Adaptive local refinement of the electron density, one-particle density matrices, and electron orbitals by hierarchical wavelet decomposition

2005 ◽  
Vol 123 (14) ◽  
pp. 144107 ◽  
Author(s):  
János Pipek ◽  
Szilvia Nagy
Keyword(s):  
Electron Density ◽  
Wavelet Decomposition ◽  
Particle Density ◽  
Density Matrices ◽  
Local Refinement ◽  
Adaptive Local Refinement

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

2018 ◽  
Vol 71 (4) ◽  
pp. 295 ◽  
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.

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

2001 ◽  
Vol 215 (10) ◽  
Author(s):  
T. Asthalter ◽  
M. Walter
Keyword(s):  
Single Particle ◽  
Organic Molecules ◽  
Graphical Representation ◽  
Particle Density ◽  
Electron System ◽  
Covalent Bonding ◽  
Density Matrices ◽  
Multiple Bonds ◽  
Single Particle Density ◽  
Isoelectronic Series

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.

scholarly journals Adaptive Local Refinement with Octree Load Balancing for the Parallel Solution of Three-Dimensional Conservation Laws

1997 ◽  
Vol 47 (2) ◽  
pp. 139-152 ◽  
Author(s):  
J.E. Flaherty ◽  
R.M. Loy ◽  
M.S. Shephard ◽  
B.K. Szymanski ◽  
J.D. Teresco ◽  
...  
Keyword(s):  
Load Balancing ◽  
Conservation Laws ◽  
Three Dimensional ◽  
Local Refinement ◽  
Parallel Solution ◽  
Adaptive Local Refinement

Reduced fermion density matrices. II. Electron density of Kr

1974 ◽  
Vol 61 (8) ◽  
pp. 3394-3400 ◽  
Author(s):  
Jian‐M. Yuan ◽  
Soo‐Y. Lee ◽  
J. C. Light
Keyword(s):  
Electron Density ◽  
Density Matrices
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