Showing papers in "Journal of Computational Chemistry in 1991"

A rapid finite difference algorithm, utilizing successive over-relaxation to solve the Poisson-Boltzmann equation

Abstract: An efficient algorithm is presented for the numerical solution of the Poisson–Boltzmann equation by the finite difference method of successive over-relaxation. Improvements include the rapid estimation of the optimum relaxation parameter, reduction in number of operations per iteration, and vector-oriented array mapping. The algorithm has been incorporated into the electrostatic program DelPhi, reducing the required computing time by between one and two orders of magnitude. As a result the estimation of electrostatic effects such as solvent screening, ion distributions, and solvation energies of small solutes and biological macromolecules in solution, can be performed rapidly, and with minimal computing facilities.

Optimization of parameters for semiempirical methods. III. Extension of PM3 to Be, Mg, Zn, Ga, Ge, As, Se, Cd, In, Sn, Sb, Te, Hg, Tl, Pb, and Bi

Abstract: Using a recently developed procedure for optimizing parameters for semiempirical methods,1 PM3 has been extended to a total of 28 elements. Average ΔHf errors for the newly parameterized elements are Be: 8.6, Mg: 8.4, Zn: 5.8, Ga: 14.9, Ge: 11.4, As: 8.5, Se: 11.1, Cd: 2.6, In: 11.3, Sn: 9.0, Sb: 13.7, Te: 11.3, Hg: 6.8, Tl: 6.5, Pb: 7.4, and Bi: 10.9 kcal/mol. For some elements the paucity of data has resulted in a method, which, while highly accurate, is likely to be only poorly predictive.

Frequency dependent nonlinear optical properties of molecules: formulation and implementation in the HONDO program

Abstract: This article summarizes the detailed equations for the time-dependent Hartree-Fock treatment of nonlinear properties for perturbations made up of a static electric field and an oscillating field. Explicit expressions for all nonlinear processes up to third order are obtained in terms of the density matrices at the same order. For processes at second and third order in perturbation, expressions in terms of lower order quantities are also obtained by applying the (2n+1) theorem of perturbation theory. The corresponding computer implementation in the HONDO program is described

Vectorization of the general Monte Carlo classical trajectory program VENUS

Abstract: The general chemical dynamics computer program VENUS is used to perform classical trajectory simulations for large polyatomic systems, with many atoms and complicated potential energy functions. To simulate an ensemble of many trajectories requires a large amount of CPU time. Since each trajectory is independent, it is possible to parallel process a large set of trajectories instead of processing the trajectories by the conventional sequential approach. This enhances the vectorizability of the VENUS program, since the integration of Hamilton's equations of motion and the gradient evaluation, which comprise 97.8% of the CPU, can each be parallel processed. In this article, the vectorization and ensuing optimization of VENUS on the CRAY‐YMP and IBM‐3090 are presented in terms of both global strategies and technical details. A switching algorithm is designed to enhance the vector performance and to minimize the memory storage. A performance of 140 MFLOPS and a vector/scalar execution rate ratio of 10.6 are observed when this new version of VENUS is used to study the association of CH3 with the H(Ar)12 cluster on the CRAY‐YMP.

A simple approximation for the vibrational partition function of a hindered internal rotation

Abstract: A simple formula is presented for calculating the approximate partition function of a hindered internal rotational mode of a polyatomic molecule. The formula gives useful accuracy over the whole range from harmonic oscillator to hindered rotator to free rotator.

Dispersion and repulsion contributions to the solvation energy: Refinements to a simple computational model in the continuum approximation

Abstract: A computational method for the evaluation of dispersion and repulsion contributions to the solvation energy is here presented in a formulation which makes use of a continuous distribution of the solvent, without introducing additional assumptions (e.g., local isotropy in the solvent distribution). The analysis is addressed to compare the relative importance of the various components of the dispersion energy (n = 6, 8, 10) and of the repulsion term, to compare several molecular indicators (molecular surface and volume, number of electrons) which may be put in relation to the dispersion-repulsion energy, and to define simplified computational strategies. The numerical examples refer to saturated hydrocarbons in water, treated with the homogeneous approximation of the distribution function which for this type of solution appears to be acceptable.

