skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: SCDM-k: Localized orbitals for solids via selected columns of the density matrix

Authors:
ORCiD logo; ;
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1398570
Grant/Contract Number:
FC02-13ER26134/DESC0009409
Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 334; Journal Issue: C; Related Information: CHORUS Timestamp: 2017-10-07 03:25:10; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English

Citation Formats

Damle, Anil, Lin, Lin, and Ying, Lexing. SCDM-k: Localized orbitals for solids via selected columns of the density matrix. United States: N. p., 2017. Web. doi:10.1016/j.jcp.2016.12.053.
Damle, Anil, Lin, Lin, & Ying, Lexing. SCDM-k: Localized orbitals for solids via selected columns of the density matrix. United States. doi:10.1016/j.jcp.2016.12.053.
Damle, Anil, Lin, Lin, and Ying, Lexing. Sat . "SCDM-k: Localized orbitals for solids via selected columns of the density matrix". United States. doi:10.1016/j.jcp.2016.12.053.
@article{osti_1398570,
title = {SCDM-k: Localized orbitals for solids via selected columns of the density matrix},
author = {Damle, Anil and Lin, Lin and Ying, Lexing},
abstractNote = {},
doi = {10.1016/j.jcp.2016.12.053},
journal = {Journal of Computational Physics},
number = C,
volume = 334,
place = {United States},
year = {Sat Apr 01 00:00:00 EDT 2017},
month = {Sat Apr 01 00:00:00 EDT 2017}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1016/j.jcp.2016.12.053

Citation Metrics:
Cited by: 1work
Citation information provided by
Web of Science

Save / Share:
  • Ab initio calculations were performed on selected first-row hydrides with a large Gaussian basis set. Energy localized molecular orbitals (LMOs) were computed and analyzed in terms of their sizes and shapes. The total molecular electronic energy was partitioned into components which may be associated with a LMO, and the relation between the sizes and energies of such orbitals was examined. It was found that a simple energy-size relation exists for core LMOs but only approximately holds for bond LMOs.
  • A coherent, intrinsic, basis-set-independent analysis is developed for the invariants of the first-order density matrix of an accurate molecular electronic wavefunction. From the hierarchical ordering of the natural orbitals, the zeroth-order orbital space is deduced, which generates the zeroth-order wavefunction, typically an MCSCF function in the full valence space. It is shown that intrinsically embedded in such wavefunctions are elements that are local in bond regions and elements that are local in atomic regions. Basis-set-independent methods are given that extract and exhibit the intrinsic bond orbitals and the intrinsic minimal-basis quasi-atomic orbitals in terms of which the wavefunction can bemore » exactly constructed. The quasi-atomic orbitals are furthermore oriented by a basis-set independent method (viz. maximization of the sum of the fourth powers of all off-diagonal density matrix elements) so as to exhibit clearly the chemical interactions. The unbiased nature of the method allows for the adaptation of the localized and directed orbitals to changing geometries.« less
  • The density operator (density matrix) of a quantum mechenical system can be decomposed into operators which transform as irreducible representations of the symmetry group in coordinate and spin space. Each of these components has a physical meaning connected with the expectation values of certain operators. The reduced density matrices can be decomposed in a completely analogous way. The symmetry properties of the total wave function give rise to degeneracies of the eigenvalues of the reduced density matrices. These degeneracies can be removed by requiring that the natural spin orbitals (NSO, defined as the eigenfunctions of the first-order density matrix), asmore » well as the natural spin geminals (NSG, the eigenfunctions of the second-order density matrix) and their spinless counterparts transform as irreducible representations of the symmetry group and are eigenfunctions of S/sup 2/ and S/sub z/. In many cases this requirement is compatible with the original definition of the NSO, the NSG, etc., e.g., when there is no spatial degeneracy of the total wave function and when the Z- component of the total spin vanishes. When these conditions are not fulfilled an alternative definition of the NSO and the NSG is proposed. (auth)« less
  • The half-projected Hartree--Fock function for singlet states (HPHF) is analyzed in terms of natural electronic configurations. For this purpose the HPHF spinless density matrix and its natural orbitals are first deduced. It is found that the HPHF function does not contain any contribution from odd-times excited configurations. It is seen in addition, in the case of the singlet ground states, this function is approximately equivalent to two closed-shell configurations, although the nature of the excited one depends on the nuclear geometry. An example is given in the case of the LiH ground state. Finally, the application of this model formore » studying systems of more than two atoms is criticized.« less
  • We describe the theory and implementation of two extensions to the density-matrix renormalization-group (DMRG) algorithm in quantum chemistry: (i) to work with an underlying nonorthogonal one-particle basis (using a biorthogonal formulation) and (ii) to use non-Hermitian and complex operators and complex wave functions, which occur naturally in biorthogonal formulations. Using these developments, we carry out ground-state calculations on ethene, butadiene, and hexatriene, in a polarized atomic-orbital basis. The description of correlation in these systems using a localized nonorthogonal basis is improved over molecular-orbital DMRG calculations, and comparable to or better than coupled-cluster calculations, although we encountered numerical problems associated withmore » non-Hermiticity. We believe that the non-Hermitian DMRG algorithm may further become useful in conjunction with other non-Hermitian Hamiltonians, for example, similarity-transformed coupled-cluster Hamiltonians.« less