By H.H. Greenwood
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Extra info for Computing Methods in Quantum Organic Chemistry
155) are solved and the initial width ImA(t0 ) and momentum P0 parameters are determined variationally. 3. The corrected classical path equations . These corrections are in the socalled SCF direction, that is, they correct the shape of the function in R but not the separability approximation. Using the G-H basis functions, we have also the possibility of introducing 4. The Hermite corrected classical path equations. This correction is in the “MCSCF direction” and is, therefore, the most general type of correction possible.
2 0 x/AA Fig. 6b. 2 0 x/AA Fig. 6c. 8 1 40 The Quantum Classical Theory that it was easier to solve—the opposite could be said about the “quantum dressed classical mechanics” approach which later will be derived from the TDGH formulation. 5 Mixing of Gauss-Hermite and ordinary basis sets It is possible to use traditional time-independent basis sets for some degrees of freedom while using the G-H basis for others. For simplicity, we consider just two degrees of freedom: r the quantum and R the “classical” degree of freedom.
187) m where φm (r, t0 ) = √ 1 2m m! 188) and ξ(r, t0 ) = 2ImAr (t0 )/ (r − r(t0 )). 2 shows the initial expansion coeﬃcients for a Morse-oscillator in its ground and ﬁrst excited vibrational state. 189) where H0 (r) is deﬁned through eq. 185). 2: Expansion coeﬃcients c2m for Morse-oscillator states (n = 0, 1) of hydrogen. /τ, p(t0 ) = 0, ReA(t0 ) = 0 where τ = 10−14 sec. 7416 Å. 00002 where V (t) = V (r(t)). 195) k Thus, the coeﬃcients cn (t) are coupled through the anharmonic terms of the potential.