J. Phys. Chem. 1995,99, 11659-11666
11659
Structure, Thermochemistry, and Magnetic Properties of Binary Copper Carbonyls by a Density-Functional Approach Vincenzo Barone Dipartimento di Chimica, Universith Federico 11, via Mezzocannone 4, I-80134 Napoli, Italy Received: February 16, 1995; In Final Form: May 11, 1995@
The structure, binding energy, and hyperfine coupling constants of mononuclear copper carbonyls (Cu(CO),, n = 1-3) have been studied using extended basis sets with a number of different density functionals. In the case of CuCO, all the methods agree in forecasting a bent equilibrium structure with a significant barrier to linearity (w15 kJ mol-'). Hyperfine coupling constants computed for bent and linear structures are very similar, thus ruling out the need for a linear structure to explain the electron paramagnetic resonance spectrum. In agreement with experimental data, addition of a second CO molecule leads to a 211 linear complex with vanishingly small hyperfine splittings but enhanced stability due to the reduction of two-orbital three-electron repulsive interactions. The bond pattem then remains essentially the same in Cu(CO)3, which assumes a planar trigonal equilibrium structure. From a quantitative point of view, local density functionals give extremely high binding energies and also generalized gradient corrections are not sufficient to completely rectify matters. Introduction of some Hartree-Fock exchange in the functional delivers a further significant improvement, approaching the accuracy of the most refined post Hartree-Fock computations. Purposely tailored basis sets are also introduced which are small enough to be used in molecular computations but are essentially free from basis set superposition error.
Introduction Binary complexes between CO and transition metals have been studied in detail.'-" It has been shownif that threeelectron two-orbital interactions between semifilled metal s orbitals and the CO 5u electron pair are essentially repulsive. This is usually more than counterbalanced by back-donation from metal d, orbitals to the CO 2n* orbital. Furthermore, o repulsion can be reduced by s to d promotion and sd, or sp, hybridization. As a result of these effects metal carbonyls are usually very stable. The situation is quite different for metal atoms belonging to the 1B group (Cu, Ag, and Au) in view of the extra stability of the completed ndIo configuration of these atoms, which strongly reduces the tendency to back-donation. In the case of copper monocarbonyl most calculations'-" yield a van der Waals type weak interaction with a linear CuCO arrangement. Very recently, Foumier,Io using the density functional (DF) approach, found, instead, that CuCO is nonlinear and bound by as much as 80 kJ mol-' with a Cu-C distance of 1.86 A. Sophisticatedpost-Hartree-Fock computations then confirmed the bent nature of this complex, but with a much reduced binding energy (about 20 kJ mol-') and a quite low barrier to linearity (about 2 kJ mol-').4d This latter binding energy is in agreement with the experimental estimate of 25 f 5 kJ mol-' proposed by Blitz, Mitchell, and Hackett.I2 On the other hand electron paramagnetic resonance (EPR) experiments on CuCO have been interpreted in terms of a linear equilibrium s t r u c t ~ r e . ' ~ .Addition '~ of a second CO molecule could significantly change the situation if the unpaired electron of Cu is promoted into a n orbital. In such circumstances, a 211radical would be produced with an unobservable EPR spectrumI3 but an enhanced stability connected to reduction of u repulsion. Only indirect experimental e ~ i d e n c e ' ~is, 'available ~ for this process, and no theoretical computations have been performed till now. While a low barrier to linearity would lead in both cases to properties essentially equivalent to those of a linear system, a @
Abstract published in Advance ACS Abstracts, June 15, 1995.
0022-365419512099-11659$09.00/0
contemporary computations of the structure and hyperfine coupling constants (hfcc's) by a reliable method would settle in a more direct way this problem. Another significant aspect concerns the structure and stability of the tricarbonyl, for which only indirect evidence is a ~ a i l a b l e . ' ~ . ' ~ From a theoretical point of view, a comparative study of CuCO, Cu(CO)2, and Cu(CO)3 is particularly challenging, since it requires a computational model able to describe in a balanced way both strong and weak bonds in open-shell systems. It is common practice that conventional quantum-chemical approaches of intermediate sophistication (e.g. Hartree-Fock (HF) or second-order perturbation theory (MP2)) work very well essentially for closed-shell molecules formed by main group atoms. For small systems, the most sophisticated post-HartreeFock approaches in combination with large and flexible basis sets and, when needed, a proper account of relativistic effects provide very accurate results along the whole periodic table. However, the cost of these computational tools and, especially, their scaling with the number of electrons preclude their use for large systems. In that respect the density functional (DF) approachI5 is more attractive, since it takes into account a large amount of correlation with the same resources as the HF method. The development of refined generalized gradient approximations (GGA's)I6-l8 has significantly i m p r ~ v e d ' ~the - ~results ~ provided by the so-called local spin density (LSD) appr~ximation,'~ and the very recent implementation of hybrid approaches delivers a further significant i m p r ~ v e m e n t . ~ ~Rooted * * ~ in the adiabatic connection formula,25 hybrid methods manage to combine the advantages of HF and DF models with an improved overall accuracy. A hybrid method is further qualified as selfconsistent (SCH) when gradient corrections and HF exchange are not simply computed using a converged LSD wave function but the SCF process is performed with the complete density functional. A number of studies have shown that, at least for molecules formed by second-row atoms, the B3LYP variant is particularly effective in the description of geometries, thermo0 1995 American Chemical Society
