J. CHEM. SOC. FARADAY TRANS., 1994, 90(13), 1831-1837 Transition Vector Symmetry and the Internal Pseudo-rotation and Inversion Paths of CIF,' Ruslan M. Minyaev Institute of Physical and Organic Chemistry, Rostov State University, Stachka A ve., 19413, Rostov-on- Don 344 104 , Russia David J. Wales University Chemical Laboratories, Lensfield Road, Cambridge, UK CB2 IEW A new definition of the transition vector symmetry group is suggested. The utility of the definition is demon- strated by calculations of the pathways of the internal pseudo-rotation and inversion of CIF,' (DZP and DZP/MP2 levels). The lowest internal pseudo-rotation proceeds by a Berry mechanism with an activation barrier of 6.7 kcal mol-'. The lever mechanism has a higher barrier of 39.5 kcal mol-' and would lead to more extensive fluorine scrambling.The inversion reaction that leads to enantiomerization corresponds to a planar D,, tran-sition state with an activation barrier of 60 kcal mol-'. 1. Introduction Considerable effort has been devoted to the elucidation of the connection between the symmetry elements of a transition state, and those of reactant and product. Many selection rules have been proposed.'-' ' The most important principles are probably the conservation of orbital symmetry introduced by Woodward and Hoffmann,' and selection rules for transition states due to Stanton and McIver., From a geometrical point of view, the transition-state structure is the nuclear configu- ration corresponding to a saddle point with one negative curvature2 (Hessian index, A = 1)12 on the potential-energy surface (PES) of a molecule.Any Hessian eigenvector at this point may be classified according to an irreducible representation' of the appropriate point group. Hence, the symmetry properties of the Hessian eigenvector with unique imaginary frequency (the transition ~ector)~.~ are also those of some particular irreducible representation. At the same time the transition vector considered as a local displacement vector creates an infinitesimally perturbed molecular configu- ration whose point group must be a subgroup of that of the transition state. The purpose of this paper is to focus on the symmetry properties of the transition vector in a slightly dif- ferent way to McIver and Stanton3v4 which may have some advantages.We illustrate this idea by ab initio calculations (at the DZP and DZP/MP2 levels) of the internal pseudo-rotation and inversion pathways of the ClF,+ cation. We chose this cation for the following reasons: first, inter- halogens represent a very unusual class of hypervalent stereo- chemically non-rigid molecules with different mechanisms of internal rearrangement (Berry pseudo-rotation,', turnstile rotati~n,'~*'~Bartell mechanism' etc.) and have conse-quently been much However, ClF4+ has attracted rather less attention and the internal mechanism of rearrangement remains ambiguous. The temperature dependence of the 19F NMR spectra indicates27 that rapid fluorine ligand exchange in ClF,+ occurs in a solution of ClF,-HF-AsF,.However, whether this is inter- or intra-molecular ligand exchange has not been el~cidated.~ The first ab initio (STO-6G) calculations of Guest et ~1.'~predicted a stable square pyramidal structure for ClF4+ with F-C1-F angles of 154" which was in dis- agreement with experimental observation^.^^-^* Ungemach and Schaefer' pointed out the reason for this disagreement and demonstrated the crucial influence of chlorine d basis functions. Ab initio calculations without such orbitals predict that the square-pyramidal C,, structure of ClF4+ is a minimum even with rather large DZ basis sets.*' Only when chlorine d orbitals are included do calculations find the correct C,, ClF,+ minim~m'~,~'which is consistent with vibrational28 and 19FNMR27spectra as well as with VSEPR concepts.29 Pershin and B01dyrev~~ considered the relative stability of the C2,, C,, and D,, structures of ClF,+.However, they did not consider the Hessian matrix and did not study the reaction pathways. Therefore, we decided to calculate approximate pathways for the different rearrange- ments of ClF4+. The organisation of the paper is as follows. In the second section we describe the methods of calculation. The third section is devoted to new considerations of the transition vector symmetry and its conservation along the gradient lineal1,30-33 The Berry and lever pseudo-rotations are con- sidered in Sections 4 and 5, and the inversion pathways and global topological structure of the PES are considered in Section 6.2. Methods of Calculation All the stationary point optimisations and approximate gra- dient line calculations in this work were performed by eigenvector-following34 (EF) using analytic first and second derivatives at every step which were generated by the CADPAC program.35 The particular EF implementation has been developed and discussed in some detail in previous The method enables one to follow a particular Hessian eigenvector uphill, whilst simultaneously minimising the energy in conjugate directions. This procedure is used to find transition states, while minimisation in all directions is used to locate minima. All calculations were conducted in Cartesian coordinates using a projection operator to remove overall translation and r~tation.