Linear response theory hydrogen bonds

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 ... 

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]. 

The linear response function [3], R(r, r ) = (hp(r)/hv(r ))N, is used to study the effect of varying v(r) at constant N. If the system is acted upon by a weak electric field, polarizability (a) may be used as a measure of the corresponding response. A minimum polarizability principle [17] may be stated as, the natural direction of evolution of any system is towards a state of minimum polarizability. Another important principle is that of maximum entropy [18] which states that, the most probable distribution is associated with the maximum value of the Shannon entropy of the information theory. Attempts have been made to provide formal proofs of these principles [19-21], The application of these concepts and related principles vis-a-vis their validity has been studied in the contexts of molecular vibrations and internal rotations [22], chemical reactions [23], hydrogen bonded complexes [24], electronic excitations [25], ion-atom collision [26], atom-field interaction [27], chaotic ionization [28], conservation of orbital symmetry [29], atomic shell structure [30], solvent effects [31], confined systems [32], electric field effects [33], and toxicity [34], In the present chapter, will restrict ourselves to mostly the work done by us. For an elegant review which showcases the contributions from active researchers in the field, see [4], Atomic units are used throughout this chapter unless otherwise specified. 

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. 

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