in Geometrical Parameters Taken from Crystal Diffraction Data

Oct 12, 2014 - ABSTRACT: Symmetrically independent geometrical parameters of six molecules, viz. benzene C6H6 (D6h), pyridine C5H5N (C2v), diphenyl. C...
0 downloads 4 Views 2MB Size
Download PDF
Article pubs.acs.org/crystal

A “Blind Area” in Geometrical Parameters Taken from Crystal Diffraction Data Published as part of the Crystal Growth & Design Mikhail Antipin Memorial virtual special issue. Yuri L. Slovokhotov Department of Chemistry, Lomonosov Moscow State University Institute of Organoelement Compounds, Russian Academy of Sciences, Moscow, Russia S Supporting Information *

ABSTRACT: Symmetrically independent geometrical parameters of six molecules, viz. benzene C6H6 (D6h), pyridine C5H5N (C2v), diphenyl C6H5−C6H5 (D2), 2,2′-dipyridine C5H4N−C5H4N (C2), naphthalene C10H8 (D2h), ferrocene (C5H5)2Fe (D5), and substituted (η5-C5H5)FeCp′ molecular fragment, were calculated from crystal structures deposited in the Cambridge Structural Database (CSD). Average CSD interatomic distances from low-temperature (LT) studies are systematically shortened by 0.01−0.02 Å in comparison with gas electron diffraction results for free molecules; room temperature CSD bond lengths are further reduced relative to LT ones. Bicyclic diphenyl and 2,2′-dipyridine display a similar distribution of planar (mostly in special positions) and nonplanar molecules with the interring dihedral angle varying up to 49.6° and 46.0°, respectively. A strong positive correlation between C−C and Fe−C bond lengths was observed in (η5-C5H5)Fe fragments. Bond angle values at neighboring atoms in planar cycles are negatively correlated. In all cases, distributions of CSD data contain a “blind area” where data points are randomly scattered within 0.02−0.04 Å (bond distances) and 2−3° (bond angles) independent of R-factor when R < 0.06. This area broadens with increasing temperature of a study. These observations correspond well to the model of a static and/or dynamic disorder of molecules between discrete sets of atomic positions in a crystal.

■

INTRODUCTION

structures containing the same structural fragment, retrieved from the Cambridge Structural Database (CSD).1 At the same time, high-precision X-ray diffraction studies and a comparison of their results with directly measured physical properties of crystals2 revealed a number of complications of this simplistic model of “chemical crystallography”. The influence of such factors as translation and libration movement of fragments, unrevealed positional disorder, unharmonic force field, etc., on fine details of molecular geometry obtained from diffraction data, was extensively discussed in the crystallographic literature.3−10 Although this discussion just weakly influenced structural chemistry and crystal engineering, it is indirectly reflected in a cautious attitude of chemists toward the actual precision of routine single crystal X-ray diffraction data. In structural chemistry, the empirically well-known threshold for geometrical parameters in molecular fragments composed of light atoms (C, N, O) is 1−2 pm (i.e., 0.01−0.02 Å) in bond lengths and 1−2° in bond angles. Discussion of smaller fluctuations of structural data is a “low style” in chemical

Chemists usually consider single crystal X-ray diffraction data as a source of directly measured geometrical parameters for typical polyatomic fragments such as molecules, ligands, coordination polyhedra, etc. Reliability of these data is characterized by such standard quality marks as R-factor, isotropic vs. anisotropic forms of atomic displacement parameters (ADP, or “thermal ellipsoids”), presence or absence of disordered atomic positions, and e.s.d.s. in bond lengths and bond angles. In a more sophisticated approach, indirect quality characteristics such as Rint, goodness of fit, number of observed reflections per fitting parameter, numerical ADP values, and a temperature of a study are taken into account. It is assumed that a lowtemperature single crystal X-ray study with anisotropic ADPs for all non-hydrogen atoms, H atoms revealed and refined isotropically, up to 10 symmetrically independent observed reflections per variable, unweighted R ≤ 0.03 and G.O.F. close to 1 gives absolutely reliable geometrical data in a quantitative agreement with other methodse.g., neutron diffraction, gas electron diffraction, or good quantum chemistry calculations. Even better precision is attributed to averaged geometrical parameters calculated with a set of high-quality single crystal © XXXX American Chemical Society

