bluuebunny/crossref_metadata_2025 huggingface dataset:
Stiffness‐Adaptive Taylor method for the integration of non‐stiff and stiff kinetic models
Authors: Baeza J. J. Baeza , Ramos G. Ramis , Plá F. Pérez
Published: January 2005

A systematic derivation procedure that greatly facilitates the application of the Taylor method to the integration of kinetic models is developed. In addition, an algorithm that gives the integration step as a function of the required level of accuracy is proposed. Using the Taylor method, application of this algorithm is immediate and largely reduces the integration time. In addition, a new method of integration of kinetic models, whose most important feature is the self‐adaptability to the stiffness of the system along the integration process, is developed. This “stiffness‐adaptive” Taylor method (SAT method) makes use of several algorithms, combining them to meet the particular requirements of the integration of each species along the integration process. In comparison with the Runge–Kutta–Felhberg, Runge–Kutta–Calahan, Taylor, and Gear methods, the SAT method is the best to integrate non‐stiff and stiff kinetic systems, giving the best accuracy and the smallest computing time. © 1992 by John Wiley & Sons, Inc.
Molecular electrostatic potential of substituted aromatic compounds: Factors affecting the differences between Ab Initio and semiempirical results
Authors: Bonati L. , Cosentino U. , Fraschini E. , Moro G. , Pitea D.
Published: January 2005

The molecular electrostatic potential (MEP) distribution of anisole, chlorobenzene, and fluorobenzene obtained from STO‐3G, 3‐21G, and 6‐31G* basis set ab initio and MNDO and AM1 semiempirical wave functions is investigated to explain the differences among the MEP features obtained for polychlorodibenzo‐p‐dioxins. The main topological features as well as the absoltue and relative minima location obtained from ab initio calculations are independent from the choice of the basis set. MNDO calculations are in good agreement with the ab initio ones in the case of anisole and fluorobenzene, while they incorrectly describe the MEP of chlorobenzene. The AM1 fails to localize the absolute minimum of fluorobenzene and does not find the minimum above the chlorobenzene chlorine atom. The poor agreement of both semiempirical methods with ab initio for any kind of chlorinated compounds is confirmed by results obtained for chloreothylene and chloroethane. We hypothesize that the main problem concerning these methods is that they freeze a too large amount of electrons in the atomic core of elements belonging to the second row, which makes for a wrong description of the core–valence electron interactions. Results obtained by modifying the AM1 parameters related to these interactions confirm our hypothesis. © 1992 by John Wiley & Sons, Inc.
Cumulative atomic multipole moments complement any atomic charge model to obtain more accurate electrostatic properties
Authors: Sokalski W.A. , Shibata M. , Rein R. , Ornstein R.L.
Published: January 2005

The quality of several atomic charge models based on different definitions has been analyzed using cumulative atomic multipole moments (CAMM). This formalism can generate higher atomic moments starting from any atomic charges, while preserving the corresponding molecular moments. The atomic‐charge contribution to the higher molecular moments, as well as to the electrostatic potentials, has been examined for CO and HCN molecules at several different levels of theory. The results clearly show that the electrostatic potential obtained from CAMM expansion is convergent up to the R−5 term for all atomic charge models used. This illustrates that higher atomic moments can be used to supplement any atomic charge model to obtain more accurate description of electrostatic properties. © 1992 by John Wiley & Sons, Inc.
Validation of the general purpose QUANTA ®3.2/CHARMm® force field
Authors: Momany Frank A. , Rone Rebecca
Published: January 2005

An evaluation of the CHARMm force field for small molecules is described. Using different force field conditions and computational techniques, a wide variety of compounds are analyzed. rms deviations of Cartesian coordinates for 49 diverse organic molecules taken from the Cambridge Crystallographic Data Base and internal coordinate geometries for 28 other molecules are reported. Results are described with different dielectrics, dihedral constraints, and crystal packing to allow analysis of deviations from experimental data and give precise statements of the reliability of the parameters used in the force field. Torsional barriers (rms = 0.4) and conformational energy differences (rms = 0.4) are examined and comparisons made to other force fields such as MM2, Tripos, and DREIDING. The results confirm that CHARMm is an internally consistent all purpose force field with energy terms for bonds, angles, dihedrals, and out‐of‐plane motions, as well as nonbonded electrostatic and van der Waals interactions. Reported CHARMm results (rms = 0.006 Å for bonds, rms = 1.37° for angles, and rms = 3.2° for dihedrals) are in excellent agreement with high quality electron diffraction data. © 1992 by John Wiley & Sons, Inc.
Improvements on the protein–dipole Langevin–dipole model
Authors: Xu Y.W. , Wang C.X. , Shi Y.Y.
Published: January 2005

The protein–dipole Langevin–dipole (PDLD) model developed by Warshel and co‐workers is an approach to evaluate electrostatic interactions in protein systems from microscopic sights. This model grasped the main physical factors and required little computations. But it might need the tests from every aspect. In the present work, we have chosen the solvation energies of Asp3, Glu7, Glu49, and Asp50 in bovine pancreatic trypsin inhibitor (BPTI) as a calibration to discuss the influences of parameters and conditions on the simulation results in the PDLD model. Some improvements have been proposed. The calculated solvation energies associated with ionizing the four acidic groups in BPTI and aspartic acid in solution are found in good agreement with the corresponding observed results if the improved PDLD approach and computational methods are used. © 1992 by John Wiley & Sons, Inc.
Solving the finite‐difference non‐linear Poisson–Boltzmann equation
Authors: Luty Brock A. , Davis Malcolm E. , McCammon J. Andrew
Published: January 2005

