Molecular integrals in the approximate calculation of electronic structure

A self-consistent set of new proposals is made for the calculation of the largest molecular integrals over orthogonal hybrid orbitals used in neglect of differential overlap schemes.     

Some aspects of the calculation of lattice energies

Some relations between lattice energies calculated from various simple equations are pointed out. It is found that these equations give values of the variation of compressibility with pressure that agree poorly with experiments, at least for sodium and cesium chloride, bromide, and iodide. Equations which take this variation into account are developed, and it is found that calculated values of the lattice energy vary very little with the exact equation used. On the whole these extended equations give better agreement between the calculated and observed lattice energies.     

A simple method for the approximate calculation of Hosoya's index

A simple method is developed for the approximate calculation of Hosoya's topological index Z. The two basic structural factors which determine Z are the size of the molecule and the branching of the carbon atom skeleton.     

The approximate calculation of the process of equilibrium dynamics of desorption

Conclusions The relationship between processes of equilibrium dynamics and kinetics of desorption and adsorption was discussed.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 9, pp. 1882–1886, September, 1971.     

Some aspects of the calculation of lattice energies. II

Calculations of the lattice energies, which incorporate the variation of compressibility with pressure, have been extended to a wider range of alkali halides. The present calculations deal with compounds for which the data only justify a linear relation between compressibility and pressure, and consequently equations have been used with one fewer adjustable constant that those used in an earlier paper.

In general, the calculated lattice energies are larger (absolutely) than those from equations which ignore the variation of compressibility; and these larger values are usually in better agreement with the experiment.     

Effect of nonorthogonality of electronic wave functions on the approximate calculation of transition dipole moments

We discuss a method of taking into account the nonorthogonality of independent approximations for the electronic wave functions of states of a single symmetry type in the calculation of transition dipole moments. The effectiveness of the method is illustrated for the example of the electronic transition C²_r-A²_i of the molecule BO.Translated from Teoreticheskaya i Eksperimental'naya Khimiya, Vol. 26, No. 2, pp. 215–217, March–April, 1990     

Comments on the indo calculation of hyperfine coupling in the σ phenyl radical

The relative magnitudes and signs of the hyperfine coupling constants in the phenyl radical, calculated by INDO, are explained by a combination of delocalization of electron spin density into the sigma framwork and a modification of the exchange polarization effects commonly observed for π-type radicals.     

An average fock operator technique of approximate open-shell LCAO-MO-SCF calculation

The exchange part of the usual Hartree-Fock potential in the unrestricted Hartree-Fock (UHF) theory is suitablyaveraged to construct an, average one-electron model Hamiltonian which generates a set of spin-restricted one-electron orbitals in a self-consistent manner. These orbitals are then used to calculate the electronic energy of the open-shell system by using the proper functional form for the energy which handles the exchange terms correctly. The eigenvalues ofF ^av can be used for calculating either the spin-polarised or spin-averaged ionisation potentials of different orbitals at theKoopmans’ theorem level of approximation. Comparison ofE ^ac with the UHF-energy shows thatE _UHF<E ^ac in each case revealing some kind of an upper bound nature ofE ^ac. An approximate variational argument is given. Relationship of our model with the hyper-Hartree-Fock theory of slater is explored and the general problem of eliminating ‘self-interaction’ terms in average Fock-operator based theories is discussed.     

The electronic structure of chlorine trifluoride: An approximate MO-LCAO-SCF calculation

Calculations have been performed on ClF₃ using an approximation scheme previously developed by the author. Only valence shell s and p orbitals are used in the basis. It is found that the T-shaped nuclear configuration can be satisfactory explained without the use of chlorine 3d orbitals. The calculated charge distribution is found to be similar to that postulated by the Gillespie and Nyholm model but with excess electronic charge on the fluorine atoms.

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Zusammenfassung Rechnungen am ClF₃ werden nach einem angenäherten SCF-Verfahren durchgeführt, wobei als Basis nur s- und p-Funktionen verwendet werden. Dabei zeigt sich, daß sich die T-Konfiguration des Moleküls auch ohne Einbeziehung von 3d-Zuständen des Chlors ergibt. Die erhaltene Ladungsverteilung entspricht der des Modells von Gillespie und Nyholm, jedoch mit größerer Elektronendichte am Fluor.

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Résumé ClF₃ a fait l'objet de calculs selon un schéma développé précédemment par l'auteur. La base ne contient que les orbitales s et p des couches de valence. La configuration nucléaire en forme de T peut être expliquée d'une maniére satisfaisante sans l'utilisation des orbitales 3d du chlore. La distribution de charge calculée est similaire á celle postulée dans le modéle de Gillespie et Nyholm avec cependant un excés de charge sur les atomes de fluor.

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This work was supported in part by the National Science Foundation and in part by Research Grant NsG-512 from the National Aeronautics and Space Administration.     

An approximate expression of the electrostatic molecular potential for benzenic compounds

A method for getting approximate but realistic evaluations of the electrostatic molecular potential for benzene derivatives is presented and discussed. The method is based on a partition of the whole molecular observable into directly transferable contributions, which can be calculated without a previous knowledge of the molecular wavefunction. The algorithm, which probably is applicable also to other aromatic compounds, implements a preceding study concerning only unconjugated molecules.     