Received: May 22, 2014 Revised: September 30, 2014

A

dx.doi.org/10.1021/cg5007428 | Cryst. Growth Des. XXXX, XXX, XXX−XXX

Crystal Growth & Design

Article

papers, although the corresponding standard deviations in Xray data may be 10 times less. Such disappointing limits of the instrumental power of modern X-ray crystallography probably have some physical meaning that chemists try to reveal by using high-precision structural data in chemical studies.3 In this paper, distributions of geometrical parameters calculated for several common organic molecules on the basis of high-quality crystal structures retrieved from CSD are revisited. All these distributions contain a “blind area” where bond length and bond angle values are randomly scattered, respectively, in the ranges of 0.02−0.04 Å and 2−3°. This area of uncertainty, caused by molecular translation and libration movement and/or by a nonresolved positional disorder, becomes broader at higher temperature; within it, bond angles at neighboring atoms in a planar cycle display a negative correlation. On these grounds, a hypothesis of widespread positional disorder in crystalline compounds may be suggested, in a good agreement with the results obtained by Michail Antipin and Roland Böse in structural studies of metallocenes.11,12 In particular, this hypothesis allows for a simple and natural solution of multiple minima problem in ab initio predictions of crystal structures (see Discussion).

(1) Disorder-free and error-free structures (2) No powder data (3) No polymer structures (4) R-factor less than 0.06 (5) Average e.s.d.’s in C−C bond lengths less than 0.005 Å For cocrystals with diphenyl and ferrocene molecules, the condition (4) was weakened to R ≤ 0.075 due to a small number of available data in CSD. Only molecules with revealed H atomic positions were included in the sets. For larger sets of benzene- and pyridine-containing mixed crystals, the “only organic” condition was added to the quest. In these two sets, entries with molecules on symmetry elements, unnoticed disorder in any fragment, and geometrical constraints were removed manually together with evident outliers. Data sets were processed in Microsoft Excel 2007 and Microcal Origin 7.0 programs. No factor analysis or cluster analysis of point distributions was made because independence and randomness of structural data in CSD are very doubtful.13 The resulting data sets are presented in Table 1. In most cases, entries under discussion were marked by CSD refcodes to minimize the reference list.

■

■

DETAILS OF A STATISTICAL TREATMENT To illustrate the existence of “uncertainty area” in geometrical parameters provided by single crystal X-ray studies, several sets of good crystal structures containing six well-known molecules were extracted from 2014 version of the CSD.1 The molecular components of solvates or cocrystals chosen for a statistical analysis are benzene C6H6, pyridine C5H5N, diphenyl C6H5− C6H5, 2,2′-dipyridine NC5H4−C5H4N, naphthalene C10H8, and ferrocene (C5H5)2Fe (Scheme 1). In addition, a big set of 1970

RESULTS Geometrical parameters of the molecular fragments under study, taken from CSD of corresponding cocrystals and averaged over the molecular symmetry, are shown in Tables 2−6. After disregarding structures refined with constraints and removing outliers, a number of fragments in the sets varied from 19 (naphthalene in cocrystals) and 24 (ferrocene) to 1970 (CpFeCp′). For comparison, Tables 2−6 also contain the same parameters obtained by X-ray and neutron diffraction of pure crystalline compounds, and by gas electron diffraction (ED) of free molecules. Distributions of the molecular parameters, calculated from CSD data, are shown in Figures 1−6. More data distributions for the analyzed sets are presented as Figures S1−S6 in Supporting Information. Benzene C6H6. Crystal structures of benzene solvates containing ordered C6H6 molecules in a general position were divided into four subsets according to the temperature T of the study: (a) 90−100 K, (b) 103−150 K, (c) 153−223 K, and (d) 288−300 K, or room temperature (RT) (Table 2). In each temperature interval, ca. 50% of all entries with C6H6 molecules in special positions (mostly 1)̅ were not included into analysis. For each molecule, three geometrical parameters were calculated, viz. bond length dC−C averaged according to D6h symmetry, mean deviation of six CCC bond angles from 120° Δα = abs(θCCC−120), and average deviation δ of carbon atoms from the mean plane of benzene cycle. In a “raw” set of 762 C6H6 molecules retrieved from the “organic” CSD entries with R ≤ 0.12, average dC−C values are scattered in a broad range that became narrower (ca. 0.05 Å for most data points) to R-factor ≈ 0.06. Below this value, a roughly uniform point scattering independent of R is observed in each subset (Figure 1 a,b). Although the precision in all data sets is formally equal, the magnitude of fluctuation grows from ca. 0.02 Å at T ≤ 100 K to ca. 0.04 Å in RT studies for dC−C and from ca. 0.8° to ca. 1.2° for Δα (Figure 2a). However, virtual nonplanarity of benzene cycles δC, also uniformly scattered at R < 0.06, is mostly less than 0.01 Å and similar in all subsets. Three X-ray geometrical parameters of C6H6 molecules, viz. dC−C, ΔθCCC, and δ, are not intercorrelated (see Figure S1b in Supporting Information).

