Open AccessAnharmonic temperature factors: the limitations of perturbation theory expressions. Erratum
Author(s) -
Mackenzie J. K.,
Mair S. L.
Publication year - 1985
Publication title -
acta crystallographica section a
Language(s) - English
Resource type - Journals
eISSN - 1600-5724
pISSN - 0108-7673
DOI - 10.1107/s0108767385000654
Subject(s) - anharmonicity , perturbation (astronomy) , perturbation theory (quantum mechanics) , mathematical physics , physics , mathematics , theoretical physics , statistical physics , quantum mechanics
The error in the temperature factor arising from the use of anharmonic perturbation theory is investigated for a one-dimensional one-particle potential by comparison with an exact evaluation of the Fourier transform of the Boltzmann probability density. Results are presented for a range of values of cubic and quartic coefficients for temperature factors derived from moment or cumulant expansions about the harmonic probability density function. It is found that either expansion provides an adequate approximation to the anharmonic temperature factor for moderately small anharmonicity but that both expansions become increasingly Inadequate as the anharmonicity gets larger.