An accurate analytical representation for the electron screening function

The screening function Φ [ = V_ee(R) - V_ee(∞)], a key quantity in the theory of isoelectronic molecules, has been given an accurate analytical representation for a large number of states of the species Na₂, Na₂⁺ Li₂ and Li₂⁺. The election-electron repulsion V_ee at various internuclear distances has been obtained from high-quality MC SCF/SCF wavefunctions.     

An accurate analytic potential function for ground-state N2 from a direct-potential-fit analysis of spectroscopic data

Two types of combined-isotopologue analysis have been performed on an extensive spectroscopic data set for ground-state N2 involving levels up to v=19, which is bound by half the well depth. Both a conventional Dunham-type analysis and a direct-potential-fit (DPF) analysis represent the data within (on average) the estimated experimental uncertainties. However, the Dunham-type parameters do not yield realistic predictions outside the range of the data used in the analysis, while the potential function obtained from the DPF treatment yields quantum mechanical accuracy over the data region and realistic predictions of the energies and properties of unobserved higher vibrational levels. Our DPF analysis also introduces a compact new analytic potential function form which incorporates the two leading inverse-power terms in the long-range potential.     

Calculating thermodynamic properties from perturbation theory: I. An analytic representation of square-well potential hard-sphere perturbation theory

The Barker–Henderson macroscopic compressibility approximation of the second-order perturbation term is improved by assuming that the numbers of molecules in every two neighbour shells are correlated, based upon the original assumptions. The results are better than those for the original macroscopic compressibility and local compressibility approximation, especially at high densities. A simple analytic representation of square-well potential hard-sphere perturbation theory is derived based upon this improvement. The method is tested by calculating thermodynamic properties with the four-term truncated form, and the results are in good agreement with those of Monte Carlo and Molecular Dynamics simulation.     

An accurate Ne—Ar interatomic potential

A combined analysis of experimental data on the Ne—Ar system, some from our laboratory and some from the literature, has been performed yielding an accurate interatomic potential. For this multi-property analysis a modified version of the Dunham expansion has been used as a potential model.     

An accurate and efficient empirical approach for calculating the dielectric self-energy and ion-ion pair potential in continuum models of biological ion channels

This paper presents empirical formulas for calculating the dielectric self-energy and ion-ion pair interactions in cylindrical ion channels. The proposed approach can be extended to more complex channel structures, for example, (i) a "straight" channel with variable radius and (ii) a "curved" channel with constant radius. For calibration purposes, we compare results obtained based on the approximate effective potentials developed herein to exact electrostatic calculations obtained via the algorithm of Graf et al.: the agreement is satisfactory. A dynamic lattice Monte Carlo (DLMC) technique is used to further assess the accuracy and efficiency of the proposed empirical potentials. The concentration profiles and current-voltage curves produced with our simple empirical energy formulas are in excellent agreement with numerical results obtained using the algorithm of Graf et al., which calculates all relevant electrostatic forces exactly. The use of effective ion-ion potentials greatly reduces the computer memory required to perform DLMC ion permeation simulations in dielectrically inhomogeneous environments, thus enabling treatment of larger systems than can be handled by numerically exact techniques.     

An accurate three-dimensional potential energy surface for the He-Na_2 complex

An accurate three-dimensional potential energy surface(PES) for the He-Na2 van der Waals comple was calculated at the coupled cluster singles-and-doubles with noniterative inclusion of connecte triple(CCSD(T)) level of theory.A mixed basis set,aug-cc-pVQZ for the He atom and cc-pCVQZ for th sodium atom,and an additional(3s3p2d1f) set of midbond functions were used.The computed inte action energies in 819 configurations were fitted to a 96-parameter analytic potential model by leas squares fitting.The PES has two shallow wells corresponding to the T-shaped structure and the linea configuration,which are located at 12.5a0 and 14 a0 with depths of 1.769 and 1.684 cm-1,respectivel The whole potential energy surface exhibits weak anisotropy.Based on the fitted PES,state-to-stat differential cross sections were calculated.     

