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E. K. U. Gross - One of the best experts on this subject based on the ideXlab platform.
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density Functional theory of electron transfer beyond the born oppenheimer approximation case study of lif
Journal of Chemical Physics, 2018Co-Authors: Chen Li, E. K. U. Gross, Ryan RequistAbstract:We perform model calculations for a stretched LiF molecule, demonstrating that nonadiabatic charge transfer effects can be accurately and seamlessly described within a density Functional framework. In alkali halides like LiF, there is an abrupt change in the ground state electronic distribution due to an electron transfer at a critical bond length R = Rc, where an avoided crossing of the lowest adiabatic potential energy surfaces calls the validity of the Born-Oppenheimer approximation into doubt. Modeling the R-dependent electronic structure of LiF within a two-site Hubbard model, we find that nonadiabatic electron-Nuclear coupling produces a sizable elongation of the critical Rc by 0.5 bohr. This effect is very accurately captured by a simple and rigorously derived correction, with an M−1 prefactor, to the exchange-correlation potential in density Functional theory, M = reduced Nuclear mass. Since this nonadiabatic term depends on gradients of the Nuclear Wave Function and conditional electronic density...
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exact factorization based density Functional theory of electrons and nuclei
Physical Review Letters, 2016Co-Authors: Ryan Requist, E. K. U. GrossAbstract:The ground state energy of a system of electrons (r=r_{1},r_{2},…) and nuclei (R=R_{1},R_{2},…) is proven to be a variational Functional of the electronic density n(r,R) and paramagnetic current density j_{p}(r,R) conditional on R, the Nuclear Wave Function χ(R), an induced vector potential A_{μ}(R) and a quantum geometric tensor T_{μν}(R). n, j_{p}, A_{μ} and T_{μν} are defined in terms of the conditional electronic Wave Function Φ_{R}(r). The ground state (n,j_{p},χ,A_{μ},T_{μν}) can be calculated by solving self-consistently (i) conditional Kohn-Sham equations containing effective scalar and vector potentials v_{s}(r) and A_{xc}(r) that depend parametrically on R, (ii) the Schrodinger equation for χ(R), and (iii) Euler-Lagrange equations that determine T_{μν}. The theory is applied to the E⊗e Jahn-Teller model.
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Nuclear velocity perturbation theory for vibrational circular dichroism an approach based on the exact factorization of the electron Nuclear Wave Function
Journal of Chemical Physics, 2015Co-Authors: Arne Scherrer, Federica Agostini, E. K. U. Gross, Daniel Sebastiani, Rodolphe VuilleumierAbstract: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, similar 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.
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classical Nuclear motion coupled to electronic non adiabatic transitions
Journal of Chemical Physics, 2014Co-Authors: Federica Agostini, Ali Abedi, E. K. U. GrossAbstract:Based on the exact factorization of the electron-Nuclear Wave Function, we have recently proposed a mixed quantum-classical scheme [A. Abedi, F. Agostini, and E. K. U. Gross, Europhys. Lett. 106, 33001 (2014)] to deal with non-adiabatic processes. Here we present a comprehensive description of the formalism, including the full derivation of the equations of motion. Numerical results are presented for a model system for non-adiabatic charge transfer in order to test the performance of the method and to validate the underlying approximations.
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classical Nuclear motion coupled to electronic non adiabatic transitions
arXiv: Chemical Physics, 2014Co-Authors: Federica Agostini, Ali Abedi, E. K. U. GrossAbstract:We present a detailed derivation and numerical tests of a new mixed quantum-classical scheme to deal with non-adiabatic processes. The method is presented as the zero-th order approximation to the exact coupled dynamics of electrons and nuclei offered by the factorization of the electron-Nuclear Wave Function [A. Abedi, N. T. Maitra and E. K. U. Gross, Phys. Rev. Lett., 105 (2010)]. Numerical results are presented for a model system for non-adiabatic charge transfer in order to test the performance of the method and to validate the underlying approximations.
