J. Chil. Chem. Soc., 48, N 4 (2003) ISSN 0717-9324

THEORETICAL STUDY OF COPPER-CARBONYLS INTERACTION IN
CU(CO)_N (N=1-2) COMPLEXES.*

María Luisa Cerón and Fernando Mendizabal*

Departamento de Química, Facultad de Ciencias, Universidad de Chile,
Casilla 653 -Santiago, Chile, e-mail @ hagua@uchile.cl
(Received : July 15, 2003 - Accepted: August 28, 2003)

Key Words: ab initio, Copper, van der Waals

ABSTRACT

We studied the dependence on the attraction between copper(0) and carbonyls in Cu(CO)_n (n = 1-2) complexes using ab initio methodology. Oscillation in the equilibrium Cu-C distance, as well as on the interaction energy are sensitive to the electron correlation potential. These effects were evaluated using several levels of theory, ranging from MP2 to CCSD(T). The long-distance behaviour of the CuCO interaction is related to simple induction and dispersion expressions involving the individual properties of both copper and carbonyl. The dispersion interaction is the principal contribution in the stability at long distance and an important term at short distance.

INTRODUCTION

The complexes formed with transition metals (M) can absorb small molecules, e.g., carbonyl, water, ammonia and hydrocarbons [1-5]. For the special case of metal carbonyl, they are often considered as models for CO binding to the metals surface, and they play important roles in catalysis and synthesis of complexes in the gas phase [6,7]. Spectroscopic data such as vibrational (IR and Raman), UV-visible absorption spectra and electron spin resonance (ERS) have been provided [8,9].

There have been a large number of spectroscopic and theoretical studies of the interaction of Cu group metal atoms with CO in rare-gas solids. It has been observed that they react with carbonyls to produce M(CO)_n (M = Cu, Ag, Au; n = 1,2,3) complexes [10-12] (matrix isolation) as carbonyl-metal surfaces [13,14]. Schwerdtfeger and Bowmaker [15] studied the stability and structure of open-shell monocarbonyl compounds MCO in the ground state ²A₁ at Hartree-Fock and Mf ller-Plesset second orden (MP2) levels. They reported a dissociation energy for AgCO less than 1 kJ/mol, while the metal-carbonyl interactions in CuCO and AuCO are relatively weak, with dissociation energies of about 30 kJ/mol. Furthermore, Bauschlicher studied CuCO system from DFT given a better agreement geometric with experiment, but the binding energy was significantly large [16]. Calculations bases on DFT in van der Waals interactions are not adequate due to the fact that the energy near minimum is unreliable, because the specific from of correlation energy in not properly described.

On the other hand, Mendizabal studied [17] the dependence on the attraction between gold(0) and carbonyls in Au(CO)_n (n=1,2,3) complexes using ab initio methodology. Oscillation in the equilibrium Au-C distance, as well as on the interaction energy are sensitive to the electron correlation potential. These effects were evaluated using several levels of theory, ranging from MP2 to CCSD(T). In the M(CO)_n systems, this interaction has been established to be one of the van der Waals type. We will continue the study of the cooper carbonyls due to the fact that such atom has a smaller polarization in comparison with the gold. Thus, in the systems Cu(CO)_n, the nature of the interaction Cu-CO would have to be different to the produced by the gold.

The dispersion forces that are essential in the stabilization on the complexes are not found at HF (Hartree-Fock) level. Therefore, it is necessary to use at least MP2-level methods for the complete description of the dispersion forces, which are included in the electronic correlation effects [18,19]. However, depending on the chemical system the MPn energies and several other properties namely distance, frequencies, and other, display rapid or slow convergence, monotonic or oscillatory decay [20]. Moreover, for the particular case of weak van der Waals interactions, we have found an oscillatory energy convergence [18,21]. Bearing this in mind, it might be convenient to restrict the use of MPn theory and instead coupled cluster method with perturbative treatment of triple excitations to achieve a higher degree of accuracy [20].

The van der Waals systems are frequently classified on the basis of the leading stabilisation energy term. According to this criterion, they can be denominated as ionic, electrostatic, hydrogen-bonded or charge-transfer complexes [19]. The intermolecular interactions in general can be analysed in terms of electrostatic, induction, short-range Pauli repulsion and dispersion [22]. Here, we are interested in the understanding of the nature of the intermolecular forces that contribute to stabilize the CuCO system and to prove the importance of the dispersion term a long distance.

In the present work, we undertake a theoretical study of the Cu(CO)_n (n=1-2) complexes (Figure 1). We first examine the influence of the ab initio methods and the explicit influence of relativity in the ground-state (²A₁). To our knowledge, no ab initio molecular orbital calculations on Cu(CO)₂ have been reported so far. Moreover, we try to identify the dominant contributions to the attraction forces by considering the long-range limits used CuCO as model.