An unbounded systematic search of conformational space

Abstract: A new method for searching internal coordinate conformational space systematically via a continuous-process procedure is described. Unlike previous systematic search methods, the new scheme generates torsionally remote conformers early in the search. It is also unbounded in that the extent of the search need not be specified at the outset. The search begins at low resolution (120° in torsion angle space) and then goes to higher and higher resolution as all points in space at a given resolution have been searched. The search may run without end or be terminated when new conformers cease to be found or when all space at some maximum allowable resolution has been explored. Conformational searches on several medium- and large-ring molecules using the new method are described and the results are compared with those from certain previously described search methods. It is found that the new method is significantly more efficient than previous procedures at finding all low energy conformers of organic molecules.

GEPOL: An improved description of molecular surfaces II. Computing the molecular area and volume

Abstract: The algorithm used by the program GEPOL for a finer description of molecular surface (for a fast calculation of molecular area and volume and for an efficient selection of sampling points) is presented in detail. Different types of surfaces such as van der Waals and Richard's molecular surfaces can be computed. As we described in the first article (J.L. Pascual-Ahuir and E. Silla, J. Comp. Chem., 11, 1047(1990)), GEPOL begins by building a set of spherical surfaces which fill the space which is not solvent accessible. In this second article, a triangular tessellation approach to select the parts of these spherical surfaces which form the molecular surface is described. By using a data coded generic pentakisdodecahedron, each spherical surface is divided in triangular tesserae. A simple method is used to eliminate all triangles found at the intersection volume of the spheres. The center coordinates and the surface of the remaining triangles are used in order to calculate the molecular area and volume and as starting point of the graphic representation of scalar and vector properties. We study the behavior of the method, presenting several examples of application. Special attention is given to the accuracy, spatial invariance and computer efficiency measured by CPU time. Some models of aligned spheres whose area and volume can be found exactly allow us to do a comparative study with a well-known method, analyzing their behavior in line with their respective graining parameters. A fragment of protein is used as an example of the application of the method for characterizing biomolecular surfaces. Aqueous solubility of organic compounds is studied as an example of the experimental property that depends on the molecular area obtaining a good correlation between the logarithm of the solubility and the area calculated using GEPOL.

The MM3 force field for amides, polypeptides and proteins

Abstract: The potential functions for simple amides, several peptides and a small protein have been worked out for the MM3 force field. Structures and energies were fit as previously with MM2, but additionally, we fit the vibrational spectra of the simple amides (average rms error over four compounds, 34 cm−1), and examined more carefully electrostatic interactions, including charge-charge and charge-dipole interactions. The parameters were obtained and tested by examining four simple amides, five electrostatic model complexes, two dipeptides, six crystalline cyclic peptides, and the protein Crambin. The average root-mean-square deviation from the X-ray structures for the six cyclic peptide crystals was only 0.10 A for the nonhydrogen atomic positions, and 0.011 A, 1.0°, and 4.9° for bond lengths, bond angles, and torsional angles, respectively. The parameter set was then further tested by minimizing the high resolution crystal structure of the hydrophobic protein Crambin. The resultant root-mean-square deviations for the non-hydrogen atomic data, in the presence of the crystal lattice, are 0.22 A, 0.023 A, 2.0°, and 6.4° for coordinates, bond lengths, bond angles, and torsional angles, respectively.

