Jean-Philip Piquemal

Towards a force field based on density fitting

Total intermolecular interaction energies are determined with a first version of the Gaussian electrostatic model (GEM-0), a force field based on a density fitting approach using s-type Gaussian functions. The total interaction energy is computed in the spirit of the sum of interacting fragment ab initio (SIBFA) force field by separately evaluating each one of its components: electrostatic (Coulomb), exchange repulsion, polarization, and charge transfer intermolecular interaction energies, in order to reproduce reference constrained space orbital variation (CSOV) energy decomposition calculations at the B3LYP/aug-cc-pVTZ level. The use of an auxiliary basis set restricted to spherical Gaussian functions facilitates the rotation of the fitted densities of rigid fragments and enables a fast and accurate density fitting evaluation of Coulomb and exchange-repulsion energy, the latter using the overlap model introduced by Wheatley and Price [Mol. Phys. 69, 50718 (1990)]. The SIBFA energy scheme for polarization and charge transfer has been implemented using the electric fields and electrostatic potentials generated by the fitted densities. GEM-0 has been tested on ten stationary points of the water dimer potential energy surface and on three water clusters (n = 16,20,64). The results show very good agreement with density functional theory calculations, reproducing the individual CSOV energy contributions for a given interaction as well as the B3LYP total interaction energies with errors below kBT at room temperature. Preliminary results for Coulomb and exchange-repulsion energies of metal cation complexes and coupled cluster singles doubles electron densities are discussed.

Representation of Zn(II) Complexes in Polarizable Molecular Mechanics. Further Refinements of the Electrostatic and Short-Range Contributions. Comparisons with Parallel Ab Initio Computations

We present refinements of the SIBFA molecular mechanics procedure to represent the intermolecular interaction energies of Zn(II). The two first‐order contributions, electrostatic (EMTP), and short‐range repulsion (Erep), are refined following the recent developments due to Piquemal et al. (Piquemal et al. J Phys Chem A 2003, 107, 9800; and Piquemal et al., submitted). Thus, EMTP is augmented with a penetration component, Epen, which accounts for the effects of reduction in electronic density of a given molecular fragment sensed by another interacting fragment upon mutual overlap. Epen is fit in a limited number of selected Zn(II)–mono‐ligated complexes so that the sum of EMTP and Epen reproduces the Coulomb contribution Ec from an ab initio Hartree–Fock energy decomposition procedure. Denoting by S, the overlap matrix between localized orbitals on the interacting monomers, and by R, the distance between their centroids, Erep is expressed by a S2/R term now augmented with an S2/R2 one. It is calibrated in selected monoligated Zn(II) complexes to fit the corresponding exchange repulsion Eexch from ab initio energy decomposition, and no longer as previously the difference between (Ec + Eexch) and EMTP. Along with the reformulation of the first‐order contributions, a limited recalibration of the second‐order contributions was carried out. As in our original formulation (Gresh, J Comput Chem 1995, 16, 856), the Zn(II) parameters for each energy contribution were calibrated to reproduce the radial behavior of its ab initio HF counterpart in monoligated complexes with N, O, and S ligands. The SIBFA procedure was subsequently validated by comparisons with parallel ab initio computations on several Zn(II) polyligated complexes, including binuclear Zn(II) complexes as in models for the Gal4 and β‐lactamase metalloproteins. The largest relative error with respect to the RVS computations is 3%, and the ordering in relative energies of competing structures reproduced even though the absolute numerical values of the ab initio interaction energies can be as large as 1220 kcal/mol. A term‐to‐term identification of the SIBFA contributions to their ab initio counterparts remained possible even for the largest sized complexes.