The Poisson–Boltzmann equation can be used to calculate the electrostatic potential field of a molecule surrounded by a solvent containing mobile ions. The Poisson–Boltzmann equation is a non‐linear partial differential equation. Finite‐difference methods of solving this equation have been restricted to the linearized form of the equation or a finite number of non‐linear terms. Here we introduce a method based on a variational formulation of the electrostatic potential and standard multi‐dimensional maximization methods that can be used to solve the full non‐linear equation. © 1992 by John Wiley & Sons, Inc.
Intensities of infrared bands in molecular mechanics (MM3)
Authors: Lii Jenn‐Huei , Allinger Norman L.
Published: January 2005

The MM3 molecular mechanics program calculates a fair representation of vibrational frequencies for molecules. To make this information more useful, a qualitative intensity calculation has been added, as is described herein. Because each bond in the molecule is assigned a dipole moment, and the vibrational amplitudes are known from the frequency calculation, the change in dipole moment corresponding to each normal mode is readily calculated. In some cases a charge flux has to be added empirically for bond stretchings. This relatively simple calculation has been applied to a number of different functional groups, and gives band intensities adequate for dividing the bands into very strong, strong, medium, weak, or very weak (forbidden) categories. © 1992 by John Wiley & Sons, Inc.
Ab Initio prediction of possible crystal structures for general organic molecules
Authors: Karfunkel H.R. , Gdanitz R.J.
Published: January 2005

The performance of a new crystal packing procedure for the ab initio prediction of possible molecular crystal structures is presented. The method is based upon only molecular information, i.e., no unit cell parameters are assumed to be known. The search for the global crystal energy minimum and all local minima inside an energy window is derived from Monte Carlo simulated annealing methods and has been applied to various organic molecules containing heteroatoms and polar groups. A systematic evaluation of the search method and of the quality of the potential energy function has been established. It is demonstrated that the packing of general organic molecules is possible even with standard force fields like CHARMM provided that the charges defining the electrostatic interactions are based upon physical models rather than transferable empirical parameters. Concepts of crystal packing that were based till now upon assumptions and speculations could be proved or disproved by solving directly the extended global optimization problem related to crystal packing. Crystal structures of molecules as complex as those treated in this article have not been, till now, predicted by a computational approach. In one case, a disagreement between the predicted and experimental structure was evident and, based upon the computations, we suspect that the published structure is the wrong one. © 1992 by John Wiley & Sons, Inc.
Critical analysis of electric field modeling: Formamide
Authors: Colonna François , Evleth Earl , Ángyán János G.
Published: January 2005

A detailed analysis of ab initio derived electric field and multipole modeling is presented using formamide as an example. Penetration effects, a problem encountered with most currently used modeling methods, are avoided using the Overlap Multipolar Expansion (OME) technique computed up to the hexadecapole level. This method is shown to be grid insensitive. The OME fields and subsequent atomic charge modeling are found to be more sensitive to correlation effects than to basis sets changes. Three different types of error analysis are applied to test the accuracy of regenerated fields from various multipole descriptions. It is shown that atom centered charge models, those most commonly used in the literature, have significant errors. Considerable improvement can be made by using various combinations of charge, dipole, and quadrupole atom‐ or bond‐centered models. For molecular dynamic programs it is argued that the best compromise between accuracy and efficiency is to use both atom and fictive atom charge models calculated from MP2 level density matrices using at least DZP level basis sets. © 1992 by John Wiley & Sons, Inc.
Ab Initio computed molecular structures and energies of the conformers of glucose
Authors: Polavarapu P.L. , Ewig C.S.
Published: January 2005

Ab initio computations indicate the existence of several stable and some unstable conformers in isolated α and β glucose molecules. All of the lower‐energy conformers exhibit a strikingly regular pattern of internal hydrogen bonding. Five such stable structures have been identified for each of the α and β anomers, differing primarily in the orientation of the CH2OH group. In each conformer, the α anomer is predicted to be lower in energy than the corresponding conformers of β anomer. The difference is about 2 kcal/mol in the 4‐31G basis but only 0.4 kcal/mol in the 6‐31G* basis. It is found that the electronic contributions to the free energy difference stabilize the α anomer while the nuclear motion contributions stabilize the β anomer. The implications of these predictions and the future investigations required to understand the relative stabilities of the two anomers are pointed out. © 1992 by John Wiley & Sons, Inc.
Search for nondegenerate real vertex invariants and derived topological indexes
Authors: Balaban Alexandru T. , Catana Cornel
Published: January 2005

