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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.

Supporting information


Crystallographic Information File (CIF)
Contains datablock global

Computing details top

Data collection: MXC (MAC Science) and a program IUANGLE by Tanaka (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 (K. Tanaka, 2018).

diformohydrazide top
Crystal data top
N2H4C2O2F(000) = 88
Mr = 88.07Dx = 1.631 Mg m3
Monoclinic, P21/a(originatthecenterofN¯Nbond)Mo Kα radiation, λ = 0.71073 Å
a = 8.9520 (13) ÅCell parameters from 24 reflections
b = 6.1946 (5) Åθ = 35.8–39.3°
c = 3.4927 (5) ŵ = 0.14 mm1
β = 112.19 (1)°T = 100 K
V = 179.3 (1) Å3Sphere, transparent
Z = 20.08 mm (radius)
Data collection top
2423 independent reflections
Radiation source: fine-focus rotating anode3035 reflections with F > 3.0σ(F)
Graphite monochromatorRint = 0.007
Detector resolution: 1.25x1.25 degrees pixels mm-1θmax = 74.7°, θmin = 4.1°
integrated intensities data from ω/2θ scansh = 2423
Absorption correction: for a sphere
Transmission cefficient for spheres tabulated in International Table II(1972) Table 5.3.6B was interpolated with Lagrange's method (four point interpolation)
k = 1616
Tmin = 0.984, Tmax = 1.000l = 58
4692 measured reflections
Refinement top
Refinement on FPrimary atom site location: other
Least-squares matrix: fullSecondary atom site location: other
R[F2 > 2σ(F2)] = 0.013All H-atom parameters refined
S = 0.83Weighting scheme based on measured s.u.'s
2423 reflections(Δ/σ)max = 1.98
842 parametersΔρmax = 0.002 e Å3
0 restraintsΔρmin = 0.08 e Å3
0 constraintsExtinction correction: B-C type 2 Gaussian anisotropic
Special details top

Refinement. Molecular orbitals were determined with a newly devised least-squares method. B-C anisotropic type2 extinction parameters B-C anisoropic extinction parameters will be published seperately, since the refinement is not completed yet. (But the residual density has been cleaned satisfactirily.)

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
C0.13860 (1)0.21802 (1)0.10721 (6)
N0.00323 (2)0.10455 (2)0.06475 (6)
O0.26198 (1)0.14612 (3)0.38062 (2)
H(N)0.0944 (7)0.1643 (9)0.2824 (15)
H(C)0.1298 (5)0.3720 (9)0.0129 (7)
Atomic displacement parameters (Å2) top
C0.00812 (3)0.00804 (6)0.01054 (15)0.00093 (2)0.00084 (3)0.00005 (5)
N0.00706 (1)0.00854 (4)0.00977 (1)0.00024 (4)0.00021 (4)0.00051 (12)
O0.00832 (4)0.01041 (3)0.01331 (9)0.00108 (4)0.00105 (1)0.00065 (5)
H(N)0.0162 (16)0.010 (4)0.0213 (10)0.0001 (8)0.0007 (19)0.006 (2)
H(C)0.0341 (9)0.0215 (11)0.038 (3)0.005 (2)0.0084 (18)0.007 (2)
Geometric parameters (Å, º) top
N—Ni1.3804 (2)N—H(N)0.988 (5)
N—C1.3318 (2)C—H(C)1.033 (5)
C—O1.2383 (2)
C—N—Nii119.41 (1)N—C—O123.55 (1)
Nii—N—H(N)118.0 (3)N—C—H(C)112.8 (3)
C—N—H(N)122.6 (3)O—C—H(C)123.7 (3)
Symmetry codes: (i) x, y, z; (ii) x+1/2, y+1/2, z.
Hydrogen-bond geometry (Å, º) top
N—H(N)···Oiii0.988 (5)1.810 (5)2.7644 (17)161.4 (4)
Symmetry code: (iii) x1/2, y+1/2, z1.

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