Exact factorization of the time-dependent electron-nuclear wavefunction

Abstract

We present an exact decomposition of the complete wavefunction for a system of nuclei and electrons evolving in a time-dependent external potential. We derive formally exact equations for the nuclear and electronic wavefunctions that lead to rigorous definitions of a time-dependent potential energy surface (TDPES) and a time-dependent geometric phase. For the $H_2^{+}$ molecular ion exposed to a laser field, the TDPES proves to be a useful interpretive tool to identify different mechanisms of dissociation.

4 pages, 2 figures

References in corpus (2)

• The transfer of energy between electrons and ions in solids
• Path integral formulation for quantum nonadiabatic dynamics and the mixed quantum-classical limit

Cited by in corpus (138)

• Machine learning for electronically excited states of molecules
• Correlated electron-nuclear dynamics: Exact factorization of the molecular wavefunction
• Towards high-throughput superconductor discovery via machine learning
• Cavity Born-Oppenheimer Approximation for Correlated Electron-Nuclear-Photon Systems
• A coupled-trajectory quantum-classical approach to decoherence in non-adiabatic processes
• Inclusion of machine learning kernel ridge regression potential energy surfaces in on-the-fly nonadiabatic molecular dynamics simulation
• Cavity correlated electron-nuclear dynamics from first principles
• Is the molecular Berry phase an artifact of the Born-Oppenheimer approximation?
• A brief compendium of time-dependent density-functional theory
• Real-time solutions of coupled Ehrenfest-Maxwell-Pauli-Kohn-Sham equations: fundamentals, implementation, and nano-optical applications
• The exact forces on classical nuclei in non-adiabatic charge transfer
• Excited state, non-adiabatic dynamics of large photoswitchable molecules using a chemically transferable machine learning potential
• Nuclear velocity perturbation theory for vibrational circular dichroism: An approach based on the exact factorization of the electron-nuclear wave function
• Molecular geometric phase from the exact electron-nuclear factorization
• Exact Potential Energy Surface for Molecules in Cavities
• Light-Matter Interactions via the Exact Factorization Approach
• Electronic friction-based vibrational lifetimes of molecular adsorbates: Beyond the independent atom approximation
• Exact factorization-based density functional theory of electrons and nuclei
• Accelerating Finite-temperature Kohn-Sham Density Functional Theory with Deep Neural Networks
• On the mass of atoms in molecules: Beyond the Born-Oppenheimer approximation
• Mixed quantum-classical dynamics from the exact decomposition of electron-nuclear motion
• The adiabatic limit of the exact factorization of the electron-nuclear wave function
• A Walk Through the Approximations of Ab Initio Multiple Spawning
• DFTpy: An efficient and object-oriented platform for orbital-free DFT simulations
• Classical nuclear motion coupled to electronic non-adiabatic transitions
• Mixed quantum-classical dynamics on the exact time-dependent potential energy surface: A fresh look at non-adiabatic processes
• Exact single-electron approach to the dynamics of molecules in strong laser fields
• Current-induced forces: a simple derivation
• Ultrafast dynamics with the exact factorization
• An Exact Factorization Perspective on Quantum Interferences in Nonadiabatic Dynamics
• Unitarity of quantum-gravitational corrections to primordial fluctuations in the Born-Oppenheimer approach
• Reply to "Comment on 'Correlated electron-nuclear dynamics: Exact factorization of the molecular wavefunction' [J. Chem. Phys. 137, 22A530 (2012) ]''
• On the Numerical Solution of the Exact Factorization Equations
• The Exact Potential Driving the Electron Dynamics in Enhanced Ionization
• Roadmap for Molecular Benchmarks in Nonadiabatic Dynamics
• Asymptotic analysis of the Berry curvature in the $E\otimes e$ Jahn-Teller model
• Semiclassical analysis of the electron-nuclear coupling in electronic non-adiabatic processes
• Shedding Light on Correlated Electron-Photon States using the Exact Factorization
• Incorporating Nuclear Quantum Effects in Molecular Dynamics with a Constrained Minimized Energy Surface
