Masanori Tachikawa

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.

A unified scheme for ab initio molecular orbital theory and path integral molecular dynamics

We present a general approach for accurate calculation of chemical substances which treats both nuclei and electrons quantum mechanically, adopting ab initio molecular orbital theory for the electronic structure and path integral molecular dynamics for the nuclei. The present approach enables the evaluation of physical quantities dependent on the nuclear configuration as well as the electronic structure, within the framework of Born–Oppenheimer adiabatic approximation. As an application, we give the path integral formulation of electric response properties—dipole moment and polarizability, which characterize the changes both in electronic structure and nuclear configuration at a given temperature when uniform electrostatic field is present. We also demonstrate the calculation of a water molecule using the present approach and the result of temperature and isotope effects is discussed.

Multi-component molecular orbital theory for electrons and nuclei including many-body effect with full configuration interaction treatment: isotope effects on hydrogen molecules

Abstract A multi-component molecular orbital (MC_MO) theory is developed for a combined quantum system of electrons and nuclei with the full configuration interaction (CI) scheme of Cartesian Gaussian-type functions. The technique of graphical unitary group approach (GUGA) is modified to obtain the CI matrix elements for many kinds of quantum particles efficiently. The optimum basis sets for quantum nuclei are proposed with the fully variational procedure. The average internuclear distances, dipole polarizabilities, and nuclear vibrational excitation energies for isotopic hydrogen molecules calculated with optimized basis sets are found to adequately reproduce the corresponding experimental values.

Ab initio molecular orbital calculation considering the quantum mechanical effect of nuclei by path integral molecular dynamics

Abstract We present an accurate calculational scheme for many-body systems composed of electrons and nuclei, by path integral molecular dynamics technique combined with the ab initio molecular orbital theory. Based upon the scheme, the simulation of a water molecule at room temperature is demonstrated, applying all-electron calculation at the Hartree–Fock level of theory.

Bound states of positron with urea and acetone molecules using configuration interaction ab initio molecular orbital approach

Characteristic features of the positron binding structure of the urea and acetone molecules are discussed based on the results obtained by the configuration interaction scheme of quantum chemical molecular orbital calculations. This method takes the positron–electron correlation contribution into account explicitly. We have found that the positron distribution is concentrated behind the carbonyl oxygen atom. The positron affinity of urea is larger than that of acetone, which is consistent with the stronger dipole moment of urea.

Temperature and isotope effects on water cluster ions with path integral molecular dynamics based on the fourth order Trotter expansion

Path integral molecular dynamics simulation based on the fourth order Trotter expansion has been performed to elucidate the geometrical isotope effect of water dimer anions, H(3)O(2)(-), D(3)O(2)(-), and T(3)O(2)(-), at different temperatures from 50 to 600 K. At low temperatures below 200 K the hydrogen-bonded hydrogen nucleus is near the center of two oxygen atoms with mostly O...X...O geometry (where X = H, D, or T), while at high temperatures above 400 K, hydrogen becomes more delocalized, showing the coexistence between O...X-O and O-X...O. The OO distance tends to be shorter as the isotopomer is heavier at low temperatures, while this ordering becomes opposite at high temperatures. It is concluded that the coupling between the OO stretching mode and proton transfer modes is a key to understand such a temperature dependence of a hydrogen-bonded structure.

Efficient ab initio path integral hybrid Monte Carlo based on the fourth-order Trotter expansion: Application to fluoride ion-water cluster

We propose an efficient path integral hybrid Monte Carlo (PIHMC) method based on fourth-order Trotter expansion. Here, the second-order effective force is employed to generate short trial trajectories to avoid computationally expensive Hessian matrix, while the final acceptance is judged based on fourth-order effective potential. The computational performance of our PIHMC scheme is compared with that of conventional PIHMC and PIMD methods based on second- and fourth-order Trotter expansions. Our method is applied to on-the-fly ab initio PIHMC calculation of fluoride ion-water complexes, F(-)(H(2)O) and F(-)(D(2)O), at ambient temperature, particularly focusing on the geometrical isotope effect.

Simultaneous optimization of Gaussian type function exponents for electron and positron with full-CI wavefunction – application to ground and excited states of positronic compounds with multi-component molecular orbital approach

Abstract In order to obtain the best wavefunction of positronic compound with molecular orbital (MO) treatment, the full-configuration interaction (full-CI) fully variational MO (FVMO) method is proposed for multi-component systems, in which all the variational parameters in electronic and positronic wavefunctions are optimized under the full-CI scheme. We have applied the full-CI multi-component FVMO method to the ground and positronic-excited states of [H − ;e + ] system. Our treatment gives good improvement in the basis functions for positronic compounds owing to the extension of flexibility in the variational space, though the convergence of electron–positron correlation term is slower than that of conventional electron correlation.

Ab initio quantum Monte Carlo study of the positronic hydrogen cyanide molecule

Quantum Monte Carlo methods are used to investigate the binding of a positron to the hydrogen cyanide (HCN) and lithium hydride (LiH) molecules. Our value of the adiabatic positron affinity (PA) of LiH of 1.010(3) eV is very close to the best theoretical value of 1.005 eV, obtained from variational calculations using explicitly correlated Gaussian basis sets [K. Strasburger, J. Chem. Phys. 114, 00615 (2001)]. We have obtained a reliable estimate of 0.0378(48) eV for the PA of the HCN molecule, which is almost 20 times larger than that obtained at the Hartree-Fock level, and strongly supports the binding of a positron in the electrostatic field of the HCN molecule. Our results show the importance of correlation effects for describing weakly bound positronic molecular complexes.

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.