Solving the Schrödinger and Dirac equations of hydrogen molecular ion accurately by the free iterative complement interaction method

Atsushi Ishikawa, Hiroyuki Nakashima, Hiroshi Nakatsuji

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

The nonrelativistic Schrödinger equation and the relativistic four-component Dirac equation of H2+ were solved accurately in an analytical expansion form by the free iterative complement interaction (ICI) method combined with the variational principle. In the nonrelativistic case, we compared the free ICI wave function with the so-called "exact" wave function as two different expansions converging to the unique exact wave function and found that the free ICI method is much more efficient than the exact method. In the relativistic case, we first used the inverse Hamiltonian to guarantee Ritz-type variational principle and obtained accurate result. We also showed that the ordinary variational calculation also gives a nice convergence when the g function is appropriately chosen, since then the free ICI calculation guarantees a correct relationship between the large and small components of each adjacent order, which we call ICI balance. This is the first application of the relativistic free ICI method to molecule. We calculated both ground and excited states in good convergence, and not only the upper bound but also the lower bound of the ground-state energy. The error bound analysis has assured that the present result is highly accurate.

Original languageEnglish
Article number124103
JournalJournal of Chemical Physics
Volume128
Issue number12
DOIs
Publication statusPublished - 2008
Externally publishedYes

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hydrogen ions
Dirac equation
Wave functions
molecular ions
complement
Hydrogen
Ions
Ground state
Hamiltonians
interactions
wave functions
variational principles
Excited states
Molecules
expansion
ground state
excitation
molecules

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

Solving the Schrödinger and Dirac equations of hydrogen molecular ion accurately by the free iterative complement interaction method. / Ishikawa, Atsushi; Nakashima, Hiroyuki; Nakatsuji, Hiroshi.

In: Journal of Chemical Physics, Vol. 128, No. 12, 124103, 2008.

Research output: Contribution to journalArticle

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