Algorithms for calculating excluded volume and its derivatives as function of molecular conformation and their use in energy minimization

Abstract: A numerical method for calculating the volume of a macromolecule and its first and second derivatives as a function of atomic coordinates is presented. For N atoms, the method requires about 0.3 N In@) seconds of CPI: time on a VAX-8800 to evaluate the volume and derivatives. As a test case, the method was used to evaluate a pressure-volume energy term in energy minimizations of the protein lysozyme at 1000 atm (1 atm = 1.013 x 10' Pa). R.m.s. gradients of 10 -' kcal/mol/A were obtained at convergence. The calculated structures exhibited pressure-induced changes which were qualitatively similar to the changes observed in the 1000 atm structure determined by X-ray crystallography.

Free energy difference calculations by thermodynamic integration: difficulties in obtaining a precise value

Abstract: Free energy difference calculations have been performed by the “slow growth” method of thermodynamic integration of the AMBER 3.0 molecular dynamics program for the mutation of a conformationally restricted threonine dipeptide, N-acetyl threonyl-N-methylamide, to the corresponding alanyl dipeptide. By varying the total simulation length, it has been determined that precise free energy values are obtained only for simulations of greater than 100 ps total simulation time length. By varying the starting configurations for simulations of the same length, it has been determined that averaging the free energies obtained from shorter simulations may not give precise answers. Possible reasons for this behavior are discussed.

A comparative study of the simulated-annealing and Monte Carlo-with-minimization approaches to the minimum-energy structures of polypeptides: (Met)-enkephalin

Abstract: A comparison of two methods for surmounting the multiple-minima problem, Simulated Annealing (SA) and Monte Carlo with Minimization (MCM), is presented with applications to [Met]-enkephalin in the absence and in the presence of water. SA explores a continuous space of internal variables, while MCM explores a discrete space consisting of the local energy minima on that space. Starting from random conformations chosen from the whole conformational space in both cases, it is found that, while SA converges to low-energy structures significantly faster than MCM, the former does not converge to a unique minimum whereas the latter does. Furthermore, the behavior of the RMS deviations with respect to the apparent global minimum (for enkephalin in the absence of water) shows no correlation with the observed overall energy decrease in the case of SA, whereas such a correlation is quite evident with MCM; this implies that, even though the potential energy decreases in the annealing process, the Monte Carlo SA trajectory does not proceed towards the global minimum. Possible reasons for these differences between the two methods are discussed. It is concluded that, while SA presents attractive prospects for possibly improving or refining given structures, it must be considered inferior to MCM, at least in problems where little or no structural information is available for the molecule of interest.

Molecular silverware. I.: general solutions to excluded volume constrained problems

Abstract: Molecular Silverware assists the preparation of Monte Carlo and molecular dynamics simulations at a small fraction of the total simulation time. Primary targets for applications include the study of molecular recognition mechanisms and the selective binding of DNA, RNA, peptides, saccharides and other biopolymers in solution as well as the prediction of phase separation behavior and physical properties of non-crystalline condensed phases such as bulk polymers, polymer blends, organic liquids, membranes, micelles, gels, crosslinked networks, glasses, and amorphous heterogeneous catalysts

Incorporating solvent and Ion screening into molecular dynamics using the finite-difference Poisson-Boltzmann method

Abstract: The finite difference method for solving the Poisson–Boltzmann equation is used to calculate the reaction field acting on a macromolecular solute due to the surrounding water and ions. Comparisons with analytical test cases indicate that the solvation forces can be calculated rapidly and accurately with this method. These forces act to move charged solute atoms towards the solvent where they are better solvated, and to screen interactions between charges. A way of combining such calculations with conventional molecular dynamics force fields is proposed which requires little modification of existing molecular dynamics programs. Simulations on the alanine dipeptide show that solvent forces affect the conformational dynamics by reducing the preference for internal H-bonding forms, increasing the R-alpha helix preference and reducing transition barriers. These solvent effects are similar to previous explicit solvent simulations, but require little more computation than vacuum simulations. The method should scale up with little increase in computational cost to larger molecules such as proteins and nucleic acids.

Dielectric boundary smoothing in finite difference solutions of the poisson equation: An approach to improve accuracy and convergence

Abstract: Finite difference methods are becoming very popular for calculating electrostatic fields around molecules. Due to the large amount of computer memory required, grid spacings cannot be made extremely small in relation to the size of the van der Waals radii of the atoms. As a result, the calculations make a rather crude approximation to the molecular surface by defining grid line midpoints discontinuously as either interior or exterior. We present a method which “smoothes” the boundary, but more accurately models the potential from the analytic solution of the discontinuous dielectric problem and improves convergence in electrostatic energy calculations. In addition, a small improvement in convergence rate is observed.

On computation of optimal parameters for multivariate analysis of structure-property relationship

Abstract: We outline a search for optimal parameters involving heteroatoms for use in multivariate regression analysis in structure-property and structure-activity studies. The problem consists of determining optimal numerical values for the diagonal elements of the adjacency matrix in graphs with atoms of different kind. In particular we consider weighted paths as the basic molecular descriptors and search for optimal parameters for carbon atom and oxygen atom in a correlation of molecular structure with isomeric variations in the boiling points of hexanols. Standard error is taken as the criterion for the selection of the optimal parameters. The weighting algorithm restricts the diagonal entries to values greater than −1. The selection of positive diagonal values leads to reducing the path numbers and the negative values lead to enlarging the role of path numbers relative to the zero diagonal values implied by simple graphs in which heteroatoms are not discriminated. A systematic search for optimal parameters for alcohols gave for carbon atom and oxygen atom diagonal entries: x = 1.50 and y = −0.85 respectively when a single path number is used as a descriptor and x = −0.15 and y = −0.94 when two path numbers are used. The parameters derived for 17 hexanols have been successively applied to 37 heptanols demonstrating thus transferability of the parameters.

Efficient search for all low energy conformations of polypeptides by Monte Carlo methods

Abstract: The Metropolis Monte Carlo method has been added to the program FANTOM for energy refinement of polypeptides and proteins using a Newton–Raphson minimizer in torsion angle space. With this extension, different strategies for global minimization of the semiempirical energy function ECEPP/2 by various temperature schedules and restriction of conformational space were tested for locating local minimum conformations with low energy of the pentapeptide Met-enkephalin. In total, 1881 conformations below −10 kcal/mol were found. These conformations could be represented by 77 nonidentical conformations which were analysed for their pattern of hydrogen bonds, types of tight turn, pairwise root-mean-square-deviation (rmsd), Zimmermann codes and side chain conformations. All low energy conformations below −10.4 kcal/mol show strong similarity to the global minimum conformation in the backbone structure.

Prescreening of two‐electron integral derivatives in SCF gradient and Hessian calculations

Abstract: The definition and implementation of a rigorous two-electron integral bound based on Schwarz' inequality both for gradient and hessian calculations is presented. Tests demonstrate the advantages of this easily implemented and effective bound.

On the use of electrostatic potential derived charges in molecular mechanics force fields. The relative solvation free energy of cis‐ and trans‐N‐methyl‐acetamide

Abstract: We have carried out free energy perturbation calculations on the relative solvation free energy of cis- and trans-N-methyl-acetamide (NMA). Experimentally, the solvation free energy difference has been found to be near zero. Using 6-31G* ab initio electrostatic potential derived charges for both the cis and trans conformations, we calculate a solvation free energy difference of 0.1 ± 0.1 kcal/mol. Using the 6-31G* charges derived for the trans conformation for both the cis and trans models leads to a solvation free energy difference of 0.9 ± 0.1 kcal/mol, compared to the value of 2.2 kcal/mol determined for the OPLS model for trans-NMA.

Geometry optimization in Cartesian coordinates: the end of the Z -matrix?

