Charge and Energy Transfer Dynamics in Molecular Systems

Abstract

Preface to the Third Edition XIII Preface to the Second Edition XV Preface to the First Edition XVII 1 Introduction 1 2 Electronic and Vibrational Molecular States 9 2.1 Introduction 9 2.2 Molecular Schrödinger Equation 11 2.3 Born-Oppenheimer Separation 13 2.3.1 Born-Oppenheimer Approximation 15 2.3.2 Some Estimates 17 2.4 Electronic Structure Methods 18 2.4.1 The Hartree-Fock Equations 21 2.4.2 Density Functional Theory 23 2.5 Condensed Phase Approaches 24 2.5,1 Dielectric Continuum Model 25 2.5.2 Explicit Quantum-Classical Solvent Model 31 2.6

Two-dimensional electronic spectra of the photosynthetic apparatus of green sulfur bacteria

“…The energy transport in the photosynthetic system is modeled using the Frenkel exciton description35, including the external electromagnetic field from the laser pulses in the impulsive limit25. Besides the seven single exciton states of the FMO system and the antenna chlorosome, additionally 28 two exciton states are explicitly included in the Hamiltonian and in the dipole matrix2636.…”

Open Quantum Dynamics Calculations with the Hierarchy Equations of Motion on Parallel Computers

“…Although initial correlations between system and environment would not be present in the case of instantaneous photo-excitation, 61 they can be included when modeling other processes using the HEOM. 59,65 Once the thermal average is performed, the influence of the environment enters only through the bath correlation functions given by, 4 $$C_{ab}false(tfalse)={\langle u_{a}false(tfalse)u_{b}false(0false)\rangle }_B=\frac{1}{\pi }{\displaystyle {\int }_{-\infty }^{\infty }d\omega J_{ab}(\omega )\frac{e^{-i\omega t}}{1-e^{-\beta \overline{h}\omega }},}$$ where the spectral density J ab (ω) is given by $$J_{ab}false(\omega false)=\frac{\pi }{2}{\displaystyle \sum _{\xi }\frac{c_{a\xi }{c}_{b\xi }}{m_{\xi }{\omega }_{\xi }}\delta false(\omega -{\omega }_{\xi }false)}.$$ …”

“…(6) and Eq. (7) can be expressed as a so-called Drude spectral density, 4 given by $$J_{a}false(\omega false)=2{\lambda }_a\frac{\omega {\gamma }_a}{false({\omega }^2+{\gamma }_a^{2}false)},$$ where λ a = ∫( J a (ω)/πω) d ω is the bath reorganization energy that determines the system-bath interaction strength, and 1/γ a is the bath response time. The Drude spectral density describes over-damped harmonic oscillator modes ξ.…”

Quantum Dissipative Dynamics of Electron Transfer Reaction System: Nonperturbative Hierarchy Equations Approach

“…5,6) This potential energy description is similar to that used in nonlinear ultrafast spectroscopy. 7,8) By adopting this description, one may study ET processes by nonlinear optical measurements. 9,10) A variety of approaches that have been developed to study not only ET processes but also nonlinear optical responses are used to investigate ET dynamics.…”

“…9,10) A variety of approaches that have been developed to study not only ET processes but also nonlinear optical responses are used to investigate ET dynamics. [5][6][7][8][9][10][11][12][13][14] Unlike most of the above-mentioned approaches based on the perturbative treatment of nonadiabatic transitions, the reduced equation of motion approach that describes the dynamics of density matrix of an ET system coupled to the environment can handle any strength of nonadiabatic coupling. This approach is successful in a classical case characterized by free-energy surfaces, 5,6,15) but it has to employ crucial assumptions such as rotating wave approximation and perturbative system-bath interaction in a quantum case.…”