Polarization Green's function with multiconfiguration self-consistent-field reference states

The polarization Green's-function formalism in the superoperator notation of Goscinski and Lukman is re-derived using a multiconfiguration self-consistent-field (MC -SCF ) reference state to establish the superoperator metric. The potential advantages of employing this more general reference state in Green's-function theories and certain inherent weaknesses associated with the traditional Hartree–Fock or Rayleigh–Schrödinger perturbation theory reference state choices are briefly discussed. The Hermiticity of the superoperators is analyzed within the framework of the MC –SCF reference state. Using a concept of order appropriate for this reference state choice, explicit formulas and computational procedures for the implementation of this Green's-function theory are presented and specialized to include terms consistent through second order.     

A direct CI method with a multiconfigurational reference state

A method for direct configuration–interaction (CI ) calculations with a multiconfigurational reference function is described. The reference state can contain several closed-shell electronic configurations and the CI expansion comprises all single and double replacements out of all these configurations. The resulting secular problem is solved using a variation-perturbation method. A number of examples are given showing the efficiency of the method. The largest CI expansion used in calculations with this program so far contains 76,471 spin- and space-symmetrized configurations.     

Perturbation theory for multiconfiguration reference states

Vector method procedures are adapted to evaluate Rayleigh-Schrödinger perturbation corrections to a multiconfiguration zeroth order function. If this function is sufficiently flexible, this perturbation theory can be applied to low lying excited states. The effectiveness of our theory is demonstrated on the ground state of F₂ and the low lying excited states of Mg₂. Energies calculated through fourth order are compared with appropriate CI results.     

Quasi-degenerate perturbation theory with general multiconfiguration self-consistent field reference functions

The quasi-degenerate perturbation theory (QDPT) with complete active space (CAS) self-consistent field (SCF) reference functions is extended to the general multiconfiguration (MC) SCF references functions case. A computational scheme that utilizes both diagrammatic and sum-over-states approaches is presented. The second-order effective Hamiltonian is computed for the external intermediate configurations (including virtual or/and core orbitals) by the diagrammatic approach and for internal intermediate configurations (including only active orbitals) by the configuration interaction matrix-based sum-over-states approach. The method is tested on the calculations of excitation energies of H(2)O, potential energy curves of LiF, and valence excitation energies of H(2)CO. The results show that the present method yields very close results to the corresponding CAS-SCF reference QDPT results and the available experimental values. The deviations from CAS-SCF reference QDPT values are less than 0.1 eV on the average for the excitation energies of H(2)O and less than 1 kcal/mol for the potential energy curves of LiF. In the calculation of the valence excited energies of H(2)CO, the maximum deviation from available experimental values is 0.28 eV.     

Automated generation of coupled-cluster diagrams: implementation in the multireference state-specific coupled-cluster approach with the complete-active-space reference

An algorithm for generation of the spin-orbital diagrammatic representation, the corresponding algebraical formulas, and the computer code of the coupled-cluster (CC) method with an arbitrary level of the electronic excitations has been developed. The method was implemented in the general case as well as for specific application in the state-specific multireference coupled-cluster theory (SSMRCC) based on the concept of a "formal reference state." The algorithm was tested in SSMRCC calculations describing dissociation of a single bond and in calculations describing simultaneous dissociation of two single bonds--the problem requiring up to six-particle excitations in the CC operator.     

The multiconfiguration time-dependent Hartree-Fock method for quantum chemical calculations

We apply the multiconfiguration time-dependent Hartree-Fock method to electronic structure calculations and show that quantum chemical information can be obtained with this explicitly time-dependent approach. Different equations of motion are discussed, as well as the numerical cost. The two-electron integrals are calculated using a natural potential expansion, of which we describe the convergence behavior in detail.     

Spin-conserving and spin-flipping equation-of-motion coupled-cluster method with triple excitations

We report the implementation of the spin-conserving and spin-flipping variants of the equation-of-motion (EOM) coupled-cluster (CC) model, which includes single and double excitations in the CC part and single, double, and triple excitations in the EOM part, i.e., EOM-CC(2,3) [Hirata, Nooijen, Bartlett, Chem. Phys. Lett. 326, 255 (2000)] for closed- and open-shell references. Inclusion of triples significantly improves the accuracy of EOM-CCSD for excitation energies (EOM-EE-CCSD) and its spin-flip (SF) counterpart, EOM-SF-CCSD, especially when the reference wave function is strongly spin-contaminated. A less computationally demanding active space variant with semi-internal triples has also been implemented. The capabilities of full and active space EOM-CC(2,3) are demonstrated by applications to CO(+) and CH radicals as well as to the methylene and trimethylenemethane diradicals and the dehydro-m-xylylene triradical.     