Abstract: Geometry optimization directly in Cartesian coordinates using the EF and GDIIS algorithms with standard Hessian updating techniques is compared and contrasted with optimization in internal coordinates utilizing the well known Z-matrix formalism. Results on a test set of 20 molecules show that, with an appropriate initial Hessian, optimization in Cartesians is just as efficient as optimization in internals, thus rendering it unnecessary to construct a Z-matrix in situations where Cartesians are readily available, for example from structural databases of graphical model builders

Applications of simulated annealing to the conformational analysis of flexible molecules

Abstract: We describe in this article our solution to the global minimum problem which uses the simulated annealing algorithm of Kirkpatrick. This method is a Metropolis (e-ΔE/kT) Monte Carlo sampling of conformation space with simultaneous constraint of the search by lowering the temperature T so that the search converges on the global minimum. The Anneal-Conformer program has been extensively tested with peptides and organic molecules using either the Amber or MM2 force fields. A history file of the simulated annealing process allows reconstruction of the random walk in conformation space for subsequent examination. Thus plots of distance and dihedral angle changes during the search for the global minimum can be examined to deduce molecular shape and flexibility. A separate program Conf-Gen reads the history file and extracts all low energy conformations visited during the run.

On the determination of the minimum on the crossing seam of two potential energy surfaces

Abstract: An improved gradient-based algorithm is presented for the determination of the minimum energy point on the crossing seam hypersurface between two arbitrary potential energy hypersurfaces. The Hessian matrix is updated employing the gradient information. The method is demonstrated in a study of some representative cases including charge-transfer states of a typical molecular-device molecule (a rigid spiro π – σ – π molecular cation) with, as well as without, an external electric field.

Can the Lennard—Jones 6-12 function replace the 10-12 form in molecular mechanics calculations?

Abstract: A protocol to replace «10-12» hydrogen bonding function with the «6-12» form to reproduce hydrogen bond distances, energies, and geometries in molecular mechanics calculations is described. The 6-12 function was least-squares fit to the normally employed 10-12 form of the function for the hydrogen bond types of the Weiner et al. force field by iterating over the A and B coefficients. A weighting function was used to fit the curves in the most critical areas. The 6-12 hydrogen bond model was compared with the Weiner et al. force field, OPLS/AMBER fore field, and quantum mechanical calculations on two simple systems, the water dimer and the chloride-water interaction

Atom based parametrization for a conformationally dependent hydrophobic index

Abstract: An atomic parametrization for the determination of a hydrophobicity index that depends on the molecular conformation is presented. The hydrophobicity parameter was calculated in four alternative ways based on charge densities and atomic contributions to the total molecular surface area and depending on the approach, the molecular dipole moment. The geometries required for the computations were calculated using quantum mechanical semiempirical methods as well as molecular mechanics. The charges were computed using semiempirical methods as well as the Gasteiger method.

A computer automated structure evaluation (CASE) approach to calculation of partition coefficient

Abstract: A Computer Automated Structure Evaluation (CASE) approach to the calculation of partition coefficient (log P) has been developed. A linear regression equation was obtained linking the log P value of molecules to some of their fragments as identified by a CASE analysis. The relationship was obtained for a database consisting of 935 compounds (r2 = 0.93, s = 0.39, F(39, 895, 0.05) = 316.5). It was found that this approach produced accurate log P estimations even for complex molecules and, in general, gave better results than previously described techniques.

Searching for conformers on nine- to twelve-ring hydrocarbons on the MM2 and MM3 energy surfaces: stochastic search for interconversion pathways