~' A maximum step length criterion was used to scale the steps, if necessary.Approximations to the gradient lines were calculated by displacing each transition-state geometry along the two direc- tions corresponding to the (non-mass-weighted) Hessian eigenvector associated with the unique imaginary frequency. Perturbations consisted of adding/subtracting & of the com- ponents of the normalised eigenvector in each case. Pathways were always followed downhill, i.e. by minimising the energy, and no symmetry restrictions were imposed. Calculations were considered to be converged when the maximum step size was <lop4 a, (bohr) and the rms gradient E, a, 't for two consecutive steps, which usually reduces the six 'zero' Hessian eigenvalues to the order of 0.3 cm-'.The basis sets employed were those supplied in the standard CADPAC librar~;~' the DZP basis is obtained by adding polarisation functions with exponents 1.0 (H), 0.8 (C) and 1.2 (F)to the Dunning double zeta basis.38 It is well known that pathways calculated with second- derivative-based algorithms are not quite the same as true steepest-descent or gradient-line paths ; in fact, for some pathological surfaces it is possible to converge to the wrong minimum.39 However, we have no reason to expect such dim- culties in the present case, and the algorithm adopted also means that all the Hessian eigenvectors are available at each step.Hence it was not difficult to follow the evolution of the eigenvalues and eigenvectors along the path using the overlap (dot product) of eigenvectors at successive steps to identify the correlation. We expect our calculations to remain valid for closer approximations to the gradient lines. 3. Transition Vector Symmetry A transition-state structure is a molecular configuration cor- responding to a saddle point with one imaginary frequency2 independent of the PES in neighbouring regions. Therefore, the transition-state structure is defined purely from a geo- metrical point of view, and the transition-state symmetry is given by the appropriate point group.13 All the Hessian eigenvectors must transform according to one of the irreduc- ible representations of this group.13 This is true for the eigen- vectors of both the mass-weighted and non-mass-weighted Hessian ; here we consider the latter matrix exclusively.The transition vector (Hessian eigenvector corresponding to the unique imaginary frequency) transforms according to a non- degenerate irreducible repre~entation.~.~Infinitesimal dis-placements of all atoms along the transition vector lead to a slightly distorted structure whose point group is a subgroup of the transition-state point group', which we will call the transition-vector symmetry group. This definition of the transition vector symmetry is slightly different from that introduced earlier by McIver and Stant~n.~'~ By our defini- tion the transition vector possesses a symmetry property as a real vector rather than as a vibrational m~de.~.~,~ There are several important points to note concerning the gradient-line reaction path, the transition-vector symmetry group, defined above, and the application of the Pearson6- Pechukas' (PP) theorems. First, minimum-energy pathways (MEPs) can deviate from steepest-descent paths at branching points.Since the PP results only apply to steepest-descent paths, they may not be obeyed by MEPs, which can lead to confusion. For example, the reaction-path degeneracy may not be apparent. The second point is that the PP theorems state that the molecular point group can change only at a critical point. In contrast, by our definition the transition- vector symmetry cannot change at all along a steepest-descent path.The proof of this follows in just the same way as for the PP theorem, except that it extends to the critical points because we only consider perturbed geometries. We may therefore apply the principle of conservation of transition-vector symmetry group to any gradient line ema- nating from a transition state until it reaches the next critical point (which may be also a transition state). To clarify this situation let us consider the inversion of ammonia (Scheme 1). t 1 a, (bohr) E 5.291 77 x lo-" m. 1 E, (hartree) z 4.35975 x lo-" J. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 29 D3h Scheme I The3 transition vector of TS 2 by our definition metry group C,, and this is conserved along the whole pathway from la to 16 through 2.In contrast, in the McIver- Stanton3 approach the transition vector is classified in the D,, point group which is not conserved along the pathway. Other examples are internal rotation about the C-C bond in ethane4' and internal pseudo-rotation in phos-ph~ranes;'~,~~,~'in each case the transition-vector symmetry group by our definition is conserved along the whole gradient line from one critical point to another. In the following sec- tions we will demonstrate the utility of this idea for the inter- nal pseudo-rotation and inversion pathways of ClF4+. 4. Berry Pseudo-rotation Ab initio calculations predict that ClF4+ in the ground singlet state has the stable C,, structure, 3 (see Scheme 2), with two different bonds: axial and equatorial (see Table 1 and Fig.1). These results are in agreement with previous cal- culation~,'~~~~~~~experimental data27,28 and with Gillespie's VSEPR theory.29 FL 49 c'tv Scheme 2 Calculated vibrational frequencies and assignments for 3 are given in Table 2 and compared with experimental data.28 The agreement between calculated and experimental fre-quencies is satisfactory. Significant differences are observed for o2and w6, both of which are related to the stretching of axial bonds. The disagreement seems to be due to the harmo- nic approximation, the number of basis functions and the effects of correlation. Note that the calculations predict that Table 1 Total energies (EJE,) relative energies (AElkcal mol- I), number of imaginary frequencies (I.) and values of the imaginary fre- quencies (o/cm-') calculated for structures 3-8 at the DZP/SCF level E, AE 2 37 c2v -856.472 85 0 0 4, c4v -856.462 10 6.7 1 146.8 5, c, -856.409 87 39.5 1 295.1 69 c3v -856.408 92 40.1 2 1 8 1.2( E) 7,Td -856.251 59 138.0 3 72.0(T2)87 D4h -856.378 04 59.5 1 866.3 J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 1.578 (1.638) (1.620) jF (lg,hJlq 108.1 (108.3)i F 1.514 (1.570)F 3,c2v (1.597) F (1.635) 1354 1.565 ( 1.657) i 1.653) 5, c, F 7, Td Fig. 1 Geometrical parameters of structures 3-8 calculated at DZP and DZP/MP2 (numbers in parentheses) levels. Bond lengths are given in A, bond angles in degrees.Structure 3 corresponds to a minimum (i= 0), 4, 5 and 8 to transition states (A = l), and 6 and 7 to critical points with A = 2 and 3, respectively, at the DZP level. Structures 3, 6, 7 and 8 correspond to minima (A = 0), and 4 and 5 correspond to transition states (A = 1) at the DZP/MP2 level. the co, mode is a mixture of equatorial and axial ligand dis- placements, as shown in Scheme 2, which is consistent with the assumption28 that separate modes corresponding to dis- placement of only equatorial or axial ligands do not exist. Structure 4 (C4,) corresponds to a transition state on the ClF4+PES for the Berry pseudo-rotation', with a calculated activation barrier of 6.7 kcal mol-'. This mechanism was first propo~ed'~ to explain the facile interconversion of penta- coordinated phosphoranes.' The validity of the Berry 5316,41 process has been demonstrated by X-ray structure-correlation for a large variety of five-coordinated phos-phor~~~~ (pentacoordinatedand d8-metal compo~nds~~,~~ Table 2 Vibrational assignment for ClF,' in C,, structure 3 frequency/cm-symmetry assignment exp." DZP DZP/MP2 o1 v (sym ClF, eq) 800 925 802 w, w3 v (sym ClF, ax) 6 (sciss ClF, eq) 571 510 695 585 565 497 w4 6 (sciss ClF, ax) 237 215 154 A, o5 ClF, twist 475 554 469 B1 o, w6 ClF, rocking v (asym ClF, ax) 795 537 937 611 834 518 B, O8 wg (asym C1F2 eq)6 (sciss CIF, ax)' 829 385 938 454 834 361 a Ref.28. * Out of plane. species have structures which range from trigonal bipyrami- dal to square pyramidal along the expected Berry pseudo- rotation pathway) as well as by calculations of the minimum-energy reaction paths and TSs of the topomeriza- tion of PH5,45 SiH,- 46 and SF4.47-49a It is also analogous to Lipscomb's DSD for B5H,'-.The calculated activation barrier for the Berry pseudo- rotation is consistent with the experimental observationz7 of rapid ligand exchange. Unfortunately, Christe and Sa~odny~~were not able to decrease the temperature of the ClF5-HF-SbF, mixture sufficiently (because of the freezing point of HF) to observe the fine structure of the "F NMR spectra in the absence of ligand exchange and thus obtain a value for the activation barrier. However, the similarity of the NMR spectrum behaviour for ClF4+z7 and sulfurane SF, 59,51 suggests that their activation barriers are compara- ble.The activation barrier deduced for the ligand exchange in SF, ranges from 4.5 to 16 kcal mol-' from various experi- ment~."