We consider a non-Hermitian Hamiltonian in order to effectively describe a two-level system coupled to a generic dissipative environment. The total Hamiltonian of the model is obtained by adding a general anti-Hermitian part, depending on four parameters, to the Hermitian Hamiltonian of a tunneling two-level system. The time evolution is formulated and derived in terms of the normalized density operator of the model, different types of decays are revealed and analyzed. In particular, the population difference and coherence are defined and calculated analytically. We have been able to mimic various physical situations with different properties, such as dephasing, vanishing population difference and purification.

The symplectic structure of quantum commutators is first unveiled and then exploited to introduce generalized non-Hamiltonian brackets in quantum mechanics. It is easily recognized that quantumclassical systems are described by a particular realization of such a bracket. In light of previous work, this introduces a unified approach to classical and quantum-classical non-Hamiltonian dynamics. In order to illustrate the use of non-Hamiltonian commutators, it is shown how to define thermodynamic constraints in quantum-classical systems. In particular, quantum-classical Nosé-Hoover equations of motion and the associated stationary density matrix are derived. The non-Hamiltonian commutators for both Nosé-Hoover chains and Nosé-Andersen (constant-pressure constant temperature) dynamics are also given. Perspectives of the formalism are discussed.

In 1980 Andersen introduced the use of "extended system" as a means of exploring by molecular dynamics simulation the phase space of a physical model according to a desired ensemble distribution different from the standard microcanonical function. Following his original work on constant pressure-constant enthalpy a large number of different equations of motion, not directly derivable from a Hamiltonian, have been proposed in recent years, the most notable of which is the so-called Nosé-Hoover formulation for "canonical" molecular dynamics simulation. Using a generalization of the symplectic form of the Hamilton equations of motion we show here that there is a unique general structure that underlies most, if not all the equations of motion for "extended systems." We establish a unifying formalism that allows one to identify and separately control the conserved quantity, usually known as the "total energy" of the system, and the phase-space compressibility. Moreover, we define a standard procedure to construct conservative non-Hamiltonian flows that sample the phase space according to a chosen distribution function [Tuckerman et al., Europhys. Lett. 45, 149 (1999)]. To illustrate the formalism we derive new equations of motion for two example cases. First we modify the equations of motion of the Nosé-Hoover thermostat applied to a one-dimensional harmonic oscillator, and we show how to overcome the ergodicity problem and obtain a canonical sampling of phase space without making recourse to additional degrees of freedom. Finally we recast an idea recently put forward by Marchi and Ballone [J. Chem. Phys. 110, 3697 (1999)] and derive a dynamical scheme for sampling phase space with arbitrary statistical biases, showing as an explicit application a demixing transition in a simple Lennard-Jones binary mixture.

We have investigated the structural and electronic properties of p-coumaric acid, the chromophore of the photoactive yellow protein (PYP), by means of first-principles molecular dynamics based on density functional theory (DFT). We have studied the chromophore both in the vacuum and in an extended model which includes the nearest residues in the binding pocket of PYP, as derived from crystallographic data. We have characterized the ground state of the isolated chromophore in its protonated and deprotonated forms and computed the energy barrier involved in the trans to cis isomerization process around the carbon−carbon double bond. A comparison of the optimized structures of the chromophore in the vacuum and in the extended protein model, both in the trans (ground state of PYP in the dark) and cis (first light-activated intermediate) configuration, shows how the protein environment affects the chromophore in the first step of the photocycle. Our model gives an energy storage of 25 kcal/mol associated with the trans-to-cis photoisomerization. Finally, we have elucidated the nature of the electronic excitation relevant for the photochemistry of PYP by means of time-dependent DFT calculations.

Methods for simulating the dynamics of composite systems, where part of the system is treated quantum mechanically and its environment is treated classically, are discussed. Such quantum-classical systems arise in many physical contexts where certain degrees of freedom have an essential quantum character while the other degrees of freedom to which they are coupled may be treated classically to a good approximation. The dynamics of these composite systems are governed by a quantum-classical Liouville equation for either the density matrix or the dynamical variables which are operators in the Hilbert space of the quantum subsystem and functions of the classical phase space variables of the classical environment. Solutions of the evolution equations may be formulated in terms of surface-hopping dynamics involving ensembles of trajectory segments interspersed with quantum transitions. The surface-hopping schemes incorporate quantum coherence and account for energy exchanges between the quantum and classical degrees of freedom. Various simulation algorithms are discussed and illustrated with calculations on simple spin-boson models but the methods described here are applicable to realistic many-body environments