Rationalizing the Effect of Halogenation on the Molecular Structure of

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Rationalizing the Effect of Halogenation on the Molecular Structure of Simple Cyclobutene Derivatives by Topological Real-Space Analysis of Their Electron Density Leonardo Lo Presti,*,† Arkady Ellern,‡ Riccardo Destro,*,† Raffaella Soave,6¼ and Bruno Lunelli# †

Dipartimento di Chimica Fisica ed Elettrochimica, Universita degli Studi di Milano, Via Golgi 19, 20133 Milano, Italy Chemistry Department, Iowa State University, 1711 Gilman Hall, Ames, 50011 Iowa, United States 6¼ Istituto di Scienze e Tecnologie Molecolari, CNR-ISTM, Via Golgi 19, 20133 Milano, Italy # Istituto per lo Studio dei Materiali Nanostrutturati (ISMN) CNR, Via P.Gobetti, 101, 40129 Bologna, Italy ‡

bS Supporting Information ABSTRACT: The accurate gas-phase equilibrium structures on the ground-state potential energy surface of the complete series of fluorinated and chlorinated cyclobutene derivatives with C2v symmetry have been evaluated at DFT PBE0/6-311++G(d,p) theory level. The optimized geometries have been compared with all the available experimental data reported in the literature, as obtained by microwave spectroscopy (MW) and gas-phase electron diffraction (GED) techniques. For hexafluorocyclobutene and 1,2-dichloro-3,30 ,4,40 -tetrafluorocyclobut-1-ene, the results of accurate low-temperature single-crystal X-ray diffraction experiments have also been considered. Structural changes within the cyclobutene ring, as induced by fluorination and chlorination at allylic and vinylic positions, have been correlated with changes in the corresponding theoretical charge densities. To this aim, several local and nonlocal topological descriptors provided by the quantum theory of atoms in molecules, QTAIM, have been employed, with particular emphasis on the delocalization indices and integrated source function decomposition schemes. Key factors for the resulting molecular structures are the chemical nature and the steric hindrance of the substituents, as well as quantum-mechanical effects, such as delocalization and partial conjugation. When fluorine atoms replace hydrogens at allylic or vinylic positions, the corresponding Csp3—Csp3 or Csp2dCsp2 bonds between the substituted carbons undergo a significant strengthening, while chlorination has just the opposite effect. In the latter case the steric hindrance between bulky chlorine atoms occupying vicinal positions is crucial in determining the single Csp3—Csp3 bond length. These findings are discussed in the context of the reactivity of chemically related chlorofluorocarbon compounds.

1. INTRODUCTION Since the development of processes for the massive production of fluorocarbon compounds in the early 1940s,1 halocarbons attracted a great deal of interest due to their applications in both traditional and cutting-edge technologic branches of research, including electronic and photovoltaic industry,2,3 medicine,4 pharmaceuticals5 and other crucial sectors for quality of life and industrial competitiveness. The substitution of hydrogen atoms with halogens bears dramatic consequences on the overall physical and chemical properties of the resulting materials, conferring on them features such as chemical inertness, high thermal stability, hydrophobicity and dielectric strength, all of them being attractive for a wide range of industrial applications.611 Furthermore, a wide spectrum of halocarbon derivatives with various functional groups are nowadays employed as synthetic building blocks in chemical12 and biochemical5 research. Even though the chemical properties of the C—F bond appear generally well understood,1214 it has been recently pointed r 2011 American Chemical Society

out13 that “fluorocarbon chemistry is still in an early stage of development”. In particular, a long-standing debate1519 is still open concerning the structural effects associated with the substitution of fluorine atoms for hydrogens into the simple, 4-membered hydrocarbon ring of cyclobutene (C4H6, hereinafter CB). Table 1 summarizes and compares all the experimental information available at present, to the best of our knowledge, for the molecular structure of CB and its substituted fluorinated and chlorinated derivatives of C2v symmetry (see Chart 1 for the nomenclature). At standard ambient temperature and pressure conditions, these compounds are gaseous (C4H6 and C4F6) or Special Issue: Richard F. W. Bader Festschrift Received: April 18, 2011 Revised: June 29, 2011 Published: July 26, 2011 12695

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The Journal of Physical Chemistry A

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Table 1. Summary of the Experimental Bond Distances and Angles (d, r) of Halogenated Symmetric CB Derivatives with Estimated Errors in Parentheses substance:

C4H6

C4F6 a

reference:

