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The recently developed X-ray constrained extremely localized molecular orbital (XC-ELMO) technique is a potentially useful tool for the determination and analysis of experimental electron densities. Molecular orbitals strictly localized on atoms, bonds or functional groups allow one to combine the quantum-mechanical rigour of the wavefunction-based approaches with the easy chemical interpretability typical of the traditional multipole models. In this paper, using very high quality X-ray diffraction data for the glycylglycine crystal, a detailed assessment of the capabilities and limitations of this new method is given. In particular, the effects of constraining the ELMO wavefunctions to experimental X-ray structure-factor amplitudes and the ability of the method to reproduce benchmark electron distributions have been accurately investigated. Topological analysis of the XC-ELMO electron densities and of the zero-flux surface-integrated charges and dipole moments shows that the new strategy is already reliable, provided that sufficiently flexible basis sets are used. These analyses also raise new questions and call for further improvements of the method.
Supporting information
CCDC reference: 1022150
Data collection: CrysAlis PRO, Agilent Technologies,
Version 1.171.36.28 (release 01-02-2013 CrysAlis171 .NET)
(compiled Feb 1 2013,16:14:44); cell refinement: CrysAlis PRO, Agilent Technologies,
Version 1.171.36.28 (release 01-02-2013 CrysAlis171 .NET)
(compiled Feb 1 2013,16:14:44); data reduction: CrysAlis PRO, Agilent Technologies,
Version 1.171.36.28 (release 01-02-2013 CrysAlis171 .NET)
(compiled Feb 1 2013,16:14:44); program(s) used to solve structure: SHELXS86 (Sheldrick, 1986); program(s) used to refine structure: Volkov et al., (2006); molecular graphics: Volkov et al., (2006); software used to prepare material for publication: Volkov et al., (2006).
2-[(2-Aminoacetyl)amino]acetic acid
top
Crystal data top
C4H8N2O3 | F(000) = 280 |
Mr = 132.12 | Dx = 1.549 Mg m−3 |
Monoclinic, P21/c | Mo Kα radiation, λ = 0.7107 Å |
Hall symbol: -P 2ybc | Cell parameters from 18946 reflections |
a = 7.9798 (1) Å | θ = 2.7–52.4° |
b = 9.5201 (1) Å | µ = 0.13 mm−1 |
c = 7.7643 (1) Å | T = 100 K |
β = 106.151 (1)° | Prism, colorless |
V = 566.56 (1) Å3 | 0.20 × 0.17 × 0.07 mm |
Z = 4 | |
Data collection top
SuperNova, Single source at offset, Eos diffractometer | 6597 independent reflections |
Radiation source: SuperNova (Mo) X-ray Source | 5262 reflections with I > 2σ(I) |
Mirror monochromator | Rint = 0.029 |
Detector resolution: 16.0965 pixels mm-1 | θmax = 52.6°, θmin = 2.1° |
ω scans | h = −17→17 |
Absorption correction: analytical CrysAlis PRO, Agilent Technologies,
Version 1.171.36.28 (release 01-02-2013 CrysAlis171 .NET)
(compiled Feb 1 2013,16:14:44)
Analytical numeric absorption correction using a multifaceted crystal
model based on expressions derived by R.C. Clark & J.S. Reid.
(Clark, R. C. & Reid, J. S. (1995). Acta Cryst. A51, 887-897) | k = −21→21 |
Tmin = 0.974, Tmax = 0.991 | l = −17→17 |
38933 measured reflections | |
Refinement top
Refinement on F2 | Secondary atom site location: difference Fourier map |
Least-squares matrix: full | Hydrogen site location: inferred from neighbouring sites |
R[F2 > 2σ(F2)] = 0.017 | H atoms treated by a mixture of independent and constrained refinement |
wR(F2) = 0.034 | w2 = 1/[s2(Fo2)] |
S = 0.80 | (Δ/σ)max = 0.00001 |
5467 reflections | Δρmax = 0.14 e Å−3 |
271 parameters | Δρmin = −0.14 e Å−3 |
0 restraints | Extinction correction: Becker-Coppens type 1 Lorentzian isotropic, Becker, P.J. & Coppens, P. (1974) Acta Cryst., A30, 129-153. |
Primary atom site location: structure-invariant direct methods | Extinction coefficient: 0.315 (15) |
Crystal data top
C4H8N2O3 | V = 566.56 (1) Å3 |
Mr = 132.12 | Z = 4 |
Monoclinic, P21/c | Mo Kα radiation |
a = 7.9798 (1) Å | µ = 0.13 mm−1 |
b = 9.5201 (1) Å | T = 100 K |
c = 7.7643 (1) Å | 0.20 × 0.17 × 0.07 mm |
β = 106.151 (1)° | |
Data collection top
SuperNova, Single source at offset, Eos diffractometer | 6597 independent reflections |
Absorption correction: analytical CrysAlis PRO, Agilent Technologies,
Version 1.171.36.28 (release 01-02-2013 CrysAlis171 .NET)
(compiled Feb 1 2013,16:14:44)
Analytical numeric absorption correction using a multifaceted crystal
model based on expressions derived by R.C. Clark & J.S. Reid.
