BLW-ED

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MCO+ (M+ = Cu+, Ag+, Au+) complexes have been elucidated at the DFT ... interactions, namely the σ-dative bond from the carbon lone electron pair to an empty ..... 1D (3d94s1) Ni electronic configurations in the binding, our present one- ...

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Journal of Theoretical and Computational Chemistry Vol. 7, No. 4 (2008) 639–654 c World Scientific Publishing Company 

BLOCK-LOCALIZED WAVEFUNCTION ENERGY DECOMPOSITION (BLW-ED) ANALYSIS OF σ/π INTERACTIONS IN METAL-CARBONYL BONDING

KAZUHITO NAKASHIMA∗ , XIN ZHANG∗,† , MINGLI XIANG∗,‡ , YUCHUN LIN∗ , MENGHAI LIN† and YIRONG MO∗,†,§ ∗Department of Chemistry Western Michigan University Kalamazoo, MI 49008, USA †Department

of Chemistry and State Key Laboratory of Physical Chemistry of Solid Surfaces College of Chemistry and Chemical Engineering Xiamen University, Xiamen 361005, China ‡State Key Laboratory of Biotherapy Sichuan University, Chengdu 610041, China §[email protected]

Received 18 March 2008 Accepted 8 April 2008 Dedicated to Professor Qianer Zhang on the occasion of his 80th birthday The bonding features in metal-carbonyls including neutral M CO (M = Ni, Pd, Pt) and M CO+ (M + = Cu+ , Ag+ , Au+ ) complexes have been elucidated at the DFT level with relativistic compact effective potentials for transition metals and 6-311+G(d) basis sets for C and O by the block-localized wavefunction (BLW) method. The BLW method can decompose the intermolecular interactions in terms of Heitler–London, polarization, and charge transfer energy contributions. Since the metal–CO bonding involves two synergic interactions, namely the σ-dative bond from the carbon lone electron pair to an empty dσ orbital on the metal, and the π back-donation from filled dπ orbitals to the empty 2π* orbital on CO, the present BLW-ED analyses quantitatively demonstrated that in neutral M CO complexes the π-bonding dominates over the σ-bonding, whereas in cationic M CO+ complexes, the σ-bonding plays a major role. But in both neutral and cationic species, the CO polarization induced by the metals enhances the C–O bond and increases the C–O vibrational frequencies, while the π back-donation tends to weaken the C–O bond and decrease the C–O vibrational frequencies. For neutral complexes, the latter is more prominent than the former, and consequently, there is a red-shifting of the C–O vibrational frequencies. In contrast, the π back-donation is insignificant in M CO+ cations, and the C–O eventually vibrates at higher frequencies than the free CO frequency. Keywords: Block-localized wavefunction (BLW); energy decomposition; Metal carbonyl; σ-donation; π back-donation. § Corresponding

author. 639

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1. Introduction Intermolecular interactions play a central role in chemistry as it is usually the initial step for subsequent chemical reactions. A better understanding of the nature of intermolecular interactions can help chemists tune and eventually control chemical reactions. One notable example is the rational design of inhibitors to proteins, and the mechanistic elucidation of inhibitor–substrate interactions has the potential of leading to the finding of novel inhibitors (i.e. drugs). Another outstanding example is the metal π-ligand bond,1–13 which broadly exists in chemical catalysis and is closely related to the interpretation of catalytic mechanisms and even the development of fuel cells.14 Among various ligands to transition metals, carbon monoxide is one of the most common ligands to form carbonyl complexes. The adsorption of CO on the surface of metals such as gold, iron, and cobalt is also a pre-requirement for the water–gas-shift reaction15 and the Fischer–Tropsch process.16 On the other hand, the tight binding of CO to Pt anodes results in the electrode poisoning which is a major concern in fuel cell.14 It is generally observed that there are short metal-C bonds and red-shifts of the CO stretching frequencies. Whereas this can be generally elucidated with the Dewar–Chatt–Duncanson donation/back-donation model,17–19 it was Blyholder who provided detailed descriptions for the metal–CO interactions.20–22 It is now widely accepted that there are two synergic interactions involved in the metal–CO bonding (see Scheme 1): one is the σ-dative bond formed by the partial donation of a largely lone electron pair on C to an empty d-orbital on the metal, and the other is the π-back-donation from a filled d-orbital to the empty π*-orbital on CO. Due to the reverse directions of electron flow in σ-bonding and π-back-bonding, each interaction will be enhanced by the other, and this kind of synergic bonding can be defined as a coupling energy term in our study. In most cases, the net back π-bonding predominates, and electron density is transferred from the metal dπ -orbitals to the 2π*-orbital of CO.23 As a consequence, the CO bond is weakened and lengthened and accordingly the C–O stretching frequency is shifted to a lower value. Nevertheless, it is intriguing to discriminate the σ-donation and π back-donation and quantitatively evaluate their individual interaction magnitudes. Bagus et al. proposed the constrained-space orbital variation (CSOV) method which can measure the energy contributions from various types of bonding to the

