Are you an EPFL student looking for a semester project?
Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.
Concept
Hartree atomic units
Summary
The Hartree atomic units are a system of natural units of measurement which is especially convenient for calculations in atomic physics and related scientific fields, such as computational chemistry and atomic spectroscopy. They are named after the physicist Douglas Hartree.
Atomic units are often abbreviated "a.u." or "au", not to be confused with the same abbreviation used also for astronomical units, arbitrary units, and absorbance units in other contexts.
By definition, each of the following four fundamental physical constants is expressed as the numeric value 1 multiplied by a coherent unit of this system:
Each unit in this system can be expressed as a product of powers of these four physical constants without a numerical multiplier. This makes it a coherent system of units, as well as making the numerical values of the defining constants in atomic units equal to unity.
Three of the defining constants (reduced Planck constant, elementary charge, and electron rest mass) are atomic units themselves – of action, electric charge, and mass, respectively. The two most important derived units are those of length (Bohr radius ) and energy (hartree ). The table below lists these and many other units that can be derived in the system.
Here,
is the speed of light
is the vacuum permittivity
is the Rydberg constant
is the Planck constant
is the fine-structure constant
is the Bohr magneton
≘ denotes correspondence between quantities since equality does not apply.
Atomic units, like SI units, have a unit of mass, a unit of length, and so on. However, the use and notation is somewhat different from SI.
Suppose a particle with a mass of m has 3.4 times the mass of electron. The value of m can be written in three ways:
"". This is the clearest notation (but least common), where the atomic unit is included explicitly as a symbol.
"" ("a.u." means "expressed in atomic units"). This notation is ambiguous: Here, it means that the mass m is 3.4 times the atomic unit of mass. But if a length L were 3.
Official source
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Ontological neighbourhood
Related courses (32)
MICRO-428: Metrology
The course deals with the concept of measuring in different domains, particularly in the electrical, optical, and microscale domains. The course will end with a perspective on quantum measurements, wh
ME-454: Modelling and optimization of energy systems
The goal of the lecture is to present and apply techniques for the modelling and the thermo-economic optimisation of industrial process and energy systems. The lecture covers the problem statement, th
PHYS-101(l): General physics : mechanics (flipped classroom)
Le but du cours de physique générale est de donner à l'étudiant les notions de base nécessaires à la compréhension des phénomènes physiques. L'objectif est atteint lorsque l'étudiant est capable de pr
Related lectures (56)
Energy Conservation in Fluid Flows
Explores energy conservation in fluid flows, emphasizing practical applications and the importance of fundamental physics laws.
Perturbation Theory and Variational Principle
Covers perturbation theory, variational principle, and systematic approaches to determining true energy levels.
Revision of the SI: International System of Units
Explores the revision of the International System of Units, focusing on the kilogram, ampere, kelvin, and mole, and the impact on scientific measurements.
Related publications (37)
Flux correlators and semiclassics
Riccardo Rattazzi, Alexander Monin, Eren Clément Firat, Matthew Thomas Walters
We consider correlators for the flux of energy and charge in the background of operators with large global U(1) charge in conformal field theory (CFT). It has recently been shown that the corresponding Euclidean correlators generically admit a semiclassica ...
Springer2024Advances in Magnetics Roadmap on Spin-Wave Computing
Qian Wang, Yiming Li, Dirk Grundler, Xiuwei Zhang
Magnonics addresses the physical properties of spin waves and utilizes them for data processing. Scalability down to atomic dimensions, operation in the GHz-to-THz frequency range, utilization of nonlinear and nonreciprocal phenomena, and compatibility wit ...
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2022Variability and reproducibility of multi-echo T2 relaxometry: Insights from multi-site, multi-session and multi-subject MRI acquisitions
Jean-Philippe Thiran, Friedhelm Christoph Hummel, Tobias Kober, Tom Hilbert, Erick Jorge Canales Rodriguez, Gabriel Girard, Elda Fischi Gomez, Marco Pizzolato, Gian Franco Piredda, Thomas Yu, Takuya Morishita, Elena Beanato, Alessandro Daducci, Maximilian Jonas Wessel, Chang-Hyun Park, Philipp Johannes Koch, Andéol Geoffroy Cadic-Melchior, Julia Brügger
Quantitative magnetic resonance imaging (qMRI) can increase the specificity and sensitivity of conventional weighted MRI to underlying pathology by comparing meaningful physical or chemical parameters, measured in physical units, with normative values acqu ...
2022Related concepts (16)
Gaussian units
Gaussian units constitute a metric system of physical units. This system is the most common of the several electromagnetic unit systems based on cgs (centimetre–gram–second) units. It is also called the Gaussian unit system, Gaussian-cgs units, or often just cgs units. The term "cgs units" is ambiguous and therefore to be avoided if possible: there are several variants of cgs with conflicting definitions of electromagnetic quantities and units. SI units predominate in most fields, and continue to increase in popularity at the expense of Gaussian units.
System of units of measurement
A system of units of measurement, also known as a system of units or system of measurement, is a collection of units of measurement and rules relating them to each other. Systems of measurement have historically been important, regulated and defined for the purposes of science and commerce. Instances in use include the International System of Units or () (the modern form of the metric system), the British imperial system, and the United States customary system.
Hartree
The hartree (symbol: Eh or Ha), also known as the Hartree energy, is the unit of energy in the Hartree atomic units system, named after the British physicist Douglas Hartree. Its CODATA recommended value is = The hartree energy is approximately the electric potential energy of the hydrogen atom in its ground state and, by the virial theorem, approximately twice its ionization energy; the relationships are not exact because of the finite mass of the nucleus of the hydrogen atom and relativistic corrections.
Related MOOCs (3)
The Radio Sky I: Science and Observations
Be captivated by the exotic objects that populate the Radio Sky and gain a solid understanding of their physics and the fundamental techniques we use to observe them.
Synchrotrons and X-Ray Free Electron Lasers (part 1)
Synchrotrons and X-Ray Free Electron Lasers (part 1)
Synchrotrons and X-Ray Free Electron Lasers (part 2)
The first MOOC to provide an extensive introduction to synchrotron and XFEL facilities and associated techniques and applications.