High Level ab Initio Calculations for ClF - American Chemical

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High Level ab Initio Calculations for ClFn+ (n = 1−6) Ions: Refining the Recoupled Pair Bonding Model Lina Chen, 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, United States S Supporting Information *

ABSTRACT: Based on detailed, high level ab initio calculations on a number of halogenated compounds of second row, late pblock elements, the SFn, ClFn, PFn, SCln, and SFnCl families, we found that a new type of bondthe recoupled pair bondaccounts for the ability of these elements to form hypervalent, or hypercoordinated, compounds. Hypervalent molecules are formed when it is energetically favorable for the electrons in a lone pair orbital to be recoupled, allowing each of the electrons to form chemical bonds with ligands. In this paper, we characterize the structures and energies of the ground and low-lying excited states of the ClFn+ (n = 1−6) ions, using high level ab initio methods [MRCI, CCSD(T)/RCCSD(T)] with large correlation consistent basis sets. We computed a number of quantities, including ClFn+ structures, bond dissociation energies, and ClFn ionization energies and compared our results with the available experimental data. Both the bond dissociation energies and the ionization energies oscillate, variations that are readily explained using the recoupled pair bonding model. Comparisons are drawn between the ClFn+ cations and their counterparts in the isoelectronic SFn series, which possess many similarities. We found two significant differences between the ClFn+ and the SFn series: (i) the bond dissociation energies of ClFn+ are much weaker than those of the corresponding SFn species, and (ii) there is no stable 3A2 state in ClF2+ corresponding to the stable state found in SF2. An examination of the Mulliken populations at the HF/AVTZ level for ClFn+ and SFn species predicts that the F atom in the axial (recoupled pair bonding) position is more highly charged than the F atom in the equatorial (covalent bonding) position; there is also less charge transfer to the F atoms in ClFn+ than in SFn. The positive charge on Cl+ makes it more difficult for an F atom to attract electrons from Cl+ than from S and correspondingly less favorable to recouple the electrons in the lone pair orbitals in the ClFn+ species.

1. INTRODUCTION In our previous studies of the SFn (n = 1−6),1 ClFn (n = 1−7),2 PFn (n = 1−5),3 SCln (n = 1−6),4 and SFn−1Cl (n = 1−6)5 molecules, and the low-spin excited states of the SFnClm (n + m = 1−2)6 species, we found that a new type of bondthe recoupled pair bondunderlies the formation of hypervalent compounds of the P, S, and Cl atoms, which occurs when the atoms are bound to more than three, two, and one monovalent ligands, respectively. We also found that recoupled pair bonds were present in excited states of the PXn halides with n ≤ 3, the SXn halides with n ≤ 2, and the ClXn halides with n = 1. The occurrence of recoupled pair bonds provides the basis for understanding a number of “anomalous” properties exhibited by the halogenated compounds of the second row, late p-block elements.7 Hypervalent molecules of the late p-block elements are formed when the electrons in a lone pair orbital on the central atom are recoupled via interactions with the electrons in the singly occupied orbitals of ligands with large electronegativities. The two electrons in the lone pair orbital can form bonds with the electrons in the singly occupied orbitals of two monovalent © 2013 American Chemical Society

ligand atoms, thus allowing the formation of two bonds from each lone pair. Our studies on SFn1 and ClFn2 showed that the first bond, the recoupled pair bond, is much weaker than a covalent bond formed with a singly occupied orbital of the same angular momentum on the atom in question due to the energetic cost associated with recoupling the electrons in the lone pair orbital. This penalty is manifested in the occupation of an antibonding orbital by the third “leftover” electron involved in the formation of the recoupled pair bond. On the other hand, the second bond, the bond formed by singlet coupling the electron in the antibonding orbital with the electron in the singly occupied orbital of the second ligand, is often stronger than a normal covalent bond formed with the same atom. Formation of the second bond removes much of the antibonding character associated with the orbital leftover from forming the recoupled pair bond, resulting in an unusually Received: December 9, 2012 Revised: April 16, 2013 Published: April 16, 2013 4251

dx.doi.org/10.1021/jp312103v | J. Phys. Chem. A 2013, 117, 4251−4266

The Journal of Physical Chemistry A

Article

experimental results that are available for direct comparison with our results. In this paper we report a number of observable quantities in the hope that this will stimulate new experimental explorations. Parallel to this work, we have characterized the ClFn− anions and will describe the results of this work in a follow-up paper that includes electron affinity predictions. ClFn− species are isoelectronic to ArFn compounds, where only even n species are even metastable. The paper is organized as follows. After describing the methodology, we will summarize the predictions for the ClFn+ species using the recoupled pair bonding model and then present the results: optimized structures, energies, charge distribution, and orbitals. Finally, trends in the ionization energies and bond dissociation energies will be discussed. A comparison with previous studies on the individual ions will also be summarized in the Results and Discussion section.

stable bond pair with much shorter bondswe refer to these two bonds as a recoupled pair bond dyad. There are factors that lead to variations in the strengths and other properties of recoupled pair bonds. Beyond the variations introduced by differences in the ligands, the character of the central atom also dramatically affects the strength of the recoupled pair bond. This was one conclusion of our previous work on neutral ClFn species.2 In our study of PFn species,3 we found that the 3p2 lone pair in the P(2D) excited state can be recoupled as well as the 3s2-derived lone pair in PF3, allowing the formation of PF4 and PF5. In addition, our group’s ongoing research on CHn and CFn species shows that the 2s2 lone pair in C can be recoupled [a fact noted earlier by Goddard et al. (ref 8 and references therein), although they did not use this terminology]. Because of the 2s−2p near degeneracy in C (and other early first row p-block elements), it is far easier to recouple the 2s2 pair of C than the 3p2 pair of S.8,9 The 3-center-4-electron model of Pimentel10 and Rundle11−14 is the standard model used to explain the formation of hypervalent molecules by the late p-block elements beyond the first row. The recoupled pair bonding (RPB) model provides additional insights into the existence and relative stabilities of the ground and low-lying states of species where both covalent and recoupled pair bonding can occur (and dative bonding as well). The RPB model is the realization of the “democracy principle” proposed by Cooper et al.15 The RPB model also accounts for the oscillating trend in the bond dissociation energies of SFn, as observed experimentally by Kiang and Zare,16 as well as many other anomalous properties of the compounds of the late second row p-block elements. One of the other advantages of the RPB model is that trends can be anticipated. For example, we found, as expected, that RPB is less favorable in ClFn species than in SFn species because the valence electrons of Cl are more tightly bound than those of S and, therefore, more difficult to recouple. Likewise, in the present work we compare ClFn+ species with their isoelectronic analogues in the SFn family and find that the trends are again predictable. A number of experimental studies17−24 have been reported on ClF+ and the closed shell species ClF2+, ClF4+, and ClF6+. For the open shell species, ClF3+ and ClF5+, few experimental results are available due to the (chemical) instability of the species. Charkin et al.25 calculated the structural parameters and vibrational spectra of the closed shell species ClF2±, ClF4±, and ClF6± using the Hartree−Fock (HF) and MP2 methods with 631(+)G* and 6-311(+)G* basis sets. To our knowledge, only two prior theoretical accounts have studied the entire ClFn+/ ClFn/ClFn− series. Pershin and Boldyrev26 used the Hartree− Fock−Roothaan method with Huzinaga−Dunning−Veillard basis sets,27−30 and Law et al.31 adopted the Gaussian-3/3X method. Our study is the first to characterize the entire series using high level methods with large basis sets. In this work, we compare our results for the ClFn+ cations with existing experimental and theoretical work and assess the accuracy of our calculations. In addition to examining the trends revealed by the recoupled pair bonding model, we present results for measurable quantities such as ionization energies and bond dissociation energies that might be helpful for experimentalists seeking to identify these species. While our theoretical investigations have shown that the recoupled pair bonding model provides a means of systematically understanding the nature of the bonding in halogenated compounds of the late second row p-block elements, there are few

