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

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 à 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).