Efficient solvent boundary potential for hybrid potential simulations

A common challenge in computational biophysics is to obtain statistical properties similar to those of an infinite bulk system from simulations of a system of finite size. In this work we describe a computationally efficient algorithm for performing hybrid quantum chemical/molecular mechanical (QC/MM) calculations with a solvent boundary potential. The system is partitioned into a QC region within which catalytic reactions occur, a spherical region with explicit solvent that envelops the quantum region and is treated with a MM model, and the surrounding bulk solvent that is treated implicitly by the boundary potential. The latter is constructed to reproduce the solvation free energy of a finite number of atoms embedded inside a low-dielectric sphere with variable radius, and takes into account electrostatic and van der Waals interactions between the implicit solvent and the QC and MM atoms in the central region. The method was implemented in the simulation program pDynamo and tested by examining elementary steps in the reaction mechanisms of two enzymes, citrate synthase and lactate dehydrogenase. Good agreement is found for the energies and geometries of the species along the reaction profiles calculated with the method and those obtained by previous experimental and computational studies. Directions in which the utility of the method can be further improved are discussed.     

Chemical potential for harmonically interacting particles in a harmonic potential

The chemical potential μ, as it appears in density functional theory, is examined extensively for harmonically interacting spin-½ fermions in three dimensions. For this system the energy and chemical potential are discontinuous functions of the particle number if the most straightforward equation is used to define the energy for a noninteger particle number.     

Model potential for beryllium clusters

A many-body potential is developed for beryllium based on the electronic information extracted from the total energy surface of clusters with up to 5 atoms. The cluster sequence of growth generated with the potential is in excellent agreement with the quantum mechanical calculations in the literature. The hcp lattice of bulk beryllium is correctly found to be more stable than fcc and bcc lattices.     

Local-density-functional approximation for exchange-correlation potential

Local exchange-correlation potential has been derived starting from the free electron gas model.Ab initio way of calculating the parameter of the X method is presented. Self-consistent and statistical exchange-correlation parameters have been determined. The self-consistent parameters have been used to calculate the electron binding energies of Neon, Argon and Krypton. We suggest using statistical exchange-correlation parameter in molecular calculations. The statistical exchange-correlation parameter has been applied to study the electron binding energies of the molecules H₂O and HF. It is shown that the electron binding energies calculated with the self-consistent and the statistical parameters show agreement with the experimental values.Dedicated to Professor J. Koutecký on the occasion of his 65th birthday     

Equation for the screened potential

The equation for the screened potential in the RPA has been derived by using the method of functional differentiation of Martin and Schwinger. The contribution of the “oyster” diagram has been contained in this equation.     

The intermolecular potential for nitrogen

The site—site Lennard-Jones 12-6 potential is found to fit both the second virial coefficient and the liquid properties (thermodynamic, structure, and dynamical) for nitrogen; the same is true for oxygen. This suggests that the effect of the three-body forces in these liquids is small, in contrast to the situation for atomic liquids.     

Modelling of potential energy curves for diatomics: Reference molecular potential method

A method is suggested for modelling the potential energy curves of diatomics. It involves a search for the mapping which transfers the structural details from an analytically prescribed reference potential. For the ground-state potentials of seven covalent molecules, the accuracy in describing the spectroscopic region is comparable with the best empirical potentials, and the correct asymptotic behaviour at R → 0 and R → ∞ are also obtained.     

Model potential for inversion in ammonia

It is shown that asymptotic solutions of the Schrödinger equation with a one-dimensional potential U(x) = κ(R² - x²)²/8R² can be readily applied for describing in tramolecular inversion.     

Ladder operators for the Morse potential

A realization of the raising and lowering operators for the Morse potential is presented. It is shown that these operators satisfy the commutation relations for the SU(2) group. Closed analytical expressions are obtained for the matrix elements of different operators such as 1/y and d/dy. The harmonic limit of the SU(2) operators is also studied and an approach previously proposed to calculate the Franck–Condon factors is discussed. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Ellipsoidal potential parameterization for bisphenol-A polycarbonate

We present a coarse-grained parameterization for the intra- and intermolecular potential for bisphenol-A polycarbonate (BPA-PC). The parameterization is based on the ellipsoidal-shaped monomer unit model applied to BPA-PC. Because of the symmetries of the model a Lennard-Jones type or even a mere repulsive potential with the usual parameters suffices to model the non-bonded interactions. We determined the potential parameters from ab-initio quantum calculations for the BPA-PC monomer. Results of molecular dynamics simulations using our model compare favourably with experimental data.     

An improved potential surface for formaldehyde

A potential energy surface for the ground X? ¹A₁ state of H₂CO has been derived, which reproduces the position of a recently calculated H₂ + CO transition state. The variational method for the determination of frequencies of potential energy surfaces has been extended to tetra-atomics, thus enabling the surface to be refined.     

Optical potential calculations for molecular collisions

The Feshbach optical formalism is applied to elastic, nonreactive atom-diatom scattering on a single potential energy surface. The optical potential depends on GQ, the resolvent of E-QHQ, where Q projects onto open as well as closed channels. A method for generating GQ is developed which goes beyond the free-space approximation by partitioning the radial part of the intermolecular separation into a set of intervals, on each of which the projected interaction QVQ is represented by a constant diagonal form. The resulting GQ is used in calculations on a model collinear system. The calculations are carried out with various approximations on the full nonlocal optical potential equation for Pψ Emphasis is placed on two of these, one of which is characterized by a local homogeneous equation for Pψ, and the other by a local inhomogeneous equation for Pψ.     