Barone
11660 J. Phys. Chem., Vol. 99,No. 30, 1995
particularly good performances of the BLYP model in thermochemistry, kinetics, and one-electron o b ~ e r v a b l e s . ~Also ~-~~ noncovalent interactions are well described at this l e ~ e l . ~A~ , ~ ’ chemical problems20v22and on some limits of the PW functional for one-electron proper tie^.^' Since the LYP functional contains possible drawback of SCH approaches is, however, that the both a local part3* and a gradient correction,20only the latter percentage of HF and DF exchange terms could depend on the contribution should be used to obtain a coherent implementation. particular kind of atom, interaction, and/or property investigated. However, it has been recently shown that the local part of the I thought, therefore, it would be interesting to test this approach LYP functional is very similar to the VWN parametrization of on the difficult playground represented by mononuclear copper the correlation energy in the free electron gas.38 As a carbonyls. As a first step I have tested several standard basis consequence the last term in eq 1 is approximated by sets with reference to a very large uncontracted set. A reliable and manageable set has been built, which can be used in AE, - EEWN molecular computations. I have next compare the performances of several functionals starting from the simple local spin density (LSD) level to different GGA’s, to SCH models. As we shall A number of tests showed that values of the three semiempirical see, this last family of functionals is able to provide reliable coefficients appearing in eq I near 0.80 provide the best results, structures, binding energies, and EPR parameters for copper irrespective of the particular form of the different functional^.^^ carbonyls. In particular, the hyperfine splittings of the linear I will use here the values (a0 = 0.80, ax = 0.72, and ac = and bent structures of CuCO are so similar that EPR spectra 0.81) determined by Becke from a best fitting of the heats of can be interpreted equally well in terms of both kinds of formation of a standard set of molecules.24 Note that, in the original applications by HF exchange and gradient equilibrium structures. corrections were only added in the computation of energies using Computational Details converged LSD electron densities. Furthermore single-point energy computations were performed at experimental geomAll the Kohn-Sham (KS) computations (unrestricted Kohnetries. Here I use, instead, a fully coherent implementation3* Sham (UKS) for open-shell systems) have been performed with in which the SCF process, geometry optimizations, and comthe help of the Gaussian 92” package.32 Among the putation of analytic second derivatives are performed with the characteristics of this code, I mention the use of Gaussian basis complete density functional including gradient corrections and, functions, the avoidance of auxiliary functions, the implementapossibly, HF exchange. tion of very large grids, and the availability of analytical first The formulas for calculating hyperfine parameters are oband second derivatives.20 Since the supermolecular approach tained from the spin Hamiltonian40 can be seriously affected by the basis set superposition error (BSSE), the counterpoise method of Boys and B e ~ m a r d was i~~ (3) used to estimate the BSSE on the Cu-CO dissociation energy. Although effective pruned grids are available for main group The first two contributions are the electronic and nuclear Zeeman elements of the first three rows,20bthis is not the case for terms, respectively, and arise from the interactions between a transition metals. Furthermore evaluation of the BSSE cannot magnetic field B and the magnetic moments of the unpaired be performed without specifying the same grid for all atoms electrons (S,) or the magnetic nuclei (Iz) in the system. The including ghost ones. As a consequence, I have used in all the remainder is the hyperfine interaction term and is a result of computations regular atomic grids consisting of 50 radial shells the interactions between the unpaired electrons and the nuclei. with 194 angular points each. Test computations have also been Be and BN are the electron and nuclear magnetons, and ge and performed to verify that this grid leads to converged results for g N the electron and nuclear magnetogyric ratios. the different quantities of interest in the present study. The 3 x 3 hyperfine interaction tensor T can be further Local spin density (LSD) computations have been carried out separated into its isotropic (spherically symmetric) and anisousing the exchange energy of the uniform electron gas34 and tropic (dipolar) components. Isotropic