Dipole-polarizability tensor

The dipole polarizability tensor characterizes the lowest-order dipole moment induced by a unifonu field. The a tensor is syimnetric and has no more than six independent components, less if tire molecule has some synnnetry. The scalar or mean dipole polarizability... 

Molecular dynamic studies used in the interpretation of experiments, such as collision processes, require reliable potential energy surfaces (PES) of polyatomic molecules. Ab initio calculations are often not able to provide such PES, at least not for the whole range of nuclear configurations. On the other hand, these surfaces can be constructed to sufficiently good accuracy with semi-empirical models built from carefully chosen diatomic quantities. The electric dipole polarizability tensor is one of the crucial parameters for the construction of such potential energy curves (PEC) or surfaces [23-25]. The dependence of static dipole properties on the internuclear distance in diatomic molecules can be predicted from semi-empirical models [25,26]. However, the results of ab initio calculations for selected values of the internuclear distance are still needed in order to test and justify the reliability of the models. Actually, this work was initiated by F. Pirani, who pointed out the need for ab initio curves of the static dipole polarizability of diatomic molecules for a wide range of internuclear distances. 

In the response function terminology [47] the i, j component of the frequency-dependent dipole polarizability tensor — w) (or the ij, kl component of the traceless quadrupole polarizability tensor is defined through... 

The dipole and quadrupole polarizability tensor components of LiH were calculated by MCSCF linear response theory with the basis set of Roos and Sadlej [57] which consists of 13s-, 8p-, 6d-, and 2f-type sets of uncontracted Gaussian functions on Li and 12s-, 8p-, and 5d-type sets of uncontracted Gaussians on H. Due to the small size of the molecule we could perform MCSCF calculations over the whole range of internuclear distances with a very large CAS 0000 520,10,10,4 p g present the tensor components, isotropic, and anisotropic values of the dipole polarizability tensor a as function... 

Fig. 6. HF dipole polarizability tensors (in atomic units) calculated by different linear response methods in comparison with MCSCF method.

Let us now consider the second-order molecular properties. The static electric dipole-polarizability tensor is given by the expression... 

The occurrence of Raman scattering is connected to the change in polarizability during the transition of the molecule from one vibrational state to the other. Circular polarization ROA arises from interference of the electric dipole electric dipole polarizability tensor with the electric dipole - magnetic dipole and the electric dipole electric quadrupole optical activity tensors. Due to limited space, no rigorous derivation of the theory will be given here, but only the most important results shall be shown. 

Note that a distinction is made between electrostatic and polarization energies. Thus the electrostatic term, Ue e, here refers to an interaction between monomer charge distributions as if they were infinitely separated (i.e., t/°le). A perturbative method is used to obtain polarization as a separate entity. The electrostatic and polarization contributions are expressed in terms of multipole expansions of the classical coulomb and induction energies. Electrostatic interactions are computed using a distributed multipole expansion up to and including octupoles at atom centers and bond midpoints. The polarization term is calculated from analytic dipole polarizability tensors for each localized molecular orbital (LMO) in the valence shell centered at the LMO charge centroid. These terms are derived from quantum calculations on the... 

The dynamic dipole polarizability tensor a can be expressed through eq. (1.55) when both A and B operators are the electric dipole moment... 

The ab initio theoretical quantity needed to predict molecular optical rotations is the electric dipole-magnetic dipole polarizability tensor, indexelec-tric dipole-magnetic dipole polarizability tensor given by the expression ... 

Abstract The modified equation-of-motion coupled cluster approach of Sekino and Bartlett is extended to computations of the mixed electric-dipole/magnetic-dipole polarizability tensor associated with optical rotation in chiral systems. The approach - referred to here as a linearized equation-of-motion coupled cluster (EOM-CCl) method - is a compromise between the standard EOM method and its linear response counterpart, which avoids the evaluation of computationally expensive terms that are quadratic in the field-perturbed wave functions, but still yields properties that are size-extensive/intensive. Benchmark computations on five representative chiral molecules, including (P)-hydrogen peroxide, (5)-methyloxirane, (5 )-2-chloropropioniuile, (/ )-epichlorohydrin, and (75,45)-norbornenone, demonstrate typically small deviations between the EOM-CCl results and those from coupled cluster linear response theory, and no variation in the signs of the predicted rotations. In addition, the EOM-CCl approach is found to reduce the overall computing time for multi-wavelength-specific rotation computations by up to 34%. 

Among these response properties the most known are the dipole polarizability tensors a, P, and y, that give flic first three components of flie expansion of a dipole moment t subjected to an external homogeneous field F ... 

CP. Schwerdtfeger, R. Wesendrup, G. E. Moyano, A. J. Sadlq, J. Greif, E. Hensel. The potential energy curve and dipole polarizability tensor of mercury dimer. J. Chem. Phys., 115 (2001) 7401-7412. 

It should be pointed out that there are alternative methods to calculate properties other than direct differentiation. For instance, the second-order perturbation theory correction to the energy for a perturbing electric field yields an expression for the dipole polarizability tensor, a. 

This is analogous to the usual dipole polarizability tensor which has only 3x3 components, corresponding to the perturbations g(r) = x, y, z. The second-order part of the energy in the electric field is given as... 

In order to derive a quantum mechanical expression for the mixed dynamic electric dipole magnetic dipole polarizability tensor we have to evaluate the time-dependent expectation value of the electric dipole operator ( o(t) Aa l o(f)) in the presence of the time-dependent magnetic induction of left- or right-circularly polarized radiation... 

Comparing this with the classical expansion of a time-dependent dipole moment in Eq. (7.33) we can identify the frequency-dependent mixed electric dipole magnetic dipole polarizability tensor as a linear response function or polarization propagator... 

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