-~~ predict values of l2,* Ab initio calculations48~49 and 10.6 kcal mol- '.49 All of these numbers are close to the value obtained for ClF4+, namely 6.7 kcal moi-'. Thus it seems likely that the ligand exchange in ClF4+ occurs intra- molecularly by the Berry mechanism. The Berry pseudo-rotation 3a 4 36 occurs along a gra- dient line of TS 4 that is tangential to the transition vector and enters minimum 3 tangential to the Hessian eigenvector with the smallest eigenvalue, which has A, symmetry.The C,, symmetry group of the TS 4 transition vector is con- served along the whole Berry pseudorotation pathway 3a s 4 +36 (Scheme 2). 5. 'Lever' Mechanism of Pseudo-rotation The Berry pseudo-rotation (Scheme 2) does not lead to com- plete fluorine scrambling, whereas the 'lever' mechanism (Scheme 3) proposed55 for SF, would result in sequential axial-equatorial permutations, 3a e5 e3c. The degree of scrambling can actually be made more precise in terms of the effective molecular symmetry group, as we discuss at the end of this section. The 'lever' mechanism is similar to the 'turnstile' pseudo-rotation in phosphoranes' and pro- 5916 ceeds via transition state 5 which has C, symmetry. Previous extended Hiickel and CND0/2 calculation^^^ of the lever pathway for SF, suggest that this mechanism has a slightly higher (about 2-10 kcal mol-') activation barrier than the Berry process, and under some conditions it might compete with Berry pseudo-rotation.Of course, these are only qualit- ative calculations. As far as we know the C, structure, 5, for SF, is the true transition structure for the lever mechanism and has been .~~found by Schleyer et ~1Our calculations predict that struc- ture 5 (C,)also corresponds to a true transition state (A = 1) for ClF4+ but with a rather high activation barrier of 39.5 kcal mol-'. Thus it appears that the lever mechanism cannot compete with the Berry process in this system. However, the lever rearrangement has a very interesting system of gradient-line reaction pathways; Scheme 4 shows one of four possible F' 7F4 F4ai 7.F4 Lcl,\\'' F3 -F'-ClLF3 axI F2 F2 % c,v 5, C, 3c, c,, Scheme 3.Mirror plane through 1 and 4 1834 1 1 23 3 513, c, (h=1) ,3c, c, (h= 0) 2 2 3 I 3a, C2, (h= 0) 6, C2, (h= 2) 54 c, (h= 1) 2 2I ­-1 4-1 /”\ I 31 3 5c, c, (h= 1) 3d, c,, (h= 0) Scheme 4 lever pathways from minimum 3a. For convenience, struc- tures 3, 5 and 6 in Scheme 4 are depicted with the Cl-F4 equatorial bond perpendicular to the page. The system cir- cumnavigates a rather flat hill, the top of which corresponds to C,, structure 6 with A = 2 (see Fig. 1 and Table l), and can return to starting point 3a via three equivalent steps.The gradient-line pathways along Hessian eigenvectors corre-sponding to the imaginary frequencies of structure 6 lead either to minimum 3 (C,,) or to transition state 5 (C,). The complete scrambling scheme taking into account all four dis- tinct lever pathways for each minimum, 3, is represented by the octahedral reaction graph in Fig. 2. Each vertex of the octahedron denotes one of the six ver- sions of minimum 3 that can interconvert when the lever 1 I 4-3I 1 2 I 3a, C2“(1= 1) 4 (h= 0) J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 rearrangement is the only ‘fea~ible”~ mechanism. The solid lines connecting the two vertices designate the lever path- ways. The crosses at the midpoint of these lines denote the 12 versions of TS 5 (C,)that are involved.The effective molecular symmetry (MS) group contains 24 operations for the lever mechanism, giving half the complete nuclear permutation inversion (CNPI) Hence the reaction graph in Fig. 2 contains half of the 12 distinct ver- sions of minimum 3 and half of the 24 distinct versions of TS SS8We have not attempted to represent any further connec- tions with the higher-index saddles 6 and 7in this graph. F 69, c,, (1= 2) 7,Td(1= 2) Although the Berry mechanism on its own connects only pairs of versions of the C,, minimum, if both the Berry and lever mechanism are feasible then the effective MS group becomes the CNPI group. In this case all 12 distinct C,, minima can interconvert. All of these MS group character- isations were readily carried out with a recently developed computer pr~gram.’