Density functional theory beyond the Born-Oppenheimer approximation: Accurate treatment of the ionic zero-point motion

Abstract

We introduce a method to carry out zero-temperature calculations within density functional theory (DFT) but without relying on the Born-Oppenheimer (BO) approximation for the ionic motion.Our approach is based on the finite-temperature many-body path-integral formulation of quantum mechanics by taking the zero-temperature limit and treating the imaginary-time propagation of the electronic variables in the context of DFT. This goes beyond the familiar BO approximation and is limited from being an exact treatment of both electrons and ions only by the approximations involved in the DFT component. We test our method in two simple molecules, H 2 and benzene.We demonstrate that the method produces a difference from the results of the BO approximation which is significant for many physical systems, especially those containing light atoms such as hydrogen; in these cases, we find that the fluctuations of the distance from its equilibrium position, due to the zero-point-motion, is comparable to the interatomic distances. The method is suitable for use with conventional condensed matter approaches and currently is implemented on top of the periodic pseudopotential code SIESTA. arXiv:1804.10852v4 [cond-mat.mtrl-sci]

Nonadiabatic dynamics of cobalt tricarbonyl nitrosyl for ligand dissociation induced by electronic excitation

“…As demonstrated above, the Ehrenfest dynamics allows us to perform on-the-fly simulations of the particular system without considering trajectory-based methods, such as fewest-switches surface hopping 56 although the subtle quantum nature of ion dynamics remains elusive. Regarding the zero-point motion 30 , 40 , which is neglected in the classical picture, will be insignificant because the ion temperature is 300 K or higher.…”

“…In the Ehrenfest dynamics, ions are approximated by classical particles evolving on the mean-field average of adiabatic potential energy surfaces (PESs); thus, detailed balance 39 , spontaneous phonon emission 40 , 41 , and zero-point motion 30 , 40 are missing. As to the Co(CO) 3 NO, the validity of the Ehrenfest approximation will be discussed in the following section.…”

Imaginary-Time Time-Dependent Density Functional Theory and Its Application for Robust Convergence of Electronic States

“…This is a useful result since it allows us to think about imaginary-time propagation in the Kohn–Sham system in terms of what it does in the real system, allowing the Wick-rotation connections from quantum mechanics to statistical mechanics to be employed. For example, it justifies the use of the Kohn–Sham system as a stand-in for the interacting system in our calculations performed for imaginary-time path integrals …”

“…In the present paper we transform the time-dependent KS (TDKS) equations of time-dependent density functional theory (TDDFT) − to imaginary time . We use these equations to propagate an initial state to very long imaginary time, refining it down to the KS state corresponding to its lowest energy component.…”

Two-component density functional theory for muonic molecules: Inclusion of the electron-positive muon correlation functional

“…68,69 While the e-DFT is intrinsically a single-component formalism, only assuming electrons as quantum particles, this is not an intrinsic limitation of the fundamental theorems of DFT, 70 and the multi-component versions of DFT, MC-DFT, have been also formulated for systems composed of multiple types of quantum particles. [71][72][73][74][75][76][77][78][79][80][81][82][83][84][85][86][87][88][89][90] Particularly, and relevant to present study, is the recent developments in formulation and computational applications of the MC-DFT to molecular systems where one or some numbers of protons, or other isotopes of hydrogen, are treated as quantum particles instead of clamped point charges. In fact, since usually just two components of these systems are treated as quantum particles, for example electrons and protons, the general formulation of the MC-DFT is reduced to the two-component version, TC-DFT.…”