State-selective multireference coupled-cluster theory employing the single-reference formalism: Implementation and application to the H8 model system

Piotr Piecuch, Ludwik Adamowicz

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171 Citations (Scopus)

Abstract

The new state-selective (SS) multireference (MR) coupled-cluster (CC) method exploiting the single-reference (SR) particle-hole formalism, which we have introduced in our recent paper [P. Piecuch, N. Oliphant, and L. Adamowicz, J. Chem. Phys. 99, 1875 (1993)], has been implemented and the results of the pilot calculations for the minimum basis-set (MBS) model composed of eight hydrogen atoms in various geometrical arrangements are presented. This model enables a continuous transition between degenerate and nondegenerate regimes. Comparison is made with the results of SR CC calculations involving double (CCD), single and double (CCSD), single, double, and triple (CCSDT), and single, double, triple, and quadruple (CCSDTQ) excitations. Our SS CC energies are also compared with the results of the Hilbert space, state-universal (SU) MR CC(S)D calculations, as well as with the MR configuration interaction (CI) results (with and without Davidson-type corrections) and the exact correlation energies obtained using the full CI (FCI) method. Along with the ground-state energies, we also analyze the resulting wave functions by examining some selected cluster components. This analysis enables us to assess the quality of the resulting wave functions. Our SS CC theory truncated at double excitations, which emerges through selection of the most essential clusters appearing in the full SR CCSDTQ formalism [SS CCSD (TQ) method] provides equally good results in nondegenerate and quasidegenerate regions. The difference between the ground-state energy obtained with the SS CCSD(TQ) approach and the FCI energy does not exceed 1.1 mhartree over all the geometries considered. This value compares favorably with the maximum difference of 2.8 mhartree between the SU CCSD energies and the FCI energies obtained for the same range of geometries. The SS CCSD(T) method, emerging from the SR CCSDT theory through selection of the most essential clusters, is less stable, since it neglects very important semi-internal quadruple excitations. Unlike the genuine multideterminantal SU CC formalism, our SS CC approach is not affected by the intruder state problem and its convergence remains satisfactory in nondegenerate and quasidegenerate regimes.

Original languageEnglish (US)
Pages (from-to)5792-5809
Number of pages18
JournalThe Journal of Chemical Physics
Volume100
Issue number8
StatePublished - 1994

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Charge coupled devices
formalism
Wave functions
Ground state
charge coupled devices
Geometry
Hilbert spaces
Hydrogen
energy
configuration interaction
Atoms
wave functions
excitation
ground state
geometry
Hilbert space
emerging
hydrogen atoms

