bluuebunny/crossref_metadata_2025 huggingface dataset:
Topology of conical intersections and Jahn‐Teller crossing: Application to the standard model for XY4 molecules in T2 ground states
Authors: Liotard D. , Roche M.
Published: January 2005

The topological understanding of a potential function requires a knowledge of its critical points and indices. These concepts are mathematically meaningless if the potential function is not twice continuously differentiable. When conical intersections or Jahn–Teller crossings are encountered, the adiabatic potential, defined as the lowest eigenvalue of a Hamiltonian, can be smoothed everywhere. Moreover, the limiting properties of the smoothed critical points for vanishing values of a smoothing parameter lead to a unambiguous definition of a pseudo critical point of the limiting potential. Therefore, Morse theory is readily applicable to the ground state potential function in spite of the first order discontinuities. The regularization procedure is formally and numerically applied to the simplest Hamiltonian matrix of order 3 describing the Jahn–Teller effect of XY4 molecules in the T2 ground states. Various kinds of pseudo‐critical points are encountered and are shown to satisfy the Morse theory.
Monte Carlo study of the aqueous hydration of dimethylphosphate conformations
Authors: Jayaram B. , Mezei M. , Beveridge D. L.
Published: January 2005

Monte Carlo computer simulations were performed on dilute aqueous solutions of the dimethylphosphate anion and the sodium dimethylphosphate ion pair, with the two phosphodiester torsional angles in the gauche–gauche, gauche–trans, and trans–trans conformations. The structural and energetic aspects of the aqueous hydration of each molecule were analyzed in terms of quasi component distribution functions based on the proximity criterion and partitioned into ionic, hydrophilic, and hydrophobic contributions to facilitate an understanding of the hydration pattern and conformational trends in these multifunctional solutes. Special attention was also paid to methodological issues affecting hydration, such as statistical uncertainty in the determined hydration indices, choice of partial atomic charges for the solute atoms, and solute–water interaction potentials adopted in the simulations. The results showed that gauche–trans and gauche–gauche forms are equally favorable for the dimethylphosphate anion with the trans extended form destabilized by hydration. The sodium dimethylphosphate ion pair hydration energetically favors the trans–trans conformation.
Application of SINDO1 to chlorine and sodium compounds
Authors: Jug Karl , Schulz Joachim
Published: January 2005

SINDO1 calculations are presented for ground state geometries, heats of formation, ionization potentials and dipole moments of chlorine and sodium compounds. These calculations are based on a new parametrization of SINDO1 for second‐row elements which features inclusion of 3d orbitals and zero point energies. The comparison shows a substantial improvement over MNDO in geometries and heats of formation of hypervalent compounds and ionization potentials, whereas other properties are of similar quality.
On the use of constraints in molecular mechanics. II. The Lagrange multiplier method and non‐full‐matrix Newton‐Raphson minimization
Authors: Dillen Jan L.M.
Published: January 2005

It is shown how the Lagrange Multiplier method for constrained minimization can be implemented in a molecular mechanics program using the common approximations to the full‐matrix Newton‐Raphson minimization. The method reduces the number of cycles to achieve convergence, and also stabilizes the refinement process. Increases in computer memory requirements are small. As an application, the conformational surface of cycloheptane is calculated.
Semi‐empirical calculations of molecular trajectories: Method and applications to some simple molecular systems
Authors: Stewart James J.P. , Davis Larry P. , Burggraf Larry W.
Published: January 2005

The MNDO Hamiltonian as incorporated within MOPAC has been utilized to predict dynamics for some simple reactions. In one option, the intrinsic reaction coordinate has been followed along the path of steepest descent from the transition state backward to reactants and forward to products. In a second option, dynamics of isolated molecular systems have been calculated. In each case, the potential surface (as predicted by the MNDO Hamiltonian) is calculated in situ as the atomic trajectories are calculated from Newton's Laws of Motion. Several specific examples are given and discussed.
Ab initio program for treatment of related molecules. II. Integral transformation in extended systems
Authors: Kozmutza C.
Published: January 2005

An integral transformation procedure is reported as a part of an ab initio program (named SYCETY) developed recently for spatially extended molecules. It is shown that all advantages of the program SYCETY can be kept. The procedure is especially suitable to transform the integrals to a localized basis set. By using the MBPT with localized basis the most important part of the correlation can be calculated even for large (spatially extended) systems.
A molecular mechanics‐NMR pseudoenergy approach to the solution conformation of glycolipids
Authors: Scarsdale J. N. , Ram P. , Prestegard J. H. , Yu R. K.
Published: January 2005

