bluuebunny/crossref_metadata_2025 huggingface dataset:
Comparison of compuational methods for simulating nuclear Overhauser effects in NMR spectroscopy
Authors: Forster Mark J.
Published: January 2005

Various algorithms for solving the Solomon equations describing nuclear Overhauser effects (nOes) in NMR spectroscopy have been compared. The applicability of the eigenvalue/eigenvector and the numerical integration approaches have been investigated. The eigenvalue/eigenvector approach is not a computationally efficient means of simulating nOe experiments in which a saturating radiofrequency field is applied during the time course. For experiments in which nOes develop in the absence of an RF field, this approach should only be used in simulating a full NOESY spectrum. Integration schemes have been found to be more efficient at simulating nOe experiments in which the nOe evolves in the presence of a saturating field, at simulating a partial set of initial perturbation experiments and at simulating a few rows or columns in a NOESY spectrum. Various integration schemes were applied to a two‐spin system for which an analytic solution is available and to a model B‐DNA oligonucleotide hexamer. The previously unused Taylor series algorithm was found to be superior to the Euler, midpoint, and fourth‐order Runge–Kutta methods with regard to integration accuracy/computation time. An adaptive step size control routine for the Taylor series integration scheme was developed. Integration schemes can be speeded up in a simple fashion by introducing a distance cutoff for the dipolar interaction. Using a cutoff of 8 Å the Taylor series algorithm was able to compute the NOESY spectrum more rapidly than the eigenvalue/eigenvector algorithm for large spin systems at short mixing times. At longer mixing times the eigenvalue/eigenvector approach becomes the more efficient scheme.
Conformational dynamics of polypeptides and proteins in the dihedral angle space and in the cartesian coordinate space: Normal mode analysis of deca‐alanine
Authors: Kitao Akio , Gō Nobuhiro
Published: January 2005

Effects of different treatments of the degrees of freedom of bond length stretching and bond angle bending in computational analysis of conformational dynamics of proteins and polypeptides are assessed. More specifically, the normal mode analysis of conformational dynamics of α‐helix of deca‐alanine has been carried out both in the dihedral angle space (DAS) and in the Cartesian coordinate space (CCS). Almost perfect one‐to‐one correspondence has been found between normal modes in the CCS with frequencies less than 128 cm−1 and those in the DAS with frequencies less than 164 cm−1. Patterns of atomic displacements in the corresponding modes are very similar. This indicates that the effects of fixing degrees of freedom of bond length stretching and bond angle bending on the very‐low‐frequency normal modes in the CCS with frequencies less than 128 cm−1 are almost solely to increase the frequencies by about 20%. The conclusion indicates that the different treatment of these degree does not lead to qualitatively different results as long as low‐frequency motions are concerned. Based on the results of calculation, mechanical property of the α‐helix of deca‐alanine is discussed.
New development on energetic approach to the packing in proteins
Authors: Carlacci Louis , Chou Kuo‐Chen
Published: January 2005

The energy minimization in the computer program PACK established for investigating interactions of secondary structures in proteins was based on the finite deference method. It is well known that a minimizer of finite difference method is less efficient than that of analytical gradient method. In this article the equations of the analytical energy gradients for a multiple chain system have been derived and they can be directly incorporated into the PACK program. The revised version, PACK/2, thus obtained is much more efficient. Energy minimizations carried out on the theoretical models of 4‐helix bundle, sheet‐sheet packing, and β‐barrel indicated that the CPU times were reduced 15‐ to 20‐fold if the revised PACK/2 algorithm was used. In general, the more complicated the computed structure was, the more significantly the computation time was reduced. Furthermore, for the cases demonstrated here, the final minimized energies were always lower than those obtained by the original version of PACK, indicating that a better packing structure was achieved by means of the revised program PACK/2.
A rapid finite difference algorithm, utilizing successive over‐relaxation to solve the Poisson–Boltzmann equation
Authors: Nicholls Anthony , Honig Barry
Published: January 2005

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.
Atomic multipoles and perpendicular electrostatic forces in diatomic and planar molecules
Authors: Dinur Uri
Published: January 2005

Current methods for assigning atomic multipoles focus on reproduction of the molecular electrostatic potential. Another aspect of electrostatic interaction, which is usually overlooked, is the forces that an external electric field exerts on the nuclei of a molecule. In a self‐consistent theory, both the electrostatic potential and force should be accounted for. However, in general it is not easy to meet this requirement for the force. For planar molecules, though, a formal solution is available in terms of atomic multipoles that are extracted from the molecular multipolar tensors. These Force‐Related (FR) atomic multipoles are discussed in detail for some typical diatomics and planar polyatomics, and are shown to provide a solid uniform framework for treating both aspects of the electrostatics. In contrast, the commonly used potential‐derived charges (i.e., the atomic charges obtained by fitting the electrostatic potential) can yield large deviations with respect to electrostatic forces on the nuclei, even when the electrostatic potential is very well reproduced.
An examination of intermolecular and intramolecular hydrogen bonding in biomolecules by AM1 and MNDO/M semiempirical molecular orbital studies
Authors: Khalil Maged , Woods Robert J. , Weaver Donald F. , Smith Vedene H.
Published: January 2005