2. METHODOLOGY The structures and energies of the ClFn+ (n = 1−6) species, including the ground and low-lying excited electronic states of ClF+ and ClF2+, were computed using standard coupled cluster calculations at the CCSD(T) or RCCSD(T)32 level. In these calculations, only the valence electrons were correlated; this was expected to introduce only a modest error in the calculated structures and energies. Subsequently, the energies of these species were used to determine the bond dissociation energies of ClFn+ → ClFn−1+ + F (n = 1−6). For understanding bond formation in the low-lying states of ClF+and SF, potential energy curves (PECs) were computed around the minima of these states. The PECs were obtained from complete active space self-consistent field (CASSCF) wave functions,33,34 due to the ability of these wave functions to describe both covalent and hypervalent bond formation for all values of the internuclear separation, R. A nearly full valence complete active space (CAS) treatment was chosen with the following exceptions: the 2s orbital of F was forced to be doubly occupied in all configurations, while the lowest virtual orbital was included in the active space. For ClF+/SF(2Π), degenerate configurations were state-averaged. Subsequent multireference configuration interaction (MRCI)35 calculations were performed to account for dynamical correlation, including the Davidson correction36,37 for quadruple excitations (MRCI +Q). To obtain the potential energy curves (PECs) of the lowlying excited states of ClF+/SF, state-averaged (SA) CASSCF calculations were performed (five-state calculations for Σ and Δ states and four-state calculations for Π states), followed by MRCI+Q calculations. All of the above high accuracy ab initio calculations were performed with the MOLPRO suite of programs (version 2009.1).38 To obtain accurate solutions of the electronic Schrödinger equation, augmented correlation consistent basis sets were used in all calculations: aug-cc-pVXZ (X = T, Q, 5) sets were used for F, while aug-cc-pV(X+d)Z sets that include an additional tight d function were used for Cl.39−41 We have used the shorthand notation of AVXZ for these basis sets in this paper. The complete basis set (CBS) limit for ClF+ and SF was determined by extrapolating the x = AVTZ, AQVZ, and AV5Z energies using the following functional form: E(x) = ECBS + be−x + ce−x 2

(1)

where ECBS, b, and c were obtained through a least-squares fit of the energies computed by various basis sets. 4252



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Figure 1. Atomic GVB orbital diagrams for F and Cl+.

Figure 2. Orbital diagrams for the ClFn+ (n = 1−6) series. The orbitals on the F atom are abbreviated for ClF4+ through ClF6+ with only half of the singly occupied 2p orbital of F shown.

were calculated at the B3LYP/AVTZ level using the Gaussian 03 package43 (after reoptimizing the structures). For ClF+, natural orbitals (NOs) were obtained at the CASSCF level with the AVTZ basis set. Subsequently, the NOs were transformed to approximate generalized valence bond (GVB) orbitals8 using the relationship given earlier1 (these orbitals are orthogonal to all of the other orbitals, although not orthogonal to each other). For larger ClFn+ species, Hartree− Fock orbitals obtained with the AVTZ basis sets are shown at the optimized RCCSD(T) geometries. The Pipek−Mezey method44 was used to calculate localized molecular orbitals. The 2D contour cross sections of the orbitals and 3D orbitals were plotted with gOpenMol (http://www.csc.fi/english/ research/software/gopenmol/).

For the size consistent RCCSD(T) method, the dissociation energies (De) were computed by subtracting the molecular energy from the energy of the fragments. For the MRCI and MRCI+Q methods, which are not size-consistent, De was computed by calculating the energy with the atoms separated by 100 Å and then subtracting the energy at the equilibrium bond length, Re. For the diatomic molecules, the spectroscopic parameters were determined via Dunham analysis42 (fitting an eleventh-order polynomial to 12 energy values). The computed harmonic vibrational frequencies, ωe, of the diatomic molecules were used to obtain vibrational zero point energy (ZPE) corrections to the bond energies (D0) at the same level of theory used for calculating the equilibrium energies. For the ground states of ClF2+ to ClF6+, harmonic ZPE corrections 4253



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3. AN OVERVIEW OF BONDING IN CLFn+ The atom-by-atom approach to building a family of species such as ClFn+ and anticipating their properties (structures, bond dissociation energies, low-lying excited states, etc.) begins with understanding the electronic structure of the constituent atoms. A fluorine atom bonds covalently to other atoms via its singly occupied 2p orbital, with the bond generally polarized significantly toward F (sometimes to the degree of becoming an ionic bond). The 2p pairs of F atoms are tightly bound and show little or no tendency toward participation in bonding. The valence electronic structure of the F atom, 2s22px22py22pz, is represented by the orbital diagram depicted in Figure 1, with its seven valence electrons in various singly and doubly occupied orbitals. We represent Cl+ differently, since our work has demonstrated that its 3p2 pair can be recoupled. Instead of a doubly occupied 3p orbital, the pair is treated as two GVB orbitals with the electrons in those orbitals being singlet coupled. The GVB orbitals are formed by taking linear combinations of the doubly occupied 3p orbital and a suitable correlating orbital, with the CI coefficients taken from a CASSCF wave function (see ref 1 for more details about the procedure). For Cl+, the 3s23px3py3pz2 configuration is correlated with the 3s23px3py3d2z2 configuration, thus introducing 3d character into the wave function. Although this may seem similar to Pauling’s spd hybridization model, the CI coefficient for the 3s23px3py3d2z2 configuration is very small, on the order of 0.05. So, participation of the 3dz2 orbital represents a correlation effect, not a hybridization effect. Figure 1 depicts the GVB orbitals of Cl+ and their symbolic representation: a doubly occupied 3s orbital, two singly occupied 3p orbitals, and the 3p lobe orbital pair with the orbitals localized significantly on either side of the nucleus. The small tails on the lobe orbitals serve to remind the reader that the orbitals overlap each other to a significant degree (0.865 in this case). The family of ClFn+ species is built up by successively adding an F atom to the ClFn−1+ species, taking into account the various ways in which F can be added to Cl+ and successive ClFn−1+ compounds in their low-lying electronic states. Since Cl+ is isoelectronic with S, we expected the structures and state ordering in the ClFn+ family to mirror that in the SFn family in most respects, and this was indeed found to be the case. Figure 2 depicts the orbital coupling diagrams for the ground and lowlying excited states of the ClFn+ species as built via the atom-byatom process; the process is quite similar to that reported in our study of SFn species.1 Beginning with Cl+ in its 3P ground state, one can form ground state ClF+(X2Π) by singlet coupling the electron in the singly occupied F 2pz orbital with the electron in one of the singly occupied 3pz orbitals of Cl+ to form a (polar) covalent bond. The ClF+(X2Π) state has a singly occupied 3pCl-like π orbital as well as the 3pπCl-like lobe orbitals, which in this context can be considered to be a doubly occupied 3pCl-like π orbital. If the Cl+ atom is rotated so that the 3p lobe orbital pair of Cl+ is aligned with the bond axis, excited state ClF+(a4Σ−) is formed. ClF+(a4Σ−) is formed via recoupling the Cl (3pz−, 3pz+) electron pair by the electron in the singly occupied F 2pz orbital. In this state, there is a singly occupied σ* orbital and two singly occupied 3pCl-like π orbitals; as noted earlier, the σ* orbital has considerable antibonding character. ClF 2 + (X 1 A 1 ) can be formed straightforwardly from ClF+(X2Π) by singlet coupling the electron in the remaining singly occupied 3pCl-like orbital with an electron in the singly

