Relativistic quantum crystallography of diphenyl- and dicyanomercury. Theoretical structure factors and Hirshfeld atom refinement

Quantum crystallographic refinement of heavy-element-containing compounds is a challenge, because many physical effects have to be accounted for adequately. Here, the impact and magnitude of relativistic effects are compared with those of electron correlation, polarization through the environment, choice of basis set and treatment of thermal motion effects on the structure factors of diphenylmercury(II) [Hg(Ph)₂] and dicyanomercury(II) [Hg(CN)₂]. Furthermore, the individual atomic contributions to the structure factors are explored in detail (using Mulliken population analysis and the exponential decay of atomic displacement parameters) to compare the contributions of lighter atoms, especially hydrogen atoms, against mercury. Subsequently, relativistic Hirshfeld atom refinement (HAR) is validated against theoretical structure factors of Hg(Ph)₂ and Hg(CN)₂, starting from perturbed geometries, to test if the relativistic variant of HAR leads to multiple solutions. Generally, relativistic HAR is successful, leading to a perfect match with the reference geometries, but some limitations are pointed out.

Computing details

(I)

Crystal data

C12H10Hg	V = 479.32 (1) Å^3
Mr = 354.80	Z = 2.0
Monoclinic, p121/n1	Dx = 2.458 Mg m^−3
Hall symbol: -p 2yn	Cell parameters from 1098 reflections
a = 5.622200 (1) Å	θ = 0.01–1.1°
b = 8.091200 (1) Å	µ = 0.0 mm^−1
c = 10.585200 (1) Å	T = 298 K
β = 95.485000 (1)°	This is a theoertical study, not applicable

Data collection

This is a theoertical study diffractometer	Rint = 0.1
1098 measured reflections	h = →
1098 independent reflections	k = →
1098 reflections with F > 0 & |F_calc| > 10^−3	l = ^→

Refinement

Least-squares matrix: full	3 constraints
R[F^2 > 2σ(F^2)] = 0.0000	Hydrogen site location: HAR
wR(F^2) = 0.0000	All H-atom parameters refined
S = 0.001	Weighting scheme based on measured s.u.'s w = 1/σ(F)
1098 reflections	(Δ/σ)max = 0.004
105 parameters	Δρmax = 0.001 e Å^−3
0 restraints	Δρmin = −0.001 e Å^−3

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
Hg	0.500000 (1)	0.500000 (1)	0.500000 (1)	0.018600 (1)
C1	0.771100 (1)	0.620800 (1)	0.414600 (1)	0.019599 (1)
C2	0.916700 (1)	0.739700 (1)	0.477900 (1)	0.019233 (1)
C3	1.104700 (1)	0.812600 (1)	0.423300 (1)	0.019133 (1)
C4	1.153200 (1)	0.768400 (1)	0.300300 (1)	0.018666 (1)
C5	1.009200 (1)	0.651600 (1)	0.235500 (1)	0.020466 (1)
C6	0.820600 (1)	0.577900 (1)	0.291700 (1)	0.021200 (1)
H1	0.885901 (3)	0.771901 (2)	0.561099 (1)	0.022999 (9)
H2	1.201200 (2)	0.892800 (2)	0.469300 (1)	0.022998 (10)
H3	1.282297 (2)	0.817500 (2)	0.262300 (1)	0.021997 (10)
H4	1.038799 (2)	0.621101 (2)	0.151801 (1)	0.023998 (10)
H5	0.724601 (3)	0.497401 (2)	0.245700 (2)	0.025999 (11)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Hg	0.016917 (1)	0.017900 (1)	0.022300 (1)	0.000629 (1)	0.008701 (1)	0.004500 (1)
C1	0.016192 (1)	0.018599 (1)	0.024700 (1)	0.004825 (1)	0.005547 (1)	0.005701 (1)
C2	0.024037 (1)	0.017200 (1)	0.017399 (1)	0.003053 (1)	0.006840 (1)	0.000700 (1)
C3	0.018120 (1)	0.017300 (1)	0.022500 (1)	−0.002806 (1)	0.004639 (1)	−0.000200 (1)
C4	0.017779 (1)	0.018899 (1)	0.019800 (1)	0.001667 (1)	0.004282 (1)	0.003900 (1)
C5	0.023844 (1)	0.023000 (1)	0.015399 (1)	0.001594 (1)	0.006250 (1)	0.002100 (1)
C6	0.021936 (1)	0.019000 (1)	0.022999 (1)	−0.001531 (1)	0.003891 (1)	−0.000400 (1)
H1	0.022996 (9)	0.023000 (11)	0.023002 (9)	0.000000 (8)	0.002199 (7)	0.000009 (8)
H2	0.022996 (10)	0.023000 (12)	0.022996 (9)	0.000003 (8)	0.002197 (7)	−0.000001 (8)
H3	0.021998 (10)	0.021993 (11)	0.021999 (9)	−0.000001 (7)	0.002096 (7)	0.000005 (7)
H4	0.023999 (9)	0.024002 (11)	0.023993 (9)	−0.000004 (8)	0.002291 (7)	0.000001 (8)
H5	0.025999 (11)	0.026002 (12)	0.025997 (10)	0.000009 (7)	0.002486 (8)	0.000000 (7)

Geometric parameters (Å, º)

Hg—C1	2.0878 (1)	C5—C6	1.3980 (1)
C1—C2	1.3927 (1)	C2—H1	0.9501 (1)
C1—C6	1.3998 (1)	C3—H2	0.9498 (1)
C2—C3	1.3842 (1)	C4—H3	0.9499 (1)
C3—C4	1.4019 (1)	C5—H4	0.9496 (1)
C4—C5	1.3831 (1)	C6—H5	0.9500 (1)
Hg—C1—C2	122.3378 (1)	C1—C6—H5	119.5175 (10)
Hg—C1—C6	120.2986 (1)	C2—C3—H2	119.9129 (9)
C1—C2—C3	122.0489 (1)	C3—C2—H1	118.9665 (9)
C1—C6—C5	121.0603 (2)	C3—C4—H3	120.7257 (9)
C2—C1—C6	117.2881 (1)	C4—C3—H2	119.8780 (9)
C2—C3—C4	120.2091 (2)	C4—C5—H4	119.5912 (9)
C3—C4—C5	118.5752 (1)	C5—C4—H3	120.6990 (8)
C4—C5—C6	120.8144 (1)	C5—C6—H5	119.4221 (10)
C1—C2—H1	118.9845 (9)	C6—C5—H4	119.5945 (9)