Comment on “Correlated electron-nuclear dynamics: Exact factorization of the molecular wavefunction” [J. Chem. Phys. 137, 22A530 (2012)]

Alonso, José L.; Clemente-Gallardo, Jesús; Echenique-Robba, Pablo; Jover-Galtier, J. A.

doi:10.1063/1.4818521

Cited by 40 publications

(48 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Such an exact factorisation was considered in [32,54,[57][58][59]67,68] and it avoids the complication of having to consider the dynamics of each of the ψ k states. Evidently, this factorisation is ambiguous, as one can redefine each factor as follows:…”

Section: A Critical Assessment Of the Method Non-relativistic Casementioning

confidence: 99%

“…Analogously, |ψ n | 2 is then interpreted as the conditional probability density to find the 'light' system in the q configuration given that the 'heavy' sector is in the Q configuration. In the context of molecular physics and the BO approximation, this interpretation was used in [57][58][59]67,68]. Such an interpretation was also adopted by Arce [54] in the context of the problem of time in (non-relativistic) quantum mechanics.…”

Section: Marginal and Conditional Wave Functionsmentioning

confidence: 99%

See 1 more Smart Citation

Gauge Fixing and the Semiclassical Interpretation of Quantum Cosmology

Chataignier

2019

Zeitschrift Für Naturforschung A

View full text Add to dashboard Cite

We make a critical review of the semiclassical interpretation of quantum cosmology and emphasise that it is not necessary to consider that a concept of time emerges only when the gravitational field is (semi)classical. We show that the usual results of the semiclassical interpretation, and its generalisation known as the Born-Oppenheimer approach to quantum cosmology, can be obtained by gauge fixing, both at the classical and quantum levels. By 'gauge fixing' we mean a particular choice of the time coordinate, which determines the arbitrary Lagrange multiplier that appears in Hamilton's equations. In the quantum theory, we adopt a tentative definition of the (Klein-Gordon) inner product, which is positive definite for solutions of the quantum constraint equation found via an iterative procedure that corresponds to a weak coupling expansion in powers of the inverse Planck mass. We conclude that the wave function should be interpreted as a state vector for both gravitational and matter degrees of freedom, the dynamics of which is unitary with respect to the chosen inner product and time variable.

show abstract

Section: A Critical Assessment Of the Method Non-relativistic Casementioning

confidence: 99%

Section: Marginal and Conditional Wave Functionsmentioning

confidence: 99%

Gauge Fixing and the Semiclassical Interpretation of Quantum Cosmology

Chataignier

2019

Zeitschrift Für Naturforschung A

View full text Add to dashboard Cite

show abstract

“…H n (R, t)χ(R, t) = i ∂ t χ(R, t), (15) where the PNC is inserted by means of Lagrange multipliers [45,46]. Here, the electronic and nuclear Hamiltonians are defined aŝ…”

Section: A Vibrational Circular Dichroismmentioning

confidence: 99%

Nuclear velocity perturbation theory for vibrational circular dichroism: An approach based on the exact factorization of the electron-nuclear wave function

Scherrer

Agostini

Sebastiani

et al. 2015

The Journal of Chemical Physics

View full text Add to dashboard Cite

The nuclear velocity perturbation theory (NVPT) for vibrational circular dichroism (VCD) is derived from the exact factorization of the electron-nuclear wave function. This new formalism offers an exact starting point to include correction terms to the Born-Oppenheimer (BO) form of the molecular wave function, similarly to the complete-adiabatic approximation. The corrections depend on a small parameter that, in a classical treatment of the nuclei, is identified as the nuclear velocity. Apart from proposing a rigorous basis for the NVPT, we show that the rotational strengths, related to the intensity of the VCD signal, contain a new contribution beyond-BO that can be evaluated with the NVPT and that only arises when the exact factorization approach is employed. Numerical results are presented for chiral and non-chiral systems to test the validity of the approach.

show abstract

“…What is lost is the picture of a time-dependent nuclear wave packet (or corresponding trajectories) evolving on an ensemble of static PESs; a picture that has provided important insights for the understanding of many photophysical and photochemical processes. The time evolution of the wavefunctions, Φ(r; R, t) and Ω(R, t), is described by two connected differential equations, which contain, besides the usual interaction terms, additional scalar and vector potential terms [59,60,62,63].…”

Section: The Exact Factorization-based Dynamicsmentioning

confidence: 99%

Nonadiabatic Molecular Dynamics Based on Trajectories

Carvalho

Bouduban

Curchod

et al. 2013

Entropy

View full text Add to dashboard Cite

Performing molecular dynamics in electronically excited states requires the inclusion of nonadiabatic effects to properly describe phenomena beyond the Born-Oppenheimer approximation. This article provides a survey of selected nonadiabatic methods based on quantum or classical trajectories. Among these techniques, trajectory surface hopping constitutes an interesting compromise between accuracy and efficiency for the simulation of medium-to large-scale molecular systems. This approach is, however, based on non-rigorous approximations that could compromise, in some cases, the correct description of the nonadiabatic effects under consideration and hamper a systematic improvement of the theory. With the help of an in principle exact description of nonadiabatic dynamics based on Bohmian quantum trajectories, we will investigate the origin of the main approximations in trajectory surface hopping and illustrate some of the limits of this approach by means of a few simple examples.

show abstract

Comment on “Correlated electron-nuclear dynamics: Exact factorization of the molecular wavefunction” [J. Chem. Phys. 137, 22A530 (2012)]

Cited by 40 publications

References 1 publication

Gauge Fixing and the Semiclassical Interpretation of Quantum Cosmology

Gauge Fixing and the Semiclassical Interpretation of Quantum Cosmology

Nuclear velocity perturbation theory for vibrational circular dichroism: An approach based on the exact factorization of the electron-nuclear wave function

Nonadiabatic Molecular Dynamics Based on Trajectories

Contact Info

Product

Resources

About