An accurate and simple quantum model for liquid water

The path-integral molecular dynamics and centroid molecular dynamics methods have been applied to investigate the behavior of liquid water at ambient conditions starting from a recently developed simple point charge/flexible (SPC/Fw) model. Several quantum structural, thermodynamic, and dynamical properties have been computed and compared to the corresponding classical values, as well as to the available experimental data. The path-integral molecular dynamics simulations show that the inclusion of quantum effects results in a less structured liquid with a reduced amount of hydrogen bonding in comparison to its classical analog. The nuclear quantization also leads to a smaller dielectric constant and a larger diffusion coefficient relative to the corresponding classical values. Collective and single molecule time correlation functions show a faster decay than their classical counterparts. Good agreement with the experimental measurements in the low-frequency region is obtained for the quantum infrared spectrum, which also shows a higher intensity and a redshift relative to its classical analog. A modification of the original parametrization of the SPC/Fw model is suggested and tested in order to construct an accurate quantum model, called q-SPC/Fw, for liquid water. The quantum results for several thermodynamic and dynamical properties computed with the new model are shown to be in a significantly better agreement with the experimental data. Finally, a force-matching approach was applied to the q-SPC/Fw model to derive an effective quantum force field for liquid water in which the effects due to the nuclear quantization are explicitly distinguished from those due to the underlying molecular interactions. Thermodynamic and dynamical properties computed using standard classical simulations with this effective quantum potential are found in excellent agreement with those obtained from significantly more computationally demanding full centroid molecular dynamics simulations. The present results suggest that the inclusion of nuclear quantum effects into an empirical model for water enhances the ability of such model to faithfully represent experimental data, presumably through an increased ability of the model itself to capture realistic physical effects.     

Effects of the cutoff center on the mean potential and pair distribution functions in liquid water

Molecular dynamics simulations of extended simple point charge (SPC/E) water have been performed to study the effects of the truncation of long-range interactions on some calculated bulk properties of the liquid. The mean potential calculated in liquid water is sensitive to the choice of the cutoff center in the water molecule. The pair distribution function is also dependent on this choice, although not as strongly as the mean potential. An analysis is carried out to understand the origin of these effects. A common cutoff center is at the oxygen atom in the water molecule, but our study shows that this choice does not yield a mean potential value consistent with a more accurate estimate when no cutoff is applied. © 1995 John Wiley & Sons, Inc.     

An analytic potential energy function for the amide–amide and amide–water intermolecular hydrogen bonds in peptides

An analytic potential energy function is proposed and applied to evaluate the amide–amide and amide–water hydrogen‐bonding interaction energies in peptides. The parameters in the analytic function are derived from fitting to the potential energy curves of 10 hydrogen‐bonded training dimers. The analytic potential energy function is then employed to calculate the N? H…O?C, C? H…O?C, N? H…OH₂, and C?O…HOH hydrogen‐bonding interaction energies in amide–amide and amide–water dimers containing N‐methylacetamide, acetamide, glycine dipeptide, alanine dipeptide, N‐methylformamide, N‐methylpropanamide, N‐ethylacetamide and/or water molecules. The potential energy curves of these systems are therefore obtained, including the equilibrium hydrogen bond distances R(O…H) and the hydrogen‐bonding energies. The function is also applied to calculate the binding energies in models of β‐sheets. The calculation results show that the potential energy curves obtained from the analytic function are in good agreement with those obtained from MP2/6‐31+G** calculations by including the BSSE correction, which demonstrate that the analytic function proposed in this work can be used to predict the hydrogen‐bonding interaction energies in peptides quickly and accurately. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

An analytic representation of the radial dependence of adiabatic and non-adiabatic corrections from molecular spectra of diatomic molecules

A method of determining the radial dependence of the adiabatic and non-adiabatic corrections contributing to the spectroscopie parameters Δ^a,b_kl of diatomic molecules according to an analytic representation is proposed. The method is applied to HCl and CO, and results for LiH are compared with published data.     

Calculating thermodynamic properties from perturbation theory: II. An analytic representation for the square-well chain fluid

An analytic representation of thermodynamic properties of the freely jointed square-well chain fluid is developed based on the thermodynamic perturbation theory of Barker–Henderson, Zhang and Weitheim. By using a real function expression for the radial distribution function and incorporating structural information for square-well monomer of TPT1 model, an analytic expression for the Helmholtz energy of square-well chain fluid is expanded from Zhang’s analytic expressions for thermodynamic properties of square-well monomer. The expression leads to good predictions of the compressibility factor, residual internal energy and constant-volume heat capacity for 4-mer, 8-mer and 16-mer square-well fluids when compared with the Monte Carlo (MC) simulation results. The incorporating structural information for square-well dimer of TPT-D model is also calculated. To obtain the constant-volume heat capacity needed, NVT MC simulations were performed.     

Anab initio pair potential for the interaction between a water molecule and a formate ion

The potential surface for the interaction between a rigid formate ion and a rigid water molecule has been investigated byab initio methods. An analytical potential expression was derived to fit the 591 calculated SCF energies. The global minimum on the surface is –16.3 kcal/mol and corresponds to a bifurcated bonding situation.     

