Core correlating basis functions for elements 31–118

Gaussian functions for correlation of all core shells of elements from Z = 31 to Z = 118 have been optimized in relativistic singles and doubles CI calculations, performed on the shell of highest angular momentum for each principal quantum number. The SCF functions were derived from the double-zeta, triple-zeta, and quadruple-zeta basis sets previously optimized by the author. Only those Gaussian functions that are not represented in the SCF basis sets were optimized. The functions are available from the Dirac program web site, .     

Drug efficiency indices for improvement of molecular docking scoring functions

A dataset of protein‐drug complexes with experimental binding energy and crystal structure were analyzed and the performance of different docking engines and scoring functions (as well as components of these) for predicting the free energy of binding and several ligand efficiency indices were compared. The aim was not to evaluate the best docking method, but to determine the effect of different efficiency indices on the experimental and predicted free energy. Some ligand efficiency indices, such as ΔG/W (Wiener index), ΔG/NoC (number of carbons), and ΔG/P (partition coefficient), improve the correlation between experimental and calculated values. This effect was shown to be valid across the different scoring functions and docking programs. It also removes the common bias of scoring functions in favor of larger ligands. For all scoring functions, the efficiency indices effectively normalize the free energy derived indices, to give values closer to experiment. Compound collection filtering can be done prior or after docking, using pharmacokinetic as well as pharmacodynamic profiles. Achieving these better correlations with experiment can improve the ability of docking scoring functions to predict active molecules in virtual screening. © 2009 Wiley Periodicals, Inc. J Comput Chem 2010     

Quality of correlating functions generated from commonly used basis sets

Tests have been performed on the quality of correlating functions generated from commonly used Gaussian basis sets, such as the 4-31G and MIDI-4 sets. The atoms tested were carbon, nitrogen, and oxygen. Self-consistent field and configuration interaction (CI) calculations were performed for the ground and lower excited states of neutral atoms as well as for positive and negative ions, using the original sets. Next, after adding (1) one d, and (2) two d and one f primitive Gaussian-type functions (GTFs) to the original sets, the CI calculations were repeated. In order to investigate the quality of the correlating orbitals generated from the GTF sets, parallel calculations to those for the GTF sets were carried out with an extended set of Slater-type functions. It was found that the excitation energies change in a stepwise manner as the basis sets changed from the original sets to the original set + 1d and the original set +2d1f. The improvements in excitation energies and ionization energies were almost independent of the original sets and were found to be strongly dependent on the augmented correlation functions. © 1996 by John Wiley & Sons, Inc.     

A detailed view of the Gaussian–Lorentzian sum and product functions and their comparison with the Voigt function

The Gaussian–Lorentzian sum (GLS) and product (GLP) functions remain important in X-ray photoelectron spectroscopy (XPS) peak fitting. Here, we present a detailed view of these functions, comparing them with each other and with the Voigt function (the “LA(m)” function). First, we show the GLS, GLP, and LA(m) functions as a function of their mixing parameters, m, which reveals differences between them. We then illustrate the use of these functions to fit a series of spectra acquired at different pass energies (resolutions). Next, we show the underlying Gaussian and Lorentzian components of a series of GLS and GLP functions as a function of m, which confirms that the GLS is a simple linear combination of Gaussian and Lorentzian functions. However, one of the two functions used to make the GLP can be very wide, that is, at its extremes, one of these functions has infinite width. We then discuss a plot of the areas of the GLS, GLP, and LA(m) functions as a function of m, which reveals the expected, linear increase in area of the GLS, but nonlinear changes in the areas of the other two functions. Finally, to better understand them, we fit these functions to each other. These results indicate that the GLS and GLP better match the LA(m) function at lower and higher values of the mixing parameter, respectively.     

Gaussian expansions from STOs by the distance between subspaces

Expansions of STO orbitals with GTO s for the first-row atoms have been obtained by the method of the distance between subspaces. The expansion coefficients and exponential parameters were simultaneously varied when the distance between subspaces, which are generated from STO and GTO functions, is minimized. The ζ; exponents (or scale factors) for the atomic orbitals that are optimized for these atoms are also shown to be almost independent of the number of Gaussian functions. Comparisons carried out with Stewart's least-squares method produce equivalent results when exponents for 2s and 2p functions are different. Some examples and applications for several atomic properties of the first-row atoms are included: energies and expectation values of rⁱ and pⁱ for the several expansions. These new minimal basis sets were tested for diatomic and polyatomic molecules containing these atoms. © 1993 John Wiley & Sons, Inc.     

