J . Phys. Chem. 1987, 91, 5177-5183 This reaction field is directed from A to B. As the influence of the external field, M,.F, in our treatment this reaction field changes the shape of the energy surface. In this way the potential connected with the reaction field creates a second energy minimum near the acceptor. Thus, a double minimum energy surface occurs also in hydrogen bonds between much less strong acids and bases if they are present in environments. Conclusions
The S C F calculations have shown that in the heteroconjugated BrH-N Br--.H+N bond between HBr and CH,H2N an energy -surface E(BrH,BrN) with two minima is present. The right minimum corresponds to a larger BrH and a smaller BrN distance, and with the left minimum the opposite is true. Without electrical field the right minimum is energetically lower. It is shown that the proton polarizability of this heteroconjugated bond is about 2 orders of magnitude larger than the polarizability caused by distortion of electron systems if a double minimum with energetically equal minima is present. This situation occurs at an electrical field of -0.6 X lo7 V/cm (positive field directed from Br to N ) . Hence, generally one can assume that the proton polarizability of AH-B A--H+B bonds with double minimum energy surface is largest and comparable to that of homoconjugated bonds (largest proton polarizability in the case of field zero) if the minima are energetically equalized by an electrical field. As characteristic for a system with more than one minimum many intense transitions occur in the spectra. The wavenumbers and intensities of these transitions depend sensitively on the strength of the electrical field since the upper energy levels are raised relative to the lower ones with increasing electrical field strength. (29) Onsager, L. J . Am. Chem. SOC.1936, 48, 1486. (30) Mabcki, J. In Molecular Interactions; Ratajczak, H., Orville-Thomas, T. J., eds,; Wiley: New York, 1982; pp 183-240. (31) Kramer, R.; Zundel, G. Z . Phys. Chem. (Frankfurt) 1985, 144, 265.
5177
Thus, if a distribution of electrical fields is considered, continuous absorptions should be observed in the spectra in the region 600-1600 cm-I. From experiments it is known that such a statistical distribution of local electrical fields is not the only reason for the occurrence of continua with hydrogen bonds with large proton polarizability but also the coupling of transitions of the hydrogen bond with transitions in their environments. The sum of the intensities of the transitions is, however, in the case of the heteroconjugated hydrogen bonds not largest if the proton polarizability is largest but if the residence probability of the system in the right well is higher due to an increase of the electrical field. With further increasing field the left minimum of the energy surface vanishes and only transitions between 1350 and 1600 cm-' remain besides a very weak transition at 298 cm-'. They are transitions in the remaining single minimum. The transitions at higher wavenumbers have NH' stretching vibration character and the weak transition at 298 cm-' is the hydrogen-bond stretching vibration. Our results explain why only double minimum energy surfaces occur in the case of hydrogen bonds between very strong acids and bases if these bonds are considered without environment, whereas in solutions and in solid state such energy surfaces occur with hydrogen bonds between much weaker acids and bases. The environment causes a strong reaction field at A--.H+B groups directed from A- to B. According to our calculations the potential of this reaction field creates a second minimum at the acceptor. Thus, in hydrogen bonds between weaker acids and bases double minimum energy surfaces occur if environments are present. Acknowledgment. We thank the Deutsche Forschungsgemeinschaft and the Fonds der Chemischen Industrie for providing the facilities for this work. We are much obliged to Doz. Dr. A. Karpfen for valuable discussions and especially it was particularly useful for us that we obtained details with respect to the basis set for the SCF calculations. Registry No. CH,H,N, 74-89-5; BrH, 10035-10-6.
Geometry, Bonding, and Optical and Magnetic Properties of Cu(CO),.
A Theoretical
Ramiro Arratia-Perez, Frank U. Axe, and Dennis S. Marynick* Department of Chemistry, University of Texas at Arlington, Arlington, Texas 76019-0065 (Received: January 15. 1987)
A detailed analysis of the geometry, bonding, and optical and magnetic properties of copper tricarbonyl is presented. The molecule is shown to be planar, with D3hsymmetry. The calculations show good agreement with optical spectral data and with the observed 63Cuand 13Chyperfine tensors. Spin-orbit and spin-polarization effects contribute to the axial departure of the 13Cand ''0 hyperfine tensors. Spin-orbit effects are modelled through a four-componentrelativistic molecular orbital formalism, and core spin-polarization effects are estimated from quasi-relativisticspin-unrestricted calculations. Spin-orbit effects introduce significant ligand orbital mixings, split the metal-based 3d orbitals by -0.15 eV, and introduce small but nonnegligible "orbital" contributions to the hyperfine tensors at the Cu, C, and 0 sites. The calculations predict that the unpaired electron spends most of its time on the CO ligand and has about 25% copper 4p, character.
Introduction The nature of the metal-ligand bond in metal carbonyl complexes has been studied extensively in the past two decades, mainly because of its relevance to carbon monoxide chemisorption on metal surfaces' and its implications for the mechanisms of heterogeneous catalysk2 It is generally accepted that bonding in ( I ) Plummer, E. W.; Salaneck, W. R.; Miller, J. S . Phys. Reu. B 1978, 18, 1673. (2) Muetterties, E. Chem. Reu. 1979, 79, 91.
