Showing papers in "Journal of Computational Chemistry in 1984"

An approach to computing electrostatic charges for molecules

Abstract: We present an approach for deriving net atomic charges from ab initio quantum mechanical calculations using a least squares fit of the quantum mechanically calculated electrostatic potential to that of the partial charge model. Our computational approach is similar to those presented by Momany [J. Phys. Chem., 82, 592 (1978)], Smit, Derissen, and van Duijneveldt [Mol. Phys., 37, 521 (1979)], and Cox and Williams [J. Comput. Chem., 2, 304 (1981)], but differs in the approach to choosing the positions for evaluating the potential. In this article, we present applications to the molecules H2O, CH3OH, (CH3)2O, H2CO, NH3, (CH3O)2PO, deoxyribose, ribose, adenine, 9-CH3 adenine, thymine, 1-CH3 thymine, guanine, 9-CH3 guanine, cytosine, 1-CH3 cytosine, uracil, and 1-CH3 uracil. We also address the question of inclusion of “lone pairs,” their location and charge.

Group equivalents for converting ab initio energies to enthalpies of formation

Abstract: Group equivalents which are useful for converting energies derived from ab initio calculations into enthalpies of formation have been obtained. They allow ΔHf to be estimated from 6-31G* energies with an uncertainty on the order of ±2 kcal/mol.

Molecular mechanics force‐field parameterization procedures

Abstract: A set of procedures and guidelines are presented for the estimation of bond length, bond angle, and torsional potential constants for molecular mechanics force fields. The force field constants are ultimately derived by “subtracting” nonbonded molecular mechanics energies from corresponding molecular orbital energies using a model compound containing the chemical structure to be parameterized. Case study examples of bond length, bond angle, and torsional rotation force field parameterizations are presented. A general discussion of molecular mechanics force field parameterization strategy is included for reference and completeness. Finally, a curve-fitting program to generate force field parameters from raw data is given in Appendix I.

Discrimination of isomeric structures using information theoretic topological indices

Abstract: Three newly defined information theoretic topological indices, namely “degree complexity (Id),” “graph vertex complexity (HV),” and “graph distance complexity (HD)” along with three other information indices have been used to study their discriminating power of 45 trees and 19 monocyclic graphs. It is found that the newly defined indices have satisfactory discriminating power while HD has been found to be the only index to discriminate all the graphs studied.

A combinatorial algorithm for calculating ligand binding

Abstract: We consider the problem of predicting the mode of binding of a small molecule to a receptor site on a protein. One plausible approach, given a rigid molecule and its geometry, is to search directly for the orientation in space that maximizes the degree of contact. The computation time required for such a naive procedure is proportional to n3m3, where n is the number of points in the site where binding can occur, and m is the number of atoms in the ligand. We give an alternative, combinatorial approach, in which only “contact–no‐contact” criteria are considered. We relate this problem to the well‐known combinatorial problem of finding cliques in a graph and show that we can use a solution to the clique problem not only to solve our original problem, but also the problem of avoiding energetically unfavorable matches. Our experience with this method indicates that the computation time required is proportional to nm2.8, with a lower constant of proportionality than that of the naive procedure.

A molecular mechanics treatment of the anomeric effect

Abstract: The tendency of CO bond lengths to change as a function of the torsional angles at an acetal carbon has been included in a new version of the molecular mechanics program MM2(82), based on the observed behavior of molecules of this class as indicated by ab initio calculations and experimental structural data. The experimental geometries and energies are reasonably well reproduced.

Compact contracted Gaussian‐type basis sets for halogen atoms. Basis‐set superposition effects on molecular properties

Abstract: Compact, contracted Gaussian basis sets for halogen atoms are generated and tested in ab initio molecular calculations. These basis sets have similar structure to that of Huzinaga and co-workers' (HTS) sets; however, they give both better atomic total energies and better properties of atomic valence orbitals. These sets, after splitting of valence orbitals and augmenting with polarization functions, provide molecular results that agree well with those given by extended calculations. Basis set superposition error (BSSE) is calculated using the counterpoise method. BSSE has only slight influence on calculated equilibrium geometry, shape of potential curve, and electric properties (dipole and quadrupole moments) of molecules. However, atomization energies may be significantly changed by the BSSE.