The recent NMDO/M modification and parameterization of the MNDO molecular orbital method has been used to analyze intermolecular hydrogen bonding between amino acids and water, and intramolecular hydrogen bonding in monosaccharides. The results have been compared to AM1 calculations on the same systems. The MNDO/M calculations gave values which were similar to ab initio calculations with respect to the intermolecular interactions, but yielded significantly poorer results for the intramolecular interactions. The AM1 procedure performed better on the intramolecular interactions than the MNDO/M procedure, but frequently provided unfavorable three‐centered hydrogen bonding geometries for the intermolecular interactions.
Can the Lennard–Jones 6‐12 function replace the 10‐12 form in molecular mechanics calculations?
Authors: Ferguson David M. , Kollman Peter A.
Published: January 2005

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. The 6‐12 model produced structures, energies, and geometries that were consistent with the other molecular mechanics calculations and showed reasonable agreement to the quantum mechanical results for the water dimer. The 6‐12 model was also compared with normal calculations using a 10‐12 model on several representative systems. The results indicate that the 6‐12 function, when substituted by the procedure outlined in this work, yields structures and hydrogen bond properties that are similar to the normal 10‐12 model.
A new strategy for the evaluation of force parameters from quantum mechanical computations
Authors: Alemán Carlos , Canela Enric I. , Franco Rafael , Orozco Modesto
Published: January 2005

A new strategy for the determination of force parameters is presented. The equilibrium values appearing in the force field equations representing the “stretching” and “bending” of bonds are directly determined from quantum mechanical calculations without geometrical restrictions. The determination of the force parameters is carried out by means of a rigorous fitting between the quantum mechanic and the molecular mechanical energy variations arising from the perturbation of the geometric variables. The strategy presented here has been incorporated into a computer program named PAPQMD, which was developed in order to provide nonquantum mechanical experts with a powerful tool for the determination of approximate force parameters. The program was developed upon the assumption that force parameters are not universal, but they strongly depend on the molecular environment. This implies that the parametrization procedure should be done in a molecular model close to the molecule or molecules to be studied by means of molecular mechanical or dynamic methods, and consequently, it is no longer supposed that the variation of one geometrical parameter does not affect the rest of the molecular geometry. PAPQMD performs the fitting between molecular mechanics and quantum mechanical energies considering all the perturbations that the modification in one geometric variable causes in all the others, enabling the parametrization even of large molecules. The ability of our method to reproduce experimentally derived force parameters is discussed and compared with the widely used Hopfinger's strategy. The study of the behavior of PAPQMD and Hopfinger's strategies for reproducing the force parameters of two complex molecules demonstrates the superiority of the methodology presented here.
On the additivity of basis set effects in some simple fluorine containing systems
Authors: Ignacio Edgar W. , Schlegel H. Bernhard
Published: January 2005

The reactions F + H2 → HF + H, HF → H + F, F → F+ + e− and F + e− → F− were used as simple test cases to assess the additivity of basis set effects on reaction energetics computed at the MP4 level. The 6‐31G and 6‐311G basis sets were augmented with 1, 2, and 3 sets of polarization functions, higher angular momentum polarization functions, and diffuse functions (27 basis sets from 6‐31Gd, p) to 6‐31 ++ G(3df, 3pd) and likewise for the 6‐311G series). For both series substantial nonadditivity was found between diffuse functions on the heavy atom and multiple polarization functions (e.g., 6‐31 + G(3d, 3p) vs. 6‐31 + G(d, p) and 6‐31G(3d, 3p)). For the 6‐311G series there is an extra nonadditivity between d functions on hydrogen and multiple polarization functions. Provided that these interactions are taken into account, the remaining basis set effects are additive to within ±0.5 kcal/mol for the reactions considered. Large basis set MP4 calculations can also be estimated to within ±0.5 kcal/mol using MP2 calculations, est. EMP4(6‐31 ++ G(3df, 3pd)) ≈ EMP4(6‐31G(d, p)) + EMP2(6‐31 ++ G(3df, 3pd)) – EMP2(6‐31G(d, p)) or EMP4(6‐31 + G(d, p) + EMP2(6‐31 ++ G(3df, 3pd)) – EMP2(6‐31 + G(d, p)) and likewise for the 6‐311G series.
Self‐consistent, nonorthogonal group function approximation. III. Approaches for modeling intermolecular interactions
Authors: Fülscher M. P. , Mehler E. L.
Published: January 2005

