"Vibrational spectra from atomic fluctuations in dynamics simulations: I. Theory, limitations, and a sample application." Matthias Schmitz and Paul Tavan
J. Chem. Phys. 121, 1223312246
Abstract: Hybrid molecular dynamics (MD) simulations, which combine density functional theory (DFT) descriptions of a molecule with a molecular mechanics (MM) modeling of its solvent environment, have opened the way towards accurate computations of solvation effects in the vibrational spectra of molecules. Recently, Wheeler et al. [ChemPhysChem 4, 382, (2002)] have suggested to compute these spectra from DFT/MMMD trajectories by diagonalizing the covariance matrix of atomic fluctuations. This socalled principal mode analysis (PMA) allegedly can replace the wellestablished approaches, which are based on Fourier transform methods or on conventional normal mode analyses. By scrutinizing and revising the PMA approach we identify five conditions, which must be guaranteed if PMA is supposed to render exact vibrational frequencies. Besides specific choices of (a) coordinates and (b) coordinate systems, these conditions cover (c) a harmonic
intramolecular potential, (d) a complete thermal equilibrium within the molecule, and (e) a
molecular Hamiltonian independent of time. However, the PMA conditions [(c)–(d)] and [(c)–(e)] are generally violated in gas phase DFTMD and liquid phase DFT/MMMD trajectories,
respectively. Based on a series of simple analytical model calculations and on the analysis of MD trajectories calculated for the formaldehyde molecule in the gas phase (DFT) and in liquid water (DFT/MM) we show that in both phases the violation of condition (d) can cause huge errors in PMA frequency computations, whereas the inevitable violations of conditions (c) and (e), the latter being generic to the liquid phase, imply systematic and sizable underestimates of the vibrational frequencies by PMA. We demonstrate that the huge errors, which are caused by an incomplete thermal equilibrium violating (d), can be avoided if one introduces modespecific temperatures T_{j} and calculates the frequencies from a "generalized virial" (GV) expression instead from PMA. Concerning ways to additionally remove the remaining errors, which GV still shares with PMA, we refer to Paper II of this work [M. Schmitz and P. Tavan, J. Chem. Phys. 121, 12247 (2004)].
BMO authors (in alphabetic order): Matthias Schmitz Paul Tavan