Scheme 1. Molecules Selected for Geometry Analysis

substituted ferrocene fragments CpFeCp′ (where Cp is η5C5H5 ligand, and Cp′ is a substituted η5-cyclopentadienyl) was taken from the CSD to get more data on systems with a possible rotational disorder. The structural data were retrieved from CSD under usual conditions: B

dx.doi.org/10.1021/cg5007428 | Cryst. Growth Des. XXXX, XXX, XXX−XXX

Crystal Growth & Design

Article

Table 1. CSD Data Used in Analysis number of molecules by subsets molecule

LT data

C6H6 benzene C5H5N pyridine C6H5−C6H5 diphenyl NC5H4−C5H4N 2,2′-dipyridine C10H8 naphthalene (cocrystals) C10H8 pure (NAPHTA04-36) (η5-C5H5)2Fe ferrocenea (η5-C5H5)2Fe+ ferrocenium cation (η5-C5H5)Fe fragment in CpFeCp′b a

90−100 K; 45

85−100 K; 351

103−150 K; 58 85−223 K: 79 molecules 110−200 K: 15 molecules 110−200 K: 25 molecules 90−180 K: 18 molecules 5−239 K; 19 molecules 98−220 K; 14 molecules 100−213 K; 9 cations 103−150 K; 460

153−223 K; 49

153−253 K; 453

RT data

total

288−297 K; 34 293−298 K; 39 273−298 K; 16 273−298 K; 63 298 K; 1 WUNLIA 295 K; 1 NAPHTHA36 273−298 K; 10 293−295 K; 23 267−300 K; 706

186 118 31 88 19 20 24 32 1970

b

With 10 studies of pure (C5H5)2Fe (FEROCE01-27). Cp′ denotes substituted cyclopentadienyl ring.

the temperature of the diffraction study: low-temperature 85 ≤ T ≤ 223 K (LT, 79 molecules) and 293 < T ≤ 298 K (RT, 39 molecules). Only “free” neutral solvate molecules of pyridine, not coordinated to metal atoms, were used in analysis; most of these molecules participate in H bonding in the crystal. No clear correlation of CNC bond angle at nitrogen atom involved in hydrogen bonding, to N···(H)N or N···(H)O intermolecular distances was found, so the influence of H-bonds on the molecular geometry of pyridine was not analyzed. Unlike benzene, C5H5N molecules occupied special positions only in three entries, not included in the set. The X-ray geometrical parameters of pyridine molecules were averaged over C2v molecular symmetry with three independent bond lengths and four independent bond angles (see Scheme 1). In addition, a total parameter δ of virtual nonplanarity of the cycle, i.e., averaged deviations of all non-hydrogen atoms from the mean plane, was calculated for each C5H5N molecule by analogy to C6H6. Deviations of bond lengths and bond angles from their mean values were not calculated because the corresponding parameters give no additional information in the C6H6 case. In Table 3, mean X-ray bond distances and bond angles in pyridine molecule, averaged over each subset, are compared with ED data. Distributions of some geometrical parameters are presented in Figure 3 and Figure S2 (Supporting Information). Similar to the C6H6 case, X-ray bond length and bond angle values are randomly scattered in the “blind area” without

Table 2. Geometry of C6H6 Molecule (D6h) from CSD Data on Benzene Solvates data source

d (C−C), Å

δ, Å

Δα, deg

CSD, 90−100 K CSD, 103−150 K CSD, 153−223 K CSD, 288−297 K C6H6 X-ray, 150 K (BENZEN18) C6D6 neutron, 123 K (BENZEN07) C6D6 neutron, 15 K (BENZEN06) C6H6, ED14

1.378(6) 1.374(8) 1.369(14) 1.361(11) 1.379 1.394

0.0037(28) 0.0016(28) 0.0035(28) 0.0040(24) 0.001 0.004

0.37(26) 0.54(43) 0.60(49) 0.63(33) 0.06 0.17

1.397

0.004

0.17

1.397(1)

0

0

Scatterplot of dC−C values displays a definite negative trend at temperature growth (Figure 2b, red line). The average dC−C bond length in the subsets, being substantially smaller than ED and neutron LT data (see Table 2), is reduced by ca. 0.015 Å with passing from T = 90−100 K to RT studies (Figure 2c). Extrapolation of the linear trend in LT data to 0 K in Figure 2b gives the value 1.393 Å, which corresponds better to C−C bond length in the free C6H6 molecule (1.397 Å).14 Deviations of bond lengths and bond angles in benzene molecules generally grow at higher temperature, whereas small δ values agree well with strict planarity of the benzene cycle. Pyridine C5H5N. A total of 118 ordered C5H5N molecules taken from CSD was divided into two subsets corresponding to

Figure 1. Average C−C bond length d in benzene molecules vs R-factor: (a) raw CSD data (T < 250 K, R < 0.12, 762 points), (b) 103 < T < 150 K subset, R < 0.06, 58 points (see Table 1). C

dx.doi.org/10.1021/cg5007428 | Cryst. Growth Des. XXXX, XXX, XXX−XXX

Crystal Growth & Design

Article

Figure 2. Distributions of geometrical parameters of benzene molecule from CSD data (see Table 2). (a) Scatterplots of Δα vs dC−C at 90−100 K (blue), 103−150 K (purple), and 153−233 K (red). (b) Distribution of dC−C vs temperature T; open circle − ED data. (c) Average C−C bond length at different temperatures with e.s.d. (vertical lines).

Table 3. Geometry of C5H5N Molecule (C2v) from CSD Data on Pyridine Solvates data source

d1, Å

d2, Å

d3, Å

δ, Å

α, deg

β, deg

γ, deg

φ, deg

CSD, LT CSD, RT C5H5N X-ray, 153 K (PYRDNA01) ED14

1.332(7) 1.320(10) 1.336 1.344

1.375(9) 1.367(11) 1.381 1.399

1.371(9) 1.355(12) 1.377 1.398

0.004(2) 0.005(3) 0.004 0

116.9(8) 117.2(14) 116.6 116.1

123.4(6) 123.1(9) 123.7 124.6

118.7(4) 118.8(5) 118.6 117.8

118.8(4) 119.0(6) 118.8 119.1

Averaged X-ray bond distances d1, d2, and d3 in C5H5N molecules are systematically smaller than their ED values, respectively by 0.012, 0.025, 0.028 Å in low temperature and 0.022, 0.031, and 0.042 Å in room temperature studies. Discrepancies in four independent bond angles α, β, γ, and φ are less straightforward (see Table 3). Data of an X-ray study of pure pyridine with four independent molecules in Pna21 space group and Z = 16 (PYRDNA01), made at 153 K, lie closer to ED geometry but follow the same trend. Diphenyl C6H5−C6H5 and 2,2′-Dipyridine NC5H4− C5H4N. Geometrical parameters of 31 diphenyl (PhPh) and 88 2,2′-dipyridile (dipy) molecules, ordered according to CSD criteria, are presented in Table 4. In both molecules, bond lengths and bond angles were averaged, respectively, according to D2 and C2 symmetry in nonplanar conformations (see

noticeable correlation to R factor. The spread of data points increases for higher temperature of the study: from 0.02−0.025 Å to 0.03−0.04 Å in bond lengths and from 2−2.5° to 3−5° in bond angles. As in the benzene case, the virtual nonplanarity δ of pyridine molecules is small (0.004−0.005 Å) and roughly the same in both LT and RT studies (Table 3). Similar to C6H6 molecules, no intercorrelations in X-ray geometrical parameters of different nature (i.e., bond lengths, bond angles, and δ) were observed. However, neighboring bond lengths d2 and d3 show a loose positive correlation, whereas bond angles at neighboring atoms are negatively correlated at low temperature (Figure 3a− c). The opposite α and φ bond angles in the pyridine ring do not correlate (Figure 3d). D

dx.doi.org/10.1021/cg5007428 | Cryst. Growth Des. XXXX, XXX, XXX−XXX

Crystal Growth & Design

Article

Figure 3. (a−d) Correlations of geometric parameters in pyridine molecules (see Scheme 1), low-temperature CSD data.

Table 4. Geometry of Diphenyl C6H5−C6H5 (D2) and 2,2′-Dipyridine C5H4N−C5H4N (C2) Molecules from Diffraction Data data source bond distances, Å

d1

d2

d3

d4

C6H5−C6H5, LT C6H5−C6H5, RT pure diphenyl, X-ray, 110 K (BIPHEN03) C6H5−C6H5a, ED14 C6D5−C6D5a, ED14 C5H4N−C5H4N, LT C5H4N−C5H4N, RT pure 2,2′-dipyridine, X-ray, 110 K, 123 K (BIPYRL03, 04) 2,2′-C4H4N−C5H4Na, ED15 bond angles, deg

1.489(8) 1.481(13) 1.496 1.507 1.489 1.489(4) 1.484(11) 1.490 1.496 α

1.393(6) 1.393(15) 1.397 1.404 1.403 1.347(5) 1.349(19) 1.345 1.352

1.383(7) 1.391(21) 1.388 1.395 1.396 1.339(3) 1.344(22) 1.340 1.389

1.376(7) 1.366(16) 1.385 1.396 1.398 1.380(8) 1.369(14) 1.382 1.352

C6H5−C6H5, LT C6H5−C6H5, RT pure diphenyl, X-ray, 110 K (BIPHEN03) C6H5−C6H5a, ED14 C6D5−C6D5a, ED14 C4H4N−C5H4N, LT C4H4N−C5H4N, RT pure 2,2′-dipyridine, X-ray, 110 K, 123 K (BIPYRL03, 04) 2,2′-C4H4N−C5H4Na, ED15 a

averaged geometrical parameters (see Scheme 1)

117.1(7) 117.3(17) 117.9 119.4 117.9 121.9(5) 121.8(7) 122.5 123.0

d4′

d3′

d2′

1.379(8) 1.369(15) 1.383 1.389a φ

1.384(6) 1.372(26) 1.385 1.389a γ′

1.390(7) 1.375(19) 1.393 1.389a β′

β

γ

121.4(5) 120.9(10) 120.9 119.4 121.3 117.7(5) 117.6(7) 117.4 116.2

120.5(4) 120.6(14) 120.7

119.1(6) 119.6(19) 118.9

123.8(4) 123.4(17) 123.9 124.6

118.2(3) 118.3(8) 118.3

119.1(3) 119.7(17) 119.0

119.2(4) 119.3(7) 118.9

With geometrical constraints.

E

dx.doi.org/10.1021/cg5007428 | Cryst. Growth Des. XXXX, XXX, XXX−XXX

Crystal Growth & Design

Article

Figure 4. Distribution of dihedral angle θ between cycles in (a) diphenyl and (b) 2,2′-dipyridine molecules from CSD data; ED results shown by vertical lines. (c, d) Distributions of intercycle C−C bond length d1 in the same molecules over θ. (e, f) Bond lengths d1 and d2 in diphenyl vs temperature of the study.

Scheme 1). Noteworthy, sterically nonfavored cisoid orientation of nitrogen atoms in C5H4N rings, reported in CSD for ∼10% of dipy molecules, is most probably an error. Alteration of the corresponding bond lengths d2/d2′ and d3/d3′ in “cisoid” entries boosts a scatter of data (see Table 4) and may bias their average values. It gives a didactic illustration to a bounded reliability of crystal structures taken from a database. Distributions of geometrical parameters of dicyclic PhPh and dipy molecules are shown in Figures 4 and S3 (Supporting Information). According to X-ray data, both molecules may be either planar or nonplanar. The dihedral angle θ varies from zero to 49.8° (PhPh, Figure 4a) and to 46.0° (dipy, Figure 5b),

