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Complex autocorrelation function and energy spectrum by classical trajectory calculations.

Petra R Zdánská¹, Nimrod Moiseyev

¹Institute of Organic Chemistry and Biochemistry, Academy of Sciences of the Czech Republic, Flemingovo 2, 166 10 Prague 6, Czech Republic. petra.zdanska@uochb.cas.cz

The Journal of Chemical Physics

|September 28, 2004

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A new quasiclassical method accurately calculates complex autocorrelation functions for coupled harmonic oscillators. This approach bridges classical and quantum mechanics for understanding molecular dynamics and energy spectra.

Area of Science:

Quantum Chemistry
Chemical Physics
Computational Chemistry

Background:

Classical trajectory calculations are essential for understanding molecular dynamics.
Evaluating complex autocorrelation functions is computationally challenging.
Accurate quantum-classical comparisons require robust theoretical methods.

Purpose of the Study:

To propose and validate a quasiclassical method for computing complex autocorrelation functions.
To compare classical and quantum autocorrelation functions for excited harmonic oscillators.
To assess the accuracy of classical methods in regimes of regular and chaotic motion.

Main Methods:

Development of a quasiclassical method for autocorrelation function evaluation.
Application to two nonlinearly coupled harmonic oscillators.

Related Experiment Videos

Utilizing filter diagonalization for energy level determination.

Main Results:

Good agreement between classical and quantum autocorrelation functions at short (Ehrenfest) times.
Nearly coinciding classical and quantum energy spectra obtained via Fourier transforms.
Accurate determination of energy levels using approximate short-time autocorrelation functions.

Conclusions:

The proposed quasiclassical method effectively computes complex autocorrelation functions.
The method demonstrates strong agreement with quantum mechanics for highly excited oscillators.
This approach provides a reliable tool for studying molecular dynamics and spectra.