(Clark, R. C. & Reid, J. S. (1995). Acta Cryst. A51, 887-897) | 5262 reflections with I > 2σ(I) |
Tmin = 0.974, Tmax = 0.991 | Rint = 0.029 |
38933 measured reflections | |
Refinement top
R[F2 > 2σ(F2)] = 0.017 | 0 restraints |
wR(F2) = 0.034 | H atoms treated by a mixture of independent and constrained refinement |
S = 0.80 | Δρmax = 0.14 e Å−3 |
5467 reflections | Δρmin = −0.14 e Å−3 |
271 parameters | |
Special details top
Geometry. Bond distances, angles etc. have been calculated using the rounded
fractional coordinates. All su's are estimated from the variances of the
(full) variance-covariance matrix. The cell e.s.d.'s are taken into account in
the estimation of distances, angles and torsion angles |
Refinement. Refinement of F2 against F2 > 1.5σ(F2) reflections.
The weighted R-factor wR and goodness of fit S are based
on F2, conventional R-factors R are based on F,
with F set to zero for negative F2. R-factors based on
F2 are statistically about twice as large as those based on F,
and R- factors based on ALL data will be even larger. |
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top | x | y | z | Uiso*/Ueq | |
O(1) | 0.52239 (2) | 0.29943 (2) | 0.74308 (2) | 0.012 | |
O(2) | 0.17454 (2) | −0.073257 (19) | 0.41074 (2) | 0.011 | |
O(3) | 0.02791 (2) | 0.10922 (2) | 0.25966 (2) | 0.014 | |
N(1) | 0.82464 (2) | 0.168100 (14) | 0.922223 (18) | 0.009 | |
N(2) | 0.383192 (19) | 0.092477 (17) | 0.662451 (19) | 0.009 | |
C(1) | 0.65709 (2) | 0.093814 (17) | 0.89735 (2) | 0.009 | |
C(2) | 0.515165 (19) | 0.170226 (16) | 0.757892 (19) | 0.008 | |
C(3) | 0.23607 (2) | 0.157412 (18) | 0.53382 (2) | 0.011 | |
C(4) | 0.138272 (19) | 0.055291 (15) | 0.390060 (19) | 0.008 | |
H(1) | 0.8104 (8) | 0.2717 (18) | 0.9394 (7) | 0.021 | |
H(2) | 0.9086 (16) | 0.1331 (8) | 1.032 (2) | 0.022 | |
H(3) | 0.8671 (10) | 0.1518 (6) | 0.813 (2) | 0.023 | |
H(4) | 0.6226 (9) | 0.0985 (6) | 1.024 (2) | 0.027 | |
H(5) | 0.6705 (7) | −0.0133 (16) | 0.8619 (9) | 0.027 | |
H(6) | 0.3905 (7) | −0.0115 (18) | 0.6656 (7) | 0.023 | |
H(7) | 0.1479 (17) | 0.1971 (9) | 0.5978 (13) | 0.030 | |
H(8) | 0.2795 (12) | 0.2382 (16) | 0.4727 (14) | 0.029 | |
Atomic displacement parameters (Å2) top | U11 | U22 | U33 | U12 | U13 | U23 |
