ARTICLE pubs.acs.org/JPCA
Evidence for Side-Chain π-Delocalization in a Planar Substituted Benzene: An Experimental and Theoretical Charge Density Study on 2,5-Dimethoxybenzaldehyde Thiosemicarbazone Louis J. Farrugia*,† and Aliakbar Dehno Khalaji‡ † ‡
WestCHEM, School of Chemistry, University of Glasgow, Glasgow G12 8QQ, Scotland Department of Chemistry, Faculty of Science, Golestan University, Gorgan, Iran
bS Supporting Information ABSTRACT: The charge density in 2,5-dimethoxybenzaldehyde thiosemicarbazone (1) has been studied experimentally using Mo-KR X-ray diffraction at 100 K, and by theory using DFT calculations at the B3LYP/6-311þþG(2d,2p) level. The quantum theory of atoms in molecules (QTAIM) was used to investigate the extent of π-delocalization in the thioamide side-chain, which is virtually coplanar with the benzene ring. The experimental and theoretical ellipticity profiles along the bond paths were in excellent agreement, and showed that some of the formal single bonds in the side-chain have significant π-bond character. This view was supported by the magnitudes of the topological bond orders and by the delocalization indices δ(ΩA, ΩB). An orbital decomposition of δ(ΩA, ΩB) demonstrated that there was significant π-character in all the interchain non-H chemical bonds. On the other hand, the source function referenced at the interchain bond critical points could not provide any evidence for π-delocalization, showing instead only limited σ-delocalization between nearest neighbors. Overall, the topological evidence and the atomic graphs of the oxygen atoms did not provide convincing evidence for π-delocalization involving the methoxy substituents.
’ INTRODUCTION The quantum theory of atoms in molecules (QTAIM)1 is providing a fresh outlook on many fundamental chemical concepts, by analyzing the problem in terms of the observable electron density, rather than the wave function and its composite orbitals. Good examples include the use of QTAIM in understanding concepts of aromaticity,2 and the hydrogen bond,3 as well as in the analysis of such diverse areas as Raman scattering intensities4 and active sites on extended surfaces.5 A recent monograph by Matta and Boyd1c provides numerous other examples of the use of QTAIM. Merino et al.6 have recently reviewed the concept of electron delocalization through analysis of scalar molecular fields, primarily the electron density. They conclude6 that “the electron delocalization is a notoriously difficult concept to extract directly from the topology of the electron density.” In a similar vein, Matito and Sola7 and Farrugia and Macchi8 have examined the concept of electron delocalization in transition metal complexes and metalmetal bonds using QTAIM methods. The concept of π-delocalization is a central one in organic chemistry and is used, for instance, in undergraduate explanations for the observed restricted rotation in amides and thioamides, r 2011 American Chemical Society
where a resonance form with partial CN π-character is invoked (see scheme below).9
In fact, as Laidig and Cameron10 have shown through examination of Fermi holes, there is little evidence for π-delocalization between the N and S atoms in thioamides. In their analysis, the rotation barrier arises because of a loss of CN attraction due to the lengthening of the bond. The pyramidalization energy for the N atom is greater in thioamides than in amides, hence the larger barrier to rotation in the former. The molecule 2,5-dimethoxybenzaldehyde thiosemicarbazone (1) has been shown11 to have an essentially planar arrangement for all non-H atoms. The presence of the thioamide group and Special Issue: Richard F. W. Bader Festschrift Received: March 20, 2011 Revised: April 27, 2011 Published: May 10, 2011 12512
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The Journal of Physical Chemistry A formally conjugated double bond provides the potential for more extensive π-delocalization, including the arene ring.
Since excellent quality crystals of 1 were available, the electron density and π-delocalization were examined from the experimental and theoretical charge density, using various QTAIM indicators. We show that ellipticity profiles provide a robust method of indicating preferential planes of charge accumulations in a variety of chemical bonds, with excellent agreement between experiment and theory. In combination with orbital analysis of the delocalization indices, they allow an assessment of the π-delocalization in the system, and provide good evidence that this delocalization extends over the entire thioamide substituent chain. Although some theoretical studies on free thiosemicarbazones have been reported,12 as far as we are aware, this is the first reported QTAIM analysis of the density in these molecules.
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Table 1. Experimental Crystallographic and Refinement Dataa compound formula
C10H13N3O2S
Mr
239.29
space group
Pbca
crystal system
orthorhombic
a/Å
11.0859(1)
b/Å
13.0805(1)
c/Å
15.8132(2)
V/Å3 Z
2293.06(4) 8
Dcalc/g cm3
1.386
F(000)
1008
λ/Å
0.71073
μ(MoKR)/mm1
0.272
crystal size/mm
0.50 0.34 0.28
transmission coefficients (range)
0.864 - 0.941
θ range/deg sin(θmax)/ λ
2.58 - 50.07 1.0785
no. of data used for merging
482636
no. of unique data
12054
hkl range
23 f 23; 28 f 27;
Rint
0.0501
Rσ
0.0288
34 f 34
Spherical Atom Refinement
’ EXPERIMENTAL AND COMPUTATIONAL PROCEDURES Data Collection, Processing and Spherical Atom Refinement. High quality crystals of compound 1, suitable for charge
density analysis, were grown from ethanol. Details of data collection procedures are given in Table 1. A suitable crystal of 1 was cooled from ambient temperature to 110 K over a period of 1 h, using an Oxford Instruments Cryostream. Data were collected on a Bruker-Nonius KappaCCD diffractometer, running under Nonius Collect software.13a A total of 4021 frames in 46 scan-sets were measured over a period of 44.8 h, using ω- or j-scans. An integration time of 72 s was used for scan-sets 115 (scan angle 1.8°). These scan-sets were repeated with an integration time of 7 s to remeasure the intense low angle data accurately. The high angle data were collected in scan sets 3146 with a scan angle of 1.2° and an integration time of 132 s. The unit cell dimensions used for refinement purposes were determined by postrefinement of the setting angles of a significant portion of the data set, using the Scalepack program.13b The frame images were integrated using Denzo(SMN),13b and the resultant raw intensity .x files were processed using a locally modified version of DENZOX.14 The resultant intensity measurements were corrected for absorption correction by Gaussian quadrature,15 and a second semiempirical correction16 (without a θ dependent correction) was applied to remove any residual absorption anisotropy due to the mounting medium, and account for other errors such as machine instabilities. The data were sorted and merged using SORTAV,17 giving 12054 independent data with a mean redundancy of 40.0. The data set is effectively 100% complete in the range 0 < θ e 50.07°, with just five reflections missing in the region of sin(θ)/λ around 0.56 Å. A spherical atom refinement using SHELXL97-218 was initially
no. of data in refinement
12054
no. of refined parameters
198
final R [I > 2σ(I)] (all data)
0.0321 (0.0416)
Rw2 [I > 2σ(I)] (all data)
0.0864 (0.090)
goodness of fit S
1.081
maximum features in electron
0.547(max) 0.268(min)