A new program has been developed for the implementation of the self‐consistent nonorthogonal group function (NOGF) approximation for the calculation of wavefunctions between interacting systems. The NOGF approach is based on the reformulation of a single‐determinental, closed shell wavefunction into an antisymmetrized product of nonorthogonal group functions, each of which is a single determinant of doubly occupied orbitals. The group product form of the wavefunction combined with the relaxation of the orthogonality constraints and the structure of the orbital equations allows each group's orbitals to be expanded in a local basis set, and makes it possible to modify the orbital expansions or iterative process to simplify the computation. Three models for approximating the full single‐determinental wavefunction are tested: (1) different quality basis sets for orbitals belonging to different groups, (2) variation of the types of intergroup interactions included in the wavefunction, and (3) the use of frozen orbitals which have been predetermined in a subsystem and are subsequently transferred to the system of interest. These approximations are applied to the calculation of protonation energies of formate, ammonia, imidazole, and guanidine with part of the first hydration shell being represented by two water molecules hydrogen bonded to each species. The results from different basis sets are compared. Then interaction potentials between the acid and ammonia are calculated for both neutral and charged forms, again with inclusion of part of the first hydration shell. The results show that these techniques can yield reliable wavefunctions of the same quality as obtained with the standard supermolecule approach. The effect of the basis set superposition error in the NOGF approach is briefly considered, and the reduction in computing effort resulting from the three models is discussed.
MM2 study on the conformation of N‐acetyl‐L‐amino acid N′‐methylamides with aliphatic side chain and their Nα‐methyl derivatives
Authors: Hlaváček Jan , Matějka Václav , C̆ársky Petr
Published: January 2005

φ – ψ maps have been calculated by the MM2(87) potential for the Nα‐acetyl derivatives of Gly, Ala, Val, and Tle methylamides and their Nα‐methyl substituted derivatives to interpret the 1H NMR and CD spectra of these compounds. From the critical examination of the available theoretical and experimental evidence it follows that in the series of Nα unsubstituted Ala, Val, and Tle derivatives the importance of the second lowest energy conformation (C5) is increased and that eventually it becomes the lowest energy conformation instead of C. With the Nα‐methyl substituted Ala and Val derivatives, the lowest energy conformation seems to be C. Performance of MM2(87) was tested for the φ – ψ map of the Ala derivative by comparing it with other theoretical data available in the literature.
On computation of optimal parameters for multivariate analysis of structure‐property relationship
Authors: Randić Milan
Published: January 2005

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.
The CαC internal rotation in α‐alkyl substituted carbonyls and thiocarbonyls: CH(CH3)2C(X)YH (X, Y O or S)
Authors: Teixeira‐Dias J. J. C. , Fausto R. , de Carvalho L. A. E. Batista
Published: January 2005

The CαC internal rotation in 2‐methylpropionic, 2‐methylthiopropionic (thiol and thion forms) and 2‐methyldithiopropionic acids was studied by the ab initio SCF‐MO method using 3‐21G and 3‐21G + d(0.65S) basis sets. Energies and structures of several conformations of these molecules, determined by gradient geometry refinement, are reported and used to assess the effects of oxygen‐by‐sulphur substitution on molecular properties. The nature and relative importance of intramolecular interactions involving both the α‐methyl substituents and the C(X)Y (X, Y O or S) fragment are also discussed.
Prescreening of two‐electron integral derivatives in SCF gradient and Hessian calculations
Authors: Horn Hans , Weiß Horst , Háser Marco , Ehrig Michael , Ahlrichs Reinhart
Published: January 2005

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.
A general procedure for obtaining wave functions obeying the virial theorem
Authors: Lehd Michael , Jensen Frank
Published: January 2005

The virial theorem for molecules is shown to have two different forms, one employing the energy gradient the other involving the Hellmann–Feynman force. While the former VT can be fulfilled by a uniform scaling of the basis set, the latter cannot be satisfied in certain basis sets, and can give unrealistic results in others. The scaling procedure is applied to molecules at nonstationary points on the potential energy surface and it is found that energy components can change substantially, especially at short bondlengths, while the change in total energy is small. The effects on molecular properties are also small.
Theoretical kinetic isotope effects for the hydride transfer from formate to carbon dioxide: A comparison of theory with experiment
Authors: Jones Jeffrey P. , Urbauer Jeffrey L.
Published: January 2005

