Hyperpolarizabilities calculations : strong

Our results indicate that dispersion coefficients obtained from fits of pointwise given frequency-dependent hyperpolarizabilities to low order polynomials can be strongly affected by the inclusion of high-order terms. A and B coefficients derived from a least square fit of experimental frequency-dependent hyperpolarizibility data to a quadratic function in ijf are therefore not strictly comparable to dispersion coefficients calculated by analytical differentiation or from fits to higher-order polynomials. Ab initio calculated dispersion curves should therefore be compared with the original frequency-dependent experimental data. 

Exact static optical susceptibilities are conveniently calculated as successive derivatives on an applied electric field of the gs polarization, defined, in linear aggregates, as the dipole moment per unit length. The linear polarizability (a), the first and second hyperpolarizabilities (jS and y, respectively) obtained for 16-sites clusters are shown as full lines in Fig. 5. Left, middle and right panels refer to A, B and C clusters, respectively, for the parameters that, in Fig. 4 drive the system through the neutral-zwitterionic interface. Susceptibilities show a strong and non-trivial dependence on the intermolecular distance, and, to understand the physical origin of this complex and interesting behavior we shall discuss several approximated results. 

In the above discussion, we have only considered the effects due to the CTE-CTE repulsion, which contribute to the resonant nonlinear absorption (as well as to other resonant nonlinearities) by the CTE themselves. Here, however, we want to mention a more general mechanism by which the nonlinear optical properties of media containing CTEs in the excited state can be enhanced. This influence is due to the strong static electric field arising in the vicinity of an excited CTE, If, for example, the CTE (or CT complex) static electric dipole moment is 20 Debye, at a distance of 0.5 nm it creates a field Ecte of order 107 V/cm. Such strong electric fields have to be taken into account in the calculation of the nonlinear susceptibilities, because they change the hyperpolarizabilities a, / , 7, etc. of all molecules close to the CTE. For instance, in the presence of these CTE induced static fields, the microscopic molecular hyperpolarizabilities are modified as follows... 

Note that to generate a large SHG, the material has to have laige values of the hyperpolarizabilities p and y. The THG needs a large y. In both cases, a strong laser electric field is a must. The SHG and THG therefore require support from the theoretical side we are looking for high hyperpolarizability materials and quantum mechanical calculations before an expensive... 

Yang and Su have employed the FF/B3LYP/6-31G(d) method to calculate the first hyperpolarizability of donor/acceptor derivatives of 9,10-dihydroanthracene, i.e. compounds with two D-Jt-A units that are not electronically coupled but mostly interact through electrostatics (Fig. 5). They show that these systems display remarkably large p values and that these are enhanced when using strong donor groups in combination with a CH=CH linker, rather than a N=N linker. 

The electronic and (double harmonic) vibrational contributions to the first hyperpolarizability of three merocyanine dyes have been calculated at different levels of approximation, showing a strong impact of electron correlation on the electronic counterpart . So, the dominant longitudinal p ... 

FF/DFT and SOS/TDDFT calculations have been carried out to investigate the static first hyperpolarizability of two-dimensional A-ti-D-ji-A carbazole-core chromophores. For both approaches, the B3LYP exchange-correlation functional has been employed in combination with the 6-3IG basis set. In particular, they have concluded that carbazole heterocycles containing five heteroatoms are strong auxiliary electron donors and lead to larger first... 

As an interpretating support to experimental characterizations, the first hyperpolarizabilities of metal (Zn and Cu) complexes of mcio-tetraphenyl-porphyrin have been calculated as a function of the oxidation state.In particular, upon switching to the cations and dications, the metallo-porphyrins loose their centrosymmetry and the second-order NLO responses are strongly enhanced. 

The interaction-induced (hyper)polarizability of two Kr atoms was calculated with a [8s7p6d5f] basis set at the SCF and MP2 levels of theory. At R/ao = 4, the MP2 values of the interaction (hyper)polarizability invariants are (SCF values in parentheses) a = 3.6127 (2.4113) and Aa = 24.8369 (21.8086) e ao Eii The interaction mean second hyperpolarizability at the same distance is y = 17837.0 (11719.3) e" ao" Eii . The electron correlation effects are important for all properties at short separations. The R-depen-dence of the polarizability invariants and the Cartesian components and the mean of the second hyperpolarizability are shown in Figs. 5 and 6, respectively. In both cases, the strong anisotropic character of the (hyper)polar-izability for short separations is very much obvious. 

MP4 calculations with the d-aug-cc-pVTZ basis set. Very strong correlation effects were obtained for the interaction-induced hyperpolarizability. For the HCN---HCN complex the mean jSjnt at the SCF and MP4 levels of theory is 16.37 and 23.14 e ao Eh , respectively. The mean second hyperpolarizability is yint = 7.3 (SCF) and 144.4 (MP4) e" ao" Eii. ... 

---