Optimized monopole expansions for the representation of the electrostatic properties of the nucleic acids

Abstract: Optimized monopole expansions for the subunits of the nucleic acids are developed by a reparametrizatio of the Huckel–Del Re procedure designed to reproduce closely the electrostatic properties obtained with precise overlap multipole expansions. It is shown that satisfactory values of both potential and field may be obtained for different DNA conformations and for a transfer RNA. The charge redistribution occuring between the subunits upon forming the nucleic acids is also investigated by ab initio calculations and accounted for in developing the new parametrization.

On searching neighbors in computer simulations of macromolecular systems

Abstract: Various algorithms for evaluating nonbonded interactions in molecular dynamics (MD) simulations of macromolecular systems are considered, and a combination of two techniques using a space grid for finding neighbor atoms is proposed. The application of grid search techniques to nonrectangular periodic systems is discussed. Finally, the computing time required by different algorithms is compared on a Cray-1 vector processing computer as well as on a CDC Cyber 170/760 sequential computer. Neighbor list techniques turn out to be faster than the grid search techniques for the systems considered here. However, storage requirements may exclude the use of neighbor list techniques for large systems. Finally, MD of complex macromolecular systems turned out to be about 4–14 times faster on a Cray-1 than on a Cyber 170/760.

Use of molecular symmetry in two-electron integral transformation An MP2 program compatible with HONDO 5

Abstract: A computer program is described which evaluates the second-order Moller-Plesset energy using the integral list formed by HONDO 5. In this program use may be made of full molecular symmetry for most common point groups, even if they contain two-dimensional representations. The algorithm for the integral transformation may also be applied to other methods beyond Hartree-Fock. Some numerical results and timings are presented.

A unified treatment of valence and bond order from density operators

Abstract: A generalization of the quantum chemical definition of valence of atoms in molecules is suggested. Valence is considered as expectation value of diatomic parts of density operators. It appears as a sum of contributions from occupied orbitals of all atomic pairs that contain the reference atom. This definition is applicable on self-consistent-field (SCF) and configuration interaction (CI) level in any atomic orbitals (AO) basis. Its usefulness is demonstrated in an application to special molecules. Photoelectron spectroscopy and reactivity is discussed in this context.

Computer generation of the characteristic polynomials of chemical graphs

Abstract: A computer program based on the Frame method for the characteristic polynomials of graphs is developed. This program makes use of an efficient polynomial algorithm of Frame for generating the coefficients in the characteristic polynomials of graphs. This program requires as input only the set of vertices that are neighbors of a given vertex and with labels smaller than the label of that vertex. The program generates and stores only the lower triangle of the adjacency matrix in canonical ordering in a one-dimensional array. The program is written in integer arithmetic, and it can be easily modified to real arithmetic. The coefficients in the characteristic polynomials of several graphs were generated in less than a few seconds, thus solving the difficult problem of generating characteristic polynomials of graphs. The characteristic polynomials of a number of very complicated graphs are obtained including for the first time the characteristic polynomial of an honeycomb lattice graph containing 54 vertices.

Evaluation of MNDO calculated proton affinities

Abstract: A large set of charged species arising mainly from protonation or deprotonation of hydrocarbons, alcohols, ethers, carboxylic acids, amines, imines, and nitriles has been studied by means of the semiempirical self‐consistent‐field (SCF) molecular orbital (MO) MNDO method. From the calculated heats of formation of such charged species and those of neutral molecules, MNDO‐estimated proton affinities have been obtained and the results compared with experimental gas‐phase proton affinities. If the small size anions and acetylides, for which the method predicts heats of formation too large, are ruled out, the mean absolute error in calculated proton affinities is ca. 7 kcal/mol for hydrocarbons (22 acid‐base pairs) and ca. 8 kcal/mol for oxygen‐containing compounds (25 acid‐base pairs). For nitrogen‐containing molecules it is necessary to discard, in addition, the values corresponding to the protonation of alkylamines and imines in order to achieve a reasonable mean absolute error of 7–8 kcal/mol.

An appraisal of molecular force fields for the representation of polypeptides

Abstract: A number of force fields of the molecular mechanics type have been tested for their ability to represent as an energy minimum, the observed crystal structure for three cyclic hexapeptides, cyclo-(-Ala-Ala-Gly-Gly-Ala-Gly-), cyclo-(-Ala-Ala-Gly-Gly-Ala-Gly-), and cyclo-(-D-Ala-D-Ala-Gly-Gly-Gly-Gly-). The most effective force field tested was that recently proposed by Kollman and co-workers, notwithstanding its use of “united” atoms for CH, CH2, and CH3 groups. Fields proposed by Levitt, and adaptations of that of Scheraga and co-workers, were also effective. Force fields in which hydrogens bonded to electronegative atoms were not specified explicitly were less accurate in representation.

