Hans-Beat Burgi tribute
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.
Keywords: X-ray constrained wavefunction; Hirshfeld atom; halting problem; X-ray wavefunction refinement; α-oxalic acid dihydrate.
Supporting information
Crystallographic Information File (CIF) https://doi.org/10.1107/S2052520622004103/so5075sup1.cif | |
Structure factor file (CIF format) https://doi.org/10.1107/S2052520622004103/so5075Isup2.hkl | |
Portable Document Format (PDF) file https://doi.org/10.1107/S2052520622004103/so5075sup3.pdf | |
Zip compressed file https://doi.org/10.1107/S2052520622004103/so5075sup4.zip |
CCDC reference: 2144303
Computing details top
(I) top
Crystal data top
C2H2O4·2(H2O) | c = 11.8409 (7) Å |
Mr = 126.07 | β = 103.842 (2)° |
Monoclinic, p121/c1 | V = 244.63 (3) Å3 |
Hall symbol: -p 2ybc | Z = 2 |
a = 6.0931 (4) Å | T = 100 K |
b = 3.4921 (2) Å |
Data collection top
29251 independent reflections | k = → |
29251 reflections with F > 0 and F/u(F) > 4.0 and |F_calc| > 10−3 | l = → |
h = → |
Refinement top
Refinement on F | 0 constraints |
Least-squares matrix: full | Hydrogen site location: HAR |
R[F2 > 2σ(F2)] = 0.018 | All H-atom parameters refined |
wR(F2) = 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 top
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 (Å2) top
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 (Å2) top
U11 | U22 | U33 | U12 | U13 | U23 | |
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) top
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) |