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Recoupled Pair Bonding in PFn (n ) 1-5)† David E. Woon* and Thom H. Dunning, Jr.* Department of Chemistry, UniVersity of Illinois at Urbana-Champaign, Box 92-6, CLSL, 600 S. Mathews, Urbana, Illinois 61801 ReceiVed: March 11, 2010; ReVised Manuscript ReceiVed: May 21, 2010
Following our previous studies of hypervalency in SFn (n ) 1-6) and ClFn (n ) 1-7), we have characterized the structures and energetics of PFn (n ) 1-5) species with RCCSD(T) coupled cluster calculations and triple- and quadruple-ζ quality correlation consistent basis sets. The prior studies demonstrated that hypervalent bonding occurs when it is energetically favorable to uncouple a pair of electrons to form new bonds, a process we describe as recoupled pair bonding. In contrast to S and Cl, ground state P(4S) has no 3p2 pairs that can be recoupled, but the 3s2 pair of all three elements is susceptible to recoupled pair bonding when more energetically accessible bonding pathways have been exhausted. We found that this can first occur when F is added to PF2(X2B1), which yields PF3(X1A1) via normal covalent bonding but yields PF3(a3B1) via recoupled pair bonding. PF3(a3B1) lies 92.1 kcal/mol above PF3(X1A1) but is still bound by 42.0 kcal/mol with respect to PF2(X2B1) + F at the RCCSD(T)/aug-cc-pVQZ level. We characterized both of the isomers of PF4: the more stable and familiar one that has two covalent equatorial bonds and two axial hypervalent bonds (that use both electrons of the recoupled 3s2 pair) and the less-studied one that has three covalent bonds and only one hypervalent bond. The transition state between these two minima was also located. In addition to the states that can be formed from P(4S), there is another group of low-lying excited state species that can be formed from P(2D) via various combinations of covalent and recoupled pair bonding. Additions of the latter type include PF(B3Π) formed from P(1D) + F and PF2(B2B2) formed from either PF(a1∆) + F or PF(B3Π) + F. 1. Introduction The mental grimoire that chemists use to understand molecular bonding is dominated by the two-center-two-electron bond (2c/2e): covalent singlet coupling of singly occupied orbitals originating from two moieties (atoms or radicals). It is recognized, however, that other types of bonding do not require that each moiety contributes an electron to the bond or even that two electrons are necessary for a chemical bond to form: in H2+, a single electron is shared between the two nuclei, and species such as H3O+ and BH3NH3 contain a dative bond where both electrons are contributed by one atom. One- and twoelectron bonds of this type, where one moiety participates by providing an unoccupied orbital, occur in many compounds (particularly in coordination chemistry). In several recent studies,1-3 we have described another common mode of bonding that we call “recoupled pair bonding”, which involves three electrons. In these circumstances, it is energetically favorable for a singlet coupled pair of electrons on an atom to be uncoupled to allow one of the electrons to be recoupled to a third electron from a second moiety to form a new singlet coupled pair. This results in a more extensive reorganization of the electronic structure of the combined system during bond formation than that which occurs when a normal covalent bond forms. Although recoupled pair bonds are common in molecules containing P, S, and Cl (along with the heavier elements below them in the periodic table and the heavier noble gases) and account for the formation of hypercoordinated molecules such †
Part of the “Klaus Ruedenberg Festschrift”. * To whom correspondence should be addressed. E-mail:
[email protected] (D.E.W.),
[email protected] (T.H.D.).