Theoretical analysis of gramicidin A transmembrane channel. II. Energetics of helical librational states of the channel

Abstract: The degrees of conformational freedom of poly L–D β-helical chain are analyzed consistent with the helical parameters of gramicidin A structure. From conformational energy calculations, “helical librations” that can be sustained by this structure are described and the energy of libration as a function of the cavity size is presented. Two different modes of conformational change are identified corresponding to librations of all L–D-peptide units or all D–L-peptide units while retaining the helical parameters. Such helical librations are considered relative to conformational perturbations due to the presence of an ion in the channel.

The Lagrange multiplier method for manipulating geometries. Implementation and applications in molecular mechanics

Abstract: It is shown that a Lagrange multiplier method to constrain one or several internal coordinates, or averages and combinations of these, is easily implemented in a molecular mechanics computer program that uses Newton–Raphson (NR) minimization. Results are given for constraints on nonbonded distances and torsion angles. When a potential energy surface is to be explored, it is much better to constrain the average of three torsion angles around a bond than to constrain a single torsion angle. Certain conversions can only be achieved when averages of torsion angles around different bonds are constrained. Combinations of constraints have been applied to evaluate differences between calculated and observed geometries and to obtain transition states for relatively large molecules from results for smaller molecules at relatively low costs. The efficieny of the combination of the Lagrange multiplier method and NR minimization in terms of computing time can be rated as good.

MNDO study of catenated sulfur: The molecules and ions S3 to S8

Abstract: Semiempirical molecular orbital calculations by the MNDO method are reported for sulfur rings and chains S3 through S8, for the corresponding dications, S through S, and for S. The MNDO method seems quite successful in predicting the geometries of neutral catenated sulfur molecules, even the unusual bond-length alternation and extent of coplanarity in cyclo-S7. In contrast to hydrocarbon rings, for which its prediction of strain is erratic, MNDO is consistent in its calculated strain energies in small cyclosulfur rings; unfortunately all the strain energies are overestimated by 70%. As a consequence of this error, the method must be considered unreliable in its predictions of structures for the dications S, since many of these ions could potentially exist as strained bicyclic systems. In addition, MNDO appears to have difficulty handling long, partial SS σ bonds, as are found to occur in S. It may be for this reason that MNDO predicts, apparently incorrectly, that the open-chain isomers of S are more stable than are any of the cyclic forms, at least for S to S. With respect to neutral Sn molecules, however, the MNDO predictions appear more reliable than ab initio molecular orbital (MO) calculations using small basis sets without polarization functions and without configuration interaction (CI). However, MNDO apparently underestimates by about a factor of two the strength of the three-electron π bonds present in the terminal links of sulfur diradical chains.

Calculation of energies of excited states using MNDO

Abstract: The energies of the lowest singlet (S1) and triplet (T1) states of 28 molecules have been calculated by the “half-electron” (MNDO-HE) and spin-unrestricted (UMNDO) versions of MNDO. While most of the calculated values are too negative, because of overestimation of the correlation energy in MNDO-HE and UMNDO, the errors are systematic and depend in an understandable way on the nature of the molecular orbitals (MOS) involved. When appropriate corrections are applied, the calculated energies agree with experiment almost as well as they do for ground states. This justifies the use of MNDO-HE or UMNDO for studies of excited state processes.

Ab initio calculations of the electronic structure of helical polymers

Abstract: An ab initio self-consistent-field (SCF) algorithm taking into account all the features of the one-dimensional translational periodicity and the helical symmetry is presented. This algorithm includes the long-range correction to the Coulomb potential and is designed to calculate the band structure of periodic one-dimensional polymers (planar or helical). Its efficiency in terms of computing time and numerical accuracy is tested via applications on a (LiH)n chain, polyethylene, and four conformers of polypropylene.

Analytical MCSCF energy gradients: Treatment of symmetry and CASSCF applications to propadienone

Abstract: The formula for the first derivative of the MCSCF energy with respect to a nuclear coordinate is reviewed. The efficient utilization of symmetry in programs employing symmetry-adapted basis functions is described: Advantages that are also obtained for higher derivatives and for gradients of nonself-consistent wave functions are briefly discussed. Using CASSCF wave functions, the method is applied to the question of nonlinearity in the heavy atom chain of propadienone (CH2CCO).