with no correlation to R-factor or to temperature of the study (Figure 5c−f). All 12 (PhPh) and 48 (dipy) points clustered at θ = 0° correspond to 1̅ or m special positions of the molecules. ED studies revealed the nonplanar conformation of C6H5− C6H5 (θ = 44.4°) and C6D5−C6D5 (θ = 45.5°) molecules in a gas phase.14 For 2,2′-dipyridine, a conformational equilibrium between anti- (93%, θav = 18°) and gauche- (7%, θav = 56°) forms was found in an ED study where geometrical constraints were applied because of a low molecular symmetry.15 A “blind area” of data points scattered within 0.03−0.04 Å in bond lengths and ca. 3° in bond angles is observed in CSD data for both dicyclic molecules. Intercycle C−C bond distances F

dx.doi.org/10.1021/cg5007428 | Cryst. Growth Des. XXXX, XXX, XXX−XXX

Crystal Growth & Design

Article

Figure 5. Geometrical parameters of C10H8 molecule (see Scheme 1) from CSD data of naphthalene single crystals: (a) d1 and d3 bond distance vs temperature of a study, (b) γ vs β bond angles.

Table 5. Geometry of Naphthalene C10H8 Molecule (D2h) from Diffraction Data

a

data source

d1, Å

d2, Å

d3, Å

d4, Å

α, deg

β, deg

γ, deg

C10H8 cocrystals, LT WUNLIA, 298 K pure C10H8, X-ray, LT (NAPHTA04-35) pure C10H8, X-ray, 295 K (NAPHTA36) C10H8a, ED16 C10H8a, ED17

1.422(4) 1.396 1.423(2) 1.419 1.420 1.412

1.416(4) 1.422 1.421(2) 1.416 1.422 1.422

1.364(7) 1.363 1.375(2) 1.372 1.371 1.381

1.403(8) 1.389 1.415(5) 1.412 1.412 1.417

118.7(2) 118.1 119.1(1) 119.1 118.4 119.5

120.9(3) 120.2 120.6(2) 120.7

120.4(2) 120.8 120.3(1) 120.3

With geometrical constraints.

(averaged in D2h symmetry) are presented in Table 5. Data for 19 C10H8 molecules in cocrystals determined in routine X-ray studies and 20 high-precision single crystal X-ray and neutron diffraction studies of monoclinic naphthalene (P21/a, Z = 2) with C10H8 molecule in 1̅ position (from NAPHTHA04 to NAPHTHA36 entries; see refs 6 and 7 and references therein) were separately averaged. Unlike other molecules in our analysis, geometry of C10H8 in low-temperature cocrystals and pure naphthalene coincide within error limits, whereas RT data are scarce (one entry in each subset). Bond distances in free C10H8 molecule determined by ED slightly deviate from average LT values (see Table 5). It may be partially due to the overlap of close pair interatomic distances that makes ED refinement results less reliable (see ref 17). Distributions of CSD geometrical parameters show typical features, viz. a “blind area” of randomly scattered points with no correlation to R-factor below R ≈ 0.06 and a negative correlation of bond distances to a temperature of the study, though with a small number of data points (Figure S4 in Supporting Information). Random distributions of CSD geometrical parameters persists in the unique subset of highprecision diffraction studies, but its limits reduced to 0.006− 0.010 Å in bond lengths and 0.4−0.7° in bond angles. A tendency for virtual bond shortening at higher temperature of the study is clearly seen for d1 (Figure 5a) and d3 distances and less pronounced for d2 and d4. Noteworthy, a clear negative correlation of the peripheral β, γ bond angles (Figure 5b) are observed in high-precision C10H8 data. Six-membered arene rings in the “averaged” C10H8 molecules are almost strictly planar like in the case of benzene and pyridine; the virtual

(d1) are scattered in similar ranges independent of R factor (Figure S3 in Supporting Information). A hypothetical positive correlation of d1 to θ, based on stereochemical reasons (central C−C bond in a planar molecule becomes shorter due to πconjugation of aromatic rings), is not observed; instead, a weak opposite trend may be seen in Figure 4c for diphenyl. A virtual shortening of average bond lengths with increasing temperature T of the study is seen (Figure 4e,f). No correlation of bond distances to bond angle (e.g., α) was detected, but a loose negative correlation of the neighboring bond angles α, β may be noticed even in RT data of 2,2′-dipyridine (Figure S3, Supporting Information). Distribution of geometrical parameters in C5H4N cycle of dipy (diminished α-(CCN) bond angle, Table 4) reflects a superposition of specific features observed in PhPh and pyridine molecules (see Table 3). Bond lengths of dipy molecule, determined in roomtemperature X-ray studies, are systematically shortened by 0.010−0.015 Å in comparison with low-temperature data. Splitting of PhPh structures into LT and RT subsets, in spite of a small number of entries, gives a similar result (see Table 4). The averaged values of LT geometrical parameters of diphenyl still deviate significantly from ED data; all symmetrically independent X-ray bond distances are shortened by 0.01−0.02 Å in comparison to free C 6H 5 −C 6H 5 and C 6 D5−C 6D5 molecules. In pure crystalline diphenyl (BIPHEN03) and 2,2′-dipyridine (BIPYRL03, 04) where the molecules occupy 1̅ position of virtual planarity with high off-plane libration9 (see Discussion), the corresponding bond lengths are also shorter than in ED. Naphthalene C10H8. Symmetrically independent bond distances and bond angles in naphthalene C10H8 molecule G

dx.doi.org/10.1021/cg5007428 | Cryst. Growth Des. XXXX, XXX, XXX−XXX

Crystal Growth & Design

Article

than in Fe−C distances (ca. 0.04 Å), though the former bond is stronger and therefore should be more “rigid” for chemical reasons. Broadening of bond lengths distribution and their shift to smaller distances with increasing temperature of the study give rise to a nonregular shape of total data distribution in the “blind area” (Figure 6d). The values of dihedral angle between ligands in Cp2M sandwich, obscured by imposing a strict D5 or D5d symmetry, are not negligibly small: up to 6° for sandwiches in a general position and bigger for ferrocenium cation Cp2Fe+ and substituted derivatives CpFeCp′ than for neutral Cp2Fe molecule (see Table 6 and Figure S5 in Supporting Information). In all subsets, average θ values remain actually constant in different intervals of temperature.

deviations of carbon atoms from the mean plane lie within 0.004 Å. Ferrocene (C5H5)2Fe and Its Derivatives. Three main average geometrical parameters of (C5H5)2Fe sandwich moiety are C−C and Fe−C bond lengths, and dihedral angle θ between the main planes of two rings (Table 6). Two (η5Table 6. Geometry of Ferrocene Molecule (C5H5)2Fe and Ferrocenium Cation (C5H5)2Fe+ (D5) from Diffraction Data (see Scheme 1) data source

C−Cav, Å (d1)

Fe−Cav, Å (d2)

Ferrocene (C5H5)2Fe CSD, LT data 1.419(6) 2.041(10) CSD, RT data 1.386(21) 2.033(24) pure ferrocene, X-ray, LT 1.421(5) 2.045(5) (FEROCE16, 17, 18, 24) pure ferrocene, 294 K 1.396 2.023 (FEROCE27) molecule (C5H5)2Fe, ED18 1.440(2) 2.064(3) Ferrocenium (C5H5)2Fe+ CSD, LT data 1.401(14) 2.078(12) CSD, RT data 1.385(22) 2.062(18) Substituted Ferrocenes CpFeCp′ 85−100 K 1.419(7) 2.046(6) 103−150 K 1.414(8) 2.044(6) 153−250 K 1.410(11) 2.042(8) 267−300 K (RT) 1.399(15) 2.036(10)

θ(Cp/Cp), deg

■

1.1(11) 0.9(7) 0.6(2)

DISCUSSION Structural data for six typical small molecules, ferrocenium cation, and substituted ferrocene sandwiches, taken from high quality diffraction experiments, display the following general properties: (1) All distributions contain “blind area” of uncertainty where data points are randomly scattered, instead of clustering around some limiting values. Data of routine low-temperature studies are typically distributed within 2−4 pm (0.02−0.04 Å) in bond distances and 2−3° in bond angles. High precision X-ray and neutron diffraction data of naphthalene lie in more narrow limits of ca. 0.01 Å and