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Title: Free iterative-complement-interaction calculations of the hydrogen molecule

Abstract

The free iterative-complement-interaction (ICI) method based on the scaled Schroedinger equation proposed previously has been applied to the calculations of very accurate wave functions of the hydrogen molecule in an analytical expansion form. All the variables were determined with the variational principle by calculating the necessary integrals analytically. The initial wave function and the scaling function were changes to see the effects on the convergence speed of the ICI calculations. The free ICI wave functions that were generated automatically were different from the existing wave functions, and this difference was shown to be physically important. The best wave function reported in this paper seems to be the best worldwide in the literature from the variational point of view. The quality of the wave function was examined by calculating the nuclear and electron cusps.

Authors:
;  [1];  [1];  [2]
  1. Department of Synthetic Chemistry and Biological Chemistry, Graduate School of Engineering, Kyoto University, Katsura, Nishikyo-ku, Kyoto 615-8510 (Japan)
  2. (Japan)
Publication Date:
OSTI Identifier:
20786294
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 72; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevA.72.062502; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; CONVERGENCE; ELECTRONS; HYDROGEN; ITERATIVE METHODS; MOLECULES; SCHROEDINGER EQUATION; VARIATIONAL METHODS; VELOCITY; WAVE FUNCTIONS

Citation Formats

Kurokawa, Yusaku, Nakashima, Hiroyuki, Nakatsuji, Hiroshi, and Fukui Institute for Fundamental Chemistry, Kyoto University, 34-4 Takano-Nishihiraki-cho, Sakyo-ku, Kyoto 606-8103. Free iterative-complement-interaction calculations of the hydrogen molecule. United States: N. p., 2005. Web. doi:10.1103/PHYSREVA.72.0.
Kurokawa, Yusaku, Nakashima, Hiroyuki, Nakatsuji, Hiroshi, & Fukui Institute for Fundamental Chemistry, Kyoto University, 34-4 Takano-Nishihiraki-cho, Sakyo-ku, Kyoto 606-8103. Free iterative-complement-interaction calculations of the hydrogen molecule. United States. doi:10.1103/PHYSREVA.72.0.
Kurokawa, Yusaku, Nakashima, Hiroyuki, Nakatsuji, Hiroshi, and Fukui Institute for Fundamental Chemistry, Kyoto University, 34-4 Takano-Nishihiraki-cho, Sakyo-ku, Kyoto 606-8103. Thu . "Free iterative-complement-interaction calculations of the hydrogen molecule". United States. doi:10.1103/PHYSREVA.72.0.
@article{osti_20786294,
title = {Free iterative-complement-interaction calculations of the hydrogen molecule},
author = {Kurokawa, Yusaku and Nakashima, Hiroyuki and Nakatsuji, Hiroshi and Fukui Institute for Fundamental Chemistry, Kyoto University, 34-4 Takano-Nishihiraki-cho, Sakyo-ku, Kyoto 606-8103},
abstractNote = {The free iterative-complement-interaction (ICI) method based on the scaled Schroedinger equation proposed previously has been applied to the calculations of very accurate wave functions of the hydrogen molecule in an analytical expansion form. All the variables were determined with the variational principle by calculating the necessary integrals analytically. The initial wave function and the scaling function were changes to see the effects on the convergence speed of the ICI calculations. The free ICI wave functions that were generated automatically were different from the existing wave functions, and this difference was shown to be physically important. The best wave function reported in this paper seems to be the best worldwide in the literature from the variational point of view. The quality of the wave function was examined by calculating the nuclear and electron cusps.},
doi = {10.1103/PHYSREVA.72.0},
journal = {Physical Review. A},
number = 6,
volume = 72,
place = {United States},
year = {Thu Dec 15 00:00:00 EST 2005},
month = {Thu Dec 15 00:00:00 EST 2005}
}
  • The simplest iterative complement (SIC) calculations starting from Hartree-Fock and giving full configuration interaction (CI) at convergence were performed using regular and inverse Hamiltonians. Each iteration step is variational and involves only one variable. The convergence was slow when we used the regular Hamiltonian, but became very fast when we used the inverse Hamiltonian. This difference is due to the Coulomb singularity problem inherent in the regular Hamiltonian; the inverse Hamiltonian does not have such a problem. For this reason, the merit of the inverse Hamiltonian over the regular one becomes even more dramatic when we use a better-quality basismore » set. This was seen by comparing the calculations due to the minimal and double-{zeta} basis sets. Similar problematic situations exist in the Krylov sequence and in the Lanczos and Arnoldi methods.« less
  • A local Schroedinger equation (LSE) method is proposed for solving the Schroedinger equation (SE) of general atoms and molecules without doing analytic integrations over the complement functions of the free ICI (iterative-complement-interaction) wave functions. Since the free ICI wave function is potentially exact, we can assume a flatness of its local energy. The variational principle is not applicable because the analytic integrations over the free ICI complement functions are very difficult for general atoms and molecules. The LSE method is applied to several 2 to 5 electron atoms and molecules, giving an accuracy of 10{sup -5} Hartree in total energy.more » The potential energy curves of H{sub 2} and LiH molecules are calculated precisely with the free ICI LSE method. The results show the high potentiality of the free ICI LSE method for developing accurate predictive quantum chemistry with the solutions of the SE.« less
  • The Schroedinger equation was solved very accurately for helium atom and its isoelectronic ions (Z=1-10) with the free iterative complement interaction (ICI) method followed by the variational principle. We obtained highly accurate wave functions and energies of helium atom and its isoelectronic ions. For helium, the calculated energy was -2.903 724 377 034 119 598 311 159 245 194 404 446 696 905 37 a.u., correct over 40 digit accuracy, and for H{sup -}, it was -0.527 751 016 544 377 196 590 814 566 747 511 383 045 02 a.u. These results prove numerically that with the free ICImore » method, we can calculate the solutions of the Schroedinger equation as accurately as one desires. We examined several types of scaling function g and initial function {psi}{sub 0} of the free ICI method. The performance was good when logarithm functions were used in the initial function because the logarithm function is physically essential for three-particle collision area. The best performance was obtained when we introduce a new logarithm function containing not only r{sub 1} and r{sub 2} but also r{sub 12} in the same logarithm function.« less
  • Very accurate variational calculations with the free iterative-complement-interaction (ICI) method for solving the Schroedinger equation were performed for the 1sNs singlet and triplet excited states of helium atom up to N=24. This is the first extensive applications of the free ICI method to the calculations of excited states to very high levels. We performed the calculations with the fixed-nucleus Hamiltonian and moving-nucleus Hamiltonian. The latter case is the Schroedinger equation for the electron-nuclear Hamiltonian and includes the quantum effect of nuclear motion. This solution corresponds to the nonrelativistic limit and reproduced the experimental values up to five decimal figures. Themore » small differences from the experimental values are not at all the theoretical errors but represent the physical effects that are not included in the present calculations, such as relativistic effect, quantum electrodynamic effect, and even the experimental errors. The present calculations constitute a small step toward the accurately predictive quantum chemistry.« less