We present here a protocol for the determination of oligosaccharide solution conformation from a combination of molecular mechanics calculations and NMR distance constraints treated as pseudoenergies. As an illustration of our methodology we have chosen the determination of the solution conformation of the tetrasaccharide headgroup of the glycolipid globoside. In order to test the ability of our methodology to avoid becoming trapped in local minima, we have chosen three starting structures, well displaced from one another in conformational space. The structures obtained upon convergence of the calculations with distance constraint pseudoenergies were quite similar to one another. For two of the three glycosidic linkages in globoside, the results from the calculations were virtually identical for each of the three starting structures. We also apply our protocol to a model which allows for the existence of multiple conformers in an effort to explore the possibility of conformational flexibility in the oligosaccharide headgroup of globoside.
Parallel computation of the Moller–Plesset second‐order contribution to the electronic correlation energy
Authors: Watts John D. , Dupuis Michel
Published: January 2005

We report herein, the implementation of a second‐order Moller–Plesset perturbation theory (MP2) program on the IBM LCAP parallel supercomputers. The LCAP systems comprise IBM 308X hosts and 10 FPS‐X64 attached processing units (APs). The APs are interconnected by a 512 Mbyte shared memory which allows rapid interprocessor communication. All the computationally demanding steps of the MP2 procedure execute efficiently in parallel. Parallel computation of two‐electron integrals is accomplished by distributing the loop over shell blocks among the APs. Parallel Fock matrix formation is achieved by having each AP evaluate the contribution of its own integral sublist to the total Fock matrix. The contributions are added together on the host, and the sum diagonalized either on the host or on a single AP. The parallel implementations of the integral transformation and the MP2 calculation are less straightforward. In each case, the use of the shared memory is essential for an efficient implementation. Details of the implementations and performance data are given.
Steric effects on reaction rates. XI. Solvolysis of tertiary carbon substrates rationalized by molecular mechanics calculations
Authors: Müller Paul , Mareda Jiri
Published: January 2005

The steric energy difference (ΔEst) between tertiary carbenium ions (R+) and the corresponding alcohols has been calculated by MM2 for a series of tertiary nonbridgehead substrates and correlated with their rate of solvolytic reactivity. Satisfactory correlation is obtained, except for p‐nitrobenzoates of highly congested substrates. The slope and intercept of the correlations remain almost unchanged if bridge‐head substrates are included in the plot. However, the quality of the fit is better for bridgehead substrates alone.
Computational strategies for the optimization of equilibrium geometries and transition‐state structures at the semiempirical level
Authors: Cummins Peter L. , Gready Jill E.
Published: January 2005

Several improvements have been made to the gradient algorithms commonly used to optimize equilibrium and transition‐state geometries at the semiempirical level. A gradient algorithm derived from a combination of a variable metric method (Davidon–Fletcher–Powell/Broyden–Fletcher–Goldfarb–Shanno) and Pulay's direct inversion in the iterative subspace method for geometry optimization (GDIIS) is compared with the variable metric method combined with an accurate linear search algorithm. The latter method is used routinely in the standard semiempirical program packages, MNDO, MOPAC, and AMPAC. The combined variable metric and GDIIS algorithm is also compared with GDIIS which uses a static metric. The performance of these algorithms is examined for a wide range of systems with respect to both choice of coordinate system (for cyclic molecules) and guess for the initial Hessian. The results show that the GDIIS method is up to ca. 40% more efficient than the variable metric combined with accurate line search algorithm: however, the exact savings vary depending on the coordinate system and initial Hessian. For noncyclic systems, variable‐metric GDIIS is usually equal or superior to static‐metric GDIIS, and consistently performs ca. 30% more efficiently than the variable metric combined with accurate line search algorithm. For the optimization of cyclic molecules, an improved estimate of the initial Hessian has increased the efficiency by at least a factor of two. Greater efficiencies (usually >40%) are also obtained when static‐metric GDIIS is used to refine the geometry after the initial application of a transition‐state search based on the variable metric combined with line search algorithm. On the basis of these results, we recommend several changes to the algorithms as currently implemented in the standard semiempirical program packages.
A molecular mechanics analysis of molecular recognition by cyclodextrin mimics of α‐chymotrypsin
Authors: Venanzi Carol A. , Canzius Preston M. , Zhang Zhifeng , Bunce Jeffrey D.
Published: January 2005

The method of molecular mechanics is used to investigate the structural and electrostatic features of molecular recognition by β‐cyclodextrin and capped β‐cyclodextrin models of α‐chymotrypsin. Since capped β‐cyclodextrin has been shown to be the more effective biomimetic catalyst, these features of molecular recognition can be interpreted in terms of the relationship between molecular structure and catalytic function. Calculations in vacuo show that the addition of an N‐methylformamide “cap” substituent to each glucose unit appears to change the relative orientation of some glucose fragments from that found in the X‐ray structure of the β‐cyclodextrin macrocycle. These results indicate that certain structural components of molecular recognition, such as the orientation of the secondary hydroxyls and the related orientation of the caps, may be implicated in the catalysis. In addition, the electrostatic component of molecular recognition was investigated by the analysis of molecular electrostatic potential maps calculated in planes parallel to the average plane of the glycosidic oxygen atoms. The results indicate that the addition of the caps to the β‐cyclodextrin macrocycle subtly alters the pattern of the maps in each plane. However, the general qualitative features of electrostatic recognition by β‐cyclodextrin and capped β‐cyclodextrin are similar.
SCF, MP2, and CEPA‐1 calculations on the OH ‥ O hydrogen bonded complexes (H2O)2 and (H2O‐H2CO)
Authors: Vos R. J. , Hendriks R. , Van Duijneveldt F. B.
Published: January 2005

