Effects of Ligand Electronegativity on Recoupled Pair Bonds with

Article pubs.acs.org/JPCA

Effects of Ligand Electronegativity on Recoupled Pair Bonds with Application to Sulfurane Precursors Beth A. Lindquist, David E. Woon, and Thom H. Dunning, Jr.*,‡ Department of Chemistry, University of Illinois at Urbana−Champaign, 601 South Mathews Avenue, Urbana, Illinois 61801, United States S Supporting Information *

ABSTRACT: Recoupled pair bonds (RPBs) are conditional bondsthey only form for selected central atoms and ligands. A complete theoretical description of RPBs requires an understanding of the properties of the central atom and ligands that enable such bonds to be formed. In this work, we show that ligand electronegativity is positively correlated with recoupled pair bond strength for a variety of ligands interacting with the 3p2 pair of sulfur. We also describe substituent (X) effects on the SF(a4Σ−) state by investigating X2SF species. These effects generally mirror those observed for covalently bound analogues, but we found that recoupled pair bonding can lead to breakdowns in the expected relationships among bond length, strength, and force constant for some of these species. Finally, we compare the properties of two molecules of practical interest that are bound by recoupled pair bonds: the dimethyl sulfur fluoride and hydroxide radicals (DMS−F and DMS−OH).

I. INTRODUCTION A comprehensive understanding of bonding in hypervalent species has been an active area of research for the better part of a century. As valence bond theory was being developed in the early 20th century,1 molecules such as PCl5 were recognized as outliers, but the term “hypervalent” was first defined by Musher in 1969, as a molecule possessing more bonds than the corresponding first row element.2 This definition encompasses an assortment of molecules with varying chemical properties, from highly reactive molecules such as ClF3 and SCl4 to the unusually stable SF6. In previous studies, we showed that recoupled pair bonds those resulting from interaction of a ligand with a lone pair of electrons on a central atomwere the basis for hypervalency in the late p-block elements.3−7 However, an even broader array of molecules than those traditionally classified as hypervalent exhibit this type of bonding, allowing the number of bonds formed to the central atom to exceed its nominal valence (i.e., number of singly occupied orbitals). For instance, we and others8,9 have shown that the sulfur atom (which has two unpaired electrons in the ground state) is involved in three chemical bonds in the ground state of the HSO radical. These bonds consist of a covalent S−H σ bond, a polar covalent S−O σ bond, and a recoupled pair S−O π bond.8 We have also previously noted that tri- and tetravalent carbon species (i.e., most carbon-containing molecules as well as reactive radicals such as CH3) should be collected under the umbrella of recoupled pair-bonded molecules because the carbon atom, like S, has a nominal valence of two.6 With such an extensive variety of molecules meeting this criterion, a detailed understanding of the factors influencing the formation of molecules where the central atom is able form more bonds than the nominal valence © 2014 American Chemical Society

is important. Moreover, since formation of recoupled pair bonds is dependent upon the ability of ligands to recouple a lone pair of electrons, it would be useful to identify a propertybased criterion that would reliably predict if a ligand (L) is able to induce recoupling of the lone pair in an atom. In the present work, we focus on bonding in sulfurcontaining hypervalent species. Specifically, we are interested in sulfuranes and their precursors. Sulfuranes are sawhorse-shaped compounds with four ligandstwo in equatorial positions and two in axial positionssurrounding a sulfur atom. The first hypervalent sulfur compound synthesized was a sulfurane− sulfur tetrachloride (SCl4).10 SCl4 is not particularly stable decomposing to yield SCl2 and Cl2 at temperatures above −22 °C;11 this decomposition is slightly exothermic.4 By contrast, the fluorinated analogue, SF4, while also lacking robust chemical stability, is strongly bound relative to SF2 + F2,12 and further reaction with fluorine yields the very stable SF6 molecule. Sulfuranes with nonhalogen ligands (especially involving oxygen13−15) have been synthesized as well, though they tend to be less strongly bound than SF4. For instance, several such organosulfuranes are prone to decomposition, as they are sometimes moisture-sensitive and reactive with glass.16 A variety of other ligands have been identified as participating in sulfurane chemistry: a sulfur-substituted sulfurane has recently been synthesized,16 and sulfuranes with all carbonbased ligands, such as a sulfur atom coordinated with two biphenyl ligands, have been characterized.17 Other sulfurane species have been identified as intermediates in chemical Received: April 23, 2014 Revised: June 23, 2014 Published: June 25, 2014 5709

dx.doi.org/10.1021/jp503982e | J. Phys. Chem. A 2014, 118, 5709−5719

The Journal of Physical Chemistry A

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reactions, in both organic chemistry and biology.18−22 For instance, Nakamura and co-workers recently reported an organosulfurane as an intermediate structure in the oxidation of a cysteine residue, mediated by a nearby histidine residue in a thioredoxin peroxidase.22 The axial bonds in hypervalent molecules are generally identified in the literature as 3-center 4-electron (3c-4e) bonds,23−25 whereas the equatorial bonds are described as typical 2-center 2-electron (2c-2e) covalent bonds. For the sulfur fluorides, this model would prescribe aligning the three p orbitals of F−S−F collinearly to yield an MO diagram that would include one bonding, one nonbonding, and one antibonding orbital. Combining an S 3p2 orbital with two F 2p1 orbitals would result in the former two orbitals being doubly occupied. As Á ngyán noted in 1989, the bond order predicted by this framework is 0.5. Yet, bond order calculations suggested greater bond orders (sometimes even approaching unity) for sulfuranes.26 At the time, Á ngyán rationalized the larger than expected bond orders by introducing a sulfur atomic d-orbital into the 3c-4e model; however, it has been known since at least the 1984 work of Kutzelnigg27 that the sulfur dfunctions provide only polarization and delocalization effects and do not act as valence orbitals in hypervalent systems.28−30 Previous work on the SFn (n = 1−6) family of molecules in our group showed addition of two more F atoms to ground state SF2 to yield SF4 results in an average zero-point corrected bond energy of 75.4 kcal/mol for the axial bonds, which is 87% of the average bond energy (86.5 kcal/mol) of the covalent S− F bonds in SF2(1A1).6 Experimental results mirror this trend, with an average D0 = 86.5 kcal/mol for SF2 compared to 73.6 kcal/mol for the axial bonds of SF4.31 This is a puzzling result in light of the bond order of 0.5 anticipated by the 3c-4e model. To further complicate matters, there is incredible diversity in the strengths and reactivities of the axial bonds of sulfuranes. For example, dissociation of the organosulfurane reported by Nakamura and co-workers to a sulfenic acid and an imidazole lowers the energy by 37.1 kcal/mol, indicating much weaker axial bond strengths than in SF4.22 Other nonhalogenated sulfuranes would also not be anticipated to have very strong axial bonds given their aforementioned propensity toward decomposition. Generalized valence bond theory and the resulting recoupled pair bonding model provides a theoretical framework to understand the diverse chemistry of sulfuranes. From the examples listed above, it is clear that the stability of sulfuranes is correlated with the electronegativity of the ligands. As we will show in this work, this observed relationship is a natural consequence of the recoupled pair bonding model, without prescribing any specific bond order to these interactions. The remainder of the paper is organized as follows. We describe our computational methodology in section II. In section III, we first review the connection between recoupled pair bonding and hypervalency. We then describe the correlation of recoupled pair bond strength with ligand electronegativity for a wide variety of ligands. We also investigate substituent (X) effects for X2SF molecules, and we consider two experimentally relevant examples of recoupled pair bonded species. In section IV, we offer summary conclusions.

orbital contains only one electron, and the spatial component of the orbitals and the spin couplings of the electrons in these orbitals are optimized as a function of geometry; therefore, the formation of a recoupled pair bond proceeds smoothly as the internuclear separation decreases. In its most general form, the GVB wave function is composed of the product of N spatial functions (where N is the number of electrons) multiplied by all possible linearly independent spin functions for N electrons in a state with total spin of S; this product is acted upon by an antisymmetrizer (Â ) to ensure proper behavior with respect to interchange of electrons. GVB theory has been thoroughly reviewed elsewhere,32−35 and the reader is referred to these articles for additional information. Optimization of the full GVB wave function quickly becomes computationally impractical as N increases, so the orbitals are typically partitioned into two types: doubly occupied orbitals and singly occupied, or active, orbitals. The doubly occupied orbitals are composed of a pair of GVB orbitals that are treated essentially as molecular orbitals: within each pair, they have unit overlap, are orthogonal to all other orbitals, and are described as a singlet-coupled pair with the spin function, αβ. Active orbitals, by contrast, can overlap with other active orbitals (but not with the doubly occupied orbitals), and all associated spincoupling patterns are included. This results in the following GVB wave function for Nd doubly occupied orbitals and Na active orbitals ̂ ϕ ϕ ···ϕ ϕ φ φ ···φ αβ···αβ ΘSN,aM ) ΨGVB = A( d1 d1 dN dN a1 a2 aN d

d

a

where {ϕdi} are the doubly occupied orbitals, {φai} are the f Na

a , that is, the sum of all active orbitals, and ΘNS,Ma = Σ k S csk ΘNS,M;k linear independent spin functions, of which there are f NS = (2S + 1)N!/(N/2 + S + 1)!(N/2 − S)! for a given value of N and S. The coefficients {csk} describe the importance of a given spincoupling pattern to the overall wave function. Herein we use the Kotani spin basis,36 so the square of the coefficient is equal to its weight (csk2 = wk). We will see in section III that the spincoupling pattern expressed in terms of atomic-like orbitals can change as a function of geometry; however, for the geometries examined in this work, we often find that one spin function is clearly dominant in the calculation. All calculations were performed with the Molpro suite of quantum chemical programs37 with augmented correlation consistent basis sets with tight d-functions on the P, S, and Cl atoms: aug-cc-pV(N+d)Z, where the triple-ζ (N = T) set was used for most calculations with the exception of the X2SF geometry optimizations (see below).38−40 The potential energy scans as a function of R(S−L), where L is the ligand, were performed with the multireference configuration interaction method41,42 with the Davidson correction for quadruple excitations43 (MRCI+Q) using a full valence active space in the CASSCF calculation.44,45 All other degrees of freedom were fixed at their values from the optimized geometry for the SL molecule, which was derived from an explicitly correlated coupled cluster calculation [RCCSD(T)-F12, with the “a” approximation].46−49 F12 calculations include terms that depend explicitly on the interelectronic distance to better describe the electron cusp; as a result, accuracy is typically increased by approximately one zeta relative to standard methods.50 This feature enables to us to treat larger molecules efficiently and accurately: for our investigation of substituent effects, the geometries of the X2SF molecules were optimized with the aug-cc-pV(D+d)Z basis set, and the energetics were

II. COMPUTATIONAL METHODS The generalized valence bond (GVB) wave function possesses several features that have enabled us to gain a detailed understanding of recoupled pair bonding. In particular, each 5710