Two new types of real (i.e., noninteger) local vertex invariants (LOVIs), denoted by ci and c′i and called distance‐enhanced exponential connectivities, are defined via eqs. (1)–(3) and (1′)–(3′), respectively. Only the case when the exponent z equals 1 in eqs. (3) and (3′) is discussed in detail. Both these LOVIs span the range from 0–1, but their dependence upon topology is fairly different, as seen from Table II, where ci and c′i values for all heptane and octane isomers are displayed. From these LOVIs, by simple summation over all graph vertices two new topological indexes (TIs), denoted by XC and XC′, respectively, are obtained. Their intermolecular ordering of all alkanes with four to nine carbon atoms is discussed. On their basis, correlations with boiling points and critical pressures of alkanes are presented. © 1993 John Wiley & Sons, Inc.
Microscopic and semimicroscopic calculations of electrostatic energies in proteins by the POLARIS and ENZYMIX programs
Authors: Lee Frederick S. , Chu Zhen Tao , Warshel Arieh
Published: January 2005

Different microscopic and semimicroscopic approaches for calculations of electrostatic energies in macromolecules are examined. This includes the Protein Dipoles Langevin Dipoles (PDLD) method, the semimicroscopic PDLD (PDLD/S) method, and a free energy perturbation (FEP) method. The incorporation of these approaches in the POLARIS and ENZYMIX modules of the MOLARIS package is described in detail. The PDLD electrostatic calculations are augmented by estimates of the relevant hydrophobic and steric contributions, as well as the effects of the ionic strength and external pH. Determination of the hydrophobic energy involves an approach that considers the modification of the effective surface area of the solute by local field effects. The steric contributions are analyzed in terms of the corresponding reorganization energies. Ionic strength effects are studied by modeling the ionic environment around the given system using a grid of residual charges and evaluating the relevant interaction using Coulomb's law with the dielectric constant of water. The performance of the FEP calculations is significantly enhanced by using special boundary conditions and evaluating the long‐range electrostatic contributions using the Local Reaction Field (LRF) model. A diverse set of electrostatic effects are examined, including the solvation energies of charges in proteins and solutions, energetics of ion pairs in proteins and solutions, interaction between surface charges in proteins, and effect of ionic strength on such interactions, as well as electrostatic contributions to binding and catalysis in solvated proteins. Encouraging results are obtained by the microscopic and semimicroscopic approaches and the problems associated with some macroscopic models are illustrated. The PDLD and PDLD/S methods appear to be much faster than the FEP approach and still give reasonable results. In particular, the speed and simplicity of the PDLD/S method make it an effective strategy for calculations of electrostatic free energies in interactive docking studies. Nevertheless, comparing the results of the three approaches can provide a useful estimate of the accuracy of the calculated energies. © 1993 John Wiley & Sons, Inc.
Analytical density‐dependent representation of Hartree—Fock atomic potentials
Authors: Pacios L. Fernandez
Published: January 2005

A procedure to represent atomic electron charge densities [L. Fernandez Pacios,J. Phys. Chem.,95, 10653 (1991);J. Phys. Chem.,96, 7294 (1992)] is here generalized to obtain simple analytical functions for potential energy contributions. Based upon suitable functions to describe atomic electron densities in a physically meaningful form, the procedure is developed to define density‐dependent analytical expressions for the electrostatic (classical) and exchange (quantum) potentials by means of proper approximate functionals. Calculations of correlation energies by using various density‐functional approaches are also performed. The whole scheme is used to represent Hartree–Fock limit atomic wave functions by Clementi–Roetti. This way, a set of analytically simple, nonbasis set‐dependent functions are defined with the aim to be further implemented in energy decomposition schemes for molecular interactions studies using atomic instead of electronic building blocks. © 1993 John Wiley & Sons, Inc.
Development of a restricted Hartree—Fock program INDMOL on PARAM: A highly parallel computer
Authors: Shirsat Rajendra N. , Limaye Ajay C. , Gadre Shridhar R.
Published: January 2005

Parallelization of the SCF method for closed‐shell molecules on the highly parallel transputer‐based system PARAM is described. The parallelization has been implemented on three different hardware and software environments: (1) a network of bare 64 transputers; (2) configuration 1 plus a back‐end file system (BFS); and (3) configuration 2 with one INTEL i860 processor. The evaluation of electron repulsion integrals (ERIs) and setting up of the Fock matrix is carried out in parallel on 64 nodes using minimal communication strategies. A good load balance is achieved for ERI evaluation with the help of bounds, local symmetry features, and the shell concept, as well as a data randomization technique, resulting into almost linear speedup (for ERI evaluation). In configurations 2 and 3, BFS is used for parallel storage and retrieval of ERIs. Further, in 3 matrix operations are implemented as remote procedure calls on the i860 processor. Routine techniques of level shifting and extrapolation are used for accelerating SCF convergence. The resulting package, INDMOL, has been tested for some randomly selected molecules having up to 255 contractions. Using configuration 3, a factor of 2 to 5 in computation time is obtained over 1, for the systems for which the ERIs cannot be stored in the distributed core memory. In summary, a heterogeneous system, as in configuration 3, can indeed be optimally exploited for programming peculiar diverse requirements of the SCF procedure. © 1993 John Wiley & Sons, Inc.
Computer generation of Hadamard matrices
Authors: Balasubramanian K.
Published: January 2005