21

20

19

technique:d

MW

GED

b

b

C4Cl2F4

b

c

16

17

MW

GEDe

GED

b

C4H2F4

18

24

25

26

this work

27b

GED

XRAYf

MW

GED

XRAYf

MWg

d/Å C1C4

1.566(3)

1.577

1.552(6)

1.582(8)

1.581(11)

1.595

1.564(5)

1.551(15)

1.599(10)

1.566(2)

C2dC3

1.342(4)

1.325(46)

1.333(6)

1.325(24)

1.319(23)

1.342(6)

1.326(5)

1.311(15)

1.359(9)

1.341(2)

1.349(6)

C1—C2

1.517(3)

1.517

1.478(6)

1.500(5)

1.499(5)

1.508(3)

1.487(5)

1.487(15)

1.500(6)

1.503(2)

1.501(6)

1.094(5)

1.093(15)

1.358

1.344(4)

1.341(4)

1.336(6)

1.354(15)

1.340(2)

C3—C4 C1—X2h

1.492(5) 1.354(4)

1.505(2) 1.349(2)

C1—X3h

1.350(4)

1.351(2)

C4—X4h C4—X5h

1.353(4) 1.355(4)

1.347(2) 1.350(2)

C2—X1i

1.083(3)

1.093(15)

1.311

1.309(10)

1.307(10)

1.319(12)

C3—X6i

1.316(4)

1.539(6)

1.705(15)

1.687(3)

1.316(4)

1.684(1)

1.358(2)

1.080(1)

1.687(1)

R/deg C2—C1—C4

85.8

85.7(2)

85.1(5)

85.2

C3—C4—C1 C1—C2dC3

94.2

94.0(8)

94.3(2)

94.9(5)

95.0(5)

94.8(3)

C4—C3dC2 X1—C2dC3 X6—C3dC2

85.5(2)

85.4(6)

85.4(2)

85.4(2) 94.8(3)

94.6(6)

94.6(2)

94.4(3) 133.5

140.9 j

134.6

X1—C2—C1

135.1(7)

135.2(12)

133.6(29)

130.0(11)

135.0(3) 135.6(3)

134.6(6)

133.9(3) 131.5(4)

130.0(3)

X2—C1—C2 X2—C1—C4

114.5

X2—C1—X3

109.2

109.5

94.1(1) 134.8(1) 134.6(1)

116.8(4)

115.9(5)

117.0(3)

116.5(5)

116.6(1)

114.7(3)

114.5(3)

114.5

114.7(3)

114.5(6)

115.4(1)

106.0

107.6(5)

107.6(5)

109.2

107.1(2)

132.2(3)

131.0(1)

117.0

107.1(2)

93.6(2)

131.0(1)

115.3

X4—C4—X5

86.3(2)

94.4(1)

130.3(3)

X6—C3—C4

85.9(1) 85.5(1)

106.4(6)

108.2(4)

106.9(1)

106.2(2)

107.1(1)

A single value for the three CC single bonds is reported in ref 20 as CCave = 1.537 ( 0.010 Å, together with an estimate for dC1C4 dC1C2 = 0.06 Å. b Values in parentheses are estimated 2σ from the least-squares fit. c Model A of ref 18. Uncertainties in parentheses are estimated 3σ. d MW = gasphase microwave spectroscopy; GED = gas-phase electron diffraction; XRAY = single-crystal (solid state) X-ray diffraction. e Fitting against GED data making use of structural constraints deduced from previously known rotational constants (see ref 16 for details). f Bond distances and angles have been obtained after correcting the atomic coordinates for the rigid-body motion of the molecule (see ref 29 and the Supporting Information for more details). Values in parentheses are the estimated standard deviations. g Obtained by averaging the parameter estimates as obtained from two different methods (see ref 27 for details). h Allylic bond. See also Chart 1. i Vinylic bond. See also Chart 1. j R(X1—C2dC3) = 125.25 + 0.5[125.25 R(C1—C2dC3)]. a

liquid (C4Cl2F4 and C4H2F4) with substantial vapor pressure. Hence, methods such as gas-phase electron diffraction (GED) and microwave spectroscopy (MW) provide an obvious way to investigate their molecular structure. Both techniques were in fact applied to the parent compound, C4H6, late in 1956 (GED)20 and 1969 (MW),21 but some discrepancies in terms of absolute differences in bond lengths were evident since then (see, for example, the dCdC in Table 1). Such differences are somewhat disturbing, even though the experimental uncertainties of the electron diffraction work are so large as to make null the statistical significance of the differences in the two sets of measurements (see also the discussion in section 4.1 below). Other discrepancies between the same techniques emerged more recently, when hexafluorocyclobutene (C4F6) was investigated.1619 In particular, the GED results1618 predict the C—C single bond opposite to CdC in C4F6 to be significantly longer than that obtained by the MW technique,19 with a difference exceeding by far the experimental uncertainties of the two methods. Another common method of geometry evaluation, i.e., quantum-mechanical calculations in the gas phase, initially gave results15,17 more similar to the

