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Two‐photon transition moments as determined from the quadratic response function
Author(s) -
Parkinson William A.,
Sengeløv Peter W.,
Oddershede Jens
Publication year - 1990
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560382449
Subject(s) - dipole , transition dipole moment , excitation , moment (physics) , photon , quadratic equation , physics , atomic physics , chemistry , quantum mechanics , mathematical analysis , mathematics , geometry
The matrix element for two‐photon absorption is calculated as a residue of the general quadratic response function for a system subjected to an external time‐dependent field. The matrix element is correct through first‐order in electron correlation, and includes contributions in addition to those considered in previous calculations which were based on a truncated form of the Random Phase Approximation ( RPA ). Equations of motion are derived from the spectral representation of quadratic response, leading to equivalent expressions for two‐photon absorption in the dipole length, mixed, and dipole velocity formulations. Because the transition moments evaluated in the three formalisms must be equivalent in a complete basis, the calculated results provide a measure of the adequacy of the basis set representation. As a test case, the X 1 σ g + ( v = 0) → ( E, F ) 1 Σ g + ( v = 6) two‐photon process of H 2 is considered. It is first demonstrated that agreement between length and velocity forms of the two‐photon transition moment is obtained only through the consideration of all contributing terms. The vibrationally‐averaged transition moment is decomposed into individual state contributions. It is found that the B 1 Σ u + and C 1 Π u ‐coupled matrix elements are comparable at the RPA level to values obtained at the near‐full CI limit, and, although there is some disparity as to the relative weight of the remaining states, the total transition moment in the two formalisms are in good agreement. Using the transition moment obtained at the excitation frequency 1/2ω f , the integrated two‐photon excitation cross‐section is calculated. The value is in excellent agreement with the CI result and lies near the experimental error bars of the absorption cross‐section determined from a single‐beam measurement.