Electrical response property calculations

Woon, D.E., and Duiming, T.H. Jr., Gaussian basis sets for use in correlated molecmar calculations. IV. Calcmation of static electrical response properties, J. Chem. Phys., 100, 2975-2988 (1994). 

IV. Calculation of static electrical response properties, J. Chem. Phys. 1994,100,2975. 

D. E. Woon and T. H. Dunning, Jr., /. Ghent, Phys., 100, 2975 (1994). Gaussian Basis Sets for Use in Correlated Molecular Calculations. IV. Calculation of Static Electrical Response Properties. 

In [170] the authors obtain a test set of ten molecules of specific atmospheric interest in order to evaluate the performance of various Density Functional Theory (DFT) methods in (hyper)polarizability calculations as well as established ab initio methods. The authors make their choice for these molecules based on the profound change in the physics between isomeric systems, the relation between isomeric forms and the effect of the substitution. In the evaluation analysis the authors use arguments chosen from the information theory, the graph theory and the pattern recognition fields of Mathematics. The authors mentioned the remarkable good performance of the double hybrid functionals (namely B2PLYP and mPW2PLYP) which are for the first time used in calculations of electric response properties. 

W. Zou, M. Filatov, D. Cremer. Analytic calculation of second-order electric response properties with the normalized elimination of the small component (NESC) method. /. Chem. Phys., 137 (2012) 084108. 

This equation describes a sinusoidal response at frequency, co, to the electric field component at co. This is the basis for the linear optical response. To calculate the optical properties of the Lorenz oscillator the polarization of the medium is obtained as... 

Molecular electric properties give the response of a molecule to the presence of an applied field E. Dynamic properties are defined for time-oscillating fields, whereas static properties are obtained if the electric field is time-independent. The electronic contribution to the response properties can be calculated using finite field calculations , which are based upon the expansion of the energy in a Taylor series in powers of the field strength. If the molecular properties are defined from Taylor series of the dipole moment /x, the linear response is given by the polarizability a, and the nonlinear terms of the series are given by the nth-order hyperpolarizabilities ()6 and y). 

As mentioned in section 1, the combination of the CI method and semiempirical Hamiltonians is an attractive method for calculations of excited states of large organic systems. However, some of the variants of the CI ansatz are not in practical use for large molecules even at the semiempirical level. In particular, this holds for full configuration interaction method (FCI). The truncated CI expansions suffer from several problems like the lack of size-consistency, and violation of Hellmann-Feynman theorem. Additionally, the calculations of NLO properties bring the problem of minimal level of excitation in CI expansion neccessary for the coirect description of electrical response calculated within the SOS formalism. 

Other QMC capabilities have been demonstrated on the calculation of Li 2 S- 2 P oscillator strength with significantly better agreement with experiment when compared with previous calculations [90]. Various quantities for a few electron atoms and molecules, including the electric response constants, were evaluated by Alexander et al. [91]. Study of vibrational properties of molecules has been advanced by Vrbik and Rothstein for the LiH molecule using DMC estimators for the derivatives of energy with respect to the ion positions [92]. 

Our studies on molecular response properties have been limited to the standard PCM, with the exception of the application of the lEF formalism to electric (hyper)polarizabilities. Molecular response functions are quite sensitive to the details of the calculation, by far more than energy, and can be used to test in a deeper way the various extensions of PCM we have exposed in the previous pages an example of this use of molecular response, addressed to the inclusion into HF equation of dispersion and repulsion terms, can be found in... 

Using Eqs. (4.61) and (4.63), matrix U is calculated to give the response properties in terms of the uniform electric field dipole moments, polarizabilities, hyperpolarizabilities, and so forth. Equation (4.61) is called the coupled perturbed Kohn-Sham equation. Other response properties are calculated by solving Eq. (4.61) after setting the first derivative of the Fock operator, F, in terms of each perturbation. Note, however, that this method has problems in actual calculations similarly to the time-dependent response Kohn-Sham method. For example, using most functionals, this method tends to overestimate the electric field response properties of long-chain polyenes. 

Three basic types of physical phenomenon are responsible for electroopti-cal behavior of a macromolecule in solution dipole moment, diffusion coefficients, and extinction coefficients. Amplitudes and time constants depend on both the properties of the macromolecules and experimental conditions. The sum of relaxation amplitudes is related to the linear dichroism of the solution at saturation, and depends on both the electric and optical properties of the molecule under investigation. The saturating behavior of linear dichroism calculated for a pure permanent moment, a pure induced moment or a mixed orientational mechanism is traditionally used in determining electrical responses and optical anisotropy by fitting the experimental results to a theoretical curve.Pqj. molecules with effective cylindrical symmetry (regarding their orientational behavior), the optical signal observed in the experiment can be represented as a product of orientational factor, < )(j, and a limiting reduced dichroism at infinite field. 

The response properties of molecules and clusters can easily be calculated using these equations and finite field method by applying external electric field. However, the major limitation of this approach arises because of increase in computational labor with increase in size of the system. 

An interesting application of the first case (i.e., an external oscillating field) is the study of the nonlinear properties of molecules in condensed matter. Once the approximate solutions of the corresponding time-dependent SchrOdinger equation are found, the frequency-dependent electric response functions (polarizability and hyperpolarizabilities tensors) of the molecular solute are easily calculated. 

Essentially all experimentally measured properties can be thought of as arising through the response of the system to some externally applied perturbation or disturbance. In turn, the calculation of such properties can be formulated in terms of the response of the energy E or wavefunction P to a perturbation. For example, molecular dipole moments p are measured, via electric-field deflection, in terms of the change in energy... 

The static dipole polarizability is the linear response of an atomic or molecular system to the application of a weak static electric field [1], It relates to a great variety of physical properties and phenomena [2-5]. Because of its importance, there have been numerous ab initio calculations of isolated atomic and molecular polarizabilities [6-14]. Particular theoretical attention has been dedicated to the polarizability of free atomic anions [15-21] because of its fragility and difficulty in obtaining direct experimental results. In recent years theoretical studies have... 

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