A monotone iterative technique for solution of pth order (p < 0) reaction‐diffusion problems in permeable catalysis

Abstract: The problem of determining the amount of reactant present in the steady state of a reaction‐diffusion problem with pth order reaction kinetics and slab geometry can be achieved by solving the boundary value problem \\documentclass{article}\\pagestyle{empty}\\begin{document}$$ \\begin{array}{l} u''(x) = \\phi ^2 u^p (x),\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,{\\rm 0 < }x{\\rm < 1} \\\\\\\\ u'(0) = 0{\\rm }\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,u(1) = 1 \\\\ \\end{array} $$\\end{document} where u is a normalized (dimensionless) concentration, and ϕ is the Thiele modulus. By considering the related nonlinear eigenvalue problem \\documentclass{article}\\pagestyle{empty}\\begin{document}$$ \\begin{array}{l} y''(x) = \\lambda y^p (x),\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,{\\rm 0 < }x{\\rm < 1, }\\,\\,\\,\\,\\,\\,\\,p{\\rm < 0} \\\\\\\\ y'(0) = 0,{\\rm }\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,y(1) - y'(1) = 0 \\\\ \\end{array} $$\\end{document} and constructing a sequence of functions that converges monotonically to y(x), solutions of the original boundary value problem are obtained for the negative exponent case.

Approaches to charge calculations in molecular mechanics. 2 Resonance effects in conjugated systems

Abstract: A previously published scheme of estimating atomic charges in haloalkanes is extended to include olefines, alcohols amines, acids, ethers, and amides. In the conjugated systems the effects of mesomeric transfer of charge are explicitly included. Generally good agreement with the observed dipole moments of these compounds and their substituted derivatives is found. The atomic charges so obtained are compared with those of other semiempirical and quantum-mechanical calculations for the amide group. The charges so obtained fall within the range of values obtained by these other schemes, supporting the general validity of this approach.

Examination of formamide, formamidic acid, amidine dimers, and the double proton transfer transition states involving these dimers

Abstract: Structures and relative energies were obtained for the hydrogen bonded dimers of formamide and formamidic acid using the 3-21G basis set. A double proton transfer transition state is claimed to link these two dimers. While the structure of the transition state was intermediate between those of the two dimers, the energy was only 7.6 kJ/mol greater than the less stable formamidic acid dimer. The activation energy from the formamide dimer side of the reaction was found to be 125 kJ/mol of dimer. A similar transition state was found for the amidine dimer system. The activation energy for this model reaction was found to be 66.9 kJ/mol of dimer.

Substituent effects in second‐row molecules: Basis set performance in calculations of normal valency phosphorus and sulfur compounds

Abstract: Ab inito molecular orbital calculations of the phosphorus- and sulfur-containing series PH2X, PH3X+, SHX, and SH2X+ (X = H, CH3, NH2, OH, F) have been carried out over a range of Gaussian basis sets and the results (optimized geometrical structures, relative energies, and electron distributions) critically compared. As in first-row molecules there are large discrepancies between substituent interaction energies at different basis set levels, particularly in electron-rich molecules; use of basis sets lower than the supplemented 6-31G basis incurs the risk of obtaining substituent stabilizations with large errors, including the wrong sign. Only a small part of the discrepancies is accounted for by structural differences between the optimized geometries. Supplementation of low level basis sets by d functions frequently leads to exaggerated stabilization energies for π-donor substituents. Poor performance also results from the use of split valence basis sets in which the valence shell electron density is too heavily concentrated in diffuse component of the valence shell functions, again likely to occur in electron-rich molecules. Isodesmic reaction energies are much less sensitive to basis set variation, but d function supplementation is necessary to achieve reliable results, suggesting a marginal valence role for d functions, not merely polarization of the bonding density. Optimized molecular geometries are relatively insensitive to basis set and electron population analysis data, for better-than-minimal bases, are uniform to an unexpected degree.

Ab initio studies on polymers. VI. Torsional potential in regular polyethylene chains

Abstract: Ab initio crystal orbital calculations have been performed on regular polyethylene chains applying basis sets of minimal and double-zeta quality. Relative stabilities of periodic all-trans, all-gauche, and alternating trans–gauche conformers have been evaluated, including extensive geometry optimization. Potential curves for a simultaneous rotation around CC single bonds from the all-trans to the all-gauche conformation have been computed applying the rigid-rotor approximation, the flexible-rotor approximation, and an additional reoptimization of CC distances. A rigid-rotor potential curve from the all-trans to the alternating trans-gauche conformation has been computed as well. Results obtained are compared with ab initio calculations on butane and pentane and with semiempirical and empirical force-field studies on polyethylene.

