In the upper panels shown are the dipole moments as a function of the time and the field amplitude for an excitation with “long” [, (a1)] and “short” [, (b1)] pulses. The lower panels [(a2) and (b2)] show the corresponding populations in various electronic states once the pulse is off. The TD-CISD method was employed with the aug-cc-pVDZ basis set and the laser frequency is chosen resonant with the transition.
Shown are the Kennlinien, over , due to stimulation of with pulses with different carrier frequencies (0.10, 0.20, 0.30, 0.40, and 0.44 , steeper lines correspond to larger frequencies). The TD-CISD/aug-cc-pVQZ calculations are done with and .
Shown are the dynamic polarizabilities of obtained from TD-CIS, TD-CIS(D), and TD-CISD calculations with the aug-cc-pVQZ basis set. The -shaped laser pulse [Eq. (13)] has a maximum amplitude and a width . Shown in the inset are the dynamic polarizabilities in comparison to variational calculations using different representations for the wave functions, as cited in Ref. 52: , , , and .
Demonstrated is the harmonic generation for the different TD-CI methods. The frequency-dependent dipole moment squared is plotted on a logarithmic scale. The fundamental peak and the third and fifth harmonics are shown (nonlogarithmic and magnified) as insets. The TD-CIS, TD-CIS(D), and TD-CISD signals are calculated with the aug-cc-pVDZ basis set. The incident laser has a frequency of , a maximum field amplitude of , and a width .
Shown is the frequency-dependent dipole moment squared, , for the three TD-CI methods on a logarithmic scale. The calculations are done with the aug-cc-pVDZ basis set and the laser parameters are chosen to be , , .
Shown are the areas under the harmonic signals as a function of the maximum field amplitude calculated with the TD-CISD method. Solid line, area of the fundamental peak (1HG); dashed line, area of the second harmonic (SHG) peak (amplified by a factor of 1000); dotted line, area of the third harmonic (THG) peak (amplified by a factor of 50 000). The laser parameters are as follows: polarized, shaped, , and . Shown in the subfigures are the peak areas as a function of , , and , respectively.
Shown are the components of the transition dipole moments of together with the corresponding excitation energies calculated by the CISD method with the different basis sets ( and ). Independent calculations of the excitation energies with the ACES2 program give, for the basis sets, perfect agreement for , T, and Q, while for a small discrepancy to our calculation (of about ) exists, for reasons which are not clear (Ref. 64). All values are given in atomic units ( or ).
Listed are the quasistatic diagonal polarizability components of in comparison with experimental and other theoretical values. All values given are in .
Listed are the calculated diagonal polarizability elements in comparison to experimental data. All TD-CI calculations are done with the aug-cc-pVDZ basis set. All values are determined at the same frequency of and given in . ( could not be determined more accurately.)
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