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Atomic spacing refers to the distance between the nuclei of atoms in a material. This space is extremely large compared to the size of the atomic nucleus, and is related to the chemical bonds which bind atoms together. [1] In solid materials, the atomic spacing is described by the bond lengths of its atoms.
The simplest descriptor is the set of interatomic distances from atom to its neighbours, yielding a machine-learned pair potential. However, more complex many-body descriptors are needed to produce highly accurate potentials. [ 55 ]
where () is the interatomic potential between atom i and atom j, and are the charges magnitudes, is the distance between atoms, and , and are constant parameters based on the type of atoms. [ 5 ] The BKS potential parameters for common atoms are shown below: [ 5 ]
The peaks' positions in the Patterson function are the interatomic distance vectors and the peak heights are proportional to the product of the number of electrons in the atoms concerned. Because for each vector between atoms i and j there is an oppositely oriented vector of the same length (between atoms j and i ), the Patterson function ...
For individual atoms, the equilibrium distance is between 0.3 nm and 0.5 nm, depending on the atomic-specific diameter. [7] When the interatomic distance is greater than 1.0 nm the force is not strong enough to be easily observed as it decreases as a function of distance r approximately with the 7th power (~r −7). [8]
Note: All measurements given are in picometers (pm). For more recent data on covalent radii see Covalent radius.Just as atomic units are given in terms of the atomic mass unit (approximately the proton mass), the physically appropriate unit of length here is the Bohr radius, which is the radius of a hydrogen atom.
Shorter than average C–C bond distances are also possible: alkenes and alkynes have bond lengths of respectively 133 and 120 pm due to increased s-character of the sigma bond. In benzene all bonds have the same length: 139 pm. Carbon–carbon single bonds increased s-character is also notable in the central bond of diacetylene (137 pm) and ...
The idea of relating exchange energy to inter-atomic distance was first proposed by John C. Slater in 1930, [2] [3] and illustrated as a curve on a graph in a review by Sommerfeld and Bethe in 1933. [4] For a pair of atoms, the exchange interaction w ij (responsible for the energy E) is calculated as: [5]