Energetics of Zn2+ binding to a series of biologically relevant ligands: A molecular mechanics investigation grounded on ab initio self-consistent field supermolecular computations

Detailed investigations are performed of the binding energetics of Zn²⁺ to a series of neutral and anionic ligands making up the sidechains of amino acid residues of proteins, as well as ligands which can be involved in Zn²⁺ binding during enzymatic activation: imidazole, formamide, methanethiol, methanethiolate, methoxy, and hydroxy. The computations are performed using the SIBFA molecular mechanics procedure (SMM), which expresses the interaction energy under the form of four separate contributions related to the corresponding ab initio supermolecular ones: electrostatic, short-range repulsion, polarization, and charge transfer. Recent refinements to this procedure are first exposed. To test the reliability of this procedure in large-scale simulations of inhibitor binding to metalloenzyme cavities, we undertake systematic comparisons of the SMM results with those of recent large basis set ab initio self-consistent field (SCF) supermolecule computations, in which a decomposition of the total ΔE into its four corresponding components is done (N. Gresh, W. Stevens, and M. Krauss, J. Comp. Chem., 16 , 843, 1995). For each complex, the evolution of each individual SMM energy component as a function of radial and in- and out-of-plane angular variations of the Zn²⁺ position reproduces with good accuracy the behavior of the corresponding SCF term. Computations performed subsequently on di- and oligoligated complexes of Zn²⁺ show that the SIBFA molecular mechanics (SMM) functionals, E_pol and E_ct, closely account for the nonadditive behaviors of the corresponding second-order energy contributions determined from the ab initio SCF calculations on these complexes and their nonlinear dependence on the number of ligands. Thus, the total intermolecular interaction energies computed with this procedure reproduce, with good accuracy, the corresponding SCF ones without the need for additional, extraneous terms in the intermolecular potential of polyligated complexes of divalent cations. © 1995 by John Wiley & Sons, Inc.     

Comparative binding energetics of Mg2+, Ca2+, Zn2+, and Cd2+ to biologically relevant ligands: Combined ab initio SCF supermolecule and molecular mechanics investigation

A combined ab initio SCF supermolecule and molecular mechanics investigation is carried out on the binding energetics of the divalent cations Mg²⁺, Ca²⁺, Zn²⁺, and Cd²⁺ to a series of the most common ligand functional groups found in biomolecules. The SCF binding energy components are resolved using the restricted variational space method.¹ The results show that the SIBFA molecular mechanics (SMM) procedure² reproduces the ab initio binding energies and total energy variations as a function of intermolecular variables. The model also reproduces the selectivity energetics for exchange reactions. Thus, the SMM procedure can be used without reparametrization to describe the coordination energetics of complex molecules including those subject to coordination changes. The energetic properties of divalent cation-hexahydrate complexes are compared as examples of a complete, realistic coordination system. The hexahydrates exhibit strong nonadditive effects typical of dication coordination. Nevertheless, these energetics are satisfactorily reproduced by the SMM procedure. © 1996 John Wiley & Sons, Inc.     

Atomic forces for geometry‐dependent point multipole and Gaussian multipole models

In standard treatments of atomic multipole models, interaction energies, total molecular forces, and total molecular torques are given for multipolar interactions between rigid molecules. However, if the molecules are assumed to be flexible, two additional multipolar atomic forces arise because of (1) the transfer of torque between neighboring atoms and (2) the dependence of multipole moment on internal geometry (bond lengths, bond angles, etc.) for geometry‐dependent multipole models. In this study, atomic force expressions for geometry‐dependent multipoles are presented for use in simulations of flexible molecules. The atomic forces are derived by first proposing a new general expression for Wigner function derivatives . The force equations can be applied to electrostatic models based on atomic point multipoles or Gaussian multipole charge density. Hydrogen‐bonded dimers are used to test the intermolecular electrostatic energies and atomic forces calculated by geometry‐dependent multipoles fit to the ab initio electrostatic potential. The electrostatic energies and forces are compared with their reference ab initio values. It is shown that both static and geometry‐dependent multipole models are able to reproduce total molecular forces and torques with respect to ab initio, whereas geometry‐dependent multipoles are needed to reproduce ab initio atomic forces. The expressions for atomic force can be used in simulations of flexible molecules with atomic multipoles. In addition, the results presented in this work should lead to further development of next generation force fields composed of geometry‐dependent multipole models. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Ring opening of the molecular ion of 5(4H)-oxazolone