Use of the chemical potential to improve energies from approximate wave functions

Summary An equation derived from density functional theory is used to improve energies calculated from approximate wave functions. The examples used are perturbed particle in a box and harmonic oscillators. The equation depends on the constancy of the chemical potential in these systems. The results are quite promising.     

Additive nodal increments for approximate calculation of the total π-electron energy of benzenoid hydrocarbons

An approximate method that allows efficient calculation of the total -electron energy (E ) of benzenoid hydrocarbons is presented. It is based on an additive scheme taking into account the characteristic features of variously annelated benzene rings expressed in terms of the numbers corresponding to the different nodes of the dual graph of the hydrocarbon molecule. The parameters of the model are fitted by a test calculation on 1030 hydrocarbons. The mean square error obtained in E is 0.07%. The method provides a connection between the names of hydrocarbons and their stabilities.     

Accurate calculation of the bound states of Hellmann potential

Bound states of the Hellmann potential, which is a superposition of the attractive Coulomb (?A/r) and the Yukawa (Be ^?Cr /r) potential, are calculated by using a generalized pseudospectral method. Energy eigenvalues accurate up to 13–14 significant figures, and densities are obtained through a nonuniform, optimal spatial discretization of the radial Schrödinger equation. Both ground and excited states are reported for arbitrary values of the potential parameters covering a wide range of interaction. Calculations have been made for higher states as well as for stronger couplings. Some new states are reported here for the first time, which could be useful for future works. The present results are significantly improved in accuracy over all other existing literature values and offers a simple, accurate and efficient scheme for these and other singular potentials in quantum mechanics.     

Intermolecular potential and lattice dynamics of orthorhombic acetylene

The crystal structure and lattice dynamics of orthorhombic acetylene have been calculated with an intermolecular potential consisting of atom-atom and multipole-multipole interactions and including a hydrogen bond. A new assignment of the Raman lattice vibrations is discussed and utilized in the refinement of the potential parameters. The non-transferability of the potential to the cubic phase is attributed to the breaking of the hydrogen bond at the phase transition, and to the large anharmonicity expected for the high-temperature phase.     

Model potential calculation of the electron affinity of lithium

A configuration interaction calculation, using model potential methods, is employed to evaluate the energy of the lowest ¹S state of Li⁻. The model potential describing the valence electron-core interaction is chosen so as to reproduce the observed spectra of the neutral lithium atom with high precision. The calculated result of 0.591 eV is compared with other theoretical estimates and experimental data.     

Modified Booth equation for the calculation of zeta potential

 An easy-to-use computer program based on the modified Booth equation (MBE) is developed to calculate the zeta potential of a spherical nonconducting particle from knowledge of the electrophoretic mobility, particle size, and the type and concentration of ions present in the solution. The program is applied to five sets of previously published literature data and the resulting zeta potentials are compared with the values given by the Henry equation to illustrate the extent of the relaxation effect in each case. In four cases, the output zeta potential data are compared with the corresponding values obtained from the rigorous numerical solution of O’Brien and White. Results indicate that the computer program developed here gives a reliable estimate of the zeta potential. The main advantage in using the MBE lies in its capability of calculating the zeta potential even for cases where the experimentally measured mobility exceeds the maximum theoretical mobility predicted by the O’Brien and White solution. Received: 16 June 1997 Accepted: 11 September 1997     

Adsorption voltammetric peak: approximate calculation algorithm taking into account lateral interactions

Journal of Solid State Electrochemistry - Voltammetric peak of adsorbed electroactive system with lateral interactions may be described theoretically by a parametric equation; no exact explicit...     

Perturbation-variation calculation with contact interaction.: Effect of using approximate zero-order wavefunctions

A variational method is proposed and utilised to obtain the first-order perturbed wavefunction for the contact interaction. Solutions so obtained using approximate zero-order wavefunctions are found to have an error component which becomes steadily worse with distance, making the solutions unusable beyond r ≈ 5/Z au. For symmetric molecules like HD the various variational criteria are shown to be equivalent.     

About using the approximate fields to calculate the electrostatic potential distribution of membrane channels

By the example of gramicidine channel, a comparative analysis of different approximate representations (heavy atoms, polar protons, near-by atoms) of AMBER force field has been carried out to calculate the electrostatic potential distribution of ionic channels in biological membranes. The results obtained are compared with the potential computed in a full-atom representation. The use of approximate representations is shown to lead to estimated errors of the potential.     

Monte Carlo calculation of second and third virial coefficients of small-scale comb polymers on lattice

This paper reports the first computational estimation of the comb polymers' third virial coefficients. The number of the chains in the comb polymers range from 5 to 11. An algorithm that counts the contributing terms of the third virial coefficients in an accelerated manner is presented along with its efficiency dependence on the polymers' size. In addition, the second virial coefficients are estimated for the comb polymers and compared to previously reported results.