Fig. 1. Assumed structure of the Cu(CO)n (n = 1-2) complexes.

Computational Details and Theory

Quantum Chemical Methods. The calculations were done using Gaussian 98 [23]. The 19 valence-electron (VE) quasi-relativistic (QR) pseudo-potential (PP) of Dolg [24] was employed for cooper. The f orbitals are necessary for the weak intermolecular interactions, as it has been demonstrated previously for transition metal atoms [25,26]. We employed two f-type polarization functions. This is desirable for a more accurate description of the interaction energy. Also, the carbon and oxygen atoms were treated by 4-VE and 6-VE [24], respectively. For these atoms, double-zeta basis sets were used [24], and adding one d orbital polarization functions.

We fully optimized the geometries for the Cu(CO)_n (n=1,2) complexes at MPn (n=2,4), CCSD and CCSD(T) levels. The interaction energy V(R) for the complexes were obtained according to equation (1); a counterpoise correction for the basis-set superposition error (BSSE) [27] on D E was thereby performed.

The optimized geometries, interaction energies, V(R_e), force constants and frequencies for CuCO complex are shown in Tables 1 and 2.

Theory of Intermolecular Forces. We can partition the interaction energy of the Equation (1) as,

where D E(HF) is the interaction energy evaluated from a self-consistent field (SCF) supermolecule calculation at Hartree-Fock (HF) level. The second term, D E(corr), is the electron correlation energy, which is a useful approximation to the dispersion energy at MPn, CCSD and CCSD(T) levels [19,28].

On the other hand, the total intermolecular potential V_int [21,29] can be partitioned into different contributions at long ranges [Eq. (3)] [30], where the overlap between the molecular charge clouds is insignificant.

The four terms are the short-range (V_short), electrostatic (V_elect), induction (V_ind) and dispersion (V_disp) contributions. At short distances, repulsive effects appear due to the electron clouds of the species penetrate each other and bring about charge overlap and long-range contributions. At long-range, the electrostatic and induction terms are classical. Furthermore, the dispersion (London) term also has long-range character. It is attractive, but requires a quantum mechanical interpretation [30].

The Hartree-Fock term (D E(HF)) is associated with the sum of short-range (V_short), electrostatic (V_elect) and induction (V_ind) terms; while the D E(corr) electron correlation term is associated with dispersion (V_disp) [30]. Hence, our aim is to relate the intermolecular potential at long distance (R_Cu-C) Cu-CO with the properties of the isolated Cu and CO through the dipole moment (m ), quadrupole moment (q ), polarizability (a ) and first ionization potential (IP₁). The latter property was obtained from Koopmans´s theorem [31]. These properties are given in the Table 3 for each system studied at HF, MP2 and CCSD(T) levels.

The interaction of the Cu-CO (Figure 1) will be studied using the specific configuration given for Cu and CO with respect to their dipole moment as shown in the Figure 2 [22]. The q angle (i.e. the angle formed between Cu and CO), values depend on the methodology used namely MP2 and CCSD(T). For this case, both Cu and CO do not have any formal charge, so a long-range electrostatic energy vanishes. Thus, the induction and dispersion terms remain. The induction energy (Eq.(4)) results from the interaction of the dipole of CO with the polarizability of Cu. This term is attractive, but it is not a dominant term. The dispersion term makes an important contribution to the intermolecular potential and it is attractive between Cu and CO at long and short distances. The London approximation is given in Equation (5). The leading dispersion term behaves as V_disp = -C₆/R⁶.

Fig. 2. Definition of coordinates for the CO and Cu interaction.

RESULTS AND DISCUSSION

Short-Distance Behaviour. The results obtained in this work for the CuCO (C₁) complex are similar to those of Schwerdtfeger et at [15] and Bauschlicher [16] at HF and MP2 levels. A bent structure for CuCO complex is obtained at CCSD and CCSD(T) levels. The linear structure is only 1.2 and 1.5 kJ/mol above the bent arrangement using CCSD and CCSD(T), respectively. At the HF level, the Cu-C interactions are found to be repulsive for the complexes and no real chemical bond is established. Figure 3 shows the interaction energy potential as a function of the Cu-C distance using different electron correlation methods. Similar results for Cu(CO)₂ complex were also obtained. This complex shows a linear structure (D¥ _h), independent of the calculated method. We found an oscillatory trend on the interaction energy of both complexes, as well as in other properties such as the Cu-C distance.