0022-3654/87/2091-5177$01.50/0
transition-metal carbonyls occurs via a synergistic mechanism, whereby the CO ligand forms a o-bond by electron donation from its Sa orbital to empty metal orbitals, and a back-donation occurs from filled metal d orbitals to the unoccupied 2a* orbitals of C0.3-9 It has been shown further that the valence metal orbitals (3) Baerends, E. J.; Ros, P. Mol. Phys. 1975, 30, 1735. (4) Bursten, B. E.; Freier, D. G.; Fenske, R. F. Inorg. Chem. 1980, 19, 1810.
(5) Bauschlicher, C. W.; Bagus, P. S . J . Chem. Phys. 1984, 81, 5889.
0 1987 American Chemical Society
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The Journal of Physical Chemistry, Vol. 91, No. 20, 1987
may orchestrate orbital mixings between different sets of 50. and l~ CO orbitals providing an additional component to the electronic structure of transition-metal carbonyls, which plays a fundamental role in the bonding found in the M(CO), ( M = Cr, Mo, and W ) systems.1° It has also been recognized that this 5 0 - l ~hybridization interaction becomes important in order to properly describe the dispersion of a C O layer bound to a transition-metal surface.’ Recently, with the utilization of matrix isolation techniques at cryogenic temperatures, it has been possible to generate a series of metal carbonyl radicals of group 11 (Cu, Ag, and Au), and their vibrational, electronic (UV), and electron spin resonance (ESR) spectra have been analy~ed.’~-’’In particular, C U ( C O ) ~ has attracted considerable experimenta113-17 and theoretical att e n t i ~ n . ’ * ~There ’ ~ is a general agreement that the geometry of C U ( C O ) ~is trigonal planar (D3,J with ’Az‘‘ electronic ground state.I3-l9 However, there is still controversy concerning the nature of the unpaired electron which is responsible for the paramagnetic behavior of this radical. The ESR studies disagree extensively in the location of the unpaired electron. For example, Kasai and Jones” stated that 41% of the spin population resides in the Cu 4p, orbital, while Howard et a1.16assigned a population of 110% in the 4p, orbital. T o complicate matters, the nonrelativistic scattered-wave calculationsI8 assigned the unpaired electron largely to the CO ligands, whereas a recent a b initio S C F c a l ~ u l a t i o n ~ ~ (reported during the final stages of the preparation of this article) assigned the unpaired electron to the 4p, orbital with a 51% spin population. It should be emphasized at this point that spin population is not an experimental “observable” and is normally estimated (for anisotropic hyperfine interactions) by assuming , are usually fixed values for the expectation values of ( F ~ )which taken from atomic data20 (when available). It has been shown that the molecular ( r - 3 )values vary from one orbital to another and deviate significantly (due to molecular formation) from the free atomic values. On the other hand, one way of testing the quality of wave functions determined by a molecular orbital (MO) method is to compute molecular properties from them and compare with “observable” experimental data. In this paper we apply the PRDDO and the Xa approximations to copper tricarbonyl. The purpose of this study is twofold, first, to explore the geometry of copper tricarbonyl by using the PRDDO method, and second, to use the X a method (in its different versions) to obtain a more detailed interpretation of the available experimental data. A substantial collection of experimental information exists for (6) Yang, C. Y . ;Arratia-Perez, R.; Lopez, J. P. Chem. Phys. Lert. 1984, 107, 112. (7) Rohlfing, C. M.; Hay, P. J. J . Chem. Phys. 1985, 83, 4641. (8) Rees, B.; Mitschler, A. J . Am. Chem. SOC.1976, 98, 7918. (9) Hubbard, J. L.; Litchtenberger, D. L. J . A m . Chem. Sac. 1982, 104, 2132. (10) Arratia-Perez, R.; Yang, C. Y . J. Chem. Phys. 1985, 83, 4005. ( 1 I ) Greuter, F.; Heskett, D.:Plummer, E. W.; Freund, H. J. Phys. Rec. B 1983, 27, 7117. (12) Plummer, E. W.; Eberhardt, W. Adc. Chem. Phys. 1982, 49, 533. ( 1 3) Moskovitz, M.; Ozin, G.A. Cryochemistry; Wiley-Interscience: New York, 1975. (14) Huber, H.; Kundig, E. P.; Moskovitz, M.; Ozin, G.A. J . A m . Chem. SOC.1975, 97, 2097. ( 1 5 ) Ozin, G.A. A p p l . Spectrosc. 1976, 30, 573. (16) (a) Howard, J. A,; Mile, B.; Morton, J. R.; Preston, K. F.; Sutcliffe, R. Chem. Phys. Lett. 1985, 117, 115. (b) Howard, J . A,; Mile, B.; Morton, J. R.; Preston, K. F.; Sutcliffe, R. J . Phys. Chem. 1986, 90, 1033. (c) Howard, J. A.; Mile, B.; Morton, J. R.; Preston. K. F. J . Phys. Chem. 1986, 90, 2027. ( 1 7 ) (a) Kasai, P. H.; Jones, P. M . J . Am. Chem.Soc. 1985,107, 813. (b) Kasai, P. H.; Jones, P. M. J . Phys. Chem. 1985,89, 1147. (c) Kasai, P. H.; Jones, P. M. J . Am. Chem. SOC.1985, 107, 6385. (18) McIntosh, D. F.; Ozin, G. A,; Messmer, R. P. Inorg. Chem. 1981, 20, 3640. (19) Tse, J. S. Ber. Bunsen-Ges. Phys. Chem. 1986, 90, 906. (20) Morton, J. R.; Preston, K. F. J . Magn. Reson. 1978, 30, 577. (21) Case, D. A.; Karplus, M. J . A m . Chem. SOC.1977, 99, 6182. (22) Arratia-Perez, R.; Case, D.A. J . Chem. Phys. 1983, 79, 4939. (23) (a) Case, D. A.; Lopez, J. P. J . Chem. Phys. 1984, 80, 3270. (b) Arratia-Perez, R.; Malli, G. L. J . Chem. Phys. 1986, 84, 5891. (c) Arratia-Perez, R.; Malli, G.L. J . Chem. Phys. 1986, 85, 6610. (24) Lopez, J. P.; Case, D. A . J . Chem. Phys. 1984. 81. 4554.
