Dipole hyperpolarizability, electrical properties

Among the molecular properties introduced above are the permanent electric dipole moment /xa and traceless electric quadrupole moment a(8, the electric dipole polarizability aajg(—w to) [aiso(to) = aaa(—or, o>)], the magnetizability a(8, the dc Kerr first electric dipole hyperpolarizability jBapy(—(o a>, 0) and the dc Kerr second electric-dipole hyperpolarizability yapys(— ( >, 0,0). The more exotic mixed hypersusceptibilities are defined, with the formalism of modern response theory [9]... 

The vibrational excursions of a molecule may cause it to have sharply changing electrical properties from state to state. This, of course, is essential for mechanisms of absorption and emission of radiation. How sharp these changes may be is illustrated for HF in Figure 3. The curves show the axial elements of a. A, and P in the vicinity of the equilibrium bond length as a function of the H-F distance. The types of changes that may be found in a polyatomic molecule are illustrated by Figures 4 and 5. They show contours of the dipole polarizability and hyperpolarizability elements over the two stretching coordinates of HCN. Both and P yy have zero contours... 

To understand the complete role of vibration in determining electrical properties, it is useful to consider a diatomic molecule in the harmonic oscillator approximation, where the stretching potential is taken to be quadratic in the displacement coordinate. The doubly harmonic model takes the various electrical properties to be linear functions of the coordinate. This turns out to be most reasonable in the vicinity of an equilibrium structure, but it breaks down at long separations. Letting x be a coordinate giving the displacement from equilibrium of a one-dimensional harmonic oscillator, the dipole moment, dipole polarizability, and dipole hyperpolarizability, within the doubly harmonic (dh) model, may be written in the following way ... 

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). 

Second, the development of methods and concrete numerical calculations of the constants (reduced matrix elements of the dipole and quadru-pole moments, polarizability, and hyperpolarizabilities, vibronic constant, etc.) determining the effects of electronic degeneracy on electric properties of molecules predicted in this paper seems to be one of the most up-to-date problem in the topics under consideration. Such calculations are quite possible, in principle, provided that the wave functions of the degenerate electronic term (for the calculation of the dipole moment), as well as the excited ones (for the calculation of the polarizabilities), are known. Considering the advances in quantum chemistry, the solution of the problem is quite possible from the practical point of view, especially if one takes into account that in the cases under consideration one can determine numerically the wave function of the system in the presence of an electric field instead of a calculation of excited states. 

Electron correlation plays a role in electrical response properties and where nondynamical correlation is important for the potential surface, it is likely to be important for electrical properties. It is also the case that correlation tends to be more important for higher-order derivatives. However, a deficient basis can exaggerate the correlation effect. For small, fight molecules that are covalently bonded and near their equilibrium structure, correlation tends to have an effect of 1 5% on the first derivative properties (electrical moments) [92] and around 5 15% on the second derivative properties (polarizabilities) [93 99]. A still greater correlation effect is possible, if not typical, for third derivative properties (hyperpolarizabilities). Ionic bonding can exhibit a sizable correlation effect on hyperpolarizabilities. For instance, the dipole hyperpolarizability p of LiH at equilibrium is about half its size with the neglect of correlation effects [100]. For the many cases in which dynamical correlation is not significant, the nondynamical correlation effect on properties is fairly well determined with MP2. For example, in five small covalent molecules chosen as a test set, the mean deviation of a elements obtained with MP2 from those obtained with a coupled cluster level of treatment was 2% [101]. 

The conceptually simplest NLO property is the electric first dipole hyperpolarizability 13. Nevertheless, it is a challenging property from both the theoretical and experimental side, which is related to the fact that, as third-rank tensor, it is a purely anisotropic property. Experimentally this means that (3 in isotropic media (gas or liquid phase) cannot be measured directly as such, but only extracted from the temperature dependence of the third-order susceptibilities In calculations anisotropic properties are often subject to subtle cancellations between different contributions and accurate final results are only obtained with a carefully balanced treatment of all important contributions. 

David Pugh remarked that there seemed to be very much more to write about electric and magnetic properties than when David Bounds and I wrote our own Theoretical Chemistry SPR contribution all those years ago. New techniques in non-linear optics and non-linear spectroscopy have given a new impetus to the accurate calculation of quantities such as the dipole hyperpolarizability. 

Haskopoulos and MarouUs [10] studied the interaction electric properties of H20 Rg (Rg = He, Ne, Ar, Kr, Xe). Correlation effects have been taken into account by employing M0Uer-Plesset (MP2, MP4) and coupled-cluster theories (CCSD, CCSD(T)) in connection with flexible, carefully designed basis sets. Bara-nowska et al. [11] computed the interaction-induced axial static dipole moments, polarizabilities and first hyperpolarizabilities of HCHO (HF)n (n= 1,2). They employed a series of methods (e.g. MP2, CCSD(T)) in connection with various basis sets. 

We have performed an extensive study of the dipole moment and (hy-per)polarizabilities of MeH, Me = Li, Na and K [48]. Here we shall briefly review the electronic and vibrational contributions to first and second hyperpolarizabilities, since these results show the more interesting trends. We will consider the average values [49]. The basis sets developed by Sadie] and Urban [45,49] have been used for the computations. The electric properties of interest can be expressed by ... 