Quantum chemical calculations were carried out at several theoretical levels (semi-empirical, MNDO; ab initio, 3–21G SCF, 6–311G** SCF and DZP CISD) to investigate the ring-opening process of and the loss of CO from the molecular ion of 5(4H)-oxazolone. The ring-opening process is predicted to be slightly endothermic and the loss of CO from the open-ring molecular ion to be slightly exothermic. Detailed population analysis calculations suggest the weakening of the lactonic C? O bond in the closed-ring molecular ion and weak carbon—carbon and nitrogen—(formy)—carbon bonds in the open form. Both the open-ring molecular ion and the [M–CO]^+· ion are suggested to be of distonic type.     

Molecular potential,cation binding,and hydration properties of the carboxylate anion. Ab initio studies with an extended polarized basis set

The carboxylat anion, involved in the structure of numerous compounds of biological interest, participates in a number of intermolecular interactions involving water, cations, and other cellular constituents. A set of ab initio SCF computations have been carried out with an extended polarized basis set on HCOO^–, its molecular electrostatic potential, and its interaction with Li⁺, Na⁺, K⁺, and H₂O. The results are compared with those of a minimal good quality basis set. An evaluation of the basis set superposition error is made in the two basis as well as that of the contribution of the dispersion energy to the hydration. The analogies and differences in the nucleophilic character of the formate and the phosphate groups are discussed.     

Study of the temperature‐dependent conformational averaging of 1H NMR resonances in vinylcyclopropane through the use of ab initio methodology and Boltzmann statistics

The temperature dependence of the ¹ H NMR resonance of the C‐4 olefinic proton in vinylcyclopropane was investigated through a combination of ab initio calculations and Boltzmann statistics. A torsional energy profile as a function of the 〈?〉 dihedral angle was obtained using HF methodology with a 6–311G** basis set, while the corresponding ¹ H chemical shift profiles for the C‐4 proton were computed using the GIAO approach and either HF, DFT (B3LYP) or MP2 methods at the 6–311G** level of theory. Chemical shifts at different temperatures calculated as canonical ensemble averages in which the different ab initio ¹ H chemical shift profiles and a Boltzmann factor defined by the HF/ 6–311G** energy function are employed reproduce remarkably well the temperature dependence observed experimentally. Attempts to perform a similar study using only the GIAO‐MP2 ¹ H chemical shift profile and 〈?〉 dihedral angle trajectories obtained from molecular dynamics simulations at different temperatures failed to reproduce the experimental trends. This shortcoming was attributed to the inability of the force fields employed, Tripos 6.0 and MMFF94, to reproduce properly the three‐well torsional potential of vinylcyclopropane. The application of both methodologies to the calculation of population‐dependent chemical shifts in other systems is discussed. Copyright © 2002 John Wiley & Sons, Ltd.     

Comparative analysis of molecular interactions in quaternary fluid system performed by classical and ab initio molecular dynamics

Molecular interactions in the quaternary fluid system acetic acid–n-propanol–n-propyl acetate–water were analyzed by classical and ab initio molecular dynamics methods. It was shown that ab initio molecular dynamics simulation can reproduce the molecular mobility tendency and structural features of a multicomponent system without empirical parameters.     