copper tricarbonyl, such as UV, 0ptica1,l~~’~ and ESR13,’5-17 spectra. The first of such s t ~ d i e s l provided ~ ~ ’ ~ UV optical data and information about the 63Cu(in the Cu/CO( 10%)/Ar system) hyperfine interaction (hfi). More recently, the ESR spectra of Cu(CO), observed from the Cu/C0(4%)/Ar system,” as well as from the Cu/CO/adamantane system,16 provided the anisotropic hyperfine tensors for both the 63Cuand the I3C nuclei. The analysis of the ESR spectra in each of these studies has largely ignored spin-xbit contributions to the hfi, since it is often assumed that these effects at first-row atoms may be neglected. However, recent fully relativistic results for F bound to XeZ2or NpZSand for N in copper porphyrin26casts doubt upon this assumption. In the present study the geometry of Cu(CO), has been optimized by the partial retention of diatomic differential overlap (PRDD0)27-29method. The optimization procedure indicates that the most stable ground-state structure is trigonal planar and no local minima exist for other geometries. The dipole-allowed electronic transitions have been calculated by the use of Slater’s transition-state3’ formalism through the Dirac scattered-wave (DSW) m e t h ~ d . ~ ’The - ~ ~calculated electronic transitions satisfactorily account for the optical spectra. The molecular hyperfine interactions have been calculated by the DSW and quasi-relativistic spin-unrestricted (QRU) methods to include spin-orbit and core spin-polarization effects. This approach appears to work well and yields calculated hyperfine tensors for both 63Cuand I3C that are in good agreement with the observed values. Predicted values for the I7Oare also reported. These may be of some use in interpreting spectra if the ESR spectrum of enriched samples is ever investigated.
Calculations The PRDDO method is an approximate M O treatment based upon the Hartree-Fock (HF) self-consistent field (SCF) theory.27-29 In the present study, the spin-unrestricted (UHF) theory is used in the PRDDO calculations on copper tricarbonyl. The customary procedure for evaluating the HF equations involves expanding each MO as a linear combination of atomic orbitals (AO’s). The evaluation of the required integrals over AO’s and the subsequent manipulation of these quantities during the S C F procedure may be greatly facilitated by first transforming the basis set to orthogonalized atomic orbitals (OAO’s), followed by the neglect of numerous integrals over the OAO basis, which are small. This constitutes the fundamental approximation employed in the PRDDO method. Thus, the intrinsic NJ computational dependence of the H F approach to determining molecular wave functions is reduced to a more tractable N 3 dependence. Therefore, the PRDDO method is computationally fast; however, there is little sacrifice of the qualitative and quantitative information obtained from a PRDDO calculation relative to the corresponding a b initio HF calculation. I n all the PRDDO calculations the transition-metal basis set consisted of a minimal set of Slater-type orbitals (STO’s). Orbital exponents were determined by atomic S C F optimizations for the ground-state atomic c ~ n f i g u r a t i o n .During ~~ the atomic exponent
(25) Case, D. A. J . Chem. Phys. 1985, 83, 5792. (26) Case, D. A. Porphyrins. Excited States and Dynamics; Gouterman, M., Reutzepis, P. M., Straub, K. I., Eds.; ACS Symp. Ser. 321; American Chemical Society: Washington, DC; 1986; pp 59-71. (27) Halgren, T. A,; Lipscomb, W. N. J . Chem. Phys. 1973, 58, 1569. (28) Marynick, D.S.; Lipscomb, W. N. Proc. .%’uti. Acad. Sci. U S A 1982, 79, 1341. (29) (a) Marynick, D. S.; Axe, F. U.;Kirkpatrick, C. M.;Throckmorton, L. Chem. Phys. Lett. 1982, 99, 406. (b) Marynick, D.S.: Reid, R . D. Chem. Phys. Lett. 1986, 124, 17. (30) Slater, J. C. Quantum Theory of’Molecules and Solids; McGrawHill: New York, 1974; Vol. I V . (31) Yang, C. Y.; Rabii, S. Phys. Reu. A 1975, f 2 , 362. (32) Yang, C. Y.; Case, D. A. I n Local Density Approximations in Quantum Chemistry and Solid State Physics; Dahl, J . P., Avery, J.. Eds.; Plenum: New York, 1984; p 643. (33) Yang, C. Y . In RelaficisficEffects in Atoms, Molecules and Solids; Malli, G. L., Ed.; Plenum: New York, 1983; p 335. (34) Marynick. D. S.; Kirkpatrick, C. M .J . Phys. C h e m 1983. 87. 3273.