Equation-of-motion coupled-cluster method for ionized states with spin-orbit coupling

We report implementation of the equation of motion coupled-cluster approach for ionized states (EOMIP-CC) with spin-orbit coupling (SOC) using closed-shell state as reference in this work. Ionization potentials (IPs) are calculated in the ionized 1h and 2h1p space with EOM at the CC singles (CCS) as well as the CC singles and doubles levels (CCSD). In this EOMIP-CC approach, SOC is included either in both the CC and EOM steps or only in the EOM step. It should be noted that IPs provided by the EOMIP-CC approach with SOC included only in the EOM step are not size-intensive. Time-reversal symmetry and spatial symmetry are exploited for D(2h) and its subgroups to reduce computational effort. All these approaches have been shown to be able to afford acceptable estimates for SOC splittings. The EOMIP-CCSD with SOC included only in the EOM step can provide reasonable IPs for systems containing up to 5th row elements. On the other hand, the EOMIP-CCS approach with SOC included in both CC and EOM steps could not predict a bounded (2)∑(g) (+) state for I(2) (+) and should be used with care.     

Generalized-molecular-orbital theory: Simple multiconfiguration self-consistent-field method

Even after completing a multiconfiguration self-consistent-field (MCSCF ) calculation, one must often include additional configuration interaction (CI ) to obtain quantitative or semiquantitative results. There is some question of whether the prior MCSCF calculation is worthwhile, if additional CI is needed later. We have developed a new MCSCF computational method, which, because of our assumptions about the nature of the configurations, yields one Fock-like operator for all the “filled” orbitals (high occupation numbers) and a second Fock-like operator for all the “virtual” orbitals (low occupation numbers). Since there are only two matrices to build, our method is considerably faster than other MCSCF approaches. Because of these similarities to standard molecular-orbital (MO ) calculations, we have termed our approach generalized-molecular-orbital (GMO ) theory. However, the “virtual” orbitals, unlike those of standard MO theory, are optimized to correlate the “filled” ones and can he used in a subsequent CI calculation. Results are presented for the correlation energy of H₂O, the spectroscopic constants of N₂, the singlet–triplet energy separations in CH₂, and the nature of the chromium–chromium quadruple bond. Although these results are at a very low level of CI , the GMO approach appears to correct for the gross deficiencies of the single-determinant SCF procedure.     

A coupled-cluster method for quasidegenerate states

A size-extensive, multireferences coupled-cluster method for studies of quasidegenerate states based on the Jeziorski–Monkhorst [16] ansatz for the cluster operator (Ω = ∑eP_j, where the sum is extended over the configurations spanning the model space), is presented and applied in pilot calculations. The method is referred to as multireference coupled electron-pair method (MR CEPM ), because it is assumed that the individual cluster operators can be approximated by their two-body parts, i.e., T_j ≈ T_j(2). The linear version of this method (MR L-CEPM ) is also discussed. Both methods are applied to two simple model systems: (1) a minimum basis set model involving eight hydrogen atoms in various spacial arrangements for which the degree of quasidegeneracy can be continuously varied; (2) a model involving the C_2ν insertion of Be into H₂. For the first time in multireference coupled-cluster calculations, the nonlinear parts of the equations are completely accounted for. The MR CEPM results are very encouraging for strongly quasidegenerate states. The MR L -CEPM results are slightly below the accurate (FCI ) values.     

A natural linear scaling coupled-cluster method

It is shown that using an appropriate localized molecular orbital (LMO) basis, one is able to calculate coupled-cluster singles and doubles (CCSD) wave functions and energies for very large systems by performing full CCSD calculations on small subunits only. This leads to a natural linear scaling coupled-cluster method (NLSCC), in which total correlation energies of extended systems are evaluated as the sum of correlation energy contributions from individual small subunits within that system. This is achieved by defining local occupied orbital correlation energies. These are quantities, which in the LMO basis become transferable between similar molecular fragments. Conventional small scale existing molecular CCSD codes are all that is needed, the local correlation effect being simply transmitted via the appropriate LMO basis. Linear scaling of electronic correlation energy calculations is thus naturally achieved using the NLSCC approach, which in principle can treat nonperiodic extended systems of infinite basis set size. Results are shown for alkanes and several polyglycine molecules and the latter compared to recent results obtained via an explicit large scale LCCSD calculation. (c) 2004 American Institute of Physics.     