hfcc’s Ai,,(N) are related the corresponding Vosko, Wilk, and Nusair (VWN) correlation to the spin densities @(r”N)at the corresponding nuclei by f ~ n c t i o n a l .Gradient ~~ corrections have been introduced using the Becke exchange and either the Perdew” (P) or the Lee-Yang-ParrI8 (LYP) correlation parts. In standard nomenclature, the former method is sometimes referred to as BP and the latter as BLYP. Becke has recently convincingly argued that “exact exchange Computation of these terms is straightforward and is already energy (which is essentially, though not exactly, equal in value included in most ab-initio codes. The anisotropic components to the conventional Hartree-Fock exchange energy) must play are derived from the classical expression of interacting dipoles: a role in highly accurate density-functional theories”.24 Rooted in the “adiabatic connection” formula,25 eq 1 represents the simplest possible blend of local density approximation Hartree-Fock exchange and gradient corrections to exchange (AEx) and correlation (A&) that exactly recovers the uniform electron-gas limit: These terms are more complicated to compute and also to
e
(GY),
E,, = E i F i(1 - a o ) ( E y-
(q),
eSD) + axAEx + a,AEc (1)
I will use here the Becke gradient correction to exchange, but the Perdew-Wang (PW) correlation potential36used in ref 24 has been replaced by the P or LYP ones (leading to B3P and B3LYP hybrid functionals, respectively). This is based on the
determine experimentally. They are, however, strictly related to field-gradient integrals already available in several standard ab-initio packages. For linear molecules, the molecular symmetry axis is chosen as one of the components, say 2. Since the tensor is traceless, there remains only one meaningful diagonal element, say T . with T z = -2T~u = - 2 T y y . The quantity A d i p defined by A d i p = I/~Tzzis called the dipolar hyperfine coupling constant. The observed hyperfine structures
Properties of Binary Copper Carbonyls
J. Phys. Chem., Vol. 99, No. 30, 1995 11661
Note that at this level the error in the computed hfcc is slightly less than lo%, which is typical for the best theoretical computation^^^^^^ and is sufficient for interpreting experimental results. Also the good reproduction of the experimental splitting basis set notes energy IP A,,,(Cu) between 3D (d9s') and IS (d'O) states of Cu+ (the j-averaged (23,15,8)/[23,1531 EXT -1640.591 66 8.03 5491 energy separation calculated from ref 52b is 2.81 eV) afforded -1640.598 17 8.03 5533 (24,18,9,1)/[24,18,9,1] EXT IS + by the EXT basis set (2.88 eV) is only slightly deteriorated using 3p + Id + I f smaller contracted basis sets (e.g. 2.96 eV by the HSA basis - 1640.436 55 8.00 5664 (14,11,6,1)/[8,7,4,1] WAC set and 2.90 eV by the TZVP basis set). We can, therefore, (14,11,6,1)/[8,7,4,1] HSA -1640.490 73 8.01 5512 expect a reasonable description of the copper atom also when (14,11,5,1)/[8,7,3,1] HSA without -1640.466 83 8.01 5167 carrying a not negligible positive charge andor undergoing diffuse d - 1640.466 18 8.02 5 160 (14,9,5)/[8,5,31 HSA original significant s to d promotion. from ref 37 In C, symmetry the 2F state of the CuCO complex (14,11,6,1)/[8,7,3,1] HSA'" -1640.523 30 8.03 5513 correlates with the 2S (3dI04s') ground state of atomic copper -1640.542 73 8.03 5115 (17,12,7,1)/[6,5,4,1J TZVP and the closed shell ''P ground state of CO. This is the only (1 7,12,7,1)/[8,5,4,1] TZ2P' a -1640.546 23 8.03 5534 experimental 7.72b 5 9 9 s state considered in the present paper. Due to repulsion between the singly occupied 4s copper orbital and the highest occupied See Table 5. Reference 52a. Reference 51. molecular orbital (HOMO) of CO, a localized lone pair on the carbon atom, this state of the complex is expected to be only of EPR spectra of linear molecules are often analyzed in terms weakly bonded by dipole induced dipole interactions. Bending of the components of the hyperfine tensor parallel (All) and could at the same time reduce Cu-CO repulsion and also allow perpendicular (AJ to the symmetry axis. These are related to 4s to 2n* donation, which is not possible for the linear molecule. the above Aiso and Adip All = Aiso r' 2 A d i p and A 1 = As a consequence the bent structure could correspond to the AIS, - Adip. absolute energy minimum. The results obtained by different The hfcc's are usually given in units of megahertz by functionals using the same basis set (HSA) are summarized in microwave spectroscopists and in gauss or millitesla (1 G = Table 2. All the methods agree in forecasting a bent equilibrium 0.1 mT) by EPR spectroscopists. In the present work all the structure with a substantial barrier ( ~ 1 kJ 5 mol-') to linearity. theoretical hfcc's are given in megahertz; to convert data to It is quite apparent that the B3LYP functional gives the most gauss, one has to divide by 2.8025gdge, where go is the g factor satisfactory binding energies. While the geometries obtained of the electron in individual radicals. at the LSD and BP levels are slightly different from the Several basis sets for Cu have been tested with reference to corresponding results of ref 10, the binding energies are very the isotropic hfcc computed by a very large reference set. This similar: 135.6 and 83.3 kJ mol-' with respect to 138.9 and has been obtained supplementing the (23,15,8) set optimized 84.9 kJ mol-'. This confirms that DIT is a very stable by Partridge4' (hereafter