rhe Journal of Physical Chemistry, Vol. 91, No. 20, 1987 5179
Properties of Cu(CO), optimizations the ns and np orbital exponents were constrained to be equal for computational efficiency in the molecular calculations. Also, the 3d AO’s in the atomic optimizations were represented by a double-[ description. The molecular 3d basis functions were then taken as the fixed contraction of the double-t representation. The metal 4s and 4p orbital exponents were set at a value of 2.0, which has been shownz9to be reasonable. The C and 0 atom basis sets were a minimal set of STO’s with orbital exponents given by Hehre et al.35 The X a scattered-wave (Xa-SW) technique was proposed originally by Slater36and subsequently developed by Johnson.37 This method generates approximate single-determinant wave functions, in which the nonlocal exchange interaction of the Hartree-Fock method has been replaced by a local term, as in the Thomas-Fermi-Dirac model. In the S W approach, the molecular potential is assumed to be spherically symmetric inside a cell surrounding each atom and outside of an outer sphere that surrounds the entire molecule. In the remaining intersphere region (IS), a constant potential is assumed. These approximations, and those involving the muffin-tin potential, have been described in recent reviews.,* In the present contribution, we report spinrestricted nonrelativistic ( N R ) scattered-wave calculations, in which the MO’s are determined by solving the molecular Schroedinger equation, quasi-relativistic or “scalar” relativistic spin-unrestricted (QRU) S W calculations, as well as fully relativistic Dirac scattered-wave (DSW) calculations for copper tricarbonyl. In the quasi-relativistic (QRU) method the nonrelativistic radial functions inside each atomic sphere satisfy an average Dirac equation that includes the Darwin and maswelocity corrections, but leaves out the spin-orbit term.39 Because spin is still a good quantum number, one can perform spin-unrestricted calculations in the usual manner, giving a qualitative picture of the effects of spin-polarization that is difficult to obtain in other ways. Thus, the spin-up and spin-down orbitals are distinct, so that in general the resulting wave function (which transforms according to the single point group) is not a spin eigenfunction. The DSW method begins with the Dirac equation as its point of departure and retains the four-component wave function formalism throughout the calculation. Spin-orbit interactions, as well as other relativistic effects such as Darwin and mass-velocity corrections, are then implicitly included at the SCF stage. The top two (or large) components of the wave function correspond to spin-up and spin-down character, so that the MO’s in general will be spin mixtures. The bottom two (or small) components carry information related to magnetic behavior. Thus, each orbital as well as the overall wave function transforms according to the molecular double group under study. The DSW methodology was initially developed by Yang and Rabii3’ and has been recently The size of the sphere radii were chosen according to the procedure suggested by Norman.40 The “atomic number radii” were scaled by a factor of 0.88, which has been found to be nearly optimal in many S W calculations.6~’0~z2-z6 A minimum basis of angular functions was used, with 1 = 0 through 4 on the outer sphere, I = 0 through 2 on Cu, and 1 = 0 through 1 on C and 0. The basis functions for the D3h* (double) group were generated according to Yang’s symmetrization pr~cedure.~’In our notation the two-dimensional extra irreducible representations (irrep) are related to Bethe’s notation as follows: e, y7,e2 ys, e j y9. The relationships between the single (D3h) and the double (D3h*)group irreps indicate that the nonrelativistic doubly degenerate e’ and e” representations split into ez e, and e, + e3 extra irreps, respectively. Furthermore, the nondegenerate pairs
- - +
(35) Hehre, W. J.; Stewart, R. F.; Pople, J. A. J . Chem. Phys. 1969, 51, 2657. (36) Slater, J. C. J . Chem. Phys. 1965, 43, 5228. (37) Johnson, K. H . A h . Quantum Chem. 1973, 7, 143. (38) (a) Jonhson, K. H. Annu. Reu. Phys. Chem. 1975, 26, 39. (b) Case, D.A. Annu. Reu. Phys. Chem. 1982, 33, 151. (39) (a) Koelling, D. D.; Harmon, B. N. J . Phys. C 1977, 10, 3107. (b) Wood, J. H.; Boring, A. M. Phys. Reu. B 1978, 18, 2701. (40) Norman, J. G . Mol. Phys. 1976, 31, 1191. (41) Yang, C. Y. J . Chem. Phys. 1978, 68, 2626.