M

C

O

σ donation

M

C

π back-donation SCHEM 1.

O

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metal–carbonyl bond.24–26 The realization of the energetic measure for either σ- or π-bonding results from the constraints imposed on the variational space used for the molecular orbitals (MOs) of metal–ligand clusters. Significantly, they found that the CO σ donation makes only 1/4–1/3 of the contribution from the π back-donation to the metal–CO interaction. In fact, the metal σ orbitals polarize away from CO due to the σ repulsion.23 This differs from the analysis by Blyholder and Lawless who separated the total energy into monatomic and diatomic energy terms at the semi-empirical level and reinforced the importance of the σ electrons.22 So far a variety of theoretical approaches have been proposed to probe the nature of intermolecular interactions by decomposing the interaction energy into various physically meaningful components such as electrostatic, exchange, dispersion, relaxation or polarization, charge transfer, etc.27–37 Whereas certain arbitrariness exists in these energy decomposition schemes and there are no direct experimental proofs, consensus can be drawn from the analysis of a group of similar complexes, and significant insights into the origin of intermolecular interactions can be gained. These kinds of studies are also illuminating for the development of next-generation force fields which have been extensively applied to the simulations of large systems such as proteins and nano-systems. Among the various energy decomposition schemes, the block-localized wavefunction energy decomposition (BLW-ED) method has the advantage of defining the hypothetical electron-localized state selfconsistently.34,38–40 Moreover, the BLW has the geometry optimization capability, and it has recently been extended to the DFT level.41,42 Thus, both the structural and energetic impacts by the charge transfer among interacting species can be quantitatively computed. For instance, it can be used to study the hydrogen bonds in DNA43 and evaluate the influence of π-resonance on the strengths of the hydrogen bonds.44 In this paper, we used the BLW-ED method to elucidate the characteristics of metal–carbonyl bonding by analyzing the interaction between CO and transition metals including neutral Ni, Pd, Pt, and positively charged Cu+ , Ag+ , and Au+ . Our focus was on the comparison between the σ-donation and π back-donation in these metal–CO bonds. 2. Theory The strict discrimination between polarization and charge transfer effects which coexists in intermolecular interactions requires a proper definition of the electronlocalized state, or a resonance state in the terminology of resonance theory. The comparison between electron-localized and electron-delocalized states can exclusively reveal the significance of the electron delocalization (i.e. charge transfer) effect. In the valence bond (VB) theory, a resonance state can be well expressed with a Heitler–London–Slater–Pauling (HLSP) wave function.45,46 Ab initio VB theory has been rejuvenated in the past two decades,47,48 although at present its applications are still limited due to high computational demands. Recently, we

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proposed the block-localized wavefunction (BLW) method, which can be regarded as a variant or the simplest version of the ab initio VB theory.39,41,49 The BLW method retains the characteristics and advantages of both the VB and molecular orbital (MO) theory, and thus provides a practical means to derive the wavefunction for an electron-localized state. The fundamental assumption in the BLW method is that the total electrons and primitive basis functions can be divided into a few subgroups, and each subgroup corresponds to a monomer in the study of intermolecular interactions. If we assume that there are mi basis functions {χiµ , µ = 1, 2, . . . , mi } and ni electrons for monomer i, the electron-localized state can be defined with block-localized MOs which are expanded in only one subgroup of basis functions as ϕij =

mi 

Cijµ χiµ .

