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On the termination of the X‐ray constrained wavefunction procedure: reformulation of the method for an unequivocal determination of λ
Ist Teil von
Acta crystallographica. Section A, Foundations and advances, 2022-07, Vol.78 (4), p.302-308
Ort / Verlag
5 Abbey Square, Chester, Cheshire CH1 2HU, England: International Union of Crystallography
Erscheinungsjahr
2022
Link zum Volltext
Quelle
Wiley Online Library - AutoHoldings Journals
Beschreibungen/Notizen
The X‐ray constrained/restrained wavefunction (XCW/XRW) approach of quantum crystallography is revisited by introducing the stationary condition of the Jayatilaka functional with respect to the Lagrange multiplier λ. The theoretical derivation has unequivocally shown that the right value of λ is a maximum stationary point of the functional to optimize, thus enabling the solution of the longstanding problem of establishing the point at which to halt the XCW/XRW procedure. Based on the new finding, a reformulation of the X‐ray constrained wavefunction algorithm is proposed and its implementation is envisaged. In addition to relying on more solid mathematical grounds, the new variant of the method will be intrinsically more physically meaningful, allowing a straightforward evaluation of the highest level of confidence with which the experimental X‐ray diffraction data can be possibly reproduced.
The longstanding problem of determining the correct point at which to stop the calculations in the X‐ray constrained wavefunction (XCW) approach is formally solved on solid mathematical grounds, and a new and more physically meaningful variant of the XCW method is proposed.