Complexes of thiomandelate and captopril mercaptocarboxylate inhibitors to metallo‐β‐lactamase by polarizable molecular mechanics. Validation on model binding sites by quantum chemistry

Using the polarizable molecular mechanics method SIBFA, we have performed a search for the most stable binding modes of D‐ and L‐thiomandelate to a 104‐residue model of the metallo‐β‐lactamase from B. fragilis, an enzyme involved in the acquired resistance of bacteria to antibiotics. Energy balances taking into account solvation effects computed with a continuum reaction field procedure indicated the D‐isomer to be more stably bound than the L‐one, conform to the experimental result. The most stably bound complex has the S− ligand bridging monodentately the two Zn(II) cations and one carboxylate O− H‐bonded to the Asn193 side chain. We have validated the SIBFA energy results by performing additional SIBFA as well as quantum chemical (QC) calculations on small (88 atoms) model complexes extracted from the 104‐residue complexes, which include the residues involved in inhibitor binding. Computations were done in parallel using uncorrelated (HF) as well as correlated (DFT, LMP2, MP2) computations, and the comparisons extended to corresponding captopril complexes (Antony et al., J Comput Chem 2002, 23, 1281). The magnitudes of the SIBFA intermolecular interaction energies were found to correctly reproduce their QC counterparts and their trends for a total of twenty complexes.

Intermolecular electrostatic energies using density fitting

A method is presented to calculate the electron-electron and nuclear-electron intermolecular Coulomb interaction energy between two molecules by separately fitting the unperturbed molecular electron density of each monomer. This method is based on the variational Coulomb fitting method which relies on the expansion of the ab initio molecular electron density in site-centered auxiliary basis sets. By expanding the electron density of each monomer in this way the integral expressions for the intermolecular electrostatic calculations are simplified, lowering the operation count as well as the memory usage. Furthermore, this method allows the calculation of intermolecular Coulomb interactions with any level of theory from which a one-electron density matrix can be obtained. Our implementation is initially tested by calculating molecular properties with the density fitting method using three different auxiliary basis sets and comparing them to results obtained from ab initio calculations. These properties include dipoles for a series of molecules, as well as the molecular electrostatic potential and electric field for water. Subsequently, the intermolecular electrostatic energy is tested by calculating ten stationary points on the water dimer potential-energy surface. Results are presented for electron densities obtained at four different levels of theory using two different basis sets, fitted with three auxiliary basis sets. Additionally, a one-dimensional electrostatic energy surface scan is performed for four different systems (H2O dimer, Mg2+-H2O, Cu+-H2O, and n-methyl-formamide dimer). Our results show a very good agreement with ab initio calculations for all properties as well as interaction energies.

Binding of 5‐phospho‐D‐arabinonohydroxamate and 5‐phospho‐D‐arabinonate inhibitors to zinc phosphomannose isomerase from Candida albicans studied by polarizable molecular mechanics and quantum mechanics

Type I phosphomannose isomerase (PMI) is a Zn‐dependent metalloenzyme involved in the isomerization of D‐fructose 6‐phosphate to D‐mannose 6‐phosphate. One of our laboratories has recently designed and synthesized 5‐phospho‐D‐arabinonohydroxamate (5PAH), an inhibitor endowed with a nanomolar affinity for PMI (Roux et al., Biochemistry 2004, 43, 2926). By contrast, the 5‐phospho‐D‐arabinonate (5PAA), in which the hydroxamate moiety is replaced by a carboxylate one, is devoid of inhibitory potency. Subsequent biochemical studies showed that in its PMI complex, 5PAH binds Zn(II) through its hydroxamate moiety rather than through its phosphate. These results have stimulated the present theoretical investigation in which we resort to the SIBFA polarizable molecular mechanics procedure to unravel the structural and energetical aspects of 5PAH and 5PAA binding to a 164‐residue model of PMI. Consistent with the experimental results, our theoretical studies indicate that the complexation of PMI by 5PAH is much more favorable than by 5PAA, and that in the 5PAH complex, Zn(II) ligation by hydroxamate is much more favorable than by phosphate. Validations by parallel quantum‐chemical computations on model of the recognition site extracted from the PMI‐inhibitor complexes, and totaling up to 140 atoms, showed the values of the SIBFA intermolecular interaction energies in such models to be able to reproduce the quantum‐chemistry ones with relative errors < 3%. On the basis of the PMI–5PAH SIBFA energy‐minimized structure, we report the first hypothesis of a detailed view of the active site of the zinc PMI complexed to the high‐energy intermediate analogue inhibitor, which allows us to identify active site residues likely involved in the proton transfer between the two adjacent carbons of the substrates.

