New refinement strategies for a pseudoatom databank – toward rapid electrostatic interaction energy estimations

Pseudoatom databanks, collections of parameters from the multipole model of electron densities for various atom types, are used to replace the Independent Atom Model with the more accurate Transferable Aspherical Atom Model (TAAM) in crystal structure refinements. The databanks are also employed to reconstruct the electron density of a molecule, crystal or biomacromolecular complex in a fast yet accurate way and compute various properties such as the energy of electrostatic interactions, for example. A even faster but similarly accurate model for estimations of electrostatic energy exists called aug-PROmol [Bojarowski, Kumar & Dominiak (2016). ChemPhysChem, 17, 2455–2460]. A model analogous to aug-PROmol cannot be built from the current pseudoatom databanks, as they perform badly when truncated to the monopole level. Here, new strategies for multipole model refinements were sought, leading to better parametrization at the monopole level. This would allow the creation of a pseudoatom databank in a single route of model parametrization, which would be suitable for both crystal structure refinement and rapid electrostatic energy calculations. Here it is shown that the cumulative approach to multipole model refinements, as opposed to simultaneous or iterative refinements of all multipole model parameters (P_v, κ, P_lm, κ′), leads to substantially different models of electron density. Cumulative refinement of two blocks of parameters, the first with P_v and κ and then the second with P_lm and κ′, leads to the P_vκ|P_lmκ′ model having promising properties. The P_vκ|P_lmκ′ model is as good as the University at Buffalo DataBank (UBDB) in X-ray structure TAAM refinements and electrostatic energy estimations, especially for less polar molecules. When truncated to the monopole level, the P_vκ model has a chance to replace aug-PROmol in fast yet accurate electrostatics energy calculations, although some improvements in κ parametrization for polar functional groups are still needed. The P_vκ model is also a source of point charges which behave similarly to restrained electrostatic potential (RESP) charges in electrostatic interaction energy estimations.

Computing details

Program(s) used to refine structure: Volkov et al., (2006) for cyanuricXrayMMR. Molecular graphics: Volkov et al., (2006) for cyanuricXrayMMR. Software used to prepare material for publication: Volkov et al., (2006) for cyanuricXrayMMR.

1,3,5-triazine-2,4,6-triol (cyanuricXrayMMR)

Crystal data

C3H3N3O3·2(H2O)	F(000) = 344
Mr = 165.12	Dx = 1.716 Mg m^−3
Monoclinic, I2/a	Mo Kα radiation, λ = 0.71073 Å
a = 8.6385 (1) Å	Cell parameters from 61980 reflections
b = 6.6817 Å	θ = 3.5–71.1°
c = 11.6069 (1) Å	µ = 0.16 mm^−1
β = 107.466 (1)°	T = 100 K
V = 639.06 (1) Å^3	Block, monocrystal
Z = 4	0.31 × 0.23 × 0.18 mm

Data collection

SuperNova, Single source at offset/far, Eos diffractometer	5563 reflections with I > 2σ(I)
ω scans	Rint = 0.025
Absorption correction: gaussian CrysAlisPro 1.171.39.43d (Rigaku Oxford Diffraction, 2018) Numerical absorption correction based on gaussian integration over a multifaceted crystal model Empirical absorption correction using spherical harmonics, implemented in SCALE3 ABSPACK scaling algorithm.	θmax = 71.3°, θmin = 3.6°
Tmin = 0.383, Tmax = 1.000	h = −22→22
6322 measured reflections	k = −17→17
6322 independent reflections	l = −30→30

Refinement

Refinement on F^2	6322 reflections
Least-squares matrix: full	198 parameters
R[F^2 > 2σ(F^2)] = 0.017	0 restraints
wR(F^2) = 0.034	w2 = 1/[s^2(Fo^2)]
S = 1.00	(Δ/σ)max = 0.00001

