Reikichi Itoh

Higher‐order response theory based on the quasienergy derivatives: The derivation of the frequency‐dependent polarizabilities and hyperpolarizabilities

The higher‐order response theory to derive frequency‐dependent polarizabilities and hyperpolarizabilities is examined by means of the differentiation of the ‘‘quasienergy’’ with respect to the strengths of the time‐dependent external field, which is referred to as the quasienergy derivative (QED) method. This method is the extension of the energy derivative method to obtain static polarizabilities and hyperpolarizabilities to a time‐dependent perturbation problem. The form of the quasienergy W = 〈Φ‖H − i(∂/∂t)‖Φ〉 is determined from the time‐dependent Hellmann–Feynman theorem. The QED method is accomplished when the total sum of the signed frequencies of the associated field strengths, with respect to which the quasienergy is differentiated, is equated to 0. The QED method is applied to the single exponential‐transformation (SET) ansatz (up to the fifth‐order QEDs) and the double exponential‐transformation (DET) ansatz (up to the fourth‐order QEDs), where the time‐dependent variational principle (TDVP) is...

Frequency‐dependent hyperpolarizabilities in the Mo/ller–Plesset perturbation theory

A formulation for calculating frequency‐dependent hyperpolarizabilities in the Mo/ller–Plesset perturbation theory is presented as the correlation correction to the TDHF approximation. Our quasienergy derivative (QED) method is applied, and the difference between the QED method and the pseudoenergy derivative (PED) method by Rice and Handy is discussed. The Lagrangian technique is utilized to obtain simple and practical expressions for response properties in which the TDHF orbital rotation parameters satisfy the 2n+1 rule and the Lagrange multipliers satisfy the 2n+2 rule. Explicit expressions for response properties up to third order [μ, α(−ω1;ω1), β(−ωσ;ω1,ω2)] are derived in the second‐order Mo/ller‐Plesset perturbation theory.

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.

Calculation of frequency-dependent polarizabilities and hyperpolarizabilities by the second-order Møller-Plesset perturbation theory

Abstract The QED-MP2 model based on the quasi-energy derivative method in the second-order Moller-Plesset perturbation theory is formulated, and frequency-dependent (dynamic) polarizabilities [α(−ω;ω)] for H 2 O and NH 3 are calculated. Dynamic polarizabilities obtained for H 2 O agree with experimental values. First hyperpolarizabilities for the electro-optic Pockels effect [β(−ω;ω, 0)] and second hyperpolarizabilities for the electro-optic Kerr effect [γ(−ω;ω, 0, 0)] are also calculated as the numerical derivatives of α(−ω; ω).

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.

The quadratic response function in the THFD approximation and its application to frequency-dependent hyperpolarizabilities of the FH molecule

Abstract Frequency-dependent hyperpolarizabilities of the FH molecule are calculated in the TDHF quadratic response function formalism. Various first hyperpolarizabilities β(−ω.σ, ω1, ω2) which depend on two different frequencies are calculated, as well as the case of a monochromatic optical oscillating field. The validity of Sheltons approximation is discussed. Second hyperpolarizabilities γ(−ω.σ, ω1, ω2, ω3) for the dc-induced second-harmonic generation and the dc-induced optical rectification, as well as for the static case, are calculated using a finite-difference technique to differentiate the analytical β(−ω.σ, ω1, ω2). A new type of basis set (the “smooth-tempered” basis set) is implemented, as a modification of the even-tempered basis set. The method is applied to the largest basis set P2 ([14s10p6d4f/9s8p3d]) in this work. Basis P2 almost solves the unsaturation problem of basis sets in practice, and results for dipole moment, polarizability, and first and second hyperpolarizability with P2 are near the Hartree—Fock limit.

Ab initio SCF-SDCI prediction of type II spectra and geometry of hydrogen dichloride ion, (ClHCl)−

Abstract The two-dimensional potential energy surface of linear hydrogen dichloride ion (type II complex) is calculated by the ab initio SCF-SDCI method with 6–31 + G** basis sets. The equilibrium structure has r (HCl) = 1.416Aand 1.762A(double minimum structure) with a low central barrier (59 cm −1 ). The hydrogen-bond energy is 20.1 kcal mol −1 . Type II vibrational frequencies are calculated as ν 1 = 309 cm −1 , ν 3 = 629 cm −1 and ν 1 +ν 3 = 905 cm −1 by quantal vibrational analysis (o-SCF CI method based on vibrational difference method).