Ali Abedi - One of the best experts on this subject based on the ideXlab platform.
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universal steps in quantum dynamics with time dependent potential energy surfaces beyond the born oppenheimer picture
Physical Review A, 2016Co-Authors: G Albareda, Ali Abedi, Ivano Tavernelli, Angel RubioAbstract:It was recently shown [G. Albareda, et al., Phys. Rev. Lett. 113, 083003 (2014)] that within the conditional decomposition approach to the coupled electron-Nuclear dynamics, the electron-Nuclear Wave Function can be exactly decomposed into an ensemble of Nuclear Wavepackets effectively governed by Nuclear conditional time-dependent potential-energy surfaces (C-TDPESs). Employing a one-dimensional model system we show that for strong nonadiabatic couplings the Nuclear C-TDPESs exhibit steps that bridge piecewise adiabatic Born-Oppenheimer PESs. The nature of these steps is identified as an effect of electron-Nuclear correlation. Furthermore, a direct comparison with similar discontinuities recently reported in the context of the exact factorization framework allows us to draw conclusions about the universality of these discontinuities, viz. they are inherent to all nonadiabatic Nuclear dynamics approaches based on (exact) time-dependent potential energy surfaces.
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exact potential driving the electron dynamics in enhanced ionization of h 2
Physical Review Letters, 2015Co-Authors: Ali Abedi, Elham Khosravi, Neepa T MaitraAbstract:It was recently shown that the exact factorization of the electron-Nuclear Wave Function allows the construction of a Schrodinger equation for the electronic system, in which the potential contains exactly the effect of coupling to the Nuclear degrees of freedom and any external fields. Here we study the exact potential acting on the electron in charge-resonance enhanced ionization in a model one-dimensional H(2)(+) molecule. We show there can be significant differences between the exact potential and that used in the traditional quasistatic analyses, arising from nonadiabatic coupling to the Nuclear system, and that these are crucial to include for accurate simulations of time-resolved ionization dynamics and predictions of the ionization yield.
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classical Nuclear motion coupled to electronic non adiabatic transitions
Journal of Chemical Physics, 2014Co-Authors: Federica Agostini, Ali Abedi, E. K. U. GrossAbstract:Based on the exact factorization of the electron-Nuclear Wave Function, we have recently proposed a mixed quantum-classical scheme [A. Abedi, F. Agostini, and E. K. U. Gross, Europhys. Lett. 106, 33001 (2014)] to deal with non-adiabatic processes. Here we present a comprehensive description of the formalism, including the full derivation of the equations of motion. Numerical results are presented for a model system for non-adiabatic charge transfer in order to test the performance of the method and to validate the underlying approximations.
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classical Nuclear motion coupled to electronic non adiabatic transitions
arXiv: Chemical Physics, 2014Co-Authors: Federica Agostini, Ali Abedi, E. K. U. GrossAbstract:We present a detailed derivation and numerical tests of a new mixed quantum-classical scheme to deal with non-adiabatic processes. The method is presented as the zero-th order approximation to the exact coupled dynamics of electrons and nuclei offered by the factorization of the electron-Nuclear Wave Function [A. Abedi, N. T. Maitra and E. K. U. Gross, Phys. Rev. Lett., 105 (2010)]. Numerical results are presented for a model system for non-adiabatic charge transfer in order to test the performance of the method and to validate the underlying approximations.
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mixed quantum classical dynamics from the exact decomposition of electron Nuclear motion
EPL, 2014Co-Authors: Ali Abedi, Federica Agostini, E. K. U. GrossAbstract:We present a novel mixed quantum-classical approach to the coupled electron-Nuclear dynamics based on the exact factorisation of the electron-Nuclear Wave Function, recently proposed in Abedi A., Maitra N. T. and Gross E. K. U., Phys. Rev. Lett., 105 (2010) 123002. In this framework, the correct classical limit of the Nuclear dynamics is worked out by taking the classical limit of the exact time-dependent Schr?dinger equation satisfied by the Nuclear Wave Function. The effect of the time-dependent scalar and vector potentials, representing the exact electronic back-reaction on the Nuclear subsystem, is consistently derived within the classical approximation. We examine with an example the performance of the proposed mixed quantum-classical scheme in comparison with exact calculations.