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

	x	y	z	Uiso*/Ueq
O(1)	0.386912 (5)	0.905329 (7)	0.360753 (4)	0.013
O(3)	0.440445 (18)	0.32683 (2)	0.303288 (15)	0.015
O(2)	0.25	0.31863 (5)	0.5	0.022
N(1)	0.25	0.907601 (6)	0.5	0.01
N(2)	0.319725 (4)	0.608279 (5)	0.428310 (3)	0.01
C(1)	0.323272 (4)	0.812549 (5)	0.425531 (3)	0.009
C(2)	0.25	0.500695 (7)	0.5	0.011
H(1)	0.25	1.061753	0.5	0.031
H(2)	0.364282	0.530989	0.368302	0.029
H(3A)	0.482483	0.323377	0.235751	0.028
H(3B)	0.399208	0.196164	0.311328	0.028

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
O(1)	0.019174 (15)	0.009845 (13)	0.016271 (14)	0.000185 (7)	0.012674 (15)	0.002153 (8)
O(3)	0.02085 (6)	0.01170 (5)	0.01761 (6)	−0.00029 (4)	0.01283 (5)	−0.00173 (3)
O(2)	0.03722 (8)	0.00529 (8)	0.03287 (8)	0	0.02481 (7)	0
N(1)	0.013732 (13)	0.005911 (11)	0.012857 (15)	0	0.008408 (12)	0
N(2)	0.013825 (11)	0.006731 (9)	0.012039 (12)	0.000535 (5)	0.007907 (9)	−0.000314 (6)
C(1)	0.011813 (11)	0.007043 (10)	0.010701 (12)	0.000214 (6)	0.006694 (9)	0.000640 (6)
C(2)	0.016499 (17)	0.005711 (12)	0.014882 (19)	0	0.009707 (15)	0
H(1)	0.04903	0.01103	0.043486	0	0.030924	0
H(2)	0.043491	0.019626	0.033233	0.001246	0.027244	−0.004734
H(3A)	0.036568	0.027516	0.027662	−0.000608	0.021374	−0.0022
H(3B)	0.036619	0.018967	0.033848	−0.004027	0.018806	−0.001134

Geometric parameters (Å, º)

O(1)—C(1)	1.2247 (1)	N(1)—H(1)	1.0300 (1)
O(3)—H(3A)	0.9580 (2)	N(1)—H(1)^i	1.0300 (1)
O(3)—H(3B)	0.9580 (2)	N(2)—C(1)	1.3658 (1)
O(2)—C(2)	1.2165 (6)	N(2)—C(2)	1.3685 (1)
O(2)—C(2)^i	1.2165 (6)	N(2)—C(2)^i	1.3685 (1)
N(1)—C(1)	1.3710 (1)	N(2)—H(2)	1.0300 (1)
N(1)—C(1)^i	1.3710 (1)
H(3A)—O(3)—H(3B)	107.53 (2)	O(1)—C(1)—N(1)	121.993 (7)
C(1)—N(1)—C(1)^i	124.805 (7)	O(1)—C(1)—N(1)^i	121.993 (7)
C(1)—N(1)—H(1)	117.598 (4)	O(1)—C(1)—N(2)	122.528 (6)
C(1)—N(1)—H(1)^i	117.598 (4)	N(1)—C(1)—N(2)	115.479 (5)
C(1)^i—N(1)—H(1)	117.598 (4)	N(1)^i—C(1)—N(2)	115.479 (5)
C(1)^i—N(1)—H(1)^i	117.598 (4)	O(2)—C(2)—N(2)	121.687 (3)
C(1)—N(2)—C(2)	123.805 (5)	O(2)—C(2)—N(2)^i	121.687 (3)
C(1)—N(2)—C(2)^i	123.805 (5)	O(2)^i—C(2)—N(2)	121.687 (3)
C(1)—N(2)—H(2)	118.001 (5)	O(2)^i—C(2)—N(2)^i	121.687 (3)
C(2)—N(2)—H(2)	118.022 (5)	N(2)—C(2)—N(2)^i	116.626 (7)
C(2)^i—N(2)—H(2)	118.022 (5)

Symmetry code: (i) −x+1/2, y, −z+1.

