Hyperpolarizabilities time-dependent coupled-perturbed

The experimental measures of these molecular electric properties involve oscillating fields. Thus, the frequency-dependence effects should be considered when comparing the experimental results . Currently, there are fewer calculations of the frequency-dependent polarizabilities and hyperpolarizabilities than those of the static properties. Recent advances have enabled one to study the frequency dispersion effects of polyatomic molecules by ab initio methods In particular, the frequency-dependent polarizability a and hyperpolarizability y of short polyenes have been computed by using the time-dependent coupled perturbed Hartree-Fock method. The results obtained show that the dispersion of a increases with the increase in the optical frequency. At a given frequency, a and its relative dispersion increase with the chain length. Also, like a, the hyperpolarizability y values increase with the chain length. While the electronic static polarizability is smaller than the dynamic one, the vibrational contribution is smaller at optical frequencies. ... 

Let us return to the problem of solving the response of the quantum mechanical system to an external electric field. The zeroth-order wave function of the quantum mechanical system is obtained by use of any of the standard approximate methods in quantum chemistry and the coupling to the field is described by the electtic dipole operator. There exist a number of ways to determine the response functions, some of which differ in formulation only, whereas others will be inherently different. We will give a short review of the characteristics of tire most common formulations used for the calculation of molecular polarizabilities and hyperpolarizabilities. The survey begins with the assumption that the external perturbing fields arc non-oscillatory, in which case we may determine molecular properties at zero frequencies, and then continues with the general situation of time-dependent fields and dynamic properties. 

In the following the polarizability and the first and second hyperpolarizabilities for urea calculated at the SCF level in vacuo and in water are reported. Both static and frequency dependent nonlinear properties have been calculated, with the Coupled Perturbed Hartree-Fock (CPHF) and Time Dependent-CPHF procedures that have been described above. The solvent model is the Polarizable Continuum Model (PCM) whereas vibrational averaging of the optical properties along the C-0 stretching coordinate has been obtained by the DiNa package both in vacuo and in solution. 

Using Eqs. (4.61) and (4.63), matrix U is calculated to give the response properties in terms of the uniform electric field dipole moments, polarizabilities, hyperpolarizabilities, and so forth. Equation (4.61) is called the coupled perturbed Kohn-Sham equation. Other response properties are calculated by solving Eq. (4.61) after setting the first derivative of the Fock operator, F, in terms of each perturbation. Note, however, that this method has problems in actual calculations similarly to the time-dependent response Kohn-Sham method. For example, using most functionals, this method tends to overestimate the electric field response properties of long-chain polyenes. 

Table 16 Results for hyperpolarizabilities (in a.u.) for N2- TDHF and MBPT(2) are results from time-dependent Hartree-Fock and perturbation-theory calculations, respectively, whereas CCSD and CCSD(T) are coupled-cluster results. Exp. denotes experimental results, and LDA, GGA, and LB94 are results from time-dependent density-functional calculations with different density functionals. For a description of the quantities, see the text. The results are from ref. 95...

---