Heavy atom and deuterium isotope effects for the hydride transfer from formate to carbon dioxide were determined using MNDO, AM1, and PM3 semiempirical methods and the ab initio RHF/3‐21G*, 3‐21 + G, 6‐31G*, and 6‐31 + G* basis sets. Frequencies were also determined for ground state structures using 6‐31G* basis set at the MP2 level of theory. The calculated isotope effects compared favorably with the experimentally determined values of Hermes et al. (Biochemistry, 23, 5479 (1984)). The calculated ground state frequencies were high for most vibrational modes as compared with measured values, however some ab initio methods underestimate the carbon hydrogen stretching frequencies. The heavy atom isotope effects were influenced to a large extent by the excitation factor, the mass factor and the moment of inertia factor of the Bigeleisen equation.
Unimolecular rearrangements of ethylnitrene: An exploratory theoretical study
Authors: Kakkar Rita , Walia Vibha
Published: January 2005

The products of the rearrangement of ethylnitrene are ethylideneimine via a 1,2 hydrogen shift, N‐methyl methyleneimine via a 1,2 methyl shift, and the corresponding aziridine by cyclization. The three reactions have been studied by the semiempirical MNDO method. The charge transfer effects have been investigated. Theoretically calculated vibrational frequencies and kinetic properties have been used in calculating macroscopic thermodynamic and kinetic properties. The entropies of activation, the high pressure rate constants, k∞, and the high pressure Arrhenius parameters, A∞ and E∞, have been computed. The kinetic isotope effects have also been studied.
Analytic Löwdin alpha‐function method for two‐center electron‐repulsion integrals over slater‐type orbitals
Authors: Jones Herbert W.
Published: January 2005

Using the Löwdin alpha‐function method in which displaced orbitals are expanded in spherical harmonics, two‐center, two‐electron repulsion integrals of the Coulomb, hybrid, and exchange type are done analytically using Slater‐type orbitals. Computer algebra and integer arithmetic are used to obtain analytic results and avoid cancellation errors by the generation of rational matrix elements for C, E, and F matrices that are used to express the α‐function. The formula for the exchange integral is kept simple by reversing the order of integration over each part of a split quadrant. Only two basic integrals are used that are first efficiently evaluated by using look‐up tables and then used repeatedly.
The application of symbolic computing to chemical kinetic reaction schemes
Authors: Holmes Mark H. , Bell Jonathan
Published: January 2005

Given a reaction mechanism we show how a symbolic computation approach can be used to develop the kinetic equations by identifying the reaction scheme with an equivalent matrix. Our method is also applicable in cases where the stoichiometric matrix approach fails. The specific algorithm that is written applies to schemes where individual reactions are at most ternary, but the way to generalize the procedure is also discussed. By using symbolic computing it is possible to determine general properties of the system. We demonstrate this by showing how to use the matrix to determine the system's conservation laws, which in turn can be used to reduce the number of equations in the system. As another application it is shown how to determine some of the species which have a zero equilibrium state. To illustrate the procedure, example reaction schemes are investigated.
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
Authors: Cieplak Piotr , Kollman Peter
Published: January 2005

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.
Topological analysis of complex molecular surfaces
Authors: Zachmann Carl‐Dieter , Heiden Wolfgang , Schlenkrich Micheal , Brickmann Jürgen
Published: January 2005

An algorithm for the calculation of local and global curvatures of molecular surfaces is presented. The analysis is based on a surface representation as a set of points in 3‐D space (“dotted surface” representation). The surface data are used to subdivide the surfac into domains with different curvatures. All domains are characterized by a reference point with a corresponding curvature profile specifiying the topological properties in its neighborhood. The curvature profiles provide a method for a systematic comparison of the shapes of different molecules. Such a strategy is important for the treatment of molecular recognition problems. The enzyme‐inhibitor complex trypsin/BPTI was chosen to demonstrate the scopes of the method.
Application of SINDO1 to organo‐transition metal compounds
Authors: Li Jian , Jug Karl
Published: January 2005

The recently extended SINDO1 method is used to study geometries, electronic structures, and chemical bonding of transition metal organometallic compounds. The optimized distances and angles between metal atoms and organic ligands are in fair agreement with experimental data and are comparable to ab initio results. The comparison of orbital energies between the current method and ab initio methods shows that the method can give a correct description of electronic structure and bonding patterns of organometallic compounds. The method is also used to calculate atomic and bond valence, which are defined in terms of appropriate combinations of first‐order density matrix elements for molecules. The valence indices provide a straightforward and easy‐to‐interpret way to analyze the magnitude of metal‐carbon and metal‐metal bonds.
A coarse‐grain parallel implementation of the direct SCF method
Authors: Lüthi Hans P. , Mertz John E. , Feyereisen Martin W. , Almlöf Jan E.
Published: January 2005

A coarse‐grain, parallel approach to direct Hartree–Fock calculations is presented and discussed. The suggested scheme allows for a near asymptotic speedup involving a very low parallelization overhead without compromising the vector performance of vector‐parallel architectures. A shared‐memory MIMD implementation, for which very high speeds of computation have been achieved, is discussed in detail.
Ab initio evidence for the stepwise mechanism of the McLafferty rearrangement of the butanal radical cation
Authors: Liu Ruifeng , Pulay Peter
Published: January 2005