(triptyceneXrayMMR)

Crystal data

C20H14	F(000) = 536
Mr = 254.31	Dx = 1.256 Mg m^−3
Orthorhombic, P212121	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: P 2ac 2ab	Cell parameters from 110051 reflections
a = 8.0808 (3) Å	θ = 60.7–2.7°
b = 8.1662 (3) Å	µ = 0.07 mm^−1
c = 20.3821 (8) Å	T = 100 K
V = 1345.00 (9) Å^3	Block, colourless
Z = 4	0.34 × 0.16 × 0.10 mm

Data collection

CCD detector diffractometer	20485 independent reflections
Radiation source: TXS rotating anode	16182 reflections with I > 3σ(I)
Multilayer optics monochromator	Rint = 0.035
ω–scans	θmax = 60.7°, θmin = 2.7°
Absorption correction: multi-scan R.H. Blessing, Acta Cryst. (1995), A51, 33-38	h = −19→19
Tmin = 0.956, Tmax = 0.992	k = −19→20
110051 measured reflections	l = −49→49

Refinement

Refinement on F^2	14 restraints
R[F^2 > 2σ(F^2)] = 0.022	H atoms treated by a mixture of independent and constrained refinement
wR(F^2) = 0.046	Weighting scheme based on measured s.u.'s
S = 0.94	(Δ/σ)max = −0.001
20485 reflections	Δρmax = 0.19 e Å^−3
263 parameters	Δρmin = −0.20 e Å^−3

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

	x	y	z	Uiso*/Ueq
C1	0.43212 (2)	0.38579 (2)	0.174552 (9)	0.011381 (13)
C2	0.24543 (2)	0.59430 (2)	0.112898 (9)	0.010078 (12)
C3	0.53026 (2)	0.51301 (2)	0.136182 (9)	0.010879 (12)
C4	0.42939 (2)	0.62477 (2)	0.102465 (8)	0.010009 (12)
C5	0.49907 (2)	0.74790 (2)	0.064499 (9)	0.011243 (13)
C6	0.67153 (2)	0.76066 (3)	0.060730 (9)	0.012963 (14)
C7	0.77121 (2)	0.65091 (3)	0.094708 (10)	0.014370 (15)
C8	0.70129 (2)	0.52593 (3)	0.132681 (10)	0.013730 (14)
C9	0.31903 (2)	0.48272 (2)	0.220027 (9)	0.011235 (13)
C10	0.21843 (2)	0.59582 (2)	0.186879 (9)	0.010718 (12)
C11	0.10586 (2)	0.69176 (3)	0.221141 (10)	0.013762 (14)
C12	0.09324 (3)	0.67283 (3)	0.289278 (11)	0.016663 (18)
C13	0.19369 (3)	0.56109 (3)	0.322181 (11)	0.017237 (19)
C14	0.30757 (3)	0.46504 (3)	0.287519 (9)	0.014463 (16)
C15	0.31620 (2)	0.30523 (2)	0.125093 (9)	0.011256 (13)
C16	0.21513 (2)	0.41779 (2)	0.091775 (9)	0.010608 (12)
C17	0.10040 (3)	0.36407 (3)	0.045837 (10)	0.013549 (15)
C18	0.08589 (3)	0.19622 (3)	0.033124 (11)	0.016866 (18)
C19	0.18543 (3)	0.08489 (3)	0.066420 (12)	0.017458 (17)
C20	0.30176 (3)	0.13876 (2)	0.112657 (11)	0.014981 (15)
H1	0.5128 (6)	0.2992 (6)	0.1998 (3)	0.02549
H2	0.1677 (6)	0.6821 (6)	0.0867 (3)	0.02294
H5	0.4213 (6)	0.8351 (6)	0.0378 (3)	0.02590
H6	0.7289 (8)	0.8568 (6)	0.0316 (3)	0.02975
H7	0.9060 (4)	0.6594 (8)	0.0927 (3)	0.03345
H8	0.7795 (7)	0.4412 (7)	0.1591 (3)	0.03111
H11	0.0284 (7)	0.7801 (7)	0.1955 (3)	0.02942
H12	0.0028 (7)	0.7446 (8)	0.3164 (3)	0.03507
H13	0.1823 (9)	0.5475 (9)	0.37520 (10)	0.03725
H14	0.3855 (7)	0.3753 (7)	0.3125 (3)	0.03017
H17	0.0221 (7)	0.4501 (6)	0.0196 (3)	0.02987
H18	−0.0065 (8)	0.1536 (9)	−0.0023 (3)	0.03774
H19	0.1725 (9)	−0.0455 (4)	0.0565 (3)	0.03795
H20	0.3807 (7)	0.0515 (7)	0.1388 (3)	0.03247

