Cubic-grid Gaussian basis sets for electron scattering calculations. I. Definition and construction

We propose a new type of Gaussian basis sets for use in calculations of electron scattering by molecules. Instead of locating the basis-set functions on the atomic centers of the target molecule, we place primitive s-type Gaussians at the positions of a cubic lattice with a regular grid. The grid and the Gaussian exponent are fixed so as to give the best representation of the plane-wave function. Plane-wave functions and Green functions obtained by means of the cubic-grid basis set are tested graphically against exact functions and functions expressed by means of a conventional Gaussian basis set. © 1995 John Wiley & Sons, Inc.     

Efficient computation of the exchange-correlation contribution in the density functional theory through multiresolution

A new algorithm is presented to improve the efficiency of the computation of exchange-correlation contributions, a major time-consuming step in a density functional theory (DFT) calculation. The new method, called multiresolution exchange correlation (mrXC), takes advantage of the variation in resolution among the Gaussian basis functions and shifts the calculation associated with low-resolution (smooth) basis function pairs to an even-spaced cubic grid. The cubic grid is much less dense in the vicinity of the nuclei than the atom-centered grid and the computation on the former is shown to be much more efficient than on the latter. MrXC does not alter the formalism of the current standard algorithm based on the atom-centered grid (ACG), but instead employs two fast and accurate transformations between the ACG and the cubic grid. Preliminary results with local density approximation have shown that mrXC yields three to five times improvement in efficiency with negligible error. The extension to DFT functionals with generalized gradient approximation is also briefly discussed.     

Similarity searching in files of three-dimensional chemical structures: Representation and searching of molecular electrostatic potentials using field-graphs

This paper reports a method for the identification of those molecules in a database of rigid 3D structures with molecular electrostatic potential (MEP) grids that are most similar to that of a user-defined target molecule. The most important features of an MEP grid are encoded in field-graphs, and a target molecule is matched against a database molecule by a comparison of the corresponding field-graphs. The matching is effected using a maximal common subgraph isomorphism algorithm, which provides an alignment of the target molecule's field- graph with those of each of the database molecules in turn. These alignments are used in the second stage of the search algorithm to calculate the intermolecular MEP similarities. Several different ways of generating field-graphs are evaluated, in terms of the effectiveness of the resulting similarity measures and of the associated computational costs. The most appropriate procedure has been implemented in an operational system that searches a corporate database, containing ca. 173,000 3D structures.     

A second quantization formulation of multimode dynamics

A new formalism for calculating and analyzing many-mode quantum dynamics is presented. The formalism is similar in spirit to the second quantization formulation of electronic structure theory. The similarity means that similar techniques can be employed for calculating the many-mode nuclear wave function. As a consequence a new formulation of the vibrational self-consistent-field (VSCF) method can be developed. Another result is that the formalism opens up for the construction of new methods that go beyond the VSCF level. A vibrational coupled cluster (VCC) theory is constructed using the new formalism. The size-extensivity concept is introduced in the context of multimode wave functions and the size extensivity of approximate VCC methods is illustrated in comparison with the non-size-extensive vibrational configuration interaction method.     

Model calculation of the spin density for trapped muonium in ionic solids

A previously developed perturbation formula for calculating the spin density of trapped normal muonium in diamond is applied to the trapped muonium in the ionic solids of MgO, KCl and KBr. To obtain an improved molecular electrostatic potential (MEP) inside the cubic lattice, we performed MO calculations using clusters of MgO, KCl and KBr with additional surrounding point charges. Calculated spin densities (ƒ-values) in these potentials are compared with experimental results. We also report ab initio UHF MO calculations for these clusters with a trapped hydrogen atom at the centre of the clusters.     