Fig. 3. Calculated Cu-CO potential curves V(R) at HF, MP2, MP4, CCSD and CCSD(T) levels.

The carbonyl moiety is expected to be weakly perturbed when complexing with cooper in the ground state (²A₁). For instance, we have found that the C-O bond is slightly longer in the Cu(CO)_n (n=1,2) complexes when compares with that of free CO. The increase in the distance can be attributed to weak interactions. However, there is not experimental evidence on the geometrical parameters due to the absence of crystal structures for these complexes. Moreover, there are experimental estimates of force constants for C-O stretching and vibrational frequencies in the CuCO complex [12]. As force constants depend on the matrix used (Ne, Ar, Kr or Xe), the experimental magnitudes for C-O vary between 15.93 and 16.18 mdyn/Å. The carbonyl free has an experimental force constant of 19.01 mdyn/Å [8], very close to that calculated theoretically (see Table 1). Once the complexes are formed, there is a trend to reduce this property.

Table 1. Optimized Cu-C and C-O distances, R_e, for the complexes at different levels of calculations. Distance R_e in pm; angles a _e are in degrees; interaction energy V(R_e) with BSSE and in bracket without BSSE in kJ/mol; force constants F(Cu-C) and F(C-O) in mDyn/Å.

Species	Method	Cu-C	C-O	< CuCO	-V(Re)	F(Cu-C)	F(C-O)
CuCO (C1)	MP2	181.01	114.93	180°	28.22	1.74	16.31
	MP4	168.98	118.88	180°	161.46	4.91	15.40
	CCSD	200.17	113.53	156.94°	-4.434	0.57	16.20
	CCSD(T)	193.37	114.43	157.01°	6.12	0.84	16.89
Cu(CO)2 (D¥ h)	MP2	177.97	116.00	180°	130.75	3.61	14.52
	MP4	177.02	116.94	180°	252.53	4.50	14.73
	CCSD	183.45	114.81	180°	30.11	2.39	15.10
	CCSD(T)	182.40	115.62	180°	54.31	3.22	15.52
CO(C¥ v)	MP2		114.4				17.99
	MP4		115.1				16.20
	CCSD(T)		114.1				18.57
CO	Expt.8		112.8				19.01

We have calculated the frequencies of the CuCO complex at different levels (see Table 2). In this table, it has been included some frequencies available from experiments (matrix isolation) in order to be compared with our theoretical results. The values derived from the CO n ₃ stretching frequency decreases due to the binding CO with the cooper atom. This can be observed both theoretically and experimentally, when we compare with the carbonyl free [32]. However, it is possible to observe a strong oscillation in that frequency according to the calculation method used. MP4 tends to underestimate, while CCSD (T) tends to overestimate. MP2 calculation provides better results.

Tabla 2. Vibrational frequencies of CuCO. n ₁ is the C u-C-O bend, n ₂ is the Cu-C stretch, n ₃ is the C-O stretch. All values are in cm^-1.

Compound	Method	v1	v2	v3
CuCO	MP2	115.11	399.08	2073.16
	MP4	474.42	662.30	1740.17
	CCSD	119.39	238.75	2205.14
	CCSD(T)	144.29	288.33	2108.29
	Exp[12]		320	2010
CO	MP2			2132
	MP2[15]			2126
	MP4			2023
	CCSD(T)			2165
	Expt [31]			2143-2140

We have considered the effect of the electron correlation in Cu-CO complex at MP4(SDQT) and CCSD(T) levels (see Figure 4). It can be seen a strong oscillation at the equilibrium distance Cu-C(R_e) as well as in the interaction energy, upon changing the electron correlation potential. Figure 4 also shows the minimal interaction energies in Cu(CO)_n complexes for each methodology. At HF level calculations, we have taken the Cu-C distance obtained at MP2 level as reference due to no minimum is obtained with this methodology. This interaction energy obtained at MP2 level, D E(MP2), nearly vanishes at CCSD level. However, at CCSD(T) level, this energy is recovered. The triple excitations in CCSD(T) strongly contribute to that energy in an approximately a third of the MP2 result. A similar trend is observed in the Cu(CO)₂ system.

Figure 4. Effect of the method used on the minimal interaction energy V(Re).

In general, the Cu-C interactions analysis show that for many systems, the convergence of the perturbation theory is oscillatory, indicating that higher-order terms may be important [33,34]. This oscillation occurs in transition metal systems, particularly when (n-1)d to ns transitions are involved [33]. This is especially stressed for the case of gold.

Table 3. Finite field calculations of electric properties of cooper and carbonyl at HF, MP2 and CCSD(T). All values in au.

