Prog. Theor. Phys. Vol. 34 No. 2 (1965) pp. 210-233

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Effective Spin Hamiltonian for Nonorthogonal Orbitals. I

— Linked-Cluster Expansion —

Fumiko Yonezawa

Department of Physics, Kyoto University, Kyoto

(Received May 10, 1965)

Abstract:

The Heitler-London energy is given by a quotient, both the numerator and denominator of which seem to increase without limit when the number of atoms, N, becomes large. The diagram method is used to meet the situation and to show that this difficulty of divergence is spurious; the divergent denominator cancels the corresponding factor from the numerator. As a result, the energy expression as well as the effective expectation value of any operator is represented by certain appropriate linked-clusters, each of which is proportional to N. The linked-cluster expansion not only ensures that the nonorthogonality catastrophe does not really arise but also provides the systematic way to calculate the energy spectra and other physical quantities to a desired order. Now that the present method is free from any restrictions on the magnitude of the overlap integrals, this is a rigorous and general proof on the validity of the Heitler-London scheme for infinite systems.

URL : http://ptp.ipap.jp/link?PTP/34/210/
DOI : 10.1143/PTP.34.210

References:

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Citing Article(s) :

Progress of Theoretical Physics Vol. 36 No. 3 (1966) pp. 473-487 :
Remarks on the Nonorthogonality Problem

Tadashi Arai

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