Counterpoise corrected ab initio calculations are reported for (H2O)2 and H2O‐H2CO. Geometry searches were done in the moment‐optimized basis DZP' at the SCF, MP2, and CEPA‐1 levels of theory, followed by more accurate single‐point calculations in basis ESPB, which includes bondfunctions to saturate the dispersion energy. The final equilibrium binding energies obtained are −4.7 ±0.3 kcal/mol for a near‐linear (H2O)2 structure and −4.6 ±0.3 kcal/mol for a strongly bent HOH ‥ OCH2 structure. The energy difference between these systems is much smaller than in all previous ab initio work. Cyclic (C2h) and bifurcated (C2v) transition structures for (H2O)2 are located at 1.0 ±0.1 kcal/mol and 1.9 ±0.3 kcal/mol above the global minimum, respectively. A new partitioning scheme is presented that rigorously partitions the MP2 correlation interaction energy in intra and intermolecular (dispersion) contributions. These terms are large (up to 2 kcal/mol) but of opposite sign for most geometries studied and hence their overall effect upon the final structures is relatively small. The relative merits of the MP2 and CEPA‐1 approaches are discussed are discussed and it is concluded that for economical reasons MP2 is to be preferred, especially for larger systems.
Partial optimization of large molecules and clusters
Authors: Head John D.
Published: January 2005

By examining the displacement coordinate metric three modes of constrained optimization for large molecules and clusters are suggested. The first method corresponds to a conventional optimization using internal coordinates. The second mode has applications with respect to both internal and cartesian coordinates. The final mode is particularly interesting because it can result in computational savings. A mixture of both internal and cartesian coordinates is specified where these coordinates are usually a subset of the molecules or clusters total coordinate set. In the optimization only a subset of the energy derivatives need be evaluated reducing the computational effort associated with the gradient calculation.
Hydration free energy calculations by the acceptance ratio method
Authors: Saito Minoru , Nakamura Haruki
Published: January 2005

The hydration energy difference between the alanine and glycine zwitter ions was calculated by both the free energy perturbation method and the acceptance ratio method. The calculations were carried out by using different increments of the mutation parameter λ, δλ = − 0.05, −0.10, and −0.20. The free energy difference calculated by the acceptance ratio method was found to be approximately the same as an average of the two free energy differences in the forward and the backward directions calculated by the perturbation method. The results by the perturbation method were significantly affected by large δλ as compared with that by the acceptance ratio method. The statistical error caused by decreasing the simulation time for sampling equilibrium configurations is discussed.
General quantum mechanical operators. An open‐ended approach for one‐electron integrals with Gaussian bases
Authors: Augspurger Joseph D. , Dykstra Clifford E.
Published: January 2005

A universal computational approach for evaluating integrals over gaussian basis functions for general operators of the form

is presented. The implementation is open‐ended with respect to the types of basis functions (s, p, d, f, g, h…) and with respect to the integers that specify the operator. These one‐electron integrals comprise operators associated with electrical and magnetic properties of molecules and include those needed to find multipole polarizabilities, multipole susceptibilities, chemical shifts, and so on. The scheme also generates the usual kinetic, nuclear attraction, and overlap operators.
Ab initio study of substituent effect on the addition of hydrogen fluoride to fluoroethylenes
Authors: Solà Miquel , Lledós Agustí , Duran Miquel , Bertrán Juan , Ventura Oscar N.
Published: January 2005

An ab initio 3‐21G study of the direct addition of HF to C2HnF(4–n), with n = 0 to 4, has been performed to investigate the effect of the substituent on the reaction. Geometry optimization of all charge‐transfer complexes and transition states has been done. Standard analysis of activation energies of addition reactions, vibrational and thermodynamical analysis, as well as Morokuma energy decomposition, BSSE correction, PMO analysis, and Pauling bond orders were used to explain the results. A subset of the reactions, including that of C2H4 as reference one and the two most favorable cases, was also studied at the MP2/6–31G(d,p)//HF/6–31G(d,p) level. The barriers so obtained are in agreement with the indirectly found from experimental data. It was found that the effect of the substituent is not monotonic for the additions. Decomposition of the interaction energy is shown to be adequate to explain this nonmonotonic behavior. The implications for laser chemistry of the addition of hydrogen halides to fluorosubstituted olefins is briefly discussed.
Derivation of net atomic charges from molecular electrostatic potentials
Authors: Woods Robert J. , Khalil Maged , Pell Wendy , Moffat Steven H. , Smith Vedene H.
Published: January 2005

