Molecular Electronic Hyper Polarizability

METHODS FOR MOLECULAR ELECTRONIC (HYPER)POLARIZABILITY CALCULATIONS 

This section does not provide an exhaustive survey of all possible methods and approximations in use, but rather focuses on the most common methods currently implemented and then briefly describes a few others that are important. Three methods—the finite field, sum-over-states (SOS), and time-dependent Hartree-Foclc methods—encompass the vast majority of NLO property calculations being performed today and are implemented in several readily available molecular orbital computer programs. 

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Just as a is the linear polarizability, the higher order terms p and y (equation 19) are the first and second hvperpolarizabilities. respectively. If the valence electrons are localized and can be assigned to specific bonds, the second-order coefficient, 6, is referred to as the bond (hyper) polarizability. If the valence electron distribution is delocalized, as in organic aromatic or acetylenic molecules, 6 can be described in terms of molecular (hyper)polarizability. Equation 19 describes polarization at the atomic or molecular level where first-order (a), second-order (6), etc., coefficients are defined in terms of atom, bond, or molecular polarizabilities, p is then the net bond or molecular polarization. 

We show how the response of a molecule to an external oscillating electric field can be described in terms of intrinsic properties of the molecules, namely the (hyper)polarizabilities. We outline how these properties are described in the case of exact states by considering the time-development of the exact state in the presence of a time-dependent electric field. Approximations introduced in theoretical studies of nonlinear optical properties are introduced, in particular the separation of electronic and nuclear degrees of freedom which gives rise to the partitioning of the (hyper)polarizabilities into electronic and vibrational contributions. Different approaches for calculating (hyper)polarizabilities are discussed, with a special focus on the electronic contributions in most cases. We end with a brief discussion of the connection between the microscopic responses of an individual molecule to the experimentally observed responses from a molecular ensemble... 

There are two major ways to view tlie vibrational contribution to molecular linear and nonlinear optical properties, i.e. to (hyper)polarizabilities. One of these is from the time-dependent sum-over-states (SOS) perturbation theory (PT) perspective. In the usual SOS-PT expressions [15], based on the adiabatic approximation, the intermediate vibronic states K, k> are of two types. Either the electronic wavefunction... 

This article is devoted to Are methodology of predicting the direction of the changes of molecular (hyper)polarizabilities values as a function of tire solvent polarity. Since the environmental effect on the two-photon absorption (TPA) is still poorly understood, we will consider the two-level approximation to describe the influence of the solvent effects on TPA from the ground to the CT excited state of the D-tt-A type chromophores. Only electronic contributions will be taken into account. In contrast to the TPA process, the substantial progress in theoretical description of the solvent influence on the vibrational (hyper)polarizabilities has been observed recently [64-67],... 

The reason is simple the computation of the various (hyper)polarizability elements requires the knowledge of the one-electron density matrix derivatives with respect to the external field Cartesi ln components E , with v = x,y,z] in fact, by expanding the molecular dipole in terms of powers of the external field, we can derive ... 

The second category includes the response properties which describe the effects of any external applied field on a molecular system. This category includes the electronic and vibrational dipole (hyper)polarizabilities, both static and frequency dependent, magnetic and chiro-optic properties, etc.. Response properties are essential for a deeper understanding of molecular behaviors, and they represent the basis for an ever increasing number of technical applications. 

Certain improvement in the efficiency of the CC calculations can be achieved by using the idea of local correlation effects [18, 33, 64, 67, 69]. In that approach the CC reference function is built using localized molecular orbitals (LMO) [62]. The use of the LMOs enables to significantly reduce the computational cost of the CCSD calculations [1, 32, 44, 53, 66, 70, 84]. Also, the local CC approach has been implemented in the calculations of electronic excited states [29, 30, 37, 52]. The use of the local CCSD approach in the calculations of the (hyper)polarizabilities has been described in Refs. [28, 35, 36, 38, 66]. For a description of the calculations of the frequency-dependent polarizability and dispersion-coefficients see Ref. [85]. 

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