Nuclear attraction and electron interaction integrals of exponentially decaying functions and the Poisson equation

Summary The technique proposed by O-Ohata and Ruedenberg (J Math Phys 7:547 (1966)) and by Silver and Ruedenberg (J Chem Phys 49:4306 (1968)) of computing nuclear attraction and electron interaction integrals by solving an inhomogeneous Laplace equation can also be applied ifB functions (Filter E, Steinborn EO (1978) Phys Rev A 18:1) are used as basis functions in atomic and molecular calculations. It is shown that because of the remarkable mathematical properties ofB functions the derivation of compact explicit expressions for the multicenter integrals mentioned above is particularly simple. These results are also of interest in the context of other exponentially decaying functions, since all the other commonly occurring exponentially decaying functions as, for instance, Slater functions or bound state hydrogen eigenfunctions can be expressed as simple linear combinations ofB functions. Consequently, their multicenter integrals can also be expressed in terms of multicenter integrals ofB functions.Dedicated to Prof. Klaus Ruedenberg on the occasion of his 70th birthday     

水与正丁醇二元体系最低共沸混合物的热容

Molar heat capacities of n-butanol and the azeotropic mixture in the binary system [water （x=0.716） plus n-butanol （x=0.284）] were measured with an adiabatic calorimeter in a temperature range from 78 to 320 K. The functions of the heat capacity with respect to thermodynamic temperature were estabhshed for the azeotropic mixture. A glass transition was observed at （111.9±1.2） K. The phase transitions took place at （179.26±0.77） and （269.69±0.14） K corresponding to the solid-hquid phase transitions of n-butanol and water, respectively. The phase-transition enthalpy and entropy of water were calculated. A thermodynamic function of excess molar heat capacity with respect to temperature was estabhshed, which took account of physical mixing, destructions of self-association and cross-association for n-butanol and water, respectively. The thermodynamic functions and the excess thermodynamic ones of the binary systems relative to 298.15 K were derived based on the relationships of the thermodynamic functions and the function of the measured heat capacity and the calculated excess heat capacity with respect to temperature.     

Structural properties of dilute aqueous solutions of dimethylformamide and acetone based on computer simulation

The Monte Carlo simulation of molecular configurations for aqueous solutions ofN,N-dimethylformamide and acetone was carried out. The atom-atom radial distribution functions were determined. The topological properties of the H-bond system were investigated. The concentrations of closed H-bond cycles and the radial distribution functions of their geometric centers were found. It was shown that the local arrangement of molecules and supermolecular assemblies typical of the H-bond network in neat water is retained in the solutions studied. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 592–599, April, 1998.     

Thermodynamics of Solution of Some Alkyl Acetates in Water

Summary.  The temperature dependence of the solubility of methyl acetate (MeOAc), ethyl acetate (EtOAc), 1-propyl acetate (1-PrOAc), 1-butyl acetate (1-BuOAc), 2-methyl-1-propyl acetate (iso-BuOAc), 2-butyl acetate (sec-BuOAc), and 2-methyl-2-propyl acetate (tert-BuOAc) in water in the temperature range from 298.2 to 318.2 K was determined. The experimental solubility data together with some literature values are presented as a function of temperature and given in analytical form. The solubilities of the investigated compounds at 298.2 K were correlated with the number of carbon atoms in the solute molecule. The standard thermodynamic functions for solubility, i.e. Gibbs free energy, enthalpy, heat capacity, and entropy, were calculated. The Gibbs free energy is positive and increases linearly with the number of carbon atoms, whereas the enthalpy and entropy are negative. The standard thermodynamic functions were converted to thermodynamic quantities for hydration. The Gibbs free energies of hydration of alkyl acetates, which are negative, are compared with the Gibbs free energy of hydration of some n-alkanes, 1-alcohols, and 1-alkylamines. The standard thermodynamic functions of hydration were analyzed using a modified version of the theoretical approach developed by Lee and Graziano [1]. Received October 16, 2000. Accepted May 14, 2001     

Gaussian expansions of hydrogenic functions involving few variational parameters

Fully optimized lengthy Gaussian expansions of hydrogenic 1s and 2p_z functions have been practically reproduced by generating the variational parameters by means of suitably chosen functions involving only few parameters. Hydrogenic 3d_xy and 4f_xyz functions have been approximated in a similar way. The usefulness of such generating functions is briefly discussed.     

