Unconstrained and X-ray constrained extremely localized molecular orbitals: analysis of the reconstructed electron density

Dos Santos, L.H.R.; Genoni, A.; Macchi, P.

doi:10.1107/S2053273314019652

Unconstrained and X-ray constrained extremely localized molecular orbitals: analysis of the reconstructed electron density

L. H. R. Dos Santos, A. Genoni and P. Macchi

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.

Keywords: X-ray constrained wavefunction; extremely localized molecular orbital; high-resolution X-ray diffraction; glycylglycine.

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Supporting information

	Crystallographic Information File (CIF) https://doi.org/10.1107/S2053273314019652/td5019sup1.cif Contains datablock I
	Structure factor file (CIF format) https://doi.org/10.1107/S2053273314019652/td5019Isup2.hkl Contains datablock I
	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
	Text file https://doi.org/10.1107/S2053273314019652/td5019sup4.txt Example of an ELMO input file
	Text file https://doi.org/10.1107/S2053273314019652/td5019sup5.txt Example of an ELMO output file
	Portable Document Format (PDF) file https://doi.org/10.1107/S2053273314019652/td5019sup6.pdf Notes on ELMO inputs and outputs
	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

C₄H₈N₂O₃	F(000) = 280
M_r = 132.12	D_x = 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	R_int = 0.029
Detector resolution: 16.0965 pixels mm^-1	θ_max = 52.6°, θ_min = 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
T_min = 0.974, T_max = 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(F_o²)]
S = 0.80	(Δ/σ)_max = 0.00001
5467 reflections	Δρ_max = 0.14 e Å⁻³
271 parameters	Δρ_min = −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
M_r = 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)
T_min = 0.974, T_max = 0.991	R_int = 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	Δρ_max = 0.14 e Å⁻³
5467 reflections	Δρ_min = −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	U_iso*/U_eq
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···O1^iv	0.99 (2)	1.98 (2)	2.9295 (3)	158 (1)
C1—H4···O1^v	1.09 (2)	2.29 (2)	3.3167 (3)	156 (1)
C1—H5···O1^iv	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
M_r	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)
T_min, T_max	0.974, 0.991
No. of measured, independent and observed [I > 2σ(I)] reflections	38933, 6597, 5262
R_int	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
Δρ_max, Δρ_min (e Å⁻³)	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···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···O1^iv	0.99 (2)	1.98 (2)	2.9295 (3)	158.1 (7)
C1—H4···O1^v	1.09 (2)	2.29 (2)	3.3167 (3)	156.1 (6)
C1—H5···O1^iv	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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