referred to as EXT) with one s (fs = procedure from a computational point of view and that partial 0.0124), three p (tp= 0.132 612, 0.055 109, 0.022 901), and inclusion of Hartree-Fock exchange significantly improves the one d (fd = 0.060 458) diffuse functions, whose exponents are performances of current functionals. chosen in an even-tempered sequence starting from the two most Correcting the B3LYP binding energy for BSSE (5.4 W diffuse functions of each angular quantum number in the original mol-') and zero point energy differences (2.9 kJ mol-') yields basis. One f function (ff = 0.761)46has also been added. I tested, in particular, the (14,9,5)/[8,5,3] set of W a c h t e r ~ ~ ~ a value of 32.6 W mol-', which is just above the error bar of the experimental estimate.I2 Note that more than 90% (5.0 kJ (hereafter referred to as WAC), the corresponding set recently mol-') of the total BSSE arises from the Cu atom in the presence reoptimized by Schiifer et al.43 (referred to as SHA), and the of the CO ghost basis set. The total BSSE is, furthermore, less (17,10,6)/[6,3,3] set of ref 44 (referred to as TZVP). All these than 50% of the corresponding values obtained in recent postbasis sets have been supplemented by the two p functions H a r t r e e - F ~ c k ~and ~ DFT'O studies. This shows that the basis suggested in ref 42 (scaled by 1.54d),by one diffuse d function$5 set is well balanced, at least for DFT computations. Since the and by one f function.46 role of d electrons in the binding between Cu and CO is only In all cases the C and 0 atoms were described by the TZ2P' marginal, f functions are essentially useless in this case. basis set optimized and validated in previous DFT studies The results obtained by B3LYP and several post-Hartreedealing with structures and EPR parameters of organic free Fock methods using the same basis set (WAC) are compared r a d i ~ a l s . ~ ~This , ~ basis ~ , ~ ~set, ~gives ~ energies and structures in Table 3. The bond lengths obtained by the different methods very close to those provided by the standard Huzinaga-Dunning are quite similar, taking also into account that the DIT value is TZ2P basis set49%50 used by several authors in previous DFT essentially converged, whereas extension of the basis set studies.21*22 increases the Cu-C bond length at the CCSD[T] and MCPF On the other hand, the Cu-C=O angle obtained by Results and Discussion post-Hartree-Fock methods is larger than the DFT values. At the same time the barrier to linearity obtained by DIT methods The results obtained for the ionization potential and the is more than 6 times the corresponding CCSD[T] value. isotropic hfcc of 63Cuby different basis sets are compared with Correspondingly an harmonic analysis of linear CuCO yields e ~ p e r i m e n t ~in' ,Table ~ ~ 1. It is quite apparent that the B3LYP two relatively high degenerate imaginary frequencies (40 1i functional provides reasonable ionization potentials irrespective cm-I). The other two real frequencies occur at 2184 (CO of the basis set, whereas diffuse d functions play the same stretching) and 302 cm-' (CuC stretching). It is remarkable significant role in the computation of isotropic hfcc's as diffuse that the C-0 bond length (1,128 A) and the corresponding s and p functions in the case of second-row atom^.^^,^^ On the stretching frequenc are very near to the values computed for other hand, f functions have no role, since the unpaired electron free CO (1.126 and 2210 cm-I), whereas significant is localized in an s orbital. The situation could be different for atoms with semifilled d orbitals. modifications are found for the bent structure (1.141 %, and 2033 TABLE 1: Total Energy (a.u.), First Ionization Potential (eV), and Isotropic Hyperfine Coupling Constant (MHz) of 63CuComputed with Different Basis Sets Using the B3LYP Functional
+
K
11662 J. Phys. Chem., Vol. 99, No. 30, I995
Barone
TABLE 2: Geometrical Parameters (A, deg), Dipole Moments @, D), Isotropic hfcc's (MHz), Binding Energies (De,kJ mol-'), and Barriers to Linearity (AE,kJ mol-') Computed for CuCO with Different Density Functionals Using the HSA Basis Set (See Text for Details) BP
LSD
BLYP
B3P
B3LYP
bent
lin
bent
lin
bent
lin
bent
lin
bent
lin
De
1.840 1.148 142.7 0.673 3724 214 135.6
AE
0.0
1.831 1.135 180.0 1.868 3717 219 115.5 20.1
1.900 1.158 142.1 0.636 3829 213 83.3 0.0
1.891 1.145 180.0 1.856 3811 219 65.3 18.0
1.924 1.158 141.5 0.649 3869 226 68.2 0.0
1.921 1.145 180.0 1.773 3912 23 1 49.4 18.8
1.929 1.141 141.2 0.687 3961 190 54.4 0.0
1.921 1.128 180.0 2.312 3832 198 37.2 17.2
1.957 1.142 140.2 0.651 3992 20 1 41.0 0.0
1.953 1.129 180.0 2.259 3892 207 23.4 17.6
AdCu)
5912
cu-c c=o Cu-C=O
P AdCu) AwdC)
cuco
exP
4142" 182" 25 +c 5b
cu
c-0
P a
5768
5713
5598
5512
5995'
1.125 0.119
1.127 0.099
1.12gd 0.112d
co 1.128 0.225
1.138 0.185
1.138 0.158
Reference 13. Reference 12. Reference 5 1. Reference 2 1.
TABLE 3: Comparison between the Results Obtained for CuCO by Different Methods Using the Same WAC Basis Set (See Text for Details) Cu-C C=O CU-C-0 De Do Do" fres MP2b MCPFb UCCSD[TIb B3LYP exP
1.783 1.947 1.910 1.952
1.140 1.137 1.140 1.141
180.0 156.4 152.5 140.3
55.6 19.2 23.4 41.8
52.3 17.6 7.5 21.8 9.2 38.9 33.1 25 f 5c
2086,85,408 2103, 58, 295 2094,63, 296 2033,403, 233 2014d
a Corrected for BSSE. Reference 4d. Reference 12. Fundamental band origin from ref 13; this value corresponds to an harmonic frequency of -2040 cm-I.