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computed with the aug-cc-pV(T+d)Z basis set. All X2SF species were optimized in CS symmetry. Charges presented in this work were computed from a Mulliken population analysis of the GVB wave function. For the X2SL species, the three electrons affiliated with the S−L recoupled pair bond were included in the active space, and for the (HO)2PF isomers, the two electrons associated with the P−F bond formed the active space with the doubly occupied orbitals frozen as localized Hartree−Fock orbitals. We also used RCCSD(T)-F12 calculations to compute the electronegativity of the ligands. Because many of the ligands that we investigate here are polyatomic, there is no predefined scale of electronegativity for them. As a result, we applied the Mulliken definitionthe arithmetic mean of the first ionization potential (IP) and the electron affinity (EA)to the ligand, subject to the slight modification described below. All of the ligands included in this work are monovalent, and it is the electron-withdrawing ability of the singly occupied orbital of the ligand rather than that of the ligand as a whole that is expected to influence the strength of the recoupled pair bond. As a result, when determining the ionization potential, we computed the energy gap between the neutral ligand (a doublet) and the lowest lying singlet state of the corresponding cation. We did not optimize the geometry of the ligand as a function of charge. We then applied the following linear transformation, χM = 0.168·(IP + EA − 1.23), where χM is the electronegativity and the IP and EA are in units of electron volts, to obtain values similar in magnitude to those of the Pauling scale.51 We treated a large variety of ligands in this work and endeavored to place them all on equal theoretical footing. However, a few cases required slight modifications to yield reasonable results. For the F2SF molecule, the global minimum corresponds to a T-shaped molecule that contains a recoupled pair bond dyad and a single covalent bond.6 In order to describe a single recoupled pair S−F bond with two covalent S−F bonds, we constrained the F−S−F angle associated with the covalent bonds to be fixed at its value in ground 1A1 state of SF2. For the potential energy scan of SOH(4A″), a second electronic state was included in the CASSCF calculation in order to achieve a smooth curve at larger values of R(S−OH). The SNH2 calculations were complicated by the presence of a low lying excited state of NH2 that bonded with the sulfur atom in both the 2A′ and 4A″ states. To force the sulfur atom to bond with the ground state of NH2, the geometry of the NH2 fragment and the angle of the NH2 moiety relative to the sulfur atom were fixed at their values in the 2A″ state of SNH2, which does interact with the ground state of NH2. More information on SNH2 can be found in the Supporting Information.

Figure 1. GVB orbital diagram and selected GVB orbitals for the SF(a4Σ−) state at (a) R(SF) = Re + 1.0 Å and (b) R(SF) = Re. The yellow shading in the diagram indicates that high spin coupling (here, quartet) among the electrons in the orbitals is present in the dominant spin-coupling pattern, and a dotted line separating GVB orbitals indicates singlet coupling in the dominant spin-coupling pattern. Both the MO (left) and GVB (right, φ1 and φ2) representation of the sulfur atom are shown in the diagrams in (a).

3p orbitals, (φ1, φ2), in Figure 1a indicates that they are singlet coupled in the dominant spin-coupling pattern and constitute what, in molecular orbital theory, would be the S 3p2 lone pair (shown to the left in Figure 1a). However, at R(S−F) = Re, the two S 3p-like orbitals are no longer singlet coupled into a lone pair; rather, one electron from this pair has polarized toward and delocalized onto the F atom to form a Heitler−London bond pair52 with the fluorine-centered orbital (97.8% of the wave function). The electron in the remaining S 3p-like orbital is now coupled into a quartet with the electrons in the singly occupied S 3pπ orbitals as depicted in Figure 1b. As bond formation occurs, φ1 and φ3 essentially exchange and φ2 polarizes toward and delocalizes onto the more electronegative fluorine atom. In the S atom, the two orbitals describing the S 3p lone pair have a high overlap and are singlet coupled. However, in the bound SF(a4Σ−) state, these two orbitals, now (φ2, φ3), are no longer singlet-coupled, and therefore their overlap is energetically unfavorable due to Pauli repulsion.53−56 In prior work, where nonsinglet paired orbitals were constrained to be orthogonal, this electron repulsion was manifest in the antibonding character of the unpaired orbital,6 but if we lift

III. RESULTS A. Recoupled Pair Bond and Connection to Hypervalency. A recoupled pair bond is formed when an electron in a singly occupied orbital interacts with a singlet-coupled pair of electrons on another atom. Often such three-electron interactions are repulsive. However, under some conditions, a bound state is obtained, such as the a4Σ− state of SF.6 Selected GVB orbitals for this state and the corresponding GVB orbital diagrams of the dominant spin-coupling patterns are shown in Figure 1a,b at R(S−F) = Re + 1.0 Å and R(S−F) = Re, respectively. At R(S−F) = Re + 1.0 Å, the dominant contribution to the wave function (99.9%) describes an S(3P) atom and an F(2P) atom. The dotted line separating the two S 5711



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bonds, and therefore a key component of these types of hypervalent species, is the recoupling of the electrons in the 3p lone pair of sulfur. This occurs even in the diatomic SF(4Σ−) molecule, making this type of interaction the basis for hypervalency. In the next section, we consider the properties of similar quartet states with a variety of ligands in addition to the fluorine atom. B. Properties of the Recoupled Pair Bond. The recoupling of a pair of electrons that were singlet coupled in the atomic wave function, induced by formation of one or two central atom−ligand bond pairs that utilize these electrons, can allow atoms to form a greater number of bonds than predicted by their nominal valence. In this view, the fundamental building block of a hypervalent molecule is the recoupled pair bond. Given that the weakness of the SF(4Σ−) recoupled pair bond is a consequence of the large repulsive overlaps in the σ space, ligand electronegativity is expected to be an important determining factor in the strength of these types of recoupled pair bonds, because shifting the electron density toward the ligand will reduce the electronic repulsion that results from formation of the recoupled pair bond. In the case of SF(4Σ−), this electron repulsion is manifest in the substantial overlap between the nonpaired orbitals, particularly the overlap between the two orbitals that were originally centered on the sulfur atom, S23. In Figure 1b, the electronegativity of the F atom facilitated the movement of φ2 away from φ3 as well as away from the 3s2 orbital of the sulfur atom. Our group has previously shown that as the halide ligand is taken from further down the periodic table (and therefore ligand electronegativity decreases), the recoupled pair bond strength decreases.58 The same trend is observed as the atom of the ligand bearing the singly occupied orbital is taken from further to the left of F within the first row, where ligand electronegativity also decreases. Figure 3 shows potential energy scans for the