We develop a computer code that uses elegant bit‐manipulation techniques for matrix multiplication and thus facilitates exhaustive generation of Skew‐Hadamard matrices. Hadamard matrices are useful in spectroscopic applications (Hadamard transform spectroscopy) and in balanced chemical designs. Application of our code yields several Skew‐Hadamard matrices up to order 100 × 100, although the combinatorial complexity of exhaustive generation increases exponentially. Our bit‐manipulation‐based codes took 124 h of CPU time to perform 7.79344 × 1011 matrix multiplications on an IBM RS 6000/560 system to generate all 100 × 100 matrices. This amounts to 5.7 × 10−7 s of CPU time per matrix multiplication. © 1993 John Wiley & Sons, Inc.
Madelung fields from optimized point charges for ab initio cluster model calculations on ionic systems
Authors: Sousa C. , Casanovas J. , Rubio J. , Illas F.
Published: January 2005

A simple procedure devised to obtain optimized point charges to represent the Madelung potential is reported and applied to six different crystal structures occurring in ionic systems. Their use in ab initio cluster model calculations is discussed through some selected examples and results compared with those arising from the use of the well‐known Evjen method. © 1993 John Wiley & Sons, Inc.
Relative basicities of carboxylate lone pairs in aqueous solution
Authors: Pranata Julianto
Published: January 2005

Relative basicities of the lone pairs of the acetate ion have been determined using ab initio calculations for the gas phase and Monte Carlo simulations for the aqueous phase. The syn lone pair is found to be more basic by only 1.25 pKa units. This small difference is the result of a large intrinsic preference for the syn conformer of the conjugate acid in the gas phase, offset by an almost equally large preferential solvation of the anti conformer in the aqueous phase. The better solvation of the anti conformer is due to stronger solute–solvent interactions. © 1993 John Wiley & Sons, Inc.
Conformational analysis of cocaine, the potent analog 2β‐carbomethoxy‐3β‐(4‐fluorophenyl)tropane (CFT), and other dopamine reuptake blockers
Authors: Froimowitz Mark
Published: January 2005

Using the MM2‐87 program and parameter set, conformational analyses have been performed on cocaine (1), the potent analog 2β‐carbomethoxy‐3β‐(4‐fluorophenyl)tropane (CFT, 2), and a group of dopamine reuptake blockers that contain two phenyl rings. The latter includes LU 19‐005 (3), a 1‐amino‐4‐phenyltetralin (4), a hexahydropyrrolo[2,1‐a]isoquinoline (5), diclofensine (6), and a hexahydro[1,2‐b]pyridine (7). Using different values for the dielectric constant, the global minimum of 1 and 2 is a conformer in which there is a favorable electrostatic interaction between the ammonium hydrogen and the carbonyl of the carbomethoxy group. The N‐methyl groups in 1 and 2 are found to strongly prefer the equatorial position of the piperidine ring. These results were also related to four crystal structures of 1 and its close derivatives. Compounds 3–7 are found to have a common conformation that was used to define the pharmacophore for dopamine reuptake blockers including the required orientation of the ammonium hydrogen. The pharmacophore provides an explanation for why the tertiary amine analogs of 3 and 4 are less potent than the secondary amines because the added N‐methyl group occupies the position required for the ammonium hydrogen. This explanation, however, does not work for 7, in which the tertiary amine is again less active than the secondary amine. However, this last series appears to have a number of anomalous features. Superposition of 2 with the pharmacophore suggests that its carbomethoxy may occupy the same region of the receptor as the second phenyl ring in compounds 3–7. © 1993 John Wiley & Sons, Inc.
Continuous similarity measure between nonoverlapping X‐ray powder diagrams of different crystal modifications
Authors: Karfunkel H.R. , Rohde B. , Leusen F.J.J. , Gdanitz R.J. , Rihs G.
Published: January 2005

The problem of quantifying similarity between crystal structures is transformed into the problem of comparing the associated X‐ray powder diagrams. A smooth similarity measure between two powder diagrams, termed a “fold,” is defined. In contrast to conventional comparison methods, the introduced method is still applicable when the peaks of the spectra to be compared have no overlap. The main areas of application of the method are the construction of a molecular crystal structure when only the experimental powder diagram is available and the analysis of possible crystal packings predicted on the basis of molecular information only. A suitable empirical parameterization of the fold has been derived from a large set of experimental and force‐field‐generated crystals. The analysis of the outcome of an ab initio packing of a flexible molecule is given as an example. The algorithmic details of the method are given as a FORTRAN 77 code. © John Wiley & Sons, Inc.
Shape groups of the electronic isodensity surfaces for small molecules: Shapes of 10‐electron hydrides
Authors: Walker P. Duane , Arteca Gustavo A. , Mezey Paul G.
Published: January 2005