The dependence of net atomic charges, as derived from least‐squares fitting to electrostatic potentials, on molecular orientation and potential site location is critically examined. A unique rotationally invariant algorithm, in which the charges may be constrained to reproduce the molecular dipole moment, is presented and the results for several basis sets compared to previous work. Significant improvements in dipole moments derived from the unconstrained charges are noted.
Variable step molecular dynamics: An exploratory technique for peptides with fixed geometry
Authors: Gibson Kenneth D. , Scheraga Harold A.
Published: January 2005

A new algorithm is presented for performing molecular dynamics simulations of peptides with fixed geometry, with the aim of simulating conformational changes and of exploring conformational space. The principle of the method is to expand the potential energy as a Taylor's series in the coordinates around the current point, retaining the force and its first two derivatives, and obtain a series solution of the resulting differential equations using a method due to Lyapunov. By choosing the time step so that the second term in the series is small compared to the first, the true solution can in principle be approximated to any desired degree of accuracy. The algorithm has been used to solve numerically Lagrange's equations of motion for N‐acetyl alanine amide and N‐acetyl methionide amide, regarded as fixed at their C‐termini, under the influence of the ECEPP/2 potential energy function, and time steps of 15–30 fsec have been achieved with little variation in the total energy. Possible directions for future development are discussed.
A new algorithm for solving large inhomogeneous linear system of algebraic equations
Authors: Ramasesha S.
Published: January 2005

An algorithm based on a small matrix approach to the solution of a system of inhomogeneous linear algebraic equations is developed and tested in this short communication. The solution is assumed to lie in an initial subspace and the dimension of the subspace is augmented iteratively by adding the component of the correction vector obtained from the Jacobi scheme on the coefficient matrix A (ATA, if the matrix A is nondefinite) that is orthogonal to the subspace. If the dimension of the subspace becomes inconveniently large, the iterative scheme can be restarted. The scheme is applicable to both symmetric and nonsymmetric matrices. The small matrix is symmetric (nonsymmetric), if the coefficient matrix is symmetric (nonsymmetric). The scheme has rapid convergence even for large nonsymmetric sparse systems.
Computing the electric potential of biomolecules: Application of a new method of molecular surface triangulation
Authors: Zauhar R. J. , Morgan R. S.
Published: January 2005

A new method is presented for defining a smooth, triangulated analytic surface for biological molecules. The surface produced by the algorithm is well‐suited for use with a recently developed polarizationcharge technique1 for the computation of the electrostatic potential of solvated molecules, and may also be used for calculations of molecular surface areas and volumes. The new method employs Connolly's definitions of contact, reentrant and saddle surface,2 but includes modifications that preclude the presence of self‐interesting reentrant surface, and also insure a rigorous decomposition of contact regions into curvilinear finite elements. The triangulation algorithm may be used in conjunction with the electrostatic methods described previously to compute the electric potential of molecules of arbitrary shape in solution. Applications include the estimation of hydration enthalpies, computation of the electrostatic forces associated with solvation, estimation of interactions between separate charged species in solution, and computation of the three‐dimensional form of the molecular electric potential. Test calculations are presented for a double‐stranded dinucleotide, the polypeptide enkephalin, and the protein ferredoxin.
Adaptation of D2hab initio computer code to higher‐symmetry point groups
Authors: Earl Edward
Published: January 2005

The imposition of symmetry in electronic structure calculations can be plagued by artifactual symmetry‐breaking in orbital or configuration amplitudes. While most ab initio computer code is well‐developed to impose symmetry constraints in D2h and its subgroups, the problem is not nearly as tractable in higher‐symmetry point groups. This article describes the successful modification of existing D2h ab initio computer code to handle symmetry constraints in higher‐symmetry point groups. Prospects for the development of ab initio computer code that runs fully under any point group are also discussed.
On the interaction of palladium with olefinic systems
Authors: Sellers Harrell
Published: January 2005

We have performed all electron Hartree–Fock gradient calculations and geometry optimizations on systems composed of one to three palladium atoms and: CH3 cation and anion, C2H4, C2H3NH2, C4H4, NH3, and (NH3) + (C2H4). Several basis set considerations are discussed and the binding energies of Pd to these small molecules are reported. We find the counterpoise correction to the binding energies of these systems to be large. We also present MP2 calculations of the palladium binding energy with a large uncontracted palladium spd basis set in the PdC2H4 and PdNH3 systems. The binding interaction between ethylene and palladium results in a mixing of the 4d–π* and 5s–π orbitals, and, is dissociative to the ethylene. The palladium‐butadiene and palladium‐cyclobutene relative stabilites and structures are interesting since these molecules could form from acetylene on a palladium surface. We find the Pd‐butadiene cyclic structure to be 43 kcal/mol more stable than the Pd‐cyclobutene product.
Combinatorial models and algorithms in chemistry. The expanded Wiener number—a novel topological index
Authors: Tratch S. S. , Stankevitch M. I. , Zefirov N. S.
Published: January 2005