O(1) | 0.01203 (5) | 0.00617 (5) | 0.01492 (5) | −0.00086 (4) | −0.00220 (6) | 0.00003 (4) |
O(2) | 0.01467 (5) | 0.00754 (5) | 0.00871 (4) | −0.00037 (3) | 0.00073 (4) | −0.00020 (3) |
O(3) | 0.01463 (6) | 0.01500 (6) | 0.00925 (4) | 0.00252 (4) | −0.00372 (5) | 0.00163 (4) |
N(1) | 0.00792 (4) | 0.00848 (4) | 0.00821 (4) | −0.00040 (3) | −0.00040 (3) | −0.00052 (3) |
N(2) | 0.00828 (4) | 0.00664 (5) | 0.01037 (5) | −0.00030 (3) | −0.00192 (4) | −0.00025 (3) |
C(1) | 0.00865 (5) | 0.00852 (5) | 0.00828 (5) | −0.00063 (4) | −0.00009 (4) | 0.00110 (4) |
C(2) | 0.00763 (5) | 0.00638 (5) | 0.00834 (5) | −0.00032 (3) | −0.00027 (4) | −0.00028 (3) |
C(3) | 0.00975 (5) | 0.00798 (5) | 0.01162 (5) | 0.00147 (4) | −0.00240 (5) | −0.00127 (4) |
C(4) | 0.00816 (5) | 0.00839 (5) | 0.00671 (4) | 0.00006 (4) | 0.00000 (4) | 0.00044 (4) |
H(1) | 0.022139 | 0.012909 | 0.027241 | −0.001034 | 0.005879 | −0.00234 |
H(2) | 0.017571 | 0.025762 | 0.0177 | 0.001374 | −0.002732 | 0.003858 |
H(3) | 0.022254 | 0.031527 | 0.017383 | −0.001701 | 0.008346 | −0.00548 |
H(4) | 0.024092 | 0.039383 | 0.016436 | −0.005577 | 0.005107 | 0.000438 |
H(5) | 0.028025 | 0.014228 | 0.033315 | 0.001771 | −0.001419 | −0.002627 |
H(6) | 0.026408 | 0.011544 | 0.025926 | −0.000877 | −0.002659 | 0.001579 |
H(7) | 0.020947 | 0.036523 | 0.029184 | 0.005944 | 0.003484 | −0.011311 |
H(8) | 0.03135 | 0.020489 | 0.028964 | −0.004508 | −0.000788 | 0.007698 |
Geometric parameters (Å, º) top
O(1)—C(2) | 1.2382 (3) | N(2)—H(6) | 0.992 (17) |
O(2)—C(4) | 1.2575 (2) | C(1)—C(2) | 1.5172 (2) |
O(3)—C(4) | 1.2522 (2) | C(1)—H(4) | 1.092 (18) |
N(1)—H(1) | 1.006 (18) | C(1)—H(5) | 1.070 (16) |
N(1)—H(2) | 0.985 (18) | C(3)—C(4) | 1.5217 (2) |
N(1)—H(3) | 1.006 (19) | C(3)—H(7) | 1.038 (19) |
N(2)—C(2) | 1.3311 (2) | C(3)—H(8) | 1.01 (2) |
N(2)—C(3) | 1.4511 (2) | | |
| | | |
H(1)—N(1)—H(2) | 107.0 (4) | N(2)—C(2)—C(1) | 116.653 (14) |
H(1)—N(1)—H(3) | 109.8 (4) | N(2)—C(3)—C(4) | 112.603 (13) |
H(2)—N(1)—H(3) | 111.7 (10) | N(2)—C(3)—H(7) | 110.6 (3) |
C(2)—N(2)—C(3) | 120.637 (15) | N(2)—C(3)—H(8) | 109.2 (3) |
C(2)—N(2)—H(6) | 120.6 (3) | C(4)—C(3)—H(7) | 107.8 (3) |
C(3)—N(2)—H(6) | 118.2 (3) | C(4)—C(3)—H(8) | 108.3 (3) |
C(2)—C(1)—H(4) | 107.3 (3) | H(7)—C(3)—H(8) | 108.3 (5) |