An algorithm for a detailed 3‐D characterization of the shapes of molecular charge distributions is implemented in the form of a comprehensive package of computer programs, GSHAPE, and applied to a series of 10‐electron hydrides to critically evaluate the methodology. Attention is paid to the effects of nuclear geometry and the size of basis on the molecular shape. The characterization is performed by computing a number of topological invariants (“shape groups”) associated with a continuum of molecular surfaces: the complete family of all electronic isodensity contours for the given molecules. These shape groups (the homology groups of truncated surfaces derived from isodensity contours) depend on two continuous parameters: a density value defining the density contour and a reference curvature value, to which the local curvatures of the isodensity contours are compared. The electronic charge distribution is calculated at the ab initio level using basis sets ranging from STO‐3G to 6‐31G**. No visual inspection is required for the characterization and comparison of shapes of molecular charge densities, as these are done algorithmically by the computer. However, visualization of the results is one option of our program using Application Visualization Software (AVS). For a given molecule, in a given nuclear geometry, the technique provides a 2‐D shape map, displaying the distribution of the shape gruops as a function of the local curvature and the level set value (the value of the charge density at the contour). The computer program GSHAPE performs the analysis automatically. This feature makes it potentially useful in the context of computer‐aided drug design, where unbiased, automated shape characterization methods are valuable tools. As examples, a variety of 2‐D shape maps are discussed. © John Wiley & Sons, Inc.
Generalized morse analytic function for the “true” diatomic potential of the RKR type
Authors: Dagher M. , Kobeissi H. , Kobressi M. , D'Incan J. , Effantin C.
Published: January 2005

The problem of the representation of the RKR (or IPA) diatomic potential by a simple analytic function is considered. This old problem has for a fairly good solution the Coxon‐Hajigeorgiou function U(x) = D[1 ‐ exp‐fn(x)]2 with fn(x) = Σ amxm. The problem of the determination of the disposable parameters a1 … an [in order that U(r) fits the given RKR potential] is reduced to that of a set of linear equations in am where a standard least‐squares technique is used. The application to several states (ground or excited) of several molecules shows that a fairly “good” fit is obtained for n ∼ 10, even for the state XOg—I2 bounded by 109 vibrational levels, for which the RKR potential is defined by the coordinates of 219 points. It is shown that the percentage deviation |U(r)RKR ‐ U(r)| throughout the range of r values is about 0.04% for XΣLi2, 0.0005% for XΣHCl, 0.06% for XOgI2, and 0.05% for BOuI2 (as examples). This approach shows the same success for deep and shallow potentials. The comparison of the computed Ev (vibrational energy) and Bv (rotational constant) with their corresponding experimental values shows that a good agreement is reached even for high vibrational levels close to the dissociation. © John Wiley & Sons, Inc.
Prediction of peptide conformation by multicanonical algorithm: New approach to the multiple‐minima problem
Authors: Hansmann Ulrich H. E. , Okamoto Yuko
Published: January 2005

We apply a recently developed method, the multicanonical algorithm, to the problem of tertiary structure prediction of peptides and proteins. As a simple example to test the effectiveness of the algorithm, metenkephalin is studied and the ergodicity problem, or multiple‐minima problem, is shown to be overcome by this algorithm. The lowest‐energy conformation obtained agrees with that determined by other efficient methods such as Monte Carlo simulated annealing. The superiority of the present method to simulated annealing lies in the fact that the relationship to the canonical ensemble remains exactly controlled. Once the multicanonical parameters are determined, only one simulation run is necessary to obtain the lowest‐energy conformation and further the results of this one run can be used to calculate various thermodynamic quantities at any temperature. The latter point is demonstrated by the calculation of the average potential energy and specific heat as functions of temperature. © John Wiley & Sons, Inc.
Analysis of the genetic algorithm method of molecular conformation determination
Authors: McGarrah D.B. , Judson R.S.
Published: January 2005

Many important problems in chemistry require knowledge of the 3‐D conformation of a molecule. A commonly used computational approach is to search for a variety of low‐energy conformations. Here, we study the behavior of the genetic algorithm (GA) method as a global search technique for finding these low‐energy conformations. Our test molecule is cyclic hexaglycine. The goal of this study is to determine how to best utilize GAs to find low‐energy populations of conformations given a fixed amount of CPU time. Two measures are presented that help monitor the improvement in the GA populations and their loss of diversity. Different hybrid methods that combine coarse GA global search with local gradient minimization are evaluated. We present several specific recommendations about trade‐offs when choosing GA parameters such as population size, number of generations, rate of interaction between subpopulations, and combinations of GA and gradient minimization. In particular, our results illustrate why approaches that emphasize convergence of the GA can actually decrease its effectiveness as a global conformation search method. © John Wiley & Sons, Inc.
“Full numerical” diatomic matrix elements: Simplified shooting method
Authors: Kobeissi Hafez , Trad Chafia H. , Kobeissi Majida
Published: January 2005

The problem of diatomic matrix elements Mnn′ = 〈Ψn|Q|Ψn′〉 related to the anharmonic oscillator is considered for standard operators Q of the form x = r – re (r is the radial variable), powers of x, or exponentials, or combinations of such operators; the quantum numbers (n, n′) may be equal or not. A “full numerical” method to determine Mnn′ is presented for any type of the potential U, analytic like that of Morse or numerical like the RKR potential. This numerical method is a simplified version of the standard Cooley shooting method (CSM). The present simplified shooting method (SSM): (1) shoots in one direction only (instead of two); (2) avoids starting problems and matching problems; (3) determines the “end” point automatically (without prior guesses); and (4) reduces thus the number of grid points effectively needed. Examples for analytic (Morse) and RKR potentials are presented. The numerical application to a standard example used by Delgado‐Barrio et al. [J. Comp. Chem., 7, 208 (1986)] using the CSM, and by Kobeissi et al. [J. Comp. Chem., 10, 358 (1989)] using the highly accurate “Canonical Functions” method, shows that when the SSM and CSM are used with the same integrator and the same mesh size the relative discrepancy ΔMnn′(between computed and exact M) is averaged for several (n, n′) to 5.4 × 10−4 for the CSM and to 8.5 × 10−6 for the present SSM. This improvement in accuracy is supplemented by a reduction in computer time consumption. © John Wiley & Sons, Inc.
Use of molecular dynamics simulations with ab initio SCF calculations for the determination of the deuterium quadrupole coupling constant in liquid water and bond lengths in ice
Authors: Eggenberger Rolf , Gerber Stefan , Huber Hanspeter , Searles Debra , Welker Marc
Published: January 2005