An expanded form of the Wiener number is suggested for characterization of molecular graphs and structure‐property correlations. The simple, computer‐oriented method for counting of the novel index is briefly discussed.
On the use of AM1 and MNDO wave functions to compute accurate electrostatic charges
Authors: Orozco M. , Luque F. J.
Published: January 2005

A new strategy to evaluate accurate electrostatic charges from semiempirical wave functions is reported. The rigorous quantum mechanical molecular electrostatic potentials computed from both MNDO and AM1 wave functions are fitted to the point‐charge molecular electrostatic potential to obtain the electrostatic charges. The reliability of this strategy is tested by comparing the semiempirical electrostatic charges for 21 molecules with the semiempirical Mulliken charges and with the ab initio STO‐3G and 6‐31G* electrostatic charges. The ability of the dipoles derived from the semiempirical electrostatic and Mulliken charges as well as from the SCF charge distributions to reproduce the ab initio 6‐31G* electrostatic dipoles and the gas phase experimental values is determined. The statistical analysis clearly point out the goodness of the semiempirical electrostatic charges, specially when the MNDO method is used. The excellent relationships found between the MNDO and 6‐31G* electrostatic charges permit to define a scaling factor which allows to accurately reproduce the 6‐31G* electrostatic charge distribution as well as the experimental dipoles from the semiempirical electrostatic charges.
Electronic structure and photoelectron spectra of Sb2 and Sb4 from local‐spin‐density calculations. Model potential for Sb
Authors: Musolino V. , Toscano M. , Russo N.
Published: January 2005

The geometry, electronic structure, and photoelectron spectra of Sb2 and Sb4 have been investigated employing the LCGTO‐MP‐LSD method. For both molecules the geometrical and spectroscopic constants computed using the VWN potential are in very good agreement with the available experimental data. The HeI photoelectron spectra were computed with different potentials (Xα, GL, HL, BH, and VWN). The calculated spectra are in excellent agreement with the experimental ones and the use of the VWN potential gives the most accurate results. The reliable results for molecules complement those for the Sb atom and show that the proposed LSD Model Potential is able to give an accurate description of the structural and spectroscopic properties of the title molecules.
The effect of diffuse functions on minimal basis set superposition errors for H‐bonded dimers
Authors: Alagona Giuliano , Ghio Caterina
Published: January 2005

The effect of the addition of diffuse functions of sp type on the first row atoms (and/or of d type on phosphorus) to a MINI‐1 minimal basis set is evaluated by comparing the SCF description of the interaction energy and its decomposition, counterpoise (CP) corrected and uncorrected for basis set superposition errors (BSSEs), with that produced by extended basis sets (6‐31G** and 3‐21G+) as well as by basis sets (6‐31G** + VPS and (2d)S), previously successfully tested, designed to minimize the BSSE. The systems considered are a few anions (F−, HCOO−, H2PO−4) H‐bonded to water; the basis set performance on a different geometry (bifurcated instead of linear) of the phosphate‐water adduct was also considered. An additional comparison with the interaction energy in a neutral dimer, (HF)2, was carried out. The addition of diffuse functions to the MINI‐1 basis set, instead of resorting to extended basis sets, seems to be a sensible choice for anions. The equilibrium distance is shifted towards the reference basis set value at the CP corrected level as well as at the uncorrected one. The spread of the energy due to the basis set is hardly distinguishable when the CP corrected values are plotted. The description of the interaction energy in dimers involving phosphorus is improved using d type diffuse functions.
Comparative study of imidazole hydration: Ab initio and electrostatic calculations vs. Cambridge structural database analysis
Authors: Alagona Giuliano , Ghio Caterina , Nagy Péter , Simon Kálmán , Náray‐Szabo Gábor
Published: January 2005

We studied geometries and energies of complexes between water and neutral or protonated imidazole by ab initio molecular orbital calculations using the 4‐31G basis set with and without the counterpoise correction. Positions of hydration sites and relative binding energies could be also estimated by using the electrostatic field map of imidazole as calculated by our bond increment method. The reliability of the calculations is confirmed by comparing the geometries of the imidazole‐water complex to the experimental ones from the Cambridge Structural Database. These were obtained by X‐ray diffraction studies on crystals with water bound to a molecule containing the imidazole fragment.
An ab initio method for approximation of the frozen molecular fragment
Authors: Roszak S. , Hariharan P. C. , Kaufman Joyce J.
Published: January 2005

An ab initio method for calculation on many‐electron molecular systems with the approximation of the inactive part of a molecule by frozen molecular fragment is presented. In the following method the SCF calculations are performed in two series. First the molecular orbitals resulting from the first SCF calculation (modest basis set) are localized. In the second SCF run, the basis set is extended for the active part of the molecule, while molecular orbitals of the inactive part, selected from the localized set, are kept frozen. The results are in good agreement with the extended basis set calculation.
The application of molecular similarity calculations
Authors: Burt Catherine , Richards W. Graham , Huxley Philip
Published: January 2005

