Multiresolution quantum chemistry in multiwavelet bases: excited states from timedependent Hartree–Fock and density functional theory via linear response
Abstract
Using the fully numerical method for timedependent Hartree–Fock and density functional theory (TDHF/DFT) with the Tamm–Dancoff (TD) approximation we use a multiresolution analysis (MRA) approach to present our findings. From a reformulation with effective use of the density matrix operator, we obtain a general form of the HF/DFT linear response equation in the first quantization formalism. It can be readily rewritten as an integral equation with the boundstate Helmholtz (BSH) kernel for the Green's function. The MRA implementation of the resultant equation permits excited state calculations without virtual orbitals. Moreover, the integral equation is efficiently and adaptively solved using a numerical multiresolution solver with multiwavelet bases. Our implementation of the TDHF/DFT methods is applied for calculating the excitation energies of H _{2}, Be, N _{2}, H _{2}O, and C _{2}H _{4} molecules. The numerical errors of the calculated excitation energies converge in proportion to the residuals of the equation in the molecular orbitals and response functions. The energies of the excited states at a variety of length scales ranging from shortrange valence excitations to longrange Rydbergtype ones are consistently accurate. It is shown that the multiresolution calculations yield the correct exponential asymptotic tails for the response functions, whereas those computedmore »
 Authors:
 Inst. for Molecular Science, Aichi (Japan)
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Univ. of Colorado, Boulder, CO (United States)
 Stony Brook Univ., NY (United States); Brookhaven National Lab. (BNL), Upton, NY (United States)
 Publication Date:
 Research Org.:
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)
 Sponsoring Org.:
 USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC22)
 OSTI Identifier:
 1265805
 Grant/Contract Number:
 AC0500OR22725; MDA9720010016; ACI0082982; DMS0219326; AC0376SF0098
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Physical Chemistry Chemical Physics. PCCP (Print)
 Additional Journal Information:
 Journal Name: Physical Chemistry Chemical Physics. PCCP (Print); Journal Volume: 17; Journal Issue: 47; Journal ID: ISSN 14639076
 Publisher:
 Royal Society of Chemistry
 Country of Publication:
 United States
 Language:
 English
 Subject:
 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
Citation Formats
Yanai, Takeshi, Fann, George I., Beylkin, Gregory, and Harrison, Robert J. Multiresolution quantum chemistry in multiwavelet bases: excited states from timedependent Hartree–Fock and density functional theory via linear response. United States: N. p., 2015.
Web. doi:10.1039/C4CP05821F.
Yanai, Takeshi, Fann, George I., Beylkin, Gregory, & Harrison, Robert J. Multiresolution quantum chemistry in multiwavelet bases: excited states from timedependent Hartree–Fock and density functional theory via linear response. United States. doi:10.1039/C4CP05821F.
Yanai, Takeshi, Fann, George I., Beylkin, Gregory, and Harrison, Robert J. 2015.
"Multiresolution quantum chemistry in multiwavelet bases: excited states from timedependent Hartree–Fock and density functional theory via linear response". United States.
doi:10.1039/C4CP05821F. https://www.osti.gov/servlets/purl/1265805.
@article{osti_1265805,
title = {Multiresolution quantum chemistry in multiwavelet bases: excited states from timedependent Hartree–Fock and density functional theory via linear response},
author = {Yanai, Takeshi and Fann, George I. and Beylkin, Gregory and Harrison, Robert J.},
abstractNote = {Using the fully numerical method for timedependent Hartree–Fock and density functional theory (TDHF/DFT) with the Tamm–Dancoff (TD) approximation we use a multiresolution analysis (MRA) approach to present our findings. From a reformulation with effective use of the density matrix operator, we obtain a general form of the HF/DFT linear response equation in the first quantization formalism. It can be readily rewritten as an integral equation with the boundstate Helmholtz (BSH) kernel for the Green's function. The MRA implementation of the resultant equation permits excited state calculations without virtual orbitals. Moreover, the integral equation is efficiently and adaptively solved using a numerical multiresolution solver with multiwavelet bases. Our implementation of the TDHF/DFT methods is applied for calculating the excitation energies of H2, Be, N2, H2O, and C2H4 molecules. The numerical errors of the calculated excitation energies converge in proportion to the residuals of the equation in the molecular orbitals and response functions. The energies of the excited states at a variety of length scales ranging from shortrange valence excitations to longrange Rydbergtype ones are consistently accurate. It is shown that the multiresolution calculations yield the correct exponential asymptotic tails for the response functions, whereas those computed with Gaussian basis functions are too diffuse or decay too rapidly. Finally, we introduce a simple asymptotic correction to the local spindensity approximation (LSDA) so that in the TDDFT calculations, the excited states are correctly bound.},
doi = {10.1039/C4CP05821F},
journal = {Physical Chemistry Chemical Physics. PCCP (Print)},
number = 47,
volume = 17,
place = {United States},
year = 2015,
month = 2
}
Web of Science

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