Tanaka Kiyoaki, Wasada-Tsutsui Yuko
Research Division, Nagoya Industrial Science Research Institute, Yotsuya tori 1-13, Chikusa-ku/Nagoya, 464-0819, Japan.
Department of Life Science and Applied Chemistry, Nagoya Institute of Technology, Gokiso-cho/shouwa-ku/Nagoya, 466-8555, Japan.
Acta Crystallogr A Found Adv. 2021 Nov 1;77(Pt 6):593-610. doi: 10.1107/S2053273321006495. Epub 2021 Oct 4.
The molecular orbitals (MOs) of diformohydrazide have been determined from the electron density measured by X-ray diffraction. The experimental and refinement procedures are explained in detail and the validity of the obtained MOs is assessed from the crystallographic point of view. The X-ray structure factors were measured at 100 K by a four-circle diffractometer avoiding multiple diffraction, the effect of which on the structure factors is comparable to two-centre structure factors. There remained no significant peaks on the residual density map and the R factors reduced significantly. Among the 788 MO coefficients, 731 converged, of which 694 were statistically significant. The C-H and N-H bond distances are 1.032 (2) and 1.033 (3) Å, respectively. The electron densities of theoretical and experimental MOs and the differences between them are illustrated. The overall features of the electron density obtained by X-ray molecular orbital (XMO) analysis are in good agreement with the canonical orbitals calculated by the restricted Hartree Fock (RHF) method. The bonding-electron distribution around the middle of each bond is well represented and the relative phase relationships of the π orbitals are reflected clearly in the electron densities on the plane perpendicular to the molecular plane. However, differences are noticeable around the O atom on the molecular plane. The orbital energies obtained by XMO analysis are about 0.3 a.u. higher than the corresponding canonical orbitals, except for MO10 to MO14 which are about 0.7 a.u. higher. These exceptions are attributed to the N-H...O'' intermolecular hydrogen bond, which is neglected in the MO models of the present study. The hydrogen bond is supported by significant electron densities at the saddle points between the H(N) and O'' atoms in MO7, 8, 14 and 17, and by that of O''-p extended over H(N) in MO21 and 22, while no peaks were found in MO10, 11, 13 and 15. The electron density of each MO clearly exhibits its role in the molecule. Consequently, the MOs obtained by XMO analysis give a fundamental quantum mechanical insight into the real properties of molecules.
已通过X射线衍射测量的电子密度确定了二甲酰肼的分子轨道（MOs）。详细解释了实验和精修过程，并从晶体学角度评估了所得分子轨道的有效性。通过四圆衍射仪在100 K下测量X射线结构因子，避免了多重衍射，其对结构因子的影响与双中心结构因子相当。残余密度图上没有明显的峰，R因子显著降低。在788个MO系数中，731个收敛，其中694个具有统计学意义。C-H和N-H键长分别为1.032(2) Å和1.033(3) Å。说明了理论和实验分子轨道的电子密度及其之间的差异。通过X射线分子轨道（XMO）分析获得的电子密度的总体特征与通过受限Hartree Fock（RHF）方法计算的正则轨道非常吻合。每个键中间周围的成键电子分布得到了很好的体现，并且π轨道的相对相位关系在垂直于分子平面的平面上的电子密度中清晰地反映出来。然而，在分子平面上的O原子周围差异明显。通过XMO分析获得的轨道能量比相应的正则轨道高约0.3 a.u.，除了MO10至MO14高约0.7 a.u.。这些例外归因于N-H...O''分子间氢键，在本研究的MO模型中被忽略。在MO7、8、14和17中，H(N)和O''原子之间的鞍点处有显著的电子密度支持氢键，在MO21和22中，O''-p延伸到H(N)上也有电子密度支持氢键，而在MO10、11、13和15中未发现峰。每个分子轨道的电子密度清楚地显示了其在分子中的作用。因此，通过XMO分析获得的分子轨道为分子的真实性质提供了基本的量子力学见解。