Direct configuration interaction with a reference state composed of many reference configurations

The configuration interaction method where a single reference state is composed of a linear combination of reference configurations is analyzed in detail. In this method single and double replacements are constructed by applying annihilation and creation operators on the reference state. The analysis is based on the recently derived factorization of the direct CI coupling coefficients into internal and external parts. Using the internal coupling coefficients the integrals are transformed to new entities which are used in the diagonalization step. This two-step procedure differs significantly from the usual straightforward one-step direct CI procedure. A number of operations analysis shows that calculations with the present method should be feasible even with a large number of reference configurations in the reference state. Based on first-order perturbation theory the accuracy of the method is predicted to be close to the accuracy obtained with the usual CI method with many reference configurations.     

Breaking bonds with the left eigenstate completely renormalized coupled-cluster method

The recently developed [P. Piecuch and M. Wloch, J. Chem. Phys. 123, 224105 (2005)] size-extensive left eigenstate completely renormalized (CR) coupled-cluster (CC) singles (S), doubles (D), and noniterative triples (T) approach, termed CR-CC(2,3) and abbreviated in this paper as CCL, is compared with the full configuration interaction (FCI) method for all possible types of single bond-breaking reactions between C, H, Si, and Cl (except H2) and the H2Si[Double Bond]SiH2 double bond-breaking reaction. The CCL method is in excellent agreement with FCI in the entire region R=1-3Re for all of the studied single bond-breaking reactions, where R and Re are the bond distance and the equilibrium bond length, respectively. The CCL method recovers the FCI results to within approximately 1 mhartree in the region R=1-3Re of the H-SiH3, H-Cl, H3Si-SiH3, Cl-CH3, H-CH3, and H3C-SiH3 bonds. The maximum errors are -2.1, 1.6, and 1.6 mhartree in the R=1-3Re region of the H3C-CH3, Cl-Cl, and H3Si-Cl bonds, respectively, while the discrepancy for the H2Si[Double Bond]SiH2 double bond-breaking reaction is 6.6 (8.5) mhartree at R=2(3)Re. CCL also predicts more accurate relative energies than the conventional CCSD and CCSD(T) approaches, and the predecessor of CR-CC(2,3) termed CR-CCSD(T).     

Generalized brillouin theorem multiconfiguration method for excited states

The Generalized Brillouin Theorem Multiconfiguration Method (GBT-MC) of Grein and Chang is extended and applied to the calculation of excited states. Orthogonality constraints to lower states as well as second-order interaction effects of states lying close together have been taken into account. In this way quadratic convergence can be guaranteed. Difficulties with coupling coefficients and Lagrangian multipliers of SCF methods can be circumvented. Test calculations have been performed on valence electron excited states of C, H₂O, and CH₂O, and on core excited states of Li.     

The coupled-cluster method in high sectors of the Fock space

The coupled-cluster method is applied to high sectors of the Fock space (up to five electrons outside a closed shell). Ionization potentials and excitation energies are calculated for atomic N, O, F, P, and S and their ions. The effect of virtual triple excitations is included, exactly or at several levels of appoximation. These terms are important for accurate results in the high sectors. © 1995 John Wiley & Sons, Inc.     

Excited states in the multireference state-specific coupled-cluster theory with the complete active space reference

The recently proposed multireference state-specific coupled-cluster theory with the complete active space reference has been used to study electronically excited states with different spatial and spin symmetries. The algorithm for the method has been obtained using the computerized approach for automatic generation of coupled-cluster diagrams with an arbitrary level of the electronic excitation from a formal reference determinant. The formal reference is also used to generate the genuine reference state in the form of a linear combination of determinants contracted to a configuration with the spin and spatial symmetries of the target state. The natural-orbital expansions of the one-electron configuration inferaction density matrix allowed us to obtain the most compact orbital space for the expansion of the reference function. We applied our approach in the calculations of singlet and triplet states of different spatial symmetries of the water molecule. The comparisons of the results with values obtained using other many-particle methods and with the full configuration interaction results demonstrate good ability of the approach to deal with electronic excited states.