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
C1	0.01130 (5)	0.01138 (5)	0.01146 (5)	0.00234 (4)	−0.00074 (4)	0.00127 (4)
C2	0.00869 (4)	0.01051 (5)	0.01104 (5)	0.00138 (4)	−0.00045 (4)	0.00068 (4)
C3	0.00874 (5)	0.01242 (5)	0.01148 (5)	0.00197 (4)	−0.00045 (4)	0.00080 (4)
C4	0.00846 (4)	0.01114 (5)	0.01042 (5)	0.00094 (4)	−0.00013 (4)	0.00091 (4)
C5	0.01049 (5)	0.01266 (6)	0.01059 (5)	−0.00026 (4)	0.00001 (4)	0.00113 (4)
C6	0.01076 (5)	0.01635 (6)	0.01178 (5)	−0.00160 (5)	0.00144 (4)	−0.00019 (5)
C7	0.00879 (5)	0.01892 (7)	0.01540 (6)	0.00020 (5)	0.00092 (4)	−0.00074 (5)
C8	0.00879 (5)	0.01663 (6)	0.01577 (6)	0.00251 (5)	−0.00069 (4)	0.00068 (5)
C9	0.01203 (5)	0.01197 (5)	0.00970 (5)	0.00076 (4)	0.00022 (4)	0.00063 (4)
C10	0.01015 (5)	0.01097 (5)	0.01103 (5)	0.00134 (4)	0.00091 (4)	−0.00055 (4)
C11	0.01204 (5)	0.01392 (6)	0.01533 (6)	0.00173 (5)	0.00228 (5)	−0.00294 (5)
C12	0.01660 (7)	0.01816 (7)	0.01523 (7)	−0.00062 (6)	0.00484 (5)	−0.00472 (5)
C13	0.02040 (8)	0.01993 (8)	0.01138 (6)	−0.00222 (6)	0.00362 (5)	−0.00186 (5)
C14	0.01706 (7)	0.01635 (7)	0.00999 (5)	−0.00121 (6)	0.00049 (5)	0.00117 (4)
C15	0.01179 (5)	0.01002 (5)	0.01196 (5)	0.00171 (4)	0.00000 (4)	−0.00025 (4)
C16	0.01022 (5)	0.01068 (5)	0.01093 (5)	0.00084 (4)	−0.00057 (4)	−0.00025 (4)
C17	0.01343 (6)	0.01402 (6)	0.01319 (6)	−0.00036 (5)	−0.00251 (4)	−0.00114 (5)
C18	0.01826 (7)	0.01529 (7)	0.01706 (7)	−0.00142 (6)	−0.00269 (6)	−0.00428 (5)
C19	0.01958 (8)	0.01220 (6)	0.02060 (8)	0.00036 (6)	−0.00082 (6)	−0.00462 (5)
C20	0.01662 (7)	0.01035 (6)	0.01797 (7)	0.00226 (5)	−0.00018 (5)	−0.00144 (5)
H1	0.02573	0.02391	0.02684	0.00554	−0.00515	0.00539
H2	0.01965	0.02245	0.02673	0.00486	−0.00392	0.00503
H5	0.02111	0.02719	0.02941	0.00321	−0.00227	0.00989
H6	0.02683	0.03212	0.03030	−0.00895	0.00334	0.00943
H7	0.01188	0.04388	0.04459	−0.00273	0.00280	0.00382
H8	0.02248	0.03302	0.03784	0.00710	−0.00265	0.00868
H11	0.02576	0.03079	0.03172	0.01149	−0.00108	−0.00055
H12	0.03311	0.03924	0.03286	0.00796	0.01202	−0.00938
H13	0.04969	0.04502	0.01705	0.00262	0.00601	−0.00039
H14	0.03347	0.03343	0.02361	0.00488	−0.00379	0.00649
H17	0.03093	0.02653	0.03214	0.00298	−0.01019	0.00150
H18	0.04042	0.03548	0.03732	−0.00732	−0.01395	−0.01070
H19	0.04496	0.01747	0.05142	−0.00147	−0.00872	−0.00854
H20	0.03567	0.02089	0.04085	0.00675	−0.01081	0.00176

