Hideo Sekino

Frequency dependent nonlinear optical properties of molecules

Various nonlinear optical polarizabilities are derived and evaluated by time dependent Hartree–Fock theory (TDHF). The recursive nature of the TDHF theory is exploited to develop formulas that are applicable in any order. The theory is applied to evaluate dispersion effects for the series of molecules CH4, CH3F, CH2F2, CHF3, and CF4. Comparisons are made with results obtained from dc‐induced, second‐Harmonic generation, and third‐Harmonic generation experiments. Additional applications are reported for H2 and HF.

COUPLED-CLUSTER CALCULATIONS OF INDIRECT NUCLEAR COUPLING CONSTANTS : THE IMPORTANCE OF NON-FERMI CONTACT CONTRIBUTIONS

Electron correlation effects to the four coupling mechanisms which contribute to the isotropic nuclear spin–spin coupling constant, the Fermi contact (FC), paramagnetic spin–orbit (PSO), spin‐dipole (SD), and diamagnetic spin–orbit (DSO) are studied using the equation of motion coupled‐cluster (EOM‐CC) method. The second‐order properties are expressed as a sum‐over state (SOS) using EOM‐CC intermediate state wave functions. This formulation is simple, accurate, computationally convenient, and involves no truncation. Several molecules, HF, CO, N2, H2O, NH3, and HCl which have been previously shown to have large noncontact contributions are investigated using the EOM‐CC method and the results are compared with experiment and other theoretical methods, including polarization propagator and finite‐field MBPT(2) methods. Using fairly large basis sets, the EOM‐CCSD provides results which agree with experimental indirect nuclear spin–spin coupling constants to within an average error of 13%.

Hyperpolarizabilities of the hydrogen fluoride molecule: A discrepancy between theory and experiment?

Due to the recent availability of an experimental value for the second‐ and third‐order electric polarizabilities of the HF molecule, possible errors in the previous prediction of these quantities have been considered. These include basis sets, vibrational corrections, frequency dependence, infinite‐order correlation corrections, and the effect of triple excitations. Despite the inclusion of all of these effects, the discrepancy between experiment and theory remains. Our best results predict χ(2)∥ to be −3.3 to −3.8×10−32 and χ(3)∥ to be 45 to 48×10−39 esu which are at best 81% and 69% of the experimental values, respectively. Possible additional corrections are considered with emphasis on basis set completeness. Considering the difficulty in predicting such sensitive quantities, this is rather good agreement. The paper also addresses questions of reliability of ab initio calculations for such high‐order properties as hyperpolarizabilities, while identifying some places where the experimental results are ...

Property evaluation and orbital relaxation in coupled cluster methods

Molecular electronic properties such as dipole moments, polarizabilities and hyperpolarizabilities and quadrupole moments and polarizabilities, and spin properties such as hyperfine splitting constants and nuclear magnetic coupling constants are predicted by ab initio coupled cluster (CC) methods for a variety of molecules. We compare the results of property evaluation using orbitals that have been allowed to relax in the presence of the perturbation and results obtained using nonrelaxed orbitals. It is demonstrated numerically, and proven formally, that the coupled cluster singles and doubles (CCSD) model using nonrelaxed orbitals is able to include most of the relaxation effects for the evaluation of first‐ and second‐order properties. Thus there is little reason to perform coupled (perturbed) Hartree–Fock calculations as a precursor to correlated CCSD calculations of such properties.

Comparison of MBPT and coupled-cluster methods with full CI. Importance of triplet excitation and infinite summations☆

Abstract Results from full fourth-order perturbation theory [SDTQ MBPT(4)], and the coupled-cluster single- and double-excitation model (CCSD). are compared with recent full CI results for BH, HF, NH3, and H2O. For H2O, studies include large symmetric displacements of the OH bonds, which offer a severe test for any single-reference MBPT/CC method. In every case. CCSD plus fourth-order triple-excitation terms provide agreement with the full CI to

Spin density of radicals by finite field many‐body methods

The spin densities of several small radicals CH3, NH2,CH2CH, BeH, and H2CO+ are calculated by a finite field coupled‐cluster method using a spin density operator as a finite perturbation on the systems. The calculated hyperfine coupling constants of the π radicals are in good agreement with experiment at a low level of correlation. The CH2CH radical required a higher level of correlation to obtain the experimental value. The calculations are also performed for the H2CO+ radical where theory has failed to predict the experimental splitting constants. The spin density on hydrogen calculated in the present study is lower than the result obtained by the low temperature gas ESR techniques, although the carbon spin density is well reproduced. An analysis of possible corrections for the H spin density is presented.

Hyperpolarizabilities of molecules with frequency dependence and electron correlation

Frequency dependent second hyperpolarizabilities of N2 and the prototype organic molecule trans‐butadiene are reported using generalized time dependent Hartree–Fock (TDHF) theory for several frequencies of applied fields. A monotonic increase of the values (positive dispersion) is observed for every nonlinear optical process in a range of frequencies for the applied field. Correlation effects are estimated using a second‐order many body perturbation theory and coupled cluster singles and doubles relaxed density method for the analytical determination of the induced dipole moment. Such hybrid results for DC‐induced second harmonic generation provide reasonable values in comparison with experiment for N2. However, dispersion and correlation effects in trans‐butadiene are both found to be large and could be nonadditive.

FREQUENCY-DEPENDENT HYPERPOLARIZABILITIES IN THE COUPLED-CLUSTER METHOD : THE KERR EFFECT FOR MOLECULES

Abstract Introducing frequency dependence in the equation-of-motion coupled-cluster method, we evaluate the optical Kerr effect for butadiene and ammonia. This permits a critical evaluation of dispersion estimates via the uncorrelated time-dependent Hartree-Fock theory. The percentage dispersions are similar for low frequencies, but not for larger values. We also consider other dispersion estimates based upon a power series expansion in the frequency. This leads to a possible resolution of the observed discrepancy between correlated theory and experiment for butadiene. Augmented by vibrational corrections, we offer estimates for the experimentally unknown Kerr values for NH3 and C4H6.

Nuclear coupling constants obtained by the equation-of-motion coupled cluster theory

Abstract The coupled cluster (CC) treatment of a second-order property is expressed, analytically, by a generalized sum over state formulation based upon the equation of motion CC intermediate state wavefunctions. The method is applied to calculate the Fermi contact contribution to the indirect spin-spin coupling constants (J) of several molecules; ethane, cyclopropane, cyclobutane, bicyclobutane, ethylene and hydrogen fluoride. The excellent results obtained are very close to experiment and that obtained by the full-CC response theory, but in a computationally more convenient format. We also consider, numerically, the Karplus relation for 3J(H-H).

Nuclear spin–spin coupling constants evaluated using many body methods

In nuclear spin–spin coupling constant determinations, correlation corrections to the Fermi contact term are significant. In this paper we report the coupling constants calculated for the HD and HF molecules obtained by the infinite‐order coupled cluster singles and doubles (CCSD) methods and MBPT(4). These are in good agreement with the experimentally estimated value for the Fermi‐contact term. In addition, it is well known that the coupled perturbed Hartree–Fock (CPHF) scheme fails for multiply bonded molecules because the closed shell Hartree–Fock solution is triplet unstable. A CCSD method using ordinary nonrelaxed SCF orbitals is presented in order to circumvent this problem, and illustrated by application to the C2H4 molecule. It is shown that CCSD results based upon ordinary SCF orbitals include effectively all the effect of orbital relaxation and reproduce the experimental values for most of the coupling constants. Unlike previous results, the 3J(H–H) constant is positive in agreement with experiment.