Federica Agostini - One of the best experts on this subject based on the ideXlab platform.
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on the mass of atoms in molecules beyond the born oppenheimer approximation
arXiv: Chemical Physics, 2016Co-Authors: Arne Scherrer, Rodolphe Vuilleumier, Federica Agostini, Daniel Sebastiani, E GrossAbstract:Describing the dynamics of nuclei in molecules requires a potential energy surface, which is traditionally provided by the Born-Oppenheimer or adiabatic approximation. However, we also need to assign masses to the nuclei. There, the Born-Oppenheimer picture does not account for the inertia of the electrons and only bare Nuclear masses are considered. Nowadays, experimental accuracy challenges the theoretical predictions of rotational and vibrational spectra and requires to include the participation of electrons in the internal motion of the molecule. More than 80 years after the original work of Born and Oppenheimer, this issue still is not solved in general. Here, we present a theoretical and numerical framework to address this problem in a general and rigorous way. Starting from the exact factorization of the electron-Nuclear Wave Function, we include electronic effects beyond the Born-Oppenheimer regime in a perturbative way via position-dependent corrections to the bare Nuclear masses. This maintains an adiabatic-like point of view: the Nuclear degrees of freedom feel the presence of the electrons via a single potential energy surface, whereas the inertia of electrons is accounted for and the total mass of the system is recovered. This constitutes a general framework for describing the mass acquired by slow degrees of freedom due to the inertia of light, bounded particles. We illustrate it with a model of proton transfer, where the light particle is the proton, and with corrections to the vibrational spectra of molecules. Inclusion of the light particle inertia allows to gain orders of magnitude in accuracy.
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the adiabatic limit of the exact factorization of the electron Nuclear Wave Function
arXiv: Chemical Physics, 2016Co-Authors: F G Eich, Federica AgostiniAbstract:We propose a procedure to analyze the relation between the exact factorization of the electron-Nuclear Wave Function and the Born-Oppenheimer approximation. We define the adiabatic limit as the limit of infinite Nuclear mass. To this end, we introduce a unit system that singles out the dependence on the electron-Nuclear mass ratio of each term appearing in the equations of the exact factorization. We observe how non-adiabatic effects induced by the coupling to the Nuclear motion affect electronic properties and we analyze the leading term, connecting it to the classical Nuclear momentum. Its dependence on the mass ratio is tested numerically on a model proton- coupled electron transfer in different non-adiabatic regimes.
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Nuclear velocity perturbation theory for vibrational circular dichroism an approach based on the exact factorization of the electron Nuclear Wave Function
Journal of Chemical Physics, 2015Co-Authors: Arne Scherrer, Federica Agostini, E. K. U. Gross, Daniel Sebastiani, Rodolphe VuilleumierAbstract: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, similar 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.
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coupled trajectory quantum classical approach to electronic decoherence in nonadiabatic processes
Physical Review Letters, 2015Co-Authors: Federica Agostini, Seung Kyu Min, E GrossAbstract:We present a novel quantum-classical approach to nonadiabatic dynamics, deduced from the coupled electronic and Nuclear equations in the framework of the exact factorization of the electron-Nuclear Wave Function. The method is based on the quasiclassical interpretation of the Nuclear Wave Function, whose phase is related to the classical momentum and whose density is represented in terms of classical trajectories. In this approximation, electronic decoherence is naturally induced as an effect of the coupling to the nuclei and correctly reproduces the expected quantum behavior. Moreover, the splitting of the Nuclear Wave packet is captured as a consequence of the correct approximation of the time-dependent potential of the theory. This new approach offers a clear improvement over Ehrenfest-like dynamics. The theoretical derivation presented in this Letter is supported by numerical results that are compared to quantum mechanical calculations.