Ab initio studies on vibrational spectra of XSO2NCO (X = F,Cl): harmonic force fields and frequency assignments

The harmonic vibrational force fields and the IR spectrum of XSO₂NCO (X= F, C1) molecules have been studied usingab initio HF/SCF method with the 6-31G’ basis set. Theab initio harmonic force fields are scaled empirically using the scaled quantum mechanical (SQM) method of Pulay. A set of scale factors are optimized by the least-squares fitting to the experimental frequencies of FSO₂NCO and then are transferred to CISO₂NCO to give ana priori prediction of its fundamental frequencies. The average deviations between the theoretical frequencies and the experimental values for FSO₂NCO and C1SO₂NCO are 3 and 5 cm^-1, respectively. The assignments of the fundamentals for these two molecules are also made atcording to the potential energy distributions and theab initio IR intensities Project supported by the National Natural Science Foundation of China (Grant No. 29673029)     

Cation-binding to biomolecules

Ab initio SCF computations indicate that Mg²⁺ should bind essentially to the oxygen atoms of uracil, the remaining part of the base being rather repulsive towards such an interaction. The Coulombic component predominates in the interaction, the essential feature of which may thus be deduced from the study of the molecular electrostatic potential of uracil. These ab initio results contradict an earlier CNDO prediction that the binding of uracil and Mg²⁺ should occur preferentially at the C₅=C₆ double bond of the base. It is shown that the CNDO result is an artifact due to an exaggeration by this method of the charge transfer between the ligand and the cation. The small amount of available experimental data seem in favor of the ab initio results.     

An optimum strategy for solution chemistry using semiempirical molecular orbital method: Importance of description of charge distribution

For the purpose to execute direct dynamics calculation in solution chemistry, we propose an optimum strategy for solution chemistry using semiempirical molecular orbital (MO) method with neglect of diatomic differential overlap (NDDO) approximation with specific solution reaction parameters (SSRP), i.e., the NDDO‐SSRP method. In this strategy, the empirical parameters of the semi‐empirical MO method were optimized individually for target molecule or ion by reference to the ab initio MO calculation data for many configurations on the potential energy surface near the reaction path. For demonstration, the NDDO‐SSRP method was applied to two molecules and two ions (OH^?, H₂O, NH₃, NH₄⁺) at their equilibrium states in aqueous solution, respectively. Accordingly, it was verified that both the potential energy surface and the charge distribution of these solutes in aqueous solution are dramatically improved to reproduce themselves accurately at ab initio MO calculation level. In conclusion, it is expected that the NDDO‐SSRP method should become quite useful for dynamic and statistical applications to chemical reaction systems in solution. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

On the electronic structure of N2H2. A possible triplet ground state in diazines

Within the frame of closed-shell and restricted open-shell ab initio SCF calculations 1,1-dihydrodiazine H₂N=N has a triplet ground state, ³A₂. This result, though not unsuspected from simple valence theory, is critically discussed and possible chemical implications are briefly mentioned.The ab initio calculations were performed at the IBM Research Center, San Jose, California.     

A potential function for computer simulation studies of proton transfer in acetylacetone

A potential energy model is developed to study the intramolecular proton transfer in the enol form of acetylacetone. It makes use of the empirical valence bond approach developed by Warshel to combine standard molecular mechanics potentials for the reactant and product states to reproduce the interconversion between these two states. Most parameters have been fitted to reproduce the key features of an ab initio potential surface obtained from 4-31G^* Hartree-Fock calculations. The partial charges have been fitted to reproduce the electrostatic potential surface of 6-31G^* Hartree-Fock wave functions, subject to total charge and symmetry constraints, using a fitting procedure based on generalized inverses. The resulting potential energy function reproduces the features most important for proton transfer simulations, while being several orders of magnitude faster in evaluation time than ab initio energy calculations. © 1997 by John Wiley & Sons, Inc.     

Properties of pyridine and pyrazine from ab initio molecular orbital wave functions

Various molecular properties have been calculated for pyridine and pyrazine from Gaussian lobe ab initio SCF molecular wave functions. Values are compared with available experimental data. In general, agreement is satisfactory with the exception of the rather sensitive asymmetry parameter of the quadrupole coupling tensor. The distributions of total electronic charge, and of selected molecular orbitals have been displayed as plots of the charge density contours in two dimensions.     

