Electron density and density matrix approximations using potential energy error bounds

An open quantum system is studied consisting of a particle moving in a spherical space with an infinite wall. With the theory of Lindblad the system is described by a density matrix which gets affected by operators with diffusive and dissipative properties depending on the linear momentum and density matrix only. It is shown that an infinite number of basis states leads to an infinite energy because of the infinite unsteadiness of the potential energy at the infinite wall. Therefore only a solution with a finite number of basis states can be performed. A slight approximation is introduced into the equation of motion in order that the trace of the density matrix remains constant in time. The equation of motion is solved by the method of searching eigenvalues. As a side-product two sums over the zeros of spherical Bessel functions are found.

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Application of variational reduced-density-matrix theory to the potential energy surfaces of the nitrogen and carbon dimers

The Journal of Chemical Physics ◽

10.1063/1.1901565 ◽

2005 ◽

Vol 122 (19) ◽

pp. 194104 ◽

Cited By ~ 30

Author(s):

Gergely Gidofalvi ◽

David A. Mazziotti

Keyword(s):

Potential Energy ◽

Density Matrix ◽

Potential Energy Surfaces ◽

Matrix Theory ◽

Reduced Density Matrix ◽

Energy Surfaces ◽

Reduced Density ◽

Density Matrix Theory

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Stockholder projector analysis: A Hilbert-space partitioning of the molecular one-electron density matrix with orthogonal projectors

The Journal of Chemical Physics ◽

10.1063/1.3673321 ◽

2012 ◽

Vol 136 (1) ◽

pp. 014107 ◽

Cited By ~ 10

Author(s):

Diederik Vanfleteren ◽

Dimitri Van Neck ◽

Patrick Bultinck ◽

Paul W. Ayers ◽

Michel Waroquier

Keyword(s):

Hilbert Space ◽

Density Matrix ◽

Electron Density ◽

Space Partitioning ◽

Electron Density Matrix ◽

Orthogonal Projectors

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Is it Reasonable to Obtain Information on the Polarizability and Hyperpolarizability Only from the Electron Density?

Australian Journal of Chemistry ◽

10.1071/ch17624 ◽

2018 ◽

Vol 71 (4) ◽

pp. 295 ◽

Cited By ~ 1

Author(s):

Dylan Jayatilaka ◽

Kunal K. Jha ◽

Parthapratim Munshi

Keyword(s):

Density Matrix ◽

Electron Density ◽

Ground State ◽

Density Functional ◽

Particle Density ◽

Density Matrices ◽

Hartree Fock ◽

Electron Density Matrix ◽

Ground State Electron ◽

Side Result

Formulae for the static electronic polarizability and hyperpolarizability are derived in terms of moments of the ground-state electron density matrix by applying the Unsöld approximation and a generalization of the Fermi-Amaldi approximation. The latter formula for the hyperpolarizability appears to be new. The formulae manifestly transform correctly under rotations, and they are observed to be essentially cumulant expressions. Consequently, they are additive over different regions. The properties of the formula are discussed in relation to others that have been proposed in order to clarify inconsistencies. The formulae are then tested against coupled-perturbed Hartree-Fock results for a set of 40 donor-π-acceptor systems. For the polarizability, the correlation is reasonable; therefore, electron density matrix moments from theory or experiment may be used to predict polarizabilities. By constrast, the results for the hyperpolarizabilities are poor, not even within one or two orders of magnitude. The formula for the two- and three-particle density matrices obtained as a side result in this work may be interesting for density functional theories.

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The electron density function of the Hückel (tight-binding) model

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2017.0721 ◽

2018 ◽

Vol 474 (2210) ◽

pp. 20170721 ◽

Cited By ~ 3

Author(s):

Ernesto Estrada

Keyword(s):

Density Matrix ◽

Electron Density ◽

Tight Binding ◽

High Dimensional ◽

Spin Interaction ◽

Tight Binding Model ◽

Solid State Physics ◽

Binding Model ◽

Conjugated Molecules ◽

Unpaired Electrons

The Hückel (tight-binding) molecular orbital (HMO) method has found many applications in the chemistry of alternant conjugated molecules, such as polycyclic aromatic hydrocarbons (PAHs), fullerenes and graphene-like molecules, as well as in solid-state physics. In this paper, we found analytical expressions for the electron density matrix of the HMO method in terms of odd-powers of its Hamiltonian. We prove that the HMO density matrix induces an embedding of a molecule into a high-dimensional Euclidean space in which the separation between the atoms scales very well with the bond lengths of PAHs. We extend our approach to describe a quasi-correlated tight-binding model, which quantifies the number of unpaired electrons and the distribution of effectively unpaired electrons. In this case, we found that the corresponding density matrices induce embedding of the molecules into high-dimensional Euclidean spheres where the separation between the atoms contains information about the spin–spin repulsion between them. Using our approach, we found an analytic expression which explains the bond length alternation in polyenes inside the HMO framework. We also found that spin–spin interaction explains the alternation of distances between pairs of atoms separated by two bonds in conjugated molecules.

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