Jove
Visualize
Contact Us

Related Experiment Video

Updated: Dec 1, 2025

Millifluidics for Chemical Synthesis and Time-resolved Mechanistic Studies
12:55

Millifluidics for Chemical Synthesis and Time-resolved Mechanistic Studies

Published on: November 27, 2013

11.5K

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
Summary
This summary is machine-generated.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Semiclassical descriptions of rotational transitions in natural and shifted angles: Analysis of unexpected results.

The Journal of chemical physics·2021
Same author

Erratum: "Semiclassical initial value representation: From Møller to Miller" [J. Chem. Phys. 153, 174102 (2020)].

The Journal of chemical physics·2021
Same author

Statistical properties of quantum probability fluctuations in complex-forming chemical reactions.

The Journal of chemical physics·2020
Same author

Semiclassical initial value theory of rotationally inelastic scattering: Some remarks on the phase index in the interaction picture.

The Journal of chemical physics·2018
Same author

The dynamics of the C(<sup>1</sup>D)+H<sub>2</sub>/D<sub>2</sub>/HD reactions at low temperature.

The Journal of chemical physics·2018
Same journal

The influence of chirality on the macroscopic behavior of multiferroic smectic phases.

The Journal of chemical physics·2026
Same journal

Polaron transformed canonically consistent quantum master equation.

The Journal of chemical physics·2026
Same journal

The x-ray absorption spectrum of the propargyl radical C3H3●.

The Journal of chemical physics·2026
Same journal

Transient hydroperoxyalkyl intermediates (•QOOH) in isopentane oxidation. I. Conformer- and isomer-resolved infrared spectra.

The Journal of chemical physics·2026
Same journal

Transient hydroperoxyalkyl intermediates (•QOOH) in isopentane oxidation. II. Isomer-resolved unimolecular dynamics.

The Journal of chemical physics·2026
Same journal

Quantum state-to-state dynamics studies of the C(3P) + OH(X2Π) → CO(a3Π) + H(2S) reaction based on a new HCO(12A″) potential energy surface.

The Journal of chemical physics·2026
See all related articles
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

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.

More Related Videos

Design and Use of Multiplexed Chemostat Arrays
19:40

Design and Use of Multiplexed Chemostat Arrays

Published on: February 23, 2013

23.8K
Isolation of Murine Valve Endothelial Cells
09:34

Isolation of Murine Valve Endothelial Cells

Published on: August 21, 2014

14.5K

Related Experiment Videos

Last Updated: Dec 1, 2025

Millifluidics for Chemical Synthesis and Time-resolved Mechanistic Studies
12:55

Millifluidics for Chemical Synthesis and Time-resolved Mechanistic Studies

Published on: November 27, 2013

11.5K
Design and Use of Multiplexed Chemostat Arrays
19:40

Design and Use of Multiplexed Chemostat Arrays

Published on: February 23, 2013

23.8K
Isolation of Murine Valve Endothelial Cells
09:34

Isolation of Murine Valve Endothelial Cells

Published on: August 21, 2014

14.5K
  • 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.