On the accuracy of analytical potentials: comment on ‘Accurate ab initio calculation of the Ar–CF4 intermolecular potential energy surface’

In a recent study of the Ar–CF₄ intermolecular interaction potential [Shen C-C, Chang R-Y. Accurate ab initio calculation of the Ar–CF₄ intermolecular potential energy surface. Mol Sim. 2010;36:1111–1122], Shen and Chang (SC) illustrated how the use of bond functions can improve the accuracy and basis-set saturation of electronic structure calculations employing perturbation and coupled-cluster theory. SC then used these ab initio data to derive analytic potential energy functions for use in chemical dynamics simulations. We critically examine these analytic potentials and comment on their usage in such simulations. Our analysis highlights the need for care and global validation when deriving analytic potential energy functions.     

Molecular Parameterisation and the Theoretical Calculation of Electrode Potentials

The difference in reduction potentials between ortho and para-benzoquinones has been calculated. The employs gas phase ab initio and semi-empirical computations in combination with free energy perturbation theory applied to gas and solution phase Monte Carlo simulations. The effects on calculated results of altering solute electrostatic parameterisation in solution phase simulations is examined. Atom centred charges derived from the molecular electrostatic potentials, MEPs, from optimised ab initio wavefunctions and charges generated by consideration of hydrogen bonded complexes are considered. Parameterisation of hydroxyl torsions in hydroquinone molecules is treated in a physically realistic manner. The coupled torsional system of the ortho-hydrobenzoquinone molecule is described by a potential energy surface calculated using gas phase AM1 semi-empirical computations rather than the simple torsional energy functions frequently employed in such calculations. Calculated differences in electrode potentials show that the electrostatic interactions of quinone and hydroquinone molecules in aqueous solution are not well described by atom centred charges derived from ab initio calculated MEPs. Moreover, results in good agreement with the experimental reduction potential difference can be obtained by employing high level ab initio calculations and solution phase electrostatic parameters developed by consideration of hydrogen bonded complexes.     

Accurate ab initio calculation of the Ar–CF4 intermolecular potential energy surface

Ar–CF₄ intermolecular interaction potential is studied by ab initio calculations at the MP2 and CCSD(T) levels of theory containing the so-called bond functions ({3s3p2d1f} basis set was chosen) both with and without a correction for the basis-set superposition error. The calculations were performed with Dunning's correlation consistent basis sets (aug-cc-pVXZ, X = D, T, Q, 5) to extrapolate the Ar–CF₄ potential energy minimum and intermolecular distance to their complete basis set (CBS) limits. It is shown that the addition of bond functions results in a dramatic improvement in the convergence of the calculated interaction energies at the MP2/aug-cc-pVTZ level. The MP2/{3s3p2d1f}-aug-cc-pVTZ potential energy surface even approaches the CCSD(T)/aug-cc-pVQZ potential energy surface. The potential energy minima and the intermolecular distances are both significantly closer to the CBS limit when using the bond functions, and it implies that adding bond functions in the calculation has a great effect on the interaction energies. We also find that with bond functions included in the CCSD(T)/aug-cc-pVDZ model chemistry, the potential energy minima are extremely close to the CBS limit and are better than the CCSD(T)/aug-cc-pVQZ values. Several levels of theory described in the text were used to determine pairwise analytic potential energy surfaces for Ar+CF₄. The analytic potential energy surfaces are in very good agreement with the ab initio values.     

Comparison of Different Three-site Interaction Potentials for Liquid Acetonitrile

Abstract

Computer simulations of liquid acetonitrile at normal room conditions are reported. Both static and dynamic properties are analysed. Special attention is paid to the dielectric properties. A three-site interaction potential has been derived from ab initio calculations on the gas phase dimer and a comparison with different three-site interaction potentials available in the literature is presented. The suitability of three-site models to reproduce the properties of the real liquid is discussed by comparing computer simulation results with experimental data.     