Atomic dipole moments calculated using analytical molecular second-moment gradients

We have implemented analytical second-moment gradients for Hartree-Fock and multiconfigurational self-consistent-field wave functions. The code is used to calculate atomic dipole moments based on the generalized atomic polar tensor (GAPT) formalism [Phys. Rev. Lett. 62, 1469 (1989)], and the proposal of Dinur and Hagler (DH) for the calculation of atomic multipoles [J. Chem. Phys. 91, 2949 (1989)]. Both approaches display smooth basis-set convergence toward a well-defined basis-set limit and give reasonable electron correlation effects on the calculated atomic properties. However, the atomic charges and atomic dipole moments obtained from the GAPT partitioning scheme are unable to provide even qualitatively meaningful molecular quadrupole moments for some molecules, and thus the atomic multipole moments calculated in this scheme cannot be considered well suited for analyzing the electron density in molecules and for calculating intermolecular interaction energies. In contrast, the DH approach gives atomic charges and dipole moments that by definition exactly reproduce the molecular quadrupole moments. The approach of DH is, however, restricted to planar molecules and thus suffers from not being applicable to molecules of arbitrary shape. Both the GAPT and DH approaches give rather poor results for octupole and hexadecapole moments, indicating that at least atomic quadrupole moments are required for an accurate representation of the molecular charge distribution in terms of atomic electric moments.     

Improved intermolecular force field for crystalline oxohydrocarbons including O?HO hydrogen bonding

An improved intermolecular force field of the (exp‐6‐1) type was obtained by fitting a training set of 124 observed oxohydrocarbon crystal structures and seven observed heats of sublimation. All of these structures, when energy minimized, showed cell edge length shifts of 3% or less. Especially good results were obtained for modeling carbohydrate crystal structures. The fitted crystal structures are a subset of a database of 180 structures systematically selected from the CSD library according to functional group and threshold accuracy criteria. Energy minimization results are also presented for 56 structures not in the training set, which showed cell edge length shifts larger than 3%. The previously published W99 force field, using C(4), C(3), and H(1) potentials, was slightly modified and adopted for hydrocarbon portions of the molecules. Oxygen atoms with one bond, O(1), and those with two bonds, O(2), were assigned separate parameters. Hydrogen atoms bonded to oxygen were assigned exponential repulsion functions and divided into two types: in hydroxy groups, H(2); and in carboxyl groups, H(3). Wavefunctions of HF 6‐31g** quality were calculated for every molecule and the molecular electric potential (MEP) was modeled with net atomic charges. Methylene bisector charges were used for all CH₂ and CH₃ groups, and ring center site charges were added if necessary to fit the MEP. For some structures, upward scaling of the MEP to simulate intermolecular polarization gave better results. MEP interaction generally gave a satisfactory representation of weak C HO hydrogen bonding. Medium strength C HO hydrogen bonding was modeled by reducing the repulsion of the involved hydrogen atoms. Crystal structures of several biologically interesting molecules were modeled with the force field, yielding good results. These molecules include aspirin, sucrose, β‐cellobiose, β‐lactose, progesterone, testosterone, prostaglandin E1, cholesterol acetate, and stearic acid. © 2000 John Wiley & Sons, Inc. J Comput Chem 22: 1–20, 2001     

Suitability of the PM3-derived molecular electrostatic potentials

A systematic study of the suitability of PM3-derived molecular electrostatic potentials (MEPs) is presented. Forty-six MEP minima, 81 electrostatic charges, and 17 electrostatic dipoles were determined at the PM3 level and compared with those obtained from the ab initio 6-31G* wave function, as well as from the semiempirical MNDO and AM1 wave functions. The statistical results of the comparison analysis between semiempirical and ab initio 6-31G* MEPs show that PM3 is in general reliable for the study of the MEP minima but a mediocre method as a source of electrostatic charges. © 1993 John Wiley & Sons, Inc.     

Hyperspherical slow variable discretization method for weakly bound triatomic molecules

We develop a method for calculating the bound state energies and the wave functions of weakly bound triatomic molecular systems. The method is based on the use of hyperspherical coordinates, combined with the slow variable discretization approach. The finite-element methods-discrete variable representation scheme provides an efficient means to solve the coupled-channel hyper-radial equations. Our method is applied to searching for bound states of the (20)Ne(2)H and (4)He(20)NeH triatomic molecules, using the best empirical pairwise interaction potentials. We consider not only zero total nuclear orbital momentum, J = 0, states but also J > 0 states. The (20)Ne(2)H system has been found to possess one bound state each for the J(Π)=0(+),1(-), and 2(+) symmetries, while there exist only one bound state for the (4)He(20)NeH system in the 0(+) symmetry. We shall calculate the bound state energies and analyze the molecular structures of these species in detail.     

