Real-World Predictions from Ab Initio Molecular Dynamics Simulations - Multiscale Molecular Methods in Applied Chemistry - page 111

GGA Generalized gradient approximation (GGA) functional, a functional
that depends on density and its gradient
HF Hartree-Fock, static quantum chemical method
IR Infrared red
loc Local functional depending only on r
MD Molecular dynamics, simulation method
MEP Minimum energy path
MFEP Minimum free energy path
MLWC Maximally localized Wannier centers
MLWO Maximally localized Wannier orbitals
MTD Metadynamics, method to calculate rare events
NAO Numerically tabulated atom-centered orbitals
NEMD Non-equilibrium molecular dynamics
nl Non-local, functional depending not only on r but also on r 0
NPT NPT ensemble: isothermal-isobaric ensemble; constant particle (N),
pressure (P), and temperature (T) simulation
PBC Periodic boundary conditions
QM/MM Hybrid quantum-mechanical/molecular-mechanical calculations
RPA Random phase approximation

SCF Self consistent field

vdW van der Waals, dispersion forces; usually not well-described in DFT

1 Introduction

Ab initio molecular dynamics (AIMD) simulations combine classical molecular
dynamics simulations with electronic structure calculations on the fly. The theoret-
ical foundations for ab initio molecular dynamics were laid with the work of
Ehrenfest [ 1 ] and Dirac [ 2 ] at the beginning of the twentieth century. Dirac
developed the theory of time-dependent self consistent field (SCF) equations for
nuclear and electronic motion and Ehrenfest derived mixed classical-quantum
mechanical (time-dependent electronic structure) equations [ 3 ]. In 1985 it was the
seminal article of Roberto Car and Michele Parrinello [ 4 ] which initiated the use
and further development of ab initio molecular dynamics simulations. The authors
intended to derive a new method which is able to “(1) compute ground-state
electronic properties of large and/or disordered systems using state-of-the-art
electronic structure calculations; (2) perform AIMD simulations where the only
assumptions are the validity of classical mechanics to describe ionic motion and the
Born-Oppenheimer (BO) approximation to separate nuclear and electronic
coordinates” [ 4 ]. For this purpose Car and Parrinello made use of the extended
Lagrangian technique, previously invented to simulate systems under constant
pressure [ 5 , 6 ]. This ingenious method solved the problem of the expensive self-
consistent solution to the electronic structure problem along the molecular dynam-
ics trajectory. By showing a feasible route to extensive ab initio molecular dynamics