Abstract: The stochastic search method was employed to find as many conformers on the MM2 and MM3 energy surfaces as possible for cyclic saturated hydrocarbons with ring sizes from 9 through 12. The number found was 8 MM2 (8 MM3) for 9 rings, 18 MM2 (16 MM3) for 10 rings, 40 MM2 (29 MM3) for 11 rings, and 111 MM2 (90 MM3) for 12 rings. A measure of similarity between pairs of conformers of a compound, called conformational distance, is described. It was used to correlate similar MM2 and MM3 conformers. It was discovered that some conformers on each energy surface are not close to minima on the other surface in rings larger than 9. On refinement with the other optimizer, they changed considerably—going downhill to other previously found minima on the other energy surface or (in a few cases) going to minima which had not been found by direct searches. Conformational distance was also employed as an indication of which pairs of MM2 (or MM3) conformers are likely to interconvert rapidly. A new stochastic procedure of using small kicks was used to search for the most likely interconversion processes among the conformers. There is fairly good agreement between the most facile pathways located by it and unusually short conformational distances. Several additional 12‐ring conformers (not found with previous methods) were located through application of this small kick procedure.

Calculations of molecular vibrational frequencies using semiempirical methods

Abstract: MINDO/3, MNDO, AM1, and PM3 calculations of molecular vibrational frequencies are reported for 61 molecules. All techniques were applied to both well‐behaved and badly behaved systems. Overall, MINDO/3 and MNDO were found to contain rather large errors whereas AM1 and PM3 were relatively accurate. Since no technique does well for all molecules, the technique used should be chosen based on the molecular vibration of interest. In general, AM1 and PM3 together provide fairly accurate results.

The incorporation of hydration forces determined by continuum electrostatics into molecular mechanics simulations

Abstract: A new technique is presented for incorporating hydration forces into molecular mechanics simulations. The method assumes the classical continuum approximation, where a solvated molecule is represented as a low-dielectric cavity of arbitrary shape embedded in a continuous region of high dielectric constant. Electrostatic effects are computed by first calculating the distribution of polarization charge (induced by the configuration of solute fixed charges) at the molecular surface. The hydration force at a particular atom is then found as the sum of the coulombic interaction with the induced surface charge, plus a purely mechanical contribution that arises from the pressure of the polarized solvent as it is pulled toward the solute. A procedure is developed to use the computed hydration forces in conjunction with the CHARMM molecular mechanics package to carry out energy minimizations in which the effects of solvation are explicitly included. This new technique also allows a detailed analysis of the relative balance of coulombic, hydration, and steric energies as a function of molecular conformation. The method is applied to the test case of a zwitterionic tripeptide (LYS-GLY-GLU), and the computational results suggest that hydration effects can play a significant role in determining a stable conformation for a solvated polar molecule. The future application to larger molecules is discussed.

Charges derived from distributed multipole series

Abstract: A novel method to calculate electrostatic charges is proposed. Partial charges are fitted to reproduce the electrostatic potential of a distributed multipole series without explicitly evaluating electrostatic potentials. The calculation is economical and results in charges reflecting the symmetry properties of charge centers and being independent of molecular orientation.

Quantitative comparison of molecular electrostatic potentials for structure-activity studies

Abstract: An approach for representing, efficiently calculating and comparing discrete three-dimensional molecular electrostatic potentials using a quantitative similarity index (MEP-SI) based on a Carbo-type formalism is presented. A radial-type (MACRA) grid representation is described that provides more efficient storage of MEP information than a cubic grid of similar range, appropriate emphasis, and a convenient means for restricting the comparison of MEP functions to a local molecule region. The MACRA based MEP-SI formalism was used to evaluate the suitability of a variety of approximate methods for efficiently calculating the MEP for use in MEP-SI comparison of dissimilar molecules. The Mulliken charge method was found inadequate, while the method of potential-derived charges (PDCs), with additional charges for lone electron pairs included on sulfur, provided an efficient and sufficiently accurate representation of the MEP for this purpose. Convergence of the MEP-SI with respect to MACRA grid extent and mesh size was demonstrated; the effect of MEP error and different grid point emphasis in the MACRA versus the cubic grid results was investigated, and MEP-SI results were compared for different forms of the SI equation. The methodology proposed in this study provides an efficient and practical means for comparing MEP functions for two molecules and gives discriminating results for a sample series of molecular analogues consistent with expectations.