(1)

µ=1

The final block-localized wavefunction is expressed by a Slater determinant     ΦBLW = M (N !)−1/2 det ϕ211 ϕ212 · · · ϕ21 n1 ϕ221 · · · ϕ2i1 · · · ϕ2i ni · · · ϕ2k nk , 2

2

2

(2)

where N is the total number of electrons in complex, M is the normalization constant, and k is the number of monomers (in current cases k = 2). The block-localized MOs in the same subspace are subject to the orthogonality constraint, like in conventional MO methods, while no such kind of constraint is imposed on different subspaces, like in VB methods. The energy of the localized wavefunction is determined as the expectation value of the Hamiltonian H E BLW = ΦBLW |H|ΦBLW  =

m m  

dµν hµν +

µ=1 ν=1

m m  

dµν Fµν ,

(3)

µ=1 ν=1

where hµν and Fµν are, respectively, elements of the usual one-electron and the Fock matrices, and dµν is an element of the density matrix, D = C(C+ SC)−1 C+ . Here S is the overlap matrix of the basis functions. With the definition of BLW, the binding energy between two monomers A and B can be decomposed to the deformation energy ∆Edef , Heitler–London energy ∆EHL , polarization energy ∆Epol , and charge transfer energy ∆ECT terms as ∆EB = E(AB) − E(A) − E(B) = ∆Edef + ∆EHL + ∆Epol + ∆ECT ,

(4)

where the deformation energy refers to the energetic cost to deform the monomers from their separated optimal structures to the distorted geometries in the optimal structure of dimer AB. In current cases the deformation cost is negligible. The derivation of the Heitler–London energy term is based on the construction of the directly from the MOs for initial block-localized wavefunction for the dimer ΨBLW0 AB

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separated monomers in the structure of dimer as ˆ 0A Ψ0B ). = A(Ψ ΨBLW0 AB

(5a)

The subsequent relaxation of the electron densities within each monomer results in the self-consistent form ΨBLW AB as ˆ ΨBLW AB = A(ΨA ΨB ).

(5b)

Once the initial and optimal BLWs are defined, the energy terms in Eq. (4) can be subsequently expressed as ) − E(Ψ0A ) − E(Ψ0B ), ∆EHL = E(ΨBLW0 AB

(6a)

BLW0 ∆Epol = E(ΨBLW ), AB ) − E(ΨAB

(6b)

BLW ∆ECT = E(ΨDFT AB ) − E(ΨAB ) + BSSE,

(6c)

where the BSSE refers to the basis set superposition error. The Heitler–London energy ∆EHL is defined as the energy change by bringing monomers together without disturbing their individual electron densities, while the polarization energy ∆Epol corresponds to the redistribution of electron density within each monomer due to the electric field imposed by the other monomer. This is an energy-lowering step for the complex, but there is no penetration of electrons between the monomers. By restricting the relaxation of block-localized MOs in either A or B, we can even define the individual polarization energies for A or B as 0 ˆ ∆Epol (A) = E(ΨBLW AB ) − E[A(ΨA ΨB )],

(7a)

ˆ 0 ∆Epol (B) = E(ΨBLW AB ) − E[A(ΨA ΨB )].

(7b)

Clearly, the sum of ∆Epol (A) and ∆Epol (B) will not be exactly equal to the overall polarization energy ∆Epol in Eq. (6b), and the difference however is small and generally refers to the coupling effect. The extension of electron movements from block-localized orbitals to the whole complex further stabilizes the complex and this energy variation is denoted as the charge transfer energy ∆ECT . In this step, BSSE is also introduced; thus, the correction is completely assigned to the charge transfer energy term. It should be noted that ∆EHL is a sum of electrostatic and Pauli exchange repulsion energies, as similarly defined in the Kitaura–Morokuma (KM) analysis27 and the energy decomposition analysis (EDA) implemented in ADF.35–37 Since the exchange of electrons is a quantum mechanical effect and classical force field approaches have difficulties to formulate the exchange energy separately, here we simply use ∆EHL . In previous works, we also introduced the electron correlation contribution ∆Ecor , which is estimated by the comparison between the interaction energies calculated at the HF level and higher electron-correlated levels. We also note that in the EDA method,35–37 Eq. (5a) is straightly relaxed to the adiabatic state ΨDFT AB , and the energy drop is called orbital relaxation energy ∆Eorb .