Interaction of neutral and zwitterionic glycine with Zn2+ in gas phase: ab initio and SIBFA molecular mechanics calculations

The interaction of Zn²⁺ with glycine (Gly) in the gas phase is studied by a combination of ab initio and molecular mechanics techniques. The structures and energetics of the various isomers of the Gly–Zn²⁺ complex are first established via high‐level ab initio calculations. Two low‐energy isomers are characterized: one in which the metal ion interacts with the carboxylate end of zwitterionic glycine, and another in which it chelates the amino nitrogen and the carbonyl oygen of neutral glycine. These calculations lead to the first accurate value of the gas‐phase affinity of glycine for Zn²⁺. Ab initio calculations were also used to evaluate the performance of various implementations of the SIBFA force field. To assess the extent of transferability of the distributed multipoles and polarizabilities used in the SIBFA computations, two approaches are followed. In the first, approach (a), these quantities are extracted from the ab initio Hartree–Fock wave functions of glycine or its zwitterion in its entirety, and for each individual Zn²⁺‐binding conformation. In the second, approach (b), they are assembled from the appropriate constitutive fragments, namely methylamine and formic acid for neutral glycine, and protonated methylamine and formate for the zwitterion; they undergo the appropriate vector or matrix rotation to be assembled in the conformation studied. The values of the Zn²⁺–glycine interaction energies are compared to those resulting from ab initio SCF and MP2 computations using both the all‐electron 6‐311+G(2d,2p) basis set and an effective core potential together with the valence CEP 4‐31G(2d) basis set. Approach (a) values closely reproduce the ab initio ones, both in terms of the total interaction energies and of the individual components. Approach (b) can provide a similar match to ab initio interaction energies as does approach (a), provided that the two constitutive Gly building blocks are considered as separate entities having mutual interactions that are computed simultaneously with those occurring with Zn²⁺. Thus, the supermolecule is treated as a three‐body rather than a two‐body system. These results indicate that the current implementation of the SIBFA force field should be adequate to undertake accurate studies on zinc metallopeptides. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 963–973, 2000     

Empirical force-field and ab initio calculations on delocalized open chain cations

Force-field calculations are reported for large delocalized cations. The results for the geometries, heats of formation, and π-electron densities agree well with MP2(full)/6–31G^* ab initio calculations. Both methods give similar results for the distortion of the carbon skeletons of unsubstituted cations by hyperconjugating methyl groups. Because of the SCF treatment of π-interactions, the MMP2 force-field technique enables calculations of resonance energies in delocalized cations. The additional resonance stabilization produced by extending conjugation is directly related to the π-charge on the carbon at which a vinyl group is substituted. The good agreement of MMP2 results for nonbonded resonance effects in large delocalized cationic π-systems with ab initio data suggests that MMP2 can be used to study the influence of these interactions in cationic π-systems too large to be calculated by correlated ab initio methods. © 1997 by John Wiley & Sons, Inc.     

Theoretical studies of molecular conformation. Derivation of an additive procedure for the computation of intramolecular interaction energies. Comparison withab initio SCF computations

An additive procedure (SIBFA) is developed for the rapid computation of conformational energy variations in very large molecules. The macromolecule is built out of constitutive molecular fragments and the intramolecular energy is computed as a sum of interaction energies between the fragments. The electrostatic and the polarization components are calculated using multicenter multipole expansions of theab initio SCF electron density of the fragments. The repulsion component is obtained as a sum of bond and lone pair interactions.Tests of the procedure on a series of model compounds containing ether oxygens and pyridine-like nitrogens are reported and compared with the results of correspondingab initio SCF calculations. The resulting methodology is compatible with the simultaneous computation of intermolecular interactions.     

Comparative study of the molecular electrostatic potential obtained from different wavefunctions. Reliability of the semiempirical MNDO wavefunction

A systematic analysis of the molecular electrostatic potential (MEP) is presented. This study has been performed with a twofold purpose: first, to study the MEP dependence with regard to the quality of the basis set used to compute the ab initio SCF wavefunction and second, to develop and to assess a new strategy for computing isoelectrostatic potential maps using the semiempirical MNDO wavefunction. The only differences between this procedure and the ab initio SCF MEP computation lie in the freezing of the inner electrons and in the origin of the first-order density matrix. The statistical analysis of MEPs computed for a large number of molecules from MNDO wavefunction and ab initio SCF wavefunctions obtained using STO-3G, 4-31G, 6-31G, 4-31G*, 6-31G*, and 6-31G** basis sets points out the ability of any wavefunction to reproduce the general topological characteristics of the MEP surfaces. Nevertheless, split-valence basis sets including polarization functions are necessary to obtain accurate MEP minimum energy values. MNDO wavefunction tends to overestimate the MEP minima depth by a constant factor and shows an excellent ability to reflect the relative variation of MEP minima energies derived from a rather sophisticated (6-31G*) basis set, lacking of the shortcomings detected in the semiempirical CNDO approximation.     