• Ab-Initio Molecular Dynamics with Screened Lorentz Forces. Part I. Calculation and Atomic Charge Interpretation of Berry Curvature
• Ultrafast dynamics of photoinduced charge separation
• Quantum Computing for Fusion Energy Science Applications
• Correlated Electron-Nuclear Dynamics with Conditional Wave Functions
• Density functional theory of electron transfer beyond the Born-Oppenheimer approximation: Case study of LiF
• Bohmian mechanics in the exact factorization of electron-nuclear wavefunction
• Disordered Crystals from First Principles I: Quantifying the Configuration Space
• Effects of electron-phonon interaction on thermal and electrical transport through molecular nano-conductors
• Energy, Momentum and Angular Momentum Transfer Between Electrons and Nuclei
• Molecular vibrational frequencies from analytic Hessian of constrained nuclear-electronic orbital density functional theory
• Surface hopping methodology in laser-driven molecular dynamics
• Embedding via the Exact Factorization Approach
• Time in quantum mechanics: A fresh look at the continuity equation
• Case Studies of the Time-Dependent Potential Energy Surface for Dynamics in Cavities
• The equivalent emergence of time dependence in classical and quantum mechanics
• Total Angular Momentum Conservation in Ab Initio Born-Oppenheimer Molecular Dynamics
• Efficient geometric integrators for nonadiabatic quantum dynamics. II. The diabatic representation
• Exact factorization-based density functional theory of electron-phonon systems
• Quantum-classical nonadiabatic dynamics of Floquet driven systems
• Efficient geometric integrators for nonadiabatic quantum dynamics. I. The adiabatic representation
• Energy-Conserving Coupled Trajectory Mixed Quantum Classical Dynamics
• Representation and Conservation of Angular Momentum in the Born-Oppenheimer Theory of Polyatomic Molecules
• Classification of materials with phonon angular momentum and microscopic origin of angular momentum
• Asymptotic nodal planes in the electron density and the potential in the effective equation for the square root of the density
• Non-Unitarity Problem in Quantum Gravity Corrections to Quantum Field Theory with Born-Oppenheimer Approximation
• Analysis of the Classical Trajectory Treatment of Photon Dynamics for Polaritonic Phenomena
• The Exact Wavefunction Factorization of a Vibronic Coupling System
• Quantum Dynamics with Electronic Friction
• Geometry of nonadiabatic quantum hydrodynamics
• Non-adiabatic quantum dynamics without potential energy surfaces based on second-quantized electrons: application within the framework of the MCTDH method
• Electronic Non-adiabatic Dynamics in Enhanced Ionization of Isotopologues of H${}_2^{+}$ from the Exact Factorization Perspective
• Quasi-classical approaches to vibronic spectra revisited
• Validating Fewest-Switches Surface Hopping in the Presence of Laser Fields
• Fock space embedding theory for strongly correlated topological phases
• Many-body Green's function theory of electrons and nuclei beyond the Born-Oppenheimer approximation
• Coupled nuclear and electron dynamics in the vicinity of a conical intersection
• Nonadiabatic Field: A Conceptually Novel Approach for Nonadiabatic Quantum Molecular Dynamics
• Quantum entanglement from classical trajectories
• Nonadiabatic quantum transition-state theory in the golden-rule limit. II. Overcoming the pitfalls of the saddle-point and semiclassical approximations
• First-principles derivation and properties of density-functional average-atom models
• Nuclear-Electronic Orbital Approach to Quantization of Protons in Periodic Electronic Structure Calculations
• Universal Steps in Quantum Dynamics with Time-Dependent Potential-Energy Surfaces: Beyond the Born-Oppenheimer Picture
• On Factorization of Molecular Wavefunctions
• A functional approach to the electronic and bosonic dynamics of many-body systems perturbed with an arbitrary strong electron-boson interaction
• Shortcuts to Adiabaticity Assisted by Counterdiabatic Born-Oppenheimer Dynamics
• Gauge Fixing and the Semiclassical Interpretation of Quantum Cosmology
• The bohmion method in nonadiabatic quantum hydrodynamics
• A Snapshot of Time-Dependent Density-Functional Theory
• How important are the residual nonadiabatic couplings for an accurate simulation of nonadiabatic quantum dynamics in a quasidiabatic representation?