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Apparently, this ∆Eorb term is equal to the sum of polarization and charge-transfer energy terms in our BLW-ED approach. We have ported the BLW code to the GAMESS software,50 and thus all computations were done with GAMESS at the DFT (B3LYP) level which includes certain amount of electron correlations. Since normally there is a large relativistic effect in transition metals, we used relativistic compact effective potentials (SBKJC VDZ ECP in short) for transition metals51 to treat scalar relativistic effects which mainly affect core electrons, and 6-311+G(d) basis sets for C and O.52 3. Results and Discussion 3.1. Neutral M CO (M = Ni , Pd, Pt) complexes Both experimental and computational studies have been extensively conducted on the interaction between Ni and CO.4,26,53–60 While one interesting issue related to the ground state 1 Σ+ vs 3 ∆ of NiCO is the relative significance of the 1 S (3d10 ) and 1 D (3d9 4s1 ) Ni electronic configurations in the binding, our present one-determinant DFT can be simply regarded as the optimal mixture of these two electronic configurations and no further exploration in this direction will be pursued. The geometrical optimization of NiCO (see Table 1) results in the bond distances of Ni–C and C– O to be 1.672 ˚ A and 1.151 ˚ A, respectively, in reasonable agreement with the most recent experimental values 1.641 ˚ A and 1.193 ˚ A.57 Both computations and experiments showed the red-shifting of the C–O vibrational frequency of similar magnitude. Martinez and Morse determined the C–O vibrational frequency in NiCO as 2011 cm−1 , compared with free CO 2143 cm−1 .61 Our computations indicated that CO vibrates at the frequency of 2079 cm−1 , compared with free CO 2212 cm−1 at the same theoretical level. The red-shifting of the C–O vibrational frequency is consistent with the lengthening of the CO bond in the NiCO complex.

Table 1. Optimal bond distances (˚ A) and stretching frequencies of CO (cm−1 ) for M CO (M = Ni, Pd, Pt, Cu+ , Ag+ , and Au+ ) derived with the regular DFT and the BLW-DFT methodsa . M

Ni Pd Pt Cu+ Ag+ Au+ a The

DFT

BLW-DFT

RMC

RCO

νCO

b ∆νCO

1.672 1.879 1.791 1.884 2.199 1.968

1.151 1.142 1.146 1.116 1.116 1.116

2079 2112 2120 2316 2314 2310

−133 −100 −92 +104 +102 +98

RMC

RCO

νCO

b ∆νCO

2.044 2.406 2.360 2.177 2.570 2.517

1.120 1.123 1.121 1.114 1.117 1.116

2293 2257 2280 2342 2307 2320

+81 +45 +68 +130 +95 +108

DFT optimization on free CO leads to a equilibrium distance 1.127 ˚ A and a stretching frequency of 2212 cm−1 , compared with the experimental values of 1.128 ˚ A92 and 2143 cm−1 .61 b Changes with reference to free CO stretching frequency 2212 cm −1 .