cm-I). Comparison of the experimental shift in the CO frequency upon complexation (-130 f 6 cm-I) with the computed values (-177 cm-' for the bent structure and -26 cm-' for the linear one) gives further support to the prediction of a bent equilibrium structure. I tried next to develop an effective basis set for Cu. The results obtained by different standard basis sets are shown in Table 4. As could have been expected, WAC and HSA results are very similar, whereas the TZVP basis set leads to longer Cu-C bond lengths and, correspondingly, to a lower binding energy. The BSSE of Cu is, however, particularly low at the TZVP level (1.9 kJ mol-'), so that the BSSE corrected binding energies obtained by the different basis sets differ by less than 3 kJ mol-' and are very close to the upper limit of the experimental estimate (30 kJ mol-').'* Next I reoptimized the contraction coefficients of the HSA basis set through UKS computations on the Cu atom. As mentioned above, addition of a diffuse d function to the original HSA basis set significantly improves results. On the other hand this leads to a too high number of contracted d functions (4)for molecular computations. At the Hartree-Fock level this number can be reduced to 3, optimizing the basis set on a different electronic config~ r a t i o n . I~ have ~ thus used the 35 contraction of the (6d) set given in ref 53 to develop the HSA' basis set shown in Table 5. The results of Table 1 show that the hfcc of Cu is unaffected by the above modifications, whereas the total energy is significantly lowered. The results of Table 4 show that geometrical parameters are also unaffected by the reoptimization, but the binding energy becomes essentially identical to that of the TZVP basis set with a BSSE for the Cu atom reduced from 5 to 3 kJ mol-'. On the other hand the TZVP basis set has a number of attractive features (very small BSSE, reduced number of contracted functions, lower total energies). Its only drawback is a relatively poor description of s orbitals, which is evidenced
by the hfcc of the Cu atom. As a consequence I have reoptimized the s part of the basis set and just the contraction coefficients of the p and d parts. The resulting basis set (also given in Table 5) becomes part of our standard TZ2P' set. The results obtained at this level are very encouraging both for atomic (Table 2) and molecular (Table 4) computations. Since computed binding energies are generally considered "chemically accurate" when their error is below 5 kJ mol-', correction for BSSE can be avoided with the reoptimized basis sets HSA' and TZ2P'. Although the counterpoise method33 gives in general reasonable r e s ~ l t s ?its ~ ,inclusion ~~ in geometry optimizations becomes quite cumbersome. On the other hand, the Cu-C bond length and, especially, the corresponding force constant are seriously affected by BSSE." Taking into account that BSSE-free basis sets are much more difficult to obtain for post-Hartree-Fock computations,''*56this is a further advantage of DFT-based approaches. The line shapes of the EPR spectrum of CuCO are characteristic of an ensemble of randomly oriented radicals having axially symmetric g and hyperfine coupling tensors. Taking the Z axis along the metal-carbon bond, and the molecule in the XZ plane, we get A m = -12.1, AYY = -12.5 MHz for 63Cu and Axx = -19.2, Aru = -12.3 MHz for I3C. The corresponding values for the linear structure are A n = AYY= -40.8 MHz for 63Cuand Axx = Ayy = -3.0 MHz for I3C. The difference between the two perpendicular components is, therefore, sufficiently small that interpretation in terms of an axially symmetric tensor is essentially correct also for the bent structure. Also the isotropic hfcc's computed for linear and bent structures (see Table 2) are so similar that this feature of the EPR spectra cannot be used for structural purposes. The situation is quite different for dipolar terms. In particular at the B3LYPmZ2P' level the computed difference between All and A1 (which is 3 / 2 A ~amounts ) to 37 or 122 MHz for 63Cu and to 46 or 9 MHz for I3C when considering bent or linear structures, respectively. The experimental value for 63Cu (48 MHz) is thus well compatible with the bent structure, whereas the value for I3C ( < l o MHz) suggests a larger Cu-C=O valence angle. Note that the dipole moments computed for the linear and bent form are very different (see Table 2), so that environmental effects can have some influence on the equilibrium structure. The results obtained for the whole series of mononuclear copper carbonyls at the B3LYPRZ2F" level are shown in Table 6. Computations of harmonic frequencies shows that the linear
J. Phys. Chem., Vol. 99, No. 30, 1995 11663
Properties of Binary Copper Carbonyls
TABLE 4: Geometrical Parameters (A,deg), Total Energies (a.u.), Binding Energies (kJ mol-'), Dipole Moments @), and Isotropic hfcc's (MHz) of CuCO Computed with the B3LYP Functional Using Different Basis Sets (See Text for Details) parameter cu-c C=Ob
cu-c=o E
De Do
DiC P A,so(63C~) A,s0(13C)
WAC
HSA
HSA' a
TZVP
1.952 1.141 (1.126) 140.3 -1753.812 18 41.8 38.9 33.1 0.654 3995 20 1
1.957 1.142 (1.127) 140.2 -1753.857 58 41.0 38.1 32.7 0.65 1 3992 20 1
1.957 1.142 (1.127) 140.2 -1753.888 06 35.7 32.8 29.4 0.650 2993 20 1
1.974 1.141 (1.126) 139.5 -1753.910 72 34.1 31.2 28.9 0.634 2947 198
TZ2P'
a
1.969 1.142 (1.126) 139.5 -1753.914 36 32.6 29.7 27.5 0.638 4033 198
See Table 5 . Values in parentheses are for the CO molecule. Corrected for BSSE.
