Semiclassical instanton formulation of Marcus-Levich-Jortner theory

Area of Science:

• * Theoretical Chemistry
• * Quantum Dynamics
• * Physical Chemistry

Background:

• * Marcus-Levich-Jortner (MLJ) theory is a standard for calculating electron-transfer rates, incorporating nuclear quantum effects.
• * MLJ theory models subsystems quantum-mechanically and the solvent classically, using Fermi's golden rule and Marcus theory.
• * Existing methods can introduce significant errors and may not satisfy detailed balance.

Purpose of the Study:

• * To present a "reduced" semiclassical instanton theory as an advancement over MLJ theory.
• * To develop a multiscale method for simulating quantum tunneling in molecular systems with harmonic baths.
• * To provide a more accurate and insightful approach for electron-transfer rate calculations.

Main Methods:

• * Developed a reduced semiclassical instanton theory based on path integrals.
• * Applied a multiscale approach to model quantum tunneling in molecular subsystems.
• * Utilized a harmonic bath model for solvent interactions.

Main Results:

• * Instanton theory demonstrates significantly higher accuracy than cumulant expansion or semiclassical Franck-Condon sum methods.
• * Instanton theory avoids orders-of-magnitude errors and respects detailed balance, unlike some alternative methods.
• * The method does not require solving the Schrödinger equation or global potential knowledge, enabling application to complex systems.

Conclusions:

• * Reduced semiclassical instanton theory provides accurate electron-transfer rates and detailed mechanistic insights.
• * It effectively models quantum tunneling in complex, anharmonic multidimensional subsystems.
• * The path integral foundation offers advantages over wavefunction-based methods like MLJ theory.