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The most striking findings, however, come from the BLW calculations where both the σ-donation from CO to Ni and the back-donation from Ni to CO are quenched. The BLW geometrical optimization resulted in a very long Ni–C distance, suggesting the weak interaction between the neutral species. Although the C–O bond changes only slightly, its bond shortens rather than lengthening. This is accompanied by a blue-shift of the C–O vibrational frequency by 81 cm−1 . Since there is no charge transfer, the only culprit is the polarization of the electron density in CO induced by Ni. This can be visualized by the electron density difference (EDD) maps shown in Figs. 1(b) and 1(c), which highlight the shifting of electron density in CO toward the Ni side. In the EDD maps, the red color denotes the increasing electron density and the blue color refers to the reducing electron density. The charge transfer between Ni and CO substantially weakens the C–O bond and results in the red-shifting of the C–O vibrational frequency and the lengthening of the C–O bond. From the electron density maps in Fig. 1, we can hypothesize that the π-back-donation plays a bigger role than the σ-dative donation. The subsequent BLW energy decomposition analysis confirms the above hypothesis. Table 2 lists the major energy terms while separated contributions from either Ni vs CO or σ vs π are listed in Tables 3 and 4. Table 2 showed that while the Heitler–London interaction destabilizes the system, the polarization stabilizes the system at a comparable magnitude. Ultimately, the charge transfer dominates the total binding energy, which is 66.7 kcal/mol. However, here we take the singlet state of Ni atom as a reference. For Ni, the ground state is actually triplet, and the ground state of NiCO (1 Σ+ ) dissociates Ni(3 Dg ) and CO(1 Σ+ ). The singlet–triplet gap is computed as 41.2 kcal/mol at our present theoretical level. Thus, the adjusted binding energy for Ni and CO is 25.5 kcal/mol. For comparison, there is a large range

(a) Ni polarization

(b) CO polarization

(c) overall polarization

(d) σ charge transfer

(e) π charge transfer

(f) overall charge transfer

Fig. 1. Electron density difference (EDD) maps showing the polarization and charge-transfer in the NiCO molecule where red and blue colors refer to the increase and decrease of electron density (isodensity 3×10−3 a.u.).

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∆Edef

∆EHL

∆Epol

∆ECT

∆Eb

Ni Pd Pt Cu+ Ag+ Au+

0.8 0.3 0.5 0.2 0.2 0.2

27.2 55.5 104.9 11.4 8.9 45.2

−20.3 −36.2 −67.3 −25.1 −13.6 −32.4

−74.4 −57.7 −110.6 −25.1 −18.7 −57.2

−66.7 −38.1 −72.5 −38.6 −23.2 −44.2

Table 3. Individual polarization energies for M and CO (kcal/mol). M

∆Epol (M )

∆Epol (CO)

Ni Pd Pt Cu+ Ag+ Au+

−11.6 −30.8 −54.1 −7.4 −3.6 −16.3

−9.4 −1.9 −6.5 −15.0 −8.9 −12.0

a ∆E coupling pol

a

coupling ∆Epol

0.7 −3.5 −6.7 −2.7 −1.1 −4.1

= ∆Epol −∆Epol (M )−∆Epol (CO).

Table 4. Separated σ-dative bond energy and π-back-donation stabilization energy (kcal/mol). a

M

∆ECT (σ)

∆ECT (π)

coupling ∆ECT

Ni Pd Pt Cu+ Ag+ Au+

−22.6 −20.8 −47.4 −17.1 −15.2 −41.2

−48.8 −35.5 −52.6 −7.7 −3.4 −12.8

−3.0 −1.3 −10.6 −0.3 −0.1 −3.2

a ∆E coupling CT

= ∆ECT −∆ECT (σ)−∆ECT (π).

of experimental values for the binding energy in NiCO, from 29 ± 15 kcal/mol62 to 40.5 ± 5.8 kcal/mol.63 Computations of individual polarization energies shown in Table 3 indicated that both Ni and CO make comparable contributions to the total polarization energy. But in terms of charge transfer, the π-back-donation from Ni to CO stabilizes the NiCO complex one time more than the σ-dative bond from the carbon lone pair to Ni (see Table 4). Our BLW-ED analyses are consistent with the previous works by Bauschlicher et al. and Xu et al., who found the most important interaction in the