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classical Nuclear motion coupled to electronic non adiabatic transitions
Journal of Chemical Physics, 2014Co-Authors: Federica Agostini, Ali Abedi, E. K. U. GrossAbstract:Based on the exact factorization of the electron-Nuclear Wave Function, we have recently proposed a mixed quantum-classical scheme [A. Abedi, F. Agostini, and E. K. U. Gross, Europhys. Lett. 106, 33001 (2014)] to deal with non-adiabatic processes. Here we present a comprehensive description of the formalism, including the full derivation of the equations of motion. Numerical results are presented for a model system for non-adiabatic charge transfer in order to test the performance of the method and to validate the underlying approximations.
Angel Rubio - One of the best experts on this subject based on the ideXlab platform.
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universal steps in quantum dynamics with time dependent potential energy surfaces beyond the born oppenheimer picture
Physical Review A, 2016Co-Authors: G Albareda, Ali Abedi, Ivano Tavernelli, Angel RubioAbstract:It was recently shown [G. Albareda, et al., Phys. Rev. Lett. 113, 083003 (2014)] that within the conditional decomposition approach to the coupled electron-Nuclear dynamics, the electron-Nuclear Wave Function can be exactly decomposed into an ensemble of Nuclear Wavepackets effectively governed by Nuclear conditional time-dependent potential-energy surfaces (C-TDPESs). Employing a one-dimensional model system we show that for strong nonadiabatic couplings the Nuclear C-TDPESs exhibit steps that bridge piecewise adiabatic Born-Oppenheimer PESs. The nature of these steps is identified as an effect of electron-Nuclear correlation. Furthermore, a direct comparison with similar discontinuities recently reported in the context of the exact factorization framework allows us to draw conclusions about the universality of these discontinuities, viz. they are inherent to all nonadiabatic Nuclear dynamics approaches based on (exact) time-dependent potential energy surfaces.
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conditional born oppenheimer dynamics quantum dynamics simulations for the model porphine
Journal of Physical Chemistry Letters, 2015Co-Authors: G Albareda, Ivano Tavernelli, Angel Rubio, Josep Maria Bofill, Fermin Huartelarranaga, Francesc IllasAbstract:We report a new theoretical approach to solve adiabatic quantum molecular dynamics halfway between Wave Function and trajectory-based methods. The evolution of a N-body Nuclear Wave Function moving on a 3N-dimensional Born–Oppenheimer potential-energy hyper-surface is rewritten in terms of single-nuclei Wave Functions evolving nonunitarily on a 3-dimensional potential-energy surface that depends parametrically on the configuration of an ensemble of generally defined trajectories. The scheme is exact and, together with the use of trajectory-based statistical techniques, can be exploited to circumvent the calculation and storage of many-body quantities (e.g., Wave Function and potential-energy surface) whose size scales exponentially with the number of Nuclear degrees of freedom. As a proof of concept, we present numerical simulations of a 2-dimensional model porphine where switching from concerted to sequential double proton transfer (and back) is induced quantum mechanically.
E Gross - One of the best experts on this subject based on the ideXlab platform.
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on the mass of atoms in molecules beyond the born oppenheimer approximation
arXiv: Chemical Physics, 2016Co-Authors: Arne Scherrer, Rodolphe Vuilleumier, Federica Agostini, Daniel Sebastiani, E GrossAbstract:Describing the dynamics of nuclei in molecules requires a potential energy surface, which is traditionally provided by the Born-Oppenheimer or adiabatic approximation. However, we also need to assign masses to the nuclei. There, the Born-Oppenheimer picture does not account for the inertia of the electrons and only bare Nuclear masses are considered. Nowadays, experimental accuracy challenges the theoretical predictions of rotational and vibrational spectra and requires to include the participation of electrons in the internal motion of the molecule. More than 80 years after the original work of Born and Oppenheimer, this issue still is not solved in general. Here, we present a theoretical and numerical framework to address this problem in a general and rigorous way. Starting from the exact factorization of the electron-Nuclear Wave Function, we include electronic effects beyond the Born-Oppenheimer regime in a perturbative way via position-dependent corrections to the bare Nuclear masses. This maintains an adiabatic-like point of view: the Nuclear degrees of freedom feel the presence of the electrons via a single potential energy surface, whereas the inertia of electrons is accounted for and the total mass of the system is recovered. This constitutes a general framework for describing the mass acquired by slow degrees of freedom due to the inertia of light, bounded particles. We illustrate it with a model of proton transfer, where the light particle is the proton, and with corrections to the vibrational spectra of molecules. Inclusion of the light particle inertia allows to gain orders of magnitude in accuracy.