A prescription for applying the method of molecular similarity calculations based on electrostatic potentials and fields is developed by consideration of a typical structure‐activity series. Firm conclusions are drawn about the nature of the grid of points surrounding the molecules and about the choice of geometry, but options for point charges are less clearcut.
Four‐Index transformation on distributed‐memory parallel computers
Authors: Covick Lawrence A. , Sando Kenneth M.
Published: January 2005

Because it has 𝒪(N5) operations, a low computation to data transfer ratio, and is a compact piece of code, the four‐index transformation is a good test case for parallel algorithm development of electronic structure calculations. We present an algorithm primarily designed for distributed‐memory machines. Unlike the previous algorithm of Whiteside et al., ours is not designed with a particular architecture in mind. It is a general algorithm in the sense that not only can it be used on some common architectures but it can utilize some of the advantages inherent in each. In addition, we present formulas predicting that there would be a twofold decrease in communication time if our algorithm was used instead of that of Whiteside et al., on a square array of processors and up to an N‐fold decrease if the two algorithms were implemented on a hypercube.
The bond order—bond length relationship
Authors: Paolini John P.
Published: January 2005

The difference in length between two bond orders was reported by Pauling to be essentially the same, regardless of the atoms that make up the bond. To a first approximation these differences hold not only for bond orders 1, 2 and 3 but also for six membered aromatic rings containing all carbon, carbon‐nitrogen, nitrogen‐nitrogen, carbon‐phosphorous, carbon‐arsenic, and carbon‐antimony bonds. An equation was developed (based upon these differences) that relates bond order and bond length. The output of this equation was compared with those of Gordy and Pauling. Our equation as well as the Gordy equation (with revised constants) return a bond length of 1.4 Å for bond order 1.67 which is consistent with theory. (This bond order was not used in developing either the equation or the revised Gordy constants.)
Macromolecular dynamics on a shared‐memory multiprocessor
Authors: Skeel Robert D.
Published: January 2005

This is a study of the effect of data structures and algorithms on parallelism and vectorization for the molecular dynamics package GROMOS. About 80% of the computing time (for the GROMOS benchmark) is spent on the nonbonded interactions, and an important issue is the method that is used for finding all pairs of atoms (actually atom groups) which are within a given cutoff radius of each other. Favored by the authors of GROMOS is the use of the (Verlet) neighbor list with direct calculation of all distances. Substantial restructuring of their code for the nonbonded interactions has resulted in a speedup of a factor 6.9 for the eight‐processor Alliant FX/8 through the use of concurrent subroutine calls. Vectorization gave a further improvement of 30%. However, the direct calculation of all distances does not scale up linearly with the number of atoms. (Nor would neighbor lists be needed if cutoffs were abandoned in favor of such techniques as the fast multipole method). Therefore an alternative GROMOS subroutine that implements the “gridcell plus linked list” approach without a neighbor list was also rewritten and tested. This resulted in the discovery of an apparent flaw in an early study of the relative merits of the two algorithms. It is observed that actually the neighbor list version of GROMOS is not much faster.
A comparison of conformational energies calculated by molecular mechanics (MM2(85), Sybyl 5.1, Sybyl 5.21, and ChemX) and semiempirical (AM1 and PM3) methods
Authors: Gundertofte Klaus , Palm Jonas , Pettersson Ingrid , Stamvik Anders
Published: January 2005

Conformational energies of different conformers have been calculated for a series of molecules using various molecular mechanics and semiempirical methods. The quality of the force fields has also been tested by calculating barriers to rotation about carbon‐carbon bonds. The molecular mechanics force fields used are MM2(85), Sybyl 5.1, Sybyl 5.21, and ChemX, ver. Jan 89. The semiempirical methods used are AM1 and PM3. Molecules with different functional groups, for which good experimental data exist, have been selected. The semiempirical methods generally calculate barriers to rotation which are lower than the experimentally determined. The conformational energies for hydrocarbons are reasonably well reproduced by all tested methods although MM2(85) gives the quantitatively best agreement with experiments. For compounds containing oxygen, nitrogen and halogens MM2(85) gives results which are in best agreement with the experimentally determined values.
A complete shape characterization for molecular charge densities represented by Gaussian‐type functions
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, tested and applied for a family of AB2 molecules. 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 continuously on two 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 modeled by means of Gaussian‐type functions. The method employs an explicit form of the charge density function in order to compute the curvature properties for the molecular surfaces analytically, from which the shape groups are derived by the algorithm. 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, visual inspection of the results of the shape analysis is a possible option. For a given molecule, in a given nuclear configuration, the technique provides a two‐dimensional shape map, displaying the distribution of shape groups 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 of shape maps 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, several two‐dimensional shape maps for simple systems are discussed. The changes induced in these maps by a change in the nuclear geometry, as well as by the changes of the nuclear charge, are also analyzed. The method is applicable to large biomolecules of interest if charge density information is available.
On the ab initio geometry optimization of molecular solutes
Authors: Bonaccorsi Rosanna , Cammi Roberto , Tomasi Jacopo
Published: January 2005

