Automated calculation of anharmonic vibrational contributions to first hyperpolarizabilities: Quadratic response functions from vibrational configuration interaction wave functions

Mikkel Bo Hansen1, Ove Christiansen1, and Christof Hättig2
1 Center for Oxygen Microscopy and Imaging and Lundbeck Foundation Center for Theoretical Chemistry, Department of Chemistry, Århus University, DK-8000 Århus C, Denmark
2 Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, Universitätsstrasse 150, D-44801 Bochum, Germany

J. Chem. Phys. 131, 154101 (2009).
(Received 24 June 2009; accepted 21 September 2009; published online 15 October 2009)

Quadratic response functions are derived and implemented for a vibrational configuration interaction state. Combined electronic and vibrational quadratic response functions are derived using Born-Oppenheimer vibronic product wave functions. Computational tractable expressions are derived for determining the total quadratic response contribution as a sum of contributions involving both electronic and vibrational linear and quadratic response functions. In the general frequency-dependent case this includes a new and more troublesome type of electronic linear response function. Pilot calculations for the FH, H2O, CH2O, and pyrrole molecules demonstrate the importance of vibrational contributions for accurate comparison to experiment and that the vibrational contributions in some cases can be very large. The calculation of transition properties between vibrational states is combined with sum-over-states expressions for analysis purposes. On the basis of this some simple analysis methods are suggested. Also, a preliminary study of the effect of finite lifetimes on quadratic response functions is presented. (C) 2009 American Institute of Physics. [doi: 10.1063/1.3246349]

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