that constraint, the antibonding character disappears; now, the magnitude of the repulsion is related to the orbital overlaps (here, S13 and S23, see Table 1). These large repulsive overlaps, Table 1. GVB Orbital Overlaps for the SF(4Σ−) and SF2(3Σ−) States at Rea S12 S13 S23

SF(4Σ−)

SF2(3Σ−)

0.79 0.17 0.61

0.83 0.06 0.23

a

S12 is an energetically favorable overlap correlating with bond formation; S13 and S23 correlate with Pauli repulsion between the electrons in the bond pair and electron in the left over orbital. Note the slight increase in the favorable overlap and pronounced decreases in the unfavorable overlaps when the second SF bond is formed in SF2(3Σ−).

particularly S23, result in a bond that is much weaker than the covalent analogue: De[SF(a4Σ−)] = 36.7 kcal/mol versus De[SF(X2Π)] = 84.6 kcal/mol. Moreover, the recoupled pair S−F bond is longer than the analogous covalent bond Re[SF(a4Σ−)] = 1.877 Å versus Re[SF(X2Π)] = 1.599 Å. We can demonstrate that these repulsive overlaps are the origin of the weak bond energy by adding a second electronegative ligand (another F atom) to φ3 from Figure 1b to reduce these overlaps (S23 in particular); see the associated GVB diagram in Figure 2 for the resulting SF2(3Σ−)

Figure 2. GVB orbital diagram for SF2(3Σ−). The yellow shading indicates that the electrons in these orbitals are high spin (triplet) coupled in the dominant spin function.

state. As φ3 is polarized away from the original bond pair, φ2 and φ3 become much more spatially separated. Table 1 compares the orbital overlaps for both SF(4Σ−) and SF2(3Σ−). Marked reduction in the energetically unfavorable overlaps is obvious, and the new repulsive overlap between the two F 2plike orbitals, S34, is quite small (0.02). (The 3Σ− geometry was selected to facilitate a straightforward comparison of the orbital overlaps; it is only 0.4 kcal/mol higher in energy than the 3B1 minimum, which has a bond angle of 163.0°.) Consistent with the reduction in repulsive overlaps, the bond energy for this addition (De = 107.5 kcal/mol) is stronger than even a typical 2c-2e polar covalent S−F bond. The combination of a recoupled pair bond plus a polar covalent bond formed with the electron left over from the formation of the recoupled pair bond is referred to as a recoupled pair bond dyad. As we have previously shown,6,57 SF4 can be constructed by adding two F atoms to the singly occupied orbitals of the 3B1 state of SF2 (i.e., to the S 3pπ orbitals in the GVB diagram in Figure 2). The recoupled pair bond dyad forms the axial bonds of SF4, whereas the equatorial bonds in SF4 are 2c-2e covalent bonds. In this view, it is clear that the axial bonds are two polar covalent bonds that have a somewhat higher overlap between the bond pairs than would occur between two such bonds oriented in a bent configuration. Furthermore, the central feature that allows the sulfur atom to form more than two

Figure 3. Potential energy curves for the quartet state of SL, where L = F (■), OH (●), NH2 (◆), and CH3 (▲); all other degrees of freedom are held fixed at their equilibrium values from an RCCSD(T)F12/AV(T+d)Z calculation. The zero of energy is set to the potential energy at R(S−L) = Re(S−L) + 100.0 Å. For the unbound species, Re was estimated as described in the text. Calculation: MRCI+Q/aug-ccpV(T+d)Z.

quartet states of S−L, where L = F, OH, NH2, and CH3. The SF(4Σ−) curve is the most strongly bound, with SOH(4A″) being weakly bound. The quartet states of SNH2 and SCH3 are purely repulsive, with the SCH3 curve being notably more repulsive than the SNH2 curve. The SNH2 curve has a slightly flatter area at longer values of R(S−NH2); this is potentially a consequence of stabilizing effects of a certain amount of 5712



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recoupling in the σ orbitals even though the curve is repulsive overall. Again, we can understand this trend in terms of recoupled pair bonding because ligand electronegativity is a key aspect to reducing the repulsion in the three-electron interaction in the σ system. To get a more comprehensive view of recoupled pair bonds, we have performed geometry optimizations of the quartet state for various monovalent ligands bonding with sulfur. Table 2

Table 3. Calculated Electronegativities of the Ligands with the Methodology Described in Section II, with Comparison to the Pauling Scale When the Ligand Is an Atom

Table 2. Bond Dissociation Energies for the S−L Bond with Various Ligands on the Quartet Surface for SL, Where L Is the Liganda L

De (kcal/mol)

F Cl Br CCH CN OH SCH3 SH OCH3 NH2 H CH3 CHCH2

36.7 22.5 18.7 14.5 14.1 12.8 9.8 8.6 4.2 −4.8 −13.2 −18.3 −21.5

L

EN (this work)

EN (Pauling)

F Cl Br CCH CN OH SCH3 SH OCH3 NH2 H CH3 CHCH2

3.77 2.85 2.61 2.68 2.78 2.72 1.91 2.18 2.19 2.03 2.22 1.55 1.62

3.98 3.16 2.96

2.20

a

See the main text for a description of the computed negative bond energies. Calculation: RCCSD(T)-F12/AV(T+d)Z.

reports the S−L bond energies [RCCSD(T)-F12/AV(T+d)Z] of the resulting species. For the bound quartet geometries, the recoupled pair bonds were between 17% and 44% longer than the analogous doublet (covalent) species, with an average increase in length of 26%. We used this value to estimate the degree of repulsion in the unbound quartet species (such as NH2 and CH3) by performing a geometry optimization constraining the S−L bond length to be 126% of the covalent bond length. These values are reported as negative numbers in Table 2 and should be regarded as simple estimates. The SL molecules listed in Table 2 possess widely varying bond strengths. Consistent with the fact that the fluorine atom is the most electronegative ligand, the S−F recoupled pair bond has the largest bond energy, 36.7 kcal/mol. Ligands yielding the next strongest bonds are the other halides: the Cl atom (22.5 kcal/mol) followed by the Br atom (18.7 kcal/mol). More weakly (but still appreciably) bound are the alkyne ligands, CCH and CN, with S−L bond strengths of 14.5 and 14.1 kcal/ mol, respectively. The most weakly bound ligands are OH (12.8 kcal/mol), SCH3 (9.8 kcal/mol), SH (8.6 kcal/mol), and OCH3 (4.2 kcal/mol), respectively. The NH2, CH3, H, and CHCH2 ligands are unbound on the quartet surface, with the degree of repulsion estimated as described above. To correlate recoupled pair bond strength with ligand electronegativity, we calculated this property of the ligand using a slight modification of Mulliken’s definition of electronegativity (see section II). The calculated electronegativities, as well as the corresponding value from the Pauling scale for the atomic ligands, are listed in Table 3. There are some differences between the two scales, which reflect both the lack of a perfect correlation between the unmodified Mulliken and Pauling scales as well as our focus on the properties of the singly occupied orbital and not the ligand as a whole. However,

Figure 4. Comparison of the computed electronegativity of the ligand versus the bond energy of the quartet state of SL, with the best-fit line shown. The dotted lines mark one standard deviation with respect to this fit.

the qualitative ordering of the ligands in terms of electronegativity is preserved. The comparsion between the calculated electronegativity and recoupled pair bond strength is shown in Figure 4. There is clearly a correlation between these quantites (R2 = 0.79), but it is not perfect, and there are a few outliers. It seems that ligand electronegativity is an important factor in determining recoupled pair bond strength, but it is not the only one. For instance, the various ligands and the sulfur atom have different interactions in the π system, and the size of the ligands varies significantly. Figure 4 shows dotted lines corresponding to one standard deviation from the best-fit line. Some of the departures from linearity in this plot appear to be systematic in nature, with the more polarizable ligands often being more strongly bound than would be expected based on ligand electronegativity and vice versa. The SCH3 ligand in particular is the most polarizable ligand (see Table S1 in the Supporting Information for the calculated ligand polarizabilities) and is also the most strongly bound relative to what the ligand electronegativity predicts. Conversely, the two least polarizable ligands (H and F) are the most weakly bound relative to what would be anticipated based on the ligand electronegativity and lie outside of one standard deviation. It seems that recoupled pair bonds are sufficiently weak and long that effects generally 5713



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regarded as weak intermolecular forces may play a greater relative role in determining their bond energy. The ligand electronegativities were computed from the first ionization potential (IP) and the electron affinity (EA) of the singly occupied orbital of the ligand, as described in section II. In Figure 5, we show the correlation between bond dissociation

Figure 6. Comparison of the electronegativity of the ligand versus the bond energy of the ground (doublet) state of SL.

perfect in Figure 4, it is not coincidental nor due to an inherent property of the ligand. Figure S3 in the Supporting Information shows the potential energy scans analogous to those in Figure 3 for the doublet states, where the dependence on the identity of the ligands is dramatically reduced. C. Applications. 1. Substituent Effects. Although many of the quartet states examined in the previous section are physically stable, they will not be chemically stable and would be difficult to study experimentally. While also very reactive, the X2SF molecules (X = H, CH3, NH2, OH, and F) might be easier to characterize. Here, we examine substituent effects on the S−F recoupled pair bond present in these species; the values for De(SF) are given in Table 4. The X2SF molecules can Table 4. Bond Dissociation Energies for the S−F Bond in X2SF, Where X is the Substituenta

Figure 5. Comparison of the ionization potential (IP; a) and electron affinity (EA; b) of the ligand versus the bond energy of the quartet state of SL.

energy of the SL quartet state and IP and EA of the ligand, respectively. For the IP, the qualitative trends present in Figure 4 (ligands more strongly bound than their predicted values tend to be more polarizable and vice versa) remain, but the spread in the correlation is markedly larger (R2 = 0.57 for IP versus 0.79 for electronegativity). For the EA, although the R2 value is equal to that of Figure 4 (both 0.79), the plot is overall less satisfying for several reasons. The outliers are not as systematic in nature as they are for Figures 4 and 5a (e.g., the CN ligand is significantly more weakly bound than the EA predicts, but CCH is relatively consistent with its EA). Similarly, for the halogens (L = F, Cl, Br), where differences among the ligands that might disrupt the correlation should be minimal, the qualitative ordering is incorrect (the EA of F is less than that of Cl). These results suggest that both the energetic penalty for donating electron density and the energetic gain from accepting electron density with respect to the neutral ligand play a role in determining recoupled pair bond strength. It is worth noting that the observed dependence on electronegativity is particular to recoupled pair bonds. For the covalently bound species, there is effectively no correlation between ligand electronegativity and bond strength; see the analogous comparison for the doublet states in Figure 6. This result underscores that even though the correlation is not

a

X

De (kcal/mol)

none H CH3 NH2 OH (cis) OH (trans) F

36.7 21.8 34.7 39.1 51.2 38.6 41.9

Calculation: RCCSD(T)-F12/AV(T+d)Z.

be formed via covalent bond formation involving the S 3px and S 3py orbitals in Figure 1b with the substituent X. Note that there are two minima for (HO)2SF, one where the hydrogen atoms are pointed at the F atom (cis) and one where they are pointed away from the F atom (trans). Overall, there is a small increase in bond strength as the electronegativity of the substituents increases. Again, reduction of electronic repulsion is undoubtedly the driving force; here the dominant repulsive interactions are between the electrons of the two S−X bond pairs and the S−F bond. Table S2 in the Supporting Information gives the Mulliken spin population analysis for the X2SF species at Re. This metric indicates that as the electronegativity of X is increased, localization of the singly occupied orbital on the sulfur atom is enhanced, owing to the reduced electron density surrounding the sulfur atom. In the previous section, we calculated that H and CH3 have similar electronegativities; however, the longer S−C bond length relative to that of S−H also reduces repulsion with the recoupled pair bond. As a result, the H2S−F bond is by far the weakest of the X2SF molecules. 5714



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The recoupled pair bond in H2SF is appreciably weaker than the one in SF(4Σ−), owing to the loss of favorable exchange interactions with the electrons in the singly occupied π orbitals. For SF(4Σ−), at large internuclear separation on the quartet surface, the singly occupied σ orbital of the F atom is coupled into high spin with the triplet pair on sulfur. At Re, the σ orbital coupled into α spin is centered on the S atom, and the bond energy is augmented by the favorable exchange energy among these three orbitals. (As noted above, these spin-coupling patterns are depicted in Figure 1.) Adding covalently bound hydrogen atoms to the sulfur-centered singly occupied orbitals negates this effect, significantly weakening the bond. However, for the remaining substituents, the increased length and polarity of the S−X bonds reduces electron repulsion sufficiently that the bond energies of these X2SF species are comparable to or even greater than those of the SF(4Σ−) state. Additionally, the presence of hydrogen atoms bearing partial positive charges near the partially negatively charged F atom for X = CH3, NH2, and OH is expected to stabilize the recoupled pair bond. To discern whether the observed substituent effects are peculiar to recoupled pair bonds, we compare the S−F bond strengths of the X2SF molecules to those of the covalently bound X2PF species. This comparison is not straightforward for three reasons. (1) The covalent P−F bond is much stronger than the recoupled pair S−F bond. (2) The effect of adding any substituent to PF(3Σ−) is less deleterious to the bond energy relative to SF(4Σ−) because of the differences in exchange energy. In PF(3Σ−), the electron in the incoming singly occupied 2p orbital of fluorine is low spin coupled relative to the quartet-coupled 3p orbitals of phosphorus. So as bond length decreases, there is no favorable contribution from the exchange energy in the phosphorus analogues like there is in SF(4Σ−). (3) The difference in electronegativity between the central atom (P or S) and the incoming F atom results in bonds of differing polarity. To try to compensate for these differences, we first subtracted the bond energies of the X2PF and X2SF species from their corresponding diatomic bond energy to account for one of the bonds being covalent and the other being a recoupled pair bond and for the difference in the polarity of the P−F and S−F bonds. Then we set the bond energy of H2SF and H2PF equal to one another and applied that constant shift to the X2PF bond energies to account for the different effects of exchange. The result of this analysis is shown in Figure 7. (The untransformed PF bond strengths are given in Table S3 in the Supporting Information.) When these differences are accounted for, the substituent effects are nearly equivalent for every species (with X = H being equivalent by construction), except for the (HO)2YF (Y = P, S) structures, particularly the cis conformer (which we will consider below). But beyond this special case, effects present in both X2YF species, such as the additional electron repulsion resulting from adding an F atom to the X2Y molecule and interactions of the partially positively charged hydrogen atom of X with the partially negatively charged incoming F atom, seem to dictate the role of substituent effects. As mentioned above, the anomaly in this correlation is (HO)2YF, particularly for the cis orientation of the hydrogen atoms. (HO)2SF (cis) is much more strongly bound than would be anticipated based on the (HO)2PF (cis) analogue; however, (HO)2SF (trans) is reasonably similar to (HO)2PF (trans). (HO)2SF (cis) and (HO)2SF (trans), along with their Mulliken charges derived from the GVB wave function are shown in Figure 8a, as are the phosphorus analogues in Figure 8b. In the

Figure 7. Comparison of substituent (X) effects on the S−F and P−F bonds of X2SF (■) and X2PF (●), where the bond energies of SF(4Σ−) and PF(3Σ−) have been subtracted from the X2S−F and X2P−F bond energies. The H2P−F and H2S−F bond energies have been set equal to one another, and all values of the X2P−F bond energies have been shifted by this difference (−21.2 kcal/mol).

Figure 8. Structures and Mulliken charges for (HO)2YF (cis) and (HO)2YF (trans) for (a) Y = S and (b) Y = P.

(HO)2SF (cis) molecule, the polar OH bonds are in a nearperfect alignment with the polar S−F bond at the equilibrium geometry (FSOH dihedral = 1.1°), and the H−F distance is quite short, 1.879 Å. The long (2.010 Å) recoupled pair S−F bond reduces repulsion between the F atom and the OH bond pairs. These dipolar interactions are expected to be quite energetically favorable. Furthermore, the associated bonds are significantly more polar in the (HO)2SF (cis) molecule than in the (HO)2SF (trans) molecule; the interaction of the dipole moments likely stabilizes charge separation. In principle, (HO)2PF (cis) could adopt this configuration as well; however, the P−F bond is a 2c-2e covalent interaction, and therefore is much shorter (Re = 1.606 Å). Apparently, the loss in energy that would accompany lengthening of the P−F bond to the degree required to reduce electronic repulsion between the F atom and the OH bond pairs is greater than the energy gained from these dipolar interactions. The sulfur analogue is more strongly bound than would be expected based on (HO)2PF (cis); however, the SF bond is weaker than the PF bond by 84.4 kcal/mol. The two trans species are much more similar in geometry, with the phosphorus species seemingly having greater flexibility with respect to positioning of the H atoms. This is likely due to reduced electronic repulsion between the OH groups and the two-electron P−F bond versus the three-electron S−F bond. The net result is that (HO)2SF (trans) is somewhat less strongly bound than would be expected based on the 5715



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Figure 9b shows the SF bond energy of (HO)2SF (cis), (HO)2SF (trans), and SF(4Σ−) as a function of R(S−F). At R(S−F) ≈ 2.2 Å, the cis curve begins to turn over to yield a structure where the H atoms are shared between the F and O atoms that is not of interest in this work. To avoid this feature, we calculated ke by fitting the three data points around Re(S− F) to a Morse oscillator, where Re and De were fixed at their calculated values. The comparison of Re, De, and ke is shown in Table 5. Generally, Re is inversely correlated to both De and ke,

phosphorus analogue as shown in Figure 7. Interestingly, the (HO)2SF (trans) species, despite possessing a weaker S−F bond than the cis confomer, has a significantly shorter S−F bond (1.717 Å). This is an unusually short bond for a single recoupled pair bond; for example, SF(4Σ−) has a bond length of 1.877 Å. This feature is a result of the polarity of the S−OH bonds. The singly occupied orbital left over from the recoupled pair bond can more effectively avoid the S−F bond pair by overlapping with the S−OH bonds, and, because the S−OH bonds are polarized toward the O atom, there is less energetic penalty for doing so. The GVB orbital overlaps as a function of R(S−F) for this singly occupied orbital with the sulfur-centered orbital of the S−F bond (S13), and one of the S−OH bonds (S34) is plotted in Figure 9a along with the favorable S−F

Table 5. Equilibrium Bond Lengths (Re; Å), Dissociation Energies (De; kcal/mol), and Force Constants (ke; kcal· mol−1·Å2) for the S−F Bond in SF(4Σ−), (HO)2SF (cis), and (HO)2SF (trans)a SF(4Σ−) (HO)2SF (cis) (HO)2SF (trans) a

Re

De

ke

1.8774 2.0099 1.7172

36.7 51.2 38.6

249.8 101.6 194.9

Calculation: RCCSD(T)-F12/AV(T+d)Z.

which are in turn positively correlated with one another; these relationships are widely used in chemical analyses.59 However, for the above molecules, these quantities are not correlated in any way. These deviations from the “expected” correlations are nonetheless accounted for in the preceding paragraphs by recognizing the character of recoupled pair bonds. 2. Practical Examples. Having examined the effects of both the ligands and the substituents on the recoupled S−L bond, we now consider molecules with more practical applications. In a previous work, our group showed that the reaction of dimethyl sulfide (DMS) with diatomic fluorine, which is an unusual example of a barrierless reaction between two closedshell chemical species,60−62 is mediated by formation of a recoupled pair bond between the 3p2-like lone pair orbital of DMS and one of the fluorine atoms.63 The presence of the recoupled pair bond lowers the energy along the reaction coordinate, eliminating the barrier to reaction altogether. Similarly, we can understand the stability of single addition products to DMS and related molecules if the incoming ligand is sufficiently electronegative. For instance, a possible reaction channel for DMS and the OH radical in the atmosphere involves the DMS−OH adduct.64,65 It was unclear for some time whether this species was a transition state or an intermediate, but modern quantum chemical calculations have shown this species is in fact bound (i.e., it is an intermediate in this reaction). We can understand the stability of this species in terms of recoupled pair bonding with the S 3p2-like lone pair orbital of DMS. We compare the GVB orbitals for both DMS−F and DMS− OH in Figure 10, where the impact of ligand electronegativity is clear. In Figure 10a, the GVB orbitals and their overlaps for DMS−F closely resemble those of SF(4Σ−), consistent with their similar bond energies (34.7 and 36.7 kcal/mol, respectively); compare to Figure 1b and Table 1. The SF bond is quite polar, with the F atom bearing a −0.60 partial Mulliken charge. The exchange of the sulfur-centered orbital and the incoming fluorine orbital is complete, and the perfect pairing spin-coupling pattern depicted in Figure 10a accounts for 96.5% of the wave function. By contrast, DMS−OH is more weakly bound (De = 10.3 kcal/mol). This is also slightly less than the S−OH bond energy of SOH(4A″) of 12.8 kcal/mol. Because the OH ligand is less electronegative, the OH group

Figure 9. (a) GVB orbital diagram and selected GVB orbital overlaps (S12 = ◆, S13=●, S34 = ■) for (HO)2SF (trans) as a function of R(SF). (b) Potential energy [RCCSD(T)-F12/AV(T+d)Z] as a function of R(SF) for (HO)2SF (cis) [◆], (HO)2SF (trans) [●], and SF(a4Σ−) [■] relative to the ground state (HO)2S + F energy for the former and the ground state S + F energy for the latter.

bonding overlap (S12). The bonding overlap increases linearly with decreasing R(S−F). At larger R(S−F), the repulsive overlaps are similar to that of SF(4Σ−), where the unpaired electron mainly overlaps with the S−F bond pair (S13) (compare to Table 1). However, as R(S−F) decreases, the unpaired electron moves away from the S−F bond pair (S13 decreases) and overlaps more strongly with the S−OH bond pairs (S34 increases). In the trans conformer, the trade-off between overlapping with the S−F bond or the S−OH bond pairs as a function of R(S−F) results in a more flexible S−F bond, and therefore a lower force constant (ke) than would be anticipated based on the bond length alone. The cis conformer is similarly flexible at smaller values of R(S−F), and increasingly flexible at larger R(S−F), as the dipolar interactions stabilize the bond stretch. 5716



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To connect more directly to species that might be experimentally observable, we also considered substituent (X) effects on recoupled pair bonding in X2SF molecules. We found that, in large part, the effects of the S−X bonds are nearly identical to those observed for the covalently bound X2PF species, except for where X = OH. For (HO)2SF, we found two minima associated with the orientation of the H atoms: one cis and one trans to the F atom. Intriguingly, when comparing the S−F bond in (HO)2SF (cis), (HO)2SF (trans), and SF(4Σ−), the usual direct correlations among inverse bond length, bond strength, and frequency did not hold. In this particular system, the breakdown of these relationships may not have any practical consequences. However, given that we recently reported on another case where these correlations are disrupted by recoupled pair bonding, FSSF3,66 it seems that the presence of recoupled pair bonding means that particular care must be taken when applying these relationships. Moreover, a detailed understanding of recoupled pair bonding might allow us to understandand even predictwhen these relationships are likely to break down. Finally, we showed that the (CH3)2S−OH species, which is an intermediate in the reaction between dimethyl sulfide and the hydroxyl radical, is bound by approximately 10 kcal/mol, because there is a recoupled pair bond between the S atom and OH. When this species was first examined by others, its stability was surprising, but we find that the binding energy of this species is as expected based on our study of recoupled pair bonds. As such, we argue that the recoupled pair bonding framework is useful not only to understand bonding in stable hypervalent species but also to anticipate the properties of transient species, such as reaction intermediates.

Figure 10. GVB orbitals and overlaps for (a) (CH3)2SF and (b) (CH3)2SOH.

only bears a partial charge of −0.31. As a result, there is more electronic repulsion associated with the recoupled pair bond. Instead of appearing as large unfavorable GVB orbital overlaps, here, the augmented repulsion results in the recoupling process (the exchange between the sulfur-centered and oxygencentered orbital into the singlet coupled pair) being less complete. This is particularly apparent when the high spin coupled orbital is examined; there is obvious antibonding character present and density on both the sulfur and oxygen atoms. Moreover, the spin-coupling pattern describing the SO bond pair (αβα) only accounts for 84.2% of the wave function, with the remainder of the wave function triplet coupling φ1 and φ2 (ααβ). The Mulliken spin population analysis, given in Table S4, also indicates reduced transfer of the high spin coupled orbital from ligand to DMS when L = OH versus L = F. We have found other instances of interactions that are attractive because of recoupled pair bonding but the recoupling of the pair is incomplete. Future work will focus in more detail on this “frustrated” recoupled pair bonding (see Takeshita, Woon, and Dunning, in preparation). Note that either of these molecules can undergo further bond formation to result in a sulfurane by addition of a sufficiently electronegative ligand to the unpaired orbital shown in Figure 10.

■

ASSOCIATED CONTENT

S Supporting Information *

Calculated polarizabilites of the ligands presented in this work, Mulliken spin populations for the X2SF and DMS−OH molecules, untransformed X2PF bond energies, additional material regarding SNH2 and the first excited state of the NH2 ligand, and potential energy scans for the doublet states of the molecules analogous to those shown in Figure 3. This material is available free of charge via the Internet at http:// pubs.acs.org.

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IV. DISCUSSION It is well known that hypervalent molecules typically involve weakly electronegative central atoms and very electronegative ligands. In this work, drawing on the connection between hypervalency and recoupled pair bonding, we investigated the properties of recoupled pair bonds involving the 3p2 lone pair of the sulfur atom. As noted in the introduction, recoupled pair bonds, unlike most covalent bonds, are conditional bonds they only form between certain atoms or fragments. We found that ligand electronegativity strongly stabilizes this class of bonds. This result matches the general trend observed with experimentally synthesized sulfuranes, where sulfur fluorides are strongly bound, but oxygen- and sulfur-substituted organosulfuranes are generally much more prone to decomposition. It is of course not a surprising result that ligand electronegativity correlates with the stability of molecules traditionally classified as hypervalent. However, we have begun to quantify this trend, which allows us to make predictions about what types of ligands might be feasible for future synthesis of novel sulfuranes. For instance, alkynes would likely be good choices, whereas unconjugated alkenes are not good ligands.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: 206-616-1439. Present Address

‡ University of Washington, Northwest Institute for Advanced Computing, Box 352500, Seattle, WA 98195-2500

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Distinguished Chair for Research Excellence in Chemistry and the National Center for Supercomputing Applications at the University of Illinois at Urbana−Champaign. One of the authors (B.A.L.) is the grateful recipient of a National Science Foundation Graduate Research Fellowship. This work was adapted from the first author’s Ph.D. dissertation, which is available at http://hdl. handle.net/2142/49568. 5717



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