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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.

Supporting information


Crystallographic Information File (CIF)
Contains datablocks global, I


Structure factor file (CIF format)
Contains datablock I


Portable Document Format (PDF) file
Additional tables and figures

CCDC reference: 2091337

Computing details top

Data collection: MXC(MAC Science) and a program IUANGLE by Tanaka for avoidance of multiple diffraction (Tanaka, K.,Kumazawa S., Tsubokawa, M., Maruno, S. & Shirotani, I. (Acta Cryst. A50, 246-252 (1994)); cell refinement: RSLC-3 UNICS system (Sakurai, T. & Kobayashi, K. (1979), Rep. Inst. Phys. Chem. Res. 55, 69-77); data reduction: RDEDIT (K. Tanaka); program(s) used to refine structure: QNTMO (Tanaka, K. (2018). Acta Cryst. A74, 345-356..

diformohydrazide top
Crystal data top
C2H4N2O2F(000) = 92.
Mr = 88.07Dx = 1.631 Mg m3
Monoclinic, P21/aMo Kα radiation, λ = 0.71073 Å
a = 8.9520 (13) ÅCell parameters from 24 reflections
b = 6.1946 (5) Åθ = 48.3–73.7°
c = 3.4927 (5) ŵ = 0.14 mm1
β = 112.1902 (2)°T = 100 K
V = 179.34 (5) Å3Sphere, colorless
Z = 20.08 mm (radius)
Data collection top
4692 independent reflections
Radiation source: fine-focus rotating anode3036 reflections with F > 3.0σ(F)
Graphite monochromatorRint = 0.015
Detector resolution: 1.25x1.25 degrees pixels mm-1θmax = 73.7°, θmin = 4.1°
integrated intensities data from ω/2θ scansh = 2422
Absorption correction: for a spherek = 1616
Tmin = 0.984, Tmax = 1.000l = 58
5510 measured reflections
Refinement top
Refinement on FWeighting scheme based on measured s.u.'s w = 1/u(F)
Least-squares matrix: full(Δ/σ)max = 7.53
R[F2 > 2σ(F2)] = 0.012Δρmax = 0.13 e Å3
2423 reflectionsΔρmin = 0.12 e Å3
842 parametersExtinction correction: B-C type 2 Gaussian anisotropic
All H-atom parameters refined
Special details top

Experimental. The crystal was shaped into a sphere of the averaged radius of 0.0793 mm by rolling it manually on a wet filter paper. The difference between the longest and the shortest diameters is less than 4 % of the longest one, which can be neglected since the linear absorption coefficient m=0.1355 mm-1 is small.

Refinement. Molecular orbitals were refined & determined by the XMO analysis. (K. Tanaka, Acta Cryst.(2018). A74, 345-356.) Among 788 MO coefficients, 692 of them are larger than their e.s.d.'s, 637 of which have shift/su < 1.0 and mean value of shift/su is 0.49. The largest shift/su = 7.53 listed below is the ratio of significant MO coefficient a14,106 = -0.124 (4) with shift = -0.031. When the max of the shift/su is limited to those of atomic parameters, scales and extinction parameters, the largest one is 1.11 for the extinction parameter G22. When only G22 is refined, the ratio and its e.s.d. are reduced to 0.666 and 75, respectively, though this is not a valid refinement defined in the above paper. For G22, see the second parameter below.

B-C anisotropic type 2 extinction parameters

B-C anisotropic extinction parameters are as follows 572 (15) 1252 (119) 833 (40) 0(21) -596 (16) 123 (41)

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
C0.13861 (1)0.21801 (2)0.10724 (4)0.00974 (2)
N0.00322 (1)0.10457 (2)0.06478 (4)0.00939 (2)
O0.261973 (8)0.14612 (1)0.38059 (3)0.01222 (2)
HC0.1300 (3)0.3720 (3)0.0122 (6)0.032 (1)
HN0.0993 (4)0.1660 (6)0.2918 (1)0.013 (1)
Atomic displacement parameters (Å2) top
C0.00820 (2)0.00811 (2)0.01056 (3)0.00093 (3)0.00088 (2)0.00008 (2)
N0.00714 (2)0.00858 (2)0.00985 (3)0.00029 (2)0.00027 (2)0.00046 (3)
O0.00844 (2)0.01056 (2)0.01325 (3)0.00102 (2)0.00092 (2)0.00073 (3)
HC0.029 (1)0.024 (2)0.037 (1)0.006 (1)0.0048 (9)0.005 (1)
HN0.010 (2)0.007 (2)0.015 (2)0.002 (1)0.003 (1)0.003 (1)
Geometric parameters (Å, º) top
C—N1.3318 (1)C—HC1.032 (2)
C—O1.2381 (1)N—HN1.033 (3)
Ni—N1.3806 (2)HN—Oi2.369 (3)
HN···Oii1.770 (3)N···Oii2.764 (1)
O—C—N123.562 (8)N—C—HC112.9 (1)
C—N—Ni119.388 (9)C—N—HN123.1 (2)
O—C—HC123.6 (1)Ni—N—HN117.5 (2)
Symmetry codes: (i) x, y, z; (ii) x1/2, y+1/2, z1.
Hydrogen-bond geometry (Å, º) top
N—HN···Oii1.033 (3)1.770 (3)2.764 (1)160.4 (3)
Symmetry code: (ii) x1/2, y+1/2, z1.

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