~ 6.Inversion Mechanism According to our ab initio calculations planar structure 8 (D4h) is a true TS (A = 1) at the DZP level for the inversion process with a calculated activation barrier of 59.5 kcal mol-’. The corresponding barrier for SF, is calculated to be 108.8 kcal mol-1.49” The gradient line along which the inver- sion reaction occurs emanates from TS 8 tangential to the eigenvector corresponding to the transition vector (see Scheme 5) and enters transition state 4 tangential to the eigenvector corresponding to the fourth smallest positive eigenvalue. It is important to emphasise that the C,, sym-metry group of the transition vector of TS 8 is conserved along this pathway from 4a to 4b via 8 according to our defi- nition.This gradient line connects three successive TSs ; however, there is no contradiction between the proposed inversion path and the Fernandez-Sinanoglu theorem,60 which states that a gradient line passing through a minimum cannot cross two successive saddle points. In our case the whole reaction path consists of three different gradient lines, while the Fernandez-Sinanoglu theorem holds only for a reaction path consisting of one gradient line. The complete gradient-line reaction path of Scheme 6 at the DZP level consists of three different gradient lines. Two of them are equivalent (GL1 and GL1’) and correspond to Berry pseudo-rotations 3ae4ae36 and 3f= 4b s3g passing through transition states 4a and 4b, respectively.The 1) Fig. 2 Schematic representation of the reaction graph for the gradient-line reaction path for the lever mechanism ligand exchange in CIF,+. Filled circles and crosses denote minima 3a-g (C2,)and transition states 5 (Cs), respectively. The solid lines designate the lever reaction pathways. 8,D,, (A= 1) Scheme 5 4b, C,, (A= 1) J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 1835 F’ F‘ F3 transition vector F’ F3 third gradient line (GL2) connects one transition state 4a to another 46 via the third TS, 8. Taking EF24 steps with starting displacements along one of the directions defined by the Hessian eigenvector of TS 8 corresponding to the unique imaginary frequency, we calcu-lated the pathway and energy profile from TS 8 to TS 4a.The pathway is only an approximate gradient line36 since the EF steps are not strictly parallel to the gradient vector.39 However, it is probably close enough to GL2 for our pur-poses and has the same symmetry properties, as corroborated by the evolution of the Hessian eigenvectors corresponding to the lowest Hessian eigenvalues along the pathway (Fig.3). The evolution of the five smallest Hessian eigenvalues along this path is shown in Fig. 4. The TS 8 transition vector transforms smoothly into the Hessian eigenvector of transition state 4a with A, symmetry, which has the fourth largest positive eigenvalue. The TS 4u transition vector (for Berry pseudo-rotation, see Scheme 2) is perpendicular to it, so that the gradient-line pathway changes direction in configuration space. In other words, the gradient-line path changes from GL2 to GL1 (or GLl’). Furthermore, from point 4a (or 44, there are two equivalent paths along both parts of GL1 (or GL1’) to minima 3a and 3b (or 3fand 3g).Of course, the total energy of the system decreases along the whole of the gradient-line reaction path (see Fig. 3). Note that on GL2 (from both sides of TS 8) there are two points B and B‘ (see Fig. 3 and 4) where a Hessian eigenvalue changes sign from plus to minus. These are ‘branching’61 points where the minimum-energy reaction paths and the symmetry is broken,66 i.e. the four-fold axis changes to two-fold. However, such points are not sta-tionary points, because VE does not vanish.Consequently, the minimum-energy pathway67-70 might appear to violate Pearson’s6 and Pechukas’’ theorems, except that the latter should be applied only to steepest-descent paths. The system cannot change its direction of motion at the branching points and by our definition the gradient-line reaction path con-tinues to follow GL2 and hence cannot change the point-I \\-856 4---856.41.>c -856.44 -856.41 r------h+-856.42. ‘\Y \-856 43. -856 44-\ -856 45 -a-856461 , , ‘\ /4’ c4v{ *a, -856 47 0 2 4 6 8 101214 . steps transition vector Fig. 3 Schematic three-dimensional representation of the ClF,+ PES (bottom) (no attempt has been made to show the branching points), energy profile (top) and evolution of two Hessian eigen-vectors along the gradient line from TS 8 (D4h)to TS 4a (C4J On the left is the transition vector for TS 4 which correlates with the smallest positive eigenvalue of TS 8; on the right is the transition vector for TS 8 which correlates with the fourth smallest positive eigenvalue of TS 4.0.41 a-?I9 -0.2-/ bifurcation pointal .-0 Q, -0.4-C .