• First-principles modelling for time-resolved ARPES under different pump-probe conditions
• Many-electron effects of strong-field ionization described in an exact one-electron theory
• Electronic Born-Oppenheimer Approximation in Nuclear-Electronic Orbital Dynamics
• Nonadiabatic \textit{ab initio} Quantum Dynamics without Potential Energy Surfaces
• Non-adiabatic dynamics of electrons and atoms under non-equilibrium conditions
• On the Proper Derivation of the Floquet-based Quantum Classical Liouville Equation and Surface Hopping Describing a Molecule or Material Subject to an External Field
• Local diabatic representation of conical intersection quantum dynamics
• Hamiltonian formulation of nonequilibrium quantum dynamics: geometric structure of the BBGKY hierarchy
• Nonadiabatic Van der Pol oscillations in molecular transport
• Model Hamiltonian for strongly-correlated systems: Systematic, self-consistent, and unique construction
• Which form of the molecular Hamiltonian is the most suitable for simulating the nonadiabatic quantum dynamics at a conical intersection?
• Conditional probability density functional theory
• On the Meaning of Berry Force For Unrestricted Systems Treated With Mean-Field Electronic Structure
• Ehrenfest statistical dynamics in chemistry: study of decoherence effects
• Time-resolved spectroscopy at surfaces and adsorbate dynamics: insights from a model-system approach
• Exact factorization of the many-body Green's function theory of electrons and nuclei
• Time-Dependent Multi-Component Density Functional Theory for Coupled Electron-Positron Dynamics
• Time-dependent renormalized-natural-orbital theory applied to laser-driven H${}_2^{+}$
• Geometric energy transfer in two-component systems
• Density Matrix Renormalization Group Study of a One Dimensional Diatomic Molecule beyond the Born-Oppenheimer Approximation
• Beyond semiclassical time
• Sum-rules of the response potential in the strongly-interacting limit of DFT
• Density functional theory beyond the Born-Oppenheimer approximation: Exact mapping onto an electronically non-interacting Kohn-Sham molecule
• Generation of Phonons with Angular Momentum During Ultrafast Demagnetization
• Light-matter quantum dynamics of complex laser-driven systems
• Quantum Field Theory of Electrons and Nuclei
• Fermi's golden rule rate expression for transitions due to nonadiabatic derivative couplings in the adiabatic basis
• Influence of coherent vibronic excitation on the high harmonics generation of diatomic molecules
• Two imaginarity monotones induced by unified $(\alpha ,\beta )$-relative entropy
• Quantum motion with trajectories: beyond the Gaussian beam approximation
• Floquet Engineering of a Diatomic Molecule Through a Bichromatic Radiation Field
• Semiclassical quantization of nonadiabatic systems with hopping periodic orbits
• Nucleus-electron correlation revising molecular bonding fingerprints from the exact wavefunction factorization
• Koopmon trajectories in nonadiabatic quantum-classical dynamics
• Electronic decoherence along a single nuclear trajectory
• Quantum covariant derivative
• Conditional wave theory of environmental interactions with a quantum particle
• A quantum dynamics method for excited electrons in molecular aggregate system using a group diabatic Fock matrix
• Quantum-ionic features in the absorption spectra of homonuclear diatomic molecules
• The Special Theory of Relativity as Applied to the Born-Oppenheimer-Huang Approach
• Quantum Gravity Corrections to the inflationary spectrum in a Bohmian approach
• Exactly factorized molecular Kohn-Sham density functional theory
• Geometric Phase Effect in Thermodynamic Properties and in the Imaginary-Time Multi-Electronic-State Path Integral Formulation
• Mixed quantal-semiquantal dynamics with stochastic particles for backreaction
• Symmetry-protected topological polarons
• Unifying Decoherence and Phase Evolution in Mixed Quantum-Classical Dynamics through Exact Factorization
• On the Geometric Potential and the Relationship between the Exact Electron Factorization and Density Functional Theory
• Energy density and stress fields in quantum systems
• Introducing Time-dependent Molecular Fields: Derivation of the Wave Equations
• On the breakdown of the Born-Oppenheimer approximation in LiH and LiD