Molecular Dynamics Simulation

The contributions collected in this book move from the quantum-statistical description to the validity of classical modeling; they present some perspectives in the algorithmic and in the enhanced sampling approaches, tackling some longstanding challenges to simulation in the area of non-equilibrium, rare events, mesoscale and quantum-classical simulation. Initially, the book deals with the validity of molecular dynamics modeling, starting from the adiabatic hypothesis for the electronic ground state; the first contribution explores different descriptions of the potential energy surfaces one can use in a molecular dynamics simulation; the second analyzes in detail the Born-Oppenheimer schemes for ab initio MD within Kohn– Sham density functional theory, while the third one tackles the problem from the alternative perspective of a quantum Monte Carlo approach. The next contribution dwells on how to improve the statistical ensemble properties of time integrators for Langevin dynamics by including an acceptance–rejection scheme. The subject of free energy calculations by molecular dynamics is illustrated in the next two contributions, first with a presentation of alternative dynamical approaches for performing enhanced sampling by force biasing and temperature acceleration, then using non-equilibrium path sampling within the framework of Jarzynski identity and Crooks fluctuation theorem. The general ideas behind non-equilibrium molecular dynamics are the focus of the next two contributions, regarding calculation of dynamical responses and the application of Malliavin weight sampling to dynamical trajectories. Many of the same ideas are at the core of the study of rare, reactive, events by molecular dynamics as discussed in the next two contributions, more in general in the first and then with specific reference to the Markov state models approach. The last four invited contributions are dedicated to the problem of dealing with well separated space and time scales. First, the general philosophy of multiscale approaches and the related computational strategies within molecular dynamics are discussed in a concept paper, while the other three deals with specific non-adiabatic dynamical approaches for systems with a mixed quantum- classical description, based upon alternative approaches borrowing either from the Wigner transform representation or from the Bohmian formulation of quantum dynamics. The book is completed by the contributed papers to the molecular dynamics special issue.