The deuterium quadrupole coupling constant and asymmetry parameter in heavy water were determined using ab initio SCF calculations. Snapshots from a molecular dynamics simulation were used to give liquid water cluster configurations and the influence of simulation parameters on the quadrupole coupling constant was investigated. The electronic potential model and the number of molecules in the molecular dynamics simulation and the pressure of the system were found to have only a small influence on the quadrupole coupling constant. The average value of the quadrupole coupling constant at room temperature, corrected for the known deficiency of the ab initio calculation in the gas phase, yields a quadrupole coupling constant of 253 kHz, in perfect agreement with the most recent experiments. The oxygen—deuterium bond lengths in ice Ih, ice II, and ice IX were determined using experimental quadrupole coupling constants and a model equation. An averaged bond length of 98.9 pm was obtained for the Ih form, which is approximately 2 pm shorter than that determined by neutron diffraction studies, whereas the bond lengths for the four deuterium sites in ice II and the three sites in ice IX are in fair agreement with experiment. © John Wiley & Sons, Inc.
Implementation of a data parallel, logical domain decomposition method for interparticle interactions in molecular dynamics of structured molecular fluids
Authors: Young William S. , Brooks Charles L.
Published: January 2005

In this article, we describe a domain decomposition method for the efficient parallel computation of nonbonded forces and energies in condensed‐phase molecular systems. This decomposition is based upon the monotonic logical grid (MLG) approach of Boris [J. Boris, J. Comp. Phys., 66, 1 (1986)] and yields an efficient, scalable algorithm for interparticle interaction computation on private‐memory, single‐instruction multiple‐data (SIMD) parallel computers. We illustrate the application of this technique in a molecular dynamics kernel for rigid molecular solvents by simulating the structural and thermodynamic properties of water and methanol. The performance of this algorithm on the Thinking Machines' CM‐2, private‐memory SIMD computer, is demonstrated to be good compared to conventional vector/parallel supercomputers. However, as the fluid becomes less structured performance slightly degrades. © 1994 by John Wiley & Sons, Inc.
Applicability of the WKB method in asymmetric double wells with degenerate and nondegenerate minima
Authors: Gelabert Ricard , Moreno Miquel , Lluch José M.
Published: January 2005

To test the applicability of the WKB semiclassical approximation to correctly describe the tunneling frequencies and energy levels in asymmetric double wells, we have considered the cases where the asymmetry comes from the nondegeneracy of the two minima and when it comes from the asymmetry in the shape of the barrier between both minima. To do this, we compare the tunneling frequencies and energy levels obtained through the WKB method for symmetric and asymmetric cases with exact results obtained by a basis set procedure. Our results show that the semiclassical WKB approximation has to be used with caution for asymmetric double wells. © 1994 by John Wiley & Sons, Inc.
Rationalizing nuclear overhauser effect data for compounds adopting multiple‐solution conformations
Authors: Forster Mark J. , Mulloy Barbara
Published: January 2005

An algorithm is described for refining the populations of a set of multiple‐solution conformers using experimental nuclear Overhauser effects (nOes). The method is based upon representing the effective relaxation matrix for the set of interconverting proposed conformers as a linear combination of relaxation matrices (LCORMs) due to each conformer. The conformer population derivative of the nOe is derived from a Taylor series expression for the calculated nOe. This derivative may then be used in a standard nonlinear least‐squares refinement procedure. The LCORM nOe procedure is tested using a monosaccharide system, 1‐O‐methyl‐α‐L‐iduronate, that is known to exhibit conformational variability. The measured nOes for this system are used to refine the populations of a set of three static conformers, namely, the 1C4, 4C1, and 2S0 ring conformers. The populations thus derived are compared to those previously obtained using nuclear magnetic resonance proton‐proton coupling constant information. Two possible extensions to the method are discussed: The first uses combined nOe and coupling constant data while the second removes the restrictions that the conformers used for fitting be rigid entities. © 1994 by John Wiley & Sons, Inc.
Preconditioners for distance matrix algorithms
Authors: Glunt W. , Hayden T. L. , Raydan M.
Published: January 2005

A recent gradient algorithm in nonlinear optimization uses a novel idea that avoids line searches. This so‐called spectral gradient algorithm works well when the spectrum of the Hessian of the function to be minimized has a small range or is clustered. In this article, we find a general preconditioning method for this algorithm. The preconditioning method is applied to the stress function, which arises in many applications of distance geometry, from statistics to finding molecular conformations. The Hessian of stress is shown to have a nice block structure. This structure yields a preconditioner which decreases the amount of computation needed to minimize stress by the spectral gradient algorithm. © 1994 by John Wiley & Sons, Inc.
Force field calculations (MM3) on glyoxal, quinones, and related compounds
Authors: Allinger Norman L. , Fan Yi
Published: January 2005