density map/eÅ3 max shift/esd in last cycle
1.0 103
Multipole Refinement no. of data in refinement
10515
no. of refined parameters
460
final R [I > 2σ(I)] (all data)
0.022(0.036)
Rw [I > 2σ(I)]
0.024
goodness of fit S
1.394
maximum features in electron
0.225, 0.226, 0.043(rms)
density map/eÅ3 (all data) (data truncated to resolution of 0.8 Å1) max shift/esd in last cycle
0.085, 0.096, 0.018(rms) 3σ(F) included in the refinement. The multipole expansion was truncated at the hexadecapole level for all non-H atoms and the dipole level for the isotropic H atoms. The importance of employing anisotropic displacement parameters (adp’s) for H atoms in multipole refinements has been emphasized by a number of workers.23 Since neutron diffraction data were not available for 1, the H atom adp’s were estimated by the SHADE2 program of Madsen24 from the non-H atom adp’s obtained after the multipole refinement. This method has been demonstrated to provide an excellent approximation to the H atom adp’s.25 These estimated H atom adp’s were kept fixed in all subsequent refinements, and the H atoms were expanded to the quadrupole level in the multipole model. The H atom positional parameters were fixed at the neutron-determined CH distances of 1.091 Å for the methyl H’s, 1.083 Å for the aromatic H’s, and 1.01 Å for the NH atoms. Each pseudoatom was assigned a core and spherical-valence scattering factor derived from the relativistic DiracFock wave functions of Su and Coppens26 expanded in terms of the single-ζ functions of Bunge, Barrientos, and Bunge.27 The radial fit of these functions was optimized by refinement of the expansioncontraction parameter k. The valence deformation functions used a single-ζ Slater-type radial function multiplied by the density-normalized spherical harmonics. The initial constrained model, with enforced mirror-symmetry for all non-H atoms [except the methyl carbons C(12) and C(15)] was found to provide an excellent fit. As this constrained model gave only very marginally higher R values than an unconstrained one, the enforced mirror-symmetry was retained for the final refinement. In view of comments by Coppens et al.,28 a number of radial models for the sulfur atom were examined. These differ in the values of n(l) in the exponent of the Slatertype radial function, and the (2,4,6,8) model recommended by Coppens et al.28 was found to provide the best model, though the difference between this and other models was very marginal. As some sharp features near the sulfur atom remained in the difference map, an anharmonic model was examined for this atom. The importance of considering anharmonic motion has been stressed in a number of recent charge density studies on molecular crystals.2932 The anharmonic thermal parameter T(H) is expressed as a series expansion in terms of the harmonic thermal parameter T0(H). 4 2 TðHÞ ¼ 1 π3 iCijk hi hj hk þ π4 Dijkl hi hj hk hl þ ::: T0 ðHÞ 3 3 The coefficients Cijk and Dijkl are the third- and fourth-order GramCharlier quasi-moments of the probability density function (pdf) and are refinable parameters. A significant improvement in fit was observed when third- and fourth-order GramCharlier coefficients were included for the sulfur atom in the refinement, with R(F) being reduced from 2.27% to 2.23%, and GoF from 1.411 to 1.394. Moreover, the resulting difference Fourier map
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showed no features near the sulfur atom (Figure S1, Supporting Information). In order to avoid potential correlations33 between the multipole parameters and anharmonic coefficients, they were initially refined in separate blocks. However, in the final cycles they were refined together, and no significant corrrelations between these parameters were noted. The acceptability of the resulting pdf3436 was verified using the XDPDF module of XD. In the case of harmonic (Gaussian) thermal motion, a simple mathematical check (i.e., a positive-definite Uij tensor) can verify that the pdf is physically meaningful. Such an approach is not feasible for the GramCharlier coefficients, which are just coefficients in a series expansion, and devoid of any physical significance. One way to demonstrate that the total pdf is physically meaningful is to verify that it is everywhere positive.3436 The total integrated negative probability for the sulfur atom was only 0.003%, and the negative regions were far from the nuclear position. This is a very small value, so the refined anharmonic coefficients were judged acceptable, and the anharmonicity was retained in the final model. The successful deconvolution of thermal motion was judged by the Hirshfeld rigid bond criterion for the non-H adp’s.37 The mean Δ-msda (mean square displacement amplitude) was 0.3 103 Å, with the highest individual value of 0.8 103 Å for C(12)O(12). A scatter plot of the scale factor Fobs/Fcalc against sin(θ)/λ showed no significant trends, difference Fourier maps were featureless, and a residual density analysis38 implied no unmodeled features remained in the data (see Figures S1S3, Supporting Information). The density derived from the final pseudoatom multipole model based on refinement against the experimental structure factors is designated as the “experimental multipole” density. The multipole populations are given in Tables S3S7 (Supporting Information. A similar multipole refinement was also undertaken using the 605612 theoretical static complex structure factors obtained analytically using the program DENPROP39 from the DFT wave function (see below) for reciprocal lattice points corresponding to a pseudocubic unit cell of a = 30 Å, and a resolution of sinθ/λ e 1.1 Å1. This is designated as the “theoretical multipole” density. All non-H atoms were expanded to the hexadecapole level, with mirror symmetry imposed for all atoms except the methyl carbons. The same level of multipole expansion used for the experimental multipole model was employed, but all thermal parameters were set to zero and the positional parameters were not refined. The space group is effectively P1, and in view of the well-known problems of refinement of multipole models in noncentrosymmetric space groups,40 phase-constrained refinement as implemented in XD-200622 was used to avoid any phase ambiguity. The multipole populations are given in Tables S8S12 (Supporting Information). Theoretical Studies. Gas-phase DFT calculations on 1 at the optimized geometry were undertaken with the program GAUSSIAN09,41 using the B3LYP42 functional and the 6-311þþG(2d,2p) basis for all atoms. The optimized geometry has virtually exact Cs symmetry, although this was not imposed in the optimization procedure. Topological analysis was undertaken using the programs AIMPAC,43 AIM2000,44 or AIMALL.45 The theoretical integrated source function (SF) and its orbital decomposition was obtained using a locally modified version of the program DENPROP.39 The reference points were the 29 bond critical points (bcp’s) and the single ring critical point (rcp). The discrepancy between the recovered density from the SF and the actual density at the reference point was typically less than 1%, often less than 0.1% (see Table S13, Supporting Information), 12514
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Figure 1. ORTEP plot of 1 showing the atomic labeling scheme, with thermal ellipsoids drawn at the 50% probability level.
apart from at the rcp, where the density is an order of magnitude smaller than that at the bcp’s.
