Showing papers in "Journal of Computational Chemistry in 1985"
TL;DR: The CGTO integral evaluation, SCF,SCF‐gradient, integral transformation, and MR‐CI (SD) steps of the COLUMBUS system of programs have been adapted for the CYBER 205 supercomputer.
Abstract: The CGTO integral evaluation, SCF, SCF-gradient, integral transformation, and MR-CI (SD) steps of the COLUMBUS system of programs have been adapted for the CYBER 205. A description is given of our efforts and the partly heavy modifications necessary to exploit the potential of this supercomputer and to avoid its shortcomings. Typical timings are reported, vector and scalar performance are compared.
139 citations
TL;DR: In this paper, a method for constructing compact orbital and auxiliary basis sets for LCAO-LSD calculations has been developed for first row transition metal atoms from Sc to Zn for the 3dn−14s1 and 3n−24s2 configurations.
Abstract: A method for preparing compact orbital and auxiliary basis sets for LCAO-LSD calculations has been developed. The method has been applied to construct basis sets for first row transition metal atoms from Sc to Zn for the 3dn−14s1 and 3dn−24s2 configurations. The properties of different expansion patterns have been tested in atomic calculations for the chromium atom.
129 citations
TL;DR: In this paper, a set of atom equivalents has been developed which permit the estimation of heats of formation, ΔH° f298 (g), from ab initio total energies (3−21G and 6−31G* basis sets).
Abstract: Sets of atom equivalents have been developed which permit the estimation of heats of formation, ΔH° f298 (g), from ab initio total energies (3‐21G and 6‐31G* basis sets). This extends the isodesmic reaction scheme of Pople and the group equivalents of Wiberg. A variety of small inorganic and organic molecules, including fluorocarbons, free radicals, carbocations, and protonated species give excellent agreement with experiment; average errors are less than 1 kcal/mol with unstrained hydrocarbons (both basis sets), and are on the order of 2 kcal/mol for all molecules considered (6‐31G*; the 3‐21G basis errors, as expected, usually are somewhat higher). The results substantiate Pople's early conclusions that Hartree‐Fock theory provides a generally satisfactory description of classical molecules.
119 citations
TL;DR: In this article, a computer program SURVIB is described for calculating vibrational anharmonicity constants for polyatomic molecules, and the program requires as input a grid of calculated energies in the vicinity of a stationary point, which is fit, in a least squares sense, to a polynomial function of the internal coordinates.
Abstract: A computer program SURVIB is described for calculating vibrational anharmonicity constants for polyatomic molecules. The program requires as input a grid of calculated energies in the vicinity of a stationary point. This grid is fit, in a least squares sense, to a polynomial function of the internal coordinates. This analytic representation of the energy surface is employed in a normal mode analysis, and the energy is reexpanded as a polynominal function of the normal mode coordinates (expressed as vectors in the mass-weighted atomic Cartesian coordinate space). The resulting coefficients are used in a second-order perturbation theory analysis to obtain the vibrational anharmonicity constants. Also reported is an application of this program to formaldehyde employing ab initio, RHF, MP2, MP3, and RHF-CI calculations. The spectroscopic constants obtained for H2CO are in good agreement with experimentally derived values recently reported by Reisner.
96 citations
TL;DR: A real‐time docking method using molecular graphics and high‐speed calculation of the energy of interaction between a drug and a receptor that compares well with those calculated by more orthodox means while also providing visual feedback on both molecular geometry and energy.
Abstract: We describe a real-time docking method using molecular graphics and high-speed calculation of the energy of interaction between a drug and a receptor. A three-dimensional tabulation of the potential is computed prior to the docking experiment, and the total interaction energy is calculated and updated on the display screen in real-time to provide immediate visual feedback to the user as the drug molecule is moved inside the receptor pocket. The “Simplex” method is then used to minimize the energy of interactions after each docking. Using this real-time method, it is now possible to examine rapidly the interactions of a large number of drugs and their analogues with receptor molecules. As an application, the interaction of thyroid hormone and its analogues with prealbumin is considered. The final interaction energies of this very rapid method compare well with those calculated by more orthodox means, while also providing visual feedback on both molecular geometry and energy.
88 citations
TL;DR: In this article, the authors calculated the partition coefficient, in octanol/water, for about 200 organic molecules of diverse structures and functionalities and showed that this method was successful in providing a better quantitative structure activity relationship (QSAR) than the Hansch-type approach.
