Autocorrelation function linear response theory

The linear response theory [50,51] provides us with an adequate framework in order to study the dynamics of the hydrogen bond because it allows us to account for relaxational mechanisms. If one assumes that the time-dependent electrical field is weak, such that its interaction with the stretching vibration X-H Y may be treated perturbatively to first order, linearly with respect to the electrical field, then the IR spectral density may be obtained by the Fourier transform of the autocorrelation function G(t) of the dipole moment operator of the X-H bond ... 

Using linear response theory and noting (according to the results at the end of Section 5.1.3) that the (complex) electrical conductivity a is the Fourier transform of the current density autocorrelation function, we obtain from Eqn. (5.75) (see the equivalent Eqn. (5.21))... 

Here, G(t) is the quantum autocorrelation function (ACF) of the dipole moment operator responsible for the dipolar absorption transition, whereas oo is the angular frequency and t is the time. Equation (1) has been used, for example, by Bratos [45] and Robertson and Yarwood [46] in their semiclassical studies of H-bonded species within the linear response theory. 

Linear response theory provides autocorrelation function expressions for transport properties [68] and, starting with early investigations of hard sphere [69] and Lennard-Jones [70] systems, MD has been used, and continues to be used, to estimate transport... 

At T 0 the sharp lines corresponding to the harmonic modes are broadened by anharmonic effects until, at high temperature, the simple relationship between vibrational density of states and dynamical matrix is lost. In this regime, and especially for large aggregates, MD is the most suitable tool to compute the vibrational spectrum. Standard linear response theory within classical statistical mechanics shows that the spectrum f(co) is given by the Fourier transform of the velocity-velocity autocorrelation function... 

Another approach to the calculation of IR spectra of hydrogen-bonded complexes is based on linear response theory, in which the spectral density is the Fourier transform of the autocorrelation function of the dipole moment operator involved in the IR transition [62,63]. Recently Car-Parrinello molecular dynamics (CPMD) [73] has been used to simulate IR spectra of hydrogen-bonded systems [64-72]. 

Another approach to calculate thermal conductivity is equilibrium molecular dynamics (EMD) [125] that uses the Green-Kubo relation derived from linear response theory to extract thermal conductivity from heat current correlation functions. The thermal conductivity X is calculated by integrating the time autocorrelation function of the heat flux vector and is given by... 

The thermal conductivity of a material can be calculated directly from equilibrium molecular dynamics (EMD) simulation based on the linear response theory Green-Kubo relationship. " The fluctuation-dissipation theorem provides a connection between the energy dissipation in irreversible processes and the thermal fluctuations in equilibrium. The thermal conductivity tensor. A, can be expressed in terms of heat current autocorrelation correlation functions (HCACFs),/, ... 

A general approach (VIG, GT) to a linear-response analytical theory, which is used in our work, is viewed briefly in Section V.B. In Section V.C we consider the main features of the hat-curved model and present the formulae for its dipolar autocorrelator—that is, for the spectral function (SF) L(z). (Until Section V.E we avoid details of the derivation of this spectral function L). Being combined with the formulas, given in Section V.B, this correlator enables us to calculate the wideband spectra in liquids of interest. In Section V.D our theory is applied to polar fluids and the results obtained will be summarized and discussed. 

In our variant of the response theory the spectral function (SF) L(z) of the model is linearly related to the spectrum of the dipole autocorrelation function (ACF). 

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