Dispersion formulas for real- and imaginary-frequency-dependent hyperpolarizabilities

Abstract

The dynamic second hyperpolarizability for real frequencies, yll (-oa;ol,02,03) in the limit o; + 0 can be expressed as yl10 + A1lnwLZ, where oL2 = ma2 + oI2 + w2 + 03' and yl10 is the frequency-independent (static) quantity; the parallel subscript ((1) indicates that the polarization and electric fields all lie along the same axis. In this paper the coefficient Alln is evaluated exactly for the H atom and very accurately for He, He, and Li+. A similar analysis is carried out for yll(-io; io, 0,O) in the limit o + oo.Key words: nonlinear optics, hyperpolarizabilities, dispersion formulas.RCsumC : On peut exprimer la deuxikme hyperpolarisabilitC dynamique de frCquences rCelles, y I I ( -~; o1, w , 0 3 ) dans la limite w; -0, peut Etre exprimCe sous la forme yl10 + AIIooL2, dans laquelle o~' = ma2 + oI2 + w2 + o3' et ylln est la [Traduit par la rCdaction]

A coupled cluster response study of the electric dipole polarizability, first and second hyperpolarizabilities of HCl

“…The frequency dependence of the (hyper)polarizabilities over a range of frequencies well below the first pole can be obtained fairly accurately through a limited number of frequency dispersion coefficients. [18][19][20][21][22][23][24] Their analytic calculation has been implemented efficiently up to CCSD level. [22][23][24] Here the expansion is truncated after fourth order and a [1,1] Pade ´approximant approximation-which guarantees faster convergence and a larger range of applicability with respect to usual power expansions-is employed.…”