A general force field type of calculation has been devised in connection with MM3 to treat 1,2‐ and 1,4‐diketones, both when they are not conjugated (as in derivatives of glyoxal) and when they are conjugated (as in derivatives of ortho‐ and para‐benzoquinone). The molecular structures, moments of inertia, dipole moments, and vibrational spectra have been examined for about 15 compounds, some in several conformations. Ab initio calculations (6‐31G*) have been used to determine quantities that have not been previously defined by experiment. In general, the force field permits the calculation of the structures with high accuracy, and the spectroscopic and conformational energy data with fair accuracy. © 1994 by John Wiley & Sons, Inc.
Finite‐state and reduced‐parameter representations of protein backbone conformations
Authors: Buturović Ljubomir J. , Smith Temple F. , Vajda Sandor
Published: January 2005

This article studies the representation of protein backbone conformations using a finite number of values for the backbone dihedral angles. We develop a combinatorial search algorithm that guarantees finding the global minima of functions over the configuration space of discrete protein conformations, and use this procedure to fit finite‐state models to the backbones of globular proteins. It is demonstrated that a finite‐state representation with a reasonably small number of states yields either a small root‐mean‐square error or a small dihedral angle deviation from the native structure, but not both at the same time. The problem can be resolved by introducing limited local optimization in each step of the combinatorial search. In addition, it is shown that acceptable approximation is achieved using a single dihedral angle as an independent variable in local optimization. Results for 11 proteins demonstrate the advantages and shortcomings of both the finite‐state and reduced‐parameter approximations of protein backbone conformations. © 1994 by John Wiley & Sons, Inc.
Molecular simulation of alkyl boronic acids: Molecular mechanics and solvation free energy calculations
Authors: Chen Xiannong , Bartolotti Libero , Ishaq Khalid , Tropsha Alexander
Published: January 2005

The alkyl boronic acid moiety is incorporated into many biologically interesting structures. To provide parameters for molecular mechanics and dynamics studies of compounds containing this group, we performed ab initio calculations at the 6‐31G* level to obtain bond stretching, bending, and torsion constants. The hydrodynamic formulation of the time‐dependent density functional theory was used to calculate the attractive part of van der Waals (VDW) 6–12 potential. The geometry of boronic acid moiety of the 6‐31G* optimized methyl boronic acid was similar to that of the X‐ray crystal structure of phenyl boronic acid. To test the reliability of nonbonded parameters, Monte Carlo free energy perturbation simulations and the thermodynamic cycle approach were used to estimate the differences in solvation free energy between alkyl alcohol and alkyl boronic acid, both in water and in chloroform. These free energy differences were also obtained experimentally by measuring the vapor–water and water–chloroform partition coefficients. The close agreement between experimental values and the results of our simulations suggests the reliability of new molecular mechanics force‐field parameters for alkyl boronic acids. © 1994 by John Wiley & Sons, Inc.
Variation of atomic charges during proton transfer in hydrogen bonds
Authors: FloriáN Jan , Scheiner Steve
Published: January 2005

The point atomic charges in a number of ionic H‐bonded systems are studied by ab initio calculations as functions of the proton transfer coordinate. In the proton‐bound complexes of water–water, ammonia–ammonia, formamide–water, formamide–ammonia, and dimethylether–ammonia, the net atomic charges were obtained using Mulliken population analysis and from the diagonal elements of the atomic polar tensors calculated at the HF/4–31G and MP2/6–31 + G** levels. The dependence of the atomic charges upon the coordinate of the transferring proton was found to be close (within an error of 0.02 e) to a linear function for intermolecular distances in the 2.5–2.8 Å range. The obtained charge and charge flux dependencies highlight the electron redistribution during the proton transfer process and provide insights into the source of the high infrared (IR) intensities of stretching modes of NH and OH bonds undergoing hydrogen bonding. © 1994 by John Wiley & Sons, Inc.
Interaction between carbon dioxide and naphthalene: A molecular modeling approach
Authors: Battersby P. , Dean J. R. , Hitchen S. M. , Tomlinson W. R. , Myers P. M.
Published: January 2005

The formation of a charge‐transfer complex between carbon dioxide and naphthalene was studied using a molecular modeling program, with the aim of studying the solubility of naphthalene in supercritical carbon dioxide. The orbitals involved in the formation of the complex were studied using MINDO/3 as the semi‐empirical method. A solvent cage was constructed, and the maximum number of carbon dioxide molecules to surround naphthalene was found to be 20. The heat of interaction of the complex was obtained using MINDO/3. © 1994 by John Wiley & Sons, Inc.
Structures and stabilization energies of methyl anions with main group substituents from the first five periods
Authors: El‐Nahas Ahmed M. , Schleyer Paul Von Ragué
Published: January 2005