Computation of the Electronic and Spectroscopic Properties of Carbohydrates Using Novel Density Functional and Vibrational Self-Consistent Field Methods

ABSTRACT

A novel density functional method is presented for the calculation of electronic and thermodynamical properties of oligosaccharides. This method, termed K2-BVWN, offers two advantages; it scales as N ³, where N is the number of basis functions, and there are only two adjustable parameters. The current density functional method is tested in terms of reproducing high level gas phase ab initio calculations in eleven low energy conformers of D-glucopyranose including exo-anomeric and different hydroxymethyl orientations (G ^?, G ⁺, and T). The K2-BVWN method is also tested in terms of reproducing the spectroscopic features of D-glucopyranose and D-mannopyranose (α/β) as compared with both a vibrational self-consistent field calculation (VSCF) as well as experimental infrared spectroscopy. The VSCF calculations offer the advantage that it is possible to include higher order mode coupling and anharmonic effects directly into the calculation of the vibrational frequencies. In general, the K2-BVWN method reproduces the ab initio energetic trends of the different conformers of D-glucose. While the absolute energies are not the same between the ab initio and the K2-BVWN method, both methods do predict a preference for the α-anomer in the gas phase (0.4 kcal/mol ab initio, 0.0 – 0.5 kcal/mol K2-BVWN). The K2-BVWN method was able to reproduce the experimental and VSCF calculated spectrum of both D-glucopyranose and D-mannopyranose in the frequency range between 1500 – 800 cm^?1. Because the current density functional method is both relatively quick and accurate, it represents a significant advancement in the development of oligosaccharide force fields.     

Accurate density functional theory description of binding constants and NMR chemical shifts of weakly interacting complexes of C60 with corannulene‐based molecular bowls

Density functional calculations on “catch and release” complexes of C₆₀ with corannulene derived molecular bowls show that computationally obtained ¹H nuclear magnetic resonance (NMR) chemical shifts can be used as a reliable predictor of binding constants. A wide range of functionals was benchmarked against accurate ab initio calculations to ensure a credible representation of the weak forces that dominate the interactions in these systems. The most reliable density functional theory (DFT) results were then calibrated using experimentally observed NMR data. Careful analysis and comparison of a wide range of commonly used density functionals shows that the explicit inclusion of dispersion corrections is currently the only reliable way to accurately describe the systems investigated in our study. Moreover, we are able to show that the B97‐D and ωB97X‐D functionals are not only able to reproduce ab initio benchmark calculations, but they do so accurately with a moderately sized basis sets and without the problems of numerical integration we encountered with other functionals in this study. © 2013 Wiley Periodicals, Inc.     

A polarizable electrostatic model of the N‐methylacetamide dimer

Our previously developed polarizable electrostatic model is applied to isolated N‐methylacetamide (NMA) and to three hydrogen‐bonded configurations of the NMA dimer. Two versions of the model are studied. In the first one (POL1), polarizability along the valence bonds is described by induced bond charge increments, and polarizability perpendicular to the bonds is described by cylindrically isotropic induced atomic dipoles. In the other version (POL2), the induced bond charge increments are replaced by induced atomic dipoles along the bonds. The parameterization is done by fitting to ab initio MP2/6‐31++G(d,p) electric potentials. The polarizability parameters are determined by subjecting the NMA molecule to various external electric fields. POL1 turns out to be easier to optimize than POL2. Both models reproduce well the ab initio electric potentials, molecular dipole moments, and molecular polarizability tensors of the monomer and the dimers. Nonpolarizable models are also investigated. The results show that polarization is very important for reproducing the electric potentials of the studied dimers, indicating that this is also the case in hydrogen bonding between peptide groups in proteins. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1933–1943, 2001