C(2)—C(1)—H(5) | 112.4 (3) | O(2)—C(4)—O(3) | 125.966 (17) |
H(4)—C(1)—H(5) | 109.8 (4) | O(2)—C(4)—C(3) | 118.376 (14) |
O(1)—C(2)—N(2) | 123.419 (16) | O(3)—C(4)—C(3) | 115.656 (15) |
O(1)—C(2)—C(1) | 119.851 (15) | | |
| | | |
C(3)—N(2)—C(2)—O(1) | −0.647 (17) | H(4)—C(1)—C(2)—O(1) | 84.8 (6) |
C(3)—N(2)—C(2)—C(1) | 176.15 (2) | H(4)—C(1)—C(2)—N(2) | −92.1 (6) |
C(2)—N(2)—C(3)—C(4) | 157.27 (2) | H(5)—C(1)—C(2)—O(1) | −154.4 (6) |
C(2)—N(2)—C(3)—H(7) | −82.1 (6) | H(5)—C(1)—C(2)—N(2) | 28.7 (6) |
C(2)—N(2)—C(3)—H(8) | 37.0 (7) | N(2)—C(3)—C(4)—O(2) | 10.551 (15) |
H(6)—N(2)—C(2)—O(1) | 171.1 (7) | N(2)—C(3)—C(4)—O(3) | −169.08 (2) |
H(6)—N(2)—C(2)—C(1) | −12.1 (7) | H(7)—C(3)—C(4)—O(2) | −111.7 (6) |
H(6)—N(2)—C(3)—C(4) | −14.6 (7) | H(7)—C(3)—C(4)—O(3) | 68.7 (6) |
H(6)—N(2)—C(3)—H(7) | 106.0 (9) | H(8)—C(3)—C(4)—O(2) | 131.4 (7) |
H(6)—N(2)—C(3)—H(8) | −134.9 (10) | H(8)—C(3)—C(4)—O(3) | −48.3 (7) |
Hydrogen-bond geometry (Å, º) top
D—H···A | D—H | H···A | D···A | D—H···A |
N1—H1···O2i | 1.01 (2) | 1.86 (2) | 2.7819 (3) | 150 (1) |
N1—H2···O3ii | 0.98 (2) | 1.77 (2) | 2.7285 (3) | 162 (1) |
N1—H3···O2iii | 1.01 (2) | 1.83 (2) | 2.7400 (3) | 148 (1) |
N2—H6···O1iv | 0.99 (2) | 1.98 (2) | 2.9295 (3) | 158 (1) |
C1—H4···O1v | 1.09 (2) | 2.29 (2) | 3.3167 (3) | 156 (1) |
C1—H5···O1iv | 1.07 (2) | 2.34 (1) | 3.1976 (3) | 135 (1) |
Symmetry codes: (i) −x+1, y+1/2, −z+3/2; (ii) x+1, y, z+1; (iii) −x+1, −y, −z+1; (iv) −x+1, y−1/2, −z+3/2; (v) x, −y+1/2, z+1/2. |
Experimental details
Crystal data |
Chemical formula | C4H8N2O3 |
Mr | 132.12 |
Crystal system, space group | Monoclinic, P21/c |
Temperature (K) | 100 |
a, b, c (Å) | 7.9798 (1), 9.5201 (1), 7.7643 (1) |
β (°) | 106.151 (1) |
V (Å3) | 566.56 (1) |
Z | 4 |
Radiation type | Mo Kα |
µ (mm−1) | 0.13 |
Crystal size (mm) | 0.20 × 0.17 × 0.07 |
|
Data collection |
Diffractometer | SuperNova, Single source at offset, Eos diffractometer |
Absorption correction | Analytical CrysAlis PRO, Agilent Technologies,
Version 1.171.36.28 (release 01-02-2013 CrysAlis171 .NET)
(compiled Feb 1 2013,16:14:44)
Analytical numeric absorption correction using a multifaceted crystal
model based on expressions derived by R.C. Clark & J.S. Reid.
