Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Time-dependent Hartree Approximation and Ehrenfest Dynamics

In course

CH-453: Molecular quantum dynamics

The course covers several exact, approximate, and numerical methods to solve the time-dependent molecular Schrödinger equation, and applications including calculations of molecular electronic spectra. More advanced topics include introduction to the semicl ...

Description

This lecture covers the principles of the time-dependent Hartree approximation (TDHA) and its application in the Toupe principle. It also discusses the mean-field and single-particle approximations, as well as the concept of gauge conditions and the initial conditions for the system. The lecture further explores the Ehrenfest dynamics, focusing on the mixed quantum-classical dynamics and the molecular time-dependent Schrödinger equation. Various alternative parametrizations and propositions related to the TDHA are presented, along with the concept of mean-field Hamiltonians and energy conservation. The lecture concludes with an examination of the Ehrenfest theorem and its implications in molecular dynamics.

Instructor

Jiri Vanicek

Official source

Related concepts (32)

Molecular dynamics

Molecular dynamics (MD) is a computer simulation method for analyzing the physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a fixed period of time, giving a view of the dynamic "evolution" of the system. In the most common version, the trajectories of atoms and molecules are determined by numerically solving Newton's equations of motion for a system of interacting particles, where forces between the particles and their potential energies are often calculated using interatomic potentials or molecular mechanical force fields.

Computational chemistry

Computational chemistry is a branch of chemistry that uses computer simulation to assist in solving chemical problems. It uses methods of theoretical chemistry, incorporated into computer programs, to calculate the structures and properties of molecules, groups of molecules, and solids. It is essential because, apart from relatively recent results concerning the hydrogen molecular ion (dihydrogen cation, see references therein for more details), the quantum many-body problem cannot be solved analytically, much less in closed form.

Ehrenfest theorem

The Ehrenfest theorem, named after Austrian theoretical physicist Paul Ehrenfest, relates the time derivative of the expectation values of the position and momentum operators x and p to the expectation value of the force on a massive particle moving in a scalar potential , The Ehrenfest theorem is a special case of a more general relation between the expectation of any quantum mechanical operator and the expectation of the commutator of that operator with the Hamiltonian of the system where A is some quantu

Density functional theory

Density-functional theory (DFT) is a computational quantum mechanical modelling method used in physics, chemistry and materials science to investigate the electronic structure (or nuclear structure) (principally the ground state) of many-body systems, in particular atoms, molecules, and the condensed phases. Using this theory, the properties of a many-electron system can be determined by using functionals, i.e. functions of another function. In the case of DFT, these are functionals of the spatially dependent electron density.

École Polytechnique Fédérale de Lausanne

The École polytechnique fédérale de Lausanne (EPFL; English: Swiss Federal Institute of Technology in Lausanne; Eidgenössische Technische Hochschule Lausanne) is a public research university in Lausanne, Switzerland. Established in 1853, EPFL has placed itself as a university specializing in engineering and natural sciences. EPFL is part of the ETH Domain, which is directly dependent on the Federal Department of Economic Affairs, Education and Research.

Related lectures (32)

Car-Parrinello molecular dynamics

Explores Car-Parrinello molecular dynamics, a unified approach combining molecular dynamics and density-functional theory for simulating various systems, with a focus on historical background, technical details, and challenges in atomistic simulations.

Quantum to Classical Mechanics: MD & MC Simulations

Covers Molecular Dynamics and Monte Carlo Simulations, transitioning from Quantum to Classical Mechanics in computational chemistry.

QM/MM Hybrid Methods

Explores the integration of quantum mechanics and molecular mechanics in computational chemistry using CP2K software.

Quantum Chemistry Fundamentals

Introduces the fundamentals of quantum chemistry, including Hartree-Fock wavefunctions and density functional theory.

Molecular Dynamics Simulations