Table of bond lengths in chemical molecules
Tables show length of chemical bonds in selected molecules.

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Some facts#

  • When we say about bond length in the molecule we get in mind the distance between atomic nuclei.
  • In real world, distance beetwen atoms are not constant, because atoms in mocelules are in constant motion. Effectively bonds are in longer-shorter cycle, oscillating around some particular length.
  • In general, the length of the bonds is a property of a whole molecule. It means, that the distance between the same pair of atoms (e.g., C-H) may vary depending on which compound we are dealing with.
  • Experimental methods that allow to study the bond lengths in molecules include:
    • X-ray diffraction of solids - uses X-ray diffraction during contact with the electron cloud, allows to experimentally determine the structure (geometry) of solids (crystals),
    • low-energy electron diffraction (LEED) - is a bombardment of the crystal surface (solid body) with a beam of low energy electrons (20-200 eV) and observation of their diffraction on a fluorescent screen,
    • spectroscopic methods - measuring the absorbance (degree of absorption) of electromagnetic waves at a fixed frequency during contact with the test substance.
  • The lengths of bonds can also be determined theoretically by quantum chemistry methods. These calculations consist in finding the position of atomic nuclei for which potential energy of the whole molecule reaches the minimum. Such a procedure is called geometry optimization.
  • Mathematical optimization of geometry is searching for the minimum of many variables function:
    E=f(R1,R2,R3,...)E = f(\vec{R1}, \vec{R2}, \vec{R3}, ...)
    where:
    • E - energy of a molecule at a given position of atomic nuclei,
    • Ri\vec{R_i} - position of i-th atom.
  • The quality of results obtained during geometry optimization depends on the method of calculating energy in given point. The methods currently used during routine calculations are:
    • Hertree-Fock based - solving the Schroedinger equation using a variation method with a test function in the form of one Slater determinant,
    • density functional theory (DFT).

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