TABLE 5: Orbital Exponents and Contraction Coefficients for the HSA' and T Z 2 1 Basis S e w HSA' basis set orbital contraction exponent coeff 441087.3 661 12.02 15047.01 4263.427 1396.382 5 11.9606 203.4543 82.79234 20.85429 9.041068 2.751814 1.043486 0.111723 0.04 1041
2530.097 600.0979 194.0820 73.67182 30.44737 13.1227 1 5.521483 2.145792 0.767975
65.80000 18.82000 6.538000 2.348000 0.769100 0.206500
TZ2P' basis set orbital contraction exponent coeff
s Orbitals 2942850. 441087.3 661 12.02 15047.01 4263.427 1396.382 5 11.9606 0.406 52 203.4543 0.312 72 82.79234 414.4127 1.000 00 128.3205 1.000 00 1.000 00 1.000 00 20.85429 1.ooo 00 9.04 1068 1.000 00 2.75 1814 1.O43486 0.1 11723 0.04 1041
0.000 20 0.001 55 0.007 94 0.032 55 0.105 02 0.256 80
p Orbitals 0.001 84 2034.760 0.015 27 481.9047 0.073 11 154.6748 57.74058 0.224 64 23.0991 0.417 21 9.38825 0.368 57 37.59617 1.ooo 00 5.124069 1.000 00 2.0 12000 1.000 00 0.738607
d Orbitals 0.017 08 0.099 16 0.274 75 0.404 01 1.000 00 1.000 00
74.12946 21.35984 7.499524 2.760139 0.953621 0.284209 0.100000
0.000 03 0.000 17 0.001 55 0.007 94 0.032 55 0.105 02 0.256 80 0.406 52 0.312 72 0.026 13 0.121 93 1.000 00 1.000 00 1.000 00 1.ooo 00 1.000 00 1.ooo 00 0.002 35 0.019 13 0.090 17 0.260 63 0.420 93 0.243 45 --0.028 99 0.549 19 0.937 93 1.000 00
0.014 36 0.086 63 0.256 3 1 0.403 74 1.ooo 00 1.000 00 1.000 00
a Both basis sets are supplemented by two p functions and one f function (see text).
form of Cu(CO)2 and the planar trigonal form of Cu(CO)3 correspond to true energy minima. The harmonic frequencies for inversion at the Cu atom are, however, so small (about 60 cm-' both for the 2ng mode in the dicarbonyl and the A"2 mode in the tricarbonyl) that vibrational averaging could significantly affect some observables (vide infra). Some comment is, further, in order about the frequencies of the dicarbonyl. In linear systems each n manifold should consist of two degenerate vibrations occumng in the planes XZ and YZ,respectively.
TABLE 6: Geometrical Parameters (A, deg), Binding Energies (kJ mol-'), Isotropic Hyperfine Coupling Constants (MHz), Harmonic WaveNumbers (em-'), and IR Intensities (in Parentheses in km mol-') Computed at the B3LYP/ TZ2P' Level for CuCO, Cu(CO)2 (Both in Linear Structures), and Cu(C0)s (Planar Trigonal Structure) CuCO CuC 1.964 CO 1.128 A,,,(Cu) 3946 A d C ) 217 A,,,(O) -16.3 AEl" 15.0 A&,? 15.0 CJ,: 2186,282 w(1)
n:4431'
Cu(CO)2 1.842 1.146 -39.1 -7.2 -8.9 80.0 95.0 u,: 2114(0.0), 377.6(0.0) 0,: 1998(4088), 469(0.5) n,: 354-307,66
nu:378-220 a
Cu
+ nCO - Cu(CO),.
For the process Cu(CO),-,
Cu(CO)3 1.889 1.139 -0.2 -11.4 -5.7 68.0 148.0 A',: 2165(0.0), 280(0.0) A'2: 346(0.0)
E': 2048(2300),425(0.3), 368(11.8), 57(0.2) A'$: 60(0.6) E": 292(0.0)
+ CO - Cu(CO),.
For the process
Although this is the case for the 2ng vibration (essentially involving the C-Cu-C angle), both symmetric and antisymmetric combinations of CuCO bendings are split into two nondegenerate vibrations (see Table 6). As a matter of fact, the potential energy of spatially degenerate electronic states of linear triatomic moieties splits into two components when the moiety is bent away from linearity (Renner-Teller ~ p l i t t i n g ) . ~ ~ In such circumstances, calculation of vibrational frequencies for the linear equilibrium structure can provide different combinations of real and imaginary frequencies, since bending in the XZ plane samples a different C, potential than bending in the YZ plane. This occurs because the symmetries of the openshell molecular orbitals are fixed for a particular choice of the Cartesian axes, making the two bending displacements access different components of the degenerate electronic state. In particular, the calculation of two different real frequencies for each of the two n manifolds corresponds to the case referred to as (a) in ref 57. The ground electronic state of CuCO (2Z+) is not spatially degenerate, but the same effect has been computed for the degenerate ground state of AlC0.58 All the characteristics of the di- and tricarbonyl compounds are quite similar but markedly different from those of CuCO. This is related to the very different electronic structure of copper in the monocarbonyl. In this case, in fact, the unpaired electron is essentially localized in the 4s orbital with small contributions from d orbitals. In the other two complexes there is, instead, a significant s to p promotion with the consequent reduction of repulsion and increase of stabilizing back-donation to the 2n* orbitals of carbonyl groups. These results are in line with the
11664 J. Phys. Chem., Vol. 99, No. 30, 1995
Barone