GED’s ones, while more recently a better agreement with the MW results seems to prevail.22,23 Besides large numerical differences, the conflict between GED and MW estimates poses a question of genuine chemical interest: upon fluorination, does the CC single bond opposite to the CdC double bond of CB become longer (GED results) or shorter (MW results) than that in the parent compound? At variance with his own early findings,17 and based on intensive quantum mechanical simulations up to the CCSD(T) theory level, Csaszar a few years ago presented23 for C4F6 theoretical results in agreement with the MW structure and stated that the “length of the CC bond opposite to the double bond becomes shorter upon fluorination and not longer, as the GED investigations have indicated”. During the last two decades several experimental and theoretical studies have been carried out both on the same perfluorinated compound24 and on other CB derivatives, with various degrees of fluorination,23,2527 or even bearing different functional groups.24,28 In our combined experimental/theoretical analysis of hexafluorocyclobutene24 by means of accurate 12696

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Chart 1. Synoptic of the Halogenated Cyclobutene Derivatives Considered in This Work

single-crystal X-ray diffraction and periodic optimizations in the solid state, we found29 values for the Csp3Csp3 bond very close (or even identical, in terms of our X-ray estimated standard deviations, esd’s) to both the MW outcomes for CB and the last results of Csaszar. This author has proposed to rationalize his findings in terms of a simple rehybridization model,23 “namely that the increased number of fluorines attached to a carbon atom increases the s character of the carbon bonds and tends to shorten all the bonds around the carbon. Ring strain and Coulomb repulsion effects are only needed to explain finer characteristics in the structures of fluorinated cyclobutenes”. Actually, for a complete and unbiased understanding of the effect of halogenation on the molecular structure of this class of substances, it would be necessary to uniquely identify and, above all, quantify in detail what determines a certain molecular structure, at least on a relative scale. As molecules are subject to quantum mechanical laws, such effects are primarily of electronic nature, and it is not sufficient to compare geometrical results for a limited group of compounds to fully elucidate them. In our opinion, the thorough work by Csaszar23 has the merit of providing reliable benchmark structural parameters for CB and the derivatives he investigated. However, a deep investigation of the electron-density derived properties of a complete series of chemically related compounds (even if experimental data are not yet available) seems necessary to elucidate all the mutually related factors governing the effect of halogen substitution on the chemical properties of the derived compound with respect to the parent CB. As the molecular electron density F(r) is the “glue” that keeps together the atomic nuclei through chemical bonds, a straightforward way to deal with this problem is to directly analyze the changes it undergoes in the real space upon halogenation by means of the quantum theory of atoms in molecules (QTAIM),30,31 the most complete density-based topological tool for chemical bonding studies.32 In this work, we report the accurate gas-phase equilibrium structures on the ground-state potential energy surface at the DFT PBE0/6-311++G(d,p) theory level of the complete series of fluorinated and chlorinated CB derivatives with C2v symmetry (Chart 1), with the aim of comparing their corresponding

ground-state one-electron topological properties on the same grounds and on a relative scale. Moreover, we add a new contribution to the experimental knowledge by reporting the solidstate structure of 1,2-dichloro-3,30 ,4,40 -tetrafluorocyclobut-1ene, C4Cl2F4, as obtained by single crystal X-ray diffraction at low T on an in situ grown specimen. The results of the topological analysis of the corresponding theoretical charge densities are also presented. We include in our study also the chlorinated derivatives because fluorine and chlorine, although sharing a lot of chemical properties, affect in different ways the reactivity of vicinal functional groups owing to their different atomic properties such as volume, hardness, electron affinity, and electronegativity. To emphasize the essential points, we restrict our investigation to the symmetric C2v derivatives, thus ignoring the effect of asymmetrical halogen substitutions within the CB ring, which would imply a further level of complexity due to symmetry breaking.

2. THEORETICAL METHODS 2.1. Computational Details. To test the performances of different basis sets on the final geometrical parameters, gas-phase optimizations at DFT PBE033 6-31G(d), 6-311++G(d,p), and cc-pVDZ34 theory levels have been carried out on cyclobutene and the eight derivatives considered (Chart 1). The Gaussian09 program35 has been employed throughout for such calculations. All the optimizations have been performed by imposing molecular C2v symmetry. The geometry optimizations have then been repeated by applying a MP236 perturbative MøllerPlesset correlation energy correction with the triple-ζ 6-311++G(d,p) basis set, to test the effect of the Hamiltonian on the refined geometrical parameters. Eventually, the PBE0/6-311++G(d,p) scheme has been selected to perform the subsequent topological analysis, as the geometries predicted within this scheme showed the best agreement with the X-ray derived structural models. More details on the computational strategy can be found within the Supporting Information. For both the DFT and MP2 geometry optimizations, a full frequency analysis has been carried out to ensure that a true 12697


The Journal of Physical Chemistry A minimum on the potential energy surface (PES) had been reached. No imaginary or somewhat unrealistic vibration frequencies have been found. 2.2. Topological Analysis. The topological analysis of the scalar field F(r) has been performed with a modified version of the PROAIM program package.37 In particular, the EXTREME and PROMEGA algorithms have been employed to find the critical points of F(r) and to calculate the integral properties of the atomic basins. According to QTAIM,30 the total electron density of a quantum-mechanical system is unequivocally partitioned into proper open systems, the topological atoms Ω’s. The latter are defined as three-dimensional attraction basins of the gradient of F(r), rF(r), bounded by surfaces through which the flux of the vector rF(r) is zero. Two atoms are bonded38 to one another if there exists a unique atomic interaction line (AIL), i.e., a path of maximum F(r) (also called bond path, BP), that links the corresponding nuclei. The minimum of the F(r) along the AIL is a saddle point in R3, the so-called bond critical point (hereinafter, bcp). It is usually taken as a reference point to evaluate several chemically relevant properties that bear information on both the nature and strength of the bond itself. Among other topological point descriptors that can be evaluated at the bcp, of particular relevance are the energy densities. The total electron energy density (Hbcp) is defined as the sum of the corresponding potential (Vbcp < 0) and kinetic (Gbcp > 0) energy densities. Obviously, Hbcp is negative if the Vbcp contribution prevails over Gbcp. This is exactly the case of the CC bonds considered in this work, all of them being clearly covalent. When a covalent bond strengthens, no matter the cause, more and more charge density is accumulated within the internuclear region and, therefore, at the bcp. Accordingly, Fbcp and both the Vbcp and Gbcp indicators are expected to increase (in absolute value). Therefore, a negative percent variation in Hbcp < 0 means that an augmented attractive potential energy in the internuclear region due to positively charged nuclei stabilizes the higher electron charge concentration at the bcp. Furthermore, as energy densities are related to the charge density Laplacian r2Fbcp by means of the virial theorem in its local form,30 differences in the Laplacian can highlight more subtle aspects of the balance between potential and kinetic energy contributions. By integrating the appropriate scalar field within the volume occupied by one or more basins Ω’s, integral atomic properties (charge, energy, volume, electrostatic moments) and other nonlocal descriptors are obtained, such as the integrated source function39 and delocalization indices.40 The latter two quantities help to assess how the F(r) is delocalized and redistributed upon the formation of chemical bonds. The interested reader can found a brief, although detailed, description of these indicators within the Supporting Information.

3. STRUCTURAL ANALYSIS OF C4Cl2F4 3.1. Material. The product as received from City Chemical, West Haven, CT, USA, was analyzed by gas chromatographymass spectrometry to establish an approximate initial composition and some properties of the main impurities. Overall, it indicated a purity of about 95%. An isomer of the examined compound was detected, plus other minority species. After purification (see Supporting Information for full details), the material was slowly cooled and crystallized for the following single-crystal X-ray diffraction analysis.

