### 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 language | English |
---|---|

Article number | 124103 |

Journal | Journal of Chemical Physics |

Volume | 128 |

Issue number | 12 |

DOIs | |

Publication status | Published - 2008 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Journal of Chemical Physics*,

*128*(12), [124103]. https://doi.org/10.1063/1.2842068

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

Research output: Contribution to journal › Article

*Journal of Chemical Physics*, vol. 128, no. 12, 124103. https://doi.org/10.1063/1.2842068

}

TY - JOUR

T1 - Solving the Schrödinger and Dirac equations of hydrogen molecular ion accurately by the free iterative complement interaction method

AU - Ishikawa, Atsushi

AU - Nakashima, Hiroyuki

AU - Nakatsuji, Hiroshi

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=41549152957&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=41549152957&partnerID=8YFLogxK

U2 - 10.1063/1.2842068

DO - 10.1063/1.2842068

M3 - Article

VL - 128

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 12

M1 - 124103

ER -