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Ni–CO bond to be the π-back-donation from the filled 3dπ metal orbitals to the empty 2π* CO orbitals.4,26 The PdCO molecule also has received extensive attention.64–72 It has been confirmed that PdCO has a linear 1 Σ+ ground state with little multireference character, but computational studies diverge over the internuclear distances, binding energy, and vibrational frequencies. In contrast to Ni, single Pd atom has a singlet ground state, and the excitation from 1 S(d10 ) to 3 D(d9 s1 ) requires 0.95 eV.73 Our optimal Pd–C and C–O bond lengths are 1.879 ˚ A and 1.142 ˚ A, compared with the 74 ˚ ˚ experimental values 1.843 A and 1.13 A. Filatov performed all-electron CCSD(T), QCISD(T), and MP4(SDQ) calculations including relativistic effects and estimated the Pd–CO bond dissociation energy to be 38.8 kcal/mol,69 which is very close to our 38.1 kcal/mol without zero-point energy correction. Our computed C–O vibrational frequency in PdCO is 2112 cm−1 , in good agreement with the experimental data 2080 cm−1 .68 By deactivating the charge transfer between Pd and CO, the BLW-DFT optimization leads to a much long metal–C bond and slightly shortened C–O bond compared to the free CO. Once again we confirmed that when a neutral Pd atom approaches the carbon end of CO without allowing any charge transfer, the electron density in CO polarizes toward the metal side and eventually, the electron density between C and O increases. This results in the slight shortening of the C–O bond and the blue-shifting of the C–O vibrational frequency by 45 cm−1 . Once the charge transfer is allowed, the C–O vibrational frequency red-shifts significantly by 145 cm−1 , and as a combination, the final C–O vibrational frequency in PdCO is 2112 cm−1 . The energy decomposition revealed strong Pauli repulsion between Pd and CO, which is partially offset by the polarization stabilization. The polarization is dominated by the adjustment of the electron density within Pd (see Table 3). The charge transfer plays a prominent role in the binding of PdCO. Similar to NiCO, the π-back-donation stabilizes the system by nearly one time more than the σdonation. Platinum is widely used in industry, notably in automobile catalytic converters to remove CO from the automobile exhaust. The chemisorption of CO on the Pt surface has fundamental importance in surface chemistry; thus, Pt carbonyls have been well investigated.66,70,75–81 Theoretical studies predict a linear 1 Σ+ ground state for PtCO which correlates with the Pt 1 S state instead of the 3 D ground state. Our level of theory shows that the energy gap between Pt 1 S and 3 D states is 0.39 eV. In terms of variations of bond lengths and vibrational frequencies, PtCO exhibits similar trends along the above NiCO and PdCO. The computed C–O vibrational frequency (2120 cm−1 ) in PtCO is slightly higher than the experimental value (1052 cm−1 ).79 But this difference is systematic for all complexes and our focus is on the relative shifting. The optimal Pt–C and C–O distances are 1.791 ˚ A and 1.146 ˚ A, in good agreement with the experimental data 1.760 ˚ A and ˚ 1.144 A, respectively.80 However, Pt does show higher affinity to carbonyl than Ni and Pd, and all energy terms, including Heitler–London repulsion, polarization and

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charge transfer stabilizations, are the biggest in the series. Whereas the individual polarization energy for Pt is impressively high (Table 3), both the σ-donation and π-back-donation between Pt and CO are significant and comparable in magnitude. In summary, among the above three Group 10 neutral metal–CO molecules, the metal–ligand distance increases in the order of Ni < Pt < Pd which has been ascribed to a considerable relativistic strengthening of the Pt–CO bond.66 Our predicted binding energies are similar to those in the relativistic calculations of Chung et al. and correlate well with the evolution of the metal–carbon bond force constant (FPtC > FNiC > FPdC ) determined experimentally by Manceron et al.79 The BLW-ED analyses demonstrated that Pt is different from the rest two, particularly in the σ-donation capability. 3.2. Metal carbonyl cations MCO+ (M + = Cu+ , Ag+ , Au+ ) Here we consider the Group 11 metal cations which can exert strong electric fields on CO and thus disturb (or polarize) the electron density of CO much more significantly than the neutral metal atoms.82–87 Among the metal carbonyl cations, copper carbonyl cations [Cu(CO)n ]+ (n = 1, 2) were the first one generated and studied in solution.88 Metal carbonyl cations usually have high catalytic activity in the Koch reaction which is an important acid-catalyzed carbonylation.89 Lupinetti et al. first noted that the C–O bond is shortened by nearly the same amount in HCO+ and M CO+ compared to free CO, and interpreted the changes in terms of polarization due to the strong electrostatic effect from the cations.84 Interestingly, they showed opposite effects when cations bind to the oxygen end of the carbonyl. Later, the same Frenking group systematically studied the homoleptic carbonyl complexes of the Group 11 and Group 12 d10 metal cations with up to six carbonyl ligands at the MP2 and CCSD(T) levels with relativistic effective core potentials for the metals.85 Recently, Mogi et al. examined the geometries and electronic structures of Group 10 and 11 metal carbonyl cations at the DFT and CCSD(T) levels.86 Geometry optimizations of M CO+ (M + = Cu+ , Ag+ , Au+ ) at the DFT level with relativistic compact effective potentials for metals result in the same C–O bond lengths (1.116 ˚ A), and similar vibrational frequencies. As well recognized, all these metal carbonyl cations exhibit shortened C–O bond lengths and higher C–O vibrational frequencies than free CO and thus called “nonclassical metal carbonyls”.82 For instance, our computed frequency in CuCO+ is 2316 cm−1 , compared with 2212 cm−1 for free CO; thus, the C–O vibrational frequency blue-shifts by 104 cm−1 . Experimentally, the frequency in CuCO+ is 2178 cm−1 ,90 compared with the free CO 2143 cm−1 ; so, there is only 35 cm−1 blue-shifting. But we note that the experiment on CuCO+ was conducted in the solid state. Similarly, the experimental C–O vibrational frequency in AgCO+ is 2208 cm−1 ,82 and there is 65 cm−1 blue-shifting, which is less than 102 cm−1 evaluated at the present computational level. The BLWDFT optimizations result in metal–C distances which are determined completely

