Stability (learning theory)

Physics

Aerospace engineering

Path integral formulation

Energy (signal processing)

Work (physics)

Mathematics

Optics

Absorption (acoustics)

Statistics

Mathematical optimization

Machine learning

Engineering

Mathematical analysis

Set (abstract data type)

Integral equation

Programming language

Range (aeronautics)

Path (computing)

Computer science

Spectral line

Quantum mechanics

Applied mathematics

Quantum

The Journal of Chemical Physics

In this work, we present and implement the theory for calculating fluorescence rates and absorption and emission spectra from first principles, using the path integral approach. We discuss some approximations and modifications to the full set of equations that improve speed and numerical stability for the case when a large number of modes are considered. New methods to approximate the excited state potential energy surface are also discussed and it is shown that for most purposes, these can be used instead of a full geometry optimization to obtain the rates mentioned above. A few examples are presented and the overall performance of the method is discussed. It is shown that the rates and spectra computed in this way are well within the acceptable range of errors and can be used in future predictions, particularly for screening purposes, with the only limitation on size being that of the electronic structure calculation itself.

On the theoretical prediction of fluorescence rates from first principles using the path integral approach