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J. Phys. Chem. A 2002, 106, 5660-5670
Modeling Copper(I) Complexes: SIBFA Molecular Mechanics versus ab Initio Energetics and Geometrical Arrangements N. Gresh,*,† C. Policar,*,‡ and C. Giessner-Prettre*,§ Equipe de Pharmacochimie Mole´ culaire et Cellulaire, UMR 8638, UniVersite´ Rene´ Descartes, 4, aVenue de l’ObserVatoire, 75270 Paris Cedex 06, France, Laboratoire de Chimie Bioorganique et Bioinorganique, FRE 2127, Baˆ timent 420, UniVersite´ de Paris Sud, 91405 Orsay, Cedex, France, and Laboratoire de Chimie The´ orique, UMR 7616, UniVersite´ P. & M. Curie, Case Courrier 137, 4, place Jussieu, 75252 Paris Cedex 05, France ReceiVed: February 15, 2001; In Final Form: July 13, 2001
SIBFA parametrization is extended to the closed-shell Cu(I) cation. This parametrization introduces the cation polarization up to quadrupolar effects and the metal-ligand charge transfer. The results obtained are compared to the corresponding ab initio quantum-chemical quantities given by intermolecular interaction energy decomposition and MP2 runs. Mono- and polycoordinated complexes of Cu(I) with O-, S-, and N-containing ligands are considered. An extension to systems containing two and three Cu(I) cations, found in copper metalloenzyme active sites, such as cytochrome C oxidase and hemocyanin, and supramolecular systems, is reported. The results obtained show that in such cases SIBFA is able to give geometrical arrangements in reasonable agreement with experimental data and interaction energy values close to those given by ab initio computations. With respect to MP2 results, covering interaction energy range of ≈400 kcal/mol, the interaction energy rms amounts to 7.6 kcal/mol.
Introduction The involvement of the Cu(I) cation in several enzymatic reactions1-5 has initiated numerous experimental studies on structural and functional models of mono- and binuclear Cu(I) enzymes.6 In supramolecular chemistry, Cu(I) is often a key factor in the stabilization of supramolecular complexes.7-9 In synthetic chemistry, Cu(I) complexes have been recently used as catalysts in enantioselective reactions.10 High-level quantum-chemical investigations provide essential information on the electronic, structural, and energetic properties of Cu(I) complexes.11-14 However, such computations become hardly tractable for systems of more than 100 atoms. Larger ones can only be handled by semiempirical or molecular mechanics procedures. For the latter, there exist conventional force-fields to handle Cu(I) complexes,15 but they do not embody the polarization and charge-transfer terms, whose magnitude can be quite important.16 A correct reproduction of ∆E, the intermolecular interaction energy, can be of primary importance for studies of substrate/inhibitor binding to metalloenzyme active sites. To have reliable molecular mechanics results it is essential to be able to obtain not only the value of the total ab initio ∆E value but also those of its individual contributions given by ab initio energy-decomposition of ∆E. This alone can ensure the quality of the results for other complexes than those for which the procedure was initially parametrized. It also allows that further refinements be done on the individual components without affecting the others. This is the essential objective in the formulation and calibration of the SIBFA (sum of interactions between fragments ab initio computed) polarizable molecular mechanics procedure.17 Recent * To whom correspondence should be addressed. † Universite ´ Rene´ Descartes. E-mail:
[email protected] ‡ Universite ´ Paris Sud. E-mail:
[email protected]. § Universite ´ P. & M. Curie. E-mail:
[email protected].