The mechanism of the McLafferty rearrangement of the butanal radical cation to ethylene and vinyl alcohol cation is found, by ab initio calculations, to be stepwise. The results of a previous ab initio study are inconclusive because of symmetry restriction in their geometry optimization.
Geometry optimization in Cartesian coordinates: Constrained optimization
Authors: Baker Jon
Published: January 2005

An efficient algorithm for constrained geometry optimization in Cartesian coordinates is presented. It incorporates mode‐following techniques within both the classical method of Lagrange multipliers and the penalty function method. Both constrained minima and transition states can be located and, unlike the standard Z‐matrix using internal coordinates, the desired constraints do not have to be satisfied in the initial structure. The algorithm is as efficient as a Z‐matrix optimization while presenting several additional advantages.
PEFF: A program for the development of empirical force fields
Authors: Dillen Jan L. M.
Published: January 2005

PEFF is a new computer program designed to assist in the development of empirical force fields used in molecular mechanics calculations. Its main features are: constrained and unconstrained energy minimization available with four different techniques, rigid group refinement, crystal lattice summations, calculation of normal modes, thermodynamic functions and crystallographic temperature factors, vibrational corrections of calculated crystal structures, and a multidimensional driver to scan the energy hypersurface. Used in force field optimization mode, the program employs a least‐squares method to fit the force field parameters to a set of experimental data.
Representation of molecules by atomic charges: A new population analysis
Authors: Tasi Gyula , Kiricsi Imre , Förster Horst
Published: January 2005

For the calculation of atomic charges in molecules, a new fast procedure based on extended Mulliken population analysis is presented. The reliability of the new population analysis is tested within the AM1 approximation and the results are compared in detail with those obtained by different methods reported in the literature.
Molecular docking using shape descriptors
Authors: Shoichet Brian K. , Kuntz Irwin D. , Bodian Dale L.
Published: January 2005

Molecular docking explores the binding modes of two interacting molecules. The technique is increasingly popular for studying protein‐ligand interactions and for drug design. A fundamental problem problem with molecular docking is that orientation space is very large and grows combinatorially with the number of degrees of freedom of the interacting molecules. Here, we describe and evaluate algorithms that improve the efficiency and accuracy of a shape‐based docking method. We use molecular organization and sampling techniques to remove the exponential time dependence on molecular size in docking calculations. The new techniques allow us to study systems that were prohibitively large for the original method. The new algorithms are tested in 10 different protein‐ligand systems, including 7 systems where the ligand is itself a protein. In all cases, the new algorithms successfully reproduce the experimentally determined configurations of the ligand in the protein.
Efficient algorithm for the reconstruction of a protein backbone from the α‐carbon coordinates
Authors: Rey Antonio , Skolnick Jeffrey
Published: January 2005

We present an analytical method for generating a whole protein backbone structure from the coordinates of the α‐carbons. The procedure begins by automatically positioning the β‐carbons for every residue, and then the positions of the carbonyl groups and the amide nitrogens are also computed. The method is based upon the simultaneous minimization of a number of geometrical constraints that appear in real proteins and that can be very easily formulated as a set of trigonometric relations between the coordinates of the atoms involved in the backbone reconstruction. The resulting algorithm has been tested for proteins of very different sizes and topologies, and can advantageously compete with other methods proposed for this goal both in accuracy and in computational requirements. Possible ways of further refinement of the resulting structures are discussed.
Conformational analysis of 4h‐1,3,2‐benzodioxaphosphorin 2‐sulfides with ab initio molecular orbital calculations
Authors: Kurita Yasuyuki , Takayama Chiyozo , Sasaki Mitsuru
Published: January 2005

Among some 2‐substituted 4H‐1,3,2‐benzodioxaphosphorin 2‐sulfides, the 2‐OMe derivative has the sulfur atom mainly in the quasiequatorial position. On the other hand, the conformation in which the sulfur is quasiaxial is favored in the 2‐NHMe and 2‐Et derivatives. We have done ab initio molecular orbital calculations for the model compounds, and such a substituent effect was reproduced. Moreover, the effect was discussed in terms of the intramolecular electrostatic interactions and the degree of charge distribution.
Improvements to the distance geometry algorithm for conformational sampling of cyclic structures
Authors: Peishoff Catherine E. , Dixon J. Scott
Published: January 2005

