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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

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S2053273314019652/td5019sup1.cif
Contains datablock I

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S2053273314019652/td5019Isup2.hkl
Contains datablock I

pdf

Portable Document Format (PDF) file https://doi.org/10.1107/S2053273314019652/td5019sup3.pdf
Additional experimental details, plots of electron densities and their Laplacians, charges and dipoles in tabular form, electrostatic potentials, and residual density analysis of ELMO and XC-ELMO densities

txt

Text file https://doi.org/10.1107/S2053273314019652/td5019sup4.txt
Example of an ELMO input file

txt

Text file https://doi.org/10.1107/S2053273314019652/td5019sup5.txt
Example of an ELMO output file

pdf

Portable Document Format (PDF) file https://doi.org/10.1107/S2053273314019652/td5019sup6.pdf
Notes on ELMO inputs and outputs

cml

Chemical Markup Language (CML) file https://doi.org/10.1107/S2053273314019652/td5019Isup7.cml
Supplementary material

CCDC reference: 1022150

Computing details top

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
C4H8N2O3F(000) = 280
Mr = 132.12Dx = 1.549 Mg m3
Monoclinic, P21/cMo Kα radiation, λ = 0.7107 Å
Hall symbol: -P 2ybcCell parameters from 18946 reflections
a = 7.9798 (1) Åθ = 2.7–52.4°
b = 9.5201 (1) ŵ = 0.13 mm1
c = 7.7643 (1) ÅT = 100 K
β = 106.151 (1)°Prism, colorless
V = 566.56 (1) Å30.20 × 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 Source5262 reflections with I > 2σ(I)
Mirror monochromatorRint = 0.029
Detector resolution: 16.0965 pixels mm-1θmax = 52.6°, θmin = 2.1°
ω scansh = 1717
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 = 2121
Tmin = 0.974, Tmax = 0.991l = 1717
38933 measured reflections
Refinement top
Refinement on F2Secondary atom site location: difference Fourier map
Least-squares matrix: fullHydrogen site location: inferred from neighbouring sites
R[F2 > 2σ(F2)] = 0.017H 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 reflectionsΔρmax = 0.14 e Å3
271 parametersΔρmin = 0.14 e Å3
0 restraintsExtinction 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 methodsExtinction coefficient: 0.315 (15)
Crystal data top
C4H8N2O3V = 566.56 (1) Å3
Mr = 132.12Z = 4
Monoclinic, P21/cMo Kα radiation
a = 7.9798 (1) ŵ = 0.13 mm1
b = 9.5201 (1) ÅT = 100 K
c = 7.7643 (1) Å0.20 × 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 = 0.991Rint = 0.029
38933 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0170 restraints
wR(F2) = 0.034H atoms treated by a mixture of independent and constrained refinement
S = 0.80Δρmax = 0.14 e Å3
5467 reflectionsΔρmin = 0.14 e Å3
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
xyzUiso*/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
U11U22U33U12U13U23
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)0.0221390.0129090.0272410.0010340.0058790.00234
H(2)0.0175710.0257620.01770.0013740.0027320.003858
H(3)0.0222540.0315270.0173830.0017010.0083460.00548
H(4)0.0240920.0393830.0164360.0055770.0051070.000438
H(5)0.0280250.0142280.0333150.0017710.0014190.002627
H(6)0.0264080.0115440.0259260.0008770.0026590.001579
H(7)0.0209470.0365230.0291840.0059440.0034840.011311
H(8)0.031350.0204890.0289640.0045080.0007880.007698
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···AD—HH···AD···AD—H···A
N1—H1···O2i1.01 (2)1.86 (2)2.7819 (3)150 (1)
N1—H2···O3ii0.98 (2)1.77 (2)2.7285 (3)162 (1)
N1—H3···O2iii1.01 (2)1.83 (2)2.7400 (3)148 (1)
N2—H6···O1iv0.99 (2)1.98 (2)2.9295 (3)158 (1)
C1—H4···O1v1.09 (2)2.29 (2)3.3167 (3)156 (1)
C1—H5···O1iv1.07 (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, y1/2, z+3/2; (v) x, y+1/2, z+1/2.

Experimental details

Crystal data
Chemical formulaC4H8N2O3
Mr132.12
Crystal system, space groupMonoclinic, P21/c
Temperature (K)100
a, b, c (Å)7.9798 (1), 9.5201 (1), 7.7643 (1)
β (°) 106.151 (1)
V3)566.56 (1)
Z4
Radiation typeMo Kα
µ (mm1)0.13
Crystal size (mm)0.20 × 0.17 × 0.07
Data collection
DiffractometerSuperNova, Single source at offset, Eos
diffractometer
Absorption correctionAnalytical
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, Tmax0.974, 0.991
No. of measured, independent and
observed [I > 2σ(I)] reflections
38933, 6597, 5262
Rint0.029
(sin θ/λ)max1)1.118
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.017, 0.034, 0.80
No. of reflections5467
No. of parameters271
H-atom treatmentH atoms treated by a mixture of independent and constrained refinement
Δρmax, Δρmin (e Å3)0.14, 0.14

Computer programs: CrysAlis PRO, Agilent Technologies, Version 1.171.36.28 (release 01-02-2013 CrysAlis171 .NET) (compiled Feb 1 2013,16:14:44), SHELXS86 (Sheldrick, 1986), Volkov et al., (2006).

Selected 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···AD—HH···AD···AD—H···A
N1—H1···O2i1.01 (2)1.86 (2)2.7819 (3)150.0 (3)
N1—H2···O3ii0.98 (2)1.77 (2)2.7285 (3)162.3 (7)
N1—H3···O2iii1.01 (2)1.83 (2)2.7400 (3)147.6 (8)
N2—H6···O1iv0.99 (2)1.98 (2)2.9295 (3)158.1 (7)
C1—H4···O1v1.09 (2)2.29 (2)3.3167 (3)156.1 (6)
C1—H5···O1iv1.07 (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, y1/2, z+3/2; (v) x, y+1/2, z+1/2.
 

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