Haruyuki Nakano

Quasidegenerate perturbation theory with multiconfigurational self‐consistent‐field reference functions

A quasidegenerate perturbation theory based on multiconfigurational self‐consistent‐field (MCSCF) reference functions is derived. The perturbation theory derived here is for multistate, where several MCSCF functions obtained by the state‐averaged MCSCF method are used as the reference and an effective Hamiltonian is constructed by perturbation calculation. The energies of states interested in are obtained simultaneously by diagonalization of the effective Hamiltonian. An explicit formula of the effective Hamiltonian through second order is derived as well as general formalism, and is applied to calculate potential curves of the system H2, Be–H2, CO, NO, BN, and LiF. The results agree well with those of full configuration interaction or multireference single and double excitation configuration interaction methods for both the ground and the excited states.

MCSCF reference quasidegenerate perturbation theory with Epstein—Nesbet partitioning

Abstract A quasidegenerate perturbation theory (QDPT) with Epstein—Nesbet partitioning based on MCSCF reference functions is presented. The formulas for CSF-based matrix operations are derived. They are applied to the systems BeH 2 and CO, and compared with other methods. The potential energy curves agree well with those of the full-CI or MR-CI methods.

Theoretical study of the valence π→π* excited states of polyacenes: Benzene and naphthalene

Multireference perturbation theory with complete active space self‐consistent field (CASSCF) reference functions was applied to the study of the valence π→π* excited states of benzene and naphthalene. The eigenvectors and eigenvalues of CASSCF with valence π active orbitals satisfy pairing properties for the alternant hydrocarbons to a good approximation. The excited states of polyacenes are classified into the covalent minus states and ionic plus states with the use of the alternancy symmetry. The present theory satisfactorily describes the ordering of low‐lying valence π→π* excited states. The overall accuracy of the present approach is surprisingly high. We were able to predict the valence excitation energies with an accuracy of 0.27 eV for singlet u states and of 0.52 eV or better for singlet g states of naphthalene. Our predicted triplet states spectrum provides a consistent assignment of the triplet–triplet absorption spectrum of naphthalene. For benzene we were able to predict the valence excitatio...

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 H2O, potential energy curves of LiF, and valence excitation energies of H2CO. 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 H2O and less than 1 kcal/mol for the potential energy curves of LiF. In the calculation of the valence excited energies of H2CO, the maximum deviation from available experimental values is 0.28 eV.

Theoretical study of the excitation spectra of five‐membered ring compounds: Cyclopentadiene, furan, and pyrrole

Multireference perturbation theory with complete active space self‐consistent field (CASSCF) reference functions was applied to the study of the valence and Rydberg excited states in the range of 5–8 eV of five‐membered ring compounds, cyclopentadiene, furan, and pyrrole. The spectra of these molecules have been studied extensively for many years but characterization is far from complete. The present approach can describe all kinds of excited states with the same accuracy. The calculated transition energies are in good agreement with corresponding experimental data. We were able to predict the valence and Rydberg excited states with an accuracy of 0.27 eV or better except for the B+2 of pyrrole. The valence excited states of five‐membered ring compounds were interpreted in terms of the covalent minus states and ionic plus states of the alternate symmetry. The unobserved 1A1→A−1 transition with very weak intensity, which is hidden under the strong 1A1→B+2 transition, is also discussed. Overall, the present...

Study of low‐lying electronic states of ozone by multireference Mo/ller–Plesset perturbation method

The geometry and relative energy of the seven low‐lying electronic states of ozone and the ground state of ozonide anion have been determined in C2v symmetry by the complete active space self‐consistent field (CASSCF) and the multireference Mo/ller–Plesset perturbation (MRMP) methods. The results are compared with the photodetachment spectra of O−3 observed recently by Arnold et al. The theoretical electron affinity of ozone is 1.965 eV, which is 0.14 eV below the experimental result of 2.103 eV. The calculated adiabatic excitation energies (assignment of Arnold et al. in parentheses) of ozone are 3A2 0.90 eV (1.18 eV), 3B2, 1.19 eV (1.30 eV), 3B1, 1.18 eV (1.45 eV), 1A2, 1.15 eV (∼1.6 eV), 1B1, 1.65 eV (2.05 eV), and 1B2, 3.77 eV (3.41 eV), respectively. Overall the present theory supports the assignment of Arnold et al. However, the simple considerations of geometry and energy are insufficient to determine a specific assignment of the 3B2 and 3B1 states. The dissociation energy of the ground state of oz...