studies from our laboratories devoted to polycoordinated complexes of Zn(II) have been able to give a reasonable agreement between the structures obtained from SIBFA and ab initio computations for a model of β-lactamase active site as well as for the interaction energies calculated for models of thermolysin active site and Gal4.17e,g Cu(I) parametrization requires us to include its relaxation energy within ∆E, that is, the terms originating from Cu(I) polarization and Cu(I)-to-ligand charge-transfer, whereas they are negligible in the case of isoelectronic Zn(II).16 Therefore, in addition to the calibration of Erep/Edisp terms concerning this cation, explicit formulas and parameters for Epol(Cu) and Ect(Cu) are implemented in the present work. After calibration of the various necessary parameters on small systems, computations were carried out on a variety of larger molecular assemblies such as Cu(I) polyhydrates, dinuclear copper complexes encountered in metalloenzyme active sites and Cu-stabilized supramolecular systems. Comparisons with results using the semiempirical PM3(tm)18 and ZINDO19 methods, as well as with the nonpolarizable UFF15a molecular mechanics method, were also done for representative monoand polyligated Cu(I) complexes. This comparison will provide information of the validity domain of the results that we will obtain for the systems of interest to us such as Cu(I) copper enzymes active site models, functional models, and their complexes with different inhibitors. Finally, it is worth noting that Cu(I) complexes should also be relevant for some Cu(II) metalloenzymes, because as exemplified by galactose oxidase and superoxide dismutase, the transient existence of Cu(I) was put forth during the catalytic cycle.20 Computational Procedures Ab Initio Calculations. The ab initio computations use three basis sets. The first is the coreless effective potential (CEP
10.1021/jp0106146 CCC: $22.00 © 2002 American Chemical Society Published on Web 05/15/2002
Modeling Copper(I) Complexes 4-31G(2d)) basis set derived by Stevens et al.,21 supplemented on the heavy atoms by two, uncontracted 3d orbitals, the exponents of which were given previously.22 This was the basis set used for refining and testing the SIBFA procedure.17 Two additional sets, all-electron bases, are the DZVP2 polarized splitvalence set of Godbout et al.23 and the TZVP built from the triple-valence set of Ahlrichs et al.24 to which were added the polarization functions proposed for the DZVP2 basis. The energy decompositions are performed using the reduced variational-space analysis (RVS) developed by Stevens and Fink,25 interfaced in the Gamess package.26 This procedure is related to the original Morokuma procedure27 and to the constrained space orbital variation of Bagus et al.28 It enables us to deconvolute the total ab initio HF interaction energy ∆EHF into its components and, in its present implementation, can be performed on complexes encompassing up to 10 molecules. The energy components are Coulomb (Ec) and exchange (Eexch) in the first-order energy (E1) and polarization (Epol) and charge transfer (Ect) in the second order (E2). An interesting feature of the RVS procedure is that the last two components are given for each entity of the complex. In the tables given below, E1 is the sum of Ec and Eexch. E2 is the sum of Epol and Ect. ∆E is the value of the HF intermolecular interaction energy, as computed with the RVS procedure with the basis set superposition error using the virtual orbitals.29 As commented below, ∆E is not equal to the sum of E1 and E2. Ecorr is the MP2 intermolecular correlation energy, and ∆Etot is the sum of ∆E and Ecorr. Unless otherwise specified, the reported ab initio results are those with the CEP 4-31G(2d) basis set. The DFT results reported were obtained using Gaussian9830 and the B3LYP hybrid functional.31 The complete optimization carried out for six of the systems considered in this study altogether with the single-point computation on the largest of them have been carried out using Jaguar 4.0 with the LACVP** basis set and the B3LYP functional.32 SIBFA Calculations. Within the SIBFA procedure, the intermolecular interaction energy ∆E is computed as a sum of five separate contributions:
