# On factorization of molecular wavefunctions

@article{Jecko2015OnFO, title={On factorization of molecular wavefunctions}, author={Thierry Jecko and Brian T Sutcliffe and R Guy Woolley}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2015}, volume={48} }

Recently there has been a renewed interest in the chemical physics literature of factorization of the position representation eigenfunctions {Φ} of the molecular Schrödinger equation as originally proposed by Hunter in the 1970s. The idea is to represent Φ in the form φχ where χ is purely a function of the nuclear coordinates, while φ must depend on both electron and nuclear position variables in the problem. This is a generalization of the approximate factorization originally proposed by Born…

## 10 Citations

### Corrigendum: On factorization of molecular wavefunctions (2015 J. Phys. A.: Math. Theor. 48 445201)

- Physics
- 2018

Recently there has been a renewed interest in the chemical physics literature of factorization of the position representation eigenfunctions { Φ } of the molecular Schrödinger equation as originally…

### On the numerical solution of the exact factorization equations.

- PhysicsThe Journal of chemical physics
- 2019

A first demonstration of a self-consistent solution of the exact equations is provided, with a preliminary analysis of their stability and convergence properties, that enables stable propagation long enough to witness non-adiabatic behavior in a model system before non-trivial instabilities take over.

### When the exact factorization meets conical intersections...

- PhysicsThe European Physical Journal B
- 2018

Abstract
Capturing nuclear dynamics through conical intersections is pivotal to understand the fate of photoexcited molecules. The concept of a conical intersection, however, belongs to a specific…

### Coupled-Trajectory Mixed Quantum-Classical Algorithm: A Deconstruction.

- PhysicsJournal of chemical theory and computation
- 2018

While the coupled-trajectory term in the electronic equation is essential in yielding accurate dynamics, that in the nuclear equation has a much smaller effect, and a decoherence time is extracted from the electronic equations and compared with that of augmented fewest-switches surface-hopping.

### An exact factorization perspective on quantum interferences in nonadiabatic dynamics.

- PhysicsThe Journal of chemical physics
- 2016

This work analyzes how nonadiabatic quantum interferences translate in the context of the exact factorization of the molecular wavefunction, and focuses on the shape of the time-dependent potential energy surface-the exact surface on which the nuclear dynamics takes place.

### Characterization of the continuous transition from atomic to molecular shape in the three-body Coulomb system

- PhysicsPhysical Review A
- 2022

We present an alternative, univocal characterization of the continuous transition from atomic to molecular shape in the Coulomb system constituted by two identical particles and a third particle with…

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

- PhysicsPhysical Review A
- 2018

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…

### Non-Born–Oppenheimer electron, nuclear and nuclear–electron second-order density matrices for exactly solvable four-particle model system

- PhysicsTheoretical Chemistry Accounts
- 2016

AbstractProperties of the non-Born–Oppenheimer two-matrix are examined for four-particle systems of the Coulomb–Hooke and Moshinsky types. We obtain for both these models explicit closed-form…

### Treating nuclei in molecules with quantum mechanical respect

- PhysicsTheoretical Chemistry Accounts
- 2021

An examination is made of how nuclear motion ought to be considered in solutions to the eigenvalue problem for the full Coulomb Hamiltonian and the role played by the usual clamped-nuclei electronic…

## References

SHOWING 1-10 OF 30 REFERENCES

### Correlated electron-nuclear dynamics: exact factorization of the molecular wavefunction.

- PhysicsThe Journal of chemical physics
- 2012

A one-dimensional model of the H(2)(+) molecule in a laser field shows the usefulness of the exact TDPES in interpreting coupled electron-nuclear dynamics: it is shown how features of its structure indicate the mechanism of dissociation.

### Spectral Properties of Atomic and Molecular Systems

- Mathematics
- 1980

These first two chapters are intended to give a survey of presently known methods and results in N-body Schrodinger operator theory with applications to the specific situation where interactions are…

### The exact molecular wavefunction as a product of an electronic and a nuclear wavefunction.

- Physics, ChemistryThe Journal of chemical physics
- 2013

A variational principle is introduced which shows explicitly that the exact total wavefunction can be exactly written as a product of an electronic and a nuclear wavefunction.

### Electronic non-adiabatic states: towards a density functional theory beyond the Born–Oppenheimer approximation

- PhysicsPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2014

A novel treatment of non-adiabatic couplings is proposed, based on a theorem by Hunter stating that the wave function of the complete system of electrons and nuclei can be written as a Born–Oppenheimer (BO)-type product of a nuclear wave function and an electronic one, ΦR(r), which depends parametrically on the nuclear configuration R.

### Molecular structure calculations without clamping the nuclei.

- PhysicsPhysical chemistry chemical physics : PCCP
- 2005

To what extent the very idea of molecular structure might be dependent upon treating the nuclei simply as providing a potential and the extent to which the work of Born and Oppenheimer can be used to support this position is discussed.

### On the quantum theory of molecules.

- Chemistry, PhysicsThe Journal of chemical physics
- 2012

It is suggested that the potential energy surface construction is more appropriately regarded as a legitimate and effective modification of quantum mechanics for chemical purposes.

### The quantum N-body problem

- Physics
- 2000

This selective review is written as an introduction to the mathematical theory of the Schrodinger equation for N particles. Characteristic for these systems are the cluster properties of the…

### Nodeless wave functions and spiky potentials

- Physics
- 1981

The exact (nonadiabatic) nuclear and electronic factors of a molecular wave function are expanded in the basis of eigenfunctions of the electronic Hamiltonian according to the Rayleigh–Schrodinger…

### A New Proof of the Analyticity of the Electronic Density of Molecules

- Mathematics
- 2010

We give a new proof of the regularity away from the nuclei of the electronic density of a molecule obtained by Fournais et al. (Commun. Math. Phys. 228(3):401–415, 2002; Ark. Math. 42(1):87–106,…

### Exact factorization of the time-dependent electron-nuclear wave function.

- PhysicsPhysical review letters
- 2010

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.