as PCl5, SF6, and ClF3, it is essentially equivalent to the manner in which the valence s2 pairs of electrons in Be, B, and C (along with the heavier elements below them) are able to participate in chemical bonds, expanding the nominal valence of these atoms (although the details differ to some extent). We thus observe that recoupled pair bonding is nearly as ubiquitous across the main group p-block and in the alkaline earths as covalent bonding and is not an anomaly limited to a few columns of the periodic table. It also occurs in some transition metals, at least to the extent that s2 pairs are recoupled in states such as CuF(a3Σ+).4 This new approach to understanding hypervalency in molecules is partially in accord with the Rundle-Pimentel5,6 threecenter-four-electron (3c/4e) bonding model, but, as our studies1-3 demonstrate, the recoupled pair bonding model offers far more explanatory and predictive insight than the 3c/4e model. After identifying the underlying principles of recoupled pair bonding in our initial studies of diatomic chalcogen halides1 and the SFn family,2 a subsequent paper on the ClFn species3 laid out the ground rules for making predictions using the new model. The principles enable one to predict the structures, energetics and low-lying excited states of the XFn (X ) S, Cl) species. In the present work, we treat the remaining member of the late second row p-block elements, the fluorides of phosphorus from PF through PF5 and show that these principles also apply to PFn. The first known hypervalent species, PCl5, is a close cousin of PF5 and was discovered by Davy two centuries ago.7 Hypervalence can be viewed as the ability that some atoms possess to form chemical bonds using electrons that have already been paired together. Recoupled pair bonding certainly qualifies, but it is not the only means by which hypervalence can occur under this definition. As argued in a recent study8 on species
10.1021/jp102236a 2010 American Chemical Society Published on Web 06/15/2010
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such as H2SO4 and HClO4 but established much earlier in work9 on rare gas oxides, O(1D) can form bonds through dative transfer from a lone pair. This would also qualify as hypervalence under the definition given above. We are currently studying various sulfoxy species, where covalent bonds, recoupled pair bonds, and dative bonds to O(1D) all occur. In this work, we characterize the molecular structures and bond dissociation energies for the ground and low-lying excited states of the PFn family (n ) 1-5). As noted above, the results are consistent with our previous observations and with the guidelines established in Chen et al.3 Thus, these principles apply to all of the late second row p-block fluorides. Phosphorus in its (3p3 4S) atomic ground state has no 3p2 pairs of electrons to recouple, in contrast to the ground states of atomic sulfur and chlorine, but all three elements have 3s2 pairs that can be recoupled to form bonds once the 3p electrons have become sufficiently involved in bonding to make uncoupling the 3s2 pair to form bonds energetically favorable. The rules we’ve developed for understanding hypervalent behavior led us to look for hypervalency before PF4, and it was found in PF3(a3B1), a state that has received only limited attention by one previous theoretical study.10 We also characterized the low-lying isomer of PF4 with C3V symmetry, which is known but has also not been studied extensively.11 Portions of various potential energy surfaces were characterized beyond the regions of their minima, including the PF2(X2B1) + F triplet surface and the PF3(X1A1) + F doublet surface, where the transition state (TS) for the interconversion of the two PF4 isomers was located approximately. Bonding in phosphorus has another dimension: in addition to recoupling the 3s2 pair of P(4S), recoupled pair bonding also occurs in states that arise from P(3p3 2D), where there is a 3p2 pair that can be recoupled even in the diatomic molecules. This leads to recoupled pair bonds in PF(B3Π), PF2(A2A1), PF2(B2B2), and the T-shaped PF3(1A1) transition state. The behavior of the states that arise from recoupling the 3p2 pair of P(2D) is consistent with that of the PFn species that arise from P(4S) as well as that of the SFn and ClFn families. Recoupling also occurs in fluorides formed from the excited states of other late p-block atoms, such as the weakly bound 2∆ state of SF reported by Yang and Boggs,11 which correlates with S(1D) + F(2P). In addition to a number of studies that focused on one or more members of the PFn series that will be cited in context, a number of previous theoretical papers treated all of the ground state neutral species. These include DFT studies by Gutsev12 (VWN) and Tschumper et al.13 (BHLYP) and ab initio studies by Gu and Leszczynski14 (various G2 methods), Lau and Li (G3),15 and Grant et al.10 [CCSD(T)], the last of which provides results at or above the best level of theory used in the present work for species treated by both. A study by Lugez et al.16 reported vibrational frequencies for the five PFn species but provided neither structures nor bond energies. 