X‐ray molecular orbital analysis. I. Quantum mechanical and crystallographic framework

• Published in: Acta crystallographica. Section A, Foundations and advances Vol. 74; no. 4; pp. 345 - 356
• Main Author: Tanaka, Kiyoaki
• Format: Journal Article
• Language: English
• Published: 5 Abbey Square, Chester, Cheshire CH1 2HU, England International Union of Crystallography 01.07.2018
• Subjects: least‐squares method; molecular orbitals; X‐ray molecular orbital analysis (XMO); least-squares method; molecular orbitals; X-ray molecular orbital analysis (XMO)
• ISSN: 2053-2733; 2053-2733
• DOI: 10.1107/S2053273318005478

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. Molecular orbitals of an organic compound were successfully obtained by X‐ray molecular orbital analysis. The quantum‐mechanical and crystallographic framework of the method is described.