occupied 2p orbital of a second F atom. The low-lying a3B1 state of ClF2+ can be formed from ClF+(a4Σ−) + F(2P) by singlet coupling the electron in the ClF+(a4Σ−) σ* antibonding orbital with the electron in the singly occupied 2p orbital of the second F atom. The a3B1 state of ClF2+ represents the first example in the ClFn+ family of a recoupled pair bond dyad. An RPB dyad consists of the two bonds formed from the two electrons in a lone pair orbital. The strength of the second bond partially compensates for the weakness of the recoupled pair bond in the ClF(a4Σ−) state and, as a result, the a3B1 state is the lowest lying excited state of ClF2+, lying just 42 kcal/mol above the ground state. The ClF2+(a3B1) state is slightly bent, θ = 155°, and has one singly occupied polarized 3pCl-like orbital in the molecular plane and one singly occupied 3pCl-like orbital perpendicular to the molecular plane as well as a polarized 3sCllike in-plane orbital. Recoupled pair bond dyads are unique. Unlike a pair of covalent bonds, the bonds in an RPB dyad are coupled; if one is broken, antibonding character is introduced into the remaining bond, substantially weakening it. Thus, dynamic tension is present in the recoupled pair bond dyad that is absent in a pair of covalent bonds. This affects the vibrational spectra of molecules with RPB dyads. The ClF3+(X2A′) state can be formed from the ClF2+(a3B1) state by covalently bonding a third F atom with the out-ofplane singly occupied orbital on the Cl atom. Thus, ClF3+ has a RPB dyad and a single covalent bond. The ground state of ClF3+ can also be formed by recoupling the electrons in the 3plike lone pair of ground state ClF2+(X1A1), followed by rearrangement to form a RPB dyad and one polar covalent bond. Bonding a fourth F atom to the remaining singly occupied orbital in ClF3+ yields ClF4+(X1A1), which has a RPB dyad and two polar covalent bonds. To form ClF5+, the pair derived from the electrons in the 3s2like orbital of Cl+ must be recoupled. This process is also followed by orbital rearrangement, yielding two RPB dyads and a polar covalent bond. ClF6+ is formed straightforwardly by addition of a sixth F to the singly occupied orbital of ClF5+, which is concentrated on the other side of the plane formed by the two RPB dyads. ClF6+ has three RPB dyads. Although the formation pathways of ClFn+ are similar to the isoelectronic SFn species, there is one major difference between ClF2+ and SF2the absence of a stable 3A2 state. In principle, this state would arise if a second F formed a covalent bond with one of the 3pCl-like π orbitals on Cl+ in ClF+(a4Σ−) or if F recoupled the 3pCl-like π2 pair of ClF+(2Π). This state is a resonance between the two possible combinations of one covalent bond and one recoupled pair bond. It is present in SF2 but not ClF2+, due to the greater cost of recoupling the lone pair of Cl+. Our calculations show that ClF2+(3A2) is a transition state connecting two van der Waals complexes. This will be discussed further in Section 5.2.

4. RESULTS AND DISCUSSION: GENERAL TRENDS 4.1. Structures and Energies. As mentioned in the introduction, only two systematic studies on the structures of the ClFn+ species have been published to date, and both used low level ab initio methodology.26,31 We present the first complete set of CCSD(T)/RCCSD(T) calculations on the ClFn+ series for n = 1−6, including the lowest lying excited states of ClF+ and ClF2+. The total energies and optimum geometric parameters of the states of ClFn+ that were characterized in this work are reported 4254



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Table 1. Energies and Structural Parameters for States of ClF+ through ClF6+ Compared with the Experimenta CCSD(T)/RCCSD(T) species ClF (X Π) +

2

ClF+(a4Σ−) ClF2+(X1A1)

ClF2+(a3B1)

ClF3+(X2A′)

ClF4+(X1A1)

ClF5+(X2A1)

ClF6+(X1A1g)

property

AVTZ

AVQZ

energy Re(ClF) energy Re(ClF) energy Re(ClF) θe(F−Cl−F) energy Re(ClFeq) θe(F−Cl−F) energy Re(ClFeq) Re(ClFax) θe(Feq−Cl−Fax) θe(Fax−Cl−Fax) energy Re(ClFeq) Re(ClFax) θe(Feq−Cl−Feq) θe(Fax−Cl−Fax) energy Re(ClFeq) Re(ClFax) θe(Feq−Cl−Fax) θe(Feq−Cl−Feq) energy Re

−558.937345 1.541 −558.844550 1.825 −658.658079 1.552 101.68 −658.592757 1.602 154.87 −758.292978 1.553 1.613 90.53 152.84 −857.995500 1.540 1.602 105.59 173.83 −957.626984 1.538 1.592 92.36 89.90 −1057.347597 1.560

−558.980937 1.535 −558.884510 1.808 −658.730814 1.544 101.84 −658.663527 1.596 154.78 −758.392687 1.545 1.605 90.56 152.78 −858.124171 1.533 1.595 105.73 173.87 −957.782544 1.531 1.585 92.39 89.90 −1057.531604 1.554

a

b

c

exptl

1.581b 102.2b

1.530c 1.617c 103.08c 173.92c

1.551d d

Energies in hartrees (Eh), bond lengths (Re) in Å, and bond angles (θe) in degrees. Reference 19. Reference 20. Reference 21; 1.551 Å is the average bond length reported in the paper.

Figure 3. Optimized structures and energies of ClFn+ ions obtained at the RCCSD(T)/AVQZ level. Equilibrium bond dissociation energies (De) without zero point energy correction are shown (in kcal/mol), as well as the energy differences between ground and excited states (in italics, in kcal/ mol).

in Table 1. The structures and relative energies are depicted in Figure 3. Since the ClFn+ cations are isoelectronic with the

corresponding members of the SFn family, we will draw frequent comparisons between the two series. Overall, we 4255



