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SPECTROSCOPIC INVESTIGATIONS OF METAL CLUSTERS AND METAL CARBONYLS IN RARE GAS MATRICES By STEPHAN BRUNO HEINRICH BACH A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1987 TO MY PARENTS ACKNOWLEDGEMENTS The author wishes to extend his deepest thanks and appreciation to Professor William Weltner, Jr., whose patience, understanding, encouragement, and professional guidance have made all of this possible. Thanks are also due to Professor Bruce Ault for the initial opportunity do matrix work and the encouragement to continue on to do graduate work in the field. Thanks need also be given to Professor Weltner's research group, specifically to Dr. Richard Van Zee, whose help and guidance were invaluable in completing this work. The author also wishes to acknowledge the assistance of the electronics, machine, and glass shops within the Department of Chemistry. They kept the equipment functioning, and fabricated new pieces of apparatus when necessary making it possible to perform the desired experiments. Thanks are also due to Larry Chamusco for many enlightening conversations regarding the present work and also for his help in preparing this work for publication. Thanks are also due to Ngal Wong for his assistance in preparing the final version of this publication. The author also wishes to acknowledge the support of the National Science Foundation (NSF) for this work as well as Division of Sponsored Research for support in completing the work for this project. iii TABLE OF CONTENTS page ACKNOWLEDGEMENTS ...................................... ii LIST OF TABLES .......... ......... ..................... vii LIST OF FIGURES ........................................ ix ABSTRACT .................................................. xiii CHAPTERS I INTODUCTION .................................. 1 Matrix Isolation ........................ 1 Theory of Cluster Formation ........... 19 ESR Theory .............................. 30 The Hyperfine Splitting Effect ..... 34 Doublet Sigma Molecules ............ 40 The spin Hamiltonian ............ 40 The g tensor ...................... 42 The A tensor ...................... 46 Randomly oriented molecules ...... 49 Molecular parameters and the observed spectrum .......... 51 Spin densities .................. 56 Quartet Sigma Molecules (S=3/2) .... 58 The spin Hamiltonian ............ 59 Sextet Sigma Molecules ............ 66 The spin Hamiltonian .............. 66 Infrared Spectroscopy ................ 67 Theory ................................ 70 Fourier Transform IR Spectroscopy .. 76 II METAL CARBONYLS ............................... 79 ESR of VCO, Molecules ................. 79 Introduction ..................... 79 Experimental ......................... 80 ESR Spectra ....................... 81 V CO .. .. .. .. .. 8 1 51VCO(A) and 5VCO(a) in argon ... 81 51V13CO(A) and 51V13CO(a) in argon 82 51VCO(A) in neon ................ 82 51VCO(a) in krypton .............. 88 51V(12CO)2 and V(13CO)2 in neon 89 51V(12C0)3 and 51V(13CO)3 in neon 89 Analysis ...... VCO, (A) and V(CO)2 ...... V(CO)3 ...... Discussion .... VCO ......... V(CO)2 ...... V(CO)3 ...... Conclusion .... Infrared Spectrosc Transition Metal Introduction Experimental Spectra ....... Discussion .... Conclusion .... ( ........... a ) .. . py of First Carbonyls......... ........... ........... ........... ........... ............ py of First Carbonyls . ........... ........... ........... ........... ........... III ESR STUDY OF A SILVER SEPTAMER ............. Introduction .......................... Experimental .......................... ESR Spectra ........................... Analysis and Discussion ............... IV ESR OF METAL SILICIDES ..................... ESR of AgSi and MnSi ...... Introduction ........... Experimental ........... ESR Spectra ............ AgSi ................. MnSi ................. Analysis and Discussion A gS i ...... .. ..... .... MnSi ................. ESR of HydrogenContaining Silicon Clusters ........ Introduction ........... Experimental ........... ESR Spectra ............ HScSiHn .............. H2ScSIHn ............. Analysis and Discussion HScSiHn .............. H2ScSiHn ............. ..o.. .... .... cand .... .... ,.... ... .... ... .... .... page ... ... ... .. ... Row .. o .. ... ... 96 96 98 98 100 100 106 107 108 109 109 109 110 115 119 121 121 122 123 129 137 137 137 137 138 138 139 139 139 145 148 148 149 150 150 156 157 157 166 ... .. ... ... um ... .. ... , ... .. ... page V CONCLUSION.... ............................... 172 REFERENCES ........................................... 178 BIOGRAPHICAL SKETCH .................................. 187 LIST OF TABLES Table Page II1. Observed and calculated line positions (in G) for VCO (X6E) in conformation (A) in argon at 4 K. v = 9.5596 GHz ............................. 83 112. Observed and calculated line positions (in G) for VCO (X6O) in conformation (a) in argon at 4 K. v = 9.5596 GHz ............................. 84 113. Observed line positions (in G) for VCO (X6O) in conformation (A) in neon at 4 K. v = 9.5560 GHz................................... 90 114. Observed and calculated line positions (in G) for V(CO)2 (X4 g) isolated in neon at 4 K. v = 9 .5560 GHz ................................. 91 115. Calculated and observed line positions and magnetic parameters of the V(CO)3 molecule in neon matrix at 4 K. v = 9.55498 GHz........... 92 II6. Carbonyl Stretching Frequencies for the First Row Transition Metal Carbonyls................... 112 III1. Calculated and observed ESR lines of 109Ag7 in solid neon at 4 K (v = 9.5338 GHz) See Figure III3 ................................. 125 III2. Magnetic parameters and selectron spin densities for 109Ag7 cluster in its A2 ground state.(a) ............................. 131 III3. Comparison of the magnetic parameters of 107Ag7 (this work) with those of Howard, et al s 107Ag5 cluster ......................... 135 III4. Spin densities (selectron) compared for the 2A2 ground states of the Na7, K7, and Ag7....... 136 IV1. Observed and Calculated Line Positions (in Gauss) for AgSi in argon at 14 K. (v = 9.380 GHz)...... 140 IV2. Observed and Calculated Line Positions (in Gauss) for MnSi in argon at 14 K. (v = 9.380 GHz)...... 141 IV3. Hyperfine parameters and calculated spin densities for MnSI in argon at 14 K. (v = 9.380 GHz)...... 147 vii page IV4. Observed and calculated line positions (in Gauss) for HScSiHn in argon at 14 K. (v = 9.380 GHz)... 151 IV5. Hyperfine parameters and calculated spin densities for HScSiHn in argon at 14 K. (v = 9.380 GHz)... 152 IV6. Observed and Calculated Line Positions (in Gauss) for H2ScSiHn, the (A) site, in argon at 14 K. (v = 9.380 GHz) ........................ 158 IV7. Hyperfine parameters and calculated spin densities for H2ScSiHn, site (A), in argon at 14 K. (v = 9.380 GHz)......................... 159 IV8. Observed and Calculated Line Positions (in Gauss) for H2ScSIHn, the (a) site, in argon at 14 K. (v = 9.380 GHz) ........................ 160 IV9. Hyperfine parameters and calculated spin densities for H2ScSiH,, site (a), in argon at 14 K. (v = 9.380 GHz)......................... 161 viii LIST OF FIGURES Figure Page I1. The furnace flange with copper electrodes and a tantalum cell attached......................... 10 12. The EPR cavity and deposition surface within the vacuum vessel. The apparatus is capable of cooling the rod to 4 K, because of the liquid helium transfer device (HeliTran) on the top ........................................ 11 I3. The ESR cavity and deposition surface within the vacuum vessel. The apparatus is capable of cooling to 12 K because of the closed cycle helium refrigeration device (Displex) on the t o p . . . . .. . 1 2 14. The vacuum vessel, deposition surface, Displex, and furnace assembly for infrared experiments... 13 I5. Zeeman energy levels of an electron interacting with a spin 1/2 nucleus ......................... 52 16. (a) Absorption and (b) first derivative line shapes of randomly oriented molecules with axial symmetry and gj oriented, axially symmetric molecules g 17. Energy levels for a 4E molecule in a magnetic field; field perpendicular to molecular axis.... 63 18. Energy levels for a 4E molecule in a magnetic field; field parallel to molecular axis......... 64 19. Resonant fields of a 4E molecule as a function of the zero field splitting...................... 65 110. Energy levels for a 6E molecule in a magnetic field for 9 = 0, 30, 600, and 90 ............ 68 111. Resonant fields of a 6E molecule as a function of the zero field splitting...................... 69 page II1. ESR spectrum of an unannealed matrix at 4 K containing 51VCO(A), with hfs of about 100 G, and 51VCO(a), with hfs of about 60 G. For the conformation (A) two perpendicular lines and an off principle axis line are shown. v = 9.5585 GHz.................................. 85 112. ESR spectrum of an annealed argon matrix at 4 K containing only 51VCO in conformation (a). Two perpendicular lines and off principal axis line are shown. v = 9.5585 GHz.................. 86 113. ESR spectrum of the perpendicular xy1 line of 51V13CO in conformation (a) in an argon matrix at 4 K. v = 9.5531 GHz ......................... 87 114. ESR lines in a neon matrix at 4 K attributed to 51VCO in conformation (A). v = 9.5560 GHz...... 93 115. ESR lines in a neon matrix at 4 K attributed to 51V(CO)2. v = 9.5560 GHz ....................... 94 116. (Top) ESR spectrum near g=2 in a neon matrix at 4 K attributed to an axial 51V(CO)3 molecule. v = 9.5584 GHz. (Bottom) Simulated spectrum using g, A(51V) parameters and linewidths given in the text.... 95 117. Molecular orbital scheme for the 6z VCO molecule (modeled after Fig. 543 in DeKock and Gray (84 )) .................................. 101 118. Infrared spectrum of CrCO using both 12CO and 13CO in argon. The top trace has a 1:200 CO/Ar concentration and the bottom has a 1:1:200 12C0/13CO/Ar concentration ..................... 113 119. Infrared spectrum of Mn and CO codeposited into an argon matrix. The bottom trace is after annealing the matrix to about 30 K and cooling back down to 14 K............................... 114 II10. Plot of the CO stretching frequencies in the first row transition metal monocarbonyl molecules MCO (circled points are tentative). Also shown is the variation of the energy of promotion corresponding to 4s23dn2 to 4sl3dn, where n is the number of valence electrons(91). 117 page III1. The pentagonal bipyramid structure ascribed to Ag7 in its 2A2 ground state. It has D5h symmetry with two equivalent atoms along the axis and five equivalent atoms in the horizontal plane.. 126 III2. The ESR spectrum of 109Ag in solid neon matrix at 4 K (v = 9.5338 GHz). The top trace is the overall spectrum, and the bottom traces are expansions of the three regions of interest after annealing. Notice the large intensity of the silver atom lines at 3000 G before annealing ...... ................................ 127 III3. The ESR spectrum of 109Ag7 in a solid neon matrix at 4 K (v = 9.5338 GHz). The fields indicated are the positions of the four hyperfine lines corresponding to IJ,Mj> = 11,1>, 11,0>, 10,0>, and 11,1> (see Table III1). The spacing within each of the four 6line patterns is uniformly 8.7 G. The few extra lines in the background of the lines centered at 3006 G are due to residual 109Ag atom signals.............................. 128 IV1. The ESR spectrum of AgSI is an argon matrix at 12 K. The line positions of the impurities (CH3 and SlH3) are noted. v = 9.380 GHz ............. 142 IV2. The ESR spectrum of MnSI in an argon matrix at 12 K. v = 9.380 GHz ............................ 143 IV3. The ESR spectrum of Sc codeposited with Sl into an argon matrix at 12 K. The eight sets of doublets are shown for HScSiHn. v = 9.380 GHz.. 153 IV4. The mi= 1/2 and 3/2 transitions for HScSiHn at 12 K. Two different rod orientations are shown. The top is with the rod parallel to the field and the bottom trace is for the rod perpendicular to the field. v = 9.380 GHz ....................... 154 IV5. The ESR spectrum in the g=2 region after annealing a matrix containing both Si and Sc (v = 9.380 GHz). The doublets due to HScSiHn have disappeared. The only remaining lines are due to impurities and H2ScSiHn (noted) ................ 155 page IV6. The ESR spectrum (mi=7/2 and 5/2) for H2ScSiHn in argon at 12 K after annealing to about 30 K. The top trace is for the rod perpendicular to the field and the bottom trace is for the rod parallel to the field. v = 9.380 GHz ........... 162 IV7. Same as Figure IV6 except the mi=3/2 and 3/2 transitions are shown........................... 163 IV8. Same as Figure IV6 except the m=l1/2 transition is shown........................................ 164 IV9. Same as Figure IV6 except the mi=5/2 and 7/2 transitions are shown .......................... 