Response function static

Introduction of the static density response function for a system with a constant number of electrons yields the RF - DFT model. This second approach is expected to be more useful in the analysis of chemical reactivity in condensed phases. 

They reduce to regular energy derivatives in the static limit [48,50]. The linear response function... 

In terms of the linear response theory the static scattering function (Q) relates to the static response function x(Q) by ... 

Static charge-density susceptibilities have been computed ab initio by Li et al (38). The frequency-dependent susceptibility x(r, r cd) can be calculated within density functional theory, using methods developed by Ando (39 Zang-will and Soven (40 Gross and Kohn (4I and van Gisbergen, Snijders, and Baerends (42). In ab initio work, x(r, r co) can be determined by use of time-dependent perturbation techniques, pseudo-state methods (43-49), quantum Monte Carlo calculations (50-52), or by explicit construction of the linear response function in coupled cluster theory (53). Then the imaginary-frequency susceptibility can be obtained by analytic continuation from the susceptibility at real frequencies, or by a direct replacement co ico, where possible (for example, in pseudo-state expressions). 

Multiplying Eq. (3.1) with the static limit of the KS response function (2.64),... 

An important aspect in the study of the dipole polarizability of a reference molecule in solution is related to the separability problem, i.e., the distinction between the reference and the environment. Of course, the application of an external static homogeneous electrical field affects both the reference and the solvent molecules (in the present case, atoms). The use of response function, thus avoiding the external field, minimizes this problem, but still has the conceptual problem of distinguishing the solute and the solvent. It is normally assumed that a simple separability is a reasonable first approximation, particularly for weakly interacting systems. The interaction polarizability of weakly interactive systems... 

The softness kernels are relevant to the remaining cases of two or more interacting systems. However, they do not by themselves provide sufficient information to constitute a basis for a theory of chemical reactivity. Clearly, the chemical stimulus to one molecule in a bimolecular reaction is provided by the other. That being the case, an eighth issue arises. Both the perturbing system and the responding system have internal dynamics, yet the softness kernel is a static response function. Dynamic reactivities need to be defined. 

There are also a number of theories taking into account dipolar solvation dynamics. These theories use the solvent s dielectric response function as the dynamical input and also include effects due to the molecular nature of the solvent. The most sophisticated of these theories, by Raineri et al. [136] and by Friedman [137], uses fully atomistic representations for both solute and solvent and recent comparisons have shown it to be capable of quantitatively reproducing both the static and dynamic aspects of solvation of C153 [110]. In these cases the theoretical nature of solvation dynamics is fully understood. However, it must be remembered that much of the success of these theories rests on using the dynamical content of the complicated function, dielectric response function, determined from experiment. Although there... 

The zeroth-order terms, that is, QTm and QT,a>2> give the contributions to the response function that arise from a static environment analogous to the linear response case. All the other contributions, that is, Qim, Q im, and Qs1 102, account for the dynamical response of the environment due to the periodic perturbations. 

The static response functions utilised in Appendix C are then obtained by taking the zero-frequency limit,... 

For the discussion of inhomogeneity corrections to the RLDA one also needs the inverse response function kast in the static limit,... 

Note, that (C.l) could be used as alternative definition for the static response functions. 

Owing to the static HK theorem, the initial potential Pq = ext[ o] is a functional of the unperturbed ground-state density Mq, so that the response function x, by Eq. (145), is a functional of Mq as well. 

The Kohn-Sham response function Xs is readily expressed in terms of the static unperturbed Kohn-Sham orbitals... 

The linear photoresponse of metal clusters was successfully calculated for spherical [158-160, 163] as well as for spheroidal clusters [164] within the jellium model [188] using the LDA. The results are improved considerably by the use of self-interaction corrected functionals. In the context of response calculations, self-interaction effects occur at three different levels First of all, the static KS orbitals, which enter the response function, have a self-interaction error if calculated within LDA. This is because the LDA xc potential of finite systems shows an exponential rather than the correct — 1/r behaviour in the asymptotic region. As a consequence, the valence electrons of finite systems are too weakly bound and the effective (ground-state) potential does not support high-lying unoccupied states. Apart from the response function Xs, the xc kernel /xc[ o] no matter which approximation is used for it, also has a self-interaction error. This is because /ic[no] is evaluated at the unperturbed ground-state density no(r), and this density exhibits self-interaction errors if the KS orbitals were calculated in LDA. Finally the ALDA form of /,c itself carries another self-interaction error. 

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