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
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).
Crystal data top
N_{2}H_{4}C_{2}O_{2} | F(000) = 88 |
M_{r} = 88.07 | D_{x} = 1.631 Mg m^{−}^{3} |
Monoclinic, P2_{1}/a(originatthecenterofN¯Nbond) | Mo Kα radiation, λ = 0.71073 Å |
a = 8.9520 (13) Å | Cell parameters from 24 reflections |
b = 6.1946 (5) Å | θ = 35.8–39.3° |
c = 3.4927 (5) Å | µ = 0.14 mm^{−}^{1} |
β = 112.19 (1)° | T = 100 K |
V = 179.3 (1) Å^{3} | Sphere, transparent |
Z = 2 | 0.08 mm (radius) |
Data collection top
Four-circle diffractometer | 2423 independent reflections |
Radiation source: fine-focus rotating anode | 3035 reflections with F > 3.0σ(F) |
Graphite monochromator | R_{int} = 0.007 |
Detector resolution: 1.25x1.25 degrees pixels mm^{-1} | θ_{max} = 74.7°, θ_{min} = 4.1° |
integrated intensities data from ω/2θ scans | h = −24→23 |
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 = −16→16 |
T_{min} = 0.984, T_{max} = 1.000 | l = −5→8 |
4692 measured reflections | |
Refinement top
Refinement on F | Primary atom site location: other |
Least-squares matrix: full | Secondary atom site location: other |
R[F^{2} > 2σ(F^{2})] = 0.013 | All H-atom parameters refined |
S = 0.83 | Weighting scheme based on measured s.u.'s |
2423 reflections | (Δ/σ)_{max} = 1.98 |
842 parameters | Δρ_{max} = 0.002 e Å^{−}^{3} |
0 restraints | Δρ_{min} = −0.08 e Å^{−}^{3} |
0 constraints | Extinction 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 (Å^{2}) top | x | y | z | B_{iso}*/B_{eq} | |
C | 0.13860 (1) | 0.21802 (1) | 0.10721 (6) | | |
N | 0.00323 (2) | 0.10455 (2) | −0.06475 (6) | | |
O | 0.26198 (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 (Å^{2}) top | U^{11} | U^{22} | U^{33} | U^{12} | U^{13} | U^{23} |
C | 0.00812 (3) | 0.00804 (6) | 0.01054 (15) | −0.00093 (2) | 0.00084 (3) | −0.00005 (5) |
N | 0.00706 (1) | 0.00854 (4) | 0.00977 (1) | −0.00024 (4) | 0.00021 (4) | 0.00051 (12) |
O | 0.00832 (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—N^{i} | 1.3804 (2) | N—H(N) | 0.988 (5) |
N—C | 1.3318 (2) | C—H(C) | 1.033 (5) |
C—O | 1.2383 (2) | | |
| | | |
C—N—N^{ii} | 119.41 (1) | N—C—O | 123.55 (1) |
N^{ii}—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) |
| | | |
O—C—N—N^{i} | 0.31 | H(C)—C—N—N^{i} | −179.97 |
O—C—N—H(N) | 179.86 | H(C)—C—N—H(N) | −0.42 |
C^{i}—N^{i}—N—H(N) | 0.43 | | |
Symmetry codes: (i) −x, −y, −z; (ii) x+1/2, −y+1/2, z. |
Hydrogen-bond geometry (Å, º) top
D—H···A | D—H | H···A | D···A | D—H···A |
N—H(N)···O^{iii} | 0.988 (5) | 1.810 (5) | 2.7644 (17) | 161.4 (4) |
Symmetry code: (iii) x−1/2, −y+1/2, z−1. |