165 xil Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy SPECTROSCOPIC INVESTIGATIONS OF METAL CLUSTERS AND METAL CARBONYLS IN RARE GAS MATRICES By STEPHAN BRUNO HEINRICH BACH December, 1987 Chairman: Professor William Weltner, Jr. Major Department: Chemistry Three vanadium carbonyls were formed by codeposition of vanadium vapor and small amounts of 12CO and 13CO in neon, argon, and krypton. Two of the species were high spin (S>1) molecules. For VCO (S=5/2) two conformations of almost equal stability were trapped in various matrices. The dicarbonyl was also observed and found to have an S=3/2 ground state and a zero field splitting parameter DI = 0.30 cm1. Also observed only in a neon matrix was V(CO)3. The ground state 2 2 depending on for this axial molecule is either A or 2A depending on whether it has planar D3h or pyramidal C3V symmetry. Other first row transition metal carbonyls were studied using Fourier transform infrared spectroscopy. When chromium and CO were codeposited into an argon matrix, a molecule was formed with CO for which a stretching frequency at 1977 cm1 xiii was observed. An attempt is made to relate the bonding of first row transition metal monocarbonyl molecules to the observed infrared CO stretching frequencies of these molecules. A cluster of seven silver atoms was produced when the 109 isotope of silver was vaporized and deposited into a neon matrix and analyzed using electron spin resonance spectroscopy. The product signals were strongest after the matrix had been annealed. From the observed hyperfine splitting it was determined that the cluster has a 2 " pentagonal bipyramidal (D5h symmetry) structure with a A2 ground state. Its properties are shown to be similar to those found by other workers for the Group IA alkali metal septamers. Pure metal clusters were isolated when silicon was codeposited with silver and manganese. Silver silicide was isolated in an argon matrix and found to have a doublet ground state. Manganese silicide was observed in both argon and neon matrices and found to have an S=3/2 ground state. Hyperfine parameters have been determined for both species. Siliconcontaining scandium hydrides have also been observed in argon matrices upon codeposition of silicon and scandium vapor. The two species identified contained one and two hydrogens attached to the scandium. Both molecules were found to have doublet ground states. Hyperfine parameters were determined for both species. xiv CHAPTER I INTRODUCTION Matrix Isolation Matrix isolated metal clusters and metal carbonyls can be studied in a variety of ways and are thought to aid in the understanding of metal catalysts. The methods of studying these compounds are as diverse as the compounds themselves, varying from optical methods such as infrared. Raman, uvvisible, to electron spin resonance and magnetic circular dichroism spectroscopies which probe the cluster for its magnetic and electronic properties. Using these varied techniques, it is possible to determine the electronic structure of the metal clusters. This information can then be tied together with theoretical calculations to elucidate the properties of the metal cluster. Before the advent of matrix isolation, the study of metal clusters was carried out either in the gas phase or in solutions. Matrix isolation was developed in the mid1950's by George Pimentel and coworkers (1). The technique was developed as a means of studying highly unstable reaction intermediates which would, under standard conditions, be too short lived to be observed. It has since been applied to a wide variety of systems which have one thing in common: The species of interest are too unstable to be studied under normal laboratory conditions. 2 Several things are required in order to do matrix isolation. First, the experiments require a high vacuum environment. This means a pressure below 1x106 torr must be maintained in order to minimize the amount of atmospheric impurities that will be trapped within the matrix. This type of a vacuum is usually achieved using an oil diffusion and a mechanical pump with a liquid nitrogen cold trap. Matrix isolation experiments are usually carried out between 4 and 15 K. This temperature range can be achieved by one of two methods depending upon the desired minimum temperature. Using commercially available closed cycle helium refrigerators is one way to cool the deposition surface to the desired temperature. The only drawback of this system is that the minimum temperature the refrigerator can achieve lies at about 12 K (Recent advances have produced a closed cycle system which is capable of 4 K, but their cost is prohibitive). An alternative to this method is to simply use liquid helium to cool the deposition surface. This can be done by using either a dewar or a commercially available transfer device such as the Air Products Helltran. These devices can achieve a low temperature in the neighborhood of 4 K. The final consideration in setting up this type of experiment is the substrate on which to deposit the matrix. Types of material for this surface range from CsI (or other suitable alkali halide salts), to sapphire, or to polished 3 metal surfaces. Factors to be considered when choosing the substrate depend on the type of experiment being done, but all such solids must have high thermal conductivity. Also, optical properties must be considered when doing absorption or emission studies, whereas magnetic susceptibilities are of concern in ESR and MCD. Obviously, the purity of the solid substrate is important since even small amounts of some impurities can cause strong absorptions or magnetic perturbations. The term "matrix isolation" comes about because the molecules of interest are trapped in a matrix of inert material, usually a noble gas such as neon, argon, krypton, or nitrogen. The trapping site is usually a substitutional site or an imperfection in the crystalline structure of the solid gas, and the trapped species, seeing only inert nearest neighbors, are isolated and can not react further. Trapping the metal atom in the matrix is fairly straightforward once the method of atomizing the metal has been determined. But, a problem arises in producing metal dl, tri, and higherorder species. It is unusual to simply deposit a matrix and get a species other than a monomer or a dimer. In order to get these higher order species of interest several techniques can be used. The most common technique used is to simply anneal the matrix. Annealing involves depositing the matrix, and then warming it. The amount that the matrix is warmed depends on 4 two things, the matrix gas being used and the trapped species. A matrix can usually be annealed up to a temperature equal to approximately one third that of its melting point without solid state diffusion occurring. The problem that occasionally arises is that once the temperature of the matrix has begun to rise, it is possible for some reactions to occur due to diffusion of smaller atoms or molecules that are trapped. This might induce an exothermic reaction, causing the matrix to heat more rapidly than intended, exceeding the capability of the cooling system to dissipate the heat produced. The pressure then rises and rapid evaporation of the matrix occurs (2). Photoaggregation is another method employed to produce metal clusters after the matrix has been deposited. This method usually involves photoexcitation of the metal which causes local warming of the matrix as the metal atom dissipates the excess energy. This partial warming loosens the matrix around the metal atom allowing it to diffuse and possibly interact with other metal atoms in the vicinity. This method has been used to successfully produce silver clusters by Ozin and coworkers (3). Using different matrix gases can also give differing results as to the size of the metal molecules formed. These differences arise for several reasons. The most obvious is that the different solid "gases" will have different sized substitutional and interstitial spaces. Another consideration is the rate at which the matrix freezes. This will depend not only on the capacity of the cooling system to dissipate the excess energy, but also on the freezing point of the gas. It is important to remember that the amount of energy that the cooling system can dissipate depends on the temperature to which it must cool the deposition surface. The Displex or Helium dewar can dissipate substantially more energy at a higher temperature, such as that necessary to freeze krypton (melting point 140 K) rather than neon, which freezes at about 20 K. This difference in freezing rates will allow a varying amount of time for the atoms to move around on the surface of the matrix which is in a semiliquid state. The longer the atoms can move on the surface of the matrix, the greater the chance for the aggregation and formation of small metal molecules (2). The kinetics of cluster formation will be discussed later in greater detail. In the last 30 years a wide variety of methods has been applied to the study of molecules and atoms which have been trapped in matrices. One technique used to obtain data is resonance Raman spectroscopy. In this case a polished aluminum surface is used as the deposition surface for the matrix. The metal is vaporized by electrically heating a metal ribbon filament and codepositing the vapor with the matrix gas. The aluminum deposition surface is contained in a pyrex or quartz bell to facilitate viewing and irradiating the matrix with an argon laser (4). In this type of an experiment one can limit the amount of metal entering the matrix to half of the aluminum surface, leaving the other half virtually free of metal atoms. It is then possible to probe various parts of the matrix to determine the distribution of metal in the matrix (Moskovits purposely screened part of the metal stream so as to achieve a concentration gradient within the matrix) (4). From resonance Raman experiments it is possible to determine the vibrational frequency (at the equilibrium internuclear separation (we)), and the first order anharmonicity constant (oexe). Typical molecules which have been investigated using this technique are Fe2, NiFe, V2, Ti2, Ni3, Sc2, Sc3, and Mn2. Another common way of determining the presence of metal in the matrix is the color of the matrix. Most matrices containing metal atoms or molecules will have a characteristic color (4). Magnetic circular dichroism (MCD) spectroscopy is another technique which has been used to study matrix isolated metal clusters. MCD is the differential absorbance of left and right circularly polarized light by a sample subjected to a magnetic field parallel to the direction of propagation of the incident radiation. A one inch diameter CaF2 deposition window is used, and the magnet (.55T) is rolled up around the vacuum shroud surrounding the deposition surface. Before an MCD spectrum is taken, a double beam absorption spectrum is usually taken, the reference beam 7 being routed around the vacuum shroud through the use of mirrors, in order to maximize the signal to noise ratio of the MCD spectrum. The optimum absorbance value has been found to be 0.87, and deposition times are controlled accordingly (5). The information gained from this type of experiment is very useful in assigning the electronic ground state of the species under study. The MCD technique also has the advantage of being able to assign spinforbidden electronic transitions. Properties of excited electronic states have also been investigated utilizing MCD (5). Optical absorption spectroscopy has also been done on matrix isolated samples; for example, PtO and Pt2 have been studied in argon and krypton. Atomic platinum lines were also observed. A KBr cold surface was used as a deposition surface. A hollow cathode arrangement was used to vaporize platinum wire, which was being used as the anode. This was then put into a stainless steel vacuum vessel equipped with an optical pathway. Deposition times were varied from a few minutes for Pt up to two hours to make PtO and Pt2. The absorption spectrum was then taken (6). The present work has utilized two types of analysis, namely electron spin resonance spectroscopy and Fourier transform infrared spectroscopy. When doing ESR, two types of deposition surfaces are usually used, either a copper or a singlecrystal sapphire rod. Both are magnetically inert, and they, like other deposition surfaces, have good thermal 8 transport properties. In order to do ESR the sample has to be placed into a homogeneous magnetic field. This is usually accomplished by mounting the vacuum shroud surrounding the deposition surface on rails. The matrix can then be deposited outside of the confines of the magnet's pole faces (7,8). In order to perform a typical matrix isolation experiment using electron spin resonance to analyze the matrix, several pieces of specialized equipment are necessary. Measurements on the matrix take place between the pole faces of an electromagnet. This inherently restricts the size of the vacuum chamber and deposition surface. The setup used is typically in two parts. One half contains the metal deposition setup or "furnace" (Figure I1). The second part contains the deposition surface and the ESR cavity (Figures I2 and 13). Figure I2 shows the system