Abstract: The values of log10P (partition coefficient, in octanol/water) were calculated for about 200 organic molecules of diverse structures and functionalities The method involves a simple procedure and appears accurate enough for semiquantitative applications Further, this method of calculating log10P values was shown to be successful in providing a better quantitative structure activity relationship (QSAR) than the Hansch-type approach in the study of inhibitory activity of substituted phenols on Bacillus Subtilis spore germination
80 citations
TL;DR: In this paper, the Hartree-Fock-level geometry of formamide and methylamine with basis sets ranging up to ones that are triple-zeta plus two sets of polarization functions in the valence shell was computed at Hartree level.
Abstract: Fully optimized geometries are computed at the Hartree–Fock level for formamide and methylamine with basis sets ranging up to ones that are triple-zeta plus two sets of polarization functions in the valence shell. The effect of very diffuse s and p functions is also examined. The relation of basis set size and composition to the computed amino group out-of-plane angle and to the related localized molecular orbitals is systematically investigated and compared with scattered results previously reported for other systems. It is concluded that the amino group angle is the result of a delicate balance between lone pair character of the nitrogen electrons and delocalization of these electrons into other portions of the molecule. Polarization functions in the nitrogen basis set are necessary to provide for proper description of the lone pair character, but even in methylamine the delocalization is not properly described without an extensive basis set, either polarization functions or very diffuse s and p functions, on the other heavy atoms. The effect is extreme for molecules such as formamide, aniline, and PF2NH2, where very large basis sets are required to obtain the correct out-of-plane angle.
65 citations
TL;DR: The matching polynomials generated are potentially useful in several applications such as lattice statistics, aromaticity, valence bond methods, and in the calculation of grand canonical partition functions, in the computation of thermodynamic properties of saturated hydrocarbons, and on chemical documentation.
Abstract: A computer program in Pascal is developed for computing the matching polynomials of graphs and lattices. This program is based on the recursive relation for matching polynomials outlined by Hosoya [Bull. Chem. Soc. Jpn., 44, 2332 (1971)], Gutman and Hosoya [Theor. Chim. Acta, 48, 279 (1978)], and others. The graph whose matching polynomial is of interest is reduced recursively until the graph reduces to several trees. The characteristic polynomial of a tree is the same as the matching polynomial. The characteristic polynomials of resulting trees are computed using the computer program based on Frame's method developed by Balasubramanian [Theor. Chim. Acta, 65, 49 (1984)]; J. Comput. Chem., 5, 387 (1984). The resulting polynomials are then assembled to compute the matching polynomial of the initial graph. The program is especially useful in generating the matching polynomials of graphs containing a large number of vertices. The matching polynomials thus generated are potentially useful in several applications such as lattice statistics (dimer covering problem), aromaticity, valence bond methods (enumeration of perfect matchings) in the calculation of grand canonical partition functions, in the computation of thermodynamic properties of saturated hydrocarbons, and in chemical documentation.
60 citations
TL;DR: An iterative algorithm for finding topological equivalence, ordering, and canonical numbering of vertexes (atoms) in molecular graphs based on extended connectivities but there is no “best name” search.
Abstract: An iterative algorithm is described for finding topological equivalence, ordering, and canonical numbering of vertexes (atoms) in molecular graphs. Like the Morgan algorithm, it is based on extended connectivities but: (i) the latter are used hierarchically, i. e., the discrimination in the next iteration is carried out only for the vertices having the same extended connectivities (ranks) at the previous iteration; (ii) at equal extended connectivities, additional discrimination is introduced by the ranks of adjacent vertices; (iii) there is no “best name” search; (iv) three levels of complexity of chemical structures are distinguished and handled by different procedures.
Two schemes of application of HOC procedures are presented: one directed towards a fast canonical numbering for coding systems, and another one yielding levels of topological equivalence allowing a unique topological representation of the molecule with possible applications to similarity search, structure-activity correlations, etc.
55 citations
TL;DR: In this paper, a general recursion formula for trees of any kind is presented, which is valid irrespective of the valence of the vertices of the tree or the degree of branching in the tree.