Geometric parameters (Å, º)

C1—C3	1.5231 (3)	C9—C14	1.3863 (3)
C1—C9	1.5234 (3)	C10—C11	1.3889 (3)
C1—C15	1.5253 (3)	C11—C12	1.4011 (3)
C1—H1	1.090 (3)	C11—H11	1.089 (3)
C2—C4	1.5222 (2)	C12—C13	1.3933 (4)
C2—C10	1.5237 (3)	C12—H12	1.088 (3)
C2—C16	1.5241 (3)	C13—C14	1.4004 (3)
C2—H2	1.093 (3)	C13—H13	1.0902 (19)
C3—C4	1.4034 (2)	C14—H14	1.092 (3)
C3—C8	1.3878 (3)	C15—C16	1.4046 (3)
C4—C5	1.3881 (3)	C15—C20	1.3878 (3)
C5—C6	1.3996 (3)	C16—C17	1.3888 (3)
C5—H5	1.095 (3)	C17—C18	1.3999 (3)
C6—C7	1.3899 (3)	C17—H17	1.086 (3)
C6—H6	1.089 (3)	C18—C19	1.3907 (4)
C7—C8	1.4000 (3)	C18—H18	1.095 (4)
C7—H7	1.092 (3)	C19—C20	1.4019 (3)
C8—H8	1.080 (3)	C19—H19	1.089 (3)
C9—C10	1.4037 (3)	C20—H20	1.095 (3)
C3—C1—C9	105.687 (14)	C2—C10—C9	112.833 (14)
C3—C1—C15	105.939 (14)	C2—C10—C11	126.584 (15)
C3—C1—H1	111.9 (3)	C9—C10—C11	120.562 (16)
C9—C1—C15	104.939 (14)	C10—C11—C12	118.938 (16)
C9—C1—H1	114.1 (3)	C10—C11—H11	120.6 (3)
C15—C1—H1	113.5 (3)	C12—C11—H11	120.4 (3)
C4—C2—C10	106.066 (13)	C13—C12—C11	120.458 (19)
C4—C2—C16	105.783 (13)	C13—C12—H12	120.0 (3)
C4—C2—H2	112.7 (3)	C11—C12—H12	119.6 (3)
C10—C2—C16	105.324 (13)	C12—C13—C14	120.453 (19)
C10—C2—H2	113.3 (3)	C12—C13—H13	119.6 (3)
C16—C2—H2	113.0 (3)	C14—C13—H13	119.9 (3)
C1—C3—C4	113.111 (14)	C9—C14—C13	119.090 (17)
C1—C3—C8	126.639 (16)	C9—C14—H14	119.6 (3)
C4—C3—C8	120.248 (15)	C13—C14—H14	121.3 (3)
C2—C4—C3	113.113 (14)	C1—C15—C16	113.227 (14)
C2—C4—C5	126.330 (14)	C1—C15—C20	126.501 (16)
C3—C4—C5	120.557 (15)	C16—C15—C20	120.253 (16)
C4—C5—C6	119.238 (15)	C2—C16—C15	112.886 (14)
C4—C5—H5	121.0 (3)	C2—C16—C17	126.612 (15)
C6—C5—H5	119.7 (3)	C15—C16—C17	120.492 (15)
C7—C6—C5	120.114 (16)	C16—C17—C18	119.339 (16)
C7—C6—H6	119.4 (3)	C16—C17—H17	121.1 (3)
C5—C6—H6	120.5 (3)	C18—C17—H17	119.6 (3)
C6—C7—C8	120.772 (17)	C19—C18—C17	120.087 (19)
C6—C7—H7	121.2 (3)	C19—C18—H18	120.5 (4)
C8—C7—H7	118.0 (3)	C17—C18—H18	119.4 (4)
C3—C8—C7	119.065 (16)	C18—C19—C20	120.714 (19)
C3—C8—H8	120.5 (3)	C18—C19—H19	119.6 (3)
C7—C8—H8	120.4 (3)	C20—C19—H19	119.7 (3)
C1—C9—C10	113.356 (14)	C15—C20—C19	119.112 (17)
C1—C9—C14	126.137 (15)	C15—C20—H20	120.0 (3)
C10—C9—C14	120.494 (16)	C19—C20—H20	120.9 (3)