Properties	Cu	CO
m (HF)	0	0.1213
m (MP2)	0	0.1116
m (CCSD(T))	0	0.0476
a (HF)	42.5329	9.4981
a (MP2)	39.6094	9.8213
a (CCSD(T))	47.8112	9.7410
a II-a ^ (HF)	0	4.1098
a II-a ^ (MP2)	0	4.5399
a II-a ^ (CCSD(T))	0	4.5035
q (HF)	0	1.6052
q (MP2)	0	1.5592
q (CCSD(T))	0	1.6007
IP1(HF)	0.2486	0.5545
IP1(MP2)	0.2486	0.5523
IP1(CCSD(T))	0.2484	0.5532

The natural bond orbital (NBO) [35] population analysis results for the complexes are shown in 4. This analysis is based on the correlated densities. The data show a small charge transfer from gold toward the carbonyl (0.086e) in the CuCO complex. This would suggest a weak interaction in the complex with a dative interaction, similar to that found in the classical Dewar-Chatt-Duncanson model [36,37]. The gross population per atom shell shows that for 4s and 4p orbitals belonging to gold tend to take benefit of this charge transfer by increasing their occupation. However, 3d orbitals are populated. In this complex does not exist hybridization between Cu and CO orbitals. Moreover, electron paramagnetic resonance (EPR) results [11] fully support the conclusion that the unpaired spin is mostly located on the cooper atom.

Table 4. NBO analysis to MP2 density for Cu(CO)_n (n=1-2), CO and Cu.

	Atom	NBO charge	NBO electron configuration
CuCO	Cu	0.0858	4s1.10 3d9.58 4p0.07 4d0.14 5p 0.02
	C	0.2688	2s1.49 2p2.11 3s0.07 3p0.04 3d 0.02
	O	-0.3684	2s1.71 2p4.59 3s0.01 3p0.02 3d 0.04
Cu(CO)2	Cu	0.4766	4s0.50 3d9.80 4p0.22 4d0.01
	C	0.3284	2s1.42 2p2.18 3s0.02 3p0.04 3d 0.01
	O	-0.5667	2s1.71 2p4.82 3s0.03
CO	C	0.6305	2s1.64 2p1.68 3s0.02 3p0.01 3d 0.01
	O	-0.6305	2s1.74 2p4.86 3d0.03
Cu	Cu	0.0000	6s1.0 5d10.0

On the other hand, Cu(CO)₂ complex showed charge transfer from cooper toward the carbons of carbonyls in 0.477e. Such transfer is has to the donation from the 4s orbital of the Cu atom to a 2p orbital on C.

Long-distance behaviour. The long-distance attraction between Cu and CO is shown in Figures 5 and 6 at MP2 and CCSD(T) levels, respectively for the CuCO complex. Energy minima occur at R_e (Table 1). The main repulsive term, the Pauli repulsion, it is already occurs at HF level. When we included electron correlation at MP2 and CCSD(T) levels, several energy minima are generated. At this level of calculations, the difference (to the HF contribution) is dominated by the repulsive Pauli and induction terms.

Figure 5. Interaction energy, V(R), long-range behaviour at MP2 level.

Figure 6. Interaction energy, V(R), long-range behaviour at CCSD(T) levels.

The long-range behaviour can be compared with the sum of the induction and dispersion terms, which were estimated with Equations (4) and (5), respectively. The induction term is small and attractive, without any effect at all distances (see Figure 5). The dominant long-range force is expected to be a London-type dispersion force. The extrapolation from large values R to R_e tend to be an attractive dispersion term (as R^-6), being the main contribution to the Cu-CO attraction. We can see from Figures 5 and 6 a good relationship between the dispersion (or London) formula (Eq.(5)) and the contribution of electron correlation term. The dispersion term for the Cu-CO is approximately a third that obtained it for the analogous gold system [17].

CONCLUSIONS

The present study provides further information about the nature of the interactions in Cu(CO)_n (n = 1-2) complexes. We have found that the energy interaction is mainly due to an electronic correlation effect. This energy shows a strong oscillation upon changing at higher levels in electron correlation, when going from MP2 to MP4(SDQT), CCSD to CCSD(T) models. The CuCO system shows a R^-6 behaviour at large distances. This result provides a proof that the binding in Cu(CO)_n complexes are essentially due to dispersion forces. Moreover, the NBO analysis in the CuCO complex showed a small charge transfer from Cu toward the carbonyl, but we cannot understand this dative interaction (Dewar-Chatt-Duncanson model). Otherwise, the HF calculations should show energy minimum.

ACKNOWLEDGEMENT

This work was supported by Fondecyt Project Nº 1020141.

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