Structure and properties of transition-metal compounds. A systematic study of basis set effects in ab initioSCF calculations

The recently developed Gaussian basis functions [2] were used in calculations on the ground electronic states of molecules containing transition-metal atoms: ScF₃, TiCl₄, ZrCl₄, Cr(CO)₆, Ni(CO)₄, CuF, CuCl, Zn(CH₃)₂, and Cd(CH₃)₂. The usefulness of minimal basis sets, the importance of splitting of the valence part of the minimal basis sets, the role of the triple splitting of the d-block functions, and the need for p-, d-, and f-type polarization functions were discussed in the context of the geometrical structure and the firstorder electronic properties of the transition-metal atom compounds.     

Contracted polarization functions for B to Ar

Using optimal exponents for B through Ne given by Dunning and those for Al through Ar by Woon and Dunning, d-type contracted polarization functions (2d/1d), (3d/1d), and (3d/2d) are generated from natural orbitals of atomic single and double excitation configuration interaction (SDCI) calculations, where the numbers before and after the slash are those of the primitive and contracted Gaussian type functions. The resulting contracted functions are tested on N₂ and P₂ molecules by self-consistent field and SDCI calculations, which clarify characteristics of the present polarization functions. Received: 5 June 1997 / Accepted: 20 August 1997     

Toward Exact Analytical Wave Function of Helium Atom: Two Techniques for Constructing Homogeneous Functions of Kinetic Energy Operator

We discuss two general techniques for constructing homogeneous functions c of the kinetic energy operator T for the helium atom in a state of symmetry S. The first technique is based on algebraic identification of the kernel of T in a space spanned by some predetermined set of basis functions. The second technique, analytic in nature, constructs the homogeneous functions of T as formal power series with coefficients deduced from recurrence relations stemming from the requirement Tc=0. Both approaches are capable of producing a great variety of homogeneous functions c with arbitrary homogeneity that can prove useful for constructing the exact ground state wave function for the helium atom.     

Thermodynamics of Solution of Some Alkyl Acetates in Water

 The temperature dependence of the solubility of methyl acetate (MeOAc), ethyl acetate (EtOAc), 1-propyl acetate (1-PrOAc), 1-butyl acetate (1-BuOAc), 2-methyl-1-propyl acetate (iso-BuOAc), 2-butyl acetate (sec-BuOAc), and 2-methyl-2-propyl acetate (tert-BuOAc) in water in the temperature range from 298.2 to 318.2 K was determined. The experimental solubility data together with some literature values are presented as a function of temperature and given in analytical form. The solubilities of the investigated compounds at 298.2 K were correlated with the number of carbon atoms in the solute molecule. The standard thermodynamic functions for solubility, i.e. Gibbs free energy, enthalpy, heat capacity, and entropy, were calculated. The Gibbs free energy is positive and increases linearly with the number of carbon atoms, whereas the enthalpy and entropy are negative. The standard thermodynamic functions were converted to thermodynamic quantities for hydration. The Gibbs free energies of hydration of alkyl acetates, which are negative, are compared with the Gibbs free energy of hydration of some n-alkanes, 1-alcohols, and 1-alkylamines. The standard thermodynamic functions of hydration were analyzed using a modified version of the theoretical approach developed by Lee and Graziano [1].     

Application of Maclaurin Series in Relating Interatomic Potential Functions: A Review

This paper provides a short review on the application of Maclaurin series in relating potential functions within the same category of interatomic interaction. The potential functions covered are those commonly adopted in computational chemistry softwares. While various mathematical approaches have been employed in generating relationships amongst potential functions, the use of Maclaurin series has been prevalent recently due to the increasing application of polynomial series-type potential functions. In the case of covalent bond-stretching, the Maclaurin series for the exponential function is used to transform the Morse potential into the polynomial series potential, and vice versa. For covalent bond-bending, Maclaurin series for the sine and cosine functions were employed to extract polynomial angle series potential from the Fourier series and harmonic cosine potential functions, and vice versa. Finally, both the exponential and the 1/(1 – x) expressions in Maclaurin series were used in obtaining the exact relationship for the repulsive terms between two potential functions.     

