Hiroshi Nakatsuji

Cluster expansion of the wavefunction. Electron correlations in ground and excited states by SAC (symmetry-adapted-cluster) and SAC CI theories

Abstract We have summarized the solutions of the SAC (symmetry-adapted-cluster) and SAC CI theories for the study of electron correlations in ground and excited states, respectively. Variational and non-variational solutions are considered for both theories and their features are discussed.

Cluster expansion of the wavefunction. Calculation of electron correlations in ground and excited states by SAC and SAC CI theories

Abstract The SAC and SAC CI theories are formulated for actual calculations of singlet ground states and their states of arbitrary spin multiplicity. Approximations are considered for the variational methods since time-consuming terms are involved. The results of test calculations for singlet states have shown, with much smaller numbers of variables (sizes of the matrices involved), excellent agreement with the full CI and close-to-full CI results. This shows the utility of the SAC theory for ground states and especially of the SAC CI theory for excited states, since the slow convergence of the CI theory is much more critical for excited states than for ground states.

Cluster expansion of the wavefunction, valence and rydberg excitations, ionizations, and inner-valence ionizations of CO2 and N2O studied by the sac and sac CI theories

Abstract Valence and Rydberg excitations, ionizations, and inner-valence ionizations of CO 2 and N 2 O, which are isoelectronic, are studied by the SAC and SAC CI theories. We have given a systematic assignment of the electronic spectra of these molecules, though there were some controversial situations in the assignment of the spectra. The broad and overlapping features of the spectra of the inner-valence ionizations are due to the existence of a large number of ionization-excitation states mixing with the singly ionized states. The theoretical origins of the similarities and differences in the photoelectron spectra of CO 2 and N 2 O are clarified.

Description of two- and many-electron processes by the SAC-CI method

Abstract The accuracy of the SAC-CI (symmetry-adapted-cluster configuration-interaction) method for two- and many-electron processes is improved by including triple, quadruple and higher excitation terms in the R† operators of the SAC-CI formalism. This is confirmed by comparing SAC-CI results with full-CI ones for various excited, ionized, and anion states of CO and C2.

Variational calculations of fermion second-order reduced density matrices by semidefinite programming algorithm

The ground-state fermion second-order reduced density matrix (2-RDM) is determined variationally using itself as a basic variable. As necessary conditions of the N-representability, we used the positive semidefiniteness conditions, P, Q, and G conditions that are described in terms of the 2-RDM. The variational calculations are performed by using recently developed semidefinite programming algorithm (SDPA). The calculated energies of various closed- and open-shell atoms and molecules are excellent, overshooting only slightly the full-CI energies. There was no case where convergence was not achieved. The calculated properties also reproduce well the full-CI results.

General SCF operator satisfying correct variational condition

We have shown that the correct variational equations for the general SCF orbitals are [Fi−Σj |ψj〉 〈 ψj |Gji] |ψi〉=0, where Gji=λjiFj+(1−λji)Fi; λji≠ 0 and how these may be combined into simple eigenvalue problems. In the course of discussions, we re‐examined whether the coupling operators suggested previously are based on the correct variational conditions.

Excited and ionized states of free base porphin studied by the symmetry adapted cluster‐configuration interaction (SAC‐CI) method

The SAC(symmetry adapted cluster)/SAC‐CI method is applied to the calculations of the ground, excited, and ionized states of the free base porphin. The electronic spectrum of porphin is well reproduced and new assignments for the B (Soret), N, L, and M bands are proposed. The present result shows that the four‐orbital model is strongly perturbed for the B and N bands by the excitations from the lower 4b1u MO and that the σ electron correlations are important for the description of the excited states. The absorption peaks in the ionization spectrum are assigned and the reorganization effect is found to be large especially for the n and σ electron ionizations.

Cluster expansion of the wave function. Valence and Rydberg excitations and ionizations of pyrrole, furan, and cyclopentadiene

The symmetry‐adapted cluster (SAC) expansion and the SAC‐CI theory have been applied to the calculations of the valence and Rydberg excitations and ionizations of the five‐membered ring compounds, pyrrole, furan, and cyclopentadiene. For almost all cases, the experimental values were reproduced to within 0.3 eV for the excitation energy, and to within 0.5–0.7 eV for the ionization potential. We have given several new assignments for the excitation spectra of pyrrole and furan, and the first ab initio assignments for cyclopentadiene. However, there were remarkable disagreements of about 1.2 eV for the singlet π → π* excitations of 2 1A1 state for furan, and of 1 1B2 state for cyclopentadiene. This is the same tendency as those due to the MRSD‐CI method. For ionization potential, our assignments of the peaks are essentially the same as those due to the Green’s function method by von Niessen et al., but the present SAC‐CI method reproduces the experimental data better than this method.

Quasirelativistic theory for the magnetic shielding constant. I. Formulation of Douglas-Kroll-Hess transformation for the magnetic field and its application to atomic systems

has been developed to study magnetic properties of molecules. The proposed Hamiltonian includes the relativistic magnetic vector potential in the framework of the DKH theory, and is applicable to the calculations of magnetic properties without further expansion in powers of c 21 . By combining with the finite-perturbation theory and the generalized-UHF method, new pictures of the magnetic shielding constant are derived. We apply the theory to calculations of the magnetic shielding constants of He isoelectronic systems, Ne isoelectronic systems, and noble gas atoms. The results of the present theory compare well with those of the four-component Dirac‐Hartree‐Fock calculations; the differences were within 3%. We note that the quasirelativistic theory that handles the magnetic vector potential at a nonrelativistic level greatly underestimates the relativistic effect. The so-called ‘‘picture change’’ effect is quite important for the magnetic shielding constant of heavy elements. The change in the orbital picture plays a significant role in the valence-orbital magnetic response as well as the core-orbital one. The effect of the finite nucleus is also studied using Gaussian nucleus model. The present theory reproduces the correct behavior of the finite-nucleus effect that has been reported with the Dirac theory. In contrast, the nonrelativistic theory and the quasirelativistic theory with the nonrelativistic vector potential underestimate the finite-nucleus effect.

Quasirelativistic theory for magnetic shielding constants. II. Gauge-including atomic orbitals and applications to molecules

Quasirelativistic theory of magnetic shielding constants based on the Douglas–Kroll–Hess transformation of the magnetic potential presented in a previous paper is extended to molecular systems that contain heavy elements. The gauge-including atomic orbital method is adapted to the quasirelativistic Hamiltonian to allow origin-independent calculations. The present theory is applied to the proton and halogen magnetic shielding constants of hydrogen halides and the 199Hg magnetic shielding constants and chemical shifts of mercury dihalides and methyl mercury halides. While the relativistic correction to the magnetic interaction term has little effect on the proton magnetic shielding constants, this correction is a dominant origin of the heavy atom shifts of the magnetic shielding constants of heavy halogens and mercury. The basis set-dependence of mercury shielding constants is quite large in the relativistic calculation; it is important to use the basis functions that are optimized by the relativistic metho...