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coupled trajectory quantum classical approach to electronic decoherence in nonadiabatic processes
Physical Review Letters, 2015Co-Authors: Federica Agostini, Seung Kyu Min, E GrossAbstract:We present a novel quantum-classical approach to nonadiabatic dynamics, deduced from the coupled electronic and Nuclear equations in the framework of the exact factorization of the electron-Nuclear Wave Function. The method is based on the quasiclassical interpretation of the Nuclear Wave Function, whose phase is related to the classical momentum and whose density is represented in terms of classical trajectories. In this approximation, electronic decoherence is naturally induced as an effect of the coupling to the nuclei and correctly reproduces the expected quantum behavior. Moreover, the splitting of the Nuclear Wave packet is captured as a consequence of the correct approximation of the time-dependent potential of the theory. This new approach offers a clear improvement over Ehrenfest-like dynamics. The theoretical derivation presented in this Letter is supported by numerical results that are compared to quantum mechanical calculations.
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mixed quantum classical dynamics on the exact time dependent potential energy surface a fresh look at non adiabatic processes
arXiv: Chemical Physics, 2013Co-Authors: Federica Agostini, Ali Abedi, Yasumitsu Suzuki, E GrossAbstract:The exact Nuclear time-dependent potential energy surface arises from the exact decomposition of electronic and Nuclear motion, recently presented in [A. Abedi, N. T. Maitra, and E. K. U. Gross, Phys. Rev. Lett. 105, 123002 (2010)]. Such time-dependent potential drives Nuclear motion and fully accounts for the coupling to the electronic subsystem. We investigate the features of the potential in the context of electronic non-adiabatic processes and employ it to study the performance of the classical approximation on Nuclear dynamics. We observe that the potential, after the Nuclear Wave-packet splits at an avoided crossing, develops dynamical steps connecting different regions, along the Nuclear coordinate, in which it has the same slope as one or the other adiabatic surface. A detailed analysis of these steps is presented for systems with different non-adiabatic coupling strength. The exact factorization of the electron-Nuclear Wave-Function is at the basis of the decomposition. In particular, the Nuclear part is the true Nuclear Wave-Function, solution of a time-dependent Schroedinger euqation and leading to the exact many-body density and current density. As a consequence, the Ehrenfest theorem can be extended to the Nuclear subsystem and Hamiltonian, as discussed here with an analytical derivation and numerical results.
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dynamical steps that bridge piecewise adiabatic shapes in the exact time dependent potential energy surface
Physical Review Letters, 2013Co-Authors: Ali Abedi, Federica Agostini, Yasumitsu Suzuki, E GrossAbstract:We study the exact time-dependent potential energy surface (TDPES) in the presence of strong nonadiabatic coupling between the electronic and Nuclear motion. The concept of the TDPES emerges from the exact factorization of the full electron-Nuclear Wave Function [A. Abedi, N. T. Maitra, and E. K. U. Gross, Phys. Rev. Lett. 105, 123002 (2010)]. Employing a one-dimensional model system, we show that the TDPES exhibits a dynamical step that bridges between piecewise adiabatic shapes. We analytically investigate the position of the steps and the nature of the switching between the adiabatic pieces of the TDPES.