configured with the HellTran liquid helium transfer device from Air Products, and Figure I3 has the setup configured with the Air Products Displex closed cycle helium refrigeration system. The two halves are separated by a set of gate valves so that they can be disconnected from each other without compromising the high vacuum conditions maintained in each. Once separated the rod is lowered into the ESR cavity with the aid of pneumatic pistons. After the rod is in the cavity, the half containing the ESR cavity and the rod is rolled into the magnet so that the ESR cavity and rod are located between the pole faces of the magnet. Infrared work can also be done in a fashion similar to that used for ESR. The primary difference is that the deposition surface is usually CsI or quartz because of their optical properties (No significant absorptions between 4000 and 200 wavenumbers). For this type of work the vacuum shroud containing the deposition window usually sits in the sample compartment of the infrared spectrometer aligned so that the sample beam passes through the deposition window. The apparatus for doing infrared experiments has some similarities to that used for the ESR experiments. There is a furnace and a dewar, and gate valves separating the two (Figure 14). But a much smaller vacuum shroud can be used because only a deposition window is contained inside of it. It is important that the infrared beam passes into the vacuum vessel, through the deposition surface (in most cases), and back out again so that the beam can reach the detector, which means that the matrix, as well as the windows through which the infrared beam must pass, needs to be able to transmit radiation in the infrared region. The deposition window usually remains in the infrared instrument for the entire experiment, which then enables one to follow the deposition of the matrix. Several options are available to vaporize the metal sample. The usual method is resistive heating. The metal is Figure I1. The furnace flange with copper electrodes and a tantalum cell attached. Figure I2. The EPR cavity and deposition surface within the vacuum vessel. The apparatus is capable of cooling the rod to 4 K, because of the liquid helium transfer device (HeliTran) on the top. I Figure 13. The ESR cavity and deposition surface within the vacuum vessel. The apparatus is capable of cooling to 12 K because of the closed cycle helium refrigeration device (Displex) on the top. ELECTRICAL He GAS C THERMOCOUPLE and HEATING WIRES EXPANDER Ist STAGE 2nd STAGE COPPER COLD TIP TARGET WINDOW RADIATION SHIELD MATRIX GAS INLET GATE VALVES ROTATABLE JOINT FURNACE ASSEMBLY VACUUM PUMPS Figure 14. The vacuum vessel, deposition surface, Displex, and furnace assembly for infrared experiments. placed into a cell made of a high melting metal with good electrical properties. (Mixed metal species may sometimes arise in high temperature work because a significant portion of the cell may also vaporize with the sample.) Heating in this fashion, it is possible to achieve temperatures in excess of 2000 C. An alternative method is to put the sample cell into an inductive heating coil; in this manner, comparable temperatures can usually be attained. The temperature of the furnace is estimated by using an optical pyrometer; more accurate measurements require an estimate of the emissivity of the hot surface. The determination of what has been trapped can sometimes be simple or, at other times, rather complex. In the case of Sc2 it was rather straightforward. The ESR spectrum was measured by Knight and coworkers (9). Since the Sc nucleus has a spin of 7/2 (1=7/2), the hyperfine structure observed identified the trapped species. A resonance Raman experiment determined the vibrational frequency of the ground state molecule to be 238.9 cm1 (10). From this information it was then possible to determine whether a chemical bond exists between the trapped species. In the case of discandium, a single bond and not van der Waals forces binds the two atoms (11). A more controversial diatomic molecule, dichromium, is not quite as straightforward; it has a singlet ground state and is therefore not observable using ESR. Theoretical studies of Cr2 indicate a variety of bonding configurations. A resonance Raman study has examined both di and tri chromium (10). For the dichromium species it was first necessary to decide which of the spectral features belonged to dichromium and which belonged to trichromium. This was done in two ways. The change in relative intensities of the bands was observed as the concentration was varied (the assumption being that a more concentrated matrix would favor a larger cluster), and a high resolution scan of one of the observed lines was fit with the calculated isotopic finestructure spectrum, assuming the carrier of the line to be Cr2. The vibrational frequency could then be determined from the spectra, and from this a force constant indicating the strength of bonding. The results from the experiment indicate that multiple bonding does exist (k=2.80 mdyne/A). (Dicopper with a single bond has a k=1.3 mdyne/A.) The extent of the multiple bonding can not be determined from these results (11). Divanadium has also been investigated using the resonance Raman technique to yield an equilibrium vibrational constant of 537.5 cm1 (4), but mass spectrometric data were needed to complete the picture. It was determined that the dissociation energy for divanadium is about 1.85 eV (11). From spectroscopy done in a twophotonlonization mass selective experiment, on a supersonically expanded metal 0 beam, a value of 1.76 A for the equilibrium distance was measured (12). The short bond distance coupled with a high vibrational frequency shows that the molecule is strongly bonded by 3d electrons (11). Higher order metal clusters such as Mn5 have also been trapped, and ESR spectra measured in matrices. In this case several equally spaced (300 G) lines were observed in the spectrum. From the number of these finestructure lines it was determined that the molecule has 25 unpaired electrons (Hyperfine splitting were not resolved.). On this basis it is possible to postulate the cluster size. Smaller clusters are improbable on the basis of S=25/2. It is also important to remember that the larger clusters are unlikely to form in the matrix initially. The structure of Mn5 is thought to be pentagonal with single bonds between each of the manganese atoms and with each of the atoms having five unpaired electrons. The ESR spectrum indicates that all of the manganese atoms in the molecule are equivalent; a pentagonal structure fulfills this requirement (13). A similar problem arises in the case of doing a high concentration scandium experiment. In this case it is thought that a molecule with 13 Sc atoms is made. The ESR spectrum contains over 60 lines in the g=2 region of the spectrum, which usually indicates one unpaired electron in the molecule. Because the intensity of the lines drops off at the fringes of the hyperfine structure, it is difficult to ascertain exactly how many lines exist. With the observed lines there are at least nine Sc atoms in the molecule. The Sc13 molecule seems likely because of theoretical calculations done on transition metal clusters with 13 atoms. A single SelfConsistent Field XaScattered wave calculation has been done for Sc13 giving a single unpaired electron, in agreement with the ESR results (14). Matrix isolation is more of a technique than a method of analysis. It can be used in conjunction with various analytical tools which then can be used to determine the composition and structure of the trapped compound. It is important to use some forethought in choosing the method of analyzing the trapped molecule because the method chosen will determine what information can be obtained from the experiment. Data from various methods will tend to complement each other. For example, if the molecule of interest does not contain an unpaired electron, then it would not be worthwhile to do ESR since this method requires the presence of at least one unpaired electron in order to produce a spectrum. Analyzing the molecule for its vibrational structure by using resonance Raman or infrared spectroscopy will only give the molecule's vibrational modes. From these modes it may or may not be possible to determine the molecule's structure, depending on the complexity of the molecule and the degeneracy of the modes. Another problem, when dealing with clusters, is that it is sometimes difficult to determine the size of the cluster from the observed 18 spectra. Also, once the molecule is trapped, its trapping environment may not be uniform throughout the matrix. This will cause splitting in the observed lines of the spectrum due to different trapping sites. The trapping site may also cause a lowering of the observed point group of the molecule, which will cause lines to split because they are no longer degenerate. Matrix isolation is a useful tool which aids in determining the structure of unstable species, but it is best used in conjunction with other techniques if accurate structures are to be determined. As can be seen from what other workers have done, matrix isolation can be used to trap very reactive and also very interesting species. We set out to use this technique to further elucidate the properties of transition metals and transition metal carbonyls. Following this line of interest has lead us to study various first row transitionmetal carbonyls using both ESR and FTIR. We continued our work with transition metals by investigating the group IB metals and attempted to produce larger clusters. We finally turned our attention to the first row transitionmetal silicides. Our hope in these endeavors was to produce various metal containing species in order to determine structure and to obtain possible enlightenment as to the reaction processes occurring to form them. Producing these metal species as well as analyzing the resultant spectra tends to be a rather complicated process. A review of the kinetics of cluster formation is very helpful in pointing out and understanding some of the processes involved in producing these exotic species. The analysis of the ESR spectra can sometimes be rather simple when one is dealing with only a few lines. But when the trapped species produces many lines, the analysis rapidly becomes complicated and a review of relevant theory becomes mandatory. A brief review of infrared spectroscopy will also be presented. Theory of Cluster Formation In recent years the area of metal cluster chemistry has become rather active. The main reason behind this is the hope that the metal cluster will be useful in the investigation of the chemistry that occurs at metal surfaces. This interest has lead to two major thrusts, one involving the reproducible production of these clusters and the other concerning itself with the mechanisms involved in the evolution of the clusters. Both of these areas are now being actively pursued by various workers (1519). Experimentally, the production of these clusters and their identification have proven extremely challenging. Three primary methods of vaporizing the metal exist, laser vaporization, resistively heating of a cell containing the metal of interest, or heating a wire made of the appropriate metal. Of these the most successful has been the use of lasers. A major problem in determining the kinetics involved 20 in cluster formation is the reproducibility of the distribution of cluster sizes from experiment to experiment. Several groups have had some success at this and even have begun to react these metal clusters with various types of reactants (20,21). In developing a general meanfield kinetic model of cluster formation one must look first at the aggregation process in the thermal vaporization source. Second, a method needs to be found to calculate probabilities for cluster formation taking into account atomatom collisions to form dimers as well as collisions between clusters. This would have to include not only aggregation but also cluster fragmentation from collisions, structural stabilities of certain clusters, how energy is dissipated upon collision, and possible transition states of the clusters. It should also be able to explain the cluster distribution found in mass spectra of these systems. The metal clusters are produced by laser vaporization in a supersonic nozzle source and then allowed to enter a fastflow reactor, before being mass analyzed. The source of the metal of interest is a rod about 0.63 cm in diameter. The rod is placed in the high pressure side of a pulsed supersonic nozzle, operating with a ten atmosphere back pressure. The frequency doubled output of a Qswitched Nd:YAG laser (30 to 40 mJ/pulse, 6 ns pulse duration) is focused to a spot approximately 0.1 cm in diameter on the 21 target rod, and fired at the time of maximum density in the helium carrier gas pulse. The target rod is continually rotated and translated, thus preventing the formation of deep pits, which would otherwise result in erratic fluctuations in the sizes of the metal clusters. The heliummetal vapor mixture then flows at near sonic velocity through a clusterformation and thermalizatlon channel, 0.2 cm in diameter and 1.8 cm in length, before expanding into a 1 cm diameter, 10 cm long reaction tube. Effectively, all cluster formation in such a nozzle source is accomplished in the thermalization channel since expansion into the 1 cm diameter reaction tube produces a 25 fold decrease in density of both the metal vapor and the helium buffer gas (20). The reaction tube has four needles which can be used to inject various reactants into the flowing mixture of carrier gas and metal. Following the reaction tube, the reaction gas mixture is allowed to expand freely into a large vacuum chamber. A molecular beam is extracted from the resulting supersonic free jet by a conical skimmer and collimated by passage through a second skimmer. The resulting well collimated, collisionless beam is passed, without obstruction, through the ionization region of a timeof flight mass spectrometer (TOFMS). Detection of the metal clusters and their reaction products is accomplished by direct one photon ionization in the extraction region of the TOFMS (20). 