Transition state barrier height for the reaction H2CO→H2+CO studied by multireference Mo/ller–Plesset perturbation theory

The second-order multireference Mo/ller–Plesset perturbation method (MRMP) was applied to the accurate estimation of the transition state barrier height of H2CO→H2+CO reaction. The best estimate for the classical barrier height is 84.5 kcal/mol at the highest level of MRMP theory with the quadruple zeta plus triple polarization basis set and with the active space of 12 electrons in 11 active orbitals. The inclusion of zero-point vibrational energy correction reduces the activation energy to 79.1 kcal/mol, which is in excellent agreement with the experimental value of 79.2±0.8 kcal/mol [Polik, Guyer, and Moore, J. Chem. Phys. 92, 3453 (1990)]. Analysis of the second-order energies in terms of internal, semi-internal, and external contributions shows that the present MRMP provides a well balanced treatment for the estimation of the energy difference between the equilibrium and transition state structures.

A study of the ground state of manganese dimer using quasidegenerate perturbation theory

We study the electronic structure of the ground state of the manganese dimer using the state-averaged complete active space self-consistent field method, followed by second-order quasidegenerate perturbation theory. Overall potential energy curves are calculated for the 1Sigmag+, 11Sigmau+, and 11Piu states, which are candidates for the ground state. Of these states, the 1Sigmag+ state has the lowest energy and we therefore identify it as the ground state. We find values of 3.29 A, 0.14 eV, and 53.46 cm(-1) for the bond length, dissociation energy, and vibrational frequency, in good agreement with the observed values of 3.4 A, 0.1 eV, and 68.1 cm(-1) in rare-gas matrices. These values show that the manganese dimer is a van der Waals molecule with antiferromagnetic coupling.

Second-order quasi-degenerate perturbation theory with quasi-complete active space self-consistent field reference functions

A quasi-degenerate perturbation theory (QDPT) is presented that is based on quasi-complete active space self-consistent field (QCAS-SCF) reference functions. The perturbation method shown here is an extension of a previously proposed QDPT with CAS-SCF reference functions (CAS-QDPT) but is a more compact perturbation method that can employ a much smaller reference configuration space with the same number of active electrons and orbitals as the CAS case. A computational scheme to second-order using a diagrammatic approach is described. The second-order effective Hamiltonian consists of the contribution from external excitations, which involve core or/and virtual orbitals, and internal excitations, which involve only active orbitals. The importance of the internal excitation contribution is emphasized. The method is tested on the potential energy curves of the LiF molecule, the Rydberg excitation energies of furan, and the transition state barrier height of the reaction, H2CO→H2+CO. The results are in very g...

Relativistic quasidegenerate perturbation theory with four-component general multiconfiguration reference functions

Relativistic quasidegenerate perturbation theory (QDPT) using general multiconfiguration (GMC) reference functions is developed and implemented. It is the relativistic counterpart of the nonrelativistic QDPT with GMC reference and thus retains all the advantages of the nonrelativistic GMC reference QDPT, such as applicability to any configuration space and small computational cost compared to the complete configuration-space case. The method is applied to the potential-energy curves of the ground states of I(2) and Sb(2) molecules, the excitation energies of CH(3)I, and the energies of the lowest terms of C, Si, and Ge atoms, and is shown to provide a balanced description of potential-energy curves and accurate transition energies for systems containing heavy elements and to provide much better results compared to the reference function (i.e., active space configuration interaction) level.