Response function theory frequency-dependent

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). 

MCT can be best viewed as a synthesis of two formidable theoretical approaches, namely the renormalized kinetic theory [5-9] and the extended hydrodynamic theory [10]. While the former provides the method to treat both the very short and the very long time responses, it often becomes intractable in the intermediate times. This is best seen in the calculation of the velocity time correlation function of a tagged atom or a molecule. The extended hydrodynamic theory provides the simplicity in terms of the wavenumber-dependent hydrodynamic modes. The decay of these modes are expressed in terms of the wavenumber- and frequency-dependent transport coefficients. This hydrodynamic description is often valid from intermediate to long times, although it breaks down both at very short and at very long times, for different reasons. None of these two approaches provides a self-consistent description. The self-consistency enters in the determination of the time correlation functions of the hydrodynamic modes in terms of the... 

The frequency dependence of SHG at simple metal surface has been the focus of a recent theoretical study of Liebsch [100]. Time-dependent density functional theory was used in these calculations. The results suggest that the perpendicular surface contribution to the second harmonic current is found to be significantly larger than had been assumed previously. He also concludes that for 2 a> close to the threshold for electron emission, the self-consistently screened nonlinear electronic response becomes resonantly enhanced, analogous to local field enhancement in the linear response near the bulk plasma frequency. 

R. Cammi and J. Tomasi, Nonequilibrium solvation theory for the polarizable continuum model - a new formulation at the SCF level with application to the case of the frequency-dependent linear electric-response function, Int. J. Quantum Chem., (1995) 465-74 B. Mennucci, R. Cammi and J. Tomasi, Excited states and solvatochromic shifts within a nonequilibrium solvation approach A new formulation of the integral equation formalism method at the self-consistent field, configuration interaction, and multiconfiguration self-consistent field level, J. Chem. Phys., 109 (1998) 2798-807 R. Cammi, L. Frediani, B. Mennucci, J. Tomasi, K. Ruud and K. V. Mikkelsen, A second-order, quadratically... 

The extension of density functional theory (DFT) to the dynamical description of atomic and molecular systems offers an efficient theoretical and computational tool for chemistry and molecular spectroscopy, namely, time-dependent DFT (TDDFT) [7-11]. This tool allows us to simulate the time evolution of electronic systems, so that changes in molecular structure and bonding over time due to applied time-dependent fields can be investigated. Its response variant TDDF(R)T is used to calculate frequency-dependent molecular response properties, such as polarizabilities and hyperpolarizabilities [12-17]. Furthermore, TDDFRT overcomes the well-known difficulties in applying DFT to excited states [18], in the sense that the most important characteristics of excited states, the excitation energies and oscillator strengths, are calculated with TDDFRT [17, 19-26]. 

Gross, E.K.U. and Kohn, W. (1985). Local density-functional theory of frequency-dependent linear response, Phys. Rev. Lett. 55, 2850-2852. 

Molecular polarizabilities and hyperpolarizabilities are now routinely calculated in many computational packages and reported in publications that are not primarily concerned with these properties. Very often the calculated values are not likely to be of quantitative accuracy when compared with experimental data. One difficulty is that, except in the case of very small molecules, gas phase data is unobtainable and some allowance has to be made for the effect of the molecular environment in a condensed phase. Another is that the accurate determination of the nonlinear response functions requires that electron correlation should be treated accurately and this is not easy to achieve for the molecules that are of greatest interest. Very often the higher-level calculation is confined to zero frequency and the results scaled by using a less complete theory for the frequency dependence. Typically, ab initio studies use coupled-cluster methods for the static values scaled to frequencies where the effects are observable with time-dependent Hartree-Fock theory. Density functional methods require the introduction of specialized functions before they can cope with the hyperpolarizabilities and higher order magnetic effects. 

The ab initio calculation of NLO properties has been a topic of research for about three decades. In particular, response theory has been used in combination with a number of electronic structure methods to derive so-called response functions [41 8], The latter describe the response of a molecular system for the specific perturbation operators and associated frequencies that characterize a particular experiment. For example, molecular hyperpolarizabilities can be calculated from the quadratic and cubic response functions using electric dipole operators. From the frequency-dependent response functions one can also determine expressions for various transition properties (e.g. for multi-photon absorption processes) and properties of excited states [42]. 

The approach outlined above combines the calculation of response functions (i.e. of frequency-dependent properties) with the theory of analytic derivatives developed for static higher-order properties. In the limit of a static perturbation all equations above reduce to the usual equations for (unrelaxed) coupled cluster energy derivatives. This is an invaluable advantage for the implementation of frequency-dependent properties in quantum chemistry programs. 

Analytic response theory, which represents a particular formulation of time-dependent perturbation theory, has constituted a core technology in much of the this development. Response functions provide a universal representation of the response of a system to perturbations, and are applicable to all computational models, density-functional as well as wave-function models, and to all kinds of perturbations, dynamic as well as static, internal as well as external perturbations. The analytical character of the theory with properties evaluated from analytically derived expressions at finite frequencies, makes it applicable for a large range of experimental conditions. The theory is also model transferable in that, once the computational model has been defined, all properties are obtained on an equal footing, without further approximations. 

The general theory of time-dependent response functions has been described in many publications.2,18,19 The response is non-local in time and the Fourier transforms of the general time-dependent functions lead to the definitions of the frequency-dependent response functions which are the quantities most easily related to experimental measurements and potential applications. The notation... 

Reis et al. report theoretical studies of the urea250 and benzene251 crystals. Their calculations start from MP2 ab initio data for the frequency-dependent molecular response functions and include crystal internal field effects via a rigorous local-field theory. The permanent dipolar fields of the interacting molecules are also taken into account using an SCF procedure. The experimental linear susceptibility of urea is accurately reproduced while differences between theory and experiment remain for /2). Hydrogen bonding effects, which prove to be small, have been estimated from a calculation of the response functions of a linear dimer of urea. Various optoelectronic response functions have been calculated. For benzene the experimental first order susceptibility is accurately reproduced and results for third order effects are predicted. Overall results and their comparison with studies of liquid benzene show that for compact nonpolar molecules environmental effects on the susceptibilities are small. 

Solvents with vanishing molecular dipole moments but finite higher order multipoles, such as benzene, toluene, or dioxane, can exhibit much higher polarity, as reflected by its influence on the ET energetics, than predicted by the local dielectric theory [228], Full spatially dispersive solvent response formulation is required in this case [27-29, 104, 229-233], There are different approaches to the problem of spatial dispersion. The original formulation by Kornyshev and co-workers [27c, 28] introduces the frequency-dependent screening effect on the basis of heuristic arguments. More recent approaches are based on the density-function theory [104,197],... 

R. Cammi and J. Tomasi, Int. J. Quantum Chem., 29, 465 (1995). Nonequilibrium Solvation Theory for the Polarizable Continuum Model A New Formulation at the SCF Level with Application to the Case of the Frequency-Dependent Linear Electric Response Function. 

---