Dipole moments, computational procedures

DFT calculations show that the dipole moment is due to not only CT between the molecules, but also the polarization of the electronic clouds within each molecule. For example, upon increasing the intermolecular distance between the TTF and TCNQ molecules the value of the M(Z) dipole moment computed from the Mulliken charges decreases almost to zero already for an intermolecular distance of 5 A. However, the dipole moment obtained directly from the SCF procedure decreases much slower. In the systems exhibiting weak CT, the dipole moment mostly originates from polarization interactions. 

The second procedure, several aspects of which are reviewed in this paper, consists of directly computing the asymptotic value by employing newly-developed polymeric techniques which take advantage of the one-dimensional periodicity of these systems. Since the polarizability is either the linear response of the dipole moment to the field or the negative of the second-order term in the perturbation expansion of the energy as a power series in the field, several schemes can be proposed for its evaluation. Section 3 points out that several of these schemes are inconsistent with band theory summarized in Section 2. In Section 4, we present the main points of the polymeric polarization propagator approaches we have developed, and in Section 5, we describe some of their characteristics in applications to prototype systems. 

As a consequence, field methods, which consist of computing the energy or dipole moment of the system for external electric field of different amplitudes and then evaluating their first, second derivatives with respect to the field amplitude numerically, cannot be applied. Similarly, procedures such as the coupled-perturbed Hartree-Fock (CPHF) or time-dependent Hartree-Fock (TDHF) approaches which determine the first-order response of the density matrix with respect to the perturbation cannot be applied due to the breakdown of periodicity. 

Spectroscopic measurement. Specifically, if the induced dipole moment and interaction potential are known as functions of the intermolecular separation, molecular orientations, vibrational excitations, etc., an absorption spectrum can in principle be computed potential and dipole surface determine the spectra. With some caution, one may also turn this argument around and argue that the knowledge of the spectra and the interaction potential defines an induced dipole function. While direct inversion procedures for the purpose may be possible, none are presently known and the empirical induced dipole models usually assume an analytical function like Eqs. 4.1 and 4.3, or combinations of Eqs. 4.1 through 4.3, with parameters po, J o, <32, etc., to be chosen such that certain measured spectral moments or profiles are reproduced computationally. 

Table 5.1. Comparison of binary spectral moments calculated from classical (C.), semi-classical (S.) and quantum (Q.) calculations, based on line shapes (.LS) and sum formulae (.SF), for He-Ar at 295 K. Moments computed from the classical line shape after desymmetrization procedures P-2 and P-4 (scaled) had been applied are also shown. Computations are based on the ab initio dipole, Table 4.3, and an advanced potential [12].

The approaches to this problem follow along two general lines. In the first approach, one computes derivatives of the dipole moment with respect to the applied field and relates them to the terms in the polarization expansion of equation 8. Inspection of equation 8 suggests that the second derivative of the dipole moment with respect to the field gives p. The choice of the exact form of the Hamiltonian, which incorporates the optical field and the atomic basis set, determines the accuracy of this procedure. In one popular version of this approach, the finite field method, the time dependence of the Hamiltonian is ignored for purposes of simplification and the effects of dispersion on p, therefore, cannot be accounted for. 

The parametrization procedure that we have opted for in the most recent works is as follows (1) Compute the intermolecular dynamic correlation energy for the ground state with a second-order Mpller-Plesset (MP2) expression that only contains the intermolecular part and which uses monomer orbitals. Fit the dispersion parameters to this potential. To aid in the distribution of the parameters, a version of the exchange-hole method by Becke and Johnson is sometimes used [154,155], Becke and Johnson show that the molecular dispersion coefficient can be obtained fairly well by a relation that involves the static polarizability and the exchange-hole dipole moment ... 

We now turn to discussion of the computer dynamical procedure, which shows great promise for calculations of static permittivity. The model of Rahman and Stillinger contains sufficient information in the computer program to enable the mean dipole moment A of a sphere of known radius to be calculated at a known temperature. This moment is related to the Kirkwood correlation parameter g by equations (9) and (10), with g defined as in equation (10). 

The prediction of mK for a given molecule requires an a priori estimation of the principal polarizabilities, 6X, b2, and b3 and a knowledge of the components of the resultant dipole moment along the principal axial directions these quantities are then united via equations (26), (27), and (30) to yield the mK sought. Computational procedures are as outlined by Le Fevre and Le Fevre (1960) and described in detail by Eckert and Le Fevre (1962a). Cartesian axes (X, Y, and Z) are arbitrarily set up within the frame-work of the three-dimensional structure to be examined, and the angles made by each bond with X, Y, and Z calculated (or measured by hand, in which case the models introduced by Barton. 

Several attempts have been made to compute the atomic charge distributions (both ir-charges and total charges) and electric dipole moment216 0f oxazole, and thus to check the accuracies of the various MO procedures (see Table III). It is apparent from Table III that all-valence-electron calculations228 232 including the atomic polarization terms yield dipole moments very close to the experimental value.218 233... 

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