Some opinions on MD-based vibrational spectroscopy of gas phase molecules and their assembly: An overview of what has been achieved and where to go

Vibrational spectroscopy by means of first‐principles molecular dynamics simulations

“…While in principle an exact solution of Equation ( 1) would be desirable, in practice further approximations have to be employed to make the solution tractable. Among the possible approximations for the time independent Schrödinger equation are tightbinding, [41][42][43][44] the Hartree-Fock method, 45 DFT, 46,47 Moller-Plesset perturbation theory, [48][49][50] approximations to relativistic quantum mechanics, 51,52 coupled cluster, [53][54][55] configuration interaction, 56 as well as combinations of methods either by embedding (e.g., hybrid quantum mechanics/molecular mechanics QM/MM 57 ) or by applying additional electronic structure methods to trajectories obtained from DFT-MD. MD calculations are carried out at finite temperatures.…”

Algorithmic graph theory for post-processing molecular dynamics trajectories

“…[4,12,13] continued on the same routes for IR and Raman spectroscopies with various types of observables being learned. In the context of vibrational spectroscopy based on MD simulations, we developed a theoretical route based on atomic polar tensors (APTs) and Raman tensors [14][15][16][17], in which the APT and Raman tensors can be machine learned from high level quantum calculations. Vibrational spectra can also be directly machine learned in order to predict very fastly a spectrum associated to a given molecular system.…”

Unsupervised Machine Learning Neural Gas Algorithm for Accurate Evaluations of the Hessian Matrix in Molecular Dynamics

“…Specifically, Hessians are employed for higher than second-order MD time-integrators, − for geometry optimization calculations, , for instantaneous normal mode analysis, , for accurate force field constructions, for semiclassical dynamics, and other applications, such as reaction rate constants with the instanton method. , While integration of Hamilton’s equations of motion is doable for any number of degrees of freedom, assuming that the interacting potential is readily available as well as that there is suitable computational power, computing properties that depend on the second or even higher coordinate derivatives of the potential is a challenging task since these calculations usually scale polynomially with the system size. The task may become prohibitive in ab initio MD where the potential and its derivatives are evaluated on-the-fly, that is, by solving the electronic structure problem and using the Hellman–Feynman theorem, or by the finite difference formula using the forces or the potential. To address this issue, a number of approximate methods have been introduced. − Usually, these are of the type of updating schemes, where the Hessian is approximated in a step-wise fashion using the latest information available .…”

“…10,11 While integration of Hamilton's equations of motion is doable for any number of degrees of freedom, assuming that the interacting potential is readily available as well as that there is suitable computational power, computing properties that depend on the second or even higher coordinate derivatives of the potential is a challenging task since these calculations usually scale polynomially with the system size. The task may become prohibitive in ab initio MD 12 where the potential and its derivatives are evaluated on-the-fly, that is, by solving the electronic structure problem and using the Hellman−Feynman theorem, or by the finite difference formula using the forces or the potential. To address this issue, a number of approximate methods have been introduced.…”