The open shell single reference size-consistent self-consistent singles and doubles configuration interaction method: Application to ionization potentials

Block Effective Hamiltonian Theory and Its Application

Block effective Hamiltonian theory (BEHT) is presented in this work. Configuration interaction functions are divided into P, Q, and R spaces. Effective Hamiltonian is constructed with the partitioning technique within the P space. The eigenvalue problem of the effective Hamiltonian is then solved iteratively. It is demonstrated that the ground-state energies of N₂, HF, and F₂ calculated with BEHT converge to the multireference configuration interaction energies from below and the iteration number becomes smaller as BEHT energy becomes closer to the exact energy. The accuracy of BEHT is better than that of the second-order multireference perturbation theory, although the matrix elements in both methods are the same. The ionization potentials of the singlet state of HF, the doublet state of F, and the triplet state of NH and the potential energy curves of CH₄, C₂, and N₂ are calculated with BEHT and compared with experiments and results of CASSCF, CCSD, and CCSD(T) and the results of the full configuration interaction if available. The iteration numbers are all less than 10 in this study. These calculations show the good performances of BEHT in comparison with other theoretical approximation methods.

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 alpha and beta 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 A 2Sigma- 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 X 2Pi and a 4Sigma- states of NH+ also requires IP-EOM-CCSDTQ for a quantitative prediction (0.06 eV) when the a 4Sigma- 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).

Vertical spectrum of the C2H2+ system. An open shell (SC)2-CAS-SDCI study

The open shell (SC)(2)-CAS-SDCI method along with a basis set of atomic natural orbitals (ANO) has been applied for calculating the main ionization potentials of acetylene, as well as the manifold of excited states of the different symmetries up to 32 eV. In this method, the single and double excitations of a CAS space are generated and the corresponding CI matrix is corrected by means of the (SC)(2) procedure that cancels the size-extensivity error and adds some high order contributions. The mean absolute error for the outer-valence X (2)Pi(u)(1pi(u) (-1)), A (2)Sigma(g) (+)(3sigma(g) (-1)), and B (2)Sigma(u) (+)(2sigma(u) (-1)) states, and the inner-valence C (2)Sigma(g) (+)(2sigma(g) (-1)) state is 0.1 eV. The excited states of C(2)H(2) (+) corresponding to the Sigma(g) (+), Sigma(u) (+), Pi(g), Pi(u), Delta(g), and Delta(u) symmetries are reported and their composition is discussed. The results are thoroughly compared to the best available multireference CI calculations. Recent multichannel CI results by Wells and Lucchese [J Chem Phys 1999, 110, 6365] have been used also as a guide for the discussion of the results. Discrepancies in the description of many multiconfigurational states by means of the (SC)(2)-CAS-SDCI wave function as compared to previous large MR-CI calculations are significant and are, consequently, remarked on. A large mixing of the 3sigma(g) (-1) and 2sigma(g) (-1) processes is found in the A (2)Sigma(g) (+) and C (2)Sigma(g) (+) states, provided that the basis set is augmented with Rydberg functions.

Reducing CAS-SDCI space. Using selected spaces in configuration interaction calculations in an efficient way

A new method is presented, which allows an important reduction of the size of some Configuration Interaction (CI) matrices. Starting from a Complete Active Space (CAS), the numerous configurations that have a small weight in the CAS wave function are eliminated. When excited configurations (e.g., singly and doubly excited) are added to the reference space, the resulting MR-SDCI space is reduced in the same proportion as compared with the full CAS-SDCI. A set of active orbitals is chosen, but some selection of the most relevant excitations is performed because not all the possible excitations act as SDCI generators. Thanks to a new addressing technique, the computational time is drastically reduced, because the new addressing of the selected active space is as efficient as the addressing of the CAS. The presentation of the method is followed by two test calculations on the N(2) and HCCH molecules. For the N(2) the FCI results are taken as a benchmark reference. The outer valence ionization potentials of HCCH are compared to the experimental values. Both examples allow to test the accuracy of the MR-SDCI compared to that of the corresponding CAS-SDCI, despite the noticeable reduction of the CI space. The algorithm is suitable for the dressing techniques that allow for the correction of the size-extensivity error. The corrected results are also shown and discussed.