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7σL orbital exhibits a fair amount of delocalization of the 3p orbital of Cl+ onto the F atom. This is the hallmark of a polar bond. Using GVB orbitals makes it easier to see where the bond polarization originates: in the case of ClF+(X2Π), it is dominated by the original Cl 3p orbital polarizing toward and delocalizing onto the F atom. Examining the GVB orbitals provides even more insight in the case of recoupled pair bonding (RPB). Figure 4b shows the orbitals for the ClF+(a4Σ−) state at its equilibrium bond length. The GVB 7σR is again dominated by F 2p character, although there is a small amount of amplitude on Cl that is not present in the orbital for the covalent state. The 7σL orbital of the excited state, however, is much more delocalized onto F than in the ground state. Together 7σR and 7σL constitute a bond pair that is more polarized toward F than in the ground state. In the ClF+(a4Σ−) state the antibonding orbital is singly occupied and the strength of the bond in this state is dramatically reduced compared to the ground state. Interestingly, the Mulliken populations show the charge on F in the ClF+ ground state (Feq) is −0.179 and that on F in the excited state (Fax) is −0.096. This is the only case where Feq gains more negative charge than Fax in the ClFn+ (n = 1−6) series, and there is no such exception in the isoelectronic SFn (n = 1−6) series. The lower electron density on Fax is probably due to two factors: (a) the positive charge on Cl leads to back-donation of electron density from F atom toward Cl atom in 7σR and (b) the significant delocalization of the electronic density in antibonding orbital 8σ onto Cl atom. For the rest of the of ClFn+ species, the antibonding character is removed when the recoupled pair bond dyad is formed, and the electron density tends to localize more toward the terminal Fax atoms. To better understand why we describe the bonding in the excited state as recoupled pair bonding, Figure 4c depicts the three GVB orbitals for ClF+(a4Σ−) at a distance 2 Å longer than Re. At large separations the pair of electrons in the singlet coupled orbitals are centered on Cl+ (see Figure 1), not on F and Cl+ as they are at Re. As the bond forms, the character of all three orbitals shifts dramatically. Both Cl+ orbitals polarize toward F as bond orbitals, while the F orbital delocalizes onto Cl+ and builds in antibonding character. The character of the Cl+ orbital that pointed away from F is present in the antibonding character of 8σ at Re, while the F atom character is found in 7σL. The coupling in the pair of electrons has thus changed from the Cl+ 3p lobe pair to a σ bond pair polarized toward/delocalized onto F. Because the singly occupied antibonding orbital has significant amplitude on the side of the Cl atom away from the F atom, we expect the second F to add to this state to form a linear or quasilinear compound. Figure 5 depicts localized orbitals of interest for ClFn+(n = 2−6) at the HF/AVTZ level. For ClF2+ through ClF4+, the electron pair derived from the Cl+ 3s2 lone pair is polarized away from the bonding orbitals, but it is more centered on Cl than is the case for their isoelectronic SFn counterparts.1 The difference can be attributed to the larger nuclear charge of Cl+ holding its electrons more tightly than S does. All of the ions studied in this work except ClF+(X2Π) and ClF2+(X1A1) have one or more recoupled pair bond dyads. The orbitals for the recoupled pair bonds are shown in the middle column of Figure 5a and b, while covalent bonds are depicted in the rightmost column. To make it easier to see the amount of bond polarization in both covalent and RPB bonds, we took a linear combination of the in- and out-of-phase orbitals, which localizes a bond pair between each Cl−F atom pair (the

found both series have similar optimum structures. They also possess the same ordering of low-lying electronic states, although the relative energies are very different. The difference between the individual species will be discussed in more detail in section 5. 4.2. Charge Distributions on Different Types of Terminal Atoms, Fax vs Feq. In addition to the structures and energies, we calculated Mulliken populations at the HF/ AVTZ level. We found a trend shared by both SFn and ClFn+ regarding the charge distribution on the two types of F atoms, equatorial (Feq) and axial (Fax). Equatorial F atoms are those F atoms that participate in normal (polar) covalent bonds, while axial F atoms are involved in recoupled pair bonds or RPB dyads. The lengths of the S/Cl+−Feq bonds are generally shorter than the S/Cl+−Fax bonds. As shown in Table 2, except Table 2. Mulliken Populations of ClFn+ and SFn Calculated at the HF/AVTZ Level state

Q(X = S,Cl+)

Q(Feq/Faq)

SF(X Π) ClF+(X2Π) SF(a4Σ−) ClF+(a4Σ−) SF2(X1A1) ClF2+(X1A1) SF2(a3B1) ClF2+(a3B1) SF2(b3A2) SF3(X2A′) ClF3+(X2A′) SF4(X1A1) ClF4+(X1A1) SF5(X2A1) ClF5+(X2A1) SF6(X1A1g) ClF6+(X1A1g)

0.475 1.179 0.585 1.096 0.948 1.406 1.098 1.444 0.962 1.477 1.642 1.816 1.949 2.314 2.257 2.754 2.643

−0.475 −0.179

2

Q(Fax/Fba)

−0.585 −0.096 −0.474 −0.203 −0.548 −0.222 −0.481 −0.421 −0.180 −0.398 −0.174 −0.374 −0.224 −0.459 −0.274

−0.528 −0.231 −0.510 −0.300 −0.485 −0.258

for ClF+, F atoms involved in recoupled pair bonds or dyads are more negatively charged than covalently bonded F atoms, indicating that recoupled pair bonds have more ionic character and are more polarized than (polar) covalent bonds. We will discuss more about the special case of ClF+ in section 4.3. One difference between SFn and ClFn+ compounds is the amount of density withdrawn from the central atom in each case. The electrons in the Cl+ ion are held more tightly than in the S atom. It is thus more difficult for F atoms in the ClFn+ species to withdraw electron density from the central atom than is the case in SFn species. As a result, the F atoms in ClFn+ are less negatively charged than those in SFn. 4.3. Orbitals. Figure 4 shows the principal bonding orbitals for the ground and first excited state of ClF+ in order to illustrate the fundamental difference between covalent and recoupled pair bonding. In Figure 4a, we compare the natural and GVB orbitals at the equilibrium bond length for ClF+(X2Π) as computed at the MCSCF/AVTZ level. For the natural orbitals, 7σ is a nearly doubly occupied bonding orbital with the orbital polarized toward the F atom, while 8σ is an antibonding orbital with a small occupation number of 0.069. The NOs were transformed into approximate GVB orbitals 7σL and 7σR using the CI coefficients as described in the previous papers.1 In the GVB representation, these orbitals are singly occupied. The 7σR orbital is very similar to the 2p orbital of F atom, while the 4256



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Figure 4. MCSCF/AVTZ 2D plots of the natural orbitals (NO) and GVB orbitals for states of ClF+ at various MRCI+Q/AVTZ geometries: (a) ClF+(X2Π) at Re, (b) ClF+(a4Σ−) at Re, and (c) ClF+(a4Σ−) at Re + 2.0 Å.

coefficients of ±1/√2 maintains the normality and orthogonality of the orbitals). Because axial F atoms attract more electron density than the equatorial F atoms, the RPB orbitals are more polarized toward the F atom than the ones for the corresponding covalent bonds. For example, in the ClF3+ (2A′) state, the RPB dyad orbitals 9a′ and 6a″ are very delocalized onto the Fax atoms, while the covalent 12a′ orbital has greater density located on Cl. The recoupled pair bonding in ClF5+ and ClF6+ (Figure 5b) is quite different from that in the smaller species in the family (Figure 5a). This type of RPB requires recoupling the polarized 3s2-like lone pair of Cl. We can demonstrate how the orbitals change by using a reverse process of ClF5+ dissociating to ClF4+ and F as shown in Figure 6. In such a scan, we began with the optimized structure of the ClF5+ at RCCSD(T)/AVTZ level. Except for the scanned ClFax coordinate, all other geometry parameters were fixed. (The purpose here is to examine the way the orbitals change qualitatively during the addition of the fifth F atom; full optimizations would add little to the analysis.) Although the HF wave function dissociates properly for ClF5+

→ ClF4+ + F, we used MCSCF/AVTZ calculations for the description of the orbitals in the bond breaking process. In Figure 6, the doubly occupied 21a orbital resembles the polarized Cl+ 3s2 lone pair at large distance while the singly occupied 22a orbital represents the singly occupied F 2p orbital. As F approaches ClF4+, the doubly occupied orbital becomes a bond pair between Cl+ and the F atom. The singly occupied orbital changes smoothly into an orbital polarized on the opposite side of the ClFeq bond, but retaining significant Cl 3s character. As in the case of the Cl 3p2 pair, we expect it to be more difficult to decouple the 3s2 lone pair of electrons in ClF5+ than in SF5, as the positive charge on Cl+ again holds this pair of electrons more tightly than in the case of S and thus makes them more difficult to recouple. This prediction is supported by comparing the sequential bond dissociation energies of ClF5+ and SF5, as detailed in section 4.5. To form ClF6+, the singly occupied orbital on a sixth F atom interacts with the singly occupied 15a1 orbital of ClF5+ (equivalent to the 22a orbital in C1 symmetry). The six equivalent bonds in ClF6+ and SF6 are a mixture of s and p 4257



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Figure 5. Important orbitals for (a) ClF2+, ClF3+, and ClF4+ ions, in most of which the Cl+ 3p2 lone pair is recoupled, and (b) ClF5+ and ClF6+, in which Cl+ 3s2 lone pair is recoupled. The superscripts 1 and 2 indicate that an orbital is singly occupied or doubly occupied, respectively.