conclusion reached in a recent CCSD(T) study of the simpler HCuCO The Cu-C bond strength is consequently much larger in di- and tricarbonyl compounds, and there is a nice correspondence between the Cu-C binding energy and the Cu-C bond length. It is remarkable that the energy gain connected to addition of the second carbonyl group is more than 4 times that of the first one, whereas a slightly lower stabilization is obtained upon addition of the third carbonyl. This trend is in line with the available kinetic and spectroscopic data. In fact the experimental determination of the binding energy of CuCO is based on the hypothesis that the Cu(CO)2 complex is sufficiently strongly bound that its dissociation to CuCO CO does not occur.'* On the other hand, the primary CO stretching force constant of copper carbonyls plotted as a function of the coordination number shows a very unusual "V"-shaped curve.* Since C=O and Cu-C bond strengths have, of course, opposite trends, the IR results are in line with an oscillatory behavior of binding energies in copper carbonyls. From another point of view, only the formation of CuCO and Cu(CO)3 from Cu and CO in matrices at low temperature has been confirmed by EPR ~ p e c t r o s c o p y . ~It~ .is' ~remarkable in this connection that the computed hyperfine couplings of Cu(C0)2 are so small that the EPR spectrum would be essentially undetectable. The situation is more involved for the 2A"2 electronic state of planar trigonal Cu(CO)3. In fact the most recent experimental investigation^'^.'^ agree in suggesting that -60% of the unpaired spin population is located on the ligands and -40% at the metal center. On the other hand DFT computations61%62 indicate a contribution of about 25% from the metal, whereas UHF ab-initio computation^^^ gave a contribution of -50%. The B3LYPmZ2P' model indicates a 30% contribution from the metal, whereas UHF computations with the same basis set give again a contribution of -50%. The better agreement between UHF and experimental results is somewhat puzzling, since several studies suggest that UKS values should be more reliable than UHF ones.@ It must be remembered in this connection that the only experimental technique directly providing spin densities involves the use of polarized neutrons,64 whereas relationships between spin populations and isotropic65 or anisotropic62hyperfine splittings (such as those used in the experimental estimates for Cu(CO),) are very questionable. In such a situation, the only meaningful procedure is the direct comparison between theoretical and experimental EPR parameters. The very large discrepancy between B3LYPmZ2P' and experimental values (see Table 6 ) is quite surprising in view of the results obtained for Cu, CuCO, and a number of organic JC I decided, therefore, to investigate more deeply the sensitivity of computations to structural and dynamical aspects. In a previous papefil it was suggested that overestimation of Cu-C bond lengths could lead to a very small isotropic hfcc on copper. Modification of the Cu-C bond length between 1.8 and 1.95 8, gives, however, only modest variations of A,,,(Cu) (between 19 and 10 MHz). Previous experience on organic radicalP suggests, on the other hand, that vibrational averaging significantly increases the isotropic hyperfine couplings of the central atom in D3h systems with low out of plane frequencies. The inversion at the radical center was, therefore, investigated optimizing Cu-C and C - 0 bond lengths at fixed values of the out of plane angle a. Figure 1 shows that the isotropic splitting of Cu changes dramatically, increasing the pyramidality of the system, whereas C and 0 atoms are only slightly affected. The corresponding potential energy is shown in Figure 2 together with the vibrational levels obtained by our standard numerical approach.67 From these data it is straightforward to compute vibrationally averaged hfs at different temperatures.66
+
0 - - - - - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ -
..........................................................
- 50
--
i
I
:
6-
\
h
-
3
L
x 4OI L
m c m
2-
-15
-5 out o f
5 plane
15
angle
Figure 2. Potential energy and lower vibrational wave functions (normalized to 2) for the inversion at Cu in Cu(CO)3 computed at the B3LYPRZZP' level.
10
1
0
1
, 2h0
400
600
800
1000
T (K) Figure 3. Temperature dependence of Ai,,(63C~)in Cu(CO)3.
Figure 3 shows a significant increase of AiSo(Cu)with temperature, but at the temperature of the EPR measurements (4.7 K) the increase with respect to the value of the planar minimum structure is only 3 MHz. This is due to the very small amplitude of vibration ((a2)"* = 2") connected to the significant mass of carbonyl groups. On the other hand, a value compatible with the experimental determination is obtained for a as small as 7". Since this distortion requires only 5 kT mol-', matrix effects could easily stabilize this C3" structure, as already advocated
J. Phys. Chem., Vol. 99, No. 30, 1995 11665
Properties of Binary Copper Carbonyls
TABLE 7: Magnetic Properties (in MHz) of Binary Copper Carbonyls Obtained by Different Methods
cuco UHF A,,,(Cu) A,,,(C) Ad,p(Cu)
Adip(C) 8 spin dens (Cu)
UMP2
B3LYP
CU(CO)2 exp
UHF
CU(CO)3
UMP2 B3LYP
3611 3700 4020 4142 173.6 36.3 150.7 183.8 214.4 182 -66.1 -15.6 6.5 7.7 15.1 16.0 68.0 68.0 13.0 6.9 15.8 e10 15.0 17.1 90 88 75 75 26 22
-18.7 -9.0 63.9 21.2 19
UHF
UMP2
178.9 77.5 -68.3 -20.5 79.2 77.0 6.9 9.6 38 32
LSD
BP
5.7 20.3 -17.1 -19.1 72.2 69.0 12.9 13.1 24 25
BLYP
B3P
B3LYP
exp
-5.3 -8.3 68.7 13.5 23
37.4 -22.6 70.8 12.1 26
14.5 -13.0 70.8 12.2 24
71.0 -18.7 81.0 12.3 40
TABLE 8: Natural Population Analysis for B3LYPmZ2P' Wave Functions of CuCO, Cu(C0)z (Both in Linear Structures), and Cu(CO)3 (Planar Trigonal Structure)
cu C
0
natural D O D U ~ natural spin popul net charge natural popul natural spin popul net charge natural popul natural spin popul net charge
cuco
Cu(CO)2)
CU(CO)3
3d9.82.4sI .094D0.03 4s0 3d0 0.058 2sl 57,2p206 2so '1,2paO02 0.357 2s' 71,2p467 2soo1,2paO01 -0.415
