The second-order nonlinear (or cubic) response function is derived from the Ehrenfest theorem with inclusion made of the finite lifetimes of the excited states, representing the extension of the derivation of the quadratic response function in the same framework [P. Norman et al., J. Chem. Phys. 123, 194103 (2005)]. The resulting damped response functions are physically sound and converging also in near-resonance and resonance regions of the spectrum. Being an accurate approximation for small complex frequencies (defined as the sum of an optical frequency and an imaginary damping parameter), the polynomial expansion of the complex cubic response function in terms of the said frequencies is presented and used to validate the program implementation. In terms of approximate state theory, the computationally tractable expressions of the damped cubic response function are derived and implemented at the levels of Hartree–Fock and Kohn–Sham density functional theory. Numerical examples are provided in terms of studies of the intensity-dependent refractive index of para-nitroaniline and the two-photon absorption cross section of neon. For the latter property, a numerical comparison is made against calculations of the square of two-photon matrix elements that are identified from a residue analysis of the resonance-divergent quadratic response function.
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Resonant-convergent second-order nonlinear response functions at the levels of Hartree–Fock and Kohn–Sham density functional theory
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14 October 2017
Research Article|
October 12 2017
Resonant-convergent second-order nonlinear response functions at the levels of Hartree–Fock and Kohn–Sham density functional theory

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JCP Editors' Choice 2017
Tobias Fahleson;
Tobias Fahleson
a)
Division of Theoretical Chemistry and Biology, School of Biotechnology, KTH Royal Institute of Technology
, SE-106 91 Stockholm, Sweden
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Patrick Norman
Patrick Norman
b)
Division of Theoretical Chemistry and Biology, School of Biotechnology, KTH Royal Institute of Technology
, SE-106 91 Stockholm, Sweden
Search for other works by this author on:
a)
Electronic mail: [email protected]
b)
Electronic mail: [email protected]
J. Chem. Phys. 147, 144109 (2017)
Article history
Received:
June 22 2017
Accepted:
August 31 2017
Connected Content
A companion article has been published:
Derivation of complex cubic response function to guide development of nonlinear optical molecular materials
Citation
Tobias Fahleson, Patrick Norman; Resonant-convergent second-order nonlinear response functions at the levels of Hartree–Fock and Kohn–Sham density functional theory. J. Chem. Phys. 14 October 2017; 147 (14): 144109. https://doi.org/10.1063/1.4991616
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