(Clark, R. C. & Reid, J. S. (1995). Acta Cryst. A51, 887-897) |
Tmin, Tmax | 0.974, 0.991 |
No. of measured, independent and observed [I > 2σ(I)] reflections | 38933, 6597, 5262 |
Rint | 0.029 |
(sin θ/λ)max (Å−1) | 1.118 |
|
Refinement |
R[F2 > 2σ(F2)], wR(F2), S | 0.017, 0.034, 0.80 |
No. of reflections | 5467 |
No. of parameters | 271 |
H-atom treatment | H atoms treated by a mixture of independent and constrained refinement |
Δρmax, Δρmin (e Å−3) | 0.14, −0.14 |
Selected geometric parameters (Å, º) topO(1)—C(2) | 1.2382 (3) | N(2)—H(6) | 0.992 (17) |
O(2)—C(4) | 1.2575 (2) | C(1)—C(2) | 1.5172 (2) |
O(3)—C(4) | 1.2522 (2) | C(1)—H(4) | 1.092 (18) |
N(1)—H(1) | 1.006 (18) | C(1)—H(5) | 1.070 (16) |
N(1)—H(2) | 0.985 (18) | C(3)—C(4) | 1.5217 (2) |
N(1)—H(3) | 1.006 (19) | C(3)—H(7) | 1.038 (19) |
N(2)—C(2) | 1.3311 (2) | C(3)—H(8) | 1.01 (2) |
N(2)—C(3) | 1.4511 (2) | | |
| | | |
H(1)—N(1)—H(2) | 107.0 (4) | N(2)—C(2)—C(1) | 116.653 (14) |
H(1)—N(1)—H(3) | 109.8 (4) | N(2)—C(3)—C(4) | 112.603 (13) |
H(2)—N(1)—H(3) | 111.7 (10) | N(2)—C(3)—H(7) | 110.6 (3) |
C(2)—N(2)—C(3) | 120.637 (15) | N(2)—C(3)—H(8) | 109.2 (3) |
C(2)—N(2)—H(6) | 120.6 (3) | C(4)—C(3)—H(7) | 107.8 (3) |
C(3)—N(2)—H(6) | 118.2 (3) | C(4)—C(3)—H(8) | 108.3 (3) |
C(2)—C(1)—H(4) | 107.3 (3) | H(7)—C(3)—H(8) | 108.3 (5) |
C(2)—C(1)—H(5) | 112.4 (3) | O(2)—C(4)—O(3) | 125.966 (17) |
H(4)—C(1)—H(5) | 109.8 (4) | O(2)—C(4)—C(3) | 118.376 (14) |
O(1)—C(2)—N(2) | 123.419 (16) | O(3)—C(4)—C(3) | 115.656 (15) |
O(1)—C(2)—C(1) | 119.851 (15) | | |
| | | |
C(3)—N(2)—C(2)—O(1) | −0.647 (17) | H(4)—C(1)—C(2)—O(1) | 84.8 (6) |
C(3)—N(2)—C(2)—C(1) | 176.15 (2) | H(4)—C(1)—C(2)—N(2) | −92.1 (6) |
C(2)—N(2)—C(3)—C(4) | 157.27 (2) | H(5)—C(1)—C(2)—O(1) | −154.4 (6) |
C(2)—N(2)—C(3)—H(7) | −82.1 (6) | H(5)—C(1)—C(2)—N(2) | 28.7 (6) |
C(2)—N(2)—C(3)—H(8) | 37.0 (7) | N(2)—C(3)—C(4)—O(2) | 10.551 (15) |
H(6)—N(2)—C(2)—O(1) | 171.1 (7) | N(2)—C(3)—C(4)—O(3) | −169.08 (2) |
H(6)—N(2)—C(2)—C(1) | −12.1 (7) | H(7)—C(3)—C(4)—O(2) | −111.7 (6) |
H(6)—N(2)—C(3)—C(4) | −14.6 (7) | H(7)—C(3)—C(4)—O(3) | 68.7 (6) |
H(6)—N(2)—C(3)—H(7) | 106.0 (9) | H(8)—C(3)—C(4)—O(2) | 131.4 (7) |
H(6)—N(2)—C(3)—H(8) | −134.9 (10) | H(8)—C(3)—C(4)—O(3) | −48.3 (7) |
Hydrogen-bond geometry (Å, º) top
D—H···A | D—H | H···A | D···A | D—H···A |
N1—H1···O2i | 1.01 (2) | 1.86 (2) | 2.7819 (3) | 150.0 (3) |
N1—H2···O3ii | 0.98 (2) | 1.77 (2) | 2.7285 (3) | 162.3 (7) |
N1—H3···O2iii | 1.01 (2) | 1.83 (2) | 2.7400 (3) | 147.6 (8) |
N2—H6···O1iv | 0.99 (2) | 1.98 (2) | 2.9295 (3) | 158.1 (7) |
C1—H4···O1v | 1.09 (2) | 2.29 (2) | 3.3167 (3) | 156.1 (6) |
C1—H5···O1iv | 1.07 (2) | 2.34 (1) | 3.1976 (3) | 135.4 (7) |
Symmetry codes: (i) −x+1, y+1/2, −z+3/2; (ii) x+1, y, z+1; (iii) −x+1, −y, −z+1; (iv) −x+1, y−1/2, −z+3/2; (v) x, −y+1/2, z+1/2. |
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