Hydrogen bonding contribution to the water pair interaction potential: Effects on the model liquid structure

Empirical pair potentials of water that take into account the contribution of the OH nonelectrostatic interaction in the hydrogen bond are considered. The effects of this contribution on the radial distribution functions derived by computer simulation are analyzed. Model potentials have been obtained for which the height and position of the first and second peaks of the oxygen-oxygen radial distribution function are comparable with experimental data.Original Russian Text Copyright © 2004 by A. V. Borovkov, M. L. Antipova, V. E. Petrenko, and Yu. M. KesslerTranslated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 4, pp. 678–682, July–August, 2004.Deceased.This revised version was published online in April 2005 with a corrected cover date.     

Energy-switching potential energy surface for the water molecule revisited: A highly accurate singled-sheeted form

A global ab initio potential energy surface is proposed for the water molecule by energy-switching/merging a highly accurate isotope-dependent local potential function reported by Polyansky et al. [Science 299, 539 (2003)] with a global form of the many-body expansion type suitably adapted to account explicitly for the dynamical correlation and parametrized from extensive accurate multireference configuration interaction energies extrapolated to the complete basis set limit. The new function mimics also the complicated Sigma/Pi crossing that arises at linear geometries of the water molecule.     

Modified Morse potential for unification of the pair interactions

We designed a novel model potential that unifies the pair interactions including the well known Morse and Lennard-Jones potentials. Using two parameters, the interactions at the minimum, short range, and long range of the new model potential can be controlled separately, so the potential is very flexible to fit various systems. It is found that for potentials with similar range with the Lennard-Jones potential at the minimum, due to the difference at the short and long ranges, the favorite structures can be very different, and some previously unknown magic numbers are located.     

Very accurate potential energy curve of the LiH molecule

We present very accurate calculations of the ground-state potential energy curve (PEC) of the LiH molecule performed with all-electron explicitly correlated Gaussian functions with shifted centers. The PEC is generated with the variational method involving simultaneous optimization of all Gaussians with an approach employing the analytical first derivatives of the energy with respect to the Gaussian nonlinear parameters (i.e., the exponents and the coordinates of the shifts). The LiH internuclear distance is varied between 1.8 and 40 bohrs. The absolute accuracy of the generated PEC is estimated as not exceeding 0.3 cm(-1). The adiabatic corrections for the four LiH isotopologues, i.e., (7)LiH, (6)LiH, (7)LiD, and (6)LiD, are also calculated and added to the LiH PEC. The aforementioned PECs are then used to calculate the vibrational energies for these systems. The maximum difference between the computed and the experimental vibrational transitions is smaller than 0.9 cm(-1). The contribution of the adiabatic correction to the dissociation energy of (7)LiH molecule is 10.7 cm(-1). The magnitude of this correction shows its importance in calculating the LiH spectroscopic constants. As the estimated contribution of the nonadiabatic and relativistic effects to the ground state dissociation energy is around 0.3 cm(-1), their inclusion in the LiH PEC calculation seems to be the next most important contribution to evaluate in order to improve the accuracy achieved in this work.     

A numerical basis for the accurate representation of the continuum spectrum of atomic Hamiltonians

We present a method for the accurate calculation of the complete spectrum of the Schrödinger equation in terms of B-splines polynomial basis. The method is capable to represent numerically the bound and continuum spectrum of complex atomic systems. The theoretical method is discussed, and an application to hydrogenic Hamiltonian is given.AMS subject classification: 65705, 34L40     

An empirical boundary potential for water droplet simulations

An empirical modified boundary potential has been derived to correct the structural perturbations arising from the presence of the vacuum boundary in the simulation of spherical TIP4P water systems. The potential is parameterized for a 12.0-Å sphere of TIP4P water and gives improved number density and orientational sampling behavior. It is also transferable to both larger and smaller simulation systems with only a moderate degradation in performance. Free-energy calculations have been conducted for the perturbation of a TIP4P water molecule to methane under aqueous conditions, and the modified boundary potential gives results consistent with those from simulations using periodic boundary conditions. However, simple half-harmonic boundary potentials give unsatisfactory number density, orientational sampling, and free-energy results. Moreover, use of the modified boundary potential results in a negligible increase in simulation time. It is envisaged that the modified boundary potential will find use in free-energy perturbation calculations on proteins with a solvent sphere centered on the active site. © 1995 by John Wiley & Sons, Inc.     

An accurate spectrophotometric method for determination of small amounts of water in acidic methanol

The method is based on u.v. measurement of the keto—ketal equilibrium of substituted acetophenones; 4-methoxyacetophenone proved most satisfactory, the standard deviation for 67 ppm of water in hydrobromic acid-containing methanol being 3 ppm.