Electron correlation and structure dependencies of the second hyperpolarizability of ethylene

We investigated an interesting behavior in electron correlation and structure dependencies of the second hyperpolarizability (γ) of the ethylene model. The γ values of the ethylene model with plain and twisted structures were examined using various ab initio MO methods. γ was found to be largely changed depending on the rotation angle of the CH₂ group in ethylene. The rotation‐angle dependence of γ is remarkably different among Hartree–Fock and higher‐order electron‐correlation results. By applying hyperpolarizability density analysis, it was found that there are negative and positive contributions to γ and that, especially, σ electrons play an important role to determine the rotation‐angle dependence of γ at high‐order electron correlation levels. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 177–183, 1999     

DFT calculations of static dipole polarizabilities and hyperpolarizabilities for the boron clusters Bn (n=3–8,10)

The static electric dipole polarizabilities and second‐order hyperpolarizabilities of several bare boron clusters have been calculated with density functional theory. The average second‐order hyperpolarizability γ_av reaches a saturation limit of about 50,000 a.u. already with B₅ for a given type of structure. The average polarizability per atom shows overall a decrease with increasing cluster size, while the average second hyperpolarizability per atom first increases from B₃ to B₆, and then starts to decrease. For the noncentrosymmetric clusters dipole moments and first‐order hyperpolarizabilities are reported. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 131–135, 2000     

Third‐order nonlinear optical properties of dendritic molecular aggregates: Effects of fractal architecture

We investigate the microscopic third‐order nonlinear optical properties, i.e., the second hyperpolarizabilities (γ), of two different sizes of molecular aggregates with a dendritic, i.e., Bethe‐lattice, structure. One possesses a nonfractal structure, while the other has a fractal structure. The aggregate is treated in a two‐exciton model composed of two‐state monomers coupled to each other by the dipole–dipole interaction. The off‐resonant γ of the aggregates are calculated by the numerical Liouville approach, including relaxation effects. The total γ value is partitioned into the contribution of virtual exciton generation, and its spatial contribution to γ is analyzed in relation to the virtual excitation processes in the perturbation theory. It is found that the intermolecular‐interaction effect enhances both one‐ and two‐exciton‐generation contributions, while the relaxation effect reduces those, although the one‐ and two‐exciton‐generation contributions have mutually opposite signs. From the comparison of spatial contributions to γ between the nonfractal and fractal aggregates, an enhancement of the contribution to γ from the periphery to the core is observed in the fractal structure, while such a feature is not observed in the nonfractal structure. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

CAS–SCF and density functional calculations of second hyperpolarizabilities for a nitronyl nitroxide radical

In this study, we investigated a multireference‐based nondynamical electron correlation dependence of the second hyperpolarizability, γ. We performed complete active space self‐consistent‐field (CAS–SCF) calculations including the effect of π electrons. Although the sign of γ obtained by CAS–SCF calculation was found to be negative, the magnitude of γ was found to be much larger than that at the CCSD(T) level. We also applied density functional (DF) methods with different exchange–correlation functionals (BLYP and B3LYP) to the calculation of γ. Although the B3LYP method is found to provide negative γ, its magnitude is much smaller than that at the CCSD(T) level. This feature is discussed in detail by using γ density plots. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 329–336, 1999     

Self‐energy fields solutions to the generalized reduced Liouville equation in the perturbative approach

A direct approach for the generalized reduced Liouville equation of motion decoupling problem associated with open quantum systems within the superoperator formalism is presented. The procedure is based on inversion of the perturbation series for the energy representation of the density operator so as to obtain one for the proper self‐energy fields that emerge as a consequence of the analytic character of the associated spectral representation. Thus, the perturbation series that arises from the iteration of the energy‐dependent matrix elements hierarchy involved in the statistical operator allows, upon further expansion of the inverse of such series, to get formally exact expressions for the corrections to all orders of the self‐energy fields. The lower order corrections of these fields are discussed in terms of resonant and nonresonant contributions. The present approach provides matrix equations that show the close relation between the environment effects represented by the self‐energy fields and the relaxation kernel that drives the system–reservoir interaction. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 79: 280–290, 2000     

Lie algebraic approach to multiphoton excitation of diatomic molecules in intense laser fields

The quadratic anharmonic oscillator Lie algebraic model is used to study the multiphoton transition of the diatomic molecule placed in intense laser fields. The multiphoton excitation of vibration and vibration‐rotation of diatomic molecules in intense laser fields are discussed. In the pure vibration transition we calculate the transition probability versus the frequency of the laser fields for the CO molecule. We also investigate the roles of rotational motion in multiphoton processes and compare with pure vibration for the LiH molecule. The influences of the angular quantum number l and the molecular orientations in laser fields on the multiphoton processes are discussed. The averaged absorb energy changing with the laser field's frequency is calculated. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 201–207, 1999     

The polarizability and the second hyperpolarizability of tetrakis(phenylethynyl)ethene and several of its lithiated derivatives

The polarizability (α) and the second hyperpolarizability (γ) of tetrakis(phenylethynyl)ethene (TPEE) are compared and analyzed in connection with the properties (α, γ) of a series of selected/designed molecules having different conjugation patterns. Several lithiated derivatives of TPEE are designed and shown to have very enhanced second hyperpolarizabilities; for example, one of the lithiated TPEE has a 1.6×10³ times larger second hyperpolarizability than that of benzene. The potential of the proposed derivatives for applications in photonics is noted. The polarizabilities and the hyperpolarizabilities of the considered molecules have been computed employing the PM3 method which has been proven to be adequate for the present comparative study. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 177–187, 1999     

