Ryoichi Fukuda

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...

Formulation and implementation of direct algorithm for the symmetry-adapted cluster and symmetry-adapted cluster–configuration interaction method

We present a new computational algorithm, called direct algorithm, for the symmetry-adapted cluster (SAC) and SAC-configuration interaction (SAC-CI) methodology for the ground, excited, ionized, and electron-attached states. The perturbation-selection technique and the molecular orbital index based direct sigma-vector algorithm were combined efficiently with the use of the sparse nature of the matrices involved. The formal computational cost was reduced to O(N(2)xM) for a system with N-active orbitals and M-selected excitation operators. The new direct SAC-CI program has been applied to several small molecules and free-base porphin and has been shown to be more efficient than the conventional nondirect SAC-CI program for almost all cases. Particularly, the acceleration was significant for large dimensional computations. The direct SAC-CI algorithm has achieved an improvement in both accuracy and efficiency. It would open a new possibility in the SAC/SAC-CI methodology for studying various kinds of ground, excited, and ionized states of molecules.

Symmetry-adapted cluster and symmetry-adapted cluster-configuration interaction method in the polarizable continuum model: Theory of the solvent effect on the electronic excitation of molecules in solution

In this paper we present the theory and implementation of the symmetry-adapted cluster (SAC) and symmetry-adapted cluster-configuration interaction (SAC-CI) method, including the solvent effect, using the polarizable continuum model (PCM). The PCM and SAC/SAC-CI were consistently combined in terms of the energy functional formalism. The excitation energies were calculated by means of the state-specific approach, the advantage of which over the linear-response approach has been shown. The single-point energy calculation and its analytical energy derivatives are presented and implemented, where the free-energy and its derivatives are evaluated because of the presence of solute-solvent interactions. We have applied this method to s-trans-acrolein and metylenecyclopropene of their electronic excitation in solution. The molecular geometries in the ground and excited states were optimized in vacuum and in solution, and both the vertical and adiabatic excitations were studied. The PCM-SAC/SAC-CI reproduced the known trend of the solvent effect on the vertical excitation energies but the shift values were underestimated. The excited state geometry in planar and nonplanar conformations was investigated. The importance of using state-specific methods was shown for the solvent effect on the optimized geometry in the excited state. The mechanism of the solvent effect is discussed in terms of the Mulliken charges and electronic dipole moment.

Nonequilibrium solvation for vertical photoemission and photoabsorption processes using the symmetry-adapted cluster-configuration interaction method in the polarizable continuum model

In this paper, we present the theory and implementation of a nonequilibrium solvation model for the symmetry-adapted cluster (SAC) and symmetry-adapted cluster-configuration interaction (SAC-CI) method in the polarizable continuum model. For nonequilibrium solvation, we adopted the Pekar partition scheme in which solvent charges are divided into dynamical and inertial components. With this nonequilibrium solvation scheme, a vertical transition from an initial state to a final state may be described as follows: the initial state is described by equilibrium solvation, while in the final state, the inertial component remains in the solvation for the initial state; the dynamical component will be calculated self-consistently for the final state. The present method was applied to the vertical photoemission and absorption of s-trans acrolein and methylenecyclopropene. The effect of nonequilibrium solvation was significant for a polar solvent.

Excited-State Geometries of Heteroaromatic Compounds: A Comparative TD-DFT and SAC-CI Study

The structures of low-lying singlet excited states of nine π-conjugated heteroaromatic compounds have been investigated by the symmetry-adapted cluster-configuration interaction (SAC-CI) method and the time-dependent density functional theory (TDDFT) using the PBE0 functional (TD-PBE0).In particular, the geometry relaxation in some ππ* and nπ* excited states of furan, pyrrole, pyridine, p-benzoquinone, uracil, adenine, 9,10-anthraquinone, coumarin, and 1,8-naphthalimide as well as the corresponding vertical transitions, including Rydberg excited states, have been analyzed in detail. The basis set and functional dependence of the results was also examined. The SAC-CI and TD-PBE0 calculations showed reasonable agreement in both transition energies and excited-state equilibrium structures for these heteroaromatic compounds.