TABLE I: Parameters for the SW Calculationso ~(CU-C) d(C-0) b(Cu) b(C) NO) b(0ut)
1.89’ 1.16’ 1.15 0.85 0.84 3.79
4CU)
.(C)
do)
ol(Is,Out)
0.70697 0.75928 0.74447 0.73874
“ b denotes sphere radii (in A) and a is the exchange-correlation parameter. T h e interatomic distance, d , is also given in A. ’Obtained from the P R D D O calculation; see text.
0
5
10
15
20
25
ANGLE a Figure 1. Plot of P R D D O calculated potential energy surface for the C,, distortion.
(a]’ and a i ) and (a,” and a2”) of single group representations correlate with the two-dimensional e, and e2 extra irreps of the D3h*double group, respectively. The S W parameters used for the calculations are given in Table I.
Results and Discussion Geometries. A quantitative structural determination of Cu(CO), by routine physical methods has not been performed due to the inability to experiment with this species outside of a frozen gas matrix. All optical, vibrational, and ESR studies to date have inferred that the geometry of copper tricarbonyl is trigonal planar.I3-l9 The PRDDO method has been shown to yield excellent optimized geometries for a wide range of first series transitionmetal complexes.z9 In particular, PRDDO works especially well for calculating equilibrium geometries in metal-carbonyl systems. For instance, PRDDO optimized metal-ligand bond lengthsz9for Cr(C0)6, Fe(CO)5, and Ni(CO)4 have an average error of f0.02 A, with a maximum error of 0.05 A in Fe(CO),. Also, PRDDO has proven to predict qualitatively and quantitatively correct conformational preferences in transition-metal c o m p l e x e ~ . ~ ~ * ~ ~ Therefore, we used the PRDDO method to analyze the possible conformations and to obtain a theoretical estimate of the equilibrium bond distances in C U ( C O ) ~ . We began our structure determination by first optimizing the trigonal planar D3* structure. The resulting optimized Cu-C and (42) Axe, F. U.; Marynick, D. S. J . A m . Chem. Sac. 1984, 106, 6230. (43) Axe, F. U.; Marynick, D. S. Organometallics 1987, 6 , 572. (44) Case, D. A,; Karplus, M. Chem. Phys. Lett. 1976, 39, 33.
5180 The Journal of Physical Chemistry, Vol. 91, No. 20, 1987
Arratia-Perez et al.
-2 \
a
-5
i QRU -7
I
i
1
sa
* a
DSW
v
-10
U
C
d
e
f
W
z w
-12
-15
i -17
Figure 2. Ground-state upper valence energy levels of CU(CO)~ and CO.
Abbreviations: NR, nonrelativistic;QRU, quasi-relativistic spin-unrestricted; and DSW, Dirac scattered wave, relativistic. The highest occupied orbital is marked with a n asterisk in each case. C - 0 bond lengths were 1.89 and 1.16 A, respectively. Starting with our optimized D3, geometry we analyzed the carbonyl out-of-plane bending potential to a pyramidal (C30)structure. A series of fully optimized geometries and total energies along the C3, bending potential was generated by using an out-of-plane angular increment of 5.0' followed by reoptimization of the Cu-C and C - 0 bond lengths at each new value of the angle. The results of this procedure are displayed graphically in Figure 1. The distortion of c u ( C o ) , from the D3, structure to a c3u structure is found to be energetically unfavorable. Therefore, no local minimum possessing C3, symmetry was found. However, it should be pointed out that the energy required to distort the trigonal planar geometry (by 5 - 1 5 O ) is relatively small (see Figure 1). This relatively weak bending potential may be responsible for the apparent C3Lstructure of the isovalent Ag(C0)3 molecule due to matrix effects.'& We also examined the possibility of an in-phase distortion of two of the carbonyl groups relative to one, giving , geometry. Both possibilities of the simultaneous the molecule a C carbonyl in-plane bendings were studied, and each was found to be energetically less stable than the initial D j h structure. A structure of C, symmetry was also found to be energetically less stable than the D3, structure. The conclusion based on our theoretical model is that the ground-state structure for Cu(CO), is trigonal planar and no other local minima exists. Molecular Orbitals and Transition-State Results. The nonrelativistic electronic structure of copper tricarbonyl has been reported Although no detailed bonding analysis was given in these studies, the main conclusions were that the Cu-CO bond involves the participation of the 5u and 2 ~ ligand * orbitals, as well as the 4s, 4p, and 3d copper AO's, through a synergistic mechanism. In the present study we report quasi-relativistic spin-unrestricted (QRU) and fully relativistic (DSW) scattered-
Figure 3. (a) PRDDO wave function contour plot of the HOMO. (b) NR-SW wave function contour plot of the HOMO. (c) PRDDO contour plot of 3a,'. (d) NR-SW contour plot of 3a,'. (e) PRDDO contour plot of 5e'. (f) NR-SW contour plot of 5e'. Contour values in (electron/ bohr3)'/*: f0.5, 10.4, f0.3, 10.2, f O . l , f0.05, 10.02, 10.01, f0.005.