Revisiting the geometry of nd10 (n+1)s0 [M(H2O)]p+ complexes using four‐component relativistic DFT calculations and scalar relativistic correlated CSOV energy decompositions (Mp+ = Cu+, Zn2+, Ag+, Cd2+, Au+, Hg2+)

Hartree–Fock and DFT (B3LYP) nonrelativistic (scalar relativistic pseudopotentials for the metallic cation) and relativistic (molecular four‐component approach coupled to an all‐electron basis set) calculations are performed on a series of six nd10 (n+1)s0 [M(H2O)]p+ complexes to investigate their geometry, either planar C2v or nonplanar Cs. These complexes are, formally, entities originating from the complexation of a water molecule to a metallic cation: in the present study, no internal reorganization has been found, which ensures that the complexes can be regarded as a water molecule interacting with a metallic cation. For [Au(H2O)]+ and [Hg(H2O)]2+, it is observed that both electronic correlation and relativistic effects are required to recover the Cs structures predicted by the four‐component relativistic all‐electron DFT calculations. However, including the zero‐point energy corrections makes these shallow Cs minima vanish and the systems become floppy. In all other systems, namely [Cu(H2O)]+, [Zn(H2O)]2+, [Ag(H2O)]+, and [Cd(H2O)]2+, all calculations predict a C2v geometry arising from especially flat potential energy surfaces related to the out‐of‐plane wagging vibration mode. In all cases, our computations point to the quasi‐perfect transferability of the atomic pseudopotentials considered toward the molecular species investigated. A rationalization of the shape of the wagging potential energy surfaces (i.e., single well vs. double well) is proposed based on the Constrained Space Orbital Variation decompositions of the complexation energies. Any way of stabilizing the lowest unoccupied orbital of the metallic cation is expected to favor charge‐transfer (from the highest occupied orbital(s) of the water ligand), covalence, and, consequently, Cs structures. The CSOV complexation energy decompositions unambiguously reveal that such stabilizations are achieved by means of relativistic effects for [Au(H2O)]+, and, to a lesser extent, for [Hg(H2O)]2+. Such analyses allow to numerically quantify the rule of thumb known for Au+ which, once again, appears as a better archetype of a relativistic cation than Hg2+. This observation is reinforced due to the especially high contribution of the nonadditive correlation/relativity terms to the total complexation energy of [Au(H2O)]+.

[Pb(H2O)]2+ and [Pb(OH)]+: four-component density functional theory calculations, correlated scalar relativistic constrained-space orbital variation energy decompositions, and topological analysis.

Within the scope of studying the molecular implications of the Pb(2+) cation in environmental and polluting processes, this paper reports Hartree-Fock and density functional theory (B3LYP) four-component relativistic calculations using an all-electron basis set applied to [Pb(H(2)O)](2+) and [Pb(OH)](+), two complexes expected to be found in the terrestrial atmosphere. It is shown that full-relativistic calculations validate the use of scalar relativistic approaches within the framework of density functional theory. [Pb(H(2)O)](2+) is found C(2v) at any level of calculations whereas [Pb(OH)](+) can be found bent or linear depending of the computational methodology used. When C(s) is found the barrier to inversion through the C(infinityv) structure is very low, and can be overcome at high enough temperature, making the molecule floppy. In order to get a better understanding of the bonding occurring between the Pb(2+) cation and the H(2)O and OH(-) ligands, natural bond orbital and atoms-in-molecule calculations have been performed. These approaches are supplemented by a topological analysis of the electron localization function. Finally, the description of these complexes is refined using constrained-space orbital variation complexation energy decompositions.

Lead Substitution in Synaptotagmin: A Case Study

Quantum chemistry computations have been used to investigate the possibility of a Pb(2+)/Ca(2+) substitution in the three calcium sites of the synaptotagmin enzyme. Provided explicit cation solvation is taken into account, it is shown that the substitution is energetically feasible and induces a strong reorganization of the Ca(2+)-coordinating sites, which may preclude the enzyme for any efficient role when lead poisoning occurs.

Towards scalable and accurate molecular dynamics using the SIBFA polarizable force field

We present a short overview of the recent developments and applications of the SIBFA (Sum of Interactions Between Fragments Ab initio computed) polarizable force field.