22 With the advent of this type of a device, it is now possible to produce metal clusters under relatively controlled conditions with a fairly reproducible distribution of cluster sizes. The reproducibility of cluster size distribution between experiments has made it possible to compare the results to kinetic studies dealing with the formation of metal clusters. The kinetic analysis of the clusters has been able to explain why some cluster sizes are favored, to suggest the relative importance of kinetic and thermodynamic effects, and to shed some light on the possible influence of ionization of the clusters. The kinetic theory applicable is that of aggregation and nucleation. The meanfield rate equations governing the aggregation of particles developed by Smoluchowski (22) are i1 x i = N (I1) Xi j~1Kjii Xj X i_ 1 Xj X I = 1,...,N In equation I1, Xi denotes the concentration of clusters of size i. The aggregation kernel, Kij, determines the timedependent aggregation probability. The first term on the right hand side of the equation describes the increase in concentration of clusters size I due to the fusion of two clusters size j and ij. The second term describes the reduction of clusters size i due to the formation of larger clusters. The equation must be generalized in order that the neutralpositive, neutralnegative, and positivenegative cluster fusions are included because the vaporization process will produce some ions. But, since the electrons and the ions are attracted by long range Coulomb forces, the recombination processes are very fast, leading to a population of neutral atoms that is much larger than the population of ions. Therefore, the probability for positivenegative cluster fusion is much smaller than that of neutralpositive and neutralnegative cluster fusion and can be neglected (15). The terms due to the formation of positive clusters are .0 0+ 0 + (12) Xi = Xi Kij Xi Xj and .+ 1i1 0+ 0 + N 0+ 0 + (13) Xi j 1 Kji X Xij Kji X Xi i = 1,.....N where Xi is defined by the right hand side of equation I1 .0 .+ and Xi and Xi denote the concentration of the neutral and positively charged clusters, respectively. The kernels Kij 0+ and Kij describe the neutralneutral and neutralpositive aggregation probabilities. Analogous terms are introduced due to the presence of the negatively charged clusters (15). During cluster growth, there is also the possibility of charge transfer between the charged and the neutral clusters without the accompanying cluster fusion. The probability of electron transfer between the negatively charged and the 24 neutral clusters is much greater than the probability of electron transfer between the neutral and the positively charged species since electron affinities are much smaller than the ionization potentials for small and medium sized clusters. Therefore, only the electron transfer terms from the negatively charged to the neutral clusters are included .0 .0 0 T 0  (I4) X i J= Tij Xi Xj + j Tji Xj Xi and S 0 0 (15) Xi = Xi + = Ti X X Tji Xj X J=J ij i j ji where Tij is the nonsymmetric charge transfer kernel. The coupled rate equations I(2 through 5) can then be solved simultaneously for the concentrations of the neutral and the charged clusters (15). Classically, the aggregation probability for clusters I and j with diffusion coefficients Di and Dj is proportional to DijRij, where Dij = Di + Dj is the joint coefficient for the two clusters, and Rij is the catching radius within which the clusters will stick with unit probability. In a reactive aggregation, one has to consider the reaction probability within the interaction radius. The expression for reactive aggregation becomes Kiu = 4nDijRij[Pij/(Pij+PD)] (16) 25 where P.j is the reaction probability per unit time and PD is the probability of the reactants to diffuse away. One has PD = 1/tij, where rij is the average time in which the clusters remain within the reaction distance Rij. From the diffusion equation, (17) D = (kBT)3/2/(apmO.5 He one can easily show that 1/rij= 6Dij/(Rj)2 leading to (18) Kij = 4DIRijRj[Pij/(Pij+(6Dij/Rij2))] The limiting forms of equation I8 are of particular interest. If PIj>PD, Kij z 4xDijRj and the distribution of cluster sizes is governed by the classical aggregation kinetics. No reactioninduced magic numbers will arise in this case. The true solution to equation I1 can be approximated in this case by the ones corresponding to the exactly solvable simple kernels. Since the variation of the kernels with cluster size is not very strong in the classical limit, a constant kernel solution may be used where Kij = 2C and xl(t=O) = x0 may be used for qualitative purposes. (I9) Xi(t) = X0(CXot)i1/(l+CXOt)1+1 A more accurate solution can be obtained provided one includes the variation of the diffusion coefficients and the 26 catching radii with cluster size. Since cluster reactivity varies with its structure, the uniqueness of the structure explains the reproducibility of the reactivity data for small transition metal clusters (15). The application of classical kinetics is best exemplified by transition metal clusters. The mass distribution spectra of these clusters are essentially featureless. This is what is predicted by classical kinetics. However, although the distribution of transition metal clusters is classical, the small and medium size clusters will probably have unique or nearly unique shapes. This will result in a certain amount of nonclassical behavior which will cause certain cluster sizes to be favored (15). In the other limit of equation I8, where PD = 6Dij/(Rij)2 > Pij, the growth of clusters is reaction limited. In this case, one can neglect Pij in the denominator. Since the diffusion constants cancel, the equation becomes (I10) Ku = 4x/[6(Rij)3Pij]. Thus the aggregation probability in the reaction limited regime is dependent only on the reaction probability and does not depend on the value of the diffusion coefficient. Therefore, the aggregating clusters will undergo several collisions before fusion. Significant variations in cluster 27 size are likely to occur since the reaction probabilities depend on structure, symmetry, and the stability of the reacting clusters. This is the reason why magic numbers are observed. The reproducibility of the measured magic numbers under a wide variety of experimental conditions is due to the independence of the rate of fusion on the diffusion coefficient (15). The knowledge of reaction probabilities for each pair of reacting clusters, including their charge dependence, is required to calculate the cluster distribution in the reaction limited regime. Since this is computationally prohibitive, one is forced to make several approximations in order to make the calculation feasible. The final expression for the aggregation kernel becomes (I3 e(AGI+AGJ)/KBTav (111) Kj = GRije v after using the PolanylBronsted relationship to estimate the relative differences between transition state energies. Also, since the reactants are probably going to undergo considerable structural rearrangement after initial attachment, scaled derivatives are used to describe the energy gained upon addition of a single atom. Gibbs free energies can be used to account for the possible temperature dependent structures which can arise due to the dependence of cluster entropy with structure (15). The charge transfer kernel is approximated by 3 e(Ai+Aj)/KBTav (I12) Tij= oR1e Since the electronic wave function of a negatively charged cluster has a relatively large radius, the PolanyiBronsted proportionality factor, C, in the charge transfer kernel is significantly larger than the corresponding factor in the aggregation kernel (15). The final two equations require electronic structure calculations for only the end products (those observed in a mass spectrum). The average temperature, Tay, is not known at the outset, but the analysis of experimental spectra provides an upper bound. The spectra of positively charged clusters are thus determined by two adjustable parameters, where as those of negatively charged clusters require an additional parameter (C) (15). Ziff and coworkers (16) have studied the validity of using the Smoluchowski equation for clustercluster aggregation kinetics. They investigated the validity of the meanfield assumption by looking at the concentrations of the cluster species and also by investigating the asymptotic behavior of the equations. They found the meanfield Smoluchowski equation to be appropriate in describing the 29 aggregation of particles which form fractal clusters. The only problem was in determining the fractal properties of the kernel. Even though these properties are difficult to determine, once they are known the entire description of the kinetics follows Smoluchowski, as presented by Bernholc and Phillips (15). The kinetic theory for clustering as presented by Bernholc and Phillips (15) has been able to model the cluster distributions found for carbon by Smalley and coworkers (23). Bernholc and Phillips used the calculated formation energies with a semiempirical estimate of the entropy difference between chains and rings as input for the kinetic energy calculations. They found that the cluster distributions were in good agreement with the experimental work of Smalley. This includes the data for both the positive and negative ions produced directly in the source. The magic numbers in the range of n equal 10 to 25 were well reproduced. They also found that electron transfer effects have a strong effect on the measured distributions of small and medium clusters of the negative ions. For the positive ions produced from photolonization of neutral clusters, the calculated cluster distributions show that photofragmentation and/or photothreshold and photolonization cross section dependence on cluster size have a major effect on the measured spectra up to about n equals 25. This was not found to be true for larger clusters. 30 Even though these are just beginnings in the understanding of what is involved in cluster formation, it is essential to realize that the clusters which are seen by experimentalists are the products of a complicated set of circumstances which may possibly be at the control of the experimentalist. With this type of background it may be possible in the future to produce a desired cluster size by finely tuning the experimental conditions. To be able to do this, it will be necessary to understand what the critical factors are in the formation of clusters. Is it the overall flux of metal in the carrier gas? Can the amount of ionization be controlled in order to produce the desired cluster sizes? Or will the inherent stabilities of certain clusters override these factors and limit the variation of cluster size which can be easily produced? These are questions which will only be answered through a close synergic relationship between experiment and theory. ESR Theory Electron Spin Resonance (ESR) spectroscopy is concerned with the analysis of paramagnetic substances containing permanent magnetic moments of atomic or nuclear magnitude. The theory of ESR spectroscopy has been dealt with by many authors, and if desired a more in depth treatment can be found there (2429). In the absence of an external field such dipoles are randomly oriented, but application of a field results in a redistribution over the various orientations in such a way that the substance acquires a net magnetic moment. If an electron or nucleus possesses a resultant angular momentum or spin, a permanent magnetic dipole results and the two are related by (113) _= TP_ where g is the magnetic dipole moment vector, pis the angular momentum (an integral or halfintegral multiple of h/2x = f, where h is Planck's constant), and T is the magnetogyric ratio. The motion of these vectors in a magnetic field H consists of uniform precession about H at the Larmor precession frequency (114) w= rH. The component of u along H remains fixed