X-ray constrained wavefunctions based on Hirshfeld atoms. II. Reproducibility of electron densities in crystals of α-oxalic acid dihydrate

The Hirshfeld atom-based X-ray constrained wavefunction fitting (HA-XCW) procedure is tested for its reproducibility, and the information content of the fitted wavefunction is critically assessed. Fourteen different α-oxalic acid dihydrate data sets are used for this purpose, and the first joint fitting to 12 of these data sets is reported. There are systematic features in the electron density obtained from all data sets which agree with higher level benchmark calculations, but there are also many other strong systematic features which disagree with the reference calculations, most notably those associated with the electron density near the nuclei. To enhance reproducibility, three new protocols are described and tested to address the halting problem of XCW fitting, namely: an empirical power-function method, which is useful for estimating the accuracy of the structure factor uncertainties; an asymptotic extrapolation method based on ideas from density functional theory; and a `conservative method' whereby the smallest value of the regularization parameter is chosen from a series of data sets, or subsets.

Computing details

(I)

Crystal data

C2H2O4·2(H2O)	c = 11.8409 (7) Å
Mr = 126.07	β = 103.842 (2)°
Monoclinic, p121/c1	V = 244.63 (3) Å^3
Hall symbol: -p 2ybc	Z = 2
a = 6.0931 (4) Å	T = 100 K
b = 3.4921 (2) Å

Data collection

29251 independent reflections	k = →
29251 reflections with F > 0 and F/u(F) > 4.0 and |F_calc| > 10^−3	l = →
h = →

Refinement

Refinement on F	0 constraints
Least-squares matrix: full	Hydrogen site location: HAR
R[F^2 > 2σ(F^2)] = 0.018	All H-atom parameters refined
wR(F^2) = 0.023	Weighting scheme based on measured s.u.'s w = 1/σ(F)
S = 1.34	(Δ/σ)max = 0.008
29251 reflections	Δρmax = 0.10 e Å^−3
75 parameters	Δρmin = −0.16 e Å^−3
0 restraints

Special details

Refinement. . If constraints were applied they are defined by zero eigenvalues of the least-squares hessian, see the value of _refine_ls_SVD_threshold

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

	x	y	z	Uiso*/Ueq
O1	0.434843 (6)	0.444113 (11)	0.349875 (3)	0.013296 (12)
O2	0.242444 (6)	0.742551 (11)	0.463699 (3)	0.013083 (12)
C1	0.403061 (6)	0.558829 (11)	0.448007 (3)	0.009745 (12)
H1	0.3003 (4)	0.5213 (6)	0.27715 (18)	0.0221 (10)
O5	0.130058 (6)	0.631165 (11)	0.178524 (3)	0.012943 (12)
H3	0.1903 (3)	0.6987 (6)	0.11297 (17)	0.0303 (10)
H4	0.0062 (3)	0.4561 (6)	0.14983 (16)	0.0280 (10)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
O1	0.012827 (11)	0.018637 (14)	0.008030 (11)	0.004463 (9)	0.001718 (8)	−0.000636 (9)
O2	0.011235 (11)	0.018065 (13)	0.009269 (12)	0.005241 (9)	0.001111 (8)	−0.000655 (9)
C1	0.009367 (11)	0.011626 (13)	0.007895 (12)	0.001769 (8)	0.001381 (9)	−0.000076 (9)
H1	0.0233 (9)	0.0277 (11)	0.0181 (12)	−0.0011 (9)	0.0105 (8)	−0.0038 (10)
O5	0.010789 (11)	0.017895 (14)	0.009309 (11)	−0.001605 (9)	0.000757 (8)	0.000995 (9)
H3	0.0253 (9)	0.0318 (10)	0.0324 (11)	0.0000 (8)	0.0039 (7)	0.0058 (9)
H4	0.0258 (8)	0.0304 (10)	0.0272 (10)	0.0009 (8)	0.0052 (7)	0.0008 (8)

Geometric parameters (Å, º)

O1—C1	1.2868 (1)	O5—H3	0.964 (2)
O2—C1	1.2210 (1)	O5—H4	0.9676 (18)
O1—H1	1.072 (2)
O1—C1—O2	126.887 (4)	H3—O5—H4	106.70 (15)
C1—O1—H1	113.32 (10)
O2—C1—O1—H1	−1.02 (13)