The oscillation of the IEs of the ClFn species is a direct consequence of recoupled pair bonding. When the electron is removed from an orbital that arises from the doubly occupied 3p orbital of Cl, the IE is comparable to that of the Cl atom. This occurs in ClF(X1Σ+) and ClF3(X1A1). Although the remaining lone pair orbital on ClF5 is derived from the Cl 3s2 pair, it has acquired considerable 3p character. The admixture of 3p character results in an IE for ClF5 that is comparable to that of Cl, ClF, and ClF3. Very different behavior occurs when an electron is removed from ClF2 and ClF4 to yield singlet state cations. In both cases, large changes in geometry occur, and the bonding reorganizes substantially. When the electron is removed from the singly occupied Cl 3p-like orbital of both ClF2 and ClF4, a RPB dyad is replaced by a pair of covalent bonds. It is perhaps easier to understand what drives these large changes by considering the reverse process of adding an electron to ClF2+ and ClF4+. These are both closed-shell species: reorganizing two covalent bonds into a RPB dyad is an energetically favorable way to accommodate an extra electron in ClF2+ and ClF4+, where no

character, as shown in the representative localized orbitals depicted in Figure 5b. Overall, the orbitals illustrate the presence of recoupled pair bonds and RPB dyads in the ClFn+ species and distinguish them from the normal covalent bonds. They also illustrate two types of RPB bonds, where 3p2 and 3s2 lone pairs are decoupled. 4.4. Ionization Energies (IE). In Table 3, we report the ionization energies of the neutral ClFn species. To aid in visualization, Figure 7 depicts the orbital diagrams for ground state ClFn neutrals that are ionized to the ground state ClFn+ ions; the corresponding IEs are plotted in Figure 8 (IE0 values at the RCCSD(T)/AVQZ level). The IEs oscillate as the number of F atoms increases, with those of even n compounds [the open shell species ClF2(2A1), ClF4(2A1), and ClF6(2A1g)] about 2 eV less than those of odd n compounds [the closed shell species ClF(1Σ+), ClF3(1A1), and ClF5(1A1)]. For reference, the first ionization energies of Cl and F are 12.90 and 17.35 eV, respectively. Due to the much larger IE of F, ionization from F orbitals will not occur at the energies of interest here. 4258



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Table 3. Ionization Potentials for States of ClFn (n = 2−6) Calculated with the CCSD(T)/RCCSD(T) Methoda IPe (IP0) ClF(1Σ+)a → ClF+(2Π) + e−

AVTZ

AVQZ

expt’l.

12.58 (12.59)

12.66 (12.67)

12.60 ± 0.05b 12.66 ± 0.01c 12.74 ± 0.01c

ClF(3Π)a → ClF+(2Π) + e− ClF(3Π)a → ClF+(4Σ−) + e− ClF2(2A1) → ClF2+(1A1) + e−

10.21

10.21

12.68

12.80

10.65 (10.69)

10.66 (10.70)

11.0d 12.8 ± 0.3d 12.77 ± 0.05b

ClF2(2A1) → ClF2+(3B1) + ClF2(2B1) → ClF2+(1A1) + ClF2(2B1) → ClF2+(3B1) + ClF2(2A′) → ClF2+(1A1) + ClF2(2B1) → ClF2+(3B1) + ClF3(1A1) → ClF3+(2A′) +

Figure 6. Highest doubly occupied 21a orbital and singly occupied 22a orbital along the approximate dissociation pathway for ClF5+ → ClF4+ + F. The geometric parameters of the ClF4+ moiety are fixed at the optimized RCCSD(T)/AVTZ values of ClF5+. The natural orbitals were obtained at the MCSCF/AVTZ level.

e− e− e− e− e− e−

ClF4(2A1) → ClF4+(1A1) + e− ClF5(1A1) → ClF5+(2A1) + e− ClF6(2A1g) → ClF6+(1A1g) + e−

singly occupied orbital is available. In the case of ClF6, the open-shell molecule has an octahedral structure probably because such a structure minimizes the repulsions between the bonds and the ligands. Its singly occupied orbital has a near spherical shape with strong Cl 3s character and some 3p character.2 This orbital is destabilized by the antibonding character resulting from its overlap with other bonding and nonbonding F−Cl−F orbitals. As a result, removing the electron from this singly occupied orbital thus requires relatively low energy. In addition, the delocalization of the electron over all the atoms suggests the change is geometry neutral. The ClF6+ cation maintains a structure similar to that of ClF6 because it possesses three RPB dyads, all of which have a preference for a linear F−Cl−F configuration. Excited states of ClF2+ can also be formed through ionizations of ClF2 in its various states, as shown in Figure 9. From the ground state ClF2 (X2A1), electrons can be removed from two different orbitals. Removal of an electron from the first orbital, discussed above, yields ClF2+ in its X1A1 ground state. However, an electron can also be removed from the doubly occupied orbital 3p2-like orbital, resulting in the excited state ion ClF2+ (a3B1). The IE for this, 12.49 eV, is comparable to the IEs of ClF, ClF3, and ClF5, where similar processes occur. ClF2 also has a linear 2B1 state (which is part of a Renner−Teller system with the 2A1 state) with a very similar IE of 12.33 eV. The final case is the bent ClF2 (2A′) state, which is combination of both covalent and recoupled pair bonding. As such, its singly occupied orbital has strong antibonding character from decoupling the 3p2 lone pair of electrons in Cl. Removing the electron from this orbital to form ground state ClF2+ is more favorable than any of the other IEs, at just 9.90 eV.

12.43

12.49

10.49

10.50

12.26

12.33

9.90

9.90

9.61

9.57

12.49 (12.50)

12.54 (12.55)

12.65 ± 0.05e

10.89 (10.96)

10.87 (10.95)

13.0 ± 0.2d 13.05 ± 0.05b ≤12.13 ± 0.11f

12.68 (12.70)

12.70 (12.72)

10.20 (10.37)

10.15 (10.31)

a The MRCI+Q values for ClF+ were reported in our previous paper, see ref 2; IPe and IP0 are in eV; IP0 in parentheses; ZPE are calculated at B3LYP/AVTZ level. bReference 17. cReference 15. dReference 14. e Reference 16. fReference 18.

