Nonlinear ground-state dipole moment

Our calculations predict only minor differences between the ground state dipole moments for molecules containing nitro electron acceptors versus those possessing methylsulfonyl. In contrast, the hyperpolarizabilities behave much differently, in that calculated J3Z for the aminonitrostilbenes is about twice that of the aminosulfonylstilbenes and the nitroanilines are more than 5 times more nonlinear than the sulfonylanilines. The hyperpolarizabilities appear to be very sensitive to the details of the electron donors-acceptor interaction and hence accentuate the differences in the a values for nitro and methylsulfonyl. 

Another method is to use the molecules with relatively small ground state dipole moment (2). Weak dipole-dipole interaction can lead to non-centrosymmetric crystallization. However, it may decrease polarizability of molecules and result in low optical nonlinearities of molecular crystals. 

For an isotropic, poled polymer film of essentially one-dimensional NLO molecules, the orientational average is expressed in terms of the average angle between the ground-state dipole moments of the chromophores and the direction in the film they would be pointing if perfectly aligned (83). For a polymer film in which the nonlinear component or moiety is rotationally symmetric about the film normal (z-axis), the only two nonzero susceptibility components can be... 

It follows from the preceding results that the electro-optical properties of molecules in degenerate electronic states should have unusual temperature dependence, which is absent in the case of nondegenerate states. Even for nondipolar degenerate electronic states (e.g., for states in which the reduced matrix elements of the dipole moment are zero) for certain relationships between the vibronic constant and the temperature, there may be a quadratic dependence of the Kerr effect on p, similar to that observed in the case of molecules that are simultaneously anisotropic polarizable and possess a proper dipole moment. The nonlinear dependence on p under consideration is due exclusively to the vibronic interaction that redetermines the vibronic spectrum and leads to different polarizability in different vibronic states. This dependence on p has to be distinguished from that which arises due to the nonzero value of the dipole moment in the initial ground electronic state (e.g., as in the case of the E term in molecules with D3h symmetry). The two sources of the... 

Density matrices of the state functions provide a compact graphical representation of important microscopic features for second order nonlinear optical processes. The transition moment y is expressed in terms of the transition density matrix p jji(r,r ) by nn " /j, ptr Pjj t(r,r )dr and the dipole moment difference Ay by the difference density function p - p between the excited and ground state functions = -e / r( p -p )dr where p is the first order reduced density matrix. 

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