Apax: A Flexible and Performant Framework for the Development of Machine-Learned Interatomic Potentials
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An atomic orbital represents the three-dimensional regions in an atom where an electron has the highest probability to reside. The radial distribution function indicates the total probability of finding an electron within the thin shell at a distance r from the nucleus. The atomic orbitals have distinct shapes which are determined by l, the angular momentum quantum number. The orbitals are often drawn with a boundary surface, enclosing densest regions of the cloud.
The angular momentum...
VSEPR Theory for Determination of Electron Pair Geometries
The following procedure uses VSEPR theory to determine the electron pair geometries and the molecular structures:
Write the Lewis structure of the molecule or polyatomic ion.
Count the number of electron groups (lone pairs and bonds) around the central atom. A single, double, or triple bond counts as one region of electron density.
Identify the electron-pair geometry based on the number of electron groups: linear, trigonal planar,...
An atom comprises protons and neutrons, which are contained inside the dense, central core called the nucleus, with electrons present around the nucleus. Taking into account the wave–particle duality of electrons and the uncertainty in position around the nucleus, quantum mechanics provides a more accurate model for the atomic structure. It describes atomic orbitals as the regions around the nucleus where electrons of discrete energy exist, characterized by four quantum...
Thermodynamic potentials are state functions that are extremely useful in analyzing a thermodynamic system. They have dimensions of energy. The four important thermodynamic potentials are internal energy, enthalpy, Helmholtz free energy, and Gibbs free energy. These thermodynamic potentials can be expressed using two of the following variables: pressure, volume, temperature, and entropy. These two variables are expressed as the rate of change of the thermodynamic potential with respect to other...
Force can be calculated from the expression for potential energy, which is a function of position. The component of a conservative force, in a particular direction, equals the negative of the derivative of the corresponding potential energy with respect to the displacement in that direction. For regions where potential energy changes rapidly with displacement, the work done and force is maximum. Also, when force is applied along the positive coordinate axis, the potential energy decreases with...
Overview of Molecular Orbital Theory
Molecular orbital theory describes the distribution of electrons in molecules in the same way as the distribution of electrons in atoms is described using atomic orbitals. Quantum mechanics describes the behavior of an electron in a molecule by a wave function, Ψ, analogous to the behavior in an atom. Just like electrons around isolated atoms, electrons around atoms in molecules are limited to discrete (quantized) energies. The region of space in which...