in magnitude, so the energy of the dipole in the field (the Zeeman energy) (115) W= f*H is a constant of the motion. The relationship between the angular momentum and the 32 magnetic moment is expressed by the magnetogyric ratio in equation 113 and is defined by (I16) r = g[e/(2mc)] where e and m are the electronic charge and mass, respectively, and c is the speed of light. The g factor is equal to one for orbital angular momentum and is equal to 2.0023 (ge) for spin angular momentum. Defining the Bohr magneton as 3=ef/2mc and combining the g factor with equation 113 we have (along the field direction) (117) PS = germs Only 2p+l orientations are allowed along the magnetic field and are given by mSh where mS is the magnetic quantum number taking the values (118) mS = s, s1,..., 8 because the angle of the vector g_is space quantized with respect to the applied field H. This accounts for the appearance in Eq. (117) of the mS factor for spin angular momentum. In the case of an atom in a 2S1/2 state where only spin 33 angular momentum arises, the 2S+1 energy levels separate in a magnetic field. Each level will have an energy of (119) EM= gem"SH which will be separated by geSH. The g factor is an experimental value and mS an "effective" spin quantum number because the angular momentum does not usually enter into the experiment as purely spin, i.e. some orbital angular momentum usually enters into the observed transitions. For orbitally degenerate states described by strong coupling scheme (RussellSaunders), J=L+S, L+S1, ..., ILS) and (120) Ej = gjpmjH where (121) gj = 1 + [S(S+1)+ J(J+1) L(L+1)]/[2J(J+1)] is the Lande splitting factor. This reduces to the free electron value for L=O. The simplest case of a free spin where mj = mS = +1/2 will give two energy levels. The equation for the resonance condition follows: (122) hv = geAHo 34 where HO is the static external field and v is the frequency of the oscillating magnetic field associated with the microwave radiation. In this research a frequency of about 9.3 GHz (Xband) was employed. The transitions observed can be induced by application of magnetic dipole radiation obtained from a second magnetic field at right angles to the fixed field which has the correct frequency to cause the spin to flip. The Hyperfine Splitting Effect As described above, an ESR spectrum would consist of only one line. This would allow one to determine only a value for the g factor for the species. Fortunately, this is not the only interaction which can be observed via ESR spectroscopy. These other interactions tend to greatly increase the observed number of lines. One of the most important of these interactions is the nuclear hyperfine interaction. ESR experiments are usually designed so that at least one nucleus in the species under investigation has a nonzero magnetic moment. The magnetic moment of the odd electron can interact with this nuclear moment and split the single ESR line into hyperfine structure. In the simplest case of a nucleus having a spin 1=1/2 interacting with a single electron, the magnetic field sensed by the electron is the sum of the applied fields (external and local). A local field would be one caused by the moment of the magnetic nucleus. This local field is controlled by the nuclear spin state (I=1/2, in this case). Because there are two nuclear levels (21+1), the electron will find itself in one of two local fields due to the nucleus. This allows two values of the external field to satisfy the resonance condition, which is (123) Hr = (H' + (A/2)) = (H' AMI) where A/2 is the value of the local magnetic field (A being the hyperfine coupling constant), and H' is the resonant field for A=O. A good example of an ESR spectrum is that of the hydrogen atom with the Zeeman energy levels shown in Figure I5. Hydrogen has one unpaired electron for which a transition at about ge should be observed. Because of the spin angular momentum of the electron interacting with the spin angular momentum of the nucleus (1=1/2), two lines are observed. The lines are split around the "g" value for a free electron which is ge = 2.0023 and occurs at about 3,400 Gauss in an XBand experiment. The magnitude of the splitting hyperfinee interaction) of the two lines about the free electron position at ge is due to the interaction of the free electron with the nuclear moment of the hydrogen atom. The spin angular momentum of the unpaired electron can also be split by several nuclei that have spins, as is the case 36 with CH3. The carbon nuclei (99%) are 12C which has zero spin (1=0). The hyperfine interaction in this case arises from the three equivalent hydrogen nuclei (each with 1=1/2) which gives an overall 1=3/2, and four lines are observed (30,31). Several interactions are involved when a paramagnetic species with a nonzero nuclear spin interacts with a magnetic field. The obvious one is the direct interaction of the magnetic moment with the external field. The precession of the nuclear magnetic moment in the external field results in a similar term. The equation (124) gi1l= /9N relates the nuclear magnetic moment Iy to the nuclear g factor (gy). In the equation the nuclear magneton, ON, is defined as ei/2Mc where M is the proton mass and is about 1/2000th of the Bohr magneton. The Hamiltonian can be written as (125) {H) = gjeH__*{J} + hA{Ij*{Jj gPNHL*{ji where { } indicates that the term is an operator. Small effects such as the nuclear electric quadrupole interaction, as well as the interaction of the nuclear moment with the 37 external magnetic field (Nuclear Zeeman term), which is the last term in equation 125, are small and will be neglected. The Zeeman effect in weak fields is characterized by an external field splitting which is small compared to the natural hyperfine splitting (hA{IJ)*({ > gSH*()J) in equation 125. The orbital electrons and the nuclear magnet remain strongly coupled. The total angular momentum F = I+J orients itself with the external field and can take the values I+J, I+J1,..., IJj. The component of F_along the field direction, mF, has 2F+1 allowed values. In a weak field the individual hyperfine levels can split into 2F+1 equidistant levels which gives a total of (2J+1)(2I+1) Zeeman levels. (Not all levels are degenerate even at zero field.) The splitting becomes large compared to the natural hyperfine splitting in the strong field (PaschenBack) region. Decoupling of I and J occurs because of strong interaction with the external field. Therefore F is no longer a good quantum number. Since J and I have components along the field direction, the Zeeman level of the multiple characterized by a fixed mj is split into as many Zeeman hyperfine lines as there are possible values of mi (21+1). The total energy states are still given by (2J+1)(2I+1) since there are still (2J+1) levels for a given J. The levels in this case form a completely symmetric pattern around the energy center of gravity of the hyperfine multiple. 38 Intermediate fields are somewhat more difficult to treat. The transition between the two limiting cases takes place in such a way that the magnetic quantum number, m, is preserved (In a strong field m = mi + mj, in a weak field m = mF). The Zeeman splitting is of the order of the zero field hyperfine splitting in this region. With so many possible levels, the observed ESR spectrum needs to be explained in terms of selection rules. The transition between Zeeman levels involves changes in magnetic moments so it is necessary to consider magnetic dipole transitions and the selection rules pertaining to them. A single line is observed for the mS = 1/2 <> 1/2 transition in the pure spin system (I=0). A change in spin angular momentum of +f is necessary. This corresponds to selection rule of Amj = +1. A photon has an intrinsic angular momentum equal to f. Conservation of angular momentum therefore dictates that only one spin can flip (electronic or nuclear) upon absorption of a photon. The transitions usually observed with fields and frequencies employed in the standard ESR experiment are limited to the selection rules Amj = +1, and AmI = 0 (The opposite of NMR work). These interactions can be categorized as isotropic and anisotropic, and are related to the kind interactions of the electron with the nucleus, and can be deduced from the ESR spectrum. The isotropic interaction is the energy of the nuclear moment in the magnetic field produced at the nucleus 39 by electric currents associated with the spinning electron. This interaction only occurs with s electrons because they have a finite electron density at the nucleus. The isotropic hyperfine coupling term is given by (126) as = (86/3)geSgNON1((0O)2 where the final term represents the electron density at the nucleus. There is no classical analog to this term. The as value, also known as the Fermi contact term, is proportional to the magnetic field, and can be of the order of 105 gauss. It is obvious then very large hyperfine splitting can arise from unpaired s electrons interacting with the nucleus. Classical dipolar interactions between two magnetic moments are the basis for describing the anisotropic interaction. This interaction can be described by (127) E = (pe*jU)/r3 [3 (je*r) ("*rj_)]/r5 where r_ is the radius vector from the moment ge to an, and r is the distance between them. Substituting the operators, g{S_) and gNN{I), for .e and Aj respectively, gives the quantum mechanical version of equation 127 as (I28) Hdip = gSgNPN[{I~*({L){S})/r3 3(({I)*r ({SJ*r)/r5]. Then a dipolar term arises (129) a = gepgIPN[(3cos201)/r3] where 0 is the angle between the line connecting the two dipoles and the direction of the magnetic field. The angular term found in Eq. (129) needs to be averaged over the electron probability distribution function because the electron is not localized. The average of cos20 over all 0 vanishes for an s orbital because of the spherical symmetry of the orbital. Doublet Sigma Molecules The spin Hamiltonian The full spin Hamiltonian involves all the interactions of the unpaired spin within the molecule, not just the ones directly affected by the magnetic field. The full Hamiltonian contains the terms below, (130) H = HF + HZe + HLS + Hhf + HZn the magnitude of the terms on the right side of Eq. (130) tend to decrease going from left ot right. The first term in equation 130 is the total kinetic energy of the electrons. The "Ze" and "Zn" terms describe the electronic and nuclear Zeeman interactions, respectively. The energy, HLS, is due 41 to the spinorbit coupling interaction. The term, Hhf, accounts for the hyperfine interaction due to the electronic angular momentum and magnetic moment interacting with a nearby nuclear magnetic moment. These terms have been adequately described in detail by several authors (2427). This full Hamiltonian is rather complicated and difficult to use in calculations, and the higher order terms which could be observed in crystals have not been included. Using a spin Hamiltonian in a simplified manner, it is possible to interpret experimental ESR data. This was first done by Abragam and Pryce (32). The ESR data are usually of the lowestlying spin resonance levels which are commonly separated by a few cm1. All other states lie considerably higher in energy and are generally not observed. The behavior of this smaller group of levels in the spin system can be described by a simplified Hamiltonian. The splitting are the same as if one ignored the orbital angular momentum and replaced its effect by an anisotropic coupling between the spin and the external magnetic field. Since (S_ cannot represent a true spin, it represents an "effective" spin. This is related to the anisotropy found in the g factor which does not necessarily equal ge. By convention, the "effective" g factor is defined so that the observed number of levels equals 2S+1, just like the real spin multiple. Therefore all the magnetic properties of a system can be related to this effective spin by the spin Hamiltonian. This is possible because the spin Hamiltonian combines all of the terms in the full Hamltonian that are effected by spin. Nuclear spins can be treated in a similar fashion, so that the spin Hamiltonian which corresponds to Eq. (130) can be written as (131) HSpin = AHO*g*{S. + (I)*A*{S) where g and A are tensor quantities and the nuclear Zeeman term has been neglected. The g tensor The anisotropy of the gtensor arises from the orbital angular momentum of the electron through spinorbit coupling. The anisotropy occurs even in the sigma states which nominally have zero orbital angular momentum. Apparently the pure spin ground state interacts with lowlying excited states which add a small amount of orbital angular momentum to the ground state. This small amount is enough to change the values of the g tensor. The interaction is generally inversely proportional to the energy separation between the states. This spinorbit interaction is given by (132) {H)LS = = A(L}x{S}x + {L}y(S)y + (L)z{S)z) This term is added to the Zeeman term in the spin Hamiltonian (133) {H)= BH*({L)+g({S)) + (L)*{S). For an orbitally nondegenerate