Semiclassical initial value representation: From Møller to Miller.

Area of Science:

• Quantum mechanics
• Chemical physics
• Computational chemistry

Background:

• The initial value representation (IVR) was developed by Miller in 1970 to enhance semiclassical (SC) scattering calculations.
• Møller operators are crucial in quantum scattering theory but were absent in Miller's early IVR formulation.
• Garashchuk and Light later incorporated Møller operators into SC-IVR calculations in Cartesian coordinates, improving numerical efficiency.

Purpose of the Study:

• To demonstrate that Møller operators were implicitly part of Miller's original IVR formulation.
• To investigate the impact of Møller operators on the numerical efficiency of semiclassical scattering calculations.

Main Methods:

• Utilized a simplified model of light-induced rotational transitions.
• Analyzed Miller's original IVR formulation in action-angle coordinates.
• Compared calculations with and without the explicit inclusion of Møller operators.

Main Results:

• Møller operators were found to be intrinsically underlying Miller's pioneering IVR formulation.
• Excluding Møller operators from Miller's theory led to a substantial decrease in numerical efficiency.
• This confirms the findings of Garashchuk and Light regarding the efficiency boost provided by Møller operators.

Conclusions:

• Møller operators play a vital, albeit implicit, role in the efficiency of semiclassical calculations using the initial value representation.
• The explicit introduction of Møller operators, as shown by Garashchuk and Light, enhances computational performance.
• Understanding the underlying role of Møller operators deepens the comprehension of semiclassical scattering theory.