Suitability of density functional methods for calculation of electrostatic properties

A systematic analysis was performed on the suitability of the molecular electrostatic potential (MEP) and MEP-derived properties determined by means of density functional (DFT) methods. Attention was paid to the electrostatic potential (ESP) derived charges, the ESP and exact quantum mechanical dipole moments, the depth of MEP minima, and the MEP distribution in layers around the molecule for a large series of molecules. The electrostatic properties were determined at either local or nonlocal DFT levels using different functionals. The results were compared with the values estimated from quantum mechanical calculations performed at Hartree–Fock, Møller–Plesset up to fourth order, and CIPSI levels. The suitability of the MEP-derived properties estimated from DFT methods is discussed for application in different areas of chemical interest. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 980–991, 1997     

Mapped grid methods for long-range molecules and cold collisions

The paper discusses ways of improving the accuracy of numerical calculations for vibrational levels of diatomic molecules close to the dissociation limit or for ultracold collisions, in the framework of a grid representation. In order to avoid the implementation of very large grids, Kokoouline et al. [J. Chem. Phys. 110, 9865 (1999)] have proposed a mapping procedure through introduction of an adaptive coordinate x subjected to the variation of the local de Broglie wavelength as a function of the internuclear distance R. Some unphysical levels ("ghosts") then appear in the vibrational series computed via a mapped Fourier grid representation. In the present work the choice of the basis set is reexamined, and two alternative expansions are discussed: Sine functions and Hardy functions. It is shown that use of a basis set with fixed nodes at both grid ends is efficient to eliminate "ghost" solutions. It is further shown that the Hamiltonian matrix in the sine basis can be calculated very accurately by using an auxiliary basis of cosine functions, overcoming the problems arising from numerical calculation of the Jacobian J(x) of the R-->x coordinate transformation.     

Energy‐linearized variational cellular method for large molecules and solids

Multiple scattering theory (MST) is the mainstay of Kohn–Sham calculations of the electronic structure of solids and alloys. MST formalism solves one‐electron equations within each atomic cell, using a Green function to propagate solutions across cell boundaries, while standard methodology for molecules expands wave functions in a Gaussian orbital basis. An energy‐linearized version of MST (LMTO) is efficient but restricted to an atomic‐sphere model. Full‐potential MST extends the formalism to space‐filling Wigner–Seitz polyhedra. The variational cellular method (VCM) solves full‐potential equations, replacing Green‐function propagation (structure constants) by variational matching at the interfaces of adjacent atomic cells. VCM provides a common formalism for molecules and solids but cannot easily be converted to an energy‐linearized method. A new variational principle is derived here that extends the VCM to a straightforward procedure for energy linearization. This formalism eliminates false solutions from the VCM. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

The MIDI! basis set for quantum mechanical calculations of molecular geometries and partial charges

We present a series of calculations designed to identify an economical basis set for geometry optimizations and partial charge calculations on medium-size molecules, including neutrals, cations, and anions, with special emphasis on functional groups that are important for biomolecules and drug design. A new combination of valence basis functions and polarization functions, called the MIDI! basis set, is identified as a good compromise of speed and accuracy, yielding excellent geometries and charge balances at a cost that is as affordable as possible for large molecules. The basis set is optimized for molecules containing H, C, N, O, F, P, S, and Cl. Although much smaller than the popular 6-31G* basis set, in direct comparisons it yields more accurate geometries and charges as judged by comparison to MP2/cc-pVDZ calculations.     