-cn8 -0.6-,iI -1.0 ! , 0 2 4 6 8 10 12 14 16 steps Fig. 4 Evolution of the five lowest eigenvalues of the projected Hessian (non-mass-weighted) along the approximate DZP/SCF gra-dient line path from TS 8 (D4h) to TS 4a (C4v),as determined by overlap of the corresponding Hessian eigenvectors. The steps corre-spond to the energy profile in Fig.3. group symmetry. Although a displacement in the direction corresponding to the new negative curvature would lead to a further decrease in energy, such steps are not taken because the gradient has no component in this direction. Thus, at points B and B' the gradient-line path deviates from the bifurcating minimum-energy paths which follow the valley bottoms, rather than moving along the ridge,39 and avoid transition-state structures 4a and 46. On the pathway 4aeSe46 the reaction follows one gra- dient line (GL2) which conserves C,, symmetry. Then, at point 4a (or 46) corresponding to the other transition state (for Berry pseudo-rotation), the pathway follows another gra- dient line (GL1 or GL1') and descends to minimum 3a or 3b (3f or 3g).In this case, we should apply Pearson's and Pechukas' theorems separately to the three gradient lines, GL1, GL1' and GL2, whose symmetry properties are differ- ent, and thus no contradiction arises. The schematic three-dimensional shape of the ClF4+ PES is depicted in Fig. 3. The main feature of this PES is that GL2, which connects TS 4a to the second saddle point 46 via saddle point 8, does not lead to any of the minima 3a-g directly. These minima are interconnected by GL1 or GL1' passing through saddle points 4a or 46, respectively. There- fore, by our definition the complete gradient-line reaction pathway consists of the three gradient lines GL1, GLl', and GL2. During the course of the reaction in Scheme 6, the scheme first moves along GL1, then at point 4a changes direction to GL2, and moves along GL2 to TS 46 via TS 8.Finally, the system can descend either part of GL1' to minimum 3for 3g. The observed topology of the ClF,+ PES in the inversion region may be quite common in organic, inorganic and other reactions. For example, the rearrangement of cyclo-octatetraene seems to follow a reaction pathway similar to that in Scheme 2. The reason for this is very simple: the gra- dient line emanating from the D8h transition structure along the single imaginary mode, as reported by Hrovat and B~rden,~'has B,, symmetry and should lead to the planar D4h structure. The same is true also for the 1,3 H shift from nitrogen to oxygen in sulfamic acid in the rearrangement reaction from the neutral (H,N-S0,OH) to the zwitterionic (H,H+-SO,-) form.72 The high activation barrier of the ClF, inversion reaction + suggests that derivatives might be obtained in an optically active form similar to cyclic ~ulfuranes.~~ Furthermore, the synthesis of a stable 10-1-4 periodonium ion by Dess and Martin7, supports this assumption.7. DZP/MP2 Calculations We also performed DZP/MP2 calculations (see Table 3 and Fig. 1) for structures >S. The agreement between experimen- Table 3 Total energies (EJE,), relative energies (AElkcal mol- '), number of imaginary frequencies (I)and values of the imaginary fre- quencies (w/cm-') calculated for structures 3-8 at the DZP/MP2 level reference E, AE il o/i weight" (%) 3, C," -857.521 33 0 0 90 4, C4" -857.5 16 34 3.1 1 86.6 89 5, c, -857.498 55 14.3 1 84.7 88 6, c,, -857.39451 79.6 0 88 7,Td -857.481 54 25.0 0 84 8, D,, -857.54708 -16.2 O 72 The reference weight is the contribution of the ground-state con- figuration to the perturbed wavefuncti~n.~~~~~ J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 tal and theoretical frequencies for structure 3 is improved but at this level of theory structures 8 (D4h), 6 (D3h) and 7 (7'J correspond to minima. Furthermore, structure 8 becomes lower in energy than 3 which is not consistent with experi- mental data27.28 and VSEPR theory.,' These results testify that for structures >8 there are numerous low-lying elec- tronic states, and that application of configuration inter- action might be necessary to obtain the correct results.22 This must be a matter for future investigation. 8.Conclusions There are two different topomerization mechanisms in ClF,+: the Berry and lever pseudo-rotations. At the DZP level the Berry process is lower in energy, although only the lever mechanism leads to significant ligand scrambling. Taking into account the quite low activation barrier calcu- lated for the Berry pseudo-rotation in ClF4+ we expect that the ligand exchange in ClF,+ occurs intramolecularly by this mechanism. Of course, these calculations do not rule out intermolecular ligand exchange, and the surface changes sig-nificantly at the DZP/MP2 level. 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