(triptyceneNeutr)

Crystal data

C80H56	F(000) = 322.296
Mr = 1017.3	Dx = 1.245 Mg m^−3
Orthorhombic, P212121	Neutron radiation, λ = 0.69- 6.94 Å
Hall symbol: P 2xab;2ybc;2zac	Cell parameters from 550 reflections
a = 8.1019 (13) Å	θ = 2.0–78.1°
b = 8.1922 (13) Å	µ = 0 mm^−1
c = 20.442 (3) Å	T = 100 K
V = 1356.8 (4) Å^3	Block
Z = 1	8.00 × 2.00 × 2.00 mm

Data collection

SXD diffractometer	Rint = 0.0000
Radiation source: ISIS spallation source	θmax = 78.1°, θmin = 2.0°
time–of–flight LAUE scans	h = −16→6
21802 measured reflections	k = −20→21
21802 independent reflections	l = −56→52
21749 reflections with I > 3σ(I)

Refinement

Refinement on F	All H-atom parameters refined
R[F^2 > 2σ(F^2)] = 0.063	Weighting scheme based on measured s.u.'s w = 1/(σ^2(F) + 0.0001F^2)
wR(F^2) = 0.099	(Δ/σ)max = 0.008
S = 4.39	Δρmax = 4.37 e Å^−3
21802 reflections	Δρmin = −2.09 e Å^−3
316 parameters	Extinction correction: B-C type 1 Lorentzian isotropic (Becker & Coppens, 1974)
0 restraints	Extinction coefficient: 76.3 (12)
0 constraints	Absolute structure: 4176 of Friedel pairs used in the refinement

