Second order electrical properties

These findings imply that our basis sets are definitely more reliable than those adopted in Ref. 16 and Ref. 18 for studying second-order electric properties. Accordingly, it seems quite difficult to understand that theoretical obtained via... 

We then turn to the question of how to eliminate the spin-orbit interaction in four-component relativistic calculations. This allows the assessment of spin-orbit effects on molecular properties within the framework of a single theory. In a previous publication [13], we have shown how the spin-orbit interaction can be eliminated in four-component relativistic calculations of spectroscopic properties by deleting the quaternion imaginary parts of matrix representations of the quaternion modified Dirac equation. We show in this chapter how the application of the same procedure to second-order electric properties takes out spin-forbidden transitions in the spectrum of the mercury atom. Second-order magnetic properties require more care since the straightforward application of the above procedure will extinguish all spin interactions. After careful analysis on how to proceed we... 

First and second order electrical property LiH molecule... 

Five large basis sets have been employed in the present study of benzene basis set 1, which has been taken from Sadlej s tables [37], is a ( ()s6pAdl6sAp) contracted to 5s >p2dl >s2p and contains 210 CGTOs. It has been previously adopted by us in a near Hartree-Fock calculation of electric dipole polarizability of benzene molecule [38]. According to our experience, Sadlej s basis sets [37] provide accurate estimates of first-, second-, and third-order electric properties of large molecules [39]. 

Nonlinear second order optical properties such as second harmonic generation and the linear electrooptic effect arise from the first non-linear term in the constitutive relation for the polarization P(t) of a medium in an applied electric field E(t) = E cos ot. 

In this chapter, we therefore consider whether it is possible to eliminate spin-orbit coupling from four-component relativistic calculations. This is a situation quite different from that of more approximate relativistic methods where a considerable effort is required for the inclusion of spin-orbit coupling. We have previously shown that it is indeed possible to eliminate spin-orbit coupling from the calculation of spectroscopic constants [12,13]. In this chapter, we consider the extension of the previous result to the calculation of second-order electric and magnetic properties, i.e., linear response functions. Although the central question of this article may seem somewhat technical, it will be seen that its consideration throws considerable light on the fundamental interactions in molecular systems. We will even claim that four-component relativistic theory is the optimal framework for the understanding of such interactions since they are inherently relativistic. 

On matrix form the non-unitary transformations (27) and (30) of the previous section are easily extended to the complete Hamiltonian and have therefore allowed relativistic and non-relativistic spin-free calculations of spectroscopic constants and first-order properties at the four-component level (see, for instance. Refs. [45 7]). In this section, we consider the elimination of spin-orbit interaction in four-component calculations of second-order electric and magnetic properties. Formulas are restricted to the Hartree-Fock [48] or Kohn-Sham [49] level of theory, but are straightforwardly generalized. 

Non-linear second-order optical properties such as second harmonic generation (SHG) and the linear electrooptic effect are due to the non-linear susceptibility in the relation between the polarization and the applied electric field. SHG involves the... 

Many of the different susceptibilities in Equations (2.165)-(2.167) correspond to important experiments in linear and nonlinear optics. x<(>> describes a possible zero-order (permanent) polarization of the medium j(1)(0 0) is the first-order static susceptibility which is related to the permittivity at zero frequency, e(0), while ft> o>) is the linear optical susceptibility related to the refractive index n" at frequency to. Turning to nonlinear effects, the Pockels susceptibility j(2)(- to, 0) and the Kerr susceptibility X(3 —to to, 0,0) describe the change of the refractive index induced by an externally applied static field. The susceptibility j(2)(—2to to, to) describes frequency doubling usually called second harmonic generation (SHG) and j(3)(-2 to, to, 0) describes the influence of an external field on the SHG process which is of great importance for the characterization of second-order NLO properties in solution in electric field second harmonic generation (EFISHG). 

Having considered the general expressions for first- and second-order molecular properties, we now restrict ourselves to properties associated with the application of static uniform external electric and magnetic fields. For such perturbations, the Hamiltonian operator may be written in the manner (in atomic units)... 

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

In this equation, po is the permanent dipole moment of the molecule, a is the linear polarizability, 3 is the first hyperpolarizability, and 7 is the second hyperpolarizability. a, and 7 are tensors of rank 2, 3, and 4 respectively. Symmetry requires that all terms of even order in the electric field of the Equation 10.1 vanish when the molecule possesses an inversion center. This means that only noncentrosymmetric molecules will have second-order NLO properties. In a dielectric medium consisting of polarizable molecules, the local electric field at a given molecule differs from the externally applied field due to the sum of the dipole fields of the other molecules. Different models have been developed to express the local field as a function of the externally applied field but they will not be presented here. In disordered media,... 

The principles of nonlinear optics and the main techniques used to evaluate the second-order NLO properties are briefly presented here. Major details can be found in more specialised reviews and books. At the molecular level, the interaction between polarisable electron density and the alternating electric field of the laser light beam (E) induces a polarisation response (Afi) that can be expressed following Equation 1.1 ... 

Fig. 5.15 Light-induced generation of second-order NLO properties in an electric field-poled PMMA film doped with 25 wt% of a spiropyran (see Chart 5.14). Alternating irradiation at 7 = 355 nm and 7 = 514 nm.

The second-order NLO properties are of interest for a variety of NLO processes [1-3]. One of the most relevant is the SHG, originated by the mixing of three waves two incident waves with frequency co interact with the molecule or the bulk material with NLO properties, defined by a given value of the quadratic hyperpolarizability, fi, or of the second-order electrical susceptibility, respectively, to produce a new electrical wave, named SH, of frequency 2co. Another important second-order NLO process is the electrooptic Pockels effect which requires the presence of an external d.c. electric field, E(0), in addition to the optical E co) electrical field. This effect produces a change in the refractive index of a material proportional to the applied electric field, and can be exploited in devices such as optical switches and modulators [1-3]. 

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. 

By combining classical samplings with quantum chemistry semiempirical TDHF calculations the impact of dynamic fluctuations on the first hyperpolarizability of helical strands has been evidenced . In particular, these fluctuations are responsible for relative variations of 20% in the hyper-Rayleigh responses in both pyridine-pyrimidine (py-pym) and hydrazone-pyrimidine (hy-pym) strands. Dynamical disorder has an even more important impact on the electric field-induced second harmonic generation responses, whose variations can reach 2 (py-pym) or 5 (hy-pym) times their mean value. These results demonstrate that geometrical fluctuations have to be taken into account for a reliable description of the second-order NLO properties in flexible structures such as helical strands. This work has also highlighted the relationships between the nature of the unit cell and the helical conformation of foldamers and their second-order NLO responses. In particular, the value of the hyper-Rayleigh depolarization ratio, which is characteristics of octupolar symmetry, is related to the helix periodicity, of three unit cells per turn in both compounds. 

In general, as-deposited organic materials are centrosymmetric on a macroscopic scale and they are not endowed of second order nonlinear properties. Poling, i.e. the orientation of the microscopic molecular dipoles, is required in order to break this symmetry. The polymer is heated close to its glass transition temperature (Tg), so as to increase the molecular mobility, while application of a DC electric field results in statistical polar orientation of the molecular dipoles along the field direction. 

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