WKB and MAF quantization rules for spatially confined quantum mechanical systems

A formalism is developed to obtain the energy eigenvalues of spatially confined quantum mechanical systems in the framework of the usual Wentzel–Kramers–Brillouin (WKB) and modified airy function (MAF) methods. To illustrate the working rule, the techniques are applied to three different cases, viz. the confined one‐dimensional harmonic and quartic oscillators and a boxed‐in charged particle subject to an external electric field. The energies thus obtained are compared with those from shifted 1/N expansion, variational, and other methods, as well as the available exact numerical results. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 497–504, 1999     

Retarded intermolecular interactions involving diamagnetic molecules

Second‐ and third‐order time‐dependent perturbation theory within the multipolar framework of nonrelativistic quantum electrodynamics is used to calculate the retarded dispersion interaction between two diamagnetic molecules, a diamagnetic molecule and a magnetic‐dipole susceptible molecule, and a diamagnetic molecule and an electric‐quadrupole polarizable molecule. New expressions for the energy shift valid for all intermolecular separation distances, R, beyond the region of overlap of molecular electronic wave functions and applicable to a pair of randomly oriented molecules in the ground electronic state are given. The R‐dependent behavior of the far‐zone limit of the interaction energies is also examined. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 437–442, 2000     

A quantum‐mechanical study of oxidized oligopyrroles

The geometry and band‐gap values of oligopyrroles of increasing chain length were calculated using different semiempirical quantum‐chemical methods (AM1, PM3, SAM1, INDO/1 CI). The oxidative doping results in large changes in the geometry and conductive properties of oligomers. The properties of doped polypyrrole are extrapolated from the calculated data for oligomers. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 101–109, 1999     

Computing a molecule in its environment: A mathematical viewpoint

This article is the sequel of a previous survey where we presented the mathematical results rigorously known on the models used in quantum chemistry to simulate an isolated molecular system. The emphasis here is on the models that take into account the environment of the molecule, namely, the models of the condensed phase and the models of interaction with electromagnetic fields. Some related issues are also dealt with. A bibliography of more than 150 references are provided. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 227–250, 1999     

Relations between DFT and CI approximation

Relations between the two quantum chemical methods density functional theory (DFT) and configuration interaction (CI) are studied. As a result a new expression of the density functional based on CI approximation is presented. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 74: 55–58, 1999     

Calculation of molecular response properties with the second‐order coupled perturbed electron propagator

We present the theory of the electron propagator perturbed by an external electric field and show how it can be used to calculate a variety of one‐electron linear response properties that are accurate through second order in electron correlation. Some illustrative calculations are discussed. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 625–640, 2000     

Integral evaluation in the case of a helium atom positioned off‐center in a spherical box

A variational approach to the problem of multielectron atoms placed off‐center in a spherical box leads to the difficult evaluation of electron repulsion integrals in an environment where spherical symmetry is no longer present. A technique for the evaluation of the electron repulsion integrals generated by this situation is developed and tested for the case of a helium atom placed off‐center in a spherical box. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 459–467, 1999     

Volume‐dependent potential approach for tungsten

A scheme to produce density‐of‐states‐(DOS)‐dependent potentials for d‐metals on the basis of the local density approximation calculations is suggested. As an example this scheme is applied to construct a DOS‐dependent potential for tungsten. The second moment of the tungsten DOS is calculated. We show that the obtained potentials give a good agreement of cohesive properties with the experimental data. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 343–348, 1999     

A quantum mechanical approach to electrochemical behavior of spirochromics

Fully optimized semiempirical quantum‐chemical calculations of photochromic spiropyrans are presented. The vertical ionization potentials are calculated and their variation with substitutions are correlated to experimental oxidation potentials. The effects of the substitutions are studied and the partial charges on indoline and pyran components generated by HOMO are found to be responsible for the variations. The deactivating groups on the indoline ring system and deactivating groups on the pyran system increase the ionization potential and, consecutively, the oxidation potential. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 75: 111–117, 1999     

Generalized potentials: Free particle,harmonic, and Morse partner potentials

In this work, we propose a very simple procedure to find the partner to specific potentials. According to our method, partner potentials are those obtained in the generalization of standard potentials, for which they are generalized potentials whose Hamiltonian match the so‐called isospectral Hamiltonian. The proposed approach is straightforward and basically takes into consideration the use of three well‐established relationships: The first one is used to identify the particular potential; the second, to find the adjoint or modified potential; and the third, to obtain the corresponding generalized or partner potential. As a useful application of the proposed procedure, we give explicitly the generalized and modified free‐particle, harmonic oscillator, and Morse one‐dimensional potentials. As expected, it is shown that the adjoint and partner potentials are isospectral with respect to the particular or former potential. This procedure can be easily applied to the generalization of any other known potential, as well as to obtain new potentials that can be advantageously used for modeling important quantum interactions. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 465–472, 1999     

Modified hybridization displacement charge scheme for π‐electron systems: Study of molecular electrostatic potential maps

A modified form of the hybridization displacement charge scheme (HDC‐PI) suitable for application to molecules where π‐electrons play the dominant role in controlling molecular electrostatic potential (MEP) features is presented. This modified scheme does not only preserve the atomic contributions to molecular dipole moment but also it represents the two opposing components of atomic hybridization dipole moment arising due to π‐electrons, one due to the π‐electrons located above the molecular plane and the other due to those located below the plane, so as to reproduce MEP features appropriately. The method has been applied within the framework of the AMl and MNDO methods to several different types of molecules containing π‐electrons demonstrating its very satisfactory performance. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 191–200, 1999     

Gamow dyads and expectation values

We analyze the possibilities to define density operators for the Gamow vectors in order to extend this concept to the Liouville space. We shall study the properties of the dyadic products of Gamow vectors and see that there exist difficulties if we try to obtain a Gamow density in Liouville space by factorizing Gamow vectors. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 307–320, 2001