MEPSIM: A computational package for analysis and comparison of molecular electrostatic potentials

Summary MEPSIM is a computational system which allows an integrated computation, analysis, and comparison of molecular electrostatic potential (MEP) distributions. It includes several modules. Module MEPPLA supplies MEP values for the points of a grid defined on a plane which is specified by a set of three points. The results of this program can easily be converted into MEP maps using third-parties graphical software. Module MEPMIN allows to find automatically the MEP minima of a molecular system. It supplies the cartesian coordinates of these minima, their values, and all the geometrical relationships between them (distances, angles, and dihedral angles). Module MEPCOMP computes a similarity coefficient between the MEP distributions of two molecules and finds their relative position that maximizes the similarity. Module MEPCONF performs the same process as MEPCOMP, considering not only the relative position of both molecules but also a conformational degree of freedom of one of them. The most recently developed module, MEPPAR, is another modification of MEPCOMP in order to compute the MEP similarity between two molecules, but only taking into account a particular plane. The latter module is particularly useful to compare MEP distributions generated by systems of aromatic rings. MEPSIM can use several wavefunction computation approaches to obtain MEP distributions. MEPSIM has a menu type interface to simplify the following tasks: creation of input files from output files of external programs (GAUSSIAN and AMPAC/MOPAC), setting the parameters for the current computation, and submitting jobs to the batch queues of the computer. MEPSIM has been coded in FORTRAN and its current version runs on VMS/VAX computers.     

Using inverted indices for accelerating LINGO calculations

The ever growing size of chemical databases calls for the development of novel methods for representing and comparing molecules. One such method called LINGO is based on fragmenting the SMILES string representation of molecules. Comparison of molecules can then be performed by calculating the Tanimoto coefficient, which is called LINGOsim when used on LINGO multisets. This paper introduces a verbose representation for storing LINGO multisets, which makes it possible to transform them into sparse fingerprints such that fingerprint data structures and algorithms can be used to accelerate queries. The previous best method for rapidly calculating the LINGOsim similarity matrix required specialized hardware to yield a significant speedup over existing methods. By representing LINGO multisets in the verbose representation and using inverted indices, it is possible to calculate LINGOsim similarity matrices roughly 2.6 times faster than existing methods without relying on specialized hardware.     

Modeling vibrational spectra using the self-consistent charge density-functional tight-binding method. I. Raman spectra

An extension of the self-consistent charge density-functional tight-binding (SCC-DFTB) method is presented that allows for calculating intensities of peaks in vibrational Raman spectra for very large molecules. The extension is based on a simple ansatz: an extra term, which describes interaction of an external electric field with induced atomic charges, is added to the SCC-DFTB energy expression. We apply the modified SCC-DFTB formalism for reproducing vibrational Raman spectra of 17 organic molecules. The calculated spectra are compared with experiment and with spectra obtained from density functional theory (DFT) calculations. We find that the SCC-DFTB method is capable of reproducing most of the features of experimental Raman spectra. Limitations and advantages of this approach are analyzed and suggestions for interpreting calculated SCC-DFTB Raman spectra are given.     

Class IV charge models: A new semiempirical approach in quantum chemistry

Summary We propose a new criterion for defining partial charges on atoms in molecules, namely that physical observables calculated from those partial charges should be as accurate as possible. We also propose a method to obtain such charges based on a mapping from approximate electronic wave functions. The method is illustrated by parameterizing two new charge models called AM1-CM1A and PM3-CM1P, based on experimental dipole moments and, respectively, on AM1 and PM3 semiempirical electronic wave functions. These charge models yield rms errors of 0.30 and 0.26 D, respectively, in the dipole moments of a set of 195 neutral molecules consisting of 103 molecules containing H, C, N and O, covering variations of multiple common organic functional groups, 68 fluorides, chlorides, bromides and iodides, 15 compounds containing H, C, Si or S, and 9 compounds containing C-S-O or C-N-O linkages. In addition, partial charges computed with this method agree extremely well with high-level ab initio calculations for both neutral compounds and ions. The CM1 charge models provide a more accurate point charge representation of the dipole moment than provided by most previously available partial charges, and they are far less expensive to compute.     

Analytic calculation of isotropic hyperfine structure constants using the normalized elimination of the small component formalism

Based on the normalized elimination of the small component relativistic formalism, a new approach to the calculation of hyperfine structure parameters of paramagnetic molecules is developed and implemented. The new method is tested in the calculation of the isotropic hyperfine structure constant for a series of open-shell molecules containing mercury. The results of calculations carried out in connection with ab initio methods of increasing complexity demonstrate the high accuracy of the formalism developed. In view of its computational simplicity, the new approach provides the basis for an efficient and accurate calculation of the HFS parameters of large molecules.