Can the interaction density be measured? The example of the non-standard amino acid sarcosine

The experimental charge density ρ(r) of the non-standard amino acid sarcosine has been determined based on an extensive and complete data set measured at 100 K to high resolution (sin θ/λ = 1.18 Å⁻¹) by single-crystal X-ray diffraction. Anisotropic thermal motion of the H atoms, obtained from TLS + ONIOM cluster methods, was included in the structural model. Based on the multipole-model geometry, the theoretical Hartree–Fock interaction density of a molecule in the crystal has been calculated with CRYSTAL98. It manifests itself in local rearrangements of ρ(r) and can be reproduced with a multipole projection via simulated structure factors. An attempt has also been made to obtain the interaction density from a combination of experimental and theoretical charge densities using either a whole-molecular calculation or the invariom database. Agreement with the periodic Hartree–Fock interaction density is qualitative. It is shown that invarioms reproduce the features of the theoretical multipole-projected whole-molecular electron density, and can be used to approximate it.

Computing details

Program(s) used to refine structure: Koritsanszky et al., (2003); molecular graphics: Koritsanszky et al., (2003); software used to prepare material for publication: Koritsanszky et al., (2003).

Figures

(sarcosine)

Crystal data

C3H7NO2	F(000) = 192.0
Mr = 89.10	Dx = 1.309 Mg m^−3
Orthorhombic, P212121	? radiation, λ = 0.71073 Å
Hall symbol: P 2ac 2ab	Cell parameters from 48765 reflections
a = 6.6558 (1) Å	θ = 3.1–57.2°
b = 7.8903 (1) Å	µ = 0.11 mm^−1
c = 8.6069 (1) Å	T = 100 K
V = 452.01 (1) Å^3	Tetrahedron, colorless
Z = 4.0	0.48 × 0.39 × 0.32 mm

Data collection

Oxford Diffraction Xcalibur S diffractometer	2927 reflections with F > 2.5u(σ)F
ω scans	Rint = 0.027
Absorption correction: analytical CrysAlis RED, Oxford Diffraction Ltd., Version 1.171.31.7 (release 18-10-2006 CrysAlis171 .NET) 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)	θmax = 57.8°, θmin = 3.1°
Tmin = 0.969, Tmax = 0.977	h = −15→15
78770 measured reflections	k = −18→18
3555 independent reflections	l = −20→20

Refinement

Refinement on F	0 restraints
Least-squares matrix: full	All H-atom parameters refined
R[F^2 > 2σ(F^2)] = 0.017	w1 = 1/[s^2(Fo)]
wR(F^2) = 0.010	(Δ/σ)max < 0.001
S = 1.71	Δρmax = 0.17 e Å^−3
2927 reflections	Δρmin = −0.16 e Å^−3
156 parameters

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
O(1)	0.77985 (3)	0.18119 (2)	0.17238 (2)	0.014
O(2)	0.76653 (3)	−0.09296 (2)	0.23721 (2)	0.018
N(1)	1.01610 (3)	−0.06195 (2)	0.47965 (2)	0.01
C(1)	0.82272 (3)	0.05492 (3)	0.25761 (2)	0.011
C(2)	0.95498 (3)	0.09441 (3)	0.39760 (2)	0.011
C(3)	1.18181 (4)	−0.03359 (3)	0.59155 (3)	0.017
H(1)	1.0576 (7)	−0.1511 (6)	0.4049 (6)	0.024
H(2)	0.8981 (8)	−0.1059 (6)	0.5387 (6)	0.033
H(3)	1.0843 (8)	0.1638 (6)	0.3583 (6)	0.032
H(4)	0.8722 (8)	0.1719 (6)	0.4761 (6)	0.031
H(5)	1.3186 (8)	0.0054 (7)	0.5326 (7)	0.042
H(6)	1.2092 (8)	−0.1506 (7)	0.6522 (6)	0.037
H(7)	1.1388 (8)	0.0621 (8)	0.6749 (7)	0.045
DUM1	1.08006	0.05094	0.49785	0	0

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
O(1)	0.01736 (7)	0.01148 (6)	0.01315 (6)	−0.00181 (6)	−0.00362 (6)	0.00387 (5)
O(2)	0.02510 (9)	0.00983 (5)	0.01828 (8)	−0.00150 (6)	−0.00887 (7)	0.00061 (6)
N(1)	0.01281 (7)	0.00894 (6)	0.00962 (6)	0.00028 (5)	−0.00115 (5)	0.00007 (5)
C(1)	0.01345 (7)	0.00932 (6)	0.01003 (7)	0.00016 (6)	−0.00089 (6)	0.00104 (6)
C(2)	0.01473 (8)	0.00944 (7)	0.00987 (7)	−0.00042 (6)	−0.00099 (6)	0.00017 (6)
C(3)	0.01940 (10)	0.01370 (10)	0.01760 (10)	0.00030 (10)	−0.00720 (10)	−0.00010 (10)
H(1)	0.028 (2)	0.02	0.025	0.007	0	−0.006
H(2)	0.040 (3)	0.02	0.039	−0.003	0.008	0.005
H(3)	0.035 (3)	0.029	0.032	−0.007	−0.004	0.013
H(4)	0.048 (3)	0.022	0.023	0.011	0	−0.004
H(5)	0.021 (3)	0.051	0.054	−0.016	−0.003	−0.001
H(6)	0.037 (3)	0.033	0.04	0.007	−0.018	0.012
H(7)	0.051 (3)	0.046	0.038	0.015	−0.018	−0.025

Geometric parameters (Å, º)

O(1)—C(1)	1.2697 (3)	C(2)—H(3)	1.075 (5)
O(2)—C(1)	1.2378 (3)	C(2)—H(4)	1.065 (5)
N(1)—H(1)	0.993 (5)	C(3)—H(5)	1.087 (5)
N(1)—H(2)	0.997 (5)	C(3)—H(6)	1.077 (5)
C(1)—C(2)	1.5244 (3)	C(3)—H(7)	1.080 (6)
H(1)—N(1)—H(2)	107.6 (4)	C(1)—C(2)—H(4)	108.7 (3)
O(1)—C(1)—O(2)	126.14 (2)	H(3)—C(2)—H(4)	108.8 (4)
O(1)—C(1)—C(2)	115.215 (18)	H(5)—C(3)—H(6)	109.1 (4)
O(2)—C(1)—C(2)	118.640 (19)	H(5)—C(3)—H(7)	109.5 (4)
C(1)—C(2)—H(3)	108.5 (3)	H(6)—C(3)—H(7)	108.8 (4)