Just as the much larger ionization energy of F compared to Cl precludes low energy ionization from F ligand 2p2 lone pairs, it also means the lowest dissociation channels for ClFn+ yield ClFn−1+ and a neutral F atom. These bond dissociation energies are discussed in the next section. 4.5. Bond Dissociation Energies (BDE). Figure 10 and Table 4 depict the bond dissociation energies (BDE, D0) with respect to the ClFn−1+ + F limit. As in the SFn and ClFn series, the BDEs of the ground state ClFn+ compounds oscillate. The ClFn+ bond dissociation energies are consistently less than those of the SFn species, as shown in the figure. The oscillation of BDEs is easily understood from the recoupled pair bonding model. Smaller bond energies occur in steps in which a lone pair of electrons is recoupled, such as the formation of ClF3+/SF3 and ClF5+/SF5. The electron leftover after the lone pair is recoupled is normally in an antibonding orbital, but the orbitals in ClF3+/SF3 and ClF5+/SF5 rearrange in favor of the formation of recoupled pair bond dyads and a single polar covalent bond, placing the odd electron in a singly occupied nonbonding orbital. In the case of ClF3+/SF3, the singly occupied orbital is a Cl 3p-like orbital. When ClF4+/SF4 is subsequently formed, the new bond is covalent and has a much larger bond energy than the one in ClF3+. In ClF5+/SF5, however, the singly occupied orbital has significant antibonding character. As another F atom bonds with ClF5+/SF5, the 4259



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Figure 7. Orbital diagrams for the ground state ClFn (n = 1−6) compounds ionized to ground state ClFn+ (n = 1−6).

antibonding character is largely removed, and the bond is very strong. The differences between the ClFn+ and the SFn BDEs are due to the positive charge on Cl+, which holds the electrons much more tightly than S does. Kiang and Zare16 and others have accounted for the oscillating bond dissociation energies in SFn and other families as due to the formation of 2-center, 3-electron (2c−3e) bonds followed by 3-center, 4-electron (3c−4e) bonds.10−14 Although recoupled pair bonding shares some similarity with the 2c−3e/ 3c−4e theory, the pictures of bonding that the models provide is quite different. For example, in the 4-electron system, the recoupled pair bond dyad is simply a pair of very ionic bonds, in agreement with the detailed analysis of Ponec et al.45 The 3c−4e model, on the other hand, treats the orbitals as inherently delocalized. Harcourt46 has recently compared the 3c−4e and recoupled bond pair models. We have also calculated the reaction energies for ClFn+ → ClFn−2+ + F2. As shown in Table 5, the channel for dissociating to the F2 molecule is more favorable for ClF4+ and ClF6+ than the channel for dissociating to ClFn−1+ + F. This means it

Figure 8. Ionization energies of the F atom and the ClFn (n = 1−6) species calculated at the RCCSD(T)/AVQZ level; ZPE corrections for the molecules were calculated at the B3LYP/AVTZ level.

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Figure 9. Orbital diagrams for the various states of ClF2 ionized to ClF2+ and the corresponding ionization energies (in eV) at the RCCSD(T)/ AVQZ level, without ZPE corrections.

Table 5. Bond Dissociation Energies with Zero Point Energy Corrections (D0) Calculated with the CCSD(T)/RCCSD(T) Method for the ClFn+ → ClFn−2+ + F2 (n = 2−6) Reactions Δ[D0(ClFn−2++F2) − D0(ClFn−1++F)]

D0a bond ClF2+ ClF3+ ClF4+ ClF5+ ClF6+ a

Table 4. Bond Dissociation Energies (De) of ClFn+ → ClFn−1+ + F, Zero Point Energies (ZPE) of ClFn+ Species, and Bond Dissociation Energies with Zero Point Energy Correction (D0) in the Ground States of ClFn+ De (D0)

ZPE B3LYP

B3LYP

bonda

AVTZ

AVQZ

AVTZ

AVTZ

Cl+−F ClF+−F ClF2+−F ClF3+−F ClF4+−F ClF5+−F

63.86 (62.53) 58.41 (56.82) 4.54 (3.10) 46.98 (44.22) 2.40 (1.02) 58.33 (54.66)

66.92 (65.59) 60.97 (59.38) 5.74 (4.30) 49.43 (46.67) 3.55 (2.17) 60.46 (56.79)

69.73 (68.40) 55.91 (54.32) 10.83 (9.39) 36.94 (34.18) 3.96 (2.58) 41.11 (37.44)

1.33 2.92 4.36 7.12 8.50 12.17

Cl+ + F2 ClF+ + F2 ClF2+ + F2 ClF3+ + F2 ClF4+ + F2

AVTZ

AVQZ

AVQZ

84.25 24.82 12.23 10.14 20.49

88.64 27.35 14.64 12.50 22.62

29.26 23.05 −32.03 10.33 −34.17

D0 in kcal/mol.

5. RESULTS AND DISCUSSION: STATES OF ClFn+ SPECIES 5.1. ClF+. The ionization energy of ClF to various states of ClF+ has been measured using mass spectrometric methods,17 mass spectrometric/photoionization methods,47 and photoelectron methods.18,19 Both the experimental data and our calculated adiabatic ionization energies are summarized in Table 3 for the X1Σ+ and a3Π states of ClF and Table 7 for the vertical ionization energies from the ground state of ClF to a number of other low-lying excited states (2Δ, 2Σ+, 2Π(II), 2Σ−) of ClF+. We also calculated potential energy curves for important low-lying doublet and quartet states. The curves at the MRCI+Q level with extrapolation to the complete basis set (CBS) limit are shown in Figures 11 and 12, while the spectroscopic parameters at the MRCI+Q/CBS level are reported in Table 6. Comparison of the ClF+ and SF Curves. Similar to the calculations of Yang and Boggs,48 we performed potential scans for both species at the MRCI+Q/CBS level as detailed in the methodology section. For SF, we obtained four bound states (2Π, 4Σ−, 2Δ, 2Σ−) that could be correlated with the S(3P) + F(2P) separated atom limit. The bond energies, De, for the ground state (X2Π) and first excited state (a4Σ−) of SF are 83.93 and 35.30 kcal/mol, respectively. The equilibrium

Figure 10. Bond dissociation energies of ClFn+ → ClFn−1+ + F calculated at the RCCSD(T)/AVQZ level compared with the isoelectronic species SFn → SFn−1 + F.

CCSD(T)/RCCSD(T)

→ → → → →

a De, D0, and ZPE are in kcal/mol. D0 are in parentheses and are obtained using the ZPE value at the B3LYP/AVTZ level.

would be difficult to observe the open-shell ClF3+ and ClF5+ molecules in a mass spectroscopy experiment. 4261



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separation, as shown in Figure 11 and Table 6. The 2Δ and 2Σ− states of ClF+, as shown in Figure 12, are very weakly bound with De’s of 3.38 and 3.39 kcal/mol, respectively, and are probably the result of ion-induced dipole interactions. Both the 2 Π and the 4Σ− states of ClF+ have shorter equilibrium bond lengths than SF due to the more contracted orbitals of Cl+. The 2 Π and 4Σ− state separation is 53.41 kcal/mol for ClF+, about 5 kcal/mol more than it is for SF. Ground State ClF+(X2Π). Our results show good agreement with the experimental data. At the RCCSD(T)/AVQZ level, our calculated IP0 is 12.67 eV, which is in excellent agreement with the value of 12.66 ± 0.01 eV for ClF(1Σ+,ν = 0) to ClF+(2Π3/2,ν = 0) reported by both Anderson et al.18 and DeKock et al.19 Anderson et al.18 argued that the ground state of ClF+ should have a larger bond energy and greater vibrational frequency than ground state ClF because the ClF+(X2Π) state results from ejecting an electron from an antibonding orbital, 3πg, the highest occupied orbital in ClF(X1Σ+). The removal of an electron in the π system reduces the electron−electron repulsions and stabilizes the ionic species. Indeed, our calculations at RCCSD(T)/AVQZ level show that the bond energy of ground state ClF+ is 66.92 kcal/mol, 5.41 kcal/mol more than that for the corresponding ClF(1Σ+) state.2 To the best of our knowledge, no experimental measurement has been reported for the bond length of ClF+(X2Π). However, DeKock et al.19 estimated the change of the bond length ΔRe from the ground state of ClF to ground state ClF+ to be −0.10 Å. This value agrees well with our calculations, where ΔRe is −0.091 Å at the MRCI+Q/AV5Z level2 and −0.098 Å at RCCSD(T)/AVQZ level. The ground state of ClF+ has multireference character and is preferably calculated using MCSCF and MRCI methods, as showed in our previous work.2 The reason that we also performed the RCCSD(T) calculations is to compare the bond energies and ionization energies of ClFn/ClFn+ species consistently. Second Bound State (a4Σ−). As reported in our previous paper,2 the 4Σ− state is the first excited state of ClF+ and is bound (D0) by 5.86 kcal/mol at the RCCSD(T)/AV5Z level. Its formation can be explained using the recoupled pair bonding modelthe 3p2 lone pair of Cl+ is decoupled, and one of the electrons is recoupled with the singly occupied F 2p orbital. 2 Δ and 2Σ−. In SF, Yang and Boggs48 found that the 2Δ and 2 − Σ states are bound (De) by 6.9 kcal/mol (2Δ) and 5.3 kcal/ mol (2Σ−) with bond lengths (Re) that were comparable to, if somewhat longer than, that for the a4Σ− state (1.885 and 1.954 Å, respectively, versus 1.861 Å). In contrast, the MRCI+Q calculations on ClF+ predict bond energies of just 3.38 and 3.39 kcal/mol for these two states with the bond lengths for both states being 0.7 Å longer than in the a4Σ− state (see Table 6 and Figure 12). This suggests that the interactions responsible for the binding in ClF+ are much different than in SFthe dominant contribution is probably the interaction between the charged Cl+ ion and the dipole induced in F by that ion, with smaller contributions from dispersion. 2 Π(II) and 2Σ+. Anderson et al.18 noted that it was difficult to assign the ionization energies to higher excited states of ClF+. Based on the assumption that the energy levels of ClF should be similar to Cl2 and F2, they assigned the energies for ionizing ClF to ClF+(2Π) and ClF+(2Σ+) to be 16.39 ± 0.01 and 17.80