2. Methodology The calculations presented in this study were performed with the MOLPRO suite of quantum chemical programs (versions 2002.6 and 2009.1)17 and Gaussian 03.18 Structures and energies were determined for minima and transition states of most of the PFn species with single-reference restricted singles and doubles coupled cluster theory19 with perturbative triples [CCSD(T), RCCSD(T)]. Zero-point energy (ZPE) corrections were computed by reoptimizing the geometries with density functional theory at the B3LYP level,20 followed by calculation of the harmonic vibrational frequencies. The resulting errors in
Woon and Dunning, Jr. the ZPEs are expected to be small relative to the errors in De. Complete active space self-consistent field (CASSCF) and subsequent multireference configuration interaction (MRCI) calculations21 (including the “+Q” Davidson correction22) were performed in some cases: (i) to characterize the low-lying 3Σ-, 1 ∆, and 3Π states of PF; and (ii) to compute the approximate generalized valence bond (GVB) orbitals along the minimum energy pathways for the PF2(X2B1) + F and PF3(X1A1) + F reactions (see ref 2 for details about the conversion of natural orbitals to GVB orbitals). To yield the proper symmetry in the CASSCF wave functions for the 1∆ and 3Π states of PF, the respective degenerate contributions for each state were averaged together (1A1 and 1A2 for 1∆, 3B1 and 3B2 for 3Π). Energy differences reported below at the MRCI+Q level are at MRCI optimized geometries (MRCI+Q//MRCI). Unrestricted secondorder perturbation theory (UMP2) calculations23 were used for one of the scans described below. Augmented correlation consistent basis sets (aug-cc-pVXZ) of triple- and quadruple-ζ quality were used for F, and the corresponding d-function augmented sets [aug-cc-pV(X+d)Z] were used for P.24 The shorthand notation AVXZ (X ) T,Q) will be used to represent the sets of a specific quality. All orbital plots were generated with gOpenMol (http:// www.csc.fi/gopenmol). 3. Covalent and Hypervalent Bonding in PFn At first glance, bonding in the PFn family might appear to be much simpler than it is in the SFn and ClFn families. It is clear that (polar) covalent bonding will be favored for the first three additions of F to P(4S). Hypervalency might not be expected to occur until PF4 is formed, when the 3s-derived pair (hereafter referred to as the 3s2 pair) must be recoupled to form the fourth P-F bond. However, we found that hypervalent bonding occurs in at least one state of all of the PFn species. In fact, recoupling of the 3s2 pair occurs before PF4, in an excited state of PF3. Furthermore, the low-lying P(2D) excited state (Te ) 11 361.7 cm-1 ) 32.5 kcal/mol to the J ) 3/2 state25) has a 3p2 pair that can be recoupled, leading to hypervalent states of PF, PF2, and a transition state structure of PF3. Figure 1 depicts the orbital coupling diagrams for the ground and several low-lying states of PF, PF2, and PF3 that arise from P(4S,2D) + F(2P), as well as energetics (De or ∆Ee) through PF5. Details about each of the PFn species are discussed below. ZPE-corrected bond dissociation energies (D0) for the ground state species are collected in Table 1 and compared to available experimental and selected previous theoretical results (Grant et al.10 also reported values of bond dissociation energies for the first three F additions to P at a higher level of theory than those given in Table 1, but they are essentially the same as the values in the table). Optimized structures are shown in Figure 2, and selected orbitals are depicted in Figure 3. Measured bond energies are available26,27 for PF, PF2, and PF3; experimental structural data is available for the ground and excited states of PF28-30 and the ground states of PF2,31 PF3,32 and PF5.33 3.1. States of PF. Latifzadeh and Balasubramanian34 provided a thorough study of the manifold of states that arise from F(2P) interacting with P(4S,2D); in light of their study, we do not include potential energy curves in the present work and refer the reader to Figure 1 of their study. Subsequent work by de Broucke`re35 treated the 3Σ- ground state and 1∆ state at a higher level of theory than used by Latifzadeh and Balasubramanian. As shown in Figure 1, F can be bonded in various ways with P(4S,2D). The ground state (X3Σ-) and lowest-lying excited state (a1∆) arise from covalent singlet couplings between singly
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Figure 1. Coupling diagrams and energy differences (De, ∆Ee) for PFn species. Numbers in italics were computed at the MRCI+Q level; the remainder were computed at the RCCSD(T) level [except the three values indicated with an asterisk, which were computed with a combination of both RCCSD(T) and MRCI+Q].