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

	x	y	z	Uiso*/Ueq
C1	0.43235 (18)	0.38552 (13)	0.17460 (6)	0.0098 (3)
C2	0.24548 (18)	0.59429 (13)	0.11278 (6)	0.0085 (3)
C3	0.53057 (19)	0.51308 (14)	0.13614 (6)	0.0100 (3)
C4	0.42955 (18)	0.62482 (13)	0.10246 (6)	0.0087 (3)
C5	0.49920 (18)	0.74799 (14)	0.06439 (6)	0.0097 (3)
C6	0.67148 (19)	0.76072 (15)	0.06070 (6)	0.0117 (3)
C7	0.77144 (19)	0.65059 (16)	0.09477 (7)	0.0129 (3)
C8	0.7014 (2)	0.52599 (15)	0.13273 (6)	0.0124 (3)
C9	0.31878 (19)	0.48258 (13)	0.22011 (6)	0.0100 (3)
C10	0.21858 (18)	0.59596 (13)	0.18690 (6)	0.0094 (3)
C11	0.1062 (2)	0.69154 (15)	0.22122 (6)	0.0126 (3)
C12	0.0937 (2)	0.67289 (16)	0.28936 (6)	0.0150 (4)
C13	0.1938 (2)	0.56118 (15)	0.32224 (6)	0.0160 (4)
C14	0.3073 (2)	0.46511 (15)	0.28759 (6)	0.0130 (3)
C15	0.3163 (2)	0.30510 (13)	0.12510 (6)	0.0099 (3)
C16	0.21506 (18)	0.41781 (13)	0.09175 (6)	0.0092 (3)
C17	0.1003 (2)	0.36432 (15)	0.04584 (6)	0.0122 (3)
C18	0.0857 (2)	0.19627 (15)	0.03309 (6)	0.0152 (4)
C19	0.1851 (2)	0.08492 (15)	0.06637 (7)	0.0159 (3)
C20	0.3013 (2)	0.13877 (14)	0.11270 (6)	0.0140 (3)
H1	0.5103 (5)	0.2978 (3)	0.20030 (14)	0.0242 (8)
H2	0.1679 (4)	0.6826 (3)	0.08712 (14)	0.0217 (8)
H5	0.4194 (4)	0.8344 (4)	0.03856 (15)	0.0247 (8)
H6	0.7274 (5)	0.8582 (4)	0.03215 (15)	0.0285 (9)
H7	0.9048 (5)	0.6626 (4)	0.09234 (18)	0.0323 (10)
H8	0.7799 (5)	0.4405 (4)	0.15877 (18)	0.0299 (10)
H11	0.0273 (5)	0.7799 (4)	0.19625 (16)	0.0282 (9)
H12	0.0033 (5)	0.7459 (4)	0.31613 (17)	0.0339 (11)
H13	0.1848 (6)	0.5481 (5)	0.37520 (15)	0.0361 (11)
H14	0.3839 (5)	0.3762 (4)	0.31299 (15)	0.0290 (10)
H17	0.0210 (5)	0.4493 (4)	0.01979 (17)	0.0287 (10)
H18	−0.0038 (6)	0.1535 (4)	−0.00316 (18)	0.0366 (12)
H19	0.1737 (6)	−0.0448 (3)	0.0564 (2)	0.0368 (11)
H20	0.3802 (5)	0.0510 (4)	0.13840 (17)	0.0313 (10)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
C1	0.0076 (7)	0.0114 (4)	0.0102 (4)	0.0031 (4)	−0.0006 (4)	0.0012 (3)
C2	0.0055 (6)	0.0098 (4)	0.0104 (4)	0.0012 (4)	−0.0004 (4)	0.0007 (3)
C3	0.0064 (7)	0.0120 (4)	0.0116 (4)	0.0018 (4)	−0.0008 (4)	0.0005 (3)
C4	0.0052 (6)	0.0106 (4)	0.0103 (4)	0.0008 (4)	−0.0008 (4)	0.0010 (3)
C5	0.0067 (7)	0.0124 (4)	0.0101 (4)	0.0001 (4)	0.0002 (4)	0.0007 (3)
C6	0.0083 (7)	0.0154 (4)	0.0114 (4)	−0.0012 (4)	0.0014 (5)	0.0000 (4)
C7	0.0045 (7)	0.0187 (5)	0.0155 (5)	0.0004 (4)	0.0011 (5)	−0.0005 (4)
C8	0.0062 (7)	0.0157 (5)	0.0153 (5)	0.0027 (4)	−0.0009 (5)	0.0003 (4)
C9	0.0100 (7)	0.0113 (4)	0.0087 (4)	0.0008 (4)	−0.0001 (4)	0.0007 (3)
C10	0.0069 (7)	0.0103 (4)	0.0110 (4)	0.0017 (4)	0.0006 (4)	−0.0007 (3)
C11	0.0098 (7)	0.0131 (4)	0.0149 (5)	0.0015 (4)	0.0021 (5)	−0.0030 (4)
C12	0.0127 (8)	0.0173 (5)	0.0149 (5)	−0.0005 (5)	0.0048 (5)	−0.0044 (4)
C13	0.0179 (9)	0.0191 (5)	0.0109 (5)	−0.0016 (5)	0.0033 (5)	−0.0017 (4)
C14	0.0134 (8)	0.0160 (5)	0.0097 (4)	−0.0004 (5)	−0.0001 (5)	0.0012 (3)
C15	0.0085 (7)	0.0094 (4)	0.0120 (4)	0.0018 (4)	0.0000 (4)	−0.0001 (3)
C16	0.0072 (7)	0.0102 (4)	0.0103 (4)	0.0011 (4)	−0.0005 (4)	0.0001 (3)
C17	0.0099 (7)	0.0138 (4)	0.0128 (4)	−0.0006 (4)	−0.0024 (5)	−0.0010 (3)
C18	0.0141 (8)	0.0146 (5)	0.0169 (5)	−0.0008 (5)	−0.0023 (5)	−0.0045 (4)
C19	0.0157 (8)	0.0112 (4)	0.0208 (5)	0.0007 (5)	−0.0008 (6)	−0.0041 (4)
C20	0.0147 (8)	0.0095 (4)	0.0178 (5)	0.0020 (4)	0.0010 (5)	−0.0014 (4)
H1	0.0227 (18)	0.0234 (12)	0.0266 (12)	0.0058 (11)	−0.0053 (12)	0.0055 (10)
H2	0.0166 (16)	0.0219 (11)	0.0265 (12)	0.0051 (10)	−0.0040 (11)	0.0051 (9)
H5	0.0181 (18)	0.0267 (12)	0.0292 (13)	0.0034 (11)	−0.0024 (13)	0.0100 (10)
H6	0.024 (2)	0.0317 (14)	0.0301 (14)	−0.0089 (13)	0.0033 (14)	0.0096 (11)
H7	0.0087 (18)	0.0436 (18)	0.0445 (18)	−0.0026 (13)	0.0028 (16)	0.0039 (14)
H8	0.019 (2)	0.0326 (14)	0.0377 (16)	0.0073 (13)	−0.0027 (15)	0.0088 (11)
H11	0.023 (2)	0.0304 (14)	0.0315 (14)	0.0118 (13)	−0.0012 (13)	−0.0005 (11)
H12	0.030 (2)	0.0389 (17)	0.0327 (15)	0.0082 (15)	0.0121 (15)	−0.0094 (13)
H13	0.047 (3)	0.0447 (18)	0.0167 (11)	0.0028 (18)	0.0060 (15)	−0.0004 (11)
H14	0.031 (2)	0.0330 (14)	0.0233 (12)	0.0051 (14)	−0.0039 (14)	0.0066 (10)
H17	0.028 (2)	0.0260 (13)	0.0320 (15)	0.0032 (12)	−0.0104 (14)	0.0015 (11)
H18	0.038 (3)	0.0351 (17)	0.0372 (17)	−0.0072 (16)	−0.0142 (17)	−0.0108 (13)
H19	0.042 (2)	0.0169 (11)	0.051 (2)	−0.0013 (13)	−0.0089 (19)	−0.0086 (12)
H20	0.033 (2)	0.0204 (11)	0.0408 (17)	0.0070 (12)	−0.0110 (16)	0.0018 (11)

