Dipole moment operator, 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]. 

Trouton s rule states that for most normal liquids the entropy of vaporization per mole 21 e.u. By a normal liquid, we mean which is not associated. In general association in the liquid state may be expected when intermolecular forces of a dominant type operate. Dipole moments, hydrogen bonding etc., lead to this situation. Abnormally high boiling points are a consequence of molecular association in the liquid state. 

An apolar aprotic solvent is characterized by a low relative permittivity (sr < 15), a low dipole moment [ju < 8.3 10 Cm = 2.5 D), a low value ca. 0.0... 0.3) cf. Table A-1, Appendix), and the inability to act as a hydrogen-bond donor. Such solvents interact only slightly with the solute since only the non-specific directional, induction, and dispersion forces can operate. To this group belong aliphatic and aromatic hydrocarbons, their halogen derivatives, tertiary amines, and carbon disulfide. 

In the framework of our model, the dipole operator takes the form P = au ai,i), where d is the dipole moment of a hydrogen bond. 

The hydrogen fluoride molecule may be used as a simple example of this approach. Using the 6-31G basis the PA charge on F is -0.395 e. This monopole value yields, when combined with the bond distance of 1.733 au, a dipole moment of 0.685. However, the exact operator dipole obtained from the wavefunction is 0.776. In the cumulative procedure, the difference between these two values is made up with atomic dipoles. From [13] one obtains (w)f = + 0.330 and [w] = +0.446, which of course sum to the exact molecular dipole. Application of Eq. [14] yields cumulative atomic dipoles Mj. = -0.012 and Mh = 0.103. The sum of the PA charge dipole plus the atomic dipoles equals the exact molecular dipole. Analogous procedures are used for higher moments. 

Another technique for estimating the dipole moment in the excited state, suggested by Ito [35] is the study of the solvent shift in a mixture of two polar solvents that have practically the same refractive index, but quite different dielectric constants, and also, do not tend to form hydrogen bonds. Under these circumstances, when the interactions between the fixed dipole of the solvent and the induced dipole of the solute can be neglected, and when the contributions of the dispersion interactions are identical, the following interaction is operative [26, 35]. 

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