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

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title = "State-selective multireference coupled-cluster theory employing the single-reference formalism: Implementation and application to the H8 model system",
abstract = "The new state-selective (SS) multireference (MR) coupled-cluster (CC) method exploiting the single-reference (SR) particle-hole formalism, which we have introduced in our recent paper [P. Piecuch, N. Oliphant, and L. Adamowicz, J. Chem. Phys. 99, 1875 (1993)], has been implemented and the results of the pilot calculations for the minimum basis-set (MBS) model composed of eight hydrogen atoms in various geometrical arrangements are presented. This model enables a continuous transition between degenerate and nondegenerate regimes. Comparison is made with the results of SR CC calculations involving double (CCD), single and double (CCSD), single, double, and triple (CCSDT), and single, double, triple, and quadruple (CCSDTQ) excitations. Our SS CC energies are also compared with the results of the Hilbert space, state-universal (SU) MR CC(S)D calculations, as well as with the MR configuration interaction (CI) results (with and without Davidson-type corrections) and the exact correlation energies obtained using the full CI (FCI) method. Along with the ground-state energies, we also analyze the resulting wave functions by examining some selected cluster components. This analysis enables us to assess the quality of the resulting wave functions. Our SS CC theory truncated at double excitations, which emerges through selection of the most essential clusters appearing in the full SR CCSDTQ formalism [SS CCSD (TQ) method] provides equally good results in nondegenerate and quasidegenerate regions. The difference between the ground-state energy obtained with the SS CCSD(TQ) approach and the FCI energy does not exceed 1.1 mhartree over all the geometries considered. This value compares favorably with the maximum difference of 2.8 mhartree between the SU CCSD energies and the FCI energies obtained for the same range of geometries. The SS CCSD(T) method, emerging from the SR CCSDT theory through selection of the most essential clusters, is less stable, since it neglects very important semi-internal quadruple excitations. Unlike the genuine multideterminantal SU CC formalism, our SS CC approach is not affected by the intruder state problem and its convergence remains satisfactory in nondegenerate and quasidegenerate regimes.",
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N2 - The new state-selective (SS) multireference (MR) coupled-cluster (CC) method exploiting the single-reference (SR) particle-hole formalism, which we have introduced in our recent paper [P. Piecuch, N. Oliphant, and L. Adamowicz, J. Chem. Phys. 99, 1875 (1993)], has been implemented and the results of the pilot calculations for the minimum basis-set (MBS) model composed of eight hydrogen atoms in various geometrical arrangements are presented. This model enables a continuous transition between degenerate and nondegenerate regimes. Comparison is made with the results of SR CC calculations involving double (CCD), single and double (CCSD), single, double, and triple (CCSDT), and single, double, triple, and quadruple (CCSDTQ) excitations. Our SS CC energies are also compared with the results of the Hilbert space, state-universal (SU) MR CC(S)D calculations, as well as with the MR configuration interaction (CI) results (with and without Davidson-type corrections) and the exact correlation energies obtained using the full CI (FCI) method. Along with the ground-state energies, we also analyze the resulting wave functions by examining some selected cluster components. This analysis enables us to assess the quality of the resulting wave functions. Our SS CC theory truncated at double excitations, which emerges through selection of the most essential clusters appearing in the full SR CCSDTQ formalism [SS CCSD (TQ) method] provides equally good results in nondegenerate and quasidegenerate regions. The difference between the ground-state energy obtained with the SS CCSD(TQ) approach and the FCI energy does not exceed 1.1 mhartree over all the geometries considered. This value compares favorably with the maximum difference of 2.8 mhartree between the SU CCSD energies and the FCI energies obtained for the same range of geometries. The SS CCSD(T) method, emerging from the SR CCSDT theory through selection of the most essential clusters, is less stable, since it neglects very important semi-internal quadruple excitations. Unlike the genuine multideterminantal SU CC formalism, our SS CC approach is not affected by the intruder state problem and its convergence remains satisfactory in nondegenerate and quasidegenerate regimes.

AB - The new state-selective (SS) multireference (MR) coupled-cluster (CC) method exploiting the single-reference (SR) particle-hole formalism, which we have introduced in our recent paper [P. Piecuch, N. Oliphant, and L. Adamowicz, J. Chem. Phys. 99, 1875 (1993)], has been implemented and the results of the pilot calculations for the minimum basis-set (MBS) model composed of eight hydrogen atoms in various geometrical arrangements are presented. This model enables a continuous transition between degenerate and nondegenerate regimes. Comparison is made with the results of SR CC calculations involving double (CCD), single and double (CCSD), single, double, and triple (CCSDT), and single, double, triple, and quadruple (CCSDTQ) excitations. Our SS CC energies are also compared with the results of the Hilbert space, state-universal (SU) MR CC(S)D calculations, as well as with the MR configuration interaction (CI) results (with and without Davidson-type corrections) and the exact correlation energies obtained using the full CI (FCI) method. Along with the ground-state energies, we also analyze the resulting wave functions by examining some selected cluster components. This analysis enables us to assess the quality of the resulting wave functions. Our SS CC theory truncated at double excitations, which emerges through selection of the most essential clusters appearing in the full SR CCSDTQ formalism [SS CCSD (TQ) method] provides equally good results in nondegenerate and quasidegenerate regions. The difference between the ground-state energy obtained with the SS CCSD(TQ) approach and the FCI energy does not exceed 1.1 mhartree over all the geometries considered. This value compares favorably with the maximum difference of 2.8 mhartree between the SU CCSD energies and the FCI energies obtained for the same range of geometries. The SS CCSD(T) method, emerging from the SR CCSDT theory through selection of the most essential clusters, is less stable, since it neglects very important semi-internal quadruple excitations. Unlike the genuine multideterminantal SU CC formalism, our SS CC approach is not affected by the intruder state problem and its convergence remains satisfactory in nondegenerate and quasidegenerate regimes.

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