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(a) Cu+ polarization

(b) CO polarization

(c) overall polarization

(d) σ charge transfer

(e) π charge transfer

(f) overall charge transfer

649

Fig. 2. Electron density difference (EDD) maps showing the polarization and charge-transfer in the CuCO+ molecule where red and blue colors refer to the increase and decrease of electron density (isodensity 2 × 10−3 a.u.).

by the electrostatic and van der Waals interactions. Due to the strong electrostatic attraction, the electron density in CO moves from the oxygen side to the carbon side (see Fig. 2(b)), and this movement increases the electron density between C and O, and finally shortens the C–O bonds and increases the C–O vibrational frequencies. However, unlike neutral M CO complexes discussed in the previous section where the charge transfer remarkably lengthens the C–O bonds and red-shifts the C–O vibrational frequencies, the charge transfer between metal cations and CO changes both the C–O bond lengths and vibrational frequencies very little, although the metal–C distances decrease dramatically. The comparison between Figs. 1 and 2 may provide some clues. For both NiCO and CuCO+ , we observe that the σ-donation results from the lone pair on the carbon atom to the dσ orbitals of metals (see Fig. 1(d) and Fig. 2(d)) , and there is little variation on the oxygen end. For the π-back-donation, noticeable disparity occurs (see Fig. 1(e) and Fig. 2(e)). While the back-donation is generally regarded as the electron flow from the metal dπ orbitals to the 2π* of CO, it is indeed the case in NiCO where both C and O gain certain amount of electrons with the decreasing of electron density between C and O. In a sharp contrast, the π-back-donation in CuCO+ essentially occurs from Cu to C alone, and there is little change on the oxygen end as well as the bonding region between C and O. As a result, the π-back-donation reduces the C–O vibrational frequency in CuCO+ at a much smaller magnitude than in NiCO. Our computed binding energies are also in good agreement with available experimental data. For example, the binding energies in CuCO+ and AgCO+ are 38.6 kcal/mol and 23.2 kcal/mol, compared with the experimental data of 36 kcal/mol and 21 kcal/mol determined by Meyer and coworkers.91 This further confirmed the appropriateness of the computational level used in this work. Whereas the Heitler–London energy terms are repulsive for all cations (see Table 2), both