Modifications to the distance geometry algorithm as embodied in the program DGEOM have been made to improve sampling capabilities. Specifically, torsion angle sampling replaces distance sampling for 1,4 atomic relationships and correlated distance sampling is disabled. The effects of these modifications are illustrated by comparing the different sets of conformations produced for butane. In addition, these changes are shown to increase the conformational sampling of two medium‐sized rings, cycloheptadecane and caprylolactam. The current results for these molecules are compared to those of other conformational searching methods.
Powerful simulated‐annealing algorithm locates global minimum of protein‐folding potentials from multiple starting conformations
Authors: Snow Mark E.
Published: January 2005

Protein‐folding potentials, designed with the explicit goal that the global energy minimum correspond to crystallographically observed conformations of protein molecules, may offer great promise toward calculating native protein structures. Achieving this promise, however, depends on finding an effective means of dealing with the multiple‐minimum problem inherent in such potentials. In this study, a protein‐folding‐potential test system has been developed that exhibits the properties of general protein‐folding potentials yet has a unique well‐defined global energy minimum corresponding to the crystallographically determined conformation of the test molecule. A simulated‐annealing algorithm is developed that locates the global minimum of this potential in four of eight test runs from random starting conformations. Exploration of the energy‐conformation surface of the potential indicates that it contains the numerous local minima typical of protein‐folding potentials and that the global minimum is not easily located by conventional minimization procedures. When the annealing algorithm is applied to a previously developed actual folding potential to analyze the conformation of avian pancreatic polypeptide, a new conformer is located that is lower in energy than any conformer located in previous studies using a variety of minimization techniques.
Alternative expressions for energies and forces due to angle bending and torsional energy
Authors: Swope William C. , Ferguson David M.
Published: January 2005

We have derived alternative expressions for computing the energies and forces associated with angle bending and torsional energy terms commonly used in molecular mechanics and molecular dynamics computer programs. Our expressions address the problems of singularities that are intrinsic in popular angle energy functions and that occur from other chain rule derivations of force expressions. Most chain rule derivations of expressions for Cartesian forces due to angle energies make use of relations such as

where ϕ is a bond or torsion angle, E(ϕ) is energy, and ∂/∂x represents a derivative with respect to some Cartesian coordinate. This expression leads to singularities from the middle term, −1/sin ϕ, when ϕ is 0 or π. This is a problem that prevents the use of torsional energy expressions that have phase angles, ϕ°, other than 0 or π, such as in E(ϕ) = κ[1 + cos(nϕ − phsi;°)]. Our derivations make use of a different, but equivalent, form of the chain rule:

This form still possesses singularities for the bond angle forces since the last factor is undefined when ϕ is 0 or π. However, the alternate form may be used to great advantage for the torsional angle forces where no such problem arises. The new expressions are necessary if one desires the use of torsional energy expressions with general phase angles. Even for energy expressions in common use, i.e., with phase angles of 0 or π, our force expressions are as computationally efficient as the standard ones. The new expressions are applicable to all molecular simulations that employ restrained, or phase‐shifted, torsional angle energy expressions.
An ab initio and molecular mechanical investigation of ureas and amide derivatives
Authors: Kontoyianni Maria , Phillip Bowen J.
Published: January 2005

Ab initio molecular orbital theory with the 6‐31G* basis set has been used to investigate the geometries and preferred conformations for urea, derivatives of urea, and a few complicated amide derivatives. The results from the ab initio calculations provide insight into the gas‐phase rotational barrier about the CN bond and have been used to generate parameters for the MM2(87) molecular mechanics program. When applicable, theoretical structures are compared with corresponding previously reported experimental geometries. Urea is predicted to be nonplanar with pyramidal amino groups.
Effective internal rotation potential energy function of acryloyl fluoride, CH2  CH  CF O
Authors: Bock Charles W. , Abramenkov Alexander V. , De Maré George R. , Panchenko Yurii N.
Published: January 2005

The geometry of acryloyl fluoride was optimized completely at the RHF/6‐31G* level of theory at 10 points on the theoretical potential energy curve for internal rotation. The energies obtained were used to determine a six term cosine expansion of the torsional potential energy function. This function was then refined using the experimental torsional transition frequencies in the s‐trans and s‐cis wells in conjunction with the geometrical parameters optimized at the RHF/6‐31G* level. The effective potential function obtained is compared with previous results. The necessity of accounting for relaxation of the geometry upon internal rotation is stressed. © 1992 by John Wiley & Sons, Inc.
Long time dynamics of a polymer with rigid body monomer units relating to a protein model: Comparison with the rouse model
Authors: Knapp E.W.
Published: January 2005