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3.2. X-ray Diffraction Analysis41. A full sphere of data within

2ϑ = 61° (for a total of 4724 reflections) was collected on the selected specimen (crystal dimensions: 0.38 0.20 0.20 mm3) at T = 173(2) K, using a three-circle APEX-2 CCD diffractometer with graphite-monochromated Mo KR radiation (λ = 0.710 73 Å). The data were corrected for absorption using an empirical procedure (see the Supporting Information). The structure was solved by direct methods using the SHELX software,42 finding the position of almost all the atoms in the asymmetric unit. The remaining atoms were located in an alternating series of least-squares cycles on difference Fourier maps. Final crystallographic agreement indices on all the 1800 unique reflections were R1 = 0.0344, wR2 = 0.0820, with gof = 1.076 and maximum residual difference Fourier peaks of +0.459/ 0.313 e Å3. The atomic coordinates, as well as the bond distances and angles reported in Table 1, have been corrected for the rigid-body libration of the asymmetric unit.29,43 C4Cl2F4 crystallizes in the space group P1 (no. 2), with one molecule in the asymmetric unit and two formulas per cell (Z = 2). So, the point C2v symmetry is no more conserved in the solid state, analogously to what previously observed for C4F6.24 Cell parameters: a = 6.244(2), b = 6.380(2), c = 9.007(2) Å; R = 70.572 (3), β = 72.248(4), γ = 75.975(4)°; V = 318.3(1) Å3; calculated density = 2.034 g 3 cm3.

4. RESULTS AND DISCUSSION Following standard organic nomenclature, in our discussion atoms C1 and C4 (and their substituents, labeled from X2 to X5) will be referred to as “allylic”, whereas atoms C2 and C3 (and their substituents, labeled X1 and X6) will be named “vinylic” (Chart 1). The four-membered CB ring has the shape of a regular isosceles trapezoid, with all the carbon atoms plus the vinylic X1 and X6 substituents sharing the same main molecular plane. Accordingly, in the following sections the term “oblique bonds” will be used to indicate the C1C2 and C3C4 bonds. Full tables reporting all the computed geometrical and topological indicators can be found within the Supporting Information (Tables S1S19). In section 4.1, the performance of the gas-phase optimizations will be discussed by comparison with experimental MW, GED, and X-ray results available in the literature. In the remaining sections, the topology of F(r) will be analyzed as a function of the halogenation degree, taking into account the relative positions of chlorine and fluorine atoms within the carbon backbone and the steric hindrance among vicinal substituents. 4.1. Comparison of Gas-Phase Optimized Geometries with Results Provided by Experimental Techniques. Table 1

summarizes the results obtained so far by experimental techniques on the known molecular structures of chlorinated and fluorinated C2v CB derivatives. All the experimental estimates of the bond angles in C4H6, C4F6 and C4Cl2F4 agree well, in most cases showing deviations well below 1.0° when corresponding angles in the same compound are compared. At the same time, the agreement between our theoretical estimates and all the experimental results is quantitative, with (for example) rootmean-square deviations for the bond angles of CB never exceeding 0.5°. A completely different panorama emerges when the covalent bond lengths are considered. For such quantities, the differences may exceed 0.04 Å (depending on the experimental techniques that are being compared), much more than the corresponding 12698



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4.2. Effect of Halogen Substitution at Vinylic Positions. 4.2.1. QTAIM Point Descriptors. Figure 2 shows the effects of vinylic fluo-

Figure 1. Differences between the gas-phase computed bond distances and those experimentally determined by MW, GED, and X-ray diffraction techniques for C4Cl2F4 and C4F6. Error bars corresponding to the experimental errors are superimposed onto the graph. The lines serve only as eye guides (dotted, MW; dashed, GED; full, X-ray). For the sake of clarity, only the comparison with GED most recent results by Hedberg and Hedberg16 on C4F6 is shown.