On the additivity of basis set effects in some simple fluorine containing systems

The reactions F + H₂ → HF + H, HF → H + F, F → F⁺ + e^? and F + e^? → F^? were used as simple test cases to assess the additivity of basis set effects on reaction energetics computed at the MP4 level. The 6-31G and 6-311G basis sets were augmented with 1, 2, and 3 sets of polarization functions, higher angular momentum polarization functions, and diffuse functions (27 basis sets from 6-31Gd, p) to 6-31 ++ G(3df, 3pd) and likewise for the 6-311G series). For both series substantial nonadditivity was found between diffuse functions on the heavy atom and multiple polarization functions (e.g., 6-31 + G(3d, 3p) vs. 6-31 + G(d, p) and 6-31G(3d, 3p)). For the 6-311G series there is an extra nonadditivity between d functions on hydrogen and multiple polarization functions. Provided that these interactions are taken into account, the remaining basis set effects are additive to within ±0.5 kcal/mol for the reactions considered. Large basis set MP4 calculations can also be estimated to within ±0.5 kcal/mol using MP2 calculations, est. E_MP4(6-31 ++ G(3df, 3pd)) ≈ E_MP4(6-31G(d, p)) + E_MP2(6-31 ++ G(3df, 3pd)) – E_MP2(6-31G(d, p)) or E_MP4(6-31 + G(d, p) + E_MP2(6-31 ++ G(3df, 3pd)) – E_MP2(6-31 + G(d, p)) and likewise for the 6-311G series.     

Syntheses and reactions of porphyrin and metalloporphyrin polymers

Various porphyrin functions such as protoporphyrin IX and chlorin a as well as metalloporphyrin functions such as Mg(II)– and Cu(II)–chlorophyllin a and Fe(III)– and Co(II)–protoporphyrin IX were incorporated into vinyl polymers by preparation and polymerization of their p-vinylbenzyl esters. The porphyrin function was also incorporated by reaction of poly-p-chloromethylstyrene with porphyrins or metalloporphyrins or by the reaction of p-aminostyrene polymers with chlorophyll b through Schiff-base formation. Mg(II)–porphyrin polymers were found to be remarkably effective as catalysts in photoredox systems; porphyrin polymers without central metal atoms were also effective to a lesser extent.     

Brownian dynamics of grafted polymer chains: time dependent properties

Results of computer simulations of polymer layers consisting of chains grafted by one end on an unpenetrable plane are presented. Characteristics of translational and rotational motion of different chain segments and correlation functions of chain radii were calculated both for single layers at different grafting densities s and for two interacting layers at different distances D between parallel grafting planes. Two values of grafting density were used in the latter case. The behavior of different correlation times as function of s and D and the interplay between the interpenetration of the brushes and rotational and translational motion are discussed. Both relaxation functions and mean square displacements are discussed in terms of stretched exponentials, and the behavior of the resulting “Kohlrausch exponents” γ is presented in detail.     

Supplementary d and f functions in molecular wave functions: Optimum and nonoptimum exponents

Energy optimization calculations have been carried out to determine the variability of optimum p, d, and f polarization function exponents in molecules containing first- and second-row elements and in normal valency and hypercoordinate species. Optimum exponents were determined for single sets of higher-order functions at both Hartree–Fock and correlated (Moller–Plesset) levels of theory using the Dunning–Hay double zeta and the McLean–Chandler triple zeta basis sets. More detailed calculations were used to test the response to nonoptimum d and f function exponents of the total energy, the optimum geometry, and harmonic stretching frequencies. The variability in optimum exponents and the size of the energy penalties incurred by adopting nonoptimum values reduces the utility of standard exponents for p, d, and f polarization functions. © 1993 John Wiley & Sons, Inc.     

One-Parameter double-zeta atomic functions for the hartree–fock energies of helium isoelectronic sequence

The double-zeta atomic functions are characterized by the nuclear charge z of the two-electron atomic system. The Hartree–Fock total energies and the corresponding orbital energies are calculated using various atomic wave functions for the helium isoelectronic sequence. The expectation values rⁿ of various wave functions are also examined. It is found that the accuracy of our one-parameter double-zeta functions corresponds to the accuracy of the usual five-parameter double-zeta functions.