Simulation data from an off‐lattice polymer model are compared with data from the Rouse model. The polymer model is built of sequentially connected rigid monomer units that represent the amide planes of a protein backbone. The time propagation of the dynamics of the polymer model is performed by a Monte Carlo method. The elementary Monte Carlo steps correspond to local confomational changes in a window of three consecutive monomer units. The time autocorrelation functions of end‐to‐end distances from segments within the linear chain molecule are considered in detail. Both models exhibit a stretched exponential decay pattern. A comparison of the data from the Rouse model and the computer simulation provide an estimate of the time unit of 15 ps for a full scan of the algorithm for local conformational changes along the chain. With a conservative estimate of the parameters governing the Rouse model this time unit is four orders of magnitude longer than the elementary time step of a conventional computer simulation of polymer dynamics based upon the classical equations of motion for all atoms. © 1992 by John Wiley & Sons, Inc.
Conformational analysis of carbonyl and thiocarbonyl ethyl esters: The HC(X) (X, Y = O or S) internal rotation
Authors: Fausto R. , De Carvalho L.A.E. Batista , Teixeira‐Dias J.J.C.
Published: January 2005

The internal rotation in the HC(X)YCH2CH3 (X, Y = O or S) series of molecules was studied by the ab initio SCF‐MO method using 3‐21G and 3‐21G + d(ζ = 0.65S) basis sets. Energies and structures of several conformations of these molecules, determined by gradient geometry refinement, are reported and used to assess the effects of oxygen‐by‐sulphur substitution on molecular properties. The nature and relative importance of intramolecular interactions involving both the CH2CH3 and the HC(X)Y (X, Y = O or S) fragments are also discussed. © 1992 by John Wiley & Sons, Inc.
NDDO fragment self‐consistent field approximation for large electronic systems
Authors: Ferenczy György G. , Rivail Jean‐Louis , Surján Péter R. , Náray‐Szabó Gábor
Published: January 2005

A semi‐empirical NDDO method, generalized from a similar scheme at the CNDO/2 level developed previously, is presented to treat very large molecules. The extended molecular system is divided into a relatively small subsystem where substantial chemical changes take place and an environment remaining more‐or‐less unperturbed during the process. Expanding the wave function on an atomic hybrid basis an SCF procedure is performed for the subsystem in the field of the iteratively determined electronic distribution of the environment. A computer program has been written for the IBM RISC System/6000 530 computer and several test calculations were done for a variety of large classical molecules, like substituted aliphatic hydrocarbons, water oligomers, and a heptapeptide. Protonation energies, proton transfer potential curves, rotational barriers, atomic net charges, and HOMO and LUMO energies, as computed by the exact version of the NDDO method, are fairly well reproduced by our approximation if the subsystem is appropriately defined. © 1992 by John Wiley & Sons, Inc.
Heats of formation of organic molecules by Ab Initio calculations: Carboxylic acids and esters
Authors: Allinger Norman L. , Schmitz Lawrence R. , Motoc Ioan , Bender Charles , Labanowski Jan K.
Published: January 2005

A bond and group equivalent scheme that allows the calculation of heats of formation for carboxylic acids and esters from ab initio 6‐31G* energies has been developed. For a group of 16 compounds, the rms error for the calculated heats of formation was 0.64 kcal/mol. Heats of formation have been predicted for an additional seven compounds for which the experimental values are either unknown or suspect. © 1992 by John Wiley & Sons, Inc.
Molecular mechanics study of conformational trends in simple alcohols and ethers. II. Intramolecular hydrogen bonding
Authors: Vázquez Saulo A. , Ríos Miguel A. , Carballeira LuíS
Published: January 2005

In this article we present an extension of our modified MM2(80) force field MM2MOD in which a potential function for hydrogen bonding in alcohols and ethers is included. The results of applying MM2(85), MM2(87), and MM2MOD on ethylene glycol, 2‐methoxyethanol and 1,3‐propanediol are reported and compared with available experimental data and ab initio results. It is concluded that hydrogen bonding plays an important role in determining the molecular conformations of these systems. © 1992 by John Wiley & Sons, Inc.
Semiempirical study of electronic and bonding properties of cobalt silicide clusters
Authors: Urbina‐Villalba German , Rodriguez Leonardo J. , Castro German R. , Ruette Fernando
Published: January 2005

The electronic structure of cobalt silicide clusters Co7Si7 and Si7Co7 was studied in comparison to that of Co19 and Si17 clusters under the scope of the MINDO/SR method. Clusters Co7Si7 and Si7Co7 represent the environment of a cobalt atom and that of a silicon atom in the cobalt monosilicide bulk, respectively. It is found that the CoSi bond is essentially sp in character with an indirect participation (by electrostatic interaction) of the cobalt d orbitals. Our calculations show a charge transfer from silicon to the d orbitals of cobalt via sp–sp interaction with an internal sp–d hybridization. The theoretical density of states for cobalt silicide clusters are reported and compared with experimental results of surface spectroscopies. © 1992 by John Wiley & Sons, Inc.
Localized electron pair theory for the calculation of ground state energies of large molecules
Authors: Cullen J.M.
Published: January 2005

