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X‐ray molecular orbital analysis. I. Quantum mechanical and crystallographic framework
Author(s) -
Tanaka Kiyoaki
Publication year - 2018
Publication title -
acta crystallographica section a
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.742
H-Index - 83
ISSN - 2053-2733
DOI - 10.1107/s2053273318005478
Subject(s) - molecular orbital , atomic orbital , diffraction , crystallography , electron density , atom (system on chip) , orthonormal basis , chemistry , molecular physics , gaussian , ab initio , materials science , computational chemistry , electron , molecule , physics , optics , quantum mechanics , organic chemistry , computer science , embedded system
Molecular orbitals were obtained by X‐ray molecular orbital analysis (XMO). The initial molecular orbitals (MOs) of the refinement were calculated by the ab initio self‐consistent field (SCF) MO method. Well tempered basis functions were selected since they do not produce cusps at the atomic positions on the residual density maps. X‐ray structure factors calculated from the MOs were fitted to observed structure factors by the least‐squares method, keeping the orthonormal relationship between MOs. However, the MO coefficients correlate severely with each other, since basis functions are composed of similar Gaussian‐type orbitals. Therefore, a method of selecting variables which do not correlate severely with each other in the least‐squares refinement was devised. MOs were refined together with the other crystallographic parameters, although the refinement with the atomic positional parameters requires a lot of calculation time. The XMO method was applied to diformohydrazide, (NHCHO) 2 , without using polarization functions, and the electron‐density distributions, including the maxima on the covalent bonds, were represented well. Therefore, from the viewpoint of X‐ray diffraction, it is concluded that the MOs averaged by thermal vibrations of the atoms were obtained successfully by XMO analysis. The method of XMO analysis, combined with X‐ray atomic orbital (AO) analysis, in principle enables one to obtain MOs or AOs without phase factors from X‐ray diffraction experiments on most compounds from organic to rare earth compounds.