Introducing a novel method based on the imperialistic competitive algorithm to determine fluorine intermolecular potential from ab initio calculations and calculation of some properties via MD simulations

In this work, the possibility of obtaining an accurate site-site potential model suitable for use in molecular dynamics (MD) simulations of fluorine from ab initio calculations has been explored. The exploration was made on ab initio calculations. To reduce the ab initio pair potentials into a site-site potential, a higher significance was assigned to the configuration which is more stable. For this purpose, the imperialistic competitive algorithm (ICA) was implemented as a powerful optimisation tool. The calculated second virial coefficients were compared to the experimental values to test the quality of the presented intermolecular potential. The relative error for the calculated second virial coefficient ranged from 0.1 to 5.6%. MD simulations were used to evaluate the ability of the proposed intermolecular potential function. The relative error for the MD simulations ranged from 0.5 to 5.2%. The results are in good agreement with experimental data.     

Pair Potentials from ab initio Calculations for use in MD Simulations of Molten Alkali Carbonates

Ab initio calculations at the Hartree-Fock SCF level have been carried out to determine the pair interaction between the alkali ions and the carbonate ion. A distinction has been made between terms in the metal ion - carbonate ion interaction which have different physical origins, such as static coulomb interaction, short-range repulsion and electronic polarization. The additivity of the pair interaction is investigated in 3-body calculations. It is shown that for these 3-body systems pairwise addition of 2-body interactions from which polarization effects have been omitted is superior to pairwise addition of the full Hartree-Fock interactions. A model potential based on these modified interactions has been constructed. Results of MD simulations show that both structural and dynamical properties are well described by these pair potentials.     

Theoretical study of the intermolecular potential energy and second virial coefficient in the mixtures of CH4 and Kr gases: a comparison with experimental data

The intermolecular potential energy surface (IPS) in the mixtures of CH₄–Kr gases from ab initio calculations has been explored. The ab initio calculation was performed at the second-order Møller–Plesset perturbation theory (MP₂), with the 6-311+G(2df,2pd) basis set, for three relative orientations of two CH₄–Kr molecules as a function of CH₄–Kr separation distance. In this work, the IPS, U(r), of the CH₄–Kr complex has been investigated, where the vertex (V), edge (E) and face (F) of CH₄ approaches to Kr have been considered. Then, adjustable parameters of the Lennard-Jones and Buckingham potential energy function are fitted to the ab initio MP2/6-311+G(2df,2pd) interaction energies for three different orientations. Assuming a given set of parameters, we theoretically obtained second virial coefficients for the CH₄–Kr system, and compared with the experimental data at different temperatures. Trivial differences can be observed between the experimental and computational results.     

Hydrogen-bonded Trimers of DNA Bases and their Interaction with Metal Cations: Ab initio Quantum-chemical and Empirical Potential Study

Abstract

Neutral (G.GC, A. AT, G.AT, T. AT, and C (imino).GC) and protonated (CH⁺.GC and AH⁺.GC) hydrogen-bonded trimers of nucleic acid bases were characterized by ab initio methods with the inclusion of electron correlation. In addition, the influence of metal cations on the third-strand binding in Purine-Purine-Pyrimidine (Pu.PuPy) reverse-Hoogsteen triplets has been studied. The ab initio calculations were compared with those from recently introduced force fields (AMBER4.1, CHARMM23, and CFF95). The three-body term in neutral trimers is mostly negligible, and the use of empirical potentials is justified. The only exception is the neutral G.GC Hoogsteen trimer with a three-body term of -4 kcal/mol. Protonated trimers are stabilized by molecular ion—;molecular dipole attraction and the interaction within the complex is nonadditive, with the three-body term on the order of -3 kcal/mol. There is a significant induction interaction between the third-strand protonated base and guanine. The calculations indicate an enhancement of the third-strand binding in the G.GC reverse-Hoogsteen trimer due to metal cation coordination to the N7/06 position of the third-strand guanine. Interactions between metal cations and complexes of DNA bases are in general highly nonadditive; the three-body term is above -10 kcal/mol in a complex of a divalent cation (Ca²⁺) with the GG reverse-Hoogsteen pair. The pairwise additive empirical potentials qualitatively underestimate the binding energy between cation and base.     

