Anharmonic electron-phonon coupling in condensed media: 1. Formalism

Area of Science:

• * Theoretical Chemistry
• * Molecular Spectroscopy
• * Quantum Mechanics

Background:

• * Accurate calculation of molecular line shapes is essential for interpreting spectroscopic data.
• * Existing models often simplify potential energy surfaces, limiting their applicability to anharmonic systems.
• * The Franck-Condon factor (FCF) is key to understanding transition probabilities.

Purpose of the Study:

• * To develop and present three distinct schemes for calculating anharmonic line shape functions using eigenstate representation.
• * To investigate molecular transitions between harmonic and anharmonic (Morse potential) electronic states.
• * To derive and analyze Franck-Condon factors (FCFs) for various anharmonic scenarios.

Main Methods:

• * Derivation of linear dipole-moment time correlation function (DMTCF) and homogeneous absorption line shape functions.
• * Calculation of FCFs for transitions involving harmonic, anharmonic (Morse), and displaced/distorted anharmonic potentials.
• * Utilizing eigenstate representation and exact closed-form solutions involving Appell's hypergeometric function.

Main Results:

• * Reported FCFs for zero-phonon lines across three different anharmonic calculation schemes.
• * Demonstrated mathematical complexities in calculating overlaps between Morse and harmonic oscillator eigenfunctions.
• * Presented model calculations illustrating the application and challenges of the developed methods.

Conclusions:

• * The study provides a foundational framework for calculating anharmonic line shape functions.
• * The derived methods offer enhanced accuracy for spectroscopic analysis of complex molecular systems.
• * Further model calculations are needed to fully explore the implications of functional disparities in eigenfunction overlaps.