We present several variants of methods for the automatic search of optimum geometries of solutes via ab initio SCF procedures. The physical meaning of geometry optimization in solution is discussed. Advantages and disadvantages of the different variants are shown making use of calculations on the HF dimer with different basis sets, supplemented by information on the computational times. Suggestions for the most convenient strategies (which in part depend on the nature of the solute) are also done.
Construction of molecular mechanics energy functions by mathematical transformation of ab initio force fields and structures
Authors: Palmö K. , Pietilä L.‐O. , Krimm S.
Published: January 2005

A method is presented by which ab initio (or empirical) force fields and structures can be converted to molecular mechanics energy parameters. Using Cartesian coordinates, the effect of van der Waals and other nonquadratic interactions is eliminated from the original spectroscopic force field, and molecular mechanics force constants and reference geometry parameters are derived. The computed parameters yield molecular structure and vibrational frequencies that are identical to the original ones. The transformation produces a complete general valence force field, which in most cases is impractical, and a procedure to reduce the number of force constants is therefore described. Different ways of applying the transformation are outlined.
Frequency dependent nonlinear optical properties of molecules: Formulation and implementation in the HONDO program
Authors: Karna S. P. , Dupuis M.
Published: January 2005

This article summarizes the detailed equations for the time‐dependent Hartree–Fock treatment of nonlinear properties for perturbations made up of a static electric field and an oscillating field. Explicit expressions for all nonlinear processes up to third order are obtained in terms of the density matrices at the same order. For processes at second and third order in perturbation, expressions in terms of lower order quantities are also obtained by applying the (2n + 1) theorem of perturbation theory. The corresponding computer implementation in the HONDO program is described.
Computation of spectroscopic properties of van der Waals systems from post‐SCF ab initio potentials including the EICP alternative counterpoise technique
Authors: Tolosa S. , Espinosa J. , del Valle F. J. Olivares
Published: January 2005

The basis set superposition error (BSSE) is studied using the Counterpoise (CP) technique at SCF and post‐SCF level in weakly bonded systems, with the aim of making manifest the overestimate introduced by the Boys and Bernardi method which does not facilitate a valid ab initio construction of potentials in van der Waals systems. The results show that the excess correction introduced by the CP method is to a large extent corrected using the version called the Indirect Counterpoise (ICP) method. The extension of this method to the exchange‐polarization and exchange‐charge transfer coupling terms provides good ab initio potentials from which quite satisfactory spectroscopic properties can be extracted.
A method for modeling icosahedral virions: Rotational symmetry boundary conditions
Authors: Çağin Tahir , Holder Michael , Pettitt B. Montgomery
Published: January 2005

We present two techniques for implementing a new method of simulating an entire virion. Earlier computer simulations of a capsid protein revealed large edge effects due to the use of free standing boundaries. Because of the size of a given protomer, conventional three‐dimensional periodic boundary conditions would be extremely wasteful. This would require an extremely large number of solvent molecules, and therefore would be computationally feasible for only a fragment of the entire virion. The new method employs non‐space‐filling computational cells in molecular modeling and molecular dynamics with the boundary conditions based on the icosahedral group. The method is general and could be used for any molecular system with a point group symmetry. With this method, the dynamical and spatial intra and interprotomer correlations can be studied at atomic levels. The technique is applicable to any virion with icosahedral symmetry. A sample calculation involving a geometry optimization of the human rhinovirus coat proteins is given to demonstrate the technique.
Atom based parametrization for a conformationally dependent hydrophobic index
Authors: Kantola Angelina , Villar Hugo O. , Loew Gilda H.
Published: January 2005

An atomic parametrization for the determination of a hydrophobicity index that depends on the molecular conformation is presented. The hydrophobicity parameter was calculated in four alternative ways based on charge densities and atomic contributions to the total molecular surface area and depending on the approach, the molecular dipole moment. The geometries required for the computations were calculated using quantum mechanical semiempirical methods as well as molecular mechanics. The charges were computed using semiempirical methods as well as the Gasteiger method.
Bond functions, covalent potential curves, and the basis set superposition error
Authors: Wright James S. , Barclay V. J.
Published: January 2005

