Linear response properties

The region from A to D is called the dynamic range. The regions 2 and 4 constitute the most imfwrtant difference with the hard delimiter transfer function in perceptron networks. These regions rather than the near-linear region 3 are most important since they assure the non-linear response properties of the network. It may... 

An alternative theory is the popular time-dependent density functional theory [44], in which transition energies are obtained from the poles of dynamic linear response properties. There are several excellent reviews on time-dependent density functional theory. See, for instance, Ref. [45]. 

When Jens Oddershede was elected a Fellow of the American Physical Society in 1993, the citation read For contribution to the theory, computation, and understanding of molecular response properties, especially through the elucidation implementation of the Polarization Propagator formalism. Although written more than a decade ago, it is still true today. The common thread that has run through Jens work for the past score of years is development of theoretical methods for studying the response properties of molecules. His primary interest has been in the development and applications of polarization propagator methods for direct calculation of electronic spectra, radiative lifetime and linear and non-linear response properties such as dynamical dipole polarizabilities and... 

The calculation of frequency-dependent linear-response properties may be an expensive task, since first-order response equations have to be solved for each considered frequency [1]. The cost may be reduced by introducing the Cauchy expansion in even powers of the frequency for the linear-response function [2], The expansion coefficients, or Cauchy moments [3], are frequency independent and need to be calculated only once for a given property. The Cauchy expansion is valid only for the frequencies below the first pole of the linear-response function. 

The response matrix depends only on intrinsic characteristics of the solute-solvent system, and it permits one to obtain linear response properties of a solute with respect to any applied perturbation in a unifying and general way. The poles ( ) of the response function give an approximation of the transition energies of the molecules in solution these are obtained as eigenvalues of the system... 

Jensen, L., Duijnen P.Th. van and Snijders J.G., A discrete solvent reaction field model for calculating molecular linear response properties in solution. J.Chem.Phys. (2003) 119 12998-13006. 

Our present focus is on density functional theory and coupled cluster methods for describing molecular systems interacting with a structured environment, and we focus on the derivation of linear response properties and compare the expressions that we obtain for the two different electronic structure methods. Based on linear response... 

The benzene and azabenzenes form iso-electronic series of molecules, as naphthalene and the azanaphthalenes also do. The ground state electronic and geometric structures are therefore quite similar within one series. The substitution of CH groups with nitrogens introduces lone-pair to 7r transitions, and lowers the benzene and naphthalene symmetries. Small and systematic trends are found for linear response properties of the azabenzenes [189]. Each molecule is, however, very specific with respect to phosphorescence due to the delicate nature of the SOC and electric dipole activity interactions. 

When written with the help of the Tl matrix as in (19), from (20) the OR parameter and other linear response properties are seen to afford singularities where co = coj, just like in the SOS equation (2). Therefore, at and near resonances the solutions of the TDDFT response equations (and response equations derived for other quantum chemical methods) yield diverging results that cannot be compared directly to experimental data. In reality, the excited states are broadened, which may be incorporated in the formalism by introducing dephasing constants 1 such that o, —> ooj — iT j for the excitation frequencies. This would lead to a nonsingular behavior of (20) near the coj where the real and the imaginary part of the response function varies smoothly, as in the broadened scenario at the top of Fig. 1. 

Although many of the potential optical applications of LB films are in transmission optics, employing the linear response properties of molecules, the... 

All CS manifolds in based on the one-particle group U 2s) are families of AGP states, some of these manifolds are irreducible Riemannian manifolds and correspond to cosets formed by the maximal compact subgroups U 2M) XU 2s - 2M) and USp(25), while others are reducible and correspond to non-maximal compact subgroups USp(2basic physical properties, e.g., U 2M) X U 2s - 2M) invariant manifold describes uncorrelated IPSs, the USp(2s) invariant manifold describes highly correlated extreme AGP states that are superconducting, while the USp(2a>i) X X USp(2wp) X SU(2) X SU(2 ) invariant manifold for general (Oj,..., cr, describe intermediate types of correlation and linear response properties, see, for a particular example. Ref. [35], most of which have not been explored in any depth. 

Kama and A. T. Yeates, Eds., American Chemical Society, Washington, DC, 1996, pp. 78-101. Sum-Over-State Representation of Non-linear Response Properties in Time-Dependent Hartree-Fock Theory The Role of State Truncation. 

The polarizability (a) of an atom or a molecule means the lowest order response of its electron cloud to an external weak electric field [277, 278]. The static dipole polarizability (a), a linear response property, is defined as the second derivative of the total electronic energy ( ) with respect to the external homogeneous electric field as... 

Jalkanen KJ, Jiirgensen VW, Degtyarenko IM (2005) Linear response properties required to simulate vibrational spectra of biomolecules in various media (R)-phenyloxirane (a comparative theoretical and spectroscopic vibrational study). Adv Quantum Chem 50 91-124... 

An interesting alternative approach is the direct calculation by polarization propagator, or linear response, methods.The poles of the propagator yield the transition frequencies, the residues yield the corresponding transition moments, and the propagator itself determines linear response properties such as the frequency-dependent (or dynamic) polarizability. 

In this chapter we will therefore discuss the contributions from the nuclear wave-function to the molecular properties derived in the previous chapters. However, in doing so we will still make use of the Born-Oppenheimer approximation. In the following, we will use the static polarizability as example and illustrate how these vibrational corrections can be incorporated (Bishop and Cheung, 1980 Bishop et al., 1980). The expression, which we are going to derive, can then easily be transferred to all linear response properties. A detailed description of vibrational corrections to static and frequency-dependent hyperpolarizabilities can be found in the reviews by Bishop (1990 1998). 

For all the magnetic linear response properties derived in Chapters 5 and 6 one would obtain expressions similar to the electronic-vibrational polarizability, Eq. (8.7). On the other hand, the diamagnetic contributions to the magnetic properties as well as all first-order properties, i.e. properties defined as first derivatives of the energy, will take the following simple expectation value form... 

Pickup, B. T. (1992). The propagator theory of non-linear response properties. In Methods in computational chemistry Theory and computation of molecular properties (ed. S. Wilson), pp. 107—265. Plenum Press, New York. 

The square matrix on the right completely determines the linear response of the system, at any frequency, to the applied force corresponding to any perturbation operator A. This response matrix is an intrinsic characteristic of the system itself and depends in no way on the applied perturbation its determination (using an approximate wavefunction of any suitable form) provides a practicable route to the study of all linear response properties. 

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