Abstract: : Contemporary chemistry is focusing to an ever-increasing extent on the relationships between the structure of molecules and their physicochemical properties. In particular, there has been widespread usage of topological graphs and matrices for the characterization of both individual molecular species and a variety of intermolecular interactions. Our prime focus of interest here will center on the distance matrix, and more especially on its derivation for the important class of graphs commonly referred to as chemical trees. The many applications of the distance matrix, D(G), and the Wiener branching index, W(G), in chemistry are briefly outlined. W(G) is defined as one half the sum of all the entries in D(G). A recursion formula is developed enabling W(G) to be evaluated for any molecule whose graph G exists in the form of a tree. This formula, which represents the first general recursion formula for trees of any kind, is valid irrespective of the valence of the vertices of G or of the degree of branching in G. Several closed expressions giving W(G) for special classes of tree molecules are derived from the general formula. One illustrative worked example is also presented. Finally, it is shown how the presence of an arbitrary number of heteroatoms in tree-like molecules can readily be accommodated within our general formula by appropriately weighting the vertices and edges of G.
52 citations
TL;DR: Optimized monopole expansions for the peptide subunits of proteins are developed by a reparameterization of the Huckel-Del Re procedure designed to reproduce closely the electrostatic properties obtained with ab initioOMTP multipole expansions.
Abstract: Optimized monopole expansions for the peptide subunits of proteins are developed by a reparameterization of the Huckel–Del Re procedure designed to reproduce closely the electrostatic properties obtained with ab initioOMTP multipole expansions. It is shown that satisfactory values of both potential and field may be obtained for different conformations of the peptide backbone as well as for the common side chains. A comparison is presented for the pentadecapeptide Gramicidin A.
TL;DR: In this article, the complete molecular structure of biphenyl was derived by ab initio gradient techniques using a STO-3G basis set for coplanar, perpendicular, and minimum energy conformations with the constraint of planar phenyl ring units and a C2 symmetry axis along the CC interring bond.
Abstract: The complete molecular structure of biphenyl, characterized by 12 independent parameters, has been derived by ab initio gradient techniques using a STO-3G basis set for coplanar, perpendicular, and minimum energy conformations with the constraint of planar phenyl ring units and a C2 symmetry axis along the CC interring bond. The minimum torsional angle obtained was ϕ = 38.63° with torsional energy barriers of 8.59 and 10.04 kJ/mol for ϕ = 0° and ϕ = 90°, respectively.
TL;DR: In this paper, the problem of chance correlations in studies of structure-activity relationships using multivariate linear regression techniques is addressed, and the statistical parameters of these correlations are compared to those obtained using the actual potency/compound data pairs and the most noticeable differences are in the magnitude of the F values for the overall regression.
Abstract: The problem of chance correlations in studies of structure—activity relationships using multivariate linear regression techniques is addressed. Random correlations are simulated by scrambling real potency values in data bases consisting of molecules possessing various biological properties. The statistical parameters of these correlations are compared to those obtained using the actual potency/compound data pairs and it is noted that the most noticeable differences are in the magnitude of the F values for the overall regression. Cutoff points for this parameter are suggested, which, when implemented in the recently introduced CASE method that correlates biological activity with substructural descriptors, can serve to weed out effectively the majority of meaningless correlations.
TL;DR: In this paper, the atomic charges obtained with a previously published charge scheme are given for amino acids and peptides, both in the form of the N-acetyl-N′-methyl amino acid amides, used as models for the amino acid residues in enzymes, and as the free zwitterionic amino acids.
Abstract: Atomic charges obtained with a previously published charge scheme are given for amino acids and peptides. In order to do this, a method of handling charged species with the basic scheme2,3 has been developed. The charges obtained for alkylammonium ions and carboxylate ions with the scheme are presented and compared with CNDO and ab initio values. The calculated experimental dipole moments of the zwitterionic forms of glycine, alanine and β-alanine are then discussed. Finally, the atomic charges obtained for the naturally occurring amino acids are given, both in the form of the N-acetyl-N′-methyl amino acid amides, used as models for the amino acid residues in enzymes, and as the free zwitterionic amino acids. The charges obtained show a good correlation with n. m. r. chemical shifts of both carbon and hydrogen atoms.
TL;DR: In this article, it is shown that the Frame's method for characteristic polynomials of chemical graphs can be extended to periodic graphs and structures, where the finite periodic structures are represented by cyclic structures in the Born-von Khnan boundary condition which leads to complex matrices.
