Localized orbitals based on the fermi hole

The Fermi hole provides a direct (non-iterative) method for tansforming canonical SCF molecular orbitals into localized orbitals. Except for simple overlap integrals required to maintain orthogonality, this method requires no integrals over orbitals or basis functions. This method is demonstrated by application to a furanone (C₄H₄O₂), methylacetylene, and boron trifluoride. The results of these calculations are compared to those determined by the orbital centroid criterion of localization.     

Electron correlation forms in the LiH molecule—fermi correlation

Correlation forms for electrons of the same spin small molecules are analyzed by taking the LiH molecule as an example. The analyses are carried out on the basis of the reduced density matrix theory and for both the ground state and the first excited state. It turns out that although there is a certain similarity, the correlated motions of parallel-spin electrons in this four-electron molecule are more complicated than those found for the two-electron molecule. The correlation forms are not always constant. They vary essentially from one state to another, but are insensitive to fairly large changes of the internuclear distance for a given state.     

Fukui function as correlation hole

The Fukui Function concept of the theory of chemical reactivity is identified as the negative asymptotic exchange-correlation hole, when one electrons wanders far away from the rest of the molecule. The appropriate two-electron measures of the electron density responses for an electrophilic, nucleophilic, and radical attacks are proposed, and the exact correspondence with the electron density of the Frontier Orbitals is established for the hypothetical Kohn–Sham system.     

Kinetic energy as functional of the correlation hole

Using the marginal decomposition of the many-body probability distribution the electronic kinetic energy is expressed as the functional of the electron density and correlation hole. The analysis covers both the molecule as a whole and its constituent subsystems. The importance of the Fisher information for locality is emphasized.     

Angular correlation of electrons in the ground state of helium

The spatial angular correlation of electrons in the ground state of the helium atom has been examined using configuration interaction and Hylleraas wave-functions. It was found that, in general, the average angle between the electrons is not a maximum when the two electrons are at the same distance from the nucleus. For configuration interaction wave-functions there is a position of the electrons for which the average value of the angle between the electrons is a maximum. Hylleraas wave-functions do not show this behavior.     

The intensity and polarization aspects of photochemical hole burning

Hole-burning spectra are considered, taking into account averaging over molecular orientations. Dependence of hole-burning spectra on the polarization of the probing laser is found. A method for finding the correct Debye-Waller factor from hole-burning and fluorescence line-narrowing spectra is suggested.     

Angular correlation functions of perpendicular bands of linear molecules

The angular correlation functions of the perpendicular infrared transitions of linear polyatomic molecules in the diluted gas phase and in dense media are represented as limiting cases of the angular correlation functions of the perpendicular infrared transitions of symmetric-top molecules with the Coriolis coupling constant 3z equal + 1.     

Parallel electron correlation effect and Fermi hole structure

Based on the charge density functional theory, a simple method is proposed to calculate the parallel electron correlation coefficient, correlation charge, and exchange correlation energy. In contrast to the result in the literature, our analysis reveals that the Fermi hole has its fine structure which is different from the model suggested in the literature. © 1996 John Wiley & Sons, Inc.     

The optimal size of the exchange hole and reduction to one-particle Hamiltonians

We use the concept of the exchange hole introduced by Slater to bound the energy of atoms, molecules, and other systems interacting by Coulomb forces from below by one-particle Hamiltonians with an effective screening potential and an exchange hole around each electron. Interestingly enough the optimal size of the exchange hole is smaller than Slater proposed: the best lower bound is obtained when the exchange hole carries charge 1/2 instead of 1. To highlight the quality of our estimate we show that the Dirac exchange energy with a slightly different constant bounds the exchange–correlation energy from below, an estimate previously derived by Lieb and later improved by Lieb and Oxford. Acknowledgements The authors thank Walter Farkas and Christian Hainzl for helpful discussions. Financial support by the European Union under its IHP network program, grant HPRN-CT-2002-00277, is gratefully acknowledged.© By the authorsThe author A.M. Klaus Müller is deceased     

