Multiresolution quantum chemistry in multiwavelet bases: excited states from timedependent Hartree–Fock and density functional theory via linear response
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 computed with Gaussian basis functions aremore »
 Authors:

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 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:
 OSTI Identifier:
 1265805
 Grant/Contract Number:
 AC0500OR22725; MDA9720010016; ACI0082982; DMS0219326; AC0376SF0098
 Type:
 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
 Research Org:
 Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)
 Sponsoring Org:
 USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC22)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY