Azulene revisited: solid-state structure, invariom modeling and lattice-energy minimization of a classical example of disorder

The molecular and solid-state structure of azulene both raise fundamental questions. Therefore, the disordered crystal structure of azulene was re-refined with invariom non-spherical atomic scattering factors from new single-crystal X-ray diffraction data with a resolution of d = 0.45 Å. An unconstrained refinement results in a molecular geometry with C_s symmetry. Refinements constrained to fulfill C_2v symmetry, as observed in the gas phase and in high-level ab initio calculations, lead to similar figures of merit and residual densities as unconstrained ones. Such models are consistent with the structures from microwave spectroscopy and electron diffraction, albeit they are not the same. It is shown that for the disorder present in azulene, the invariom model describes valence electron density as successfully as it does for non-disordered structures, although the disorder still leads to high correlations mainly between positional parameters. Lattice-energy minimizations on a variety of ordered model structures using dispersion-corrected DFT calculations reveal that the local deviations from the average structure are small. Despite the molecular dipole moment there is no significant molecular ordering in any spatial direction. A superposition of all ordered model structures leads to a calculated average structure, which explains not only the experimental determined atomic coordinates, but also the apparently unusual experimental anisotropic displacement parameters.

Computing details

Program(s) used to solve structure: SHELXS97 (Sheldrick, 2008); program(s) used to refine structure: Koritsanszky et al., (2003); software used to prepare material for publication: enCIFer 1.3, CCDC, 2008.

(I)

Crystal data

C10H8	F(000) = 136.0
Mr = 128.16	Dx = 1.235 Mg m^−3
Monoclinic, P21/a	Mo Kα radiation, λ = 0.7107 Å
Hall symbol: -P 2yab	Cell parameters from 15500 reflections
a = 7.7154 (2) Å	θ = 3.4–52.2°
b = 5.9019 (1) Å	µ = 0.07 mm^−1
c = 7.6969 (2) Å	T = 100 K
β = 100.411 (2)°	Triangular, violet
V = 344.71 (1) Å^3	0.88 × 0.81 × 0.13 mm
Z = 2

Data collection

Oxford Diffraction Xcalibur S diffractometer	3834 independent reflections
Radiation source: Enhance (Mo) X-ray Source	3356 reflections with F > 2(σ)F
Graphite monochromator	Rint = 0.038
Detector resolution: 16.0009 pixels mm^-1	θmax = 51.4°, θmin = 3.4°
Absorption correction: analytical CrysAlis RED, Oxford Diffraction Ltd., Version 1.171.31.5 (release 28-08-2006 CrysAlis171 .NET) (compiled Aug 28 2006,13:05:05) 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)	h = −16→16
Tmin = 0.958, Tmax = 0.992	k = −12→12
35883 measured reflections	l = −16→12

Refinement

Refinement on F	0 restraints
Least-squares matrix: full	H-atom parameters constrained
R[F^2 > 2σ(F^2)] = 0.043	w1 = 1/[s^2(Fo)]
wR(F^2) = 0.028	(Δ/σ)max < 0.001
S = 3.04	Δρmax = 0.22 e Å^−3
3356 reflections	Δρmin = −0.16 e Å^−3
58 parameters

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

	x	y	z	Uiso*/Ueq	Occ. (<1)
C(1)	0.16540 (10)	0.20590 (10)	0.2102 (1)	0.02	0.5
C(2)	0.15098 (7)	0.04305 (8)	0.34397 (2)	0.023	0.5
C(3)	0.04490 (10)	−0.14330 (10)	0.2696 (1)	0.021	0.5
C(4)	−0.11104 (4)	−0.24314 (4)	−0.02876 (2)	0.017	0.5
C(5)	−0.17040 (10)	−0.20920 (10)	−0.2119 (1)	0.02	0.5
C(6)	−0.13861 (5)	−0.03272 (6)	−0.31700 (1)	0.023	0.5
C(7)	−0.04330 (10)	0.16140 (10)	−0.2747 (1)	0.021	0.5
C(8)	0.05260 (4)	0.23355 (4)	−0.10969 (2)	0.017	0.5
C(9)	0.06945 (4)	0.12288 (3)	0.05164 (2)	0.014	0.5
C(10)	−0.00623 (3)	−0.10001 (5)	0.08924 (2)	0.014	0.5
H(1)	0.23710	0.36360	0.2281	0.0370 (10)	0.5
H(2)	0.21118	0.05874	0.48129	0.047 (2)	0.5
H(3)	0.01170	−0.29100	0.3394	0.040 (2)	0.5
H(4)	−0.15337	−0.39883	0.02608	0.034 (2)	0.5
H(5)	−0.25200	−0.34390	−0.2791	0.0370 (10)	0.5
H(6)	−0.19919	−0.04852	−0.45521	0.047 (2)	0.5
H(7)	−0.03930	0.27600	−0.3843	0.040 (2)	0.5
H(8)	0.11938	0.39561	−0.10877	0.033 (2)	0.5

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
C(1)	0.01702 (8)	0.02016 (7)	0.02277 (8)	−0.00237 (6)	0.00275 (6)	−0.00673 (6)
C(2)	0.02090 (10)	0.02830 (10)	0.01790 (10)	0.00090 (10)	0.00270 (10)	−0.00250 (10)
C(3)	0.02099 (8)	0.02350 (10)	0.01863 (8)	0.00406 (8)	0.00464 (6)	0.00514 (6)
C(4)	0.01460 (10)	0.01210 (10)	0.0252 (2)	−0.00220 (10)	0.00540 (10)	−0.00200 (10)
C(5)	0.01702 (8)	0.02016 (7)	0.02277 (8)	−0.00237 (6)	0.00275 (6)	−0.00673 (6)
C(6)	0.02090 (10)	0.02830 (10)	0.01790 (10)	0.00090 (10)	0.00270 (10)	−0.00250 (10)
C(7)	0.02099 (8)	0.02350 (10)	0.01863 (8)	0.00406 (8)	0.00464 (6)	0.00514 (6)
C(8)	0.01650 (10)	0.01290 (10)	0.02080 (10)	−0.00010 (10)	0.00650 (10)	0.00250 (10)
C(9)	0.01290 (10)	0.01120 (10)	0.01700 (10)	−0.00070 (10)	0.00450 (10)	−0.00090 (10)
C(10)	0.01260 (10)	0.01150 (10)	0.01820 (10)	−0.00040 (10)	0.00450 (10)	0.00050 (10)

Geometric parameters (Å, º)

C(1)—C(2)	1.4274 (2)	C(4)—C(8)^i	1.0809 (2)
C(1)—C(4)^i	1.4008 (3)	C(4)—C(9)^i	0.8113 (2)
C(1)—C(5)^i	0.0434 (12)	C(4)—C(10)	1.3881 (1)
C(1)—C(6)^i	1.3507 (5)	C(4)—H(4)	1.086
C(1)—C(9)	1.3965 (1)	C(5)—C(6)	1.3679 (2)
C(1)—H(1)	1.079	C(5)—C(9)^i	1.4282 (3)
C(2)—C(3)	1.4273 (3)	C(5)—H(5)	1.086
C(2)—C(5)^i	1.4396 (4)	C(6)—C(7)	1.3686 (2)
C(2)—C(6)^i	0.2208 (1)	C(6)—H(6)	1.086
C(2)—C(7)^i	1.5069 (4)	C(7)—C(8)	1.4153 (2)
C(2)—H(2)	1.079	C(7)—C(10)^i	1.4557 (2)
C(3)—C(6)^i	1.2803 (4)	C(7)—H(7)	1.086
C(3)—C(7)^i	0.1157 (4)	C(8)—C(9)	1.3882 (1)
C(3)—C(8)^i	1.4250 (3)	C(8)—C(10)^i	0.8912 (4)
C(3)—C(10)	1.3966 (1)	C(8)—H(8)	1.086
C(3)—H(3)	1.079	C(9)—C(10)	1.4887 (2)
C(4)—C(5)	1.4152 (2)	C(9)—C(10)^i	1.1138 (3)
C(2)—C(1)—C(4)^i	140.948 (11)	C(3)^i—C(6)—C(5)	126.975 (12)
C(2)—C(1)—C(5)^i	105.5 (2)	C(5)—C(6)—C(7)	130.010 (11)
C(2)—C(1)—C(9)	107.232 (6)	C(2)^i—C(7)—C(8)	136.355 (5)
C(4)^i—C(1)—C(5)^i	108.6 (8)	C(2)^i—C(7)—C(10)^i	100.23 (2)
C(4)^i—C(1)—C(6)^i	132.42 (2)	C(3)^i—C(7)—C(8)	92.47 (11)
C(5)^i—C(1)—C(6)^i	112.6 (3)	C(3)^i—C(7)—C(10)^i	57.3 (2)
C(5)^i—C(1)—C(9)	136.5 (17)	C(6)—C(7)—C(8)	129.521 (9)
C(6)^i—C(1)—C(9)	98.708 (14)	C(6)—C(7)—C(10)^i	93.387 (11)
C(1)—C(2)—C(3)	110.066 (8)	C(3)^i—C(8)—C(4)^i	158.79 (2)
C(1)—C(2)—C(6)^i	65.45 (14)	C(3)^i—C(8)—C(9)	123.108 (15)
C(1)—C(2)—C(7)^i	113.198 (7)	C(3)^i—C(8)—C(10)^i	69.86 (3)
C(3)—C(2)—C(5)^i	111.521 (11)	C(4)^i—C(8)—C(7)	163.337 (17)
C(5)^i—C(2)—C(6)^i	66.83 (14)	C(4)^i—C(8)—C(10)^i	88.938 (19)
C(5)^i—C(2)—C(7)^i	114.637 (11)	C(7)—C(8)—C(9)	127.642 (7)
C(2)—C(3)—C(7)^i	131.8 (2)	C(7)—C(8)—C(10)^i	74.40 (2)
C(2)—C(3)—C(8)^i	144.040 (8)	C(9)—C(8)—C(10)^i	53.246 (17)
C(2)—C(3)—C(10)	107.234 (11)	C(1)—C(9)—C(4)^i	73.43 (2)
C(6)^i—C(3)—C(7)^i	138.1 (3)	C(1)—C(9)—C(8)	124.452 (13)
C(6)^i—C(3)—C(8)^i	137.08 (2)	C(1)—C(9)—C(10)	107.733 (8)
C(6)^i—C(3)—C(10)	100.280 (8)	C(1)—C(9)—C(10)^i	164.319 (10)
C(7)^i—C(3)—C(8)^i	82.88 (12)	C(4)^i—C(9)—C(5)^i	72.54 (2)
C(7)^i—C(3)—C(10)	118.7 (2)	C(4)^i—C(9)—C(8)	51.02 (2)
C(1)^i—C(4)—C(8)^i	166.13 (3)	C(4)^i—C(9)—C(10)	178.57 (3)
C(1)^i—C(4)—C(9)^i	72.85 (2)	C(4)^i—C(9)—C(10)^i	90.89 (2)
C(1)^i—C(4)—C(10)	126.200 (12)	C(5)^i—C(9)—C(8)	123.565 (7)
C(5)—C(4)—C(8)^i	167.577 (15)	C(5)^i—C(9)—C(10)	108.607 (7)
C(5)—C(4)—C(9)^i	74.30 (2)	C(5)^i—C(9)—C(10)^i	163.40 (2)
C(5)—C(4)—C(10)	127.645 (8)	C(8)—C(9)—C(10)	127.812 (5)
C(8)^i—C(4)—C(9)^i	93.28 (3)	C(10)—C(9)—C(10)^i	87.940 (15)
C(9)^i—C(4)—C(10)	53.351 (19)	C(3)—C(10)—C(4)	124.452 (12)
C(1)^i—C(5)—C(2)^i	72.80 (19)	C(3)—C(10)—C(8)^i	73.33 (2)
C(1)^i—C(5)—C(4)	69.7 (8)	C(3)—C(10)—C(9)	107.730 (8)
C(1)^i—C(5)—C(6)	65.7 (3)	C(3)—C(10)—C(9)^i	160.21 (2)
C(2)^i—C(5)—C(4)	138.032 (15)	C(4)—C(10)—C(7)^i	120.586 (19)
C(2)^i—C(5)—C(9)^i	104.88 (2)	C(4)—C(10)—C(8)^i	51.13 (2)
C(4)—C(5)—C(6)	129.537 (4)	C(4)—C(10)—C(9)	127.814 (5)
C(6)—C(5)—C(9)^i	96.385 (9)	C(7)^i—C(10)—C(8)^i	69.460 (17)
C(1)^i—C(6)—C(2)^i	106.00 (15)	C(7)^i—C(10)—C(9)	111.599 (14)
C(1)^i—C(6)—C(3)^i	125.515 (9)	C(7)^i—C(10)—C(9)^i	156.32 (3)
C(1)^i—C(6)—C(7)	128.570 (8)	C(8)^i—C(10)—C(9)	178.937 (18)
C(2)^i—C(6)—C(3)^i	128.15 (16)	C(8)^i—C(10)—C(9)^i	86.88 (3)
C(2)^i—C(6)—C(5)	104.63 (15)	C(9)—C(10)—C(9)^i	92.060 (15)
C(2)^i—C(6)—C(7)	125.24 (15)

Symmetry code: (i) −x, −y, −z.