wave (SW) calculations to ascertain the importance of spin-polarization and spin-orbit effects in the electronic structure and bonding in copper tricarbonyl. We also report nonrelativistic S W results in order to estimate quantitatively the relativistic effects in this molecule. An MO energy level diagram of the upper valence and virtual orbitals of C U ( C O )and ~ free carbon monoxide is presented in Figure 2. In this energy level diagram the results of NR-SW, QRU-SW, and DSW calculations on Cu(CO), are plotted. Some common features are apparent. For example, the valence structure is divided into six bands, namely, the unoccupied band which is comprised of C O 2a* and Cu-C u* orbitals, the partially occupied 2ai' or 7e2 MO, the occupied copper 3d crystal-field-like orbitals (the d-band), the u + a band which is comprised largely of 5 0 and l a C O orbitals, and the 40 and 30 bands. Our analysis of the nonrelativistic PRDDO and S W wave functions reveals that the metal-ligand bond consists mostly of three types of Cu-CO bonding interactions. First, the n metal-ligand bond is composed of mainly three orbitals, namely, the 2aF (which results from back-donation of the 4p, Cu to the empty 2 x * CO orbitals), the 2e" (which results from back-donation of the 3d(xz,yz) Cu to the 2a*), and the le" (which results from In donation to the 3d(xz,yz) orbitals). Second, the u metal-ligand bond is largely made up of the 3a,' MO, which results from 5 u donation to the 4s orbital. The 3d(z2)-5u interactions are largely repulsive and do not contribute to the u metal-ligand bond. Finally, the most interesting contributors to the Cu-CO bond, which has not been described in previous studies, involves participation of ligand 5u, IT, and 2a* orbital mixings through the 3d(xy,x2-y2) metal orbitals. Namely, the 3e' MO which is located close to the bottom of the u + A band (see Figure 2 ) results from ligand donation of u and a symmetry to the 3d AO's, and the 5e' MO (which is mainly 3d-like) involves orbital mixings of 5 ~ - 2 n * character. Thus, we can denote this bond as "u-n". To summarize, &,single-group symmetry requires that the s Cu-CO bond could be present in a2// and e" orbitals, the CT Cu-CO bond in a,', and the u-s Cu-CO bond in any e' orbitals. These three types of bonds can be visualized from the PRDDO and NR-SW
The Journal of Physical Chemistry, Vol. 91, No. 20, 1987 5181
Properties of C U ( C O ) ~
TABLE 11: Pauli Decomposition for Orbitals with Large Spin-Orbit MixingsO
atom
cu
I
spin
S
a
P P 3c
3 Oc
total a total P
a
P
d d
a
P
S
01
S
P
P P P P
01
P a
P
7e1 0.0742
6e I 0.0062
5e3
4e3
b
b
b b
b b
0.0025 0.0028
0.0084
0.0006
b
b 0.0080 b
0.0821 0.8138
0.8876
b
0.0718 b
0.0002
0.0005 0.0078 0.0120
0.0014 0.0097 0.01 26
0.0006
0.0014
b
b
0.1538 0.1128 0.3923 0.3124
0.1183 0.1473 0.2930 0.4097
0.0183 0.0465 0.2226 R13f6 0.5672
0.5670 0.4330
0.4333 0.5667
0.1787 0.8213
b 0.01 17
5e2
b
0.0002 0.0122 0.0027 0.0029
0.0008
0.0014 0.0304 0.0004
0.0041 0.2146 0.0488 0.6039 0.1231
0.0850 0.9150
0.9 188 0.0812
0.8210 0.1790
4e2 b 0.0126 b b
“See text for method of calculation. bIndicatesvalues that are zero because of symmetry. ‘Contributions from the oxygen 2s orbital are less than 0.0002. wave function contour plots shown in Figure 3. In Figure 3a,b we show the contour plots of the HOMO (2aF) and both methods of calculation predict that this M O is dominantly carbonyl 2a* based. In Figure 3e,f we show the contour plots of the 5e’ M O in which the 5u-2a* orbital mixings through the Cu 3d A O s can clearly be seen. In Figure 3c,d we depict the contour plot of the 3al’ M O where the u symmetry is clearly appreciated. It can be seen from Figure 2 that the relativistic shifts (due to Darwin and mass-velocity corrections) are very small, as expected, since Cu is a member of the first transition-metal series. However, the metal-ligand interactions are stabilized by relativity. In particular, the 3a,’ M O is stabilized by 0.12 eV, while the 2a2/1 M O is only slightly stabilized (by 0.04 eV). By comparing the N R and QRU orbital energies it can be observed that the 2a;’ and 3al’ orbitals are more affected by core-polarization effects (i.e., the effects of exchange-correlation forces), which split the spin-up and spin-down orbitals by 0.29 and 0.25 eV, respectively. This is expected, since these orbitals contain significant s and p metal character. The polarization forces in the MO’s that are mainly 3d are very small, ranging from 0.02 to 0.08 eV. By comparing the N R or Q R U orbital energies with those of the DSW calculation (see Figure 2) we can appreciate the effects of spin-orbit interaction in the valence electronic structure of Cu(CO),. The spin-orbit splittings are observed in the MO’s that are mainly 3d-like (in the d-band). In fact, the 2e” MO’s split into the 6eI and 6e3 orbitals by -0.14 eV, whereas, the 5e’ MO’s split into the 6e2 and 7e3 orbitals by -0.15 eV. Although