experimental uncertainty. The GED C1—C4 bond length is in general considerably greater than both the MW and X-ray estimates, whereas the same technique predicts the opposite C2dC3 bond as shorter in C4H6 and C4F6 and longer in C4Cl2F4. Anyway, for both C4F6 and C4Cl2F4 derivatives, the X-ray measure of the C1—C4 bond has an intermediate length between the MW and GED values. It should be noted, however, that the MW and GED structural parameters usually have, in terms of precision, poor statistical significance due to their very large esd values. On the contrary, the X-ray derived esd’s are significantly lower (Table 1 and Figure 1). Similarly to other techniques, MW and GED implementation generally requires explicit or implicit assumptions,4447 or the need to use information derived from other methods to extract the structural results from the collected data:48 therefore, it is not surprising that some discrepancies may exist among their results. Nevertheless, the occurrence of systematic (absolute) differences in bond lengths raises a problem. To solve the issue, and to provide a reliable check for the geometries of those halogenated cyclobutene derivatives whose experimental structures have not yet been determined, more precise experimental studies are in order, with the aim of increasing the statistical significance of both GED and MW outcomes. As regards the accuracy of the molecular geometries, the comparison among experimental results and theoretical predictions may be then extremely useful to assess unbiased (or, at least, less-biased) reference values for the investigated parameters. Figure 1 shows the differences between our theoretical results for bond lengths in C4Cl2F4 and C4F6 (that are the only derivatives studied by all three MW, GED, and X-ray techniques) and the experimental values. Vertical bars corresponding to the experimental errors (see Table 1) are superimposed to the graph. On average, the agreement between our PBE0 quantummechanical estimates and X-ray results is more than satisfactory, especially for the carboncarbon bond distances. A further test for assessing the actual accuracy of our PBE0/6-311++G(d,p) geometries resides in the comparison with the high-level theoretical outcomes provided in ref 23. In particular, the average rootmean-square deviations for bond lengths among Csaszar’s and our calculations amount to 0.003 Å (C4H6), 0.002 Å (C4H4F2 and C4H2F4), and 0.001 Å (C4F4Cl2 and C4F6).

rination and chlorination on the bond distances (d) and some topological indicators (Fbcp, r2Fbcp, and Hbcp) of the independent ring bonds. Individual values for these quantities can be found in the Supporting Information (Tables S1S4). The addition of fluorine at the X1, X6 vinylic positions (Figure 2ac) results in a strengthening of the two oblique bonds, C1—C2 and C3—C4 and, to a minor extent, also of the double C2dC3 bond. Such an effect is documented by (i) the shortening of the corresponding bond distances (up to almost 1% when F substitutes H in C4H6), (ii) the increase of F(r)bcp, and (iii) the increment of the total energy density at the bcp, Hbcp, that becomes significantly more negative for the oblique C1—C2 and C3—C4 bonds. On the contrary, the long C1—C4 bond always weakens upon vinylic fluorination. However, geometrical changes depend also on the nature of substituents X2X5 on the two allylic centers, as shown by the first three bars for each quantity in Figure 2b. When the allylic positions are occupied by another halogen (F, Cl), the C2dC3 bond remains essentially unchanged upon vinylic fluorination, whereas the oblique bonds slightly shorten and strengthen (Figure 2c). On the contrary, when F substitutes vinylic Cl (light blue and red bars in Figure 2), the above-discussed effects become significant even for the double C2dC3 bond. In most cases the changes in r2Fbcp have the same sign of those in Hbcp, indicating that the gain in potential energy upon fluorination dominates with respect to the increase of the kinetic energy density in the internuclear region. Almost an opposite picture emerges upon chlorine vinylic substitution (Figure 2df), all the point topological descriptors pointing to the weakening of both the C2dC3 double bond and the oblique bonds, with the only exception of the pair C4H6/ C4H4Cl2. In this case the effects on the F(r) topology of the C—C bonds are more similar to those occurring upon vinylic fluorination (oblique bonds strengthen, C1—C4 weakens), even if the differences with respect to CB are now less evident. 4.2.2. Nonlocal QTAIM Descriptors. By considering the integral source function (SF) percent contributions at the intraannular bcp’s (Figure 3), we note that (i) the SF contributions at the C2dC3 and oblique C1—C2 bcp’s due to C2 (and C3) atom(s) is slightly reduced upon vinylic halogenation (compare, as an example, the pink and black bars, or the pink and yellow bars, in Figure 3b,c), and (ii) the SF contribution of the X1 (and X6) substituent(s) increases. This holds true independently from the kind of halogen that is being inserted in the ring, indicating that vinylic F and Cl have qualitatively the same effect in terms of SF contribution, even if it is more pronounced upon F substitution. At first glance it may be quite surprising that fluorine, which is the most electronegative atom in the periodic table, contributes more than H and Cl to the F(r) at the bcp’s of its adjacent CC bonds. However, this behavior is just the consequence of the peculiar properties of this chemical element, and in particular of the significant greater hardness it exhibits with respect to chlorine.49 As the covalent radius of F is about 35% shorter than that of chlorine,50 the F atom is characterized by higher charge concentration in the valence region, with Laplacian values more negative than all the other halogens. According to eq S1 in the Supporting Information, higher r2F(r) values in the valence electron region imply that, overall, the atomic basin can act more and more effectively as a source of F(r) at the bcp’s lying on its zero-flux surface or even on the interatomic surfaces of its vicinal CC bonds. In other words, the large integrated SF 12699



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Figure 2. Percent differences (Δ%) of geometrical and point topological indicators at symmetry-independent C—C bcp’s upon vinylic halogenation. Negative Δ% values in d and Hbcp imply bond strengthening, whereas the same is true for positive Δ% of Fbcp. The sign of Δ% for r2Fbcp depends on the relative balance of kinetic and potential energy densities through the local form of the virial theorem (see text). Δ% upon vinylic fluorine substitution at the following bcp’s: (a) C1—C4; (b) C2dC3; (c) C1—C2. Δ% upon vinylic chlorine substitution at the following bcp’s: (d) C1—C4; (e) C2dC3; (f) C1—C2.

contributions of fluorine quantify the ability of this element to influence its chemical environment due to its higher charge-tovolume ratio. Table 2 shows the percent differences of the delocalization indices (δ(A,B)) upon vinylic halogenation, as evaluated for atoms directly involved in covalent bonds. It is seen that F and Cl have similar effects on the CC bonds, as all the δ(C,C0 ) (with C0 6¼ C) values are reduced when halogen atoms replace H1 and H6. In particular, δ(C2,C3) is the most affected, as it undergoes a 811% reduction upon halogenation. In general, halogen replacement of H atoms implies a more localized picture of F(r) within the CC bond network, with the electron pairs forming the bonds more unequally distributed among C atomic basins than in CB, due to the higher electronegativity of the F and Cl species with respect to H. The behavior of the two halogen species is no longer similar when the C2—X1 bond is considered: the δ(C2,X1) index is reduced (from 9 to 29%) when X1 = F,

whereas it increases (up to 40%) when X1 = Cl. This correlates well with the higher polarity of the CF bonds with respect to both CH and CCl bonds and confirms, from another perspective, what is stated above on the peculiar properties of the fluorine element. Low values of the δ(A,B) index are indeed associated with high bond polarity, i.e., to unequal sharing of bonded electron pairs.51,52 It is interesting to note that the delocalization index δ(C2,X1) moves from 0.97 in C4H6 to 1.15 in C4H4Cl2 (see Table S14 in the Supporting Information), i.e., it is ≈15% higher when X1 = Cl instead of H, implying that more than 1 electron pair is exchanged between the vinylic Cl and its facing C basin. This may indicate that some kind of electron coupling through the π system is taking place, involving the chlorine substituent. Such conjecture is supported by the values of bond ellipticities, ε, for C2X1, as a function of the substituent identity. Indeed, the ellipticity53 measures the asymmetry of the charge distribution with respect to the ideal, 12700



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Figure 3. Symmetry-independent integral source function percent contributions to the F(r) at the C—C bcp’s as a function of the halogenation degree: (a) C1—C4; (b) C2dC3; (c) C1—C2.

cylindrical distribution; hence, values of ε > 0 indicate partial π-bond character.30,54 For the systems here considered, ε(C2X1) = 0.014, 0.024, and 0.046 for X1 = H, X1 = F, and X1 = Cl, respectively. If the δ(A,B) values between not-directly bonded atoms are also inspected, it can be seen that δ(X1,C3) is low when X1 = H (0.05 in C4H2Cl4 and C4H2F4, 0.06 in C4H6), but it undergoes a larger increment (up to a final value of 0.14) when the vinylic X1 position is occupied by a halogen atom (Supporting Information, Table S14). That it be the π electron cloud to mediate such an increase of the electron pairing among the relatively distant X1 and C3 atoms and not, e.g., the σ bonds, is confirmed by the observation that the δ(X1,C1) indices for the equally distant X1/ C1 pair undergo significant smaller increments upon vinylic halogenation (e.g., δ(X1,C1) = 0.04 for C4H6 and 0.07 for C4H4Cl2 and C4H4F2). The existence of a π system extended even to the vinylic substituents in such compounds was also inferred in our previous study24 on two methoxy-substituted derivatives of C4F6. 4.3. Effect of Halogen Substitution at Allylic Positions. 4.3.1. QTAIM Point Descriptors. Figure 4 shows the effect of allylic halogenation on the same geometrical and topological point properties of the symmetry-independent CC bonds reported in Figure 2. Full data concerning the indicators here discussed can be found in the Supporting Information (Tables S1S4). In particular, Figure 4a focuses on the effect of fluorination on the long C1—C4 bond, i.e., just on the bond that was the subject of the controversy mentioned in the Introduction. The dC1—C4 bond distance remains almost unchanged upon introduction of fluorine as allylic substituent and a small shortening (≈3%) occurs only when F substitutes Cl. As for the topological indicators, from Figure 4a it is clear that all of them point to a

significant strengthening of the C1—C4 bond upon allylic fluorination. Indeed, a relevant increase (up to 17%) in the F(r) at the bcp is detected, together with even more significant reductions of the negative Laplacian and total energy density. This implies that the potential energy density at the bcp prevails even more on the kinetic contribution when X2X5 positions are occupied by F. Interestingly, such changes affect only marginally the opposite C2dC3 bond (Figure 4b). The oblique C1—C2 and C3—C4 bonds are generally slightly reinforced, although to a minor extent than C1—C4 (Figure 4c). The only exception is given by the pair of compounds C4Cl4F2/C4F6, i.e., in correspondence with the maximum strengthening of the C1—C4 bond (compare the light blue bars in Figure 4a,c). It should be remarked that, while the behavior of the C1—C4 bond length upon halogenation depends critically on the level of theory employed,55 both local and nonlocal topological parameters provide stable values and clear evidence that, in agreement with Csaszar’s findings,23 the aforementioned bond is significantly reinforced upon allylic fluorination. Allylic chlorine substitution has just the opposite effect (Figure 4df). In particular, the C1—C4 bond undergoes a ≈3% lengthening when X2X5 are Cl atoms. Accordingly, all the topological indices suggest a marked bond weakening, which is even more evident when Cl replaces F at allylic positions. As above (compare Figure 4b with Figure 4e and Figure 4c with Figure 4f), the opposite C2dC3 bond remains quite unaffected by the chlorine substitution at allylic positions, and the oblique bonds are in general slightly reinforced. 4.3.2. Nonlocal QTAIM Descriptors. As already observed for the vinylic system, upon allylic halogen substitution the SF % contribution from C1 to the bcp of the adjacent C1C4 bond (Figure 3a) reduces from 37.1% (C4H6, pink bar) to 34.6% 12701



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Table 2. Percent Differences (Δ%) in Delocalization Indices (δ(A,B)) upon Vinylic Halogenation, As Evaluated between Atoms Directly Involved in Covalent Bondsa

a

Vinylic substituents are highlighted in red; allylic substituents, in blue.

(C4H2F4, white bar) or to 35.2% (C4H2Cl4, red bar). On the contrary, each allylic halogen provides an amount of charge density at the same bcp greater than that of hydrogen, causing a slight increase in the F(r) at the C1C4 bcp, which is larger in the case of fluorine than in that of chlorine. Changes analogous to those of the C1—C4 bond are detected at the oblique bond (Figure 3c, same bars), whereas allylic halogenation has practically no influence on SF contributions at the distant C2dC3 bcp (Figure 3b, same bars). Table 3 summarizes the percent differences in delocalization indices (δ(A,B)) upon allylic halogenation, A and B being atoms directly involved in a covalent bond. The conclusions to be drawn are analogue to those discussed in section 4.2.1: the introduction of halogen atoms on the 4-membered ring is mirrored by a corresponding reduction of δ(C,C0 ), where C 6¼ C0 , due to an increased electron localization within the cycle (because of the electron withdrawing ability of the more electronegative halogen substituents). Such an effect is more evident when X = F, and it mainly affects the delocalization index between the C1 and C4 basins (as both of them always bear two halogens after substitution). It is seen in Table 3 that δ(C1,X2) always undergoes a significant reduction upon fluorine introduction, whereas it significantly increases when X2 = Cl. While discussing the vinylic

substitution (section 4.2), we have explained the different behavior between fluorine and chlorine by invoking electron pairing between the vinylic chlorine and its nearby carbon atoms through the π density. Such a model appears to be not justified in the case of allylic substitution. The absolute δ(C1,X2) values (Table S14 in the Supporting Information) are 0.95 (C4H6), 0.75 (C4H2F4), and 1.06 (C4H2Cl4): hence, less charge density appears to be shared between allylic Cl and C atoms with respect to the same atoms at vinylic positions, where δ is 1.15. Moreover, if the delocalization index is evaluated between the allylic substituent X2 and the double-bonded (distant) C2 atom, quite low values (

Rationalizing the Effect of Halogenation on the Molecular Structure of

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