TY - JOUR

T1 - Higher-order equation-of-motion coupled-cluster methods for ionization processes

AU - Kamiya, Muneaki

AU - Hirata, So

N1 - Funding Information:
The authors thank Professor Suehiro Iwata (Hiroshima University) for a helpful discussion. This work has been funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Science DE-FG02-04ER15621. This work used the Molecular Science Computing Facility in the William R. Wiley Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, which is supported by the U.S. Department of Energy, Office of Science, Office of Biological and Environmental Research.

PY - 2006

Y1 - 2006

N2 - Compact algebraic equations defining the equation-of-motion coupled-cluster (EOM-CC) methods for ionization potentials (IP-EOM-CC) have been derived and computer implemented by virtue of a symbolic algebra system largely automating these processes. Models with connected cluster excitation operators truncated after double, triple, or quadruple level and with linear ionization operators truncated after two-hole-one-particle (2h1p), three-hole-two-particle (3h2p), or four-hole-three-particle (4h3p) level (abbreviated as IP-EOM-CCSD, CCSDT, and CCSDTQ, respectively) have been realized into parallel algorithms taking advantage of spin, spatial, and permutation symmetries with optimal size dependence of the computational costs. They are based on spin-orbital formalisms and can describe both α and β ionizations from open-shell (doublet, triplet, etc.) reference states into ionized states with various spin magnetic quantum numbers. The application of these methods to Koopmans and satellite ionizations of N2 and CO (with the ambiguity due to finite basis sets eliminated by extrapolation) has shown that IP-EOM-CCSD frequently accounts for orbital relaxation inadequately and displays errors exceeding a couple of eV. However, these errors can be systematically reduced to tenths or even hundredths of an eV by IP-EOM-CCSDT or CCSDTQ. Comparison of spectroscopic parameters of the FH + and NH + radicals between IP-EOM-CC and experiments has also underscored the importance of higher-order IP-EOM-CC treatments. For instance, the harmonic frequencies of the Ã 2∑ - state of NH + are predicted to be 1285, 1723, and 1705 cm -1 by IP-EOM-CCSD, CCSDT, and CCSDTQ, respectively, as compared to the observed value of 1707 cm -1. The small adiabatic energy separation (observed 0.04 eV) between the X̃ 2Π and ã 4∑ - states of NH + also requires IP-EOM-CCSDTQ for a quantitative prediction (0.06 eV) when the ã 4∑ - state has the low-spin magnetic quantum number (s z= 1/2). When the state with s z=3/2 is sought, the energy separations converge much more rapidly with the IP-EOM-CCSD value (0.03 eV) already being close to the observed (0.04 eV).

AB - Compact algebraic equations defining the equation-of-motion coupled-cluster (EOM-CC) methods for ionization potentials (IP-EOM-CC) have been derived and computer implemented by virtue of a symbolic algebra system largely automating these processes. Models with connected cluster excitation operators truncated after double, triple, or quadruple level and with linear ionization operators truncated after two-hole-one-particle (2h1p), three-hole-two-particle (3h2p), or four-hole-three-particle (4h3p) level (abbreviated as IP-EOM-CCSD, CCSDT, and CCSDTQ, respectively) have been realized into parallel algorithms taking advantage of spin, spatial, and permutation symmetries with optimal size dependence of the computational costs. They are based on spin-orbital formalisms and can describe both α and β ionizations from open-shell (doublet, triplet, etc.) reference states into ionized states with various spin magnetic quantum numbers. The application of these methods to Koopmans and satellite ionizations of N2 and CO (with the ambiguity due to finite basis sets eliminated by extrapolation) has shown that IP-EOM-CCSD frequently accounts for orbital relaxation inadequately and displays errors exceeding a couple of eV. However, these errors can be systematically reduced to tenths or even hundredths of an eV by IP-EOM-CCSDT or CCSDTQ. Comparison of spectroscopic parameters of the FH + and NH + radicals between IP-EOM-CC and experiments has also underscored the importance of higher-order IP-EOM-CC treatments. For instance, the harmonic frequencies of the Ã 2∑ - state of NH + are predicted to be 1285, 1723, and 1705 cm -1 by IP-EOM-CCSD, CCSDT, and CCSDTQ, respectively, as compared to the observed value of 1707 cm -1. The small adiabatic energy separation (observed 0.04 eV) between the X̃ 2Π and ã 4∑ - states of NH + also requires IP-EOM-CCSDTQ for a quantitative prediction (0.06 eV) when the ã 4∑ - state has the low-spin magnetic quantum number (s z= 1/2). When the state with s z=3/2 is sought, the energy separations converge much more rapidly with the IP-EOM-CCSD value (0.03 eV) already being close to the observed (0.04 eV).

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U2 - 10.1063/1.2244570

DO - 10.1063/1.2244570

M3 - Article

AN - SCOPUS:33747591001

VL - 125

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 7

M1 - 074111

ER -