Maroulis calculated the interaction-induced dipole polarizability and hyperpolarizability of the He2, Ne2, Ar2 and Kr2 homodiatoms relying on finite-field Moller-Plesset perturbation theory and coupled cluster calculations. Special attention was paid to the design of flexible basis sets, suitable for interaction-induced electric property calculations. Atom-specific, prepared basis sets were used on all atoms. The construction is completed in four steps ... 

The interaction-induced dipole polarizability and second hyperpolarizability of two neon atoms was reported by Hattig et al They subsequently used the calculated values along with an accurate potential for Nc2 to estimate the refractivity and hyperpolarizability second virial coefficients of gaseous neon. The calculation of ctint, Aai t and yjnt was performed at the CCSD level of theory with a d-aug-cc-pVQZ-33211 basis set. The R-dependence of the interaction-induced electric properties was obtained at a range of internuclear separations defined by 3 < R/ao < 20. 

Li et alP reported a theoretical study of the structure and interaction-induced dipole moment, mean polarizability and mean first hyperpolarizability of the NH3-HCl-(H20)n (n = 0 ) clusters. They relied on B3LYP calculations with large standard basis sets aug-cc-pVDZ, aug-cc-pVDZ-fBF (aug-cc-pVDZ augmented with suitable placed bond functions), aug-cc-pVTZ, d-aug-cc-pVDZ and t-aug-cc-pVDZ. The authors have reached important conclusion on the magnitude of electric properties. For the non-hydrated complex NH3-HCI the first hyperpolarizability, calculated with the d-aug-cc-pVDZ basis, is jS = — 3.35 e ao Eh while the respective result for NH3-HCI-H2O is 413.52 and increases to 886.41 for NH3-HC1-(H20)4. 

Wu et al. calculated the interaction-induced electric properties of the FH-NH3 hydrogen-bonded complex. The authors relied on second-order Moller-Plesset perturbation theory with large standard basis sets. Their best values were obtained with a aug-cc-pVTZ basis augmented with bond-centered functions. The results were suitable corrected for basis set superposition errors (BSSE) with the counterpoise (CP) method. The reported values are p = 0.4762 for the dipole moment, amt= 0.8057 e ao Eh for the mean polarizability and = 3.31 e ao Eh for the mean first hyperpolarizability. It is worth noticing that without the BSSE corrections the values for the above properties are p = 0.4757 for the dipole moment, aj ,= 0.7235 e ao Eh for the mean polarizability and ) ( = 3.66... 

An interesting analysis of the performanee of DFT methods in calculations of interaction-induced electric properties was recently published by Zawada et al The analysis extended over the model compounds HF HF, H20- H2O and H2CO- HF. The properties of interest were the dipole moment, dipole polarizability and first hyperpolarizability. Diffuse Dunning (aug-cc-pVXZ) Jensen (aug-pc-Y) basis sets were employed. The performance of the DFT methods was compared to reference CCSD(T) results. The authors concluded that the LC-BLYP and PBEO methods perform best. The PBEO is proposed as the optimal choice for all interaction-induced properties studied. 

Gora et al reported systematic study of interaction-induced electric properties in linear HCN oligomer chains. The authors reported electric dipole moments, polarizabilities and hyperpolarizabilities for the sequence HCN, (HCN)2 and (HCN)3 at the HF, MP2, CCSD and CCSD(T) levels of theory with the aug-cc-pVQZ basis set. Excess electric properties were subsequently calculated at the same levels of theory. The excess mean second dipole hyperpolarizability for the dimer were found to be Ay X 10 = 0.2(HF), 2.0 (MP2), 1.0 (CCSD) and 1.2 (CCSD(T)) e ao Eh. For the trimer, the respective values are Ay x 10 = 2.8(HF), 4.6 (MP2), 2.8 (CCSD) and 3.6 (CCSD(T)) In addition, the... 

State-specific properties are best considered as describing the response of a molecule to an (external) perturbation. For example, electric properties such as dipole moment, polarizabilities, first hyperpolarizabilities, etc. determine the molecular response to an applied electric field. An important... 

The DIPOLE keyword also allows localized analysis of electric polarizability, hyperpolarizability, and other dielectric response properties, as sketched in Sidebar 6.2. However, further discussion of such higher-order electrical properties is beyond the scope of present treatment. 

In this section we turn our attention on the electric dipole moment, polarizability, and hyperpolarizability of this important species. We lean heavily for molecular data and insights on our recent paper on the electric properties of HXel [121]. 

In previous work [122] we presented an extended computational study of the interaction-induced electric properties of the water dimer (H20)2- Our findings strongly suggest that the interaction-induced mean dipole polarizability and hyperpolarizability are nearly additive, as... 

The perturbation V = H-H appropriate to the particular property is identified. For dipole moments ( i), polarizabilities (a), and hyperpolarizabilities (P), V is the interaction of the nuclei and electrons with the external electric field... 

We have shown in this paper the relationships between the fundamental electrical parameters, such as the dipole moment, polarizability and hyperpolarizability, and the conformations of flexible polymers which are manifested in a number of their electrooptic and dielectric properties. These include the Kerr effect, dielectric polarization and saturation, electric field induced light scattering and second harmonic generation. Our experimental and theoretical studies of the Kerr effect show that it is very useful for the characterization of polymer microstructure. Our theoretical studies of the NLDE, EFLS and EFSHG also show that these effects are potentially useful, but there are very few experimental results reported in the literature with which to test the calculations. More experimental studies are needed to further our understanding of the nonlinear electrooptic and dielectric properties of flexible polymers. 

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