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We present a derivation of linear response theory within polarizable embedding starting from a rigorous quantum-mechanical treatment of a composite system. To this aim, two different subsystem decompositions (symmetric and nonsymmetric) of the linear response function are introduced and the pole structures as well as residues of the individual terms are discussed. In addition to providing a thorough justification for the descriptions used in polarizable embedding models, this theoretical analysis clarifies which form of the response function to use and highlights complications in separating out subsystem contributions to molecular properties. The basic features of the presented expressions and various approximate forms are illustrated by their application to a composite model system. [ABSTRACT FROM AUTHOR]

An implementation of the second-order residue of the quadratic response function is presented in the four-component Hartree-Fock approximation, and the calculation of first-order properties of electronically excited states can thereby be achieved. Results are presented for the excited state electric dipole moments of the valence excited states in CsAg and CsAu. For CsAg, and even more so for CsAu, nonscalar relativistic effects on this property may be substantial, e.g., at the four-component level of theory, the excited-to-ground state dipole moment difference Δμ ranges from 1.994 to 4.110 a.u. for the six components of the 1 3Π state in CsAg, whereas, at the scalar relativistic level of theory, the common value of Δμ is 2.494 a.u. [ABSTRACT FROM AUTHOR]

A first implementation of the single residue of the quadratic response function in the four-component Hartree–Fock approximation is presented. The implementation is based on a Kramers paired molecular orbital basis and takes full advantage of time and spatial symmetry reductions in a quaternion formulation—in analogy with the previous work on the quadratic response function [J. Chem. Phys. 121, 6145 (2004)]. Sample calculations are given in terms of the monochromatic and coherent two-photon absorption cross sections in the noble gases. The relativistic two-photon selection rule ΔJ={0,±2} allows for nonrelativistically spin-forbidden transitions, and, even in neon, strong two-photon absorption is shown to occur for the X 1S0→2 3P2 transition. It is argued that relevant comparisons between nonrelativistic and relativistic calculations must be performed at the level of integrated absorption cross sections. [ABSTRACT FROM AUTHOR]

The second-order response function has been implemented in the time-dependent four-component Hartree-Fock approximation. The implementation is atomic orbital direct and formulated in terms of Fock-type matrices. It employs a quaternion symmetry scheme that provides maximum computational efficiency with consideration made to time-reversal and spatial symmetries. Calculations are presented for the electric dipole first-order hyperpolarizabilities of CsAg and CsAu in the second-harmonic generation optical process β(-2 ω; ω, ω). It is shown that relativistic corrections to property values are substantial in these cases-the orientationally averaged hyperpolarizabilities in the static limit &betamacr;(0;0,0) are overestimated in nonrelativistic calculations by 18% and 66% for CsAg and CsAu, respectively. The dispersion displays anomalies in the band gap region due to one- and two-photon resonances with nonrelativistically spin-forbidden states. Although weakly absorbing these states inflict divergences in the quadratic response function, since the response theoretical approach which is used adopts the infinite excited-state lifetime approximation. This fact calls for caution in applications where knowledge of the exact positioning of all excited states in the spectrum is unknown. [ABSTRACT FROM AUTHOR]

The linear response function has been derived and implemented in the time-dependent self-consistent field and multiconfigurational self-consistent field approximations with consideration made for the finite lifetimes of the electronically excited states. Inclusion of damping terms makes the response function convergent at all frequencies including near-resonances and resonances. Applications are the calculations of the electric dipole polarizabilities of hydrogen fluoride, methane, trans-butadiene, and three push–pull systems. The polarizability is complex with a real part related to the refractive index and an imaginary part describing linear absorption. The relevance of linear absorption in nonlinear optics is effectively expressed in terms of figures-of-merit. Such figures-of-merit have been calculated showing that the nonresonant linear absorption must be considered when the nonlinear optical quality of a material is to be assessed. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Proposes a semiclassical approximation model for frequency-independent properties of molecules in solution. Application of the model to test systems comprising nonpolar, polar and charged solutes; Comparison to perturbation expansion and self-consistent reaction field theory methods; Reliance of the model on gas phase calculations.

We present a reduced-space algorithm for solving the complex (damped) linear response equations required to compute the complex linear response function for the hierarchy of methods: coupled cluster singles, coupled cluster singles and iterative approximate doubles, and coupled cluster singles and doubles. The solver is the keystone element for the development of damped coupled cluster response methods for linear and nonlinear effects in resonant frequency regions. [ABSTRACT FROM AUTHOR]

A presentation of the complex polarization propagator in the restricted open-shell self-consistent field approximation is given. It rests on a formulation of a resonant-convergent, first-order polarization propagator approach that makes it possible to directly calculate the X-ray absorption cross section at a particular frequency without explicitly addressing the excited states. The quality of the predicted X-ray spectra relates only to the type of density functional applied without any separate treatment of dynamical relaxation effects. The method is applied to the calculation of the near K-edge X-ray absorption fine structure spectra of allyl and copper phthalocyanine. Comparison is made between the spectra of the radicals and those of the corresponding cations and anions to assess the effect of the increase of electron charge in the frontier orbital. The method offers the possibility for unique assigment of symmetry-independent atoms. The overall excellent spectral agreement motivates the application of the method as a routine precise tool for analyzing X-ray absorption of large systems of technological interest. [ABSTRACT FROM AUTHOR]