Dirac–Fock calculations of the magnetic shielding constants of protons and heavy nuclei in XH2 (X=O, S, Se, and Te): a comparison with quasi-relativistic calculations

Abstract Calculations of magnetic shielding constants of protons and heavy elements in HX2 molecules (X=O, S, Se, and Te) are presented based on the Dirac–Fock (DF) method in the presence of a finite magnetic field. The calculated magnetic shielding constants agree fairly well with experiments. The so-called diamagnetic, paramagnetic, Fermi-contact, and spin–dipolar terms are also presented by applying the Gordon decomposition method. The results are compared with those calculated by the quasi-relativistic (QR) method, and we found that the difference between the DF and QR methods is significant for TeH2.

Symmetry-adapted-cluster/symmetry-adapted-cluster configuration interaction methodology extended to giant molecular systems: ring molecular crystals.

The symmetry adapted cluster (SAC)/symmetry adapted cluster configuration interaction (SAC-CI) methodology for the ground, excited, ionized, and electron-attached states of molecules was extended to giant molecular systems. The size extensivity of energy and the size intensivity of excitation energy are very important for doing quantitative chemical studies of giant molecular systems and are designed to be satisfied in the present giant SAC/SAC-CI method. The first extension was made to giant molecular crystals composed of the same molecular species. The reference wave function was defined by introducing monomer-localized canonical molecular orbitals (ml-CMOs), which were obtained from the Hartree-Fock orbitals of a tetramer or a larger oligomer within the electrostatic field of the other part of the crystal. In the SAC/SAC-CI calculations, all the necessary integrals were obtained after the integral transformation with the ml-CMOs of the neighboring dimer. Only singles and doubles excitations within each neighboring dimer were considered as linked operators, and perturbation selection was done to choose only important operators. Almost all the important unlinked terms generated from the selected linked operators were included: the unlinked terms are important for keeping size extensivity and size intensivity. Some test calculations were carried out for the ring crystals of up to 10 000-mer, confirming the size extensivity and size intensivity of the calculated results and the efficiency of the giant method in comparison with the standard method available in GAUSSIAN 03. Then, the method was applied to the ring crystals of ethylene and water 50-mers, and formaldehyde 50-, 100-, and 500-mers. The potential energy curves of the ground state and the polarization and electron-transfer-type excited states were calculated for the intermonomer distances of 2.8-100 A. Several interesting behaviors were reported, showing the potentiality of the present giant SAC/SAC-CI method for molecular engineering.

Excited states and electronic spectra of extended tetraazaporphyrins

Electronic excited states, electronic absorption, and magnetic circular dichroism (MCD) spectra of free-base tetraazaporphyrin (TAP), phthalocyanine (Pc), naphthalocyanine (Nc), and anthracocyanine (Ac) were studied by quantum chemical calculations using the symmetry-adapted cluster-configuration interaction (SAC-CI) method. Not only optically allowed states including the Q- and B-bands but also optically forbidden states were calculated for transitions whose excitation energies were lower than 4.5 eV. The present SAC-CI calculations consistently assigned the absorption and MCD peaks as optically allowed π→π(∗) excitations, although these calculations using double-zeta basis limit quantitative agreement and discussion. For Nc and Ac, excited states beyond the four-orbital model appeared in the low-energy region. The low-energy shifts of the Q-bands with the extension of molecular size were explained by the orbital energies. The splitting of the Q-bands decreases with extension of the molecular size. This feature was reproduced by the SAC-CI calculations but the configuration interaction with single excitations and time-dependent density functional theory calculations failed to reproduce this trend. Electron correlation in the excited states is important in reproducing this splitting of the Q-bands and in describing the energy difference between the B(2u) and B(3u) states of free-base porphyrins.

Relativistic effects and the halogen dependencies in the 13C chemical shifts of CH4−nIn, CH4−nBrn, CCl4−nIn, and CBr4−nIn (n=0–4)

Linear and nonlinear halogen dependencies of the 13C magnetic shielding constants of CH4−nIn, CH4−nBrn, CCl4−nIn, and CBr4−nIn were fairly reproduced by the ab initio generalized unrestricted Hartree–Fock (GUHF)/finite perturbation (FP) method including spin‐orbit (SO) interaction and spin‐free relativistic (SFR) terms. As seen from the experimental trends, the calculated 13C chemical shifts in CCl4−nIn and CBr4−nIn depend linearly on n=0–4, while those in CH4−nIn and CH4−nBrn depend nonlinearly. We found that both the linear and nonlinear dependencies are due to the relativistic effects, and especially due to the Fermi–Contact (FC) term originating from the SO interaction.