ground state represented by IG,Ms>, the first order energy is given by the diagonal matrix element (134) WG = + where the first term is the spinonly electronic Zeeman effect. The term, state is orbitally nondegenerate. The second order correction to each element in the Hamiltonian is given by (135) (H) MSM = [(l + geH*SnM )/n W(0) where the prime designates summation over all states except the ground state. The matrix elements of ge.HJSj will vanish because Expanding this, it is possible to factor out a quantity (0) (0) (136) A= (E nn G 44 which is a second rank tensor. The ijth element of this tensor is given by (0) (0) (137) Aij = (E where Li and Lj are orbital angular momentum operators appropriate to the x, y, or z directions. Substituting this tensor into HMSM yields (138) HMS,MS = + 22{S)*{A}*{S})M'> S The first operator does not need to be considered any further since it represents a constant contribution to the paramagnetism. The second and third terms constitute a Hamiltonian which operates only on spin variables. The spin Hamiltonian results when the operator ge${H)*{S} is combined with the last two terms of Eq. (138). The spin Hamiltonian takes the form of (I39) HSpin = {(H}*(ge{l + 2A{A})*{S} + A2{S}*{A)*{S} = P{H}*{g}*{S} + (S)*(D}*{S} where (140) {g)= g ({1) + 2A{A} and (141) (D} = 2(A}. The final term in equation 139 Is effective only in systems with S>l. The first term is then the spin Hamiltonian for a 2E molecule. The anisotropy of the gtensor arises from the spinorbit interaction due to the orbital angular momentum of the electron which is evident from the derivation. The gtensor would be isotropic and equal to 2.0023 if the angular momentum of the system is due solely to spin angular momentum. Deviation (anisotropy) from this value results from the mixing in of orbital angular momentum from excited states which is expressed through the {A} tensor. If a molecule has axes of symmetry, they need to coincide with the principal axes of the g tensor. Three cases of interest can be outlined. The simplest case is one in which g is equal to gg. This is a spin only system for which g is isotropic. For a system containing an nfold axis of symmetry (n>3) there are two equivalent axes. The axis designated z is the unique axis and the g value for the field (H) perpendicular to z is g and gl is the value for g when H is parallel to z. The spin Hamiltonian therefore becomes (142) HSpin = $(giHx{S)} + gHy)yS} + gHz{S}z). The third case deals with the situation where the molecule L 46 contains no equivalent axes (orthorhombic symmetry), where gxx' gyy, and gzz are not equal and (143) {H)Spin = (gxxHS)x + gyyHy(S)y + gzHz(S)}). The A tensor The hyperfine tensor takes into account three types of interactions. The first term involves the interaction between the magnetic field produced by the orbital momentum and the nuclear moment, L*I which is usually small. More important terms involve the interactions due to the amount of s character of the wavefunction (the Fermi contact term) and to the nons character of the wavefunction also need to be accounted for. The isotropic interaction due to the s character is called Aiso. Fermi (33) has shown that for systems with one electron the isotropic interaction energy is approximately given by (144) Wiso = (8x/3)T(0)2 PeANPN where W(0) represents the wave function evaluated at the nucleus. The interaction arising from the dipoledipole interaction of the nucleus and electron (nons character) is called Adip. The dipolar interaction gives rise to the 47 anisotropic component of hyperfine coupling in the rigid matrix environment. The expression for the dipolar interaction energy between an electron and nucleus separated by a distance r is (145) Wdipolar = (e*N)/r3 [3(Pe*r)(PN*r)]/r5 The term, Hhf, can now be written as (146) Hhf = Hiso + Hdip = [Aiso + Hdip]l*S where Aiso has been given in Eq. (126) and Adip can be expressed by equation 129. The brackets indicate the average of the expressed operator over the wave function W. In tensor notation the term become (147) Hhf = I*A*S where A_ = Asol + T. Here 1 is the unit tensor and T is the tensor representing the dipolar interaction. The components of the A tensor becomes Aj = Aisol + Tij. (148) 48 For a completely isotropic system the components of the A tensor (Ax, Ayy, Agz) will equal Aiso. A system with axial symmetry is treated in a manner similar to that of the g tensor where Axx and Ayy are equal to A. The term, Al, is given by (149) A = Also + Txx and Azz is equal to Ag which is given by (150) A, = Azz + Tzz And finally for a system which exhibits a completely anisotropic A tensor Ax, A yy Azz are not equal to each other. In matrix isolation experiments only the absolute values of the hyperfine parameters can be determined. In most matrix isolation experiments, it is found that for the most part, the signs of A_ and A, are positive. There are two general exceptions to this. First, this may not generally be true for very small hyperfine interactions, such as the hyperfine interaction in CN where the splitting due to 14N is only 5 to 10 gauss. Second, if gI is negative, the A values will usually be negative, also (34). Randomly oriented molecules There is a very distinct difference between samples held in a single crystal and those trapped in matrices. In the case of a single crystal, the sample can be aligned to the external field and spectra recorded at various angles of the molecular axes to the field. Matrix isolated samples are usually randomly oriented within the field and the observed spectra will contain contributions from molecules at various angles. This was first considered by Bleaney (35,36), and later by others (3743) In the orthorhombic case the spin Hamiltonian can be solved (assuming the g tensor to be diagonal), and the energy levels can be given by (151) E = OSHH(g12sin20cos2 + g22sinsin20 + g32cos20)0.5 = OgHSHH where S1 is the component of the spin vector S along H, gH is the g value in the direction of H, 8 is the angle between the molecular z axis and the field direction, and 0 is the angle from the x axis to the projection of the field vector in the xy plane. Returning to axial symmetry (152) gH = (g2sin2 + g 2cos20)0.5 and the energy of the levels is given by 50 (153) E = PSHH(gL2sin20 + g12cos20). It is obvious that the splitting between the energy levels are angularly dependent. This makes the transitions between the energy levels also angularly dependent. The absorption intensity as a function of angle is proportional to the number of molecules lying between 0 and O+dO, assuming the transition probability is independent of orientation. Since g is a function of 0 for a fixed frequency v, the resonant magnetic field is (154) H = (hv/A)(g 2cos29 + g 2sin2)0*.5 and from this (155) sin20 = (g0HO/H)2 gs2)/(ge2 g12) where go equals (g, + 2g.)/3 and Ho equals hv/go0. From the above equations we have (156) H = hv/gl = go0H/g, at 0 = 00 and (157) H = hu/g#3 = g0gH/g. at 0 = 90. The absorption intensity varies from 0* to 900 and when plotted against magnetic field, takes the appearance of 51 Figure I6a, for g >g_. In a typical ESR experiment one usually measures the first derivative of the absorption signal. This spectrum appears in part b of Figure 16. The perpendicular component is generally easily determined from such a powder pattern. It is usually the strongest signal observed. The parallel component is typically much weaker and usually more difficult to detect. The values of g. and g can be determined as indicated assuming that the g tensor is not very anisotropic. Hyperfine interaction with spin containing nuclei can split the pattern shown in Figure I6b into (21+1) such patterns. A simple case would be that of a molecule containing an 1=1/2 nucleus. This is presented in Figure I6c. One important point is that the orientation of the mi=l/2 pattern is opposite to that of the mi=1/2 pattern. This is because g, is approximately equal to g, and Aj Another common situation is that of the hyperfine splitting for both parallel and perpendicular orientations are almost equal and gi is shifted upfield from g,. In this case the spectrum would contain two features like Figure I6b separated by the hyperfine splitting, A. Molecular parameters and the observed spectrum With all of this theory, the question now becomes what can be learned from an ESR spectrum? To answer this, let us begin with the solution of the spin Hamiltonian in axial hvz=g/3Ho9,500 MHz g =2.0023 HA Ho MI Ms 1/2 1/2 1/2 1/2 1/2 1/2/2 1/2 H Figure Figure 15. Zeeman energy levels of an electron interacting with a spin 1/2 nucleus. (a) T I I (c) Figure I6. (a) Absorption and (b) first derivative lineshapes of randomly oriented molecules with axial symmetry and gS (Az ( b) 54 symmetry including second order perturbations. This will then show what molecular parameters can be uncovered from an ESR spectrum. Several authors (24,26,27,38) have given detailed discussions of the spin Hamiltonian (158) H})Spin = gjHz{S)z + g(3(Hx{S)x + Hy{S}y) + AI(I)z{S)z + Az({I)x{S}x + {I)y{S)y). Considering the Zeeman term first, a transformation of axes is performed to generate a new coordinate system x', y', and z', with z' parallel to the field. If the direction of H is taken as the polar axis and 0 is the angle between z and H, then y can be arbitrarily chosen to be perpendicular to H and hence y=y'. Therefore only x and z need to be transformed. The Hamiltonian is transformed to (I59) {H} = gAH{S}z, + K{I}z,(S)z, + (AtA./K)(I)x,{S}x, + [(A 2A1 2)/K](glg_/g2)sin0cosO{I}x,{S)I , + A. I} )y,{S})y n n where 12 = AglcosO/Kg, 1x = AlgLsinx/Kg, and K22 = A 2g2cos 2 + A.22g 2sin2e. Dropping the primes and using ladder operators {S)+ = {S)x + i{S}y and {S) = {S)x i{S)y, this can be rewritten in the final form (160) HSpin = g"H{S}z + K(S)zI)z + [((A 2 Al2)/K)((gig)/g2) cos9sine(({S)+ + {S))/2){})z] + [((AIAA )/4K) + AI/4]((S)+{I)+ + {S){I) + [((A[A)/4K) + A./4]({S)+(I) + {S) I)+). This Hamiltonian can be solved for the energies at any angle by letting the Hamiltonian matrix operate on the spin kets IMS, MI>. The solution of the spin Hamiltonian is difficult to solve at all angles except at 0=00 and 90'. Elimination of some of the offdiagonal elements results in some simplification and is usually adequate. The solution is then correct to second order, and can be used when g#H >> A, and A, as is typically the case. The general secondorder solution is given by Rollman and Chan (44) and by Bleaney (36). The energy levels are given by (I61) AE(M,m) = g3H + Km + (A.2/8G)[(A 2 + K2)/K2] S[I(I+1) m2] + (A H2)(AI/K)(2M 1) where K is AI and A at 0=00 and 90, respectively, and G=gSH/2. Also, M is the electron spin quantum number of the lower level in the transition, and m is the nuclear spin quantum number. The first two terms on the right result from the diagonal matrix elements and yield equidistant hyperfine lines. The last two terms cause spacing of the hyperfine 56 lines at higher field to increase, which is referred to as a secondorder effect. This solution is routinely applied because the hyperfine energy is usually small and not comparable to the Zeeman energy. As described above, the hyperfine coupling constant consists of both an isotropic and anisotropic part. The isotropic part (Aiso) can be written as (162) Aiso = (A, + 2AL)/3 = (8x/3)ge sgNN I(0)12 The isotropic hyperfine parameter can be used to determine the amount of unpaired s spin density. The dipolar component can be written as (163) Adip = (A + AL)/3 = ge2gNN<(3cos20 1)/2r3> These then relate the fundamental quantities W((0) 2 and <(3cos201)/(2r3)> to the observed ESR spectrum. Approximate spin densities in the molecule can also be obtained from Ais and Adip. Spin densities The electron spin density, px at a nucleus X is the unpaired electron probability density at the nucleus. In the case of a single unpaired electron it is the fraction of that electron/cm3 at a particular nucleus. The spin density of the unpaired electron is generally split among s, p and d 57 orbitals. The spin density at nucleus X for an s electron is given by psXlXsX(0)l2 and for electrons in a pa orbital the spin density is given by Ppox Similar expressions can be given for px and da, etc. orbitals. The terms psX and ppaX represent the contributions of the s and pa orbitals to the spin density at nucleus X. The isotropic and anisotropic hyperfine parameters can be written as X (164) Aiso (molecule) = (8x/3)ge egiPNPsXIXsX(0)I X (165) Adip (molecule) = ge egIONPpoX Since the equations above are characteristic of atom X, it is possible to rewrite them for Aiso and Adip as given below X X (I66) Also (molecule) = PsXAlso (atom) X X (167) Adip (molecule) = PpoXAdip (atom). From Eqs. (166,67) one can easily obtain an expression relating the unpaired spin density to the isotropic and anisotropic hyperfine parameters, X X (168) PsX = Aiso (molecule)/Aiso (atom) X X (169) P2poX = Adip (molecule)/Adip (atom). The hyperfine parameters for the molecule are obtained from the ESR spectra. The hyperfine parameters for the atoms can be obtained from tables (see Weltner (24), Appendix B) and multiplied by the appropriate correction factors. The correct value of Adip is calculated by taking the free atom value of P = gepgNAN and multiplying it by an angular factor a/2 = <(3cos2al)/2>. The factor equals 2/5 for a p electron, 2/7 for a d electron and 4/15 for an f electron. The value for Aiso (atom) can be found in Table B1 (column 5) of Weltner (24) and the uncorrected value for Adip (atom) can be found in column 7 of the same Table. Quartet Sigma Molecules (S=3/2) These high spin molecules (S>1) often contain transition metals. The metal atom will generally have a large zero field splitting (D) value due to its large spinorbit coupling constant ((})). If there are only a few ligands attached to the metal atom, the unpaired electrons will be confined to a small volume which will cause a sizable spinspin interaction. A large D value will cause many predicted lines to be unobservable. The spin Hamiltonian A 4E molecule will exhibit a fine structure spectrum. A theorem due to Kramer states that in the absence of an external magnetic field the electronic states of any molecule with an odd number of electrons will be at least doubly degenerate. In the case of a quartet molecule the zero field splitting produces two Kramer's doublets, or degenerate pairs of states, with MS values of +1/2 and +3/2. The spin Hamiltonian for a quartet sigma molecule with axial symmetry can be written as (170) (H}spin = gS Hz{S}z + g.Hx{S)x + D(({S}))25/4). This equation does not take into account hyperfine structure. A 4X4 spin matrix can be calculated which upon diagonalization yields four eigenvalues (171) W(+3/2) = D + (3/2)gSH (172) W(+1/2) = D + (1/2)g,3H and at zero field the +3/2 level and the +1/2 level are separated by 2D. With H parallel to the molecular axis, the energy levels will vary linearly with the magnetic field. For the applied field perpendicular to the principal axis (Haz) with Hx = H and Hz = 0, the eigenvalues are more difficult to calculate because the offdiagonal terms are no 60 longer zero. The eigenvalue matrix can be expanded to yield a quartic equation (173) E4 1/2(1 + 15x2)E2 + 3x2E + (1/16)(1 + 6x2 + 81x4) = 0, where E = W/2D and x = gH/(2(3) O5D). Singer (45) has developed a more general form of the equation which can be applied to any angle. The eigenvalues for Hz can be expressed as (174) W(+3/2) = D + (3/8D)(gSH)2 + (175) W(+1/2) = D + g H (3/8D)(gj H )2 + ... when H/D or x is small. By expanding E it can then be given as E = a + bx + cx2 +... with the levels indexed by the low field quantum numbers. When D > gPH*({S all the matrix elements of the type <+3/2(H)Spinl1/2> = <+1/2{H})Spinl+3/2> vanish. This approach yields the eigenvalues below, (176) W(+3/2) = D + (3/2)gS3Hcose (177) W(+1/2) = D + (1/2)OzH(g12cos20 + 4gL2sin28)0.5 remembering that Hz = HcosO and Hx = Hsin6 and that the angle between the molecular axis and the applied field is 9. This 61 is used to introduce the "effective" or apparent g value. The effective g value generally indicates where the transition occurs and is defined by assuming that the resonance is occurring within the doublet, that is between MS = +1/2 levels with g = ge. The g values of the observable transitions 1+3/2> <> 13/2> and 1+1/2> <> 1/2> become (I78) MS = +3/2 g = 3g, = 6.0 g = 0.0 (179) MS = +1/2 g = go = 2.0 f. = 2gi = 4.0 for a large zero field splitting. The underlines indicate the effective g value. The derivative signal for the +3/2 transition is usually undetectable because of the low population of that level. There is not a significant population of the +3/2 level unless D is very small. Also, the absorption pattern corresponding to the g values for this transition would be very broad. Finally, assuming that H/D is large implies that the transition is forbidden. The transitions usually observed for this spin state are those between the +1/2 levels (the lower Kramer's doublet). Kasal (46) and Brom et al. (47) have analyzed 4E molecules and found the following spin Hamiltonian, (I80) (H}Spin = g$3Hz{S}z + gp(Hx{S}x + Hy{S)y) + AI(I)z(S)z + A.({I}x(S}x + (I)y{S}y) + D[(S}z)2 (1/3)S(S+1)] and rewrote it as an effective spin Hamiltonian (I81) (H)Spin = giHz({S}) + 2gpB(Hx(S)x + Hy{S}y) + A ({I)z(S)z + 2AL((I}x S})x + (I})y S)y) for the +1/2 transition. The D term vanishes and S is taken to be 1/2. The effective spin Hamiltonian can be rearranged to be diagonal. The Zeeman terms become (182) {H}spin = gOH{S}z + A(I)}{S)z + ((4(A12) (Ap)2)/A) (2glg./g2)sin0cose{I)z{S}z + (1/2)A.[(AI + A)/A]( I})+(S} + {I)(S}+) + (1/2)A.[(Al + A)/A]((I)+(S)+ + (I)(S}) where g2 = (g)2cos2O + 4(g )2sin20, and A2 = ((A )2 *(g1)2/g2) cos20 + (16(A.)2(g._)2/g2)sin2 This equation can be solved analytically at 0 = 0 and by a continued fraction method at 0 = 90". A computer program is usually used to match the observed lines with those calculated by the iterative procedure in order to come up with the values for g and A. The observed transitions and therefore the energy levels are typically very dependent on 0 and D. Figures I7 and I8 indicate the levels as a function of field for the perpendicular and parallel orientations, respectively. Two Figure 17. Energy levels for a 4Z molecule in a magnetic field; field perpendicular to molecular axis. 980 0.0 LP ,3.220 0. I1 LI 0.2 0.3  04  0 I 2 3 4 5 6 7 8 9 10 H (Kilogauss) Figure 18. Energy levels for a 4E molecule in a magnetic field; field parallel to molecular axis. 1.0 0.9  0.8 0.7 0.6 0.5 0.4 0.2 0.1 234 6 7 8 9 10 H (Kilogauss) Figure I9. Resonant fields of a 4' molecule as a function of the zero field splitting. E U 66 transitions are indicated between the same two levels at 690 and 1840 G. The reason for this can be seen in Figure 19. The xy2 line is shown as an arc which reaches a maximum at about 1000 G. Sextet Sigma Molecules The molecules considered here will have S=5/2, axial symmetry (at least a threefold symmetry axis), and a large D. Ions such as Fe3 and Mn2+ fall in this category in some coordination complexes. The spin Hamiltonian The spin Hamiltonian for a 6E molecule with axial symmetry can be given as (183) (H)Spin = geiHz(S)z + gSHx{(S)xsin + D(((S})2 35/12) including all angles. For 0 = 00 all of the off diagonal elements are zero and the eigenvalues of the 6X6 matrix are given below; (184) E(+5/2) = (10/3)D + (5/2)g,~H (185) E(+3/2) = (2/3)D + (3/2)glOH (I86) E(+1/2) = (8/3)D + (1/2)glpH. 67 Three levels appear at zero field which are separated by 2D and 4D. Applying the magnetic field will split these into three Kramers' doublets, which diverge linearly with field at high fields and with slopes proportional to Ms. A mixing of states occurs in the perpendicular case and no simple solution is possible. A direct solution is possible using a computer. This type of a solution has been done by Aasa (48), Sweeney and coworkers (49), and by Dowsing and Gibson (50). The eigenvalues of the 6X6 matrix calculated by computer are shown in Figure I10. The diagonalization of the secular determinant was done at many fields and at four angles. It is evident that the resonant field for some transitions is very dependent on the angle. The plot of zero field splitting versus the resonant field is given in Figure I11. It was prepared by solution of the Hamiltonian matrix at many fields and D values for 0 equal to 0 and 90". For the situation were D >> hv the xy, line at g=6 and the z3 line at g=2 will be most easily observed. As can be seen in Figure I10, these correspond to +1/2 transitions. Infrared Spectroscopy Sir William Herschel discovered infrared radiation in 1800, but it was not until the turn of the century that infrared absorption investigations of molecules began (51). 1.6 d 0"  300 .... .. 6 60o  1.4 90  1.2 1.0 . = 0.8 0.6  0.2 0.0 0.2 0. 2 .. .. .... ... ... ..   0.6 >O8 1.0 = ge  D = 1.32cm''' 1.2 = 9.4 GHz 0 2 4 6 8 10 12 14 16 18 20 FIELD (kG) Figure 110. Energy levels for a 6Z molecule in a magnetic field for = 0, 30, 60, and 90. ,0.5 'E %0.4 Q I 2 3 4 5 6 7 8 9 10 H (Kilogauss) Figure 111. Resonant fields of a 6E molecule as a function of the zero field splitting. 70 The typical IR source is a Nernst glower which is heated by passing electricity through it. The radiation, which is emitted over a continuous range by the source, is dispersedby using a prism, such as KBr, which is transparent over the range of interest. Various types of detectors ranging from thermocouples to photodetectors are used to analyze the light which has passed through the sample. When dealing with infrared spectroscopy, one usually deals with three specific regions of the spectrum. The region from 800 to 2500 nm is the near infrared region and adjoins the visible region of the spectrum. The infrared region is found between 2500 to 50,000 nm. And the far infrared region borders the microwave region of the spectrum and starts at 50,000 nm and extends to about 1,000,000 nm. The far infrared region is used to analyze vibrational transitions of molecules containing metalmetal bonds, as well as the pure rotational transitions of light molecules. Most spectrometers are used in the midinfrared region. This is where most molecular rotational and vibrational transitions occur (51). Theory Since infrared spectra are due to the vibration and rotations of molecules, a brief review of the theory may be useful. When a particle is held by springs between two fixed points and moved in the direction of one of the fixed points, it is constrained to move linearly. A restoring force develops as the particle is moved farther from its equilibrium position. The springs want to return to their equilibrium position. Hooke's law states that the restoring force is proportional to the displacement. (I87) f = kx where k is a constant of proportionality and called the force constant. The displacement is given by x, and the restoring force is f. The force constant is used as a measure of the stiffness of the springs. When the particle is released after the displacement, it undergoes vibrational motion. The frequency of oscillation can be written as (188) v = (1/2x)(k/m)0.5 where m is the mass of the particle. The frequency can also be expressed in wavenumbers (cm1) by dividing the right side of the equation with the speed of light. Because we are dealing with small particles (atoms in this case), it is necessary to enter into a quantum mechanical description of the oscillation. The allowed energy values are given by Ev = (v + (1/2))hy, (I89) 72 where v is found in Eq.(I88) and v is the vibrational quantum number. The equation above tells us that the energy of the harmonic oscillator can have values only of positive halfintegral multiples of hy. The energy levels are evenly spaced, and the lowest possible energy is (1/2)hv even at absolute zero (52). If one analyzes the vibrational behavior of a simple molecular system, such as a diatomic molecule, the system's oscillatory motion will be nearly harmonic and the frequency of the motion can be described by (190) v(cm1) = (1/2xc)(k/g)0.5 where p is the reduced mass of the particles and is defined as (191) p = (ml"2)/(m1 + m2) Since the motion of the atoms is not completely harmonic, we must look at the energy levels of an anharmonic oscillator. This is given by (192) Ev = (v + (1/2))hv (v + (1/2))2huvx + (v + (1/2))3hvye . where the constants Xe, Ye, ... are anharmonicity constants. These are small and typically positive and usually of the magnitude IXel > Yel > Izel >... (53). Anharmonicity in a molecule allows transitions to be observed which are called overtones. These are transitions between v=0 and v=2 or v=3 which are designated the first and second overtones, respectively. The first overtone is usually found at a frequency which is a little less than twice the fundamental frequency. Combination bands can also arise. These are caused by the sum or difference of two or more fundamentals. The force constant for a molecule is related to the bond strength between the atoms. The force constant for a molecule containing a multiple bond is expected to be larger than the force constant of a single bond. A large force constant is also usually indicative of a strong bond. For diatomic molecules there is a good correlation between (k)0.5 and u(cm1). This relationship unfortunately does not hold for polyatomic molecules. In this case force constants must be calculated by a normal coordinate analysis of the molecule. Several authors have presented detailed descriptions of this method (5154). The vibrations of a molecule depend on the motions of all of the atoms in the molecule. To describe the location of the atoms relative to each other one looks at the degrees of freedom of the molecule. In a molecule with N atoms, 3N coordinates are required to describe the location of all of the atoms (3 coordinates for each atom). The position of the entire molecule in space (its center of gravity) is determined by 3 coordinates. Three more degrees of freedom are needed to define the orientation of the molecule. Two angles are needed to locate the principal axis and 1 to define the rotational position about this