Certain aspects of heterophase ion exchange

Ion exchange between an aqueous solution of KCl and a solution of tetraoctylammonium bromide in toluene has been studied at 20–70°C. Equilibrium exchange constants were measured. The free energy of the ion exchange is determined to a large extent by Coulombic interaction, which increases with decrease in the radius of the ion. The strength of the Q⁺X^– bond is weakened on passing from the normal onium salt to the hydrate and the rate of ion exchange increases. The position of equilibrium during approach to it from different sides may be affected by different formation processes of complexes with low activity in respect to exchange.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 8, pp. 1773–1776, August, 1991.     

The antiparallel electron correlation coefficient and Coulomb hole structure

Based on the charge density functional theory, a simple method is proposed to calculate the antiparallel electron correlation coefficient, correlation charge, and correlation energy. In contrast to the result stated in the literature, our analysis reveals that the Coulomb hole has a fine structure. To our knowledge, this is the first time it has been proven that the electrons obey the curve correlation law in an intermediate separation range but the electrons obey the linear correlation law in small and large separation ranges. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 74: 1–6, 1999     

Angular correlation functions of symmetric-top molecules influenced by coriolis coupling

The influence of the Coriolis coupling on the angular autocorrelation functions (ACF's) of symmetric-top molecules is calculated starting with the angular ACF's given by St. Pierre and Steele. As an example the theoretical ACF of the v₄ transition of CHCl₃ is compared with the experiment.     

Theoretical study of the ethane ionization spectra within the correlation hole model

This work is an extension of a previous study on the assignment of the peaks of the photoionization spectrum of C₂H₆ [1]. The model of the correlation hole is reconsidered in order to carry out a new study of the states² A _1g ,² E _g ,² E _u and² A _2u of the C₂H ₆ ⁺ The qualitative relations which the average mass of the electrons in the Coulomb hole must have for the four states of the C₂H ₆ ⁺ , lead to a new criterion for the assignation of the peaks of the spectrum. The arrangement obtained for the two lower peaks is in agreement with those obtained previously [1].     

New exact relations for improving the exchange and correlation potentials

For the purpose of improving present approximations to the exchange and correlation potentials, newly derived properties of the exact exchange and correlation potentials are summarized. Present approximations are not expected to generally satisfy these properties. The summarized properties include relations at the Fermi level, low-density requirements, and a new density functional formula for computing ionization energies. © 1995 John Wiley & Sons, Inc.     

Remarks on the fermi contact interaction

It is shown by rigorous mathematical methods that the so-called Fermi contact interaction does not define any selfadjoint Hamiltonian, and the only possible form of contact interaction localized strictly at r = 0 is found. However, the Fermi contact interaction retains sense when used as a bilinear form in the perturbation theory for Dirac electrons. Some results obtained earlier by other authors are confirmed and interpreted by our analysis.     

A correlation energy calculation of the 1s hole state in neon

The Bethe-Goldstone formalism for calculating correlation energy has been applied to the 1s hole state in neon. The binding energy of the 1s electron is computed to be 870.0 eV which is in excellent agreement with experiment.     

The fermi surface of beryllium

The Fermi surface (FS ) of beryllium has been calculated using the augmented plane wave energy bands for the material. The extremum area and the FS caliper distances are in excellent agreement with the de Haas–van Alphen measurements, and are better than existing ab initio calculations.     

A perspective on the link between the exchange(-correlation) hole and dispersion forces

In a recent series of papers, Becke and Johnson have proposed an elegant model for London dispersion (van der Waals’) forces in terms of the exchange hole. A perspective on this work is presented here, showing how the exchange-correlation hole is naturally related to “conventional” perturbative approaches to dispersion. The key to establishing this link is the fluctuation-dissipation theorem, which allows the exchange-correlation hole to be related to the frequency-dependent linear response.