Abstract: It is shown that the Frame’s method (also, Le Verrier-Faddeev’s method) for characteristic polynomials of chemical graphs can be extended to periodic graphs and structures. The finite periodic structures are represented by cyclic structures in the Born-von Khnan boundary condition which leads to complex matrices. In this article we demonstrate that our earlier computer program (based on Frame’s method) can be extended to these periodic networks. The characteristic polynomials of several lattices such as polydiacetylenes, one-dimensional triangular, square, and hexagonal lattices are obtained. These polynomials can be obtained with very little computer time using this method. I. INTRODUCTION In recent years characteristic polynomials and related polynomials of graphs and other applications of graph theory to chemistry have been the subjects of a large number of inve~tigations.l-~’ Characteristic polynomials play an important role in several areas of chemistry. These polynomials are structural invariants and are thus useful in coding chemical structures. They are generating functions for dimer statistics on trees (such as Bethe lattices) and thus they play an important role in statistical mechanic^.^^.^,^^ Characteristic polynomials of graphs have applications in quantum chemistry, chemical kinetics, dynamics of oscillatory reactions, etc. They are also useful in estimating the stability of conjugated systems. The present author showed the use of Frame’s method for evaluating characteristic polynomials of graphs containing large numbers of vertices and further developed a computer program based on this meth~d.~~.~~ Krivka, Jericevib, and Trinajstib4’ have recently shown that the Frame’s method outlined in the present author’s article is similar to Le Verrier-Faddeev’s method. Other manifestations of Frame’s method could also be found in the literat~re.~~ The objective of this investigation is to show that the method and computer program
TL;DR: In this paper, the lowest potential energy surfaces of NO3 have been investigated using CASSCF and contracted CI methods, to determine if NO3 is an intermediate in the oxidation of nitric oxide.
Abstract: The lowest potential energy surfaces of NO3 have been investigated using CASSCF and contracted CI methods, to determine if NO3 is an intermediate in the oxidation of nitric oxide. This reaction is observed to be termolecular where an intermediate is almost certainly formed. The calculations, which were performed in C2v symmetry, show that the form of NO3 which has a near D3h geometry should not be possible to reach from ground state NO and O2. The energy of this isomer of NO3 is calculated to be 25 kcal/mol higher in energy than separated NO and O2. Furthermore, NO + O2 is separated from NO3 by very high barriers. The C2v constrained barrier is as high as 145 kcal/mol, which makes it very unlikely that NO3 could be formed even along less symmetric pathways. The origin of the barriers are analyzed, and it is shown that a special type of mechanism is involved for the state with the lowest barrier. In this mechanism, which was observed recently also for NiH2, the occupation in each symmetry changes only by one unit in each step of the reaction. The only isomer of NO3 which could be formed is a weak van der Waals complex with a very long bond distance of 6.5 a.u. N2O2 does, however, in this respect seem to be a more likely intermediate with its shorter bond distance of 4.5 a.u. Calculations around the D3h equilibrium further show that 2B2 is the ground state of this isomer of NO3 with 2A2 and 2B1 slightly higher in energy.
TL;DR: In this article, the effect of adding an electronegative atom (fluorine, or carbonyl oxygen) onto the framework was studied as a function of the torsional angle about the single bond.
Abstract: A series of ab initio calculations have been carried out, using the 4-21G basis set. Ethane and propane were first studied to obtain reference points. The effect of adding an electronegative atom (fluorine, or carbonyl oxygen) onto the framework was then studied as a function of the torsional angle about the single bond. Some pronounced trends in structural changes were observed, and these can in part be correlated with hyperconjugative effects. For example, fluoroethane has bond lengths which are shorter than those in ethane itself, by 0.024 Ain the CC bond, and 0.003 Ain the α CH bonds. These changes are essentially torsionally independent. On the other hand, in propionaldehyde, the CC bond length of the methyl group and the CH bond lengths of the hydrogens attached to the alpha carbon vary as a function of the torsion angle. If the methyl CC bond in the carbonyl plane is taken as a reference, the bond stretches .016 Awhen the torsion angle is increased to 90°, an α CH bond similarly stretches up to .007 A. Many of these geometric changes are large, well beyond the experimental errors in modern measurements.
TL;DR: In this paper, a very efficient algorithm for determining the geometrically feasible binding modes of a flexible ligand molecule at the receptor site is presented, which is based on distance geometry but maintains the requirements of three dimensions.
Abstract: A very efficient algorithm for determining the geometrically feasible binding modes of a flexible ligand molecule at the receptor site is presented. It is based on distance geometry but maintains the requirements of three dimensions. The distance geometry manipulation can superimpose two bodies without explicitly calculating the necessary rigid rotation and translation. The whole conformation space of a flexible molecule can be efficiently examined by considering only a finite number of conformational points. The method is suitable only when the criterion for superposition is some minimum distance limit. It cannot, however, give the exact distance between two points in two different bodies.
