On the Chemical Interpretation of the One‐Electron Density Matrix of Some Ionic Solids: LiH, LiF, and LiFHF

Asthalter, T.; Weyrich, Wolf

doi:10.1002/bbpc.19971010103

Cited by 12 publications

(7 citation statements)

References 69 publications

(8 reference statements)

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“…The experimental research has been accompanied by theoretical calculations of Compton profiles or their Fourier transforms, the so-called reciprocal form factors. The comparative analysis of experimental and theoretical data, however, has shown that even sufficiently saturated ab initio basis sets are unable to reproduce measured Compton profiles quantitatively [4][5][6]. The discrepancy between measurement and calculation exceeds the experimental uncertainty.…”

Section: Introductionmentioning

confidence: 88%

“…If the number of quantum beads N is made large enough, the quantum partition function Z as well as all quantities that are derived from Z can be evaluated with high accuracy. We have adopted the classical Metropolis approach [24] to derive the thermal properties of CÖH 6 and C 6 DÖ within the PIMC formalism. In the subsequent discussion of ensemble averaged electronic expectation values, temperatures of 50 and 750 K have been considered.…”

Section: Theoretical Background and Computational Conditionsmentioning

confidence: 99%

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New Aspects in the Calculation of Electronic Momentum Properties; an All-Quantum Study

Böhm

Ramı́rez

Schulte

1998

Zeitschrift Für Naturforschung A

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The electronic properties of the CÖHÖ and CaDö molecules have been studied by an all-quantum approach, where the classical and quantum degrees of freedom of the nuclei are taken into account in the evaluation of electronic expectation values. In the all-quantum approach suggested a Feynman path integral Monte Carlo (PIMC) formalism has been linked to an electronic ab initio Hamiltonian. The electronic expectation values have been calculated as averages over the manifold of nuclear configurations populated in thermal equilibrium. This theoretical setup leads to electronic expectation values that depend on the temperature and on the mass of the nuclei. The ensemble averaged electronic properties differ sizeably from the results derived on the basis of a single nuclear configuration of minimum energy. This behaviour should have physical implications for the theoretical calculation of electronic momentum properties such as Compton profiles, reciprocal form factors, etc. We describe an error source in the theoretical determination of electronic momentum properties which has not been commented so far.

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Section: Introductionmentioning

confidence: 88%

Section: Theoretical Background and Computational Conditionsmentioning

confidence: 99%

New Aspects in the Calculation of Electronic Momentum Properties; an All-Quantum Study

Böhm

Ramı́rez

Schulte

1998

Zeitschrift Für Naturforschung A

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“…Here we will explore these effects for the molecule LiH, which is largely ionic (Li + H − ) but less so than for example LiF. LiH was chosen since it is a useful and often studied system for exploring chemical bonding both in the gas phase and in the crystalline phase (see, e.g., [26,27] and references therein).…”

Section: Standard Exchange Hole In Lihmentioning

confidence: 99%

Phase Space, Density Matrices, Energy Densities, and Exchange Holes

Springborg¹,

Perdew²,

Schmidt³

2001

Zeitschrift Für Physikalische Chemie

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In the general case, quantum-mechanical quantities are represented by operators in position-or momentum-space representations, but in phase space they are represented by functions. The correspondence between classical mechanics and quantum mechanics is non-unique as a consequence of [x,p] = 0, and therefore the phase-space representation of quantum mechanics is also non-unique. We explain how different correspondence rules lead to different phase-space functions and how the latter are related to first-order reduced density matrices. As a special example, we discuss the phase-space representation of different terms of the total energy within the Hartree-Fock approximation for electronicstructure calculations. In particular we discuss how one may use the phase-space representation to define energy densities in position space, putting special emphasis on kinetic and exchange energy densities which are not unique. While the standard exchange energy density has an exchange hole which is normalized, the Weyl and other exchange energy densities have exchange holes which are more localized. We also make a numerical study of statistical correlations among variables commonly used in density functional theory and several energy densities, including the standard and Weyl exchange energy densities. Finally, we examine the spherical average of the standard exchange hole for the molecule LiH, finding that it reflects both the ionic and the covalent character of the bond.

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“…A check of the quality of the wavefunction for crystalline LiF by comparing to experimental Compton profiles [29] has been presented in [24]. The basis set for BeO is the same as used in [30]; the quality of this basis set with respect to the momentum-space wavefunction has been verified by comparison of experimental and theoretical isotropic Compton profiles in [31].…”

Section: Computational Detailsmentioning

confidence: 99%

“…The off-diagonal regions of the SPDM deserve special attention with respect to chemical bonding, since these regions respond in a very sensitive way to modifications of the nature, strength and range of the phase correlation between the wavefunctions of the interacting atoms or ions [22]. This has been demonstrated by discussing two-dimensional cuts along the bond axes of linear molecules [22] and solids [23,24]. In these cuts, both position coordinates r and r run along interatomic connection lines.…”

Section: Introductionmentioning

confidence: 97%

Visualizing Covalency and Multiple Bonds in Terms of the Electronic Single-Particle Density Matrix

Asthalter¹,

Walter²

2001

Zeitschrift Für Physikalische Chemie

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Two-dimensional cuts through spin-integrated single-particle density matrices (SPDMs) have proven to be a valuable tool to discuss the nature of chemical bonding independent of the degree of rotation of the underlying orbitals in Hilbert space. Starting from a straightforward concept for the interpretation of σ bonds, we briefly present how the transition from purely ionic to mainly covalent bonding is mirrored in the off-diagonal features of the SPDM in the isoelectronic series LiF, BeO and BN. Furthermore, we outline one of several possible ways to extend the graphical representation and interpretation of SPDMs to the case of π bonds in organic molecules and apply it to the conjugated π-electron system 1,6-hexadiynediol.

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On the Chemical Interpretation of the One‐Electron Density Matrix of Some Ionic Solids: LiH, LiF, and LiFHF

Cited by 12 publications

References 69 publications

New Aspects in the Calculation of Electronic Momentum Properties; an All-Quantum Study

New Aspects in the Calculation of Electronic Momentum Properties; an All-Quantum Study

Phase Space, Density Matrices, Energy Densities, and Exchange Holes

Visualizing Covalency and Multiple Bonds in Terms of the Electronic Single-Particle Density Matrix

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