∆Etot ) EMTP + Erep + Epol + Ect + Edisp EMTP denotes the electrostatic (multipolar) energy contribution, computed with distributed multipoles derived from the ab initio HF wave function of the constitutive fragments.33 Erep is the short-range repulsion energy, computed as a sum of bond-bond, bond-lone pair, and lone pair-lone pair interactions. Epol is the polarization energy contribution which uses, on the individual fragments, distributed anisotropic polarizabilities derived by a procedure by Garmer and Stevens.34 A Gaussian screening of the polarizing field is used. The field polarizing each molecule takes into account the permanent multipoles plus the dipoles induced on all of the other molecules in an iterative fashion. Ect is the charge-transfer energy contribution, in which a coupling with the polarization is accounted for.17 Edisp, the dispersion energy contribution, is computed as a sum of 1/R,6 1/R,8 and 1/R10 terms.35 A thorough description of the various terms appearing in the above formula is given in ref 17a,c-e. For consistency reasons with the RVS computations, the ab initio HF computations on the individual molecules, necessary to derive the distributed multipoles and polarizabilities, were done with the CEP 4-31G(2d) basis set. The quadrupolar polarizability tensor of Cu(I) was derived from a triple-ζ calculation using Roos’s ANO36 (21s,15p,10d,6f,4 g) f (8s,7p,5d,3f,2 g) basis set (Angyan, J.; private communication). Energy-minimization (using the Merlin package37) was performed on the set of the
J. Phys. Chem. A, Vol. 106, No. 23, 2002 5661 six intermolecular variables defining the position of each molecule in the complex. Standard internal geometries are used to construct the constitutive fragments. These geometries are not modified upon a conformational change. This is equivalent to the rigid rotor approximation. The distributed multipoles and polarizabilities on the constitutive fragments undergo matrix rotations but no changes in their intensities. In the case of Cu(I) binding by flexible ligands, intramolecular polarization effects are accounted for by computing the fragment-fragment interactions as actual intermolecular interactions, occurring simultaneously with the Cu(I)-ligand and ligand-ligand interactions. Such a procedure was recently shown to reproduce correctly the intermolecular interaction energies of the Zn(II) cation with highly polarizable and flexible ligands, such as the glycine zwitterion,38 anionic mercaptocarboxamides,39 and pyrophosphate (Gresh et al., to be published). We provide as Supporting Information the refinements brought to Epol altogether with Cu(I) parameters. The refinements to Epol were brought by introducing the dipolar and quadrupolar polarizabilities for the polarization energy of the Cu(I) cation, denoted as Epol(M) below. Those to Ect consist of including penetration effects in the monopolar component of the electrostatic potentials felt by the electron donors and acceptors. Denoting by ZB the atomic number of atom B with which A is interacting, by qB its atomic monopole, by RAB the distance between A and B, by Cs and Ds respectively the coefficient and the exponent of the exponential and by WB the van der Waals radius of atom B, the total electrostatic potential can be expressed as
VBfA ) (ZB - PelB )/RAB in which
PelB ) (ZB - qB)(1 - R′ABCs exp(-DsR′AB )) depends on the electronic population of B and
R′AB ) RAB/WB is a reduced interatomic distance. The values of Cs and Ds were calibrated to 0.09 and 3.5, respectively, to fit the radial evolution of Ect ab initio value in the monoligated complexes of Cu(I) with water and formate anion. In addition, an explicit contribution from Ect(M), the cation f ligand charge transfer, is also introduced. Its derivation is given in the Supporting Information. In the tables given hereafter, E1 is the sum of EMTP and Erep. E2 is the sum of Epol and Ect and ∆E is the sum of E1 and E2, and ∆Etot, the total interaction energy, is the sum of ∆E and Edisp. It is to be noted that, apart from the introduction of the Cu(I) parameters, no recalibration of the method was done. Results and Discussion A. Cu(I) Complexes with O and S Ligands. 1. Monoligated Complexes. The results concerning the oxygenated ligands are reported in Table 1, which lists the values of the ab initio and SIBFA energies and their components at equilibrium distances. For both H2O and formamide, the SIBFA computations closely reproduce the results of the CEP 4-31G (2d) computations, at both uncorrelated and correlated levels. E1 has a modest weight within ∆Etot, namely, 15 and 33% for the water and formamide complexes (RVS) and 15 and 40% (SIBFA). In these
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Gresh et al.