these spin-orbit splittings are not very large, the values calculated here could be useful if the photoelectron spectra of copper tricarbonyl is determined in the near future. The spin-orbit splitting of the 3d-like orbitals of C U ( C O )are ~ larger than the calculated splitting (-0.04 eV) of the 3d(t2,) orbitals in Cr(CO),.I0 This is in agreement with the notion that relativistic effects increase in going from the left side to the right side of the periodic table. Moreover, the spin-orbit mixings are significant in this molecule. One measure of the extent of spin-orbit mixings into the relativistic molecular orbitals is the amount of minority spin. These can be obtained by doing a charge breakdown in terms of a Pauli dec o m p o s i t i ~ n . In ~ ~this - ~ procedure ~ ~ ~ ~ only the two large components of the wave function are considered. We assumed that the radial wave function inside each atomic sphere is the same for 1 = j ‘ I 2 and 1 = j + The sum of two such spinors can then be interpreted as a nonrelativistic function of mixed spin, with spin-up corresponding to column 1 and spin-down to column 2. Results of our decomposition procedure reveal that the amount of minority spin is significant in the ligand-based orbitals, as indicated in Table 11. In the NR limit (not shown) pure spin states are obtained. Within the Cu sphere this spin-orbit contamination is about 9% of the 7el and 6el MO’s, while in the ligand-based orbitals (5e2, 5e3, 4e3, and 4e2, see Figure 2), the spin-orbit mixings enhance orbital mixings of l a and 5u symmetry. Fortunately, this rearrangement of ligand mixings does not affect the qualitative nature of the metal-ligand bond given by the nonrelativistic analysis presented above. This strong spin-orbit mixing is undoubtedly
TABLE 111: Excitation Energies“
---
transition 7e2 lOel 7e2 10e3 7e2 lle, 7e3 7e2
calcdb 607 368
obsdc
318
562 375 344
230
262
”All units in nm. bTransition-state calculations using the DSW method. ‘References 13 and 14.
caused by the close spacing of the energy levels in this region of the spectrum (see Figure 2). However, it is not expected to have an important effect on the strength of the metal-ligand bond.1° The analysis of each relativistic molecular orbital indicates that ligand donation to Cu amounts to 1.279 electrons (0.607 to 4s CO) and 0.672 electrons to 4p), whereas back-donation (Cu amounts to 0.928 electrons (0.753 through 4p, and 0.175 electrons through 3d). This indicates that there is a net charge transfer of 0.1 17 electrons per carbonyl from ligand to copper, smaller than in Fe(CO)5 (0.22 electron/CO) and in Cr(C0)6 (0.46 electron/CO) . l o The electronic spectrum of Cu(CO), recorded in a pure CO matrix consists of two intense visible absorptions at 562 and 375 ~ ~ ~ ~ on nm, and weak shoulders at 495, 344, and 262 1 1 1 1 1 . ~Based single point group (D3,J symmetry considerations it was concluded that the absorptions at 495 and 344 nm were due to matrix site effects. A crude assignment of the electronic transitions was made by McIntosh et all8 by taking the ground-state energy differences (Le., not allowing for electronic relaxation upon electron excitations) and their results were rather unsatisfactory. The use of the Slater’s transition-state method30 is a convenient approach within the local density theory to estimate relaxation corrections to excitation energies. In principle, the highest accuracy is obtained by doing separate transition-state calculations (until S C F convergence is reached) for every transition of interest. In the present study we have performed transition-state calculations using the DSW method (which uses double point group throughout) to estimate the first ionization potential and excitation energies. These results are given in Table 111. The first ionization potential (IP) is predicted to be 6.6 eV. This value is substantially smaller than the calculated first I P for Cr(CO),, which is 9.4 eV.Io However, we should note that the H O M O in chromium hexacarbonyl is largely 3d based, while the H O M O in copper tricarbonyl is largely ligand based. The predicted excitation energies (see Table 111) are in good agreement with the experimental observations. The two intense bands are assigned to ligand-ligand electronic transitions. The two weak shoulders are assigned to ligand-ligand transition (7e2 1 le,), and metal to ligand charge transfer (7e, 7e,). It is interesting to note that these calculated excitation energies are symmetry allowed by double group and thus we discard the experimental assignment that the weak band at 344 nm was due to matrix site effects. However, our analysis corroborated the experimental observation that the origin of the band at 495 nm is probably due to matrix effects.I4
-
-
-
5182
The Journal of Physical Chemistry, Vol. 91, No. 20, 1987