Proton Transfer in Liquid Water II; A Semiempirical Method to Describe Chemical Reactions

Abstract

A new semiempirical method is developed to deal with the proton transfer in liquid water. In the previous work, we have shown that two- and three-body charge transfer interactions and electrostatic interactions are the most important factors to describe the potential energy surfaces (PES) of the proton transfer in liquid water [Chemical Physics 180, 239–269, 1994], In order to take account of these factors, we develop a semiempirical method imposing the principle of electronegativity equalization to the Atoms in Molecule (AIM) method. The method is free from the well-known discrepancy of the traditional AIM methods, that is, the fractional molecular charges at large molecular separation, and thus can be applied to the charge transfer reactions. Intra- and intermolecular physical quantities, such as total energies, force vectors, dipole moment vectors and intermolecular charge transfer, obtained by the present method are found to be in good agreement with those by ab initio calculation.     

A force field for naproxen

A united-atom potential model for naproxen suitable for molecular dynamics (MD) simulation has been developed. The charge distribution is approximated by point charges obtained from ab initio calculations using the CHELPG method. Also the intramolecular interactions such as bond and angle vibration, and the torsion potential are obtained from ab initio calculations. The dispersive interaction contribution is taken from the literature. By MD simulation using a naproxen film in slap geometry, the temperature dependence of the density, surface tension and self-diffusion coefficient as well as the melting temperature for the developed potential model are obtained.     

Theoretical studies on radical formation in the interaction of cysteine with dicarbonyl compounds of biological relevance

A possible pathway for the interaction between cysteine and dicarbonyl compounds of glyoxal and methylglyoxal type was studied by quantum chemical methods (INDO,ab initio). The condensation reaction is likely to occur through intermediate products, formation of which competes with the dimerization reaction. Results fromab initio UHF calculation of Fermi contact interaction for the radical cation of the final product suggest an assignment of the hyperfine coupling constants for protons that differs from the one deduced from the electron spin resonance (ESR) spectrum.     

The Effect of a Crystalline Environment on Calculated Electron Densities

Abstract

Central to the calculation of useful interatomic potentials is a reliable determination of the electron densities of interacting ions. When the ions are embedded in a crystalline environment, it is reasonable to expect the effect of the crystal to be important in such calculations.

For certain ions (for example Mg²⁺ ions in MgO) the crystal has little effect on ion electron densities. Conversely, ions such as O^2? can only exist as a result of the stabilizing influence of lattice potentials; consequently, they are significantly modified by different lattice environments.

This paper will discuss the relevance of lattice effects to ions in MgO, in particular, Mg²⁺, Mg⁺, O^2? and F^?. Of these examples, the defect ions Mg⁺ and F^? are used to demonstrate how, in certain circumstances, the usual assumption that cations are not affected by lattice potentials but that anions are greatly influenced is not applicable. This work also emphasises the role of embedding electron-electron interactions in addition to the Madelung potential.     

Ab Initio Molecular Dynamics for Simple Liquid Metals Based on the Hypernetted-Chain Approximation

Abstract

We present an ab initio molecular dynamics (MD) method for simple liquid metals based on the quantal hypernetted-chain (QHNC) theory derived from exact expressions for radial distribution functions (RDF's) of the electron-ion model for liquid metals. In our method based on the QHNC equations, the classical MD is performed repeatedly to determine a self-consistent effective interionic potential, which depends on the ion-ion RDF of the system. This resultant effective ionic potential is obtained to be consistent with the density distribution of a pseudoatom and the electron-ion RDF, as well as the ion-ion RDF and the ion-ion bridge function, which are determined exactly as a result of the repeated MD simulation. We have applied this QHNC-MD method for Li, Na, K, Rb, and Cs near the melting temperature using upto 16,000 particles for the MD simulation. It is found that the convergence of the effective interionic potential is fast enough for practical applications; typically two MD runs are enough for convergence of the effective ionic potential within accuracy of 3 to 4 digits. Furthermore the resultant static structure factor is in excellent agreement with experimental data of X-ray and/or neutron scatering.     

