Gombás pseudopotential SCF calculations for atoms

The Simplified SCF Method of Gombás, in which the orbital orthogonality conditions are replaced by statistical pseudopotentials, has been tested for the first time by accurate numerical calculations without any further approximation. Whereas the original version of the method leads to characteristic error trends, a correction factor recently introduced by Gombás into the pseudopotential expression, produces surprisingly good results.

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Zusammenfassung Das sog. Vereinfachte SCF-Verfahren von Gombás, bei welchem die Orthogonalitätsbedingungen der Orbitale durch statistische Pseudopotentiale ersetzt werden, wird erstmalig durch saubere numerische Rechnungen getestet. Während die unkorrigierte Version der Methode Resultate mit charakteristischen Fehlern liefert, führt der kürzlich von Gombás abgeleitete Korrekturfaktor im Besetzungsverbotpotential zu überraschend guten Ergebnissen.

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Résumé La «méthode SCF simplifiée» de Gombás, où les conditions d'orthogonalité des orbitales sont remplacées par des pseudo potentiels statistiques, a été pour la première fois éprouvée avec des calculs numériques précis sans aucune autre approximation. Alors que la version originale de la méthode conduit à des tendances d'erreurs caractéristiques, un facteur de correction récemment introduit par Gombás dans l'expression du pseudo-potential, produit des résultats remarquablement bons.

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Dedicated to the memory of Professor Paul Gombás.

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This work has been stimulated by discussions with Prof.P. Gombás. Computer time on the IBM 7090 of the GMD at Bonn is gratefully acknowledged.     

Implementation of pseudopotential in the G3 theory for molecules containing first-, second-, and non-transition third-row atoms

Compact effective pseudopotential (CEP) is adapted in the G3 theory providing a theoretical alternative referred to as G3CEP for calculations involving the first-, second-, and non-transition third-row elements. These modifications tried to preserve as much as possible the original characteristics of G3. G3CEP was used in the study of 247 enthalpies of formation, 22 atomization energies, 104 ionization potentials, 63 electron affinities, and 10 proton affinities, resulting in the calculation of 446 species for the first-, second-, and third-row atoms. The final average total absolute deviation was of 1.29 kcal mol(-1) against 1.16 kcal mol(-1) from all-electron G3 for the same calculations. The CPU time has been reduced by 7% to 56%, depending on the size of the molecules and the type of atoms considered.     

An index of electrotopological state for atoms in molecules

A new method for molecular structure quantitation is described, in which both electronic and topological attributes are united. The method uses the hydrogen-suppressed skeleton to represent the structure and leads to a graph invariant index for the individual atoms and hydride groups of the molecular skeleton. An intrinsic atom value is calculated for each atom asI = ( + 1)/, in which and are the counts of valence and sigma electrons of atoms in the molecular skeleton, that is, exclusive of bonds to hydrogen atoms. The electrotopological state valueS _i for an atomi is defined asS _i =I _i + I _i, where the influence of atom j on atom i, I _i, is given as (I _i-j _j)/r ²;r is the graph separation between atoms i and j, counted as number of atoms, includingi andj. The information in the electrotopological state values is revealed by examples of various types of organic structures, including chain branching and heteroatom variation. The relation of the E-state value to NMR chemical shift is demonstrated for a series of carbonyl compounds.     

An application of correlation energy density functionals to atoms and molecules

Four density functionals — including that recently introduced by Perdew ((1986) Phys Rev B33: 8822)—are tested for first-row atoms, hydrides and dimers. Calculated contributions of the correlation energy to the ionization potentials and electron affinities of atoms and to the dissociation energies of molecules are compared with empirical values which were reevaluated for this purpose. An improvement over Hartree-Fock is found in all cases if the self-interaction or the gradient correction are included in the density functional, although there is a rather large variation in the accuracy of the predictions.     

An analytical expression for interatomic surfaces in the theory of atoms in molecules

Summary According to the theory of Atoms in Molecules as developed by Bader and coworkers a molecule is partitioned into atoms separated by surfaces of zero flux in the gradient of the charge density. For the first time an accurate and explicit analytical expression is given for these interatomic surfaces. They are generated by a system of differential equations which can in principle be solved by using a series expansion. Unfortunately, this expansion has a small radius of convergence and can therefore not be applied in practice. However, by a combined Chebyshev-Fourier fit to a numerically obtained surface, the interatomic surface is globally described to any given accuracy. Finally, the algorithm is tested on a set of simple molecules and on the amide interatomic surfaces of the glycyl residue |HNCH₂CO|.     

An improved iterative Extended Hückel method for conjugated molecules

The deficiencies of iterative extended Hückel theory as applied to conjugated molecules are discussed. An improved treatment is suggested which sacrifices complete rotational invariance but which is capable of a better representation of the t-electron energy levels and molecular ionization potentials.     

An improved CNDO/2 standard parametrization for bromine containing molecules

Bromine parameters are proposed, matching well the standard values of first and second row atoms, as introduced by Pople et al. This is shown by comparisons of geometries, configurations, conformations, and dipole moments, obtained with different approaches. The new parameter set was found in a very simple and efficient way that may also be useful for other tasks, e.g. in non-empirical calculations.     

Molecular orbitals for excited states of atoms and molecules

A method is described for calculating SCF wavefunctions for excited electronic states of atoms and molecules. The orthogonality conditions with the ground state wavefunction and the underlying excited states wavefunctions are introduced in the SCF process in a simplified form.     

Long-range interactions between atoms and molecules

The refractive index data for various gases are fitted to analytical formulae from which may be calculated the coefficient of the leading term of the long-range two-body interactions and the coefficient of the leading term of the long-range non-additive three-body interactions. Coefficients are obtained for mixtures of the gases He, Ne, A, Kr, Xe, H₂, N₂ and CH₄, the probable error being 5%.     

Properties of atoms in molecules

Atomic charges calculated by the population analysis method for three types of semi-empirical wave functions have been compared with charges obtained by integrating the corresponding electronic density functions over individual atomic regions. It was found that the two sets of charges compare quite well for CNDO wave functions and for extended-Hückel functions which are in terms of orthogonalized basis orbitals. However only the CNDO charges are reasonably close to those obtained by integrating near-Hartree-Fock electronic density functions.     

Properties of atoms in molecules

The electronic charges and the positions of the centers of these charges have been calculated for the atoms of a number of second- and third-row heteronuclear diatomic molecules. For both the oxygen and the fluorine atoms, the charge associated with one of these atoms can be correlated, within a series of molecules containing that atom, with both the orbital energy of the atom's 1s electrons and also with the difference in electronegativities of the atoms that comprise the molecule. The centers of electronic charge are outside of the internuclear regions, except for the positive atoms in the more ionic molecules and in HF.     

Electron pair correlation in atoms and molecules

Accurate methods for computing energies and electronic properties of atoms and molecules have been derived from direct treatment of localized pairs of electrons. The conceptual development and implementation of such methods is reviewed.     

Near ab-initio methods for the calculations of large molecules: Comparison of pseudopotential and ab-initio results

Results from pseudopotential calculations on 5-hydroxyindole, tryptamine, 5-hydroxytryptamine, 6-hydroxytryptamine and the imidazolium cation are compared to full ab-initio calculations. The localization of all molecular orbitals is found to be identical with the two methods. Orbital energies from the two methods are found to be linearly correlated for all molecules: the slope is close to unity and the orbital energies from the pseudopotential calculation show a very slight and virtually constant shift to lower values. Electron density maps and molecular electrostatic potential maps calculated from the wavefunctions show that the charge distributions and molecular reactivity characteristics predicted by the two methods are nearly identical.