’ RESULTS AND DISCUSSION Description of the Structure. Since there are no significant geometrical differences between the spherical atom and multipole refinements, we describe the results from the more accurate multipole refinement. An ORTEP plot of the molecule is shown in Figure 1. The crystal structure of 1 at 100 K has been independently reported in a recent communication.11 Apart from an increased precision in our study, there are no significant metrical differences between these two determinations. The correlation coefficient between corresponding interatomic distances from these two studies is 99.82%, with a slope of unity (see Figure S4 and Table S1, Supporting Information). The entire non-H framework is close to coplanar, with the largest deviations from the mean-plane of all non-H atoms being 0.1925(3) Å for N(5) and 0.1576(1) Å for S(1). The thioamide group is thus tilted slightly out of the plane of the remaining non-H atoms, with a torsion angle N(2)N(3) C(4)-S(1) of 175.6(1)°. Although there are only two formal double bonds in the substituent chain, i.e., C(1)N(2) = 1.2878(3) Å and C(4)S(1) = 1.6986(3) Å, all non-H XY distances are shorter than formal single XY bonds.46 This is suggestive of significant π-delocalization over the whole sidechain. The DFT-optimized structure is very similar to the experimental one, with differences between corresponding bond lengths typically being 0.01 Å, or less. The non-H framework of the optimized structure is virtually exactly coplanar, with a maximum deviation of 0.002 Å for N(5). Topological Analysis of the Electron Density. It is increasingly popular to use QTAIM1 methods to analyze the charge density, F(r), in chemical systems.47 There are two main reasons: first the profoundly useful ability of QTAIM to recover chemical structure through the analysis of the quantum observable F(r), and second this technique is applicable to densities obtained from any source. It provides a common basis to assess, on the one hand, the quality of experimental data and the efficacy of the commonly used multipole models and, on the other hand, the effects of electron correlation and the limitations of basis sets in
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theoretical calculations. We have examined the molecular charge density in 1, reconstructed from the experimental and theoretical atomic multipole populations (molecule from a crystal), and from the DFT wave function of the gas phase molecule. The topological characteristics of all bcp's in the electron density derived from the experimental multipole density, the theoretical density and the theoretical multipole density are given in Table 2. The topological structure according to QTAIM is the molecular graph, the combination of the critical points and bond paths. The molecular graphs for all density models are qualitatively identical, that obtained from experimental multipole density being shown in Figure 2. The integrated atomic charges and atomic volumes are given in the Supporting Information (Table S2). The magnitudes of F(rb) and r2F(rb) given in Table 2 are typical47d of many topological studies on organic molecules and as such merit little comment. They indicate strong covalent bonding, as the Laplacian is strongly negative. The most significant discrepancy between theory and experiment lies in the position of the bcp for the CS bond, which is noticeably closer to the C atom for the experimental graphs,48 and is especially visible in the Laplacian map (experimental, Figure 3; theoretical, Figure S4, Supporting Information). This discrepancy between experimental and theoretical topologies for polar covalent bonds is well-known49 and was probably first stated in print by Gatti et al.50 The bcp lies in a region where the curvature λ3 is varying strongly, and as a result the Laplacian r2F(rb) may differ significantly between theory and experiment, while F(rb) is much less variable. The differences between the theoretical properties and those from the theoretical multipole model arise primarily because of the inadequacies of the Hansen and Coppens21 multipole model, usually attributed49a to the deficiencies of the radial functions used. Atomic Graphs. It is now well established1ac,e that the Lewis concept of bonding pairs and lone pairs of electrons may be recovered by the Laplacian of the density in the valence shell charge concentrations (VSCC) surrounding atoms. The Laplacian map in Figure 3 clearly shows the charge concentrations from the lone pairs on the sulfur atom and indeed three (3,3) cp’s are detected in the VSCC, corresponding to a bonding pair and two lone pairs. The charge distribution in the VSCC is succinctly described in terms of the critical points in r2F(r), known as the atomic graph. This graph is a [V,E,F] polyhedron satisfying Eulers rule, such that V þ F E = 2 and where the vertices (V) are the (3,3) cp’s of charge concentration, the edges (E) are the saddle point (3,1) cp’s, and the faces (F) are the (3,þ1) cp’s of charge depletion in the negative Laplacian. Of particular interest is the situation regarding the lone and bonding pairs of the oxygen atoms of the methoxy groups. Two possibilities may be envisaged, with either one or two lone pairs, corresponding to atomic hybridizations of sp3 or sp2 respectively. Only in the latter case would delocalized π-bonding to the benzene ring be feasible. In fact, the experimental atomic graph of O(15) (Figure 4) has the form [4,5,3], with two distinct charge concentrations corresponding to two lone pairs. This in turn suggests that the hybridization of the O atoms can be considered as sp3, thus limiting the possibilities for π-delocalization involving this atom. The experimental atomic graph of O(12) (Figure S6, Supporting Information) is somewhat unusual, in that a saddlepoint (3,1) cp is found along the O(12)C(112) interatomic vector, instead of the expected (3,3) charge concentration. The reason for the differing experimental atomic graphs of two oxygen atoms is not clear, as the theoretical 12515
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Table 2. Experimental and Theoretical Topological Properties at bcp'sa bond S(1)C(4)
C(4)N(5)
C(4)N(3)
N(2)N(3)
C(1)N(2)
C(1)C(111)
C(111)C(112)
C(112)C(113)
C(113)C(114)
C(114)C(115)
C(115)C(116)
C(116)C(111)
F(rb) c
r2F(rb) d
λ1d
λ2d
λ3d
ε
ntopol
0.8930
1.42
5.60
6.33
5.60
6.33
0.13
1.59
0.9457
1.43
7.78
6.13
5.52
3.87
0.11
1.60
0.9222
1.40
6.12
5.36
4.93
4.18
0.09
1.66
0.5464
0.7847
2.37
26.10
19.83
16.37
10.11
0.21
1.17
1.3439
0.5324
0.8116
2.28
26.88
19.28
16.50
8.91
0.17
1.06
1.3439
0.5946
0.7492
2.27
18.48
19.35
15.97
16.84
0.21
1.14
1.3566(3)
0.5405
0.8161
2.30
27.44
19.85
16.78
9.19
0.18
1.06
1.3664 1.3664
0.5364 0.6011
0.8304 0.7655
2.17 2.17
25.13 16.70
18.13 18.36
15.66 15.15
8.66 16.81
0.16 0.21
0.98 1.06
Rbb
d1b
1.6986(3)
0.8057
1.6743
0.7287
1.6743
0.7521
1.3311(3)
d2b
1.3724(3)
0.6664
0.7061
2.30
5.85
19.11
17.47
30.72
0.09
1.39
1.3562
0.6668
0.6897
2.37
12.71
19.83
18.36
25.48
0.08
1.28
1.3562
0.6711
0.6854
2.28
4.09
19.45
17.36
32.73
0.12
1.38
1.2878(3)
0.4594
0.8290
2.65
32.96
23.17
18.57
8.79
0.25
1.35 1.34
1.2832
0.4618
0.8231
2.53
23.42
22.08
17.37
16.03
0.27
1.2832
0.5107
0.7728
2.55
26.55
21.81
17.40
12.66
0.25
1.34
1.4629(3) 1.4592
0.7390 0.7385
0.7239 0.7208
1.90 1.86
15.74 16.83
13.61 14.06
12.02 12.58
9.90 9.81
0.13 0.13
1.20 0.98
1.4592
0.7390
0.7202
1.84
12.48
13.53
11.85
12.90
0.14
1.15
1.4135(3)
0.6888
0.7249
2.12
19.00
16.04
13.20
10.25
0.22
1.36
1.4141
0.6916
0.7231
2.05
20.20
16.30
13.44
9.54
0.21
1.10
1.4141
0.6981
0.7164
2.02
15.32
15.61
12.67
12.96
0.23
1.28
1.3944(4)
0.7050
0.6896
2.13
18.24
16.31
12.83
10.90
0.27
1.42
1.3886
0.7166
0.6725
2.13
21.85
17.08
13.80
9.02
0.24
1.16
1.3886 1.4013(4)
0.7071 0.6677
0.6818 0.7336
2.10 2.06
16.43 16.55
16.17 15.31
12.71 12.78
12.71 11.54
0.25 0.20
1.38 1.37
1.3953
0.6980
0.6974
2.08
20.65
16.14
13.59
9.08
0.19
1.17
1.3953
0.6983
0.6971
2.06
15.67
15.54
12.83
12.70
0.21
1.37
1.3959(3)
0.6841
0.7121
2.15
18.36
16.48
12.98
11.10
0.27
1.44
1.3927
0.6788
0.7147
2.12
21.57
16.91
13.81
9.15
0.22
1.16
1.3927
0.6832
0.7100
2.09
16.36
16.01
13.01
12.66
0.23
1.37
1.3946(2)
0.7194
0.6755
2.17
20.64
17.33
13.62
10.31
0.27
1.29
1.3911 1.3911
0.7145 0.7109
0.6770 0.6803
2.14 2.11
22.23 17.23
17.25 16.42
14.14 13.40
9.17 12.59
0.22 0.22
1.13 1.33 1.34
1.3991(3)
0.6966
0.7025
2.10
18.28
15.71
13.38
10.80
0.17
1.3929
0.6901
0.7028
2.09
21.02
16.38
13.70
9.06
0.20
1.15
1.3929
0.6909
0.7020
2.06
15.65
15.57
12.94
12.85
0.20
1.36 1.04
1.3660(4)
0.5487
0.8180
2.07
21.03
17.07
15.62
11.66
0.09
1.3679
0.4777
0.8912
1.94
14.95
14.90
14.05
14.01
0.06
0.94
1.3679
0.5645
0.8037
1.98
14.30
16.11
14.58
16.38
0.10
0.93
O(12)C(12)
1.4208(4) 1.4205
0.8546 0.9162
0.5667 0.5053
1.81 1.70
15.26 13.17
13.99 11.56
12.42 11.47
11.15 9.87
0.13 0.01
0.87 0.82
1.4205
0.8269
0.5941
1.73
10.59
13.32
12.79
15.52
0.04
0.74
C(115)O(15)
1.3748(4)
0.5228
0.8522
1.97
19.32
16.11
13.95
10.73
0.15
0.98
1.3675
0.4788
0.8898
1.95
15.43
15.03
14.24
13.83
0.06
0.95
1.3675
0.5672
0.8009
1.99
14.72
16.47
14.69
16.44
0.12
0.93
C(112)O(12)
O(15)C(15)
1.4272(4)
0.8650
0.5631
1.75
14.03
13.09
11.80
10.85
0.11
0.83
1.4194
0.9137
0.5066
1.71
13.63
11.75
11.65
9.77
0.01
0.82
1.4194
0.8236
0.5962
1.75
10.83
13.54
12.96
15.67
0.04
0.75
a
Top line gives experimental values, second line gives theoretical values from B3LYP wave function, third line gives values from multipole modeling of theoretical structure factors. b Rb is the internuclear distance, d1, d2 are distance of the bcp to the nuclei in units of Å. c In units of e Å3. d In units of e Å5.
graphs of both are identical to O(15) shown in Figure 4. It is likely that experimental error is responsible, as it is known that the atomic graphs are very susceptible to errors of this type.51
Profiles of the Bond Ellipticities. It is well-known that there is a reasonable (nonlinear) correlation between interatomic distances and F(rb) for chemically similar bonds.1 12516
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Figure 4. Experimental atomic graph of O(15). The critical points of r2F(r) in the VSCC are color-coded: (3,3) cp’s in green, (3,1) cp’s in yellow, and (3,þ1) cp’s in red; interatomic OC vectors are shown in blue. Values of F at critical points are given in e Å3.
Figure 2. Molecular graph of 1 obtained from the experimental multipole model, with a section from theoretical graph inset. bcp's are shown as small red spheres, and the (3,þ1) rcp is shown as a small yellow sphere. The viewpoint is the same as in Figure 1.
Figure 3. Negative Laplacian function r2F(r) of the static density through the plane obtained from the experimental multipole model. Contours are drawn at 1.0 10-3, ( 2.0 10n, ( 4 10n, ( 8 10n (n = 3, 2, 1, 0, þ1, þ2) e Å5, negative contours are shown in red, positive in blue. Positions of the bcp's are shown as small red spheres.
This correlation has led to definitions of empirical bond indices ntopol based on the value of F(rb).52a More recently, an extension to include the eigenvalues of the Hessian matrix has been proposed.52b,c The expression of Howard and Lamarche52b ntopol ¼ a þ bðλ1 þ λ2 Þ þ cλ3 þ dFbcp was used to compute the values of ntopol given in Table 2. The values of the parameters a, b, c, and d for various types of bonds were taken from refs 52, and the values of Fbcp and λ1,2,3 (in au)
from the topological analyses. The agreement between the two multipole derived model densities is better than that with the wave function density. The values of ntopol for all the non-H bonds in the thioamide side-chain imply bond orders greater than unity; this is not so for the OC bonds of the methoxy substituents. It is noteworthy that these crudely estimated bond orders are often very similar to their corresponding delocalization indices (see below). The reader should bear in mind that an overdependence on the local properties at the bcp to extract information of chemical interest is not always profitable. As we emphasize at several points in this paper, in compound 1, F(rb) can formally have little or no contribution from π-density, as the critical point invariably lies close to the nodal plane of any π-orbitals associated with the bonded atoms. The increase in F(rb) with shorter bond distances merely reflects an increasing σ-contribution. On the other hand, the preferential accumulation of density in a plane, due to the formation of a π-bond, is detectable in the density distribution53a and may be quantified in terms of the ellipticity ε at the bcp, which is defined as (λ1/λ2) 1. Single bonds and cylindrically symmetrical π-bonds, such as in CO, typically have values of ε close to zero, whereas aromatic CC bonds have values of ε that are typically ∼0.2. In compound 1, the ellipticity ε is quite significant for most bonds, except for O(12)C(12) and O(15)C(15). The connection between the ellipticity ε at the bcp and other physicochemical properties such as electron delocalization is of course well-known, as shown, for example, by the work of Popp and co-workers.54 However, as pointed out originally by Cheeseman et al.,53a and later by Tafipolsky et al.,53b focusing on just the ellipticity at the bcp may be deceptive for polar covalent bonds, and in these cases it is better to examine the profile of ε along the entire bond path. Representative plots of such profiles for the experimental and theoretical densities are given in Figures 5 and 6, respectively. These plots also show the angle jref, which is the angle between the eigenvector of the principal axis of ellipticity λ2 (i.e., the axis of least curvature perpendicular to the bond path and λ3) and a reference plane, designated as the π-plane. In the case of 1, the reference π-plane is the mean plane of the substituent atoms C(1)N(2)N(3)-C(4)S(1)N(5). If π-delocalization is present in the side-chain, then electron density should be accumulated along the bonds, perpendicular to this reference plane, and the ideal angle jref angle should be zero. As is clear from Figures 5 and 6, there are abrupt changes of jref from small values to values approaching 90°, and these are usually associated with the maxima in ε occurring around 0.3 - 0.6 Å from the bcp. These maxima are in turn associated with the atomic charge 12517
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Figure 5. Experimental ellipticity profile plots from the multipole model.
Figure 6. Theoretical ellipticity profile plots from direct analysis of wave function density. 12518
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Table 3. Delocalization Indices δ(ΩA,ΩB) and Percentage π-Composition atom pairs, AB
δ(ΩA,ΩB)
δ(ΩA, ΩB)π
S(1)C(4)
1.540
30.6
C(1)N(2) C(4)N(3)
1.503 1.070
43.6 25.3 27.8
C(4)N(5)
1.168
N(2)N(3)
1.286
18.7
C(1)C(111)
1.069
15.2
O(12)C(12)
0.879
12.7
O(12)C(112)
0.924
20.4
O(15)C(15)
0.887
12.8
O(15)C(115) C(111)C(116)
0.925 1.351
19.9 29.6
C(111)C(112)
1.229
25.7
C(112)C(113)
1.338
30.2
C(113)C(114)
1.360
29.5
C(114)C(115)
1.315
29.0
C(115)C(116)
1.303
28.7
C(1)H(1)
0.895
2.1
N(3)H(3) av CarylH
0.769 0.944
4.1 3.2
av NamideH
0.794
4.9
av CmethylH
0.927
2.4, 48.4
S(1) 3 3 S(1) 3 3
3 N(3) 3 N(5)
0.175
45.6
0.206
56.4
N(3) 3 3 3 N(5) C(1) 3 3 3 N(3) C(4) 3 3 3 N(2)
0.155
51.4
0.125
65.4
0.047
33.6
concentrations, primarily of the N and O atoms, observable in the Laplacian map (Figure 3). At these maxima, it is commonly observed that the principal axis of ellipticity flips into (or very close to) the π-reference plane, i.e. the molecular plane. The relatively high value of ε at these points is clearly not related to any π-character of the bond, but it tends to obscure any πaccumulation along the bond. The typical profile for an aromatic CC bond53a is exemplified by that shown for C(111)C(116). For a substantial zone on either side of the bcp, the value of ε is >0.15 and the value of angle jref is constant and very close to zero. This indicates that over the central part of the CC bond, there is charge accumulation in the plane perpendicular to the molecular plane, exactly as expected for a CC π-bond. The profiles along C(4)S(1) and C(1)N(2) are essentially the same, and hence confirm the strong π-character for these (formal) double bonds. Interestingly, the profile for C(111) C(1) shows a qualitatively similar appearance, and suggests significant π-character for this (formal) single bond. This in turn may be taken as direct evidence for π-delocalization between the benzene ring and the CdN double bond. The remaining profiles in Figure 5 all show extended zones where the angle jref is low in value, but the profiles are dominated by the high values of ε associated with the charge concentrations on the O and N atoms. Because of this overwhelming influence, it is difficult to ascribe with any certainty significant π-character to these bonds, although the profiles of C(4)N(3) and C(4)N(5) are not inconsistent with some π-character. For the N(2)N(3) bond profile, however, which has a relatively large delocalization index
(see below), it is difficult to see any evidence for π-character. Nevertheless, the great similarity between the experimental and theoretical profiles is demonstrated here, and notwithstanding the variation of profiles with the basis-set as reported by Tafipolsky et al.,53a it suggests they are robust topological indicators. The use of bond ellipticity profiles has recently received some attention. For instance, Scherer and co-workers55a have proposed that CC bond ellipticity profiles are a useful indicator of agostic bonding, while Stalke and co-workers55b,c have used these profiles as indicators of bond polarizations and multiplicities . Delocalization Indices. The delocalization index, δ(ΩA, ΩB), originally defined by Bader and Stephens,56a provides a measure of the Fermi correlation shared (and hence the electrons shared) between two atomic basins ΩA and ΩB. As these basins need not share an interatomic surface, this index may be computed for any pair of atoms, regardless of whether they are formally chemically bonded. The interpretation of δ(ΩA, ΩB) at the HartreeFock (HF) level, and for homopolar bonds, is simply the number of pairs of shared electrons.56 For other situations, there is no direct relationship between this index and chemical concepts of bond order. At the DFT level the interpretation of δ(ΩA, ΩB) is even more ambiguous,57 but despite this, the DFT delocalization indices are in general quite similar numerically57,58 to those computed at the HF level and are often quoted. Table 3 gives the delocalization indices for specific atomic AB interactions in 1. For the formal single bonds, CH, NH, and CO, the index δ(ΩA, ΩB) is slightly less than unity. For the aryl CC bonds δ(ΩA, ΩB) is ∼1.3, while for the two unequivocal double bonds it is ∼1.5. The remaining bonded pairs of atoms in the side-chain have δ(ΩA, ΩB) greater than unity, suggestive of partial bond multiplicity. This is particularly so for δ(ΩN2, ΩN3), which has a value close to the aryl CC bonds. The delocalization index δ(ΩA, ΩB) unfortunately does not distinguish between a direct exchange between centers A and B, and that mediated through other atomic centers. We have suggested8 that an analysis of δ(ΩA, ΩB) in terms of contributions from individual canonical orbitals may provide some insight into this issue. On examining this decomposition for compound 1, we find that the delocalized nature of many of the Kohn Sham canonical orbitals prevents a clear picture emerging, at least in terms of dominating orbital contributions. Consider the case of the formally double CdS bond. The four predominant contributors for δ(ΩS1, ΩC4) are shown in Figure 7, but these provide only 56.4% of the total. The remainder is made up from smaller contributions from other orbitals. However, since the molecule is effectively planar, the MO’s may be divided conveniently into two classes: the A0 σ-orbitals, which are symmetric with respect to the mirror-plane, and the antisymmetric A00 orbitals of π-symmetry. The orbital contributions toward δ(ΩA, ΩB) can therefore be decomposed into global σ- and π-contributions. We define the term δ(ΩA, ΩB)π as the global contribution of all π-orbitals toward δ(ΩA, ΩB), and this is given in Table 3 as a percentage. It effectively provides a measure of the π-character of the delocalization index. As expected, all the XH bonds have a tiny contribution from the orbitals of π-symmetry (except for the out of plane methyl CH bonds). The two formal double bonds, S(1)C(4) and C(1)N(2) have the highest δ(ΩA, ΩB)π values, while those for the aryl CC bonds are of a similar magnitude. In particular, we note that the two NC bonds within the thioamide group also have similar π-contributions as the aryl CC bonds, consistent with the standard chemical viewpoint that these are partial π-bonds. Note, 12519
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Figure 7. Predominant orbital contributors to the delocalization index δ(ΩS1, ΩC4).
however, that the integrated atomic charges on the thioamide atoms (Table S2) do not provide any support for the formal polarizations implied by the resonance form shown in the Scheme. The sulfur and particularly the nitrogen atoms bear negative charges, consistent with their greater electronegativities compared with carbon. In addition, it is noteworthy that several of the “two-bond” indices δ(ΩA, ΩC) (i.e., those representing 1 3 3 3 3 interactions) have small but significant values (see Table 3). The two S 3 3 3 N “two-bond” interactions have very substantial π-contributions, further emphasizing the π-delocalization interaction in the thioamide group. This is seemingly in conflict with the results of Laidig and Cameron.10 In conclusion then, this analysis from the delocalization indices is quite supportive of extensive πdelocalization throughout the non-H atom side-chain of 1. Source Function. Bader and Gatti59 have shown that the electron density at any point r within a molecule may be viewed as being determined by a source operating at all other points r0 . The local source at position vector r from r0 , LS(r,r0 ), is given by LSðr, r0 Þ ¼ ð1=4πÞ
r2 Fðr0 Þ jr r0 j
By integrating over the regions of space bounded by the zero-flux surfaces, the density may be equated to a sum of atomic contributions S(r,Ω). Z LSðr, r0 Þdr0 Sðr, ΩÞ FðrÞ ¼
∑Ω
Ω
∑Ω
The integrated form of the SF, S(r,Ω), provides a measure of the relative importance of each atomic basin in determining the density at a specific reference point r. These reference points are normally taken at the bcp’s, as this is the least biased positions for inducing chemical bonding information from the SF, and is the method we adopt here. As an integrated property, S(r,Ω) should provide a more robust chemical descriptor than topological properties evaluated at a single point,60 although the reliance on a reference point tends to mitigate against the advantages of this indicator. Moreover, the interpretation of the SF remains a
Figure 8. Plots of the theoretical integrated SF S(r,Ω). The viewpoint is the same as in Figure 1. Reference points r (yellow spheres) are at bcp's (a) S(1)C(4), (b) C(4)N(5), (c) C(4)N(3), (d) N(2)N(3), (e) C(1)N(2), (f) C(1)C(111), (g) C(111)C(112), (h) C(113) C(114). The volume of each atomic sphere is proportional to the percentage contribution to the density at the reference point from the corresponding atomic basin.
heuristic one, and there are some difficulties if the core density makes significant contributions.61 Despite these misgivings, one could expect the SF to provide some indication of any delocalization of density along the side-chain. It has proved useful in characterizing hydrogen bonds,62ac and more recently has been used to investigate metalmetal interactions in bimetallic carbonyl complexes.62d Figure 8 shows representative plots of the integrated theoretical SF for 1, while Figure S7 shows the corresponding experimental SF (Supporting Information). The theoretically and experimentally derived SF are qualitatively identical, with only small differences between basin contributions (full details are given in Tables S13 and S14, Supporting Information). The picture that emerges is a rather homogeneous one. Almost regardless of which reference point is taken, the S(r,Ω) is highly localized, typically some 88% of the SF coming from the two atomic basins directly associated with the bcp. The remaining much smaller contributions (typically 5% or less) arise from the next nearest atomic basins. One important caveat must be made plain. As we have previously shown,61 the orbital decomposition of S(r,Ω) indicates that the A00 orbitals of π-symmetry make negligible contributions to any S(r,Ω) when the reference point lies on a π-nodal plane. This is clear from an example, the orbital decomposition of S(r,Ω) at the bcp for the S(1)C(4) interaction, which is shown in Figure 9. The four predominant orbital contributers provide 78.6% toward S(r,Ω), and these are all σ-framework orbitals. We can therefore conclude that, for the 12520
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’ ACKNOWLEDGMENT This work was supported by the University of Glasgow and the EPSRC under grant GR/M91433 for the purchase of a KappaCCD diffractometer. ’ DEDICATION Dedicated to Professor Richard F. W. Bader on the occasion of his 80th birthday, for his inspirational energy. ’ REFERENCES
Figure 9. Predominant orbital contributors to the SF S(r,Ω) at the reference point of the S1C4 bcp.
reference points close to the molecular plane, the S(r,Ω) provides little or no information about any π-delocalization. Any delocalization effects observed in the S(r,Ω) must therefore arise from σ-delocalization. The plots of S(r,Ω) shown in Figure 7 would seem to indicate that σ-delocalization is not extensive and limited to next nearest neighbors. If the reference point is moved out of the nodal plane, then the π-orbital contributions increase, as expected, but there is no strong evidence for π-delocalization.
’ CONCLUSIONS The experimental and theoretical ellipticity profiles along the bond paths of 2,5-dimethoxybenzaldehyde thiosemicarbazone (1) are in excellent agreement, indicating that they are robust topological indicators. They showed that several of the formal single bonds in the side-chain have significant π-bond character. The magnitudes of the topological bond orders and the delocalization indices δ(ΩA, ΩB), and an orbital decomposition of δ(ΩA, ΩB) provided further evidence for this view. On the other hand, the SF referenced at the interchain bcp's does not provide any evidence for π-delocalization, showing instead only limited σ-delocalization between nearest neighbors. The evidence for π-delocalization involving the methoxy substituents is less clear. While the values δ(ΩA, ΩB)π for the OC bonds would indicate some partial π-character, the ellipticity profiles and especially the atomic graphs of the oxygen atoms did not provide convincing evidence for significant π-delocalization. ’ ASSOCIATED CONTENT
bS
Supporting Information. Final refined parameters, observed and calculated structure factors in CIF format for the multipole refinements, computational details; supplementary figures (7) of plots of scale factors versus sin θ/λ, residual density maps and distribution plots, Laplacian, and SF; supplementary tables (14) of integrated atomic charges and volumes, multipole populations, SF contribution data. This material is available free of charge via the Internet at http://pubs.acs.org.
(1) (a) Bader, R. F. W. Atoms in Molecules: A Quantum Theory; International Series of Monographs in Chemistry; Oxford University Press: Oxford, 1990; Vol. 2. (b) Popelier, P. Atoms in Molecules: An Introduction; Prentice Hall: Harlow, England, 2000. (c) The Quantum Theory of Atoms in Molecules - From Solid State to DNA and Drug Design; Matta, C. F.; Boyd, R. J., Eds.; Wiley-VCH: Weinheim, Germany, 2007. (d) Koritsanszky, T. S.; Coppens, P. Chem. Rev. 2001, 101, 1583.(e) Gillespie, R. J.; Popelier, P. L. A. In Chemical Bonding and Molecular Geometry - From Lewis to Electron Densities; Oxford University Press: New York, 2001. (2) Matito, E.; Poater, J.; Sola, M. In The Quantum Theory of Atoms in Molecules - From Solid State to DNA and Drug Design; Matta, C. F.; Boyd, R. J., Eds.; Wiley-VCH: Weinheim, Germany, 2007; Chapter 15, pp 399423. (3) (a) Grabowski, S. J. In The Quantum Theory of Atoms in Molecules From Solid State to DNA and Drug Design; Matta, C. F.; Boyd, R. J., Eds.; Wiley-VCH: Weinheim, Germany, 2007; Chapter 17, pp 453469. (b) Koch, U.; Popelier, P. L. A. J. Phys. Chem. 1995, 99, 9747. (c) Rozas, I.; Alkorta, I.; Elguerdo, J. J. Am. Chem. Soc. 2000, 122, 11154. (4) Gough, K. M.; Dawes, R.; Dwyer, J. R.; Welshman, T. A. In The Quantum Theory of Atoms in Molecules - From Solid State to DNA and Drug Design; Matta, C. F.; Boyd, R. J., Eds.; Wiley-VCH: Weinheim, Germany, 2007; Chapter 4, pp 95120. (5) Aray, Y.; Rodríguez, J.; Vega, D. In The Quantum Theory of Atoms in Molecules - From Solid State to DNA and Drug Design; Matta, C. F.; Boyd, R. J., Eds.; Wiley-VCH: Weinheim, Germany, 2007, Ch. 9, pp 231256. (6) Merino, G.; Vela, A.; Heine, T. Chem. Rev. 2005, 105, 3812. (7) Matito, E.; Sola, M. Coord. Chem. Rev. 2009, 253, 647. (8) Farrugia, L. J.; Macchi, P. Struct. Bonding (Berlin) 2011in press. (9) See for example: March, J. In Advanced Organic Chemistry Reactions, Mechanisms and Structure, 3rd ed.; Wiley: New York, 1985; p 111. (10) Laidig, K. E.; Cameron, L. M. J. Am. Chem. Soc. 1996, 118, 1737. (11) Fun, H.-K.; Jebas, S. R.; D’Silva, E. D.; Patil, P. S.; Dharmaprakash, S. M. Acta Crystallogr., Sect. E 2008, 64, o2276. (12) Paiola, C.; Cammi, R.; Pelgatti, P.; Pelizzi, C. J. Mol. Struct. (THEOCHEM) 2003, 623, 105. (13) (a) COLLECT data collection software; Bruker Nonius B.V.: Delft, The Netherlands, 1999. (b) Otwinowski, Z.; Minor, W. Processing of X-ray Diffraction Data Collected in Oscillation Mode. In Macromolecular Crystallography: Methods in Enzymology; Carter, C. W., Jr., Sweet, R. M., Eds.; Elsevier Academic Press: San Diego, CA, 1997; Part A, Vol. 276, pp 307326. (14) Blessing, R. H. DENZOX - Program for processing Denzo x files (1997). Modified for KappaCCD data by Farrugia, L. J.; Muir, K. W.; University of Glasgow: Glasgow, Scotland, 2001. (15) Coppens, P.; Leiserowitz, L.; Rabinovich, D. Acta Crystallogr. 1965, 18, 1035. (16) Blessing, R. H. Acta Crystallogr., Sect. A 1995, 51, 33. (17) Blessing, R. H. J. Appl. Crystallogr. 1997, 30, 421. (18) Sheldrick, G. M. Acta Crystallogr., Sect. A 2008, 64, 112. (19) Farrugia, L. J. J. Appl. Crystallogr. 1997, 30, 565. (20) Farrugia, L. J. J. Appl. Crystallogr. 1999, 32, 837. 12521
dx.doi.org/10.1021/jp2026169 |J. Phys. Chem. A 2011, 115, 12512–12522
The Journal of Physical Chemistry A (21) Hansen, N. K.; Coppens, P. Acta Crystallogr., Sect. A 1978, 34, 909. (22) Volkov, A.; Macchi, P.; Farrugia, L. J.; Gatti, C.; Mallinson, P. R.; Richter, T.; Koritsanszky, T. XD-2006 - A computer program for multipole refinement, topological analysis of charge densities and evaluation of intermolecular energies from experimental or theoretical structure factors, 2006. (23) (a) Whitten, A. E.; Spackman, M. A. Acta. Crystallogr., Sect. B 2006, 62, 875. (b) Whitten, A. E.; Turner, P.; Klooster, W. T.; Piltz, R. O.; Spackman, M. A. J. Phys. Chem. A 2006, 110, 8763. (c) Madsen, A. Ø.; Sørensen, H. S.; Flensburg, C.; Stewart, R. F.; Larsen, S. Acta Crystallogr., Sect. A 2004, 60, 550. (d) Hoser, A. A.; Dominiak, P. M.; Wozniak, K. Acta Crystallogr., Sect. A 2009, 65, 300. (24) (a) Madsen, A. Ø. J. Appl. Crystallogr. 2006, 39, 757. (b) SHADE2 server, http://shade.ki.ku.dk/docs/index.html (accessed May 9, 2011). (25) Munshi, P.; Madsen, A. Ø.; Spackman, M. A.; Larsen, S.; Destro, R. Acta Crystallogr., Sect. A 2008, 64, 465. (26) Su, Z.; Coppens, P. Acta Crystallogr., Sect. A 1998, 54, 646–652. (27) Bunge, C. F.; Barrientos, J. A.; Bunge, A. V. At. Data Nucl. Data Tables 1993, 53, 113–162. (28) Dominiak, P. A.; Coppens, P. Acta Crystallogr., Sect. A 2006, 62, 224. (29) Meindl, K.; Herbst-Irmer, R.; Henn, J. Acta Crystallogr., Sect. A 2010, 66, 362. (30) Zhurov, V. V.; Zhurova, E. A.; Stash, A. I.; Pinkerton, A. A. Acta Crystallogr., Sect. A 2011, 67, 160. (31) Scheins, S.; Zheng, S.-L.; Benedict, J. B.; Coppens, P. Acta Crystallogr., Sect. B 2010, 66, 366. (32) Sørensen, H. O.; Stewart, R. F.; McIntyre, G. J.; Larsen, S. Acta Crystallogr., Sect. A 2003, 59, 540. (33) (a) Mallinson, P. R.; Koritsanszky, T.; Elkaim, E.; Li, N.; Coppens, P. Acta Crystallogr., Sect. A 1988, 44, 336. (b) Restori, R.; Schwarzenbach, D. Acta Crystallogr., Sect. A 1996, 52, 369. (34) (a) Scheringer, C. Acta Crystallogr., Sect. A 1988, 44, 343. (35) Trueblood, K. N.; B€urgi, H.-B.; Burzlaff, H.; Dunitz, J. D.; Gramacciaoli, C. M.; Schultz, H. H.; Shmueli, U.; Abrahams, S. C. Acta Crystallogr., Sect. A 1996, 52, 770. (36) Kuhs, W. F. Acta Crystallogr., Sect. A 1992, 48, 80. (37) Hirshfeld, F. L. Acta Crystallogr., Sect. A 1976, 32, 239. (38) Meindl, K.; Henn, J. Acta Crystallogr., Sect. A 2008, 64, 404. (39) Volkov, V.; Koritsanszky, T.; Chodkiewicz, M.; King, H. F. J. Comput. Chem. 2009, 30, 1379. (40) (a) El Haouzi, A.; Hansen, N. K.; Le Henaff, C.; Protas, J. Acta Crystallogr., Sect. A 1996, 52, 291. (b) Spackman, M. A.; Byrom, P. G. Acta Crystallogr., Sect. B 1997, 53, 553. (41) Frisch, M. J.; Gaussian 03, revision D.02; Gaussian, Inc.: Wallingford, CT, 2004. (42) (a) Stephens, P. J.; Devlin, J. F.; Chabalowski, C. F.; Frisch, M. J. J. Phys. Chem. 1994, 98, 11623. (b) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (c) Becke, A. D. Phys. Rev. A 1988, 38, 3098. (d) Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B 1988, 37, 785. (43) Biegler-K€onig, F. W.; Bader, R. F. W.; Tang, T.-H. J. Comput. Chem. 1982, 3, 317. (44) Biegler-K€onig, F. J. Comput. Chem. 2000, 12, 1040. (45) Keith, T. A. AIMAll, version 10.07.01, 2010, http:// aim.tkgristmill.com. (46) Watson, D. G.; Brammer, L.; Orpen, A. G.; Taylor, R. In International Tables for Crystallography: Mathematical, Physical and Chemical Tables; Kluwer: Dordrecht, The Netherlands, 1995; Vol. C, Chapter 9.5, pp 685706. (47) (a) Coppens, P. X-ray Charge Densities and Chemical Bonding; Oxford Science Publications: Oxford, 1997. (b) Tsirelson, V. G.; Ozerov, R. P. Electron Density and Bonding in Crystals: Institute of Physics Publishing: Bristol, U.K., 1996. (c) Coppens, P. Acta Crystallogr., Sect. A 1998, 54, 779. (d) Koritsanszky, T. S.; Coppens, P. Chem. Rev. 2001, 101, 1583. (48) The bcp in the experimental graph lies 52% along the CS distance, while in the theoretical graph it lies 56% along that distance.
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(49) (a) Volkov, A.; Abramov, Y.; Coppens, P.; Gatti, C. Acta Crystallogr., Sect. A 2000, 56, 332. (b) henn, J.; Ilge, D.; Leusser, D.; Stalke, D.; Engels, B. J. Phys. Chem. A 2004, 108, 9442. (50) Gatti, C.; Bianchi, R.; Destro, R.; Merati, F. J. Mol. Struct (THEOCHEM) 1992, 255, 409. (51) Farrugia, L. J.; Evans, C. J. Phys. Chem. A 2005, 109, 8834. (52) (a) Bader, R. F. W.; Slee, T. S.; Cremer, D.; Kraka, E. J. Am. Chem. Soc. 1983, 105, 5061. (b) Howard, S. T.; Lamarche, O. J. Phys. Org. Chem. 2003, 16, 133. (c) Tsirelson, V. G.; Bartashevich, E. V.; Stash, A.; Potemkin, V. A. Acta Crystallogr., Sect. B 2003, 63, 142. (53) (a) Cheeseman, J. R.; Carrol, M. T.; Bader, R. F. W. Chem. Phys. € Lett. 1988, 143, 450. (b) Tafipolsky, M.; Scherer, W.; Ofele, K.; Artus, G.; Pedersen, B.; Herrmann, W. A.; McGrady, G. S. J. Am. Chem. Soc. 2002, 124, 5865. (54) (a) Presselt, M.; Schnedermann, C.; M€uller, M.; Schmitt, M.; Popp, J. J. Phys. Chem. A. 2010, 114, 10287. (b) Presselt, M.; Dietzek, B.; Schmitt, M.; Rau, S.; Winter, A.; J€ager, M.; Schubert, U. S.; Popp, J. J. Phys. Chem. A 2010, 114, 13163. (c) Presselt, M.; Schnedermann, C.; Schmitt, M.; Popp, J. J. Phys. Chem. A. 2009, 113, 3210. (d) Winter, A.; Friebe, C.; Chiper, M.; Schubert, U. S.; Presselt, M.; Dietzek, B.; Schmitt, M.; Popp, J. ChemPhysChem 2009, 10, 787. (e) Presselt, M.; Dietzek, B.; Schmitt, M.; Popp, J.; Winter, A.; Chiper, M.; Friebe, C.; Schubert, U. S. J. Phys. Chem. C 2008, 112, 18651. (55) (a) Scherer, W.; McGrady, G. S. Angew. Chem., Int. Ed. 2004, 43, 1782. (b) Ott, H.; Pieper, U.; Leusser, D.; Flierler, U.; Henn, J.; Stalke, D. Angew. Chem., Int. Ed. 2009, 48, 2978. (c) Ott, H.; D€aschlein, C.; Leusser, D.; Schildbach, D.; Seibel, T.; Stalke, D.; Strohmann, C. J. Am. Chem. Soc. 2008, 130, 11901. (56) (a) Bader, R. F. W.; Stephens, M. E. J. Am. Chem. Soc. 1975, 97, 7391. (b) Fradera, X.; Austen, M. A.; Bader, R. F. W. J. Phys. Chem. A 1999, 103, 304. (57) (a) Poater, J.; Sola, M.; Duran, M.; Fradera, X. Theor. Chem. ngyan, J. G.; Sannigrahi, A. B. J. Phys. Acta 2002, 107, 362. (b) Kar, T.; A Chem. A 2000, 104, 9953. (58) (a) Poater, J.; Duran, M.; Sola, M.; Silvi, B. Chem. Rev. 2005, 105, 3911. (b) Merino, G.; Vela, A.; Heine, T. Chem. Rev. 2005, 105, 3812. (59) Bader, R. F. W.; Gatti, C. Chem. Phys. Lett. 1998, 287, 233–238. (60) Lo Presti, L.; Gatti, C. Chem. Phys. Lett. 2009, 476, 308. (61) Farrugia, L. J.; Macchi, P. J. Phys. Chem. A 2009, 113, 10058. (62) (a) Gatti, C.; Cargnoni, F.; Bertini, L. J. Comput. Chem. 2003, 24, 422. (b) Gatti, C.; Bertini, L. Acta Crystallogr., Sect. A 2004, 60, 438. (c) Overgaard, J.; Schiott, B.; Larsen, F. K.; Iversen, B. B. Chem.—Eur. J. 2001, 7, 3756. (d) Gatti, C.; Lasi, D. Faraday Discuss. 2007, 135, 55.
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