axis. For a linear molecule the rotation about the molecular axis is not an observable process. The number of vibrations of a polyatomic molecule is given then by (193) number of vibrations = 3N 6 for a nonlinear molecule and (194) number of vibrations = 3N 5 for a linear molecule. What is observed in an infrared spectrum is usually a series of absorptions. These correspond to various stretching and bending frequencies of the sample molecule. In order for an infrared transition to be observed, there needs to be a change in the dipole moment of the molecule when it undergoes a stretching or bending motion. The strongest bands are those corresponding to the selection rule (195) Avk = +1 1 and Avi = where j does not equal k and k equals 1, ..., 3N6. The most intense absorptions are those from the ground vibrational level since that is typically the most populated level. These type of transitions are called fundamental frequencies. These frequencies differ from the equilibrium vibrational frequencies, Vl,e, v2,e ..... .The fundamental frequencies are the ones generally used in force constant calculations because the available information is typically not sufficient to allow the calculation of anharmonicity constants. The fundamental frequencies of the molecule need not be the most intense absorptions. This can happen if the change in dipole moment, (6d/6Qk), is small or zero (51). The phase or environment that the molecule is in will affect the appearance of the IR spectrum. With gas phase samples it is often possible to resolve the rotational fine structure of the compound using high resolution instruments. On the other hand, when dealing with a matrix isolated sample, there usually is not much, if any, rotational fine structure even under high resolution. This is because the molecule is rigidly held (small molecules such as HC1 exhibit a rotational spectrum due to a hindered rotation within the matrix site) within the lattice of the matrix, and is not able to rotate freely as it is able to do in the gas phase. The elimination of the rotational fine structure simplifies the spectrum and enables the analysis of more complicated 76 vibrational spectra which arise when studying larger molecules. Fourier Transform IR Spectroscopy The basic components of an FTIR instrument are an infrared source, a moving mirror, a stationary mirror, and a beamsplitter. The source in a typical FTIR spectrometer is a glower which is heated to about 1100 *C by passing an electrical current through it. The beam from the glower is directed to a Michelson interferometer where the intensity of each wavelength component is converted into an ac modulated audio frequency waveform. Assuming that the source is truly monochromatic, a single frequency, A/c, hits the beamsplitter, where half is transmitted to the moving mirror and half to the fixed mirror. The two components of the light will return in phase only when the two mirrors are equidistant from the beamsplitter. In this case constructive interference occurs and they reinforce each other. Destructive interference occurs when the moving mirror has moved a distance of A/4 from the zero position. This means that the radiation which goes to the moving mirror will have to travel A/2 further than the radiation that went to the fixed mirror, and the two will be 180* out of phase. As the components go in and out of phase, the sample and the detector will experience light and dark fields as a function of the mirror traveling +x or x from its zero position. The intensity at the detector can be expressed as (I96) I(x) = B(v)cos(2nxv), where I(x) is the intensity, B(v) is the amplitude of frequency v, and x is the mirror distance from the zero position. For a broadband source the signal at the detector will be the summation of Eq.(I96) over all frequencies, and the output, as a function of mirror movement x, is called an interferogram (53). The interferogram can then be converted into the typical intensity versus frequency spectrum by performing a Fourier transformation. The signal is transformed from a time domain signal, which arises from the motion of the mirror, to a frequency domain signal which is observed in the typical IR spectrum. This can be done mathematically by using (197) C(y) = fI(x)cos(2xxv)dx, where C(v) is the intensity as a function of frequency. There are several advantages in using an FTIR instrument. The detector in a Fourier transform instrument gets the full intensity of the source without an entrance slit. This yields a 100 fold improvement over the typical prism and grating instrument. The signal to noise ratio is 78 theoretically improved by a factor of M1/2, where M is the number of resolution elements. This has been termed Fellgett's advantage since it results mathematically from one of his derivations. A direct result of Fellgett's advantage is that a dispersive instrument requires 3000 seconds to collect a spectrum, whereas an interferometer needs only about 60 seconds to collect an IR spectrum with the same signal to noise ratio. (M equals about 3000 and the observation time is about 1 sec/element) (53). A complete IR investigation, when possible, can enable one to determine the structure of the molecule of interest. The IR spectrum allows one to determine force constants of the various bonds and from that information the bond strengths can be determined. The bending frequencies even enable one to determine the bond angle between the atoms involved in the bending motion. The shift in both stretching frequencies and bending frequencies caused by the substitution of isotopes into a molecule is very useful towards this purpose since the amount of the shift is dependent on the change in mass when the isotope is substituted into the molecule. CHAPTER II METAL CARBONYLS ESR of VCOn Molecules Introduction Transitionmetal carbonyl molecules continue to be of great interest, partially because of their relevance to catalysis. The simplest molecules, those containing only one metal atom, have been studied spectroscopically, and electron spin resonance (ESR) has been applied successfully in some cases, specifically to V(CO)4, V(CO)5 (55), V(CO)6 (5659), Mn(CO)5 (60), Co(CO)3. Co(CO)4 (61.62), CuCO, Cu(CO)3 (63,64), and AgCO, Ag(CO)3 (65,66). (Ionic carbonyls have also been observed via ESR (67.68) but will not be explicitly discussed here.) Theoretical discussions of the geometries, ground states, and bonding in these types of molecules have been given by several authors beginning perhaps with Kettle (69) and then by DeKock (70), Burdett (71,72), Elian and Hoffmann (73), and Hanlan, Huber, and Ozin (74). Although a number of ab initio calculations have been made on such carbonyls, the vanadium molecules considered here apparently have not been treated in detail. The background for the present investigation was provided by the matrix work of Hanlan, Huber, and Ozin (74) who observed the infrared spectra of V(CO)n where n equals 1 80 to 5, in the solid rare gases. Most notably, those authors concluded, from experiment and theory, that [1] VCO is nonlinear, [2] V(CO)2 exists in linear, cis, and trans forms in all three matrices, argon, krypton, and xenon, [3] V(CO)3 is probably of D3h trigonal planar geometry. It should be emphasized that the supporting theory usually assumed lowspin ground states. Morton and Preston have prepared V(CO)4 and V(CO)5 in krypton matrices by irradiation of trapped V(CO)6. From ESR they assign V(CO)4 as a highspin 6A1 in tetrahedral (Td) symmetry and V(CO)5 as 2B2 with distorted trigonal bipyramid (C2v) symmetry. The V(CO)6 molecule is a well known stable free radical which has been rather thoroughly researched by infrared (75), MCD (76), ultraviolet (77), electron and Xray diffraction (78), and ESR. It is presumably a JahnTeller distorted octahedral (2T2g) molecule at low temperatures leading to a 2B2g ground state. Our ESR findings are only for V(CO)n, where n equals 1 to 3, and are not always in agreement with conclusions from optical work and semiempirical theory. The most explicit departure is in finding that VCO and V(CO)2 are highspin molecules. Experimental The vanadium carbonyls synthesized in this work were made in situ by cocondensing neon (Airco, 99.996% pure), argon (Airco, 99.999% pure), or krypton (Airco, 99.995% pure) 81 doped with 0.15 mol% 12CO (Airco, 99.3% pure) or 13C0 (Merck, 99.8% pure) with vanadium metal [99% pure, 99.8% 51V(I=7/2)] onto a flat sapphire rod maintained at 46 K but capable of being annealed to higher temperatures. The furnace, HellTran, and IBM/Bruker Xband ESR spectrometer have been previously described (79). Vanadium was vaporized from a tungsten cell at 1975 *C, as measured with an optical pyrometer (uncorrected for emissivity). ESR Spectra VCO Two ESR spectra of the VCO molecule were observed in matrices prepared by condensing vanadium into CO/argon mixtures at 4 K. We designate these two forms of VCO below as (A) and (a). This symbolism is derived from one of their distinguishing features: one has a considerably larger 51V hyperfine splitting (hfs) than the other. Only the (a) form survived after annealing the argon matrices and only it appeared in a krypton matrix. Only (A) was observed in solid neon. 51VCO(A) and 51VCO(a) in argon Upon depositing vanadium metal into an argon matrix doped with 1.0 mol% 12CO, we obtained the 4 K ESR spectrum shown in Figure II1. The two sets of eight strong, sharp lines centered near 1200 G could be attributed to separate 82 species since upon annealing one set [designated by (A)] disappeared. The hyperfine splitting (hfs) in the perpendicular xy1 and xy3 lines of the (A) species due to 51V(I=7/2) is approximately 100G, whereas that in the (a) species is about 60 G. The line centered at about 8100 G has been observed with that intensity only once, but its appearance, and disappearance upon annealing, correlates best with the (A) molecule. Its complex hfs is indicative of an offprincipal axis line where forbidden AmI not equal to zero transitions can also occur. The observed lines of both (a) and (A) are listed in Tables II1 and 112. Annealing to 16 K and quenching to 4 K converted the VCO (A) species into (a) which has the spectrum in argon in Figure 112. Again the xy1 and xy3 lines have the same hfs, now about 60 G, and an "extra" line appears but centered at about 6700 G. 51V13CO (A) and 51V13CO (a) in argon These same spectra can be observed when 13CO replaces 12CO and the effect upon the xy1 line, which is the same effect for (A) and (a), is shown in Figure 113. Each line is split into a doublet separated by about 6 G, indicating most importantly that there is only one CO in each species. 51VCO (A) in neon In neon only one VCO molecule appears to be trapped, the one designated as (A) in argon with the hfs of about Table II1. Observed and calculated line positions (in G) for VCO (X6W) in conformation (A) in argon at 4 K. (v = 9.5596 GHz) MI(51V)a xy1 xy3 Extra lines 0 = 100 Obs. Calc. Obs. Calc. Obs. Calc. 7/2 797 789 5065 5082 7906 7897 5/2 882 877 5154 5170 8015 8012 3/2 974 971 5254 5262 8119 8124 1/2 1072 1072 5364 5360 8252 8234 1/2 1174 1176 5473 5463 8346 8344 3/2 1282 1285 5584 5573 8467 8453 5/2 1396 1400 5692 5689  8562 7/2 1511 1519 5819 5814  8671 AMI=l+ transitions Derived Parameters Obs. Calc. g 2.002(37) 7944 7938 g 1.989(5) 7976 7970 IAi(51V)I 247(28)MHz 8054 8052 IA(51V)I 288(6) MHz 8083 8083 DI 0.603(2)cm1 8161 8164 Aiso(51V)a 274(13)MHz 8192 8194 Adip(55V)a 14(11)MHz 8252 8274 AL(13C)O 17(3) MHz 8304 8304 8380 8384 8423 8413  8493 8514 8521  8603  8630 a Assuming A, and A are positive () Error of the reported value Table II2. Observed and calculated line positions (in G) for VCO (X6W ) in conformation (a) in argon at 4 K. (v = 9.5596 GHz) MI(51V)a xy1 xy3 Extra lines 0 = 12* Obs. Calc. Obs. Calc. Obs. Calc. 7/2 940 940 4460 4461 6449 6448 5/2 1000 999 4520 4520 6530 6526 3/2 1061 1060 4581 4580 6603 6603 1/2 1124 1124 4645 4644 6684 6680 1/2 1191 1190 4710 4709 6756 6755 3/2 1258 1257 4777 4777 6828 6831 5/2 1326 1327 4847 4847 6906 6907 7/2 1396 1398 4918 4921  6983 AMI=l transitions Dervived gl g IA (51V) fA (51V) D I Also(51V)a Adip(51V)a IAL(13C) I Paramenters 2.002(10) 1.998(3) 165(14)MHz 183(1) MHz 0.452(2)cm1 177(5) MHz 6(5) MHz 17(3) MHz Obs. 6476 6502 6563 6590 6637 6665 6711 6782 6804 6857 6887 6934 a Assuming A, and A. are positive. () Error in the indicated value Calc. 6479 6496 6556 6573 6633 6650 6709 6726 6785 6802 6861 6877 6937 6953 6I VCO(A)/ARGON I I I I 1 I I 1 I I I I I I I VCO(a) I I I I I II .I 7.7 79 8.1 8.3 8.5 I I I I I I I I 5.0 5.2 5.4 5.6 5.8 1 1, I 1, IX Y, I I I I I I I I _I H(KG) Figure II1. ESR spectrum of an unannealed matrix at 4 K containing 51VCO(A). with hfs of about 100 G, and 51VCO(a), with hfs of about 60 G. For the conformation (A) two perpendicular lines and an off principle axis line are shown. v = 9.5585 GHz. VCO(A) I e==1i I I I I I I I I Figure 112. ESR spectrum of an annealed argon matrix at 4 K containing only 51VCO in conformation (a). Two perpendicular lines and off principal axis line are shown. v = 9.5585 GHz. 