Solvated potential energy surfaces for MePC

A conformational study of methylphosphocholine (MePC) was performed from a conformational map calculated considering the dihedral angles that most affected the energy of the system. This conformational map was obtained from interpolations of energy values found from calculations that took into account the presence of solvent through a dielectric continuum approach. We used a quantum–mechanical method based on the Density Functional Theory (DFT) and the 6-31G(d,p) basis set. Conformational samplings were performed in stability regions and the most stable conformers were identified. Comparisons of samplings in solvated and non-solvated conformational maps were performed, and although very different from each other, they furnish equivalent final conformational sets. Both the sets reproduced satisfactorily the experimental shift observed for the vibrational modes of –[P(O₂)]⁻– and –CH₂– methylene groups of MePC when the system was solvated.     

A potential bacterial carrier for bioremediation

One of the limiting factors to the effectiveness of biostimulation and bioremediation is the loss of inoculated material from the site. This can occur by a number of pathways, but is particularly problematic in open water systems where the inoculated material is simply lost in the water. It is desirable to develop new material, a matrix, within which bacteria and/or biostimulants can be incorporated. We have investigated the basic physical properties of insoluble potato starch to eventually evaluate its use as such a matrix. Insoluble starch fibers were prepared from white potato (Solanum tuberosum) and sweet potato (Ipomoea batatas) and were compared for their melting temperature by DSC and their ability to bind/aggregate bacteria. The DSC curves for white and sweet potato showed that the melting temperature is 127.34 and 133.05°C for white and sweet potato fibers, respectively. The TG curves for white and sweet potato starches exhibited one main mass loss step corresponding to the DTG peak temperature at 323.39 and 346.93°C, respectively. The two types of fibers, however, showed different binding/aggregation capacities for bacteria, with white potato approximately twice as many cells of Burkholderia cepacia (22.6 billion/g) as cells of Pseudomonas putida. The reverse was true for fibers from sweet potato, binding twice as many cells of Pseudomonas putida (23 billion/g) as cells of Burkholderia cepacia.     

Knowledge-based potential for the polypeptide backbone

A knowledge-based potential for the polypeptide backbone as a function of the dihedral angles is developed and tested. The potential includes correlations due to the conformations and compositions of adjacent residues. Its purpose is to serve as a major component of a coarse-grained protein potential by including the most relevant local interactions while averaging out nonbonded ones. A probability density estimation algorithm and a multi-resolution probability combination procedure are developed to produce smooth probability distributions and dihedral angle potentials. The potential is described by a set of two-dimensional dihedral angle surfaces involving the various combinations of amino acid triplets and duplets. Several tests are carried out to evaluate the quality of the potential. Monte Carlo simulations, using only the dihedral angle potential and a coarse-grained excluded volume potential, show that the resulting dihedral angle distributions and correlations are consistent with those extracted from protein structures. Additional simulations of unfolded proteins are carried out to measure the NMR residual dipolar coupling (RDC). Significant correlations are obtained between the simulations and the corresponding experiments consistent with other simulations in the literature. Finally, the dihedral angle entropies are calculated for the 20 amino acids. In particular, the entropy difference between alanine and glycine agrees with the ones computed from molecular dynamics simulations ( approximately 0.4 kcal/mol).     

A simple effective potential for exchange

The optimized effective potential (OEP) for exchange was introduced some time ago by Sharp and Horton and by Talman and Shadwick. The integral equation for the OEP is difficult to solve, however, and a variety of approximations have therefore been proposed. These are explicitly orbital dependent and require the same two-electron integrals as Hartree-Fock theory. We have found a remarkably simple approximate effective potential that closely resembles the Talman-Shadwick potential in atoms. It depends only on total densities and requires no two-electron integrals.     

The torsional potential function for n-butane

The energies of four different conformations for n-butane were calculated by the ab initio method using an STO-3G basis set. Fully relaxed molecular geometries obtained from molecular mechanics (MM2) were used. The two energy minima [anti (C_2h), gauche (C₂)] and the two maxima (C₂, C_2v) had the following relative energies: 0.0, 0.88, 3.56, 5.99 kcal/mole. These are approximate Hartree–Fock numbers. It is estimated that inclusion of electron correlation in the calculation would lower the last number to about 5.1 kcal/mole while leaving the first three values essentially unchanged.     

Equivalence of the Wei potential model and Tietz potential model for diatomic molecules

By employing the dissociation energy and the equilibrium bond length for a diatomic molecule as explicit parameters, we generate improved expressions for the well-known Rosen-Morse, Manning-Rosen, Tietz, and Frost-Musulin potential energy functions. It is found that the well-known Tietz potential function that is conventionally defined in terms of five parameters [T. Tietz, J. Chem. Phys. 38, 3036 (1963)] actually only has four independent parameters. It is shown exactly that the Wei [Phys. Rev. A 42, 2524 (1990)] and the well-known Tietz potential functions are the same solvable empirical function. When the parameter h in the Tietz potential function has the values 0, +1, and -1, the Tietz potential becomes the standard Morse, Rosen-Morse, and Manning-Rosen potentials, respectively.