TABLE 1: A Comparison of Ground State PFn Bond Dissociation Energies (D0) from Experiment, Selected Prior Calculations, and This Work bonda PF f P + F PF2 f PF + F PF3 f PF2 + F PF4 f PF3 + F PF5 f PF4 + F
AVTZb AVQZc 102.8 115.3 128.9 53.8 130.8
106.0 118.3 131.8 55.4 133.3
ref 13f ref 14g ref 10h
expt 106.1 ( 4.6 120.4 ( 9.9e 131.7 ( 0.5e
d
105.9 112.5 120.8 49.3 117.2
105.0 118.0 130.9 54.8 132.1
107.2 119.2 132.0 54.5 132.8
a Energies are in kcal/mol. b This work, RCCSD(T)/AVTZ results. c This work, RCCSD(T)/AVQZ results. d Reference 26. e Reference 27. f B3LYP/DZP++ results. g G2M(CC6) results. h RCCSD(T)/DTQ results (extrapolation to complete basis set limit plus corrections for core-valence and scalar relativistic effects).
occupied P 3p and F 2p orbitals. The calculated bond energy (D0) of 106.0 kcal/mol of PF(X3Σ-) at the RCCSD(T)/AVQZ level is very close to the experimental value, 106.1 ( 4.6 kcal/mol (see Table 1). The computed X3Σ- f a1∆ excitation energy (Te) at the same level of theory is 7203 cm-1 (20.6 kcal/mol), which compares well with the value of 7090.43 cm-1 reported in Huber and Herzberg.36 The predicted bond lengths of the 3 Σ state [RCCSD(T)/AVQZ level] and 1∆ state (MRCI/AVQZ level) are 1.596 and 1.598 Å, respectively, which again compare well with the measured values28,29 of 1.589329 and 1.5849 Å. The bonding in PF(a1∆) is covalent, but a hypervalent state, PF(B3Π), arises when F recouples the 3p2 pair of P(2D). Adding F to P(2D) to form PF(a1∆) is covalent bond formation because the nominal monovalence of P(2D) is satisfied by adding one F, yielding a singlet species, but adding more F atoms (or any other moiety) to PF(a1∆) requires something other than a 2c/2e bond. PF(B3Π) is hypervalent because the product is a triplet species capable of forming two covalent bonds, an increase in
Figure 2. Optimized RCCSD(T) structures for PFn species (unless otherwise noted). The structures in the top row are the ground state species. When two numbers are shown, the upper and lower values were computed with AVTZ and AVQZ basis sets, respectively.
valence of two over the releVant nonhypervalent state. Forming PF(B3Π) is not hypervalent with respect to P(4S), only with respect to P(2D), but a bound 3Π state is not formed from P(4S) + F(2P), see below. Although PF(B3Π) dissociates to ground state atoms (after considerable rearrangement of the electronic structure), the significant barrier in the potential energy curve (see Figure 1 in ref 31) is evidence of an avoided crossing with a state that dissociates to the higher P(2D) asymptote. The orbitals at re (Figure 3) diabatically correlate with those of the P(2D) state and show the same behavior present in other recoupled pair bond states,1-3 particularly SF(4Σ-): the GVB orbitals 7σR and
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Figure 3. Selected orbitals for PFn species (see text for details).
7σL constitute a PF bond pair that is heavily polarized toward F, and there is a singly occupied antibonding orbital (8σ) with much of its amplitude on P. There is also a singly occupied π orbital in this state. As in SF, the presence of the singly occupied antibonding orbital in PF(B3Π) results in a bond length that is longer than in the lower, covalently bonded states by about 0.16 Å. The computed value of re for PF(B3Π) is 1.759 Å, which is close to the measured value of 1.7517 Å.28 PF(B3Π) is bound somewhat more strongly at the MRCI+Q level than the potential curve in Latifzadeh and Balasubramanian34 indicates. The MRCI+Q/AVQZ bond energy (De) with respect to ground state atoms is 18.9 kcal/mol. The computed X3Σ- f B3Π excitation energy (Te) is 29772 cm-1 (85.1 kcal/mol), which falls among the measured substates (29543, 29686, and 29827 cm-1).36 The 3Π state lies 64.5 kcal/mol higher than the 1∆ state. This is rather larger than might be expected from considering the trends in ClF, SF, and PF, and we are continuing to investigate this trend. 3.2. States of PF2. In addition to various studies of the 2B1 ground state of PF2, a number of efforts have investigated its lowlying excited states. Several of these papersstheoretical work by Johnson and Irikura,37 Latifzadeh and Balasubramanian,38 and Lee et al.39sconcluded in common that a contemporary experimental study by Zhao and Setser40 actually observed the 2B1 f 2B2 transition rather than one involving a 4A2 state as initially concluded in ref 40. Two of the theory papers37,38 also characterized the 2A1 state and found it to be linear or quasilinear. Another theory paper by Cai41 appeared during the same time frame. Ground state PF2(X2B1) is formed by a second covalent addition of F to PF(X3Σ-), but the two excited states both involve recoupled pair bonding (see Figure 1). The computed bond energy (D0) of PF2(X2B1) is 118.3 kcal/mol at the RCCSD(T)/AVQZ level, about 2 kcal/mol below the experimental value27 of 120.4 ( 9.9 kcal/mol (Table 1) but within 1 kcal/mol of the benchmark value of Grant et el.10 The values of re and θe at this level are 1.582 Å and 98.2°, which are very close to the r0 and θ0 values of Saito et al.31 of 1.5792 Å and 98.48° deduced from microwave measurements. The singly occupied orbital (3b1) is shown in Figure 3; it still retains much of the original 3p character of atomic P. Also shown is the doubly occupied orbital (8a1), which is dominated by the P 3s orbital but has acquired considerable 3p character. The 2A1 (2B1) state of PF2 is formed by singlet coupling the singly occupied orbital of a second F to the singly occupied antibonding orbital in PF(B3Π) (8σ in Figure 3), while the 2B2 state can be formed either by covalent addition to the other singly occupied orbital of PF(B3Π) (3πx in Figure 3) or by recoupling the 3p2 pair in PF(a1∆). Unlike the 2A1 component
of the 2Π state, the 2B1 component has no minimum near 180° and relaxes to the covalent X2B1 minimum (see Figure 1 in ref 37 for bending potential energy curves). As expected from the recoupled pair bonding model (guideline A.2.b in Chen et al.3), the 2A1 state is more stable than the 2B2 state, by 15.0 kcal/mol at the RCCSD(T)/AVQZ level. The bond length in the 2A1 state has decreased to 1.639 Å, once again illustrating the favorable effect that occurs when the formation of the second PF bond pulls the amplitude of the singly occupied orbital in PF(B3Π) toward the incoming F and away from the first bond, substantially reducing its antibonding character. The 2B2 state has an acute bond angle of 85.0°, due in part to the extended antibonding character of its singly occupied b2 orbital (6b2 in Figure 3). The behavior of the 2A1 and 2B2 pair of states follows the same pattern seen in SF2 triplet states2 and ClF2 doublet states3 and provides additional evidence for the general applicability of the recoupled pair bonding model. 3.3. States of PF3. In contrast to PF and PF2, most prior theoretical studies have focused on the X1A1 ground state of PF3 and have not investigated possible excited states. Gutsev12 considered alternative singlet states with assumed geometries. Dixon et al.42 reported SCF calculations of the ground state and was the first work to indicate that PF3 inversion does not occur through a transition state with D3h symmetry but instead passes through a T-shaped planar 1A1 state with C2V symmetry. This conclusion was later confirmed with correlated calculations by various studies, such as work by Creve and Nguyen,43 and was also found to be the case in the present work. A triplet state, PF3(a3B1), was mentioned briefly by Grant el al.10 The coupling diagram and optimized structure of pyramidal PF3(X1A1) are depicted in Figures 1 and 2. The large basis set RCCSD(T) equilibrium bond length and bond angle are 1.567 Å and 97.5°, respectively, close to the values of 1.561 ( 0.001 Å and 97.6° reported by Kawashima and Cox.31 The computed bond dissociation energy (D0) of 131.8 kcal/mol is again very close to the experimental result, 131.7 ( 0.5 kcal/mol (Table 1). As in PF2(X2B1), the molecular orbital dominated by the P 3s orbital has considerable 3p character (14a′ in Figure 3). If the 2p orbital of a third F is coupled to the singly occupied orbitals of either PF2(A2A1) or PF2(B2B2), a T-shaped 1A1 species is formed. This is a transition state on the PF3 singlet surface: breaking planarity allows the structure to relax to the ground state. As noted above, the T-shaped structure is the transition state for the inversion of PF3. Although it is not a minimum, the structure is clearly a consequence of recoupled pair bonding: quasilinear bond angles occur as a consequence of recoupling p2 pairs, and bonding will rearrange to maximize three-center recoupled pair bonding (guidelines A.3 and B, respectively, in
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Figure 5. 2D scan for the dissociation of PF4 to PF3(X1A1) + F. Calculations were performed at the RCCSD(T)/AVTZ level for a fixed PF3 geometry, scanning over the distance to the departing F [r(PF)] and the F-P-F (θ) angle between that vector and the one to the apical F in the C3v minimum. The contour interval is 2 kcal/mol.
