Academic literature on the topic 'Oppenheimer Molecular'

Beginning early in the 20th century spectroscopists attributed the infrared band spectra emitted by diatomic molecules to quantum vibration and rotation modes of the molecules. Because of these relatively simple motions, band spectra offered a convenient .rst phenomenon to which to apply formulations of the new quan-tum mechanics in 1926. In his .rst paper, completed in Cambridge in May 1926, Oppenheimer presented a derivation of the frequencies and relative intensities of the observed spectral lines on the basis of Paul Dirac's new quantum commutator algebra. At the same time Lucy Mensing published a similar derivation utiliz-ing matrix mechanics, as did Edwin Fues utilizing wave mechanics. Analyses of Oppenheimer's paper and of its historical and scienti.c contexts offer insights into the new quantum mechanics and its utilization and reception during this brief period of competing formalisms, and into the characteristic features of Oppenheimer's later style of research and publication.

In Born–Oppenheimer molecular dynamics (BOMD) simulations based on the density functional theory (DFT), the potential energy and the interatomic forces are calculated from an electronic ground state density that is determined by an iterative self-consistent field optimization procedure, which, in practice, never is fully converged. The calculated energies and forces are, therefore, only approximate, which may lead to an unphysical energy drift and instabilities. Here, we discuss an alternative shadow BOMD approach that is based on backward error analysis. Instead of calculating approximate solutions for an underlying exact regular Born–Oppenheimer potential, we do the opposite. Instead, we calculate the exact electron density, energies, and forces, but for an underlying approximate shadow Born–Oppenheimer potential energy surface. In this way, the calculated forces are conservative with respect to the approximate shadow potential and generate accurate molecular trajectories with long-term energy stabilities. We show how such shadow Born–Oppenheimer potentials can be constructed at different levels of accuracy as a function of the integration time step, δt, from the constrained minimization of a sequence of systematically improvable, but approximate, shadow energy density functionals. For each energy functional, there is a corresponding ground state Born–Oppenheimer potential. These pairs of shadow energy functionals and potentials are higher-level generalizations of the original “zeroth-level” shadow energy functionals and potentials used in extended Lagrangian BOMD [Niklasson, Eur. Phys. J. B 94, 164 (2021)]. The proposed shadow energy functionals and potentials are useful only within this extended dynamical framework, where also the electronic degrees of freedom are propagated as dynamical field variables together with the atomic positions and velocities. The theory is quite general and can be applied to MD simulations using approximate DFT, Hartree–Fock, or semi-empirical methods, as well as to coarse-grained flexible charge models.