The effects of substituents (X) on the structures and stabilities of CH2X− anions for groups comprised of fourth‐ and fifth‐period main group elements (X = K, CaH, GaH2, GeH3, AsH2, SeH, Br, Rb, SrH, InH2, SnH3, SbH2, TeH, and I) have been investigated by ab initio pseudopotential calculations. Full geometry optimizations have been carried out on the CH2X− anions and the corresponding neutral parent molecules, CH3X, at HF/DZP + and MP2/DZP + levels. Results for substituents from the second (X = LiF) and third (X = NaCl) periods provide comparisons of substituent effects of the main group elements of the first four rows of the periodic table on methyl anions. Frequency calculations characterize the nature of stationary points and show pyramidal CH2X− anion structures to be the most stable unless π acceptor interactions (e.g., with BH2, AlH2, GaH2, and InH2 favor planar geometries. The CH2X− stabilization energies [at QCISD(T)/DZP + /MP2/DZP + + ZPE level for X = KI and QCISD(T)/6−31 + G*/MP2/6−31 + G* + ZPE level] for X = LiCl) also show strong π‐stabilizing effects for the same substituents. With the exception of CH3 and NH2, all substituents stabilize methyl anions, although the σ stabilization by OH and F is small. The SiH3PH2SHCl, GeH3AsH2SeHBr, and SnH3SbH2TeHI sets of substituents give stabilization energies between 19 and 30 kcal/mol. The stability of methyl anions substituted by the halogens and the chalcogens (X = OH, SH, SeH, and TeH) increases down a group in accord with the increasing substituent polarizability, while for π acceptors (BH2, AlH2, GaH2, and InH2) the stability decreases down a group in line with their π‐accepting ability. © 1994 by John Wiley & Sons, Inc.
Direct search methods for the molecular conformation problem
Authors: Meza J. C. , Martinez M. L.
Published: January 2005

An important area of research in computational biochemistry is the design of molecules for specific applications. The design of these molecules, which depends on the accurate determination of their three‐dimensional structure, can be formulated as a global optimization problem. In this article, we present results from the application of a new conformation searching method based on direct search methods. We compare these results to some earlier results using genetic algorithms and simulated annealing. © 1994 by John Wiley & Sons, Inc.
New spherical‐cutoff methods for long‐range forces in macromolecular simulation
Authors: Steinbach Peter J. , Brooks Bernard R.
Published: January 2005

New atom‐ and group‐based spherical‐cutoff methods have been developed for the treatment of nonbonded interactions in molecular dynamics (MD) simulation. A new atom‐based method, force switching, leaves short‐range forces unaltered by adding a constant to the potential energy, switching forces smoothly to zero over a specified range. A simple improvement to group‐based cutoffs is presented: Switched group‐shifting shifts the group–group potential energy by a constant before being switched smoothly to zero. Also introduced are generalizations of atom‐based force shifting, which adds a constant to the Coulomb force between two charges. These new approaches are compared to existing methods by evaluating the energy of a model hydrogen‐bonding system consisting of two N‐methyl acetamide molecules and by full MD simulation. Thirty‐five 150 ps simulations of carboxymyoglobin (MbCO) hydrated by 350 water molecules indicate that the new methods and atom‐based shifting are each able to approximate no‐cutoff results when a cutoff at or beyond 12 Å is used. However, atom‐based potential‐energy switching and truncation unacceptably contaminate group–group electrostatic interactions. Group‐based potential truncation should not be used in the presence of explicit water or other mobile electrostatic dipoles because energy is not a state function with this method, resulting in severe heating (about 4 K/ps in the simulations of hydrated MbCO). The distance‐dependent dielectric (ϵ ∝︁ r) is found to alter the temperature dependence of protein dynamics, suppressing anharmonic motion at high temperatures. Force switching and force shifting are the best atom‐based spherical cutoffs, whereas switched group‐shifting is the preferred group‐based method. To achieve realistic simulations, increasing the cutoff distance from 7.5 to 12 Å or beyond is much more important than the differences among the three best cutoff methods. © 1994 by John Wiley & Sons, Inc.

This article is a US Government work and, as such, is in the public domain in the United States of America.
Iterative methods for the calculation of a few of the lowest eigenvalues and corresponding eigenvectors of the AX = λBX equation with real symmetric matrices of large dimension
Authors: Mitin Alexander V.
Published: January 2005

New methods for the iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of a generalized eigenvalue problem are proposed. These methods use only multiplication of the A and B matrices on a vector. © 1994 by John Wiley & Sons, Inc.
Long‐time overdamped Langevin dynamics of molecular chains
Authors: Grønbech‐jensen Niels , Doniach Sebastian
Published: January 2005

We present a novel algorithm of constrained, overdamped dynamics to study the long‐time properties of peptides, proteins, and related molecules. The constraints are applied to an all‐atom model of the molecule by projecting out all components of the nonbonding interactions which tend to alter fixed bond lengths and angles. Because the overdamped dynamical equations are first order in time, the constraints are satisfied by inversion of a banded matrix at each timestep, which is computationally efficient. Thermal effects are included through a Langevin noise term in the equation of motion. Because high‐frequency components of the motion have been eliminated, the timestep of the algorithm is determined by the nonbonding forces, which are two to three orders of magnitude weaker than the bonding forces. Using polyalanine as a test example, we demonstrate that trajectories simulating a microsecond of motion can be run about 103 times faster than an equivalent molecular dynamics simulation. © 1994 by John Wiley & Sons, Inc.