Topic

# Coulomb

About: Coulomb is a research topic. Over the lifetime, 13192 publications have been published within this topic receiving 243073 citations. The topic is also known as: C.

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TL;DR: A series of auxiliary basis sets to fit Coulomb potentials for the elements H to Rn (except lanthanides) is presented and computation times for the Coulomb part are reduced by a factor of ca.15 kJ mol(-1) per atom.

Abstract: A series of auxiliary basis sets to fit Coulomb potentials for the elements H to Rn (except lanthanides) is presented. For each element only one auxiliary basis set is needed to approximate Coulomb energies in conjunction with orbital basis sets of split valence, triple zeta valence and quadruple zeta valence quality with errors of typically below ca. 0.15 kJ mol−1 per atom; this was demonstrated in conjunction with the recently developed orbital basis sets of types def2-SV(P), def2-TZVP and def2-QZVPP for a large set of small molecules representing (nearly) each element in all of its common oxidation states. These auxiliary bases are slightly more than three times larger than orbital bases of split valence quality. Compared to non-approximated treatments, computation times for the Coulomb part are reduced by a factor of ca. 8 for def2-SV(P) orbital bases, ca. 25 for def2-TZVP and ca. 100 for def2-QZVPP orbital bases.

3,397 citations

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TL;DR: In this paper, an extension of the tight-binding (TB) approach to improve total energies, forces, and transferability is presented. The method is based on a second-order expansion of the Kohn-Sham total energy in density-functional theory (DFT) with respect to charge density fluctuations.

Abstract: We outline details about an extension of the tight-binding (TB) approach to improve total energies, forces, and transferability. The method is based on a second-order expansion of the Kohn-Sham total energy in density-functional theory (DFT) with respect to charge density fluctuations. The zeroth order approach is equivalent to a common standard non-self-consistent (TB) scheme, while at second order a transparent, parameter-free, and readily calculable expression for generalized Hamiltonian matrix elements may be derived. These are modified by a self-consistent redistribution of Mulliken charges (SCC). Besides the usual ``band structure'' and short-range repulsive terms the final approximate Kohn-Sham energy additionally includes a Coulomb interaction between charge fluctuations. At large distances this accounts for long-range electrostatic forces between two point charges and approximately includes self-interaction contributions of a given atom if the charges are located at one and the same atom. We apply the new SCC scheme to problems where deficiencies within the non-SCC standard TB approach become obvious. We thus considerably improve transferability.

3,070 citations

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TL;DR: In this paper, the auxilliary basis sets for the atoms H to At were optimized for an efficient treatment of molecular electronic Coulomb interactions for molecules with up to 300 atoms and 2500 basis functions.

Abstract: We present auxilliary basis sets for the atoms H to At – excluding the Lanthanides – optimized for an efficient treatment of molecular electronic Coulomb interactions. For atoms beyond Kr our approach is based on effective core potentials to describe core electrons. The approximate representation of the electron density in terms of the auxilliary basis has virtually no effect on computed structures and affects the energy by less than 10−4 a.u. per atom. Efficiency is demonstrated in applications for molecules with up to 300 atoms and 2500 basis functions.

2,833 citations

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TL;DR: In this article, an approximate treatment of Coulomb operators based on the expansion of molecular electron densities in atom-centered auxiliary basis sets is proposed. But this approach is not suitable for all atoms and cannot be applied to all atoms.

Abstract: We demonstrate accuracy and computational efficiency resulting from an approximate treatment of Coulomb operators which is based on the expansion of molecular electron densities in atom-centered auxiliary basis sets. This is of special importance in density functional methods which separate the treatment of Coulomb and exchange-correlation terms. Auxiliary basis sets are optimized as much as possible for isolated atoms and then augmented for use in molecular electronic structure calculations. For molecules involving atoms up to Br this typically affects energies by only 10−4 au per atom, and computed structure constants by less than 0.1 pm in bond distances and 0.1° in bond angles.

2,376 citations

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TL;DR: In this paper, the Coulomb interaction between localized electrons is shown to create a soft gap in the density of states near the Fermi level, and the form of the density within the gap is discussed.

Abstract: The Coulomb interaction between localized electrons is shown to create a 'soft' gap in the density of states near the Fermi level. The new temperature dependence of the hopping DC conductivity is the most important manifestation of the gap. The form of the density of states within the gap is discussed.

1,649 citations