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polarization and charge transfer effects stabilize the systems. In the neutral M CO systems, there is strong polarization on metal atoms, but in M CO+ , the polarization on metal cations greatly reduces, as seen in Table 3. On the other hand, the polarization on CO increases by binding to metal cations. The most intriguing part is the charge transfer effect. Table 4 demonstrated that in M CO+ cations, the σ-donation dominates while the π-back-donation is relatively very weak. This is in contrast to the neutral M CO complexes, and strongly suggested that in metal carbonyl complexes both σ-donation and π-back-donation should be treated equally. In brief, the BLW-ED confirmed that metal–carbonyl σ-bonding is strongest for M + = Au+ and much weak for M + = Cu+ and Ag+ . For the metal–carbonyl π-bonding, which is much weaker than the σ-bonding, the order of strength is Au+ > Cu+ > Ag+ . 3.3. General trends in metal carbonyls Although neutral M CO (M = Ni, Pd, Pt) molecules possess different features from the M CO+ (M + = Cu+ , Ag+ , Au+ ) cations, consistent correlations can be found from them as a whole. The focus here is the carbonyl. Figure 3 shows the correlation between the C–O vibrational frequencies in the electron-localized diabatic states and the individual polarization energy of CO. Apparently, the higher the C–O vibrational frequency is, the stronger the electric field imposed on CO is, and subsequently the higher the polarization in CO is. The correlation between frequencies and bond distances has also been well documented in the literature. Figure 4 shows the linear relationship between the C–O vibrational frequencies and the C–O bond distances. A lower vibrational frequency corresponds to a longer bond distance. The excellent correlation illustrated in Fig. 4 suggests that we can predict the vibrational frequencies based on the determination of bond lengths, or vice versa.

-∆Epol (CO) (kcal/mol)

20 16

y = 0.147x - 329.5 2

R = 0.959

12 8 4 0 2240

2270

2300

2330

2360

-1

νCO (cm ) Fig. 3. Correlation between the C–O vibrational frequencies (νCO ) in diabatic states derived by BLW-DFT and the polarization energy of CO (∆Epol (CO)).

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2400

νCO (cm-1)

2350

y = -7003.6x + 10130

2300

2

R = 0.982

2250 2200 2150 2100 2050 1.11

1.12

1.13

1.14

1.15

1.16

RCO Fig. 4. Correlation between the C–O vibrational frequencies (νCO ) by regular DFT and BLW-DFT computations and the corresponding C–O bond distances (RCO ).

4. Conclusion BLW-ED has been applied to metal carbonyls to explore the binding nature between transition metals and CO. The advantage of the BLW method lies in the definition and self-consistent optimization of the wavefunction of a diabatic state where the charge transfer is deactivated. While the comparison between the optimal results from the regular DFT and BLW-DFT computations manifests the structural and energetic changes due to the charge transfer between transition metal and carbonyl, the charge transfer can be further quantitatively decomposed into the σ-bonding and π-bonding contributions. For neutral M CO (M = Ni, Pd, Pt) molecules, the π-back-donation from the metal dπ orbitals to the 2π* orbital of CO is stronger than the σ-donation from the carbon lone pair in CO to the metal dσ orbitals, but in M CO+ (M + = Cu+ , Ag+ , Au+ ) cations the σ-bonding is much more pronounced than the π-bonding. The most interesting finding in this work, however, is the elucidation of the C–O vibrational frequency shifting. On one hand, the approaching of either a neutral or cationic metal to the carbon side of carbonyl unanimously polarizes the electron density in CO from the oxygen atom to the carbon atom and consequently increases the density in the midst of C and O and blue-shifts the C–O vibrational frequency. On the other hand, the charge transfer, particularly the π-back-donation, tends to weaken the C–O bond and red-shift the C–O vibrational frequency. The relative magnitudes of these two conflicting forces determine the final frequencies. For neutral species studied in this work, the backdonation plays a bigger role than the polarization in frequencies, and eventually the red-shifting of the C–O vibrational frequencies is found. But in cations, the metal ions not only exert a strong electric field, but also are hard to back-donate electrons to the 2π* orbital of CO, and at last the C–O vibrational frequency blue-shifts.

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Acknowledgments YM would like to thank his former PhD mentor, Prof. Qianer Zhang, for his continuing advice, care, and encouragement. The block-localized wavefunction (BLW) method was initiated at Xiamen University when YM was studying the ab initio valence bond (VB) theory for a doctoral degree along with Dr Wei Wu under the guidance of Prof. Qianer Zhang, who taught us to be not only a good scientist, but also a conscientious citizen and team-player. XZ and MX acknowledge the financial support from the China Scholarship Council (CSC). References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33.

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