Kazuhide Mori

An extension of ab initio molecular orbital theory to nuclear motion

Abstract We propose an extension of the quantum chemical molecular orbital (MO) method to describe the nuclear motion. Both electronic and nuclear wavefunctions are simultaneously solved with the full variational MO method, by which exponents and centers of gaussian-type function (GTF) basis sets are optimized as well as the linear combination of GTF coefficients. Applications of the method to [F − ; e + ], FH and FD systems are carried out. The calculated bond lengths and harmonic frequencies agree well with the experimental values.

Two-dimensional vibrational analysis of the Lippincott-Schröder potential for OHO, NHO and NHN hydrogen bonds and the deuterium isotope effect

Abstract Two-dimensional vibrational analyses [i.e. crude adiabatic approximation, SCF approximation and variational method (crude adiabatic basis function)] are performed on the hydrogen bond systems consisting of the Lippincott-Schroder potentials for the OHO, NHO and NHN bonds. The OHO and NHN systems are supposed to be linear and the bent structure is considered for the NHO system. The frequency shift for the hydrogen bond length variation and its deuterium substitution effects are in good agreement with experiment. The anomalies in the frequency ratio ν OH /ν OD at an O—O distance of 2.5 A, and in the interminimum distance shift on deuteration at 2.5 A are well explained as the difference of double minimum behavior between the vibrational states of proton and deuterium. It is also shown that the Lippincott-Schroder model for the OHO system supplies the general features for proton tunneling, proton delocalization beyond the barrier and other type processes in hydrogen bonds.

Simultaneous optimization of GTF exponents and their centers with fully variational treatment of Hartree–Fock molecular orbital calculation

The authors have proposed the fully variational molecular orbital (FVMO) method by which all parameters in the molecular orbitals are optimized under the variational principle. According to the fully variational treatment within the Hartree-Fock approximation, exponents and centers in the Gaussian-type function (GTF) basis set are determined simultaneously, as well as the linear combination of atomic orbital (LCAO) coefficients. The FBMO method gives the lowest energy under the variational principle, improves the flexibility of wave function drastically, and raises the ab initio (nonempirical) feature. In the calculation of the adiabatic potential for HeH{sup +}, the electron movement for dissociation limitation is smoothly expressed due to full optimization of GTF centers and exponents under a condition that satisfies the Hellmann-Feynman and virial theorems. Properties such as dipole and polarizability of the hydrogen and helium atoms and the LiH molecule are in good agreement with the numerical Hartree-Fock values, even if only s type GTFs are used. The authors have also applied the FVMO method to H{sub 2}O and CH{sub 4} molecules.

Isotope effect of hydrated clusters of hydrogen chloride, HCl(H2O) n and DCl(H2O) n (n = 0–4): application of dynamic extended molecular orbital method

The recently proposed dynamic extended molecular orbital (DEMO) method is applied to the HCl(H2O) n and DCl(H2O) n (n = 0–4) clusters in order to explore the isotope effect on their structures, wavefunctions, and energies, theoretically. Since the DEMO method determines both electronic and nuclear wavefunctions simultaneously by optimizing all parameters including basis sets and their centres variationally, we can get the different nuclear orbitals for proton and deuteron as well as their electronic wavefunctions. The positions of the centres of nuclear orbitals show that the deuteron has weaker hydrogen bonding than the proton. There are three isomers in the case of n = 3 clusters, and less stable isomers have hydrogen transferred and non-transferred structures. In the conventional MO calculation, both hydrogen transferred and non-transferred isomers are calculated to be energy minima. When we have applied the DEMO method, only the hydrogen transferred structure is obtained for HCl(H2O)3, while both stru...

The multiconfiguration time-dependent Hartree-Fock method based on a closed-shell-type multiconfiguration self-consistent field reference state and its application to the LiH molecule

The linear response calculations in the multiconfiguration time‐dependent Hartree–Fock (MCTDHF) approximation with a closed‐shell‐type MCSCF state as the time‐independent reference state are discussed. The application to the LiH molecule with a small basis set ([4s2p1d/2s1p]) shows validity of our MCTDHF approach to the singlet ground state. Our MCSCF correlation energy is 97% of the total (=full CI) correlation energy and the MCTDHF excitation energies are in good agreements with the Δ full CI excitation energies. The Born–Oppenheimer potential energy curves for the lowest three singlet states of LiH and the corresponding vibrational level spacings, the transition moments, the oscillator strengths, and the frequency‐dependent dipole polarizabilities are reported. All of these results imply the potentiality of our MCTDHF method for the future work with the larger basis set. One of such basis sets ([9s8p4d/8s7p1d]) is referentially used only at the single‐configuration TDHF level, and the resultant near‐Hartree–Fock polarizability and Thomas–Reiche–Kuhn sum rule is very promising.

Parameters of average molecular polarizability in the MNDO, AM1 and PM3 methods

Abstract Atomic correction parameters of average molecular polarizability were determined for 16 chemical elements in the MNDO method, 13 in the AM1 method and 15 in the PM3 method using experimental polarizability data of more than 230 molecules. The above 16 elements include Li, Be, B, P, Sn and Hg whose experimental data are limited, but we tried to obtain their correction parameters for applying to a variety of molecules. The corrected polarizabilities obtained are almost in good agreement with the experimental ones. To evaluate the parameters, we calculated corrected polarizability values for molecules having multiple experimental polarizability values and those having only a theoretical polarizability. We examined 371 molecules in total.

Full-variational treatment of GTF basis sets for molecular orbitals: application to interactions in the helium dimer under an electrostatic field

Abstract The full-variational optimization method at the SCF and MP2 levels is applied to a calculation of the intermolecular interaction energy of the helium dimer under an electrostatic field. The results under an external field show that the basis set superposition errors are suppressed by this method and that the intermolecular interaction energies calculated with s functions only are comparable to those of conventional calculations with polarization functions.

Study of tunneling splitting with symmetrically-combined Morse potential model using associated Laguerre basis functions ☆

Abstract The one-dimensional symmetrical double-minimum potential is used as the vibrational tunneling splitting model in hydrogen-bonding systems. The vibrational eigenvalue and the system wave functions are calculated both by the Stormer–Levy finite difference method and the variational method, of which basis functions are associated Laguerre functions. It is well known that the former method gives the good approximate values. In the latter method, the accuracy of the solution depends on the number of basis functions. The variational method with some expansion terms is in good agreement with the finite difference method.