Isamu Shigemoto

Size‐consistent approach and density analysis of hyperpolarizability: Second hyperpolarizabilities of polymeric systems with and without defects

Various size‐consistent approaches to the calculation of molecular hyperpolarizabilities are analyzed based on the double perturbation theory. General equations for the nth‐order response property with respect to an external time‐independent field are derived on the basis of the Rayleigh–Schrodinger perturbation theory (RSPT) and the coupled‐cluster (CC) theory. The corresponding equations for the time‐dependent case are also derived by the CC formalism, which is referred to as the time‐dependent CC (TDCC) method. In order to clarify the spatial characteristics of polarizability and hyperpolarizability, we present an analysis method using a new concept ‘‘the polarizability and hyperpolarizability densities.’’ As an application of the size‐consistent methods, the static second hyperpolarizabilities (γ) of π‐conjugated polymeric systems are calculated by the use of the uncoupled (UCHF), and coupled‐Hartree–Fock (CHF) methods combined with the semiempirical INDO approximation. Characteristics of γ values cal...

Theoretical study of the second hyperpolarizabilities of three charged states of pentalene. A consideration of the structure-property correlation for the sensitive second hyperpolarizability

Abstract The static second hyperpolarizabilities (γ) for neutral, anion radical and dianion states for a symmetric condensed-ring conjugated system, i.e. pentalene, are calculated by the use of ab initio molecular orbital methods with extended basis sets. The dependence of electron correlation effects on γ is investigated by using the hyperpolarizability density analysis. Remarkable differences in the γ and the characteristics of the spatial contributions of γ densities are observed for different electron correlation results and for different charged states of this system.

Static second hyperpolarizabilities γ of nitroxide radical and formaldehyde: evaluation of spatial contributions to γ by a hyperpolarizability density analysis

Abstract The static second hyperpolarizability (γ) for a small size open-shell system containing a nitroxide radical group, H 2 NO, is studied by using ab initio molecular orbital and density functional methods. The static γ of H 2 CO is also evaluated as a reference closed-shell system. Remarkable changes in the spatial contributions of the third derivatives of the charge densities to the γ of H 2 NO, in contrast to those of H 2 CO, are observed in plots obtained by using various basis sets and correlation methods.

Intense electron correlation dependence of the first hyperpolarizabilities β of a nitroxide radical and formaldehyde

Abstract The static first hyperpolarizability (β) of a small-sized open-shell system including a nitroxide radical, H 2 NO, is studied using ab initio molecular orbital and density functional methods. The static β of H 2 CO is also evaluated as a reference closed-shell system. Intense electron correlation dependence of β for H 2 NO and H 2 CO is observed. Their tendencies are analyzed from the viewpoint of spatial contributions of electrons to β by using plots of hyperpolarizability densities.

Dynamic (hyper)polarizability density analysis based on virtual excitation processes: visualization of the dynamic electron fluctuatability of systems under time-dependent external electric fields

Abstract A novel method for the analysis of dynamic (hyper)polarizabilities of systems in the presence of arbitrary time-dependent external electric fields is developed. By using a new concept the ‘dynamic (hyper)polarizability density’, we visualize the a ability of dynamic electron fluctuation (electron fluctuatability) of systems with relaxation processes under external electric fields with arbitrary intensities, frequencies and shape of amplitudes. The (hyper)polarizability density is partitioned into that for each virtual excitation process by the numerical Liouville approach.

Free-energy analysis of water affinity in polymer studied by atomistic molecular simulation combined with the theory of solutions in the energy representation

Affinity of small molecule to polymer is an essential property for designing polymer materials with tuned permeability. In the present work, we develop a computational approach to the free energy ΔG of binding a small solute molecule into polymer using the atomistic molecular dynamics (MD) simulation combined with the method of energy representation. The binding free energy ΔG is obtained by viewing a single polymer as a collection of fragments and employing an approximate functional constructed from distribution functions of the interaction energy between solute and the fragment obtained from MD simulation. The binding of water is then examined against 9 typical polymers. The relationship is addressed between the fragment size and the calculated ΔG, and a useful fragment size is identified to compromise the performance of the free-energy functional and the sampling efficiency. It is found with the appropriate fragment size that the ΔG convergence at a statistical error of ∼0.2 kcal/mol is reached at ∼4 ns of replica-exchange MD of the water-polymer system and that the mean absolute deviation of the computational ΔG from the experimental is 0.5 kcal/mol. The connection is further discussed between the polymer structure and the thermodynamic ΔG.

Theoretical study on the geometry dependence of the second hyperpolarizability of the allyl cation based on a numerical Liouville three-type analysis

Abstract The second hyperpolarizability (γ) of the allyl cation is analyzed in terms of the virtual excitation processes by the numerical Liouville approach (NLA). The influence of molecular geometry on γ is investigated. The results indicate that molecular geometry affects the magnitude and sign of γ and that three types of virtual excitation process exhibit remarkably different dependence on the molecular geometry. A negative γ for C 2v geometry without bond alternation is shown to be converted to a positive γ for bond-alternated geometry. Implications of the results are discussed in relation to a polymeric system with a charged defect.

Theoretical study of the third-order nonlinear optical susceptibilities for the β-phase crystal of p-NPNN

Abstract The third-order nonlinear optical susceptibilities for the β-phase crystal of para-nitrophenyl nitronyl nitroxide (p-NPNN), which is an open-shell system with nitroxide radicals, are investigated by the oriented gas model. The second hyperpolarizabilities of p-NPNN are calculated by using the INDO coupled Hartree-Fock method. The largest component of the susceptibilities for the crystal is predicted to be negative as well as that of the second hyperpolarizabilities of p-NPNN.

Theoretical studies on nonlinear optical properties of organometallic conjugated systems. III: second hyperpolarizabilities of Mn(I)-carbene systems

Abstract Various ab initio electron-correlation methods are applied to calculate second hyperpolarizabilities (γs) of MnCH+, MnCH2+ and MnCH3+. These systems showed significant dependences on the electron correlations. MnCH3+, which have a single MnC bond, exhibited the larger γ than MnCH+ and MnCH2+, which have weak π bonds.

Theoretical studies for second hyperpolarizabilities of alternant and condensed-ring conjugated systems II

Abstract Alternant and condensed-ring conjugated systems are expected to have large electron correlation and structure dependencies of the second hyperpolarizabilities ( γ ). For example, cation radical triafulvalene exhibits a large negative γ at the Hartree-Fock (HF) level contrary to a large positive one at the Moller-Plesset second-order (MP2) level. In this paper, we investigate γs for different charged states (neutral, ion radical and di-ion states) of pentalene and triafulvalene to reveal their electron correlation dependencies up to the Moller-plesset fourth order.