Hyperfne Interactions. Although the electron spin resonance (ESR) spectra of copper tricarbonyl in low-temperature matrices have been extensively s t ~ d i e d , ' ~ ~still ' ~ - there '~ is controversy regarding the nature of the unpaired electron. In the present study some general features of spin-orbit and spin-polarization effects in this paramagnetic complex are discussed. Spin-orbit effects are modelled through a four-component relativistic molecular orbital (DSW) formalism, while core spin-polarization effects are estimated from quasi-relativistic spin-unrestricted (QRU) calculations. This approach, as suggested by Case,25has been shown to be successful in interpreting the ESR data of paramagnetic metalloporphyrins.26 We shall analyze the magnetic hyperfine interaction of the unpaired electron with nucleus n (n = Cu, C, or 0) in terms of a standard spin Hamiltonian: H , = In*A,*S
(1)
Here I, is a nuclear spin, A, is its associated hyperfine coupling tensor, and S is the electron spin. In nonrelativistic (or quasirelativistic) theory the connections between the H, parameters and the zero-order molecular wave function are based on a first-order perturbation treatment (excluding spin-orbit perturbation that requires a higher order).2' The hyperfine coupling tensor A, is made up of the isotropic interaction (Fermi contact term) and the anisotropic hyperfine interaction (the spin-dipolar term) between the electron and the nucleus. These are related to the nonrelativistic ( N R or QRU) electronic wave function as follows:
Bn,,, = gePegNPN((3i2- r 2 ) / r 5 ) S p i n i =
X,
Y,z
(3)
Here r is the vector from the nucleus n to the electron, and the subscript "spin" indicates that values for the spin-down orbitals are to be subtracted from those for the spin-up orbitals. Thus, spin-polarization effects may arise from differences in spin-up and spin-down orbitals. In evaluating the Fermi contact term we calculated the spin densities at the nucleus n (eq 2), and the spin-dipolar term is evaluated directly by the expectation values of the wave function as indicated in eq 3. In relativistic theory the method used for the calculation of the hyperfine interactions has been described elsewhere22,26and is based upon a first-order perturbation to the Dirac Hamiltonian, so that the effects of magnetic fields are described by the perturbation operator HD, where HD = e w A
(4)
In eq 4, a is the vector of 4 X 4 Dirac matrices and A is the electromagnetic vector potential. For the hyperfine term. A = ( p X r)/r3, where p is the nuclear magnetic dipole moment. Matrix elements of these operators are evaluated for the two rows of the e, irreducible representation of the highest occupied orbital. The resulting perturbation energies are then fitted to the usual spin Hamiltonian given in eq 1. Thus, the calculated hyperfine tensors include all the Fermi contact, spin-dipolar, and orbital contributions (due to spin-orbit); Le., there is no need to use different operators to represent these as in nonrelativistic theories (see eq 2 and 3). However, we have made an approximate decomposition of the total relativistic (DSW) value into spin-dipolar and orbital terms, which allow us to identify some interesting features of relativistic effects on hyperfine interactions.22-26 In particular, by subtracting the spin-dipolar terms from the total calculated DSW (the 63Cu Fermi contact term vanishes in an spin-restricted theory) hyperfine interaction, we determine an "orbital" contribution (that arises from unquenched orbital angular momentum), an important quantity which is difficult to estimate by other methods. Table IV gives the calculated and experimental results for 63Cu hyperfine interactions. Results at the nonrelativistic (NR) limit were obtained from the DSW code by setting the speed of light to a very large value (c = 1015au). Since the Fermi contact term vanishes by symmetry in spin-restricted (NR and DSW) theory.
Arratia-Perez et al. TABLE IV: 63CuHyperfine InteractionsQ
Fermi term
NR PRDDO QRU DSW
spin-dipolar term
emP NR QRU
DSW emP orbital terme
DSW for A , DSW for A,
total A,,
NR
total A,
QRU DSW expt NR QRU DSW
b 28.7 20.3 b 25.3' 20.6d 20.7 21.7d 28.9' 1.6 -3.0 6 1 .4df
61.6 63.1,dJ S4.4dJ,g 83.4,' 80.4,h 80.5' -0.3dkf -0.4 -3.1,dJ-1.8dJ'g -3.6,' O.O,h 8.3'
expt
"All units in G. Abbreviations: NR, nonrelativistic SW; PRDDO, nonrelativistic partial retention diatomic differential overlap; Q R U , quasi-relativistic spin-unrestricted SW; DSW, Dirac scattered wave; emp, empirical analysis for CU(CO)~ in Ar matrix (see ref 17a). bNot allowed in spin-restricted theories. Reference 17a. dCorrected for two center spin-dipolar contributions. 'See text for method of calculation. /Corrected for core spin-polarization effects. g Calculated at d(Cu-C) = 2.02 A. Reference 16a. Reference 13. TABLE V: Spin Populations of C U ( C O ) ~
atom
I
m
spin
Cu C 0
1 1 1
0 0 0
a a a
NR
QRU Pauli"
0.244, 0.5Ib 0.268
0.247
0.170 0.177 0.072, 0.05b 0.074 0.074 0.180, O . l l b
emp 0.41,