Modelling the interactions of protein side-chains

The study of small model molecules containing the relevant functional groups can help us to understand the interactions between side-chains in proteins.Ab initio quantum chemical techniques allow the interactions between the model molecules to be studied with much greater accuracy than is possible for an entire protein, where the use of simple empirical potentials is the norm. In particular, the use ofab initio methods on model molecules permits us to incorporate the atom-atom anisotropic directionality of these interactions. We survey various methods of obtaining the components of theab initio interaction energy. These are then applied to three systems of biological interest. The first of these is the arginine/aspartate pair found in salt bridges, which involves hydrogen bonding between two charged species. Secondly, we look at the arginine/phosphotyrosine interaction found in complexes between SH2 domains and peptide ligands: here we find that the arginine/phosphate part of the interaction is energetically far more important than the arginine/aromatic part. Finally, we describe a detailed study of amino/aromatic interactions in proteins: unconventional hydrogen bonds are found to be remarkably uncommon relative to stacked geometries, and the reasons for this are examined.     

Molecular Dynamics on an Excel Spreadsheet

Abstract

We discuss some of the problems that have frustrated the development of reliable model intermolecular potentials for polyatomic molecules. In particular, the usual assumption of an isotropic atom-atom model potential is analysed, and evidence for its inadequacies is presented. A new approach to designing model potentials, an anisotropic site—site model, is introduced by describing several applications to both small and organic molecules, including molecular dynamics and Monte Carlo simulations. The anisotropy required in an atom—atom potential can be directly linked to the non-spherical features in the valence electron distribution, such as lone pairs and π electrons. An accurate electrostatic model for these effects can be constructed from a distributed multipole analysis of the ab initio wavefunction. The empirically required forms of anisotropy in the repulsion potential can also be qualitatively linked to the molecular electron density difference map. Thus, consideration of the molecular bonding can be a useful indication of how to construct adequate model intermolecular pair potentials.     

A replica exchange Monte Carlo algorithm for protein folding in the HP model

Background  

The ab initio protein folding problem consists of predicting protein tertiary structure from a given amino acid sequence by minimizing an energy function; it is one of the most important and challenging problems in biochemistry, molecular biology and biophysics. The ab initio protein folding problem is computationally challenging and has been shown to be -hard even when conformations are restricted to a lattice. In this work, we implement and evaluate the replica exchange Monte Carlo (REMC) method, which has already been applied very successfully to more complex protein models and other optimization problems with complex energy landscapes, in combination with the highly effective pull move neighbourhood in two widely studied Hydrophobic Polar (HP) lattice models.     

Coordination and Thermodynamics of Stable Zn(II) Complexes in the Gas Phase

Abstract

Ab initio molecular orbital methods in combination with DFT calculations were used to study the structural and thermodynamic properties of 17 complexes containing zinc cation and four first-shell ligands as models of active site of metalloenzymes (e.g. angiotensin converting enzyme, thermolysin). The geometry of the complexes was relaxed by complete optimization by ab initio molecular orbital methods at Hertree-Fock level with 3–21G basis set. Following single point calculation with tight SCF criteria at the B3LYP level with 6–311+G(2d,p) basis set was used to calculate accurate interaction enthalpies. The structure and thermodynamics of optimized complexes are discussed from the point of view of their biological importance.     

A New Potential Model for Carbon Dioxide from AB Initio Calculations

Abstract

Ab initio quantum chemical calculations have been carried out for carbon dioxide dimer and the results have been used to establish potential functions usable in molecular simulations. Since the intermolecular interaction in carbon dioxide is fairly weak, careful treatment is required: this study uses 6–31G* basis set and takes electron correlations by the 2nd order Møller-Plesset theory into account. The potential energy surface is elucidated using the four representative relative configurations of the dimer. A new potential function model has been proposed on the basis of these ab initio data. In the super-critical region, this model is used to calculate the PVT relation of carbon dioxide fluid by the Monte Carlo simulations and confirmed to reproduce reasonably well the experimental isotherms.     

QMEANclust: estimation of protein model quality by combining a composite scoring function with structural density information

Background  

The selection of the most accurate protein model from a set of alternatives is a crucial step in protein structure prediction both in template-based and ab initio approaches. Scoring functions have been developed which can either return a quality estimate for a single model or derive a score from the information contained in the ensemble of models for a given sequence. Local structural features occurring more frequently in the ensemble have a greater probability of being correct. Within the context of the CASP experiment, these so called consensus methods have been shown to perform considerably better in selecting good candidate models, but tend to fail if the best models are far from the dominant structural cluster. In this paper we show that model selection can be improved if both approaches are combined by pre-filtering the models used during the calculation of the structural consensus.