TABLE 1: Values (kcal/mol) of the Intermolecular Interaction Energies and Their Components in the Complexes of Cu(I) with O-Containing Ligands for the Cu(I)-Ligand Distance (Given in Å) Optimized at the MP2 Level Cu+-HCOOCu+-OH2 E1 Epol(L) Epol(M)a Epol Ect(L) Ect(M) Ect E2 ∆E Edisp ∆Etot ∆Etotb d(Cu-O)c
Cu+-formamide
Cu+-CH3O-
bridge
monodentate
ab initio
SIBFA
ab initio
SIBFA
ab initio
SIBFA
ab initio
SIBFA
ab initio
SIBFA
-5.3 -9.8 -5.2
-5.4 -12.5 -2.8 (-1.9) -15.3 -4.8 -1.8 -6.6 -21.9 -27.3 -9.3 -36.6 -38.0
-17.9 -15.1 -5.2
-22.3 -16.1 -2.3 (-1.0) -18.4 -4.0 -1.3 -5.3 -23.7 -46.0 -9.8 -55.7
-117.5 -18.2 -15.3
-110.4 -27.5 -21.0 (-11.1) -48.8 -12.6 -2.2 -14.8 -53.6 -173.8 -19.1 -192.2 -196.9
-133.0 -16.1 -4.5
-131.7 -17.0 -9.0 (-4.5) -26.1 -9.7 -0.6 -10.3 -36.4 -167.6 -13.4 -181.0 -184.0
-99.7 -15.4 -10.9
-104.9 -19.7 -19.3 (-11.2) -39.0 -10.4 -1.9 -12.3 -51.3 -156.1 -15.3 -171.2 -173.8
-15.0 -4.7 -1.9 -6.6 -21.6 -28.6 -9.4 -37.9 1.9 (2.0)
-20.3 -4.6 -2.2 -6.8 -27.1 -46.7 -7.2 -53.9
-33.5 -12.6 -4.1 -16.7 -50.2 -173.2 -24.1 -197.3
1.9
1.7 (1.8)
-20.6 -7.4 -1.7 -9.1 -29.7 -164.9 -14.7 -179.6 2.13 (2.03)
-26.3 -11.1 -2.5 -13.6 -29.9 -143.4 -20.5 -163.9 1.8 (1.7)
a The value in parentheses is that of the quadrupolar polarization of Cu(I). b Value of ∆E (SIBFA) at the SIBFA-optimized distance. c The value tot in parentheses is the SIBFA-optimized Cu(I)-ligand distance.
two complexes, cation relaxation contributes -7.1 and -7.4 kcal/mol to ∆E(RVS) and -4.6 and -3.6 kcal/mol (SIBFA) at the MP2 optimized distance of 1.9 Å. For Cu(I)-H2O, at this distance, ab initio and SIBFA ∆Etot values of -37.9 and -36.6 kcal/mol, respectively, are close to the respective MP2 and CCSD(T) values of -38.9 and -37.2 kcal/mol by Hoyau and Ohanessian40 using a 6-311G (2d,2p) basis set on H and O and Wachter’s (14s11p5d/8s6p3d) basis set on Cu.40 They are also close to the experimental value of -37.5 ( 0.5 kcal/mol.40 For Cu(I)-formamide, the ab initio and SIBFA ∆Etot values of -53.9 and -55.7 kcal/mol are close to their -53.4 (CCSD(T)) value38 and to the DFT value of -56.2 kcal/mol derived by Luna et al.11f with a hybrid B3LYP functional and the 6-311+G(2df,2p) basis set. The need for polarization and charge-transfer contributions to ∆Etot is highlighted by comparison of Cu(I)H2O binding energy using the MMF94 force field15c with the corresponding ab initio results. This force field gives a ∆E value of -23.9 kcal/mol instead of -37.9, and a Cu-O equilibrium distance is 2.23 Å instead of 1.9 Å. For a 2.23 Å distance, SIBFA gives a value of ∆Etot of -34.2 kcal/mol, whereas the sum of the sole E1 and Edisp contributions is of -21.9 kcal/ mol, a value very close to that obtained using MMF94 systematics. The values reported in Table 1 concerning anionic ligands correspond to geometric arrangements depicted in Figure 1. It is observed from the tabulated values that for all three complexes ∆Etot(SIBFA) can reproduce ∆Etot(MP2) with a relative error