TL;DR: In this paper, local pseudopotential calculations have been performed for the ground state of disilane as well as for the lowest singlet and triplet states of the disilene and silylsilylene.
Abstract: Local pseudopotential calculations have been performed for the ground state of disilane as well as for the lowest singlet and triplet states of disilene and silylsilylene. Comparison with all-electron calculations shows good agreement for geometries and relative stabilities.
TL;DR: A new instrument of exploration can be used to develop unrecognized connections among points in a variety of geometric designs and is suitable for interpolation problems which arise in experimental design and the treatment of data.
Abstract: A new instrument of exploration can be used to develop unrecognized connections among points in a variety of geometric designs. Operational methods are used to derive the relationships, and a new approach to extremum location is demonstrated. The technique is suitable for interpolation problems which arise in experimental design and the treatment of data.
IBM1
TL;DR: In this article, a strategy to perform molecular dynamics simulations using parallel processing techniques on a parallel-distributed loosely coupled system consisting of IBM host computers (4341 and 4381) with attached scientific processors (FPS-164) is presented.
Abstract: This article presents a strategy to perform molecular dynamics simulations using parallel processing techniques on a parallel-distributed loosely coupled system consisting of IBM host computers (4341 and 4381) with attached scientific processors (FPS-164). This substantially enhances our ability to perform fast and more realistic large scale many-body trajectory simulations. A powerful extention of the computational range of molecular dynamics the parallel approach offers the opportunity to substantially reduce the simulation time to allow a longer simulation period to study more realistic models and larger systems. It is flexible and uses, for the most part, standard products and straightforward implementation with a broad range of applicability. The implementation of a simulation of water molecules with the inclusion of two- and three-body interactions is discussed. Some considerations in the design and implementation of parallel programs on a loosely coupled system are also presented.
TL;DR: The molecular mechanics description of the torsion of a methyl group attached to a conjugated system has been improved by using bond order dependent torsional force constants.
Abstract: The molecular mechanics (MMP2) description of the torsion of a methyl group attached to a conjugated system has been improved by using bond order dependent torsional force constants
TL;DR: In this paper, the geometrical parameters for benzene, fluorobenzene, and cyanobenzenes have been calculated using the 6-31G*(5D) and 6−31G** basis sets.
Abstract: The geometrical parameters for benzene, fluorobenzene, and cyanobenzene have been calculated using the 6–31G*(5D) and 6–31G** basis sets, and, in addition, the 6–31 + G*(5D) basis set in the case of fluorobenzene. Compared to previous results obtained using the 6‐31G basis set there are minor changes in the magnitude of the bond lengths and angles in the ring, but the relative values remain unaltered. The values for the ipso angles in fluorobenzene and cyanobenzene are again somewhat less than those reported from microwave and/or electron diffraction studies. The distortion of the ring is characterized as either an elongation or a flattening with respect to the F–C1 ⃛C4 and NCC1C4 axes, and the shape is characterized as either a broadening or a narrowing across the ring just below the F and Cn group, i.e., an increase or a decrease in the C2 ⃛C6 internuclear distance, relative of the C3 ⃛C5 distance.
TL;DR: In this paper, the authors evaluated correlation effects on computed lithium cation affinities for the oxygen and nitrogen bases CH3OH, H2CO, CO, CH3NH2, CH2NH, and HCN.
Abstract: Basis set expansion and correlation effects on computed lithium cation affinities have been evaluated for the oxygen and nitrogen bases CH3OH, H2CO, CO, CH3NH2, CH2NH, and HCN. The presence of diffuse functions on nonhydrogen atoms is found to be the most important single enhancement of double- and triple-split valence plus polarization basis sets. With the triple-split basis, enhancement effects are nearly additive. Correlation usually decreases computed lithium ion affinities, with the second order Moller-Plesset correlation term being the dominant term.
TL;DR: In this article, a stepwise computational protocol designed to identify the minimum level of theory necessary for reliable prediction of relative tautomer, reduction and ionization energies has been developed in an effort to minimize the cost of calculations for this reasonably large N−heterobicylic system.