Figure 11. Comparison between the potential energy curves for the lowest two bound states of SF and ClF+ using the MRCI+Q method at the estimated complete basis set (CBS) limit.

Figure 12. Comparison between the potential energy curves for the low-lying excited doublet states of SF and ClF+ using the MRCI+Q method at the estimated complete basis set (CBS) limit.

Table 6. Spectroscopic Constants of ClF+ States at the MRCI +Q/CBS Levela state

ωe

ωexe

Be

De

D0

Re

X2Π a4Σ− 2 Δ 2 − Σ

916.2b 377.5 118.4 119.1

5.9 7.1 1.0 3.4

0.5819 0.3642 0.1991 0.1977

68.64 15.23 3.38 3.39

67.34 14.69 3.21 3.23

1.53 1.94 2.63 2.62

a

Calculations were based on state-averaged MCSCF wave function; ωe, ωexe, and Be in cm−1; De and D0 in kcal/mol; Re in Å; CBS as complete basis set. bExperimental: 912 ± 30 (ref 15); 870 ± 30 (ref 16).

internuclear distance, Re, of SF(X2Π) is 1.595 Å and is 0.259 Å shorter than that for the SF(a4Σ−) state. We found two states for ClF+(2Π, 4Σ−) that were significantly bound at short Cl−F 4262



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± 0.01 eV, respectively. DeKock et al.19 reported the two types of ionization energies to be 16.25 ± 0.08 and 17.91 ± 0.08 eV, respectively. However, our calculations of their PECs, as shown in Figure 12, demonstrate that 2Π(II) and 2Σ+ are both dissociative states. Broad bands rather than discrete lines might

to the asymmetric stretch of the two ClF bonds; it connects two equivalent weakly bound ClF+−F complexes. 5.3. ClF3+. DeKock et al.19 reported the lowest ionization energy of ClF3(X1A1) to be 12.65 ± 0.05 eV and assigned the product as the 2B2 or 2A1 state of ClF3+. Irsa and Friedman17 and Dudin et al.20 reported the IP to be around 13.0 eV. In contrast to experimental assignment noted above, our calculation found ground state ClF3+ to have Cs symmetry; like SF3, it is a 2A′ state. The computed adiabatic ionization energy (IE0) is 12.55 eV at the RCCSD(T)/AVQZ level. Since the value is only 0.10 eV smaller than the experimental result of DeKock et al.,19 the assignment is reasonable despite the difference in symmetry assignments. There are no experimental geometry parameters reported for the ClF3+ species. As in our study, Law et al.31 reported the ground state of ClF3+ to have Cs symmetry in their G3/G3X calculations. We found our calculations are closer to their B3LYP/6-31(2df,p) results. We have listed our results in Table 1. At the RCCSD(T)/ AVQZ level, our calculated difference between the Cl−Fax and Cl−Feq bond lengths is 0.008 Å smaller than the difference calculated by Law and co-workers using their B3LYP results, and 0.052 Å larger than their MP2-(Full)/6-31G(d) result. As mentioned in the earlier section, the short equatorial bond is a normal covalent bond, while the axial bonds constitute an RPB dyad. In comparison with SF3, the Cl−Feq bond length of ClF3+ is 0.014 Å shorter, while the axial Cl−Fax bond length is 0.044 Å shorter. The Feq−Cl−Fax angle is slightly larger than 90° while the analogous angle in SF3 is 87.6°. The Fax−Cl−Fax angle is about 11° less in ClF3+ than in SF3. The difference between the two species may be due to the different polarization of the pair derived from the central atom’s 3s2-like pair in each species; this pair is more centered on Cl than on S in the respective compounds. 5.4. ClF4+. Experimental measurements by Christe et al.23,48 have shown that ClF4+ has C2v symmetry. They assigned the longer axial bonds to be ionic with the shorter equatorial bonds being covalent. The geometrical parameters from their experiment51 are listed in Table 1. There are many theoretical results25,52,53 for the structure of ClF4+ as well as its vibrational spectra and the possible internal rearrangement of its stereoactive ligands. For example, Charkin et al.25 used the HF and MP2 methods with 6-31+G* and 6-311+G* basis sets, and Cooper54 used a spin-coupled description. Both of their calculations show similar C2v structures. Our results, as listed in Table 1 and shown in Figure 3, are in good agreement with the experimental findings. At the RCCSD(T)/AVQZ level, our calculated Cl−Feq bond length is only 0.003 Å shorter than the experimental value and the Fax−Cl−Fax bond angle less than 0.1° smaller than the experimental one. Our Feq−Cl−Feq bond angle is about 3° larger than the experimental one. Christe et al.25,50 mentioned that the reported value was of ClF4+ in a solid salt, and its Feq− Cl−Feq bond angle may be compressed compared to a free gasphase ClF4+ due to fluorine bridging. This means our calculation might be closer to the gas phase result. Our calculated Feq−Cl−Feq bond angle is 4.2° larger, and the Fax−Cl−Fax bond angle is 1.7° larger than the values in SF4. The Cl−Feq bond length is 0.015 Å shorter than the S−Feq bond length, and the Cl−Fax bond length is 0.05 Å shorter than the S−Fax bond length. Overall the difference in the covalent bond lengths is smaller than the difference in the RPB dyad bond lengths. This suggests that the positive charge on the central atom more strongly influences the recoupled pair bond.