3d9.75 4s0.58 4D0.15
3d9.72 4s0.48.4D0.15
for the isovalent Ag(C0)3 molecule.68 Another possibility is, of course, that the B3LYP method performs poorly for the isotropic hyperfine splittings of n open-shell systems involving transition metals. In order to better verify this point, I have computed isotropic and anisotropic splittings with several different functionals, together with UHF and UMP2 methods using a somewhat smaller basis The results of Table 7 show that the MP2 method performs pretty well both for CuCO and Cu(CO)3, whereas the UHF method grossly overestimates isotropic splittings in n open-shell systems. This is connected to the well-known overestimation of spin polarization effects at the UHF level, whereas delocalization terms are correctly reproduced. The good performance of the UMP2 method in reproducing spin polarization effects is not u n e ~ p e c t e d ,but ~~,~~ it is gratifying that this applies also to transition metals. The most striking effect concerns, however, the poor performance of the BLYP functional with respect to both LSD and BP ones in the case of Cu(CO)3. Note that the situation is different in the case of cr open-shell systems (e.g. Cu, CuCO) where the different functionals provide comparable results. Although inclusion of some Hartree-Fock exchange improves matters, B3P and B3LYP results remain far from experiment, the former functional being somewhat better. The performances of Perdew and Lee-Yang-Parr gradient corrections to the correlation functional are thus reversed from those reported for organic radicals formed by second-row atoms.27x28-48 This suggests that the separation between core and valence electron densities afforded by the LYP functional has some limit for transition metals. The situation is different for total spin densities where all the DF-based approaches provide very similar contributions from the Cu atom, which are significantly lower than those computed using HF-based methods. The anisotropic couplings of I3C provided by all the DFT-based methods are very similar to each other and in better agreement with experiment than those computed by UHF-based methods. The situation is reversed in the case of Cu, but the Adip provided by all methods can be considered satisfactory. The ensemble of these results suggests that the performances of the B3LYP model are not worsened when global rather than pointwise spin properties are concerned. The metal-ligand interaction in copper carbonyls has been analyzed by the natural bond orbital (NBO) a p p r o a ~ h . ~ In '.~~ the bent form of CuCO the electronic configurations of Cu (4so.93,3d9,86,4po,02) and C (2s1,55,2p2,'6) confirm that bonding essentially occurs between the 4s orbital of copper and an sp
.
.
4pno l 2 0.649 2sl 44,2p226 2pno *O 0.226 70 2 4 4 0 2pno08 3P -0.442
hybrid of carbon. Also the spin distributions on Cu ( 4 P 8 , 4po.O2)and C (2s0.08,2p0.14) are in remarkable agreement with the experimental estimate^'^ of 4s0~67,4p0~08 (Cu) and 2s0.05,2p0,20 (C). A Mulliken population analysis confirms" that the metal atom is negatively charged. In particular the positive charge on carbon (0.36 1e-l) is neutralized by Cu and 0 in a ratio of about 1:2. The NBO method provides, however, a different pattern of atomic charges, namely 0.18 le-1 (Cu), 0.27 le-1 (C), and -0.45 le-1 (0). According to the NBO model, therefore, n back-donation by Cu is larger than cr donation from CO (CO is negatively charged by 0.18 le-[), whereas the opposite trend would have been predicted by the Mulliken population analysis. The situation is considerably different in Cu(CO)2 and Cu(CO)3 (see Table 8), which are instead very similar to each other. The positive net charge on Cu is, in fact, significantly enhanced (0.058, 0.520, and 0.649 le-\ for linear CuCO and Cu(CO)2 and for planar trigonal Cu(CO)3, respectively), as is the population of p orbitals. This confirms the increased role of back-donation, which, in turn, significantly stabilizes these two complexes. The unpaired electron is now localized in a n orbital, which receives significant contributions from 4p orbitals of copper. Conclusion The Cu carbonyl complexes studied in this paper can be considered as a severe test for electronic methods. In particular, binding energies appear to be influenced by fine effects and are very sensitive to the theoretical model used in the calculations. On this difficult playground, I have tested different implementations of the density functional approach. Inclusion of some Hartree-Fock exchange in gradient-corrected functionals leads to accurate structural data, harmonic frequencies, and one-electron properties. Moreover, this hybrid approach significantly reduces the overestimation of binding energies characteristic of standard density functional methods. Most of the conclusions based on partial experimental evidence are confirmed by the present computations, with the addition of significant quantitative information. This confirms the role of last generation DFT methods in complementing the data obtained from the most sophisticated spectroscopic techniques. References and Notes (1) (a) Bagus, P. S . ; Hermann, K.; Seel, M. J. Vac. Sci. Technol. 1981, 18, 435. (b) Bagus, P. S . ; Hermann, K.; Bauschlicher, C. W. J . Chem.
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