The quantum mechanical energy is examined in which groups of one, two, three, and four localized electron pairs found within a molecule are separately computed. From these results, the interaction energies of the electron pairs taken one, two, three, and four at a time form the terms of a convergent molecular mechanics like expansion of the molecular ground state energy. This procedure can be used with any size consistent quantum mechanical method. The computational time for large molecules depends chiefly upon the order needed in the energy expansion to obtain sufficient convergence and not on the particular quantum mechanical method used. Preliminary results within the framework of a semiempirical CNDO/2 model Hamiltonian show at the Hartree–Fock and Møller–Plesset perturbation levels that relative energies converge to within a few tenths of a kcal/mol of the exact values at the four body level for molecules that have little delocalization. In strained ring and aromatic systems, convergence is however not nearly as rapid. Results can be improved somewhat by using larger interacting fragments containing two or more electron pairs over three or more atomic centers. © 1992 by John Wiley & Sons, Inc.
Electronegativity and Bader's bond critical point
Authors: Hati Sanchita , Datta Dipankar
Published: January 2005

The electronegativities () of some 36 atoms/groups (including some 6 ionic ones) X are calculated from the atomic charges in the corresponding methyl species CH3X that were obtained by applying Bader's theory of atoms in molecules. The numerical values of the for the various groups studied are reasonable and correlate linearly with the two existing experimental scales for group electronegativity, Inamoto's i scale and the 1JCC (ortho‐ipso) coupling constants in the monosubstituted benzenes, to satisfactory extents. The relations between the values and some “critical properties” of the various CH3X molecules considered are also studied. It is suggested that in a molecule PX, rP/R where rP is the distance of Bader's critical point on the bond PX of length R from the atom P or the binding atom of the group P can be a very good measure of the electronegativity of the atom/group X. © 1992 by John Wiley & Sons, Inc.
Correlated molecular and multicenter multipole moments in ground and excited states from multiple reference double‐excitation configuration interaction calculations
Authors: Roszak Szczepan , Sokalski W. Andrzej , Kaufman Joyce J.
Published: January 2005

Correlated molecular mulitpole moments and compact correlated cumulative atomic multipole moment (CCAMM) representation of molecular charge distribution in ground as well as in excited states have been derived directly from multiple reference double‐excitation configuration interaction (MRD‐CI) wave functions for BH and H2CO molecules using several extended basis sets with multiple polarization functions. This approach extends previously introduced uncorrelated and correlated CAMMs, and allows obtaining inexpensive modeling of electrostatic effects involving molecules in excited electronic states. © 1992 by John Wiley & Sons, Inc.
THE weighted histogram analysis method for free‐energy calculations on biomolecules. I. The method
Authors: Kumar Shankar , Rosenberg John M. , Bouzida Djamal , Swendsen Robert H. , Kollman Peter A.
Published: January 2005

The Weighted Histogram Analysis Method (WHAM), an extension of Ferrenberg and Swendsen's Multiple Histogram Technique, has been applied for the first time on complex biomolecular Hamiltonians. The method is presented here as an extension of the Umbrella Sampling method for free‐energy and Potential of Mean Force calculations. This algorithm possesses the following advantages over methods that are currently employed: (1) It provides a built‐in estimate of sampling errors thereby yielding objective estimates of the optimal location and length of additional simulations needed to achieve a desired level of precision; (2) it yields the “best” value of free energies by taking into account all the simulations so as to minimize the statistical errors; (3) in addition to optimizing the links between simulations, it also allows multiple overlaps of probability distributions for obtaining better estimates of the free‐energy differences. By recasting the Ferrenberg–Swendsen Multiple Histogram equations in a form suitable for molecular mechanics type Hamiltonians, we have demonstrated the feasibility and robustness of this method by applying it to a test problem of the generation of the Potential of Mean Force profile of the pseudorotation phase angle of the sugar ring in deoxyadenosine. © 1992 by John Wiley & Sons, Inc.
Treatment of redundancies among internal coordinates in optimizing molecular mechanics force constants
Authors: Palmö K. , Pietilä L. ‐O. , Krimm S.
Published: January 2005

The use of redundant coordinate bases in the construction of molecular mechanics force fields is discussed. It is shown that the intrinsic indeterminacy in a force field in redundant coordinates in general stems from the squares of the first‐order redundancy relations. The necessity to use constraints in such a force field is pointed out, and a method to check whether or not a set of constraints makes the force field determinate is described. It is also explained how force fields corresponding to different sets of constraints can be transformed into one another. To facilitate the utilization of ab initio or other spectroscopic force fields, a procedure is given by which force constants pertaining to a nonredundant coordinate basis can be optimized in molecular mechanics calculations where redundant coordinates are used. © 1992 by John Wiley & Sons, Inc.