Geometric parameters (Å, º)

C1—C3	1.5310 (17)	C9—C10	1.4082 (18)
C1—C9	1.5313 (19)	C9—C14	1.3900 (18)
C1—C15	1.5307 (19)	C10—C11	1.3905 (19)
C2—C4	1.526 (2)	C11—C12	1.4049 (18)
C2—C10	1.5308 (18)	C12—C13	1.395 (2)
C2—C16	1.5285 (13)	C13—C14	1.403 (2)
C3—C4	1.4079 (18)	C15—C16	1.4105 (18)
C3—C8	1.390 (2)	C15—C20	1.3911 (13)
C4—C5	1.3940 (16)	C16—C17	1.392 (2)
C5—C6	1.402 (2)	C17—C18	1.406 (2)
C6—C7	1.398 (2)	C18—C19	1.394 (2)
C7—C8	1.402 (2)	C19—C20	1.406 (2)
C3—C1—C9	105.64 (8)	C10—C9—C14	120.52 (12)
C3—C1—C15	105.87 (10)	C2—C10—C9	112.90 (11)
C9—C1—C15	104.82 (12)	C2—C10—C11	126.71 (11)
C4—C2—C10	105.93 (11)	C9—C10—C11	120.36 (11)
C4—C2—C16	105.87 (10)	C10—C11—C12	119.11 (12)
C10—C2—C16	105.31 (8)	C11—C12—C13	120.45 (13)
C1—C3—C4	113.12 (13)	C12—C13—C14	120.39 (11)
C1—C3—C8	126.53 (12)	C9—C14—C13	119.16 (12)
C4—C3—C8	120.36 (12)	C1—C15—C16	113.27 (8)
C2—C4—C3	113.22 (10)	C1—C15—C20	126.56 (11)
C2—C4—C5	126.26 (12)	C16—C15—C20	120.15 (12)
C3—C4—C5	120.52 (14)	C2—C16—C15	112.93 (11)
C4—C5—C6	119.15 (12)	C2—C16—C17	126.52 (12)
C5—C6—C7	120.13 (11)	C15—C16—C17	120.54 (10)
C6—C7—C8	120.75 (15)	C16—C17—C18	119.30 (13)
C3—C8—C7	119.08 (13)	C17—C18—C19	120.11 (13)
C1—C9—C10	113.35 (11)	C18—C19—C20	120.64 (10)
C1—C9—C14	126.12 (11)	C15—C20—C19	119.25 (11)