The adiabatic limit of the exact factorization of the electron-nuclear wave function

Eich, F. G.; Agostini, Federica

doi:10.1063/1.4959962

Cited by 57 publications

(66 citation statements)

References 52 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…25,26 The discussed methods can be still improved, e.g. along the lines of a more accurate factorization method such as the exact factorization 54−56 known for electron–nuclear problems, or trajectory based methods 50,57 can be applied to simulate such systems dynamically. This work has direct implications on more complex correlated matter-photon problems that can be approximately solved employing the cavity Born–Oppenheimer approximation to better understand complex correlated light-matter coupled systems.…”

Section: Summary and Outlookmentioning

confidence: 99%

Cavity Born–Oppenheimer Approximation for Correlated Electron–Nuclear-Photon Systems

Flick

Appel

Ruggenthaler

et al. 2017

J. Chem. Theory Comput.

175

279

View full text Add to dashboard Cite

In this work, we illustrate the recently introduced concept of the cavity Born–Oppenheimer approximation [10.1073/pnas.1615509114PNAS2017] for correlated electron–nuclear-photon problems in detail. We demonstrate how an expansion in terms of conditional electronic and photon-nuclear wave functions accurately describes eigenstates of strongly correlated light-matter systems. For a GaAs quantum ring model in resonance with a photon mode we highlight how the ground-state electronic potential-energy surface changes the usual harmonic potential of the free photon mode to a dressed mode with a double-well structure. This change is accompanied by a splitting of the electronic ground-state density. For a model where the photon mode is in resonance with a vibrational transition, we observe in the excited-state electronic potential-energy surface a splitting from a single minimum to a double minimum. Furthermore, for a time-dependent setup, we show how the dynamics in correlated light-matter systems can be understood in terms of population transfer between potential energy surfaces. This work at the interface of quantum chemistry and quantum optics paves the way for the full ab initio description of matter-photon systems.

show abstract

Section: Summary and Outlookmentioning

confidence: 99%

Cavity Born–Oppenheimer Approximation for Correlated Electron–Nuclear-Photon Systems

Flick

Appel

Ruggenthaler

et al. 2017

J. Chem. Theory Comput.

175

279

View full text Add to dashboard Cite

show abstract

“…6 This limitation is only due to numerical reasons, as the TDPEC is defined everywhere in space. 7 The interested reader can consult for example References 36,41,85-87 for discussions on the importance of adequately selecting initial conditions for nonadiabatic dynamics. 8 Methods employing coupled trajectories, as those described in Section 5.1.1 for example, or methods based on TBFs would naturally include such decoherence effects.…”

Section: Applications Of Nonadiabatic Molecular Dynamicsmentioning

confidence: 99%

Different flavors of nonadiabatic molecular dynamics

Agostini

Curchod

2019

WIREs Comput Mol Sci

Self Cite

100

View full text Add to dashboard Cite

The Born‐Oppenheimer approximation constitutes a cornerstone of our understanding of molecules and their reactivity, partly because it introduces a somewhat simplified representation of the molecular wavefunction. However, when a molecule absorbs light containing enough energy to trigger an electronic transition, the simplistic nature of the molecular wavefunction offered by the Born‐Oppenheimer approximation breaks down as a result of the now non‐negligible coupling between nuclear and electronic motion, often coined nonadiabatic couplings. Hence, the description of nonadiabatic processes implies a change in our representation of the molecular wavefunction, leading eventually to the design of new theoretical tools to describe the fate of an electronically‐excited molecule. This Overview focuses on this quantity—the total molecular wavefunction—and the different approaches proposed to describe theoretically this complicated object in non‐Born‐Oppenheimer conditions, namely the Born‐Huang and Exact‐Factorization representations. The way each representation depicts the appearance of nonadiabatic effects is then revealed by using a model of a coupled proton–electron transfer reaction. Applying approximations to the formally exact equations of motion obtained within each representation leads to the derivation, or proposition, of different strategies to simulate the nonadiabatic dynamics of molecules. Approaches like quantum dynamics with fixed and time‐dependent grids, traveling basis functions, or mixed quantum/classical like surface hopping, Ehrenfest dynamics, or coupled‐trajectory schemes are described in this Overview. This article is categorized under: Theoretical and Physical Chemistry > Reaction Dynamics and Kinetics Software > Simulation Methods Theoretical and Physical Chemistry > Spectroscopy

show abstract

“…We call both (24) and (26) the clock-dependent Schrödinger equation (CDSE) in analogy to the TDSE, because they become TDSEs if the classical limit for the clock is taken. How to take this classical limit is discussed in [15], and we only sketch here the steps that need to be done, using some results of an analysis of the adiabatic limit in the Exact Factorization [37]. First, we introduce a parameter µ := m/M which is the ratio of the mass of the system to that of the clock.…”

Section: Of the Vector Potential A Such Thatmentioning

confidence: 99%

“…the change of the scalar potential (R) when the classical limit is taken or how to perform the classical limit in a gauge invariant way, i.e., including the vector potential A(R). While some of those details are explained in [15,37], some are still open problems and may be rewarding topics for future research. We need not be concerned with them here, however, because we keep the clock fully quantum mechanical and derive the continuity equation for such a quantum clock.…”

Section: Of the Vector Potential A Such Thatmentioning

confidence: 99%

“…The clock-dependent continuity equations (37) and (42) The clock-dependent continuity equation (42) can be useful to analyze a quantum dynamics, as illustrated in the next section. However, as we started from a stationary state of the universe, it is not obvious from (37) and (42) how to obtain a non-trivial dynamics of the system.…”

Section: The Clock-dependent Continuity Equationmentioning

confidence: 99%

See 1 more Smart Citation

Time in quantum mechanics: A fresh look at the continuity equation

Schild

2018

Phys. Rev. A

View full text Add to dashboard Cite

The local conservation of a physical quantity whose distribution changes with time is mathematically described by the continuity equation. The corresponding time parameter, however, is defined with respect to an idealized classical clock. We consider what happens when this classical time is replaced by a non-relativistic quantum-mechanical description of the clock. From the clock-dependent Schrödinger equation (as analogue of the timedependent Schrödinger equation) we derive a continuity equation, where, instead of a timederivative, an operator occurs that depends on the flux (probability current) density of the clock. This clock-dependent continuity equation can be used to analyze the dynamics of aquantum system and to study degrees of freedom that may be used as internal clocks for an approximate description of the dynamics of the remaining degrees of freedom. As an illustration, we study a simple model for coupled electron-nuclear dynamics and interpret the nuclei as quantum clock for the electronic motion. We find that whenever the Born-Oppenheimer approximation is valid, the continuity equation shows that the nuclei are the only relevant clock for the electrons.

show abstract

The adiabatic limit of the exact factorization of the electron-nuclear wave function

Cited by 57 publications

References 52 publications

Cavity Born–Oppenheimer Approximation for Correlated Electron–Nuclear-Photon Systems

Cavity Born–Oppenheimer Approximation for Correlated Electron–Nuclear-Photon Systems

Different flavors of nonadiabatic molecular dynamics

Time in quantum mechanics: A fresh look at the continuity equation

Contact Info

Product

Resources

About