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Semiclassical initial value representation: From Møller to Miller.

Laurent Bonnet1

  • 1CNRS, ISM, UMR 5255, F-33400 Talence, France.

The Journal of Chemical Physics
|November 10, 2020
PubMed
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Møller operators were implicitly present in Miller's initial value representation (IVR) for semiclassical (SC) scattering calculations. Their removal significantly reduces the numerical efficiency of these quantum scattering methods.

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.

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  • 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.