Table 7. Vertical Ionization Potentials (in eV) of the Excited Doublet States of ClF+ at MRCI+Q/CBS Level in Comparison with Experimental Data vertical IP Δ

2 +

16.83

17.40 18.41(2)a 18.36(1)b

2

MRCI+Q/CBS exptl a b

Σ

Π(II)

2

17.09 17.06(2)a 17.01(1)b

2 −

Σ (I)

17.03

2 −

Σ (II) 19.13

Reference 16; values in parentheses are standard deviations. Reference 15; values in parentheses are standard deviations.

be expected for these dissociative states. As shown in Table 7, the vertical IP without ZPE correction at MRCI+Q/CBS level is 17.09 and 17.40 eV for ClF(1Σ+) to ClF+(2Π) and ClF+(2Σ+), respectively. These values are the largest values we calculated for vertical IPs. For ClF(1Σ+)→ClF+(2Σ+) + e−, however, the vertical IP is much lower than the experimental value, 18.36 ± 0.01 eV18 or 18.41 ± 0.02 eV.19 This large difference calls for new experiments. 5.2. ClF2+. Dudin et al.20 reported the appearance potential of ClF2+ to be 12.77 ± 0.05 eV. Irsa and Friedman17 reported a very similar result, 12.8 ± 0.3 eV. The appearance potential provides an the upper limit for the vertical ionization energy of ClF2. Using the Cl−F bond energy determined by Slutsky and Bauer,49 Irsa and Friedman17 computed the ionization energy to be 11.0 eV. Our calculated value for the ionization energy of ground state of ClF2(2A1) to ClF2+(1A1) is 10.66 eV at the RCCSD(T)/AVQZ level, which is in semiquantitative agreement with the prediction of Irsa and Friedman.17 We also calculated the ionization energy from various ClF2 states to the excited state of ClF2+. As mentioned in an earlier section, the IEs have been reported in Table 3, and the coupling diagrams of the ClF2 states ionized to ClF2+ states are depicted in Figure 9. The highest ionization energy we calculated is 12.49 eV for ClF2(2A1) → ClF2+(3B1) + e−. Again, it would be interesting if new experiments were performed to verify the predictions for the ionic states obtained in this work. Gurvich22 reported the experimental bond length of ClF2+(1A1) to be 1.581 Å and the bond angle to be 102.2°. In calculations of Law et al.31 using the G3X method, the bond length was predicted to be 1.578 Å and the bond angle 102.2°. Our calculations predict that the bond length is 1.544 Å and the bond angle is 101.84°. Compared to SF2(X1A1), ground state ClF2+ has a shorter bond length (∼0.04 Å) and a slightly larger angle (∼4°). The larger bond angle may be due to greater repulsion between the bond pairs or it may be due to electrostatic effects. To the best of our knowledge, there is no experimental data for the 3B1 excited state of ClF2+. Our calculations listed in Table 1 show it has two long bonds that comprise a recoupled pair bonding dyad. The bond length is about 0.06 Å shorter than the one in the same state of SF2, while the bond angle of ClF2+(3B1) is about 8° less. This again can be attributed to the positive charge on the Cl atom. While SF2 has a stable 3A2 state, the comparable state in ClF2+ is a transition state. Its imaginary frequency corresponds 4263



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5.5. ClF5+. No experimental data appear to be available for the structure of ClF5+. In our calculations, as shown in Table 1 and Figure 3, we found it has C4v symmetry with four long axial bonds and one short equatorial bond. From the RPB perspective, it is a result of the fifth F atom decoupling the electrons derived from the Cl+ 3s2-like lone pair orbital followed by rearrangement to yield two RPB dyads. As shown in Figure 5b, the singly occupied orbital has strong Cl 3s-3p hybrid character. The Cl−Feq and Cl−Fax bond lengths are 0.009 Å and 0.01 Å shorter, respectively, than the analogous bonds lengths in SF5. The Feq−Cl−Fax angle is about 0.8° larger than the Feq−S−Fax angle. 5.6. ClF6+. ClF6+ is stable in the form of its solid salts such as [ClF6+][PtF6−]. For example, ClF6+ can be formed from reaction of ClF5 or ClO2F with a strong oxidizer like PtF6.56 ClF6+ can also be obtained in the form of [ClF6+][AsF6−] via ClF5 reacting with [KrF][AsF6].57 It has been experimentally identified to have an octahedral structure.26,55 We found the optimum structure to be octahedral as shown in Table 1 and Figure 3. The bond length is 1.554 Å at the RCCSD(T)/AVQZ level in comparison with the reported averaged bond length of 1.551 Å by Lehmann et al.24 The calculated bond length in ClF6+ is 0.007 Å shorter than the bond length of SF6. Our calculation of the energy change shows that the ClF5+ + F → ClF6+ reaction is quite exothermic (about 57 kcal/mol). This is again due to the removal of the antibonding character of the singly occupied orbital in ClF5+. The bond energy of the reaction ClF4+ + F2 → ClF6+ is about 23 kcal/mol as shown in Table 5. Even though ClF4+ is stable with respect to both the ClF3+ + F and ClF2+ + F2 dissociation channels, direct F2 addition to ClF4+ may not be a viable pathway if the behavior is analogous to what is found for the addition of F2 to similar sulfur compounds.58−60 Another pathway might be ClF4+ + F2→ ClF5+ + F followed by ClF5+ + F → ClF6+. However, ClF5+ is weakly stable with respect to ClF4+ + F (by only 2 kcal/mol). To examine whether ClF6+ can be formed via the above pathways, a future study on the potential energy surfaces around the various pathways would be desirable.

ClF2, ClF4, and ClF6 have low ionization energies (10.30−10.95 eV), because removing an electron from their singly occupied orbitals results in stable closed shell ions. On the other hand, the species with one less F, i.e., ClF, ClF3, and ClF5, are closed shell species and have high ionization energies (12.55−12.72 eV). Ionization of such species involves breaking up a lone pair of electrons. These ionization energies are comparable to that for the Cl atom (12.90 eV). Overall, our calculations of the geometric parameters and ionization energies of the ground state species show good agreement with existing experimental data. The agreement demonstrates that the RCCSD(T) method with large correlated basis sets produces results comparable to those obtained from experiment. It also suggests that our calculations are able to predict excited state species that have not yet been observed. Such states include the 4Σ− state of ClF+ and 3B1 state of ClF2+. In addition, we found the symmetry of ground state for ClF3+ is 2A′ rather than 2A1 or 2B2 as assigned in the experiment of DeKock et al.19 New experiments to reexamine the state assignment for ClF3+ are suggested by our results.

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ASSOCIATED CONTENT

S Supporting Information *

Listings of computational details and optimized structure xyz files. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; phone: +1-217-369-5790; fax: +1-217-244-3186. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Support for this work was provided by funding from the Distinguished Chair for Research Excellence in Chemistry and the National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign. Preliminary calculations on ClF5+ and ClF6+ in this work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number OCI-1053575.

6. CONCLUSIONS We have calculated the structures of various states of ClFn+ (n = 1−6) compounds. We found that the states and geometry structures of the ClFn+ family are similar to those for the isoelectronic SFn series, with only a few notable exceptions. The bond dissociation energies of ClFn−1+ + F → ClFn+ exhibit an oscillating trend similar to that for the SFn molecules. The similarity between the two species shows that the recoupled pair bond model can be used to explain and predict the bonding and structures of ClFn+. For both SFn and ClFn+, the F atoms in axial positions are associated with recoupled pair bond dyads. In most of the cases, these axial F atoms withdraw more electron density from the central atoms than F atoms in equatorial positions (polar covalent bonds), indicating that recoupled pair bonds have more ionic character and are more polarized than polar covalent Cl−F bonds. Recoupling the lone pairs of electrons of Cl+ is more difficult than is the case for the S atom, and thus the formation of recoupled pair bonds in ClFn+ species is less favorable and less complete than in SFn. For ClF4+ and ClF6+, it is energetically more favorable to dissociate to the ClF2+ + F2 and ClF4+ + F2 channels, respectively, than to the ClF3+ + F and ClF5+ + F channels. The ionization energies of ClFn to ground state ClFn+ also exhibit rather dramatic oscillations. The open-shell species

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REFERENCES

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High Level ab Initio Calculations for ClF - American Chemical

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