In the current practice of quantum chemistry, it is not clear whether corrections for basis set superposition errors should be applied to the calculation of potential energy curves, in order to improve agreement with experimental data. To examine this question, spectroscopic parameters derived from theoretical potential curves are reported for the homonuclear diatomics C2, N2, O2, and F2, using a configuration interaction method. Three different basis sets were used, including double zeta plus polarization, triple zeta plus double polarization, and double zeta polarization augmented by bond functions. The bond function basis sets, which were optimized in the preceding paper to obtain accurate dissociation energies, also gave the most accurate parameters. The potential curves were then corrected for basis set superposition error using the counterpoise correction, and the spectroscopic parameters were computed again. The BSSE‐corrected curves showed worse agreement with experiment for all properties than the original (uncorrected) curves. The reasons for this finding are discussed. In addition to the numerical results, some problems in the application of the BSSE correction to basis sets containing bond functions are shown. In particular, there is an overcounting of the lowering due to the bond functions, regardless of which type of correction is applied. Also, genuine BSSE affects cannot be separated from energy‐lowering effects due to basis set incompleteness, and we postulate that it is the latter which is strongly dominant in the calculation of covalent potential curves. Based on these arguments, two conclusions follow: (1) application of BSSE corrections to potential curves should not be routinely applied in situations where the bonding is strong, and (2) appropriate use of bond functions can lead to systematic improvement in the quality of potential curves.
Effects of hydration on scale factors for ab initio force constants
Authors: Williams Robert W. , Lowrey Alfred H.
Published: January 2005

Experimentally measured vibrational frequencies from the polar groups of peptides in aqueous solutions do not agree with frequencies calculated from scaled quantum mechanical force fields (SQMFF) using differential scale factors developed for molecules in the vapor phase. Measured stretching frequencies for carbonyl groups are more than 50 wavenumbers lower than the calculated values. On the other hand, frequencies for non‐polar groups calculated using these scale factors are relatively accurate. Our goal is to develop a SQMFF that yields accurate calculated frequencies for peptides in aqueous solutions. To this end, we have calculated scale factors for ab initio force constants for formic acid, acetic acid, and acetone using a least squares fit of calculated and experimental frequencies. We compare these scale factors with changes observed in the ab initio force constants calculated for these molecules at various states of hydration. These force constants are calculated using fully optimized geometries for these hydrated molecules using the 4‐31G basis. We present a comparison of the experimental and calculated frequencies, along with their potential energy distributions, for both vapor and aqueous phases. The results indicate that scale factors can simulate the effects of solvation on molecular force constants to yield accurate scaled ab initio force fields.
A vectorized algorithm for calculating the accessible surface area of macromolecules
Authors: Wang Huajun , Levinthal Cyrus
Published: January 2005

An algorithm is presented for calculating the solvent accessible surface area of proteins using a three‐dimensional grid. Since it requires only calculations based on single atomic positions, the algorithm is easy to be vectorized. It has been implemented on ST100 and may also be implemented on supercomputers like the CRAY or the CYBER. Results on several proteins indicate that its deviation from that of the Shrake‐Rupley algorithm is very small while the computation time is much reduced.
A molecular mechanics study of conformational trends in simple alcohols and ethers. Part I: Geometric trends
Authors: Vázquez Saulo A. , Ríos Miguel A. , Carballeira Luis
Published: January 2005

We have modified the MM2(80) molecular mechanics force field for alcohols and ethers to reproduce geometric trends predicted by ab initio calculations with the 4‐21G basis set. The results obtained with the modified force field are consistent with experimental evidence.
Force field parameters for molecular mechanical simulation of dehydroamino acid residues
Authors: Alagona Giuliano , Ghio Caterina , Pratesi Claudio
Published: January 2005

Parameters suitable to describe the conformational behavior of α – β unsaturated aminoacids and peptides in the framework of an existing force field for nucleic acids and proteins (S.J. Weiner, P.A. Kollman, D.A. Case, U. Chandra Singh, C. Ghio, G. Alagona, S. Profeta, Jr., and P. Weiner, J. Am. Chem. Soc., 106, 765 (1984)) are proposed and tested. Attention is primarily focused on dehydrophenylalanine and dehydroalanine containing peptides. The values of the parameters needed were obtained from experimental measurements available in the literature and from ad hoc quantum mechanical calculations. The selected values have subsequently been adapted and refined through molecular mechanical simulations on model compounds, such as Ac‐ΔPhe‐NMe, for which it was possible to carry out STO‐3G/SCF calculations to check selected points on the ϕ,ψ conformational map, and Ac‐ΔAla‐NMe, where the comparison was carried out at the 4‐31G level. The newly determined force field was then applied to Ac‐ΔPhe‐Ala‐ΔPhe‐NMe, whose minimal energy structures allowed us to explain the different circular dichroism behavior observed in CH2Cl2 and in dioxane. Starting from two minimum energy geometries of this tripeptide, the full optimization with AM1 produced an independent guess to their structure and stability in good agreement with the molecular mechanical one.
Counterpoise corrected calculations at the correlated level: A simplified method using LMOs
Authors: Kozmutza C. , Kapuy E.
Published: January 2005

Ab initio calculations have been performed in order to investigate the counterpoise corrections, especially at the correlated level for molecular interactions. It is pointed out that, when using a localized representation, the calculations using the MBPT/MP2 method can be simplified. The H2O + H2O system was studied, with the use of 6‐31 G* basis set. The method allows one to determine the intramolecular correlation components in a simplified way. Boys' localization procedure was applied throughout, both in the occupied as well as in the virtual spaces.