Geometry, basis set, and correlation energy dependence of computed protonation energies of imino bases

Abstract: Etude de ces influences sur l'energie de protonation a l'azote de HN=CHR avec R=H, CH 3 , NH 2 , OK ou F

The value of the π‐bond order–bond length relationship in geometry prediction and chemical bonding interpretation

Abstract: The π-bond order–bond length relationship is reintroduced to the literature and extended to heteronuclear bonds by presenting graphs derived solely by theoretical methods. π-bond order and overlap population results for carbon–carbon, carbon–nitrogen, and carbon–oxygen bonds obtained from ab initioSTO-3G calculations using theoretically-optimized geometries are reported for a series of pteridines and for a wide range of small organic molecules. The order–length correlation graphs are used in predicting the “intrinsic” single bond lengths for sp2 – sp2 and sp – sp hybridized CC, CN, and CO bonds, and in evaluating the relative importance of hybridization, π-electron delocalization and bond polarization effects in causing bond shortening in conjugated and hyperconjugated molecules. The calculated value of the π-bond order for a given bond in a molecule is shown to be relatively insensitive to moderate geometry changes: Hence, a use for the correlation graphs in geometry prediction is suggested. Some results for the extended 4-21G basis set are also presented.

Remarks on the analysis of torsional energy surfaces of cycloheptane and cyclooctane by molecular mechanics

Abstract: A modified version (MM2′) of the Allinger's 1977 force field is checked against cycloheptane and cyclooctane. Cycloheptane is characterized by two pseudorotating itineraries, chair/twist-chair and boat/twist-boat, separated by a barrier of 8.5 kcal mol−1. The activation energy in the C/TC pseudorotation is estimated to be 0.96 kcal mol−1, while B and TB transform into each other freely at an energy level 3.8 kcal mol−1 above the global energy minimum (TC). With cyclooctane the lowest energy is calculated for the boat-chair form which participates in a pseudorotational process with TBC through a saddle point lying 3.5 kcal mol−1 above BC. The chair/chair and boat/boat families contain only one local minimum, crown and BB, respectively, on the MM2′ surface. The results are presented as an illustration for quick coverage of torsional energy surface by two-bond driver calculation with the block-diagonal Newton–Raphson minimization, followed by the force search of stationary points by full-matrix Newton–Raphson optimization.

Unique description of chemical structures based on hierarchically ordered extended connectivities (HOC procedures). V. New topological indices, ordering of graphs, and recognition of graph similarity

Abstract: The vertex numbering obtained by application of the HOC algorithm can be converted into two sequences of numbers: If each vertex starting with vertex 1 is only counted once, the sums of numberings of adjacent vertices form sequence S, (i = 1-N), while the sums of S, values form sequence MI (i = 1-N). These two sequences can be used for (i) two new topological indices, and N, the latter being of extremely low degeneracy, and the former correlating with boiling points of alkanes; (ii) a criterion based on sequence S, for ordering graphs which possess the same number N of vertices; and (iii) a quantitative measure, also based on sequence S,, for appreciating the similarity or dissimilarity of pairs of graphs. Comparisons with other topological indices, ordering criteria, and similarity measures for graphs show that the newly devised procedures compare favorably with those known previously.

MNDO Study of reaction pathways for SN2 reactions. Menschutkin reaction potential energy surfaces

Abstract: MNDO molecular orbital calculations have been employed to investigate limited reaction pathways and potential energy surfaces for a series of SN2 reactions. Model calculations for X− + CH3X (X = H, F, OH, OCH3, and CN) indicate that the MNDO method gives qualitative agreement with ab initio studies except for the hydride–CH4 exchange. Studies involving alkylation of pyridine (Menschutkin reaction) were also carried out. For the reaction of pyridine with CH3Cl, which involves charge separation, our MNDO studies (which do not include solvation effects) do not produce a characteristic SN2 pathway. For the reaction of pyridine with trimethyloxonium cation [(CH3)3O+] as the alkylating agent, a well defined SN2 reaction pathway was obtained; this reaction involves charge transfer. A potential energy surface for the pyridine–trimethyloxonium cation reaction shows the presence of a saddle point transition state that resembles starting materials, in agreement with the Hammond postulate for this exothermic reaction.