Abstract: Ab initio SCF calculations with STO‐3G and 3‐21G basis sets are reported for approximately 85 pteridines of interest to the study of the reaction and inhibition mechanisms of dihydrofolate reductase. These include tautomeric, protonated, deprotonated, reduced and 6‐substituted forms of the 2‐amino‐4‐oxo‐ and 2,4‐diamino‐pteridines, many of which are not easily amenable to experimental investigation. Full geometry optimizations at the SCF/STO‐3G level for 30 such pteridines have been performed. A step‐wise computational protocol designed to identify the minimum level of theory necessary for reliable prediction of relative tautomer, reduction and ionization energies has been developed in an effort to minimize the cost of calculations for this reasonably large N‐heterobicylic system. In general, SCF/STO‐3G results were found to be inadequate while SCF/3‐21G results obtained with STO‐3G optimized geometries agreed with all available experimental evidence with the exception of the relative acidity of 6‐methyl‐7,8‐dihydropterin. Correlation graphs relating experimental pKa's to the calculated ionization energies are presented: these are of potential predictive value. An analysis is given of the importance of resonance substructures, such as the guanidinium and extended‐guanidinium groups, in stabilizing some preferred tautomeric and ionized forms, and in explaining the observed geometry changes.
TL;DR: In this paper, the Hammett σ and Taft σ 0 constants have been examined using the MNDO computational procedure and they are both best explained by using computed properties based upon the benzoate ion, especially the reciprocal of the energy of the highest occupied molecular orbital.
Abstract: The Hammett σ and Taft σ0 constants have been examined using the MNDO computational procedure. They are both best explained by using computed properties based upon the benzoate ion, especially the reciprocal of the energy of the highest occupied molecular orbital.
TL;DR: In this article, the Hartree-Fock virtual and occupied orbitals are used as one-electron functions for multireference CI calculations, and the efficiency of the computational procedure is discussed for the case of a Li6 cluster of D3h symmetry and for NaCO and PdCO complexes.
Abstract: The maximization of the exchange interaction between the canonical Hartree–Fock virtual and occupied orbitals leads to a transformed set of virtual orbitals which are well suited as one‐electron functions for CI calculations. The procedure, generally known for a long time is seldom applied, despite its simplicity and very low computational demand. However, it is found to be particularly useful in the case of multireference CI, since an improved energy is obtained with a considerable shortening of the CI expansion. Moreover, in the final CI wave function, several configurations appear with considerable weight, thus allowing an easy choice of additional configurations to be inserted in the definition of a new zero‐order wave function. The efficiency of the computational procedure is discussed for the case of a Li6 cluster of D3h symmetry and for the NaCO and PdCO complexes. Results are reported for the relative stability of four different geometrical arrangements of the Li6 cluster.
TL;DR: In this paper, general definitions of valence, degree of bonding between pairs of atoms, and atomic anisotropy and reactivity are given They can be applied to closed-or open-shell molecular wave functions (in the semiempirical, quasi or full ab initioSCF levels), as well as to GVB ones.
Abstract: General definitions of valence, degree of bonding between pairs of atoms, and atomic anisotropy and reactivity are given They can be applied to closed- or open-shell molecular wave functions (in the semiempirical, quasi or full ab initioSCF levels), as well as to GVB ones The properties and usefulness of the definitions are discussed as well as their relation to former empirical notions Examples of their application are also reported
Abstract: A computer program is developed in Pascal for the generation of king and color polynomials of graphs. The king polynomial was defined by Motoyama and Hosoya and was shown to be useful in dimer statistics, enumeration of Kekule structures, etc. We show that the king polynomial of a lattice is the same as the color polynomial of the associated dualist graph, where the color polynomial is defined here as the number of ways of coloring the vertices of a graph with one type of color (say, green) such that two adjacent vertices are not colored with the same color. Applications of these polynomials to exact finite method of lattice statistics are outlined.
TL;DR: The compact orbital and auxiliary basis sets for LCAO-LSD calculations introduced in Part I are tested in molecular calculations on Cr2 and Ni4 and the results for spectroscopic constants and valence orbital energies obtained using medium size orbital expansions with a double-zeta representation for valence orbitals are in very good agreement with those previously calculated with very extended sets as mentioned in this paper.
Abstract: The compact orbital and auxiliary basis sets for LCAO-LSD calculations introduced in Part I are tested in molecular calculations on Cr2 and Ni4. The present results for spectroscopic constants and valence orbital energies obtained using medium size orbital expansions with a double-zeta representation for valence orbitals are in very good agreement with those previously calculated with very extended sets. Since the computational time of the present calculations is reduced severalfold compared with the extended basis set calculations, the present basis sets allow increased efficiency of the LCAO-LSD calculations and allow the method to be extended to larger systems.