Figure 4. Orbitals along the addition pathway PF2(X2B1) + F f PF3(a3B1).
Chen et al.3). The energy differences (∆Ee, which are not bond energies) that result when adding F to PF2(A2A1) and PF2(B2B2) to yield the transition state are 94.9 and 110.0 kcal/mol, respectively. As in comparable cases in other hypervalent species, it is energetically more favorable to interact with the orbital with antibonding character [the 6b2 orbital of PF2(B2B2), in this case]. The angle between the covalent bond and each of the recoupled pair bonds in the PF3(1A1) transition state is 88.0°; the covalent bond is about 0.07 Å shorter than the two recoupled pair bonds. There is also a 3B1 state of PF3 that arises when F recouples the doubly occupied, 3s-derived 8a1 orbital of PF2(X2B1) [or the analogous orbital of PF2(A2A1)]. Like the PF3(1A1) transition state, PF3(a3B1) is T-shaped (see Figure 2), with a bond angle of 98.5°. However, PF3(a3B1) is stable with respect to breaking symmetry. Although it is less stable than the ground state by 92.1 kcal/mol at the RCCSD(T)/AVQZ level, it is still bound by 42.0 kcal/mol with respect to the PF2(X2B1) + F asymptote. Our results for PF3(a3B1) are very close to those of Grant et al.10 As a triplet state, PF3(a3B1) might be expected to have a reasonably long lifetime if it was formed in the laboratory. A constrained optimization at the UMP2/AVTZ level scanned along the PF separation for removing one of the F atoms in a recoupled pair bond found no barrier to dissociation (confirmed to some extent with single point RCCSD(T) calculations at the UMP2 geometries). Figure 4 shows the GVB orbitals at several geometries as the F approaches PF2(B2B1): the lone pair on P (two lobe orbitals) and the single occupied 2p orbital on F recouple to form a PF bond pair and the singly occupied orbital on PF3(a3B1) that is shown in Figure 3. 3.4. States of PF4. The formation of PF4 requires the pair in the 3s-derived orbital of P to be recoupled, either in the formation of PF3(a3B1) or upon the addition of F to PF3(X1A1). In spite of the suggestion in early work that a second minimum with C3V symmetry might also be stable, most work has focused on the sawhorse C2V global minimum. We have explored the PF4 potential energy surface and characterized the two minima, the transition state connecting them, and the dissociation to PF3(X1A1) + F.
Ground state C2V PF4(X2A1) has two covalent bonds (re ) 1.542 Å) and a pair of recoupled pair bonds (re ) 1.597 Å). The bond angle between the covalent bonds is 104.5°, and the bond angle between the recoupled pair bonds is 164.8°. The structure is similar2 to that of SF4, although the recoupled pair bonds are bent away from the covalent bonds in PF4. A likely reason for the difference is that PF4 has a singly occupied orbital (12a1 in Figure 3) influencing the structure, whereas SF4 has a doubly occupied orbital playing the analogous role (and exerting more repulsion). When a second electron is added to the orbital to form PF4-, the recoupled pair bonds are indeed bent toward the covalent bonds.13,14 The location of the singly occupied orbital anticipates the formation of a third covalent bond to form bipyramidal PF5. The bond dissociation energy (D0) for the global minimum is 55.4 kcal/mol, which is a comparably weak bond due to the cost of recoupling the pair of electrons in the 3s-derived orbital. There is a second minimum on the PF4 doublet surface with C3V symmetry. It lies only 7.3 kcal/mol higher in energy than the C2V minimum at the RCCSD(T)/AVQZ level (7.4 kcal/mol with AVTZ sets). This structure has three covalent bonds (re ) 1.574 Å) and one recoupled pair bond (re ) 1.561 Å). It is a rare case where the covalent bond length is longer than the recoupled pair bond length, which is likely a result of the large 3s component of the P bonding orbital. The bond angle is 91.6° (see Figure 2). As expected, the singly occupied orbital (18a′ in Figure 3) anticipates the formation of the second recoupled pair bond at the lower apex of bipyramidal PF5(X1A1). We located an approximate structure for the transition state connecting the C2V and C3V minima by scanning through the bond angle for pushing one of the three covalently bonded F atoms in the C3V minimum down to the second recoupled pair bond position in the C2V minimum. The maximum occurs near 118.5°. This structure has a number of interesting features. It almost has C3V symmetry, with bond lengths of about 1.57 Å for the three stable PF bonds, while the length of the bond in flux increases significantly, to about 1.8 Å. The orbitals between P and the latter F indicate a normal bond pair (16a′ in Figure 3), and the singly occupied orbital is an antibonding orbital that is aligned with the bond pair. The transition state lies 32.4 and 25.0 kcal/mol above the C2V and C3V minima, respectively. The second minimum thus appears to be fairly well isolated from the global minimum (unless there is a lower transition state not yet identified), which is promising for possible laboratory study. Figure 5 depicts a 2D constrained scan that was performed to explore the dissociative behavior of both states. The PF3
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Woon and Dunning, Jr. bipyramidal structure. In our RCCSD(T)/AVQZ calculations, the bond lengths of the three equatorial, covalent bonds are 1.537 Å, and the bond lengths of the two axial recoupled pair bonds are 1.577 Å. The experimental values of (r0)eq and (r0)ax are 1.530 and 1.576 Å, respectively.29 The final bond dissociation energy (D0) is 133.3 kcal/mol. 4. Conclusions
Figure 6. Orbitals along the addition pathway PF3(X1A1) + F f PF4(X2A1) (C2V minimum).
fragment was frozen as it is in the C2V minimum [the distortion of this moiety with respect to PF3(X1A1) is not large], and a grid of points was run in Cs symmetry over ranges of the PF distance and the angle to the apical F. Under these constraints, there is no evidence of a barrier for dissociating from either minimum. The transition state between the minima is also visible in the figure. Figure 6 shows GVB orbitals for several points along the minimum energy pathway on the surface shown above between the PF3(X1A1) + F asymptote and the global C2V minimum of PF4. The behavior is entirely consistent with other cases of recoupled pair bond formation observed in SFn, ClFn, and elsewhere. At long separations the pair of electrons in the 3sderived orbital is split into lobes due to the 3p character in the correlating orbital, and the singly occupied orbital is a localized 2p orbital on F. As the PF distance decreases, the orbitals rearrange until the PF bond pair is in place, and the singly occupied orbital is the one shown in Figure 3, where the fifth F will be able to interact to form PF5. Some of the concepts discussed in the paper by Grant et al.10 run parallel to the recoupled pair bonding model, although our approach is perhaps a bit more accessible to chemical intuition. They discuss the “reorganization energy,” estimated from the singlet-triplet separation for PF3, where there is a lone pair in PF3(X1A1) and two unpaired electrons in PF3(a3B1). In both models, it is understood than hypervalence requires making the electrons of the 3s2 pair of P available for bond formation, and there must be an energetic cost for doing that. In the recoupled pair bonding model, we show how the competition between hypervalent and nonhypervalent bond formation plays out stepby-step through the sequence. PF3(a3B1) is not just expressing the framework for forming PF4 and PF5, it is a low-lying excited state that is as stable as it is because the P 3s-derived pair in PF2(X2B1) is nearly as energetically accessible for bond formation as the unpaired 3p electron. When one then moves on to the formation of PF4, it can be anticipated that the pair will now be recoupled because there is no competitive covalent addition pathway; the energy of the new bond will be substantially less than that of the three previous covalent bond additions, but it will nevertheless be an exoergic process. 3.5. States of PF5. PF5(X1A1) can be formed by adding F to either of the two minima of PF4 to form the well-known
In this study we characterized the ground and low-lying excited states of PFn (n ) 1-5) species. Viewing the formation pathways as a combination of covalent bonding and recoupled pair bonding leads to a coherent picture of what states and structures are possible and how they are ordered energetically. As expected, recoupled pair bonding was found to be essential for the formation of hypervalent species such as PF4 and PF5, but it is present in a number of other PFn species as well. One of these is PF3(a3B1), a state which arises when the pair of electrons in the 3s-derived orbital of P in PF2(X2B1) is recoupled. But there are several states with recoupled pair bonds that occur when the 3p2 pair of P(2D) is recoupled: PF(B3Π), PF2(A2A1), PF2(B2B2), and the T-shaped PF3(1A1) transition state structure. The recoupled pair bonding model has once again demonstrated that it offers significant predictive insight into the nature of bonding in the heavier elements of the late p-block. Acknowledgment. Support for this work was provided by funding from the Distinguished Chair for Research Excellence in Chemistry at the University of Illinois at Urbana-Champaign. D.E.W. acknowledges helpful discussions with the entire Dunning group and particularly with Jeff Leiding and Dr. Lina Chen. References and Notes (1) Woon, D. E.; Dunning, T. H., Jr. Mol. Phys. 2009, 107, 991. (2) Woon, D. E.; Dunning, T. H., Jr. J. Phys. Chem. A 2009, 113, 7915. (3) Chen, L.; Woon, D. E.; Dunning, T. H., Jr. J. Phys. Chem. A 2009, 113, 12645. (4) Koukounas, C.; Mavridis, A. J. Phys. Chem. A 2008, 112, 11235. (5) Rundle, R. E. J. Am. Chem. Soc. 1947, 69, 1327. J. Am. Chem. Soc. 1963, 85, 112. (6) Pimentel, G. C. J. Chem. Phys. 1951, 19, 446. (7) Davy, H. Phil. Trans. 1810, 100, 231. (8) Kalemos, K.; Mavridis, A. J. Phys. Chem. A 2009, 113, 13972. (9) Dunning, T. H., Jr.; Hay, P. J. J. Chem. Phys. 1977, 66, 3767. (10) Grant, D. J.; Matus, M. H.; Switzer, J. R.; Dixon, D. A.; Francisco, J. S.; Christe, K. O. J. Phys. Chem. A 2008, 112, 3145. (11) Yang, X.; Boggs, J. E. J. Chem. Phys. 2005, 122, 194307. (12) (a) Gutsev, G. L. Russ. Chem. Bull. 1992, 41, 1734. (b) J. Chem. Phys. 1993, 98, 444. (13) Tschumper, G. S.; Fermann, J. T.; Schaefer, H. F. III. J. Chem. Phys. 1996, 104, 3676. (14) Gu, J.; Leszczynski, J. J. Phys. Chem. A 1999, 103, 7856. (15) Lau, J. K.-C.; Li, W.-K. J. Mol. Struct. Theochem 2002, 578, 221. (16) Lugez, C. L.; Irikura, K. K.; Jacox, M. E. J. Chem. Phys. 1998, 108, 8381. (17) Werner, H.-J.; Knowles, P. J.; Amos, R. D.; Bernhardsson, A.; Berning, A.; Celani, P.; Cooper, D. L.; Deegan, M. J. O.; Dobbyn, A. J.; Eckert, F.; Hampel, C.; Hetzer, G.; Korona, T.; Lindh, R.; Lloyd, A. W.; McNicholas, S. J.; Manby, F. R.; Meyer, W.; Mura, M. E.; Nicklass, A.; Palmieri, P.; Pitzer, R.; Rauhut, G.; Schu¨tz, M.; Schumann, U.; Stoll, H.; Stone, A. J.; Tarroni, R.; Thorsteinsson, T. Molpro, Versions 2002.6 and 2009.1; University College Cardiff Consultants Ltd.: Cardiff, UK, 2004, 2009. (18) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, Jr., J. A.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.;
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