1117
J. Phys. Chem. 1994,98, 11 17-1 120
CrFh2-: A Stable Dianion in the Gas Phase? M. Hendrickx, M. Ceulemans, and L. G. Vanquickenborne' Department of Chemistry, University of Leuuen, Celestijnenlaan 200F, B-3001 Leuven, Belgium Received: May 17, 1993; In Final Form: October 1 1 , 1993"
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T h e stability of the CrFb2- dianion toward dissociation to CrF5- F- was studied by calculating the potential energy surface both a t the RHF and a t the M C P F correlated level of approximation. For the CrF5- molecule the trigonal bipyramid was calculated to be the most stable structure. Although the energy of CrFb2- is found to be higher than that of the CrFs- F- system, the energy barrier of the reaction path is sufficiently wide and high so as to prevent the dissociation process.
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Introduction The stability of dianions in the gas phase is a subject of continuing debate in the literature. Only recently has experimental evidence on the existence of such molecules been given.' Weikert, Cederbaum, et a1.2suggested that the incorporation of atoms with large electron affinities, combined with the possibility of delocalization of the charge over a large portion of the molecule, should lead to stable molecular dianions. On the basis of ab initio calculations, they proposed BeFd2- is a likely candidate; in a later study, Scheller and C e d e r b a ~ mextended ~.~ the scope of this work by analyzing a number of other closed-shell molecules - = Li, Na, K Y = F, Cl). of the general type X Y J ~(X It is the purpose of the present paper to examine the possible stability of open-shell dianionic structures as free molecules in the gas phase. As a promising molecule, we selected a hexafluorochromate(1V) complex; indeed, it can be argued2 that two conditions have to be met in order to establish the stability of a dianion: stability toward the loss of an electron, and second stability with respect to dissociation. For CrFb2-,the first condition has already been shown to be satisfied by Sakai et al., both at the RHF5and at the CISDQ6level of approximation. The latter calculations, introducing correlation for the valence electrons, were performed by using a model potential to describe the core electrons. These calculations predict the CrF62- complex to be 56 kcal/mol more stable than CrF6-, which in turn is found to be 208 kcal/mol lower in energy than CrF6. In the geometry optimization of these three complexes, octahedral symmetry was preimposed: only the symmetric stretch coordinate was varied during the calculations and the possibility of the loss of a single fluoride ion was not examined. It is the aim of the present contribution to study the stability of the CrF62- dianion with respect to CrF5- and F-.
Method of Calculation In the first stage of our investigation we will examine the equilibrium structures of CrFb2- and CrFS-. This will allow us to gain insight into the different possible dissociation mechanisms for the dianion. It is well-known that for ionic Werner type complexes the different sndm configurations are rather well separated. The restricted HartreeFock (RHF) method may therefore be expected to be a rather reliable guide to locate the different equilibrium structures and to provide an adequate starting point to study the potential energy surface. Due to the large number of geometrical degrees of freedom during the dissociation process, a gradient method was used to optimize the intermediate structures. For the chromium ion a modified Wachters basis (15s,l lp,6d)/[9s,6p,3d] was ~ s e d . ~ J Since for the description of anions the basis sets optimized for @
Abstract published in Advance ACS Abstracts. December 15, 1993.
the neutral atoms are not appropriate, we have used an anion basis (9sSp)/[4s3p] for the F- ligand^.^ All R H F calculations are performed with the TURBOMOLE program.1° To obtain a more reliable estimation of the relative energies of the different species involved, correlation effects were taken into account. For this purpose, we used an atomic natural orbital (ANO) basis for both the chromium" (17~12p9d4f)/[Ss4p3dlfl and fluorineI2 (10~6p3d)/[3~2pld] atoms. With this basis set, we have performed open-shell R H F calculations for the different relevant states. The corresponding orbitals were subsequently used in an MCPF calculation in which the twod valence electrons of the chromium ion and all the p electrons of the F- ligands were correlated. The calculations were carried out at the R H F geometries; this procedure has been shown to produce results which compare quite well with those obtained by a geometry optimization at the correlated 1 e ~ e l . lThe ~ MCPF calculations were performed with the MOLCAS-2 program.I4 To assess the validity of the proposed methodology, two additional sets of calculations were carried out: (i) For the relevant mono- and dianionic species, the geometries were reoptimized a t the MPCF level (within certain preimposed symmetry requirements). (ii) The ability of the present level of theory to reproduce bond dissociation energies was tested for the case of CrF2, where reliable experimental dissociation energies are available: Kent et al.I5 Cr 2F report a value of 227.0 kcal/mol for the CrF2 dissociation. Using the ionic method,I6J7we find an MCPFvalue of 222.6 kcal/mol, which certainly appears to be in satisfactory agreement with the experimental value.
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Results (A) Five- and Six-CoordinatedComplexes. There can be little doubt on the nature of the ground state of CrF62- in an octahedral conformation. As can be deduced from the SuganeTanabe diagrams the lowest term of a d2system is a 3Tl,state, independent of the strength of the ligand field. Optimization of the bond length in the 3Tl,state yields a Cr-F distance of 3.47 au, which is in good agreement with the results obtained in ref 5 and 6. Optimization at the MCPF level hardly changes the picture, yielding a bond distance of 3.48 au. The calculated equilibrium bond distance is somewhat longer than the experimental value of 3.25 au, as determined by X-ray measurements for the embedded crFs2-cluster in the RbzCrF6 crystal.I8 Although the octahedral state is subject to a Jahn-Teller distortion, the corresponding energy splitting can be expected to be small, since it originates from occupation of dr(tzg) orbitals. To have an idea of the stabilization energies involved and guided by the epikernel p r i n ~ i p l e , ~we ~ . optimized ~~ the geometry for trigonal and parent. tetragonal distortions for all states originating from the 3T1g The largest stabilization energy was found for the 3A2g((eg)2) state of the D3d structure and amounted to only 4 kcal/mol at the R H F level.
0022-3654/94/2098-1117$04.50/0 0 1994 American Chemical Society
Hendrickx et al.
1118 The Journal of Physical Chemistry, Vol. 98, No. 4, 1994 TABLE 1: Total Energies and Geometry for the Relevant Conformations in the Dissociation Processs CrFs- (SP) (CrFs-F)2-(TS) CrF62CrF5- (TBP) state (configuration) enerev RHFb
MCFFC
P
Tls(t22)
3A2(b~b2)
%(a2 b2)
3A2f(ert2)
’A2(e2)
3E(ebz)
‘S
-1 640.132 736 -1 641.332 976 -1 641.333 071
-1 640.069 247 -1 641.272 757 -1 641.272 705
-1 640.066 824 -1 641.273 633 -1 641.273 814
-1 540.733 878 -1 541.771 231 -1 541.772 025
-1 540.718 001 -1 541.753 671 -1 541.755 468
-1 540.716 001 -1 541.757 408 -1 541.757 892
-99.438 079 -99.609 152
MCPFd RHF geometry (MCPF) 3.35 (3.38) 3.37 (3.40) 3.28 (3.29) 3.38 3.30 R(Cr-Fa), au 3.35 (3.38) 3.37 (3.40) 3.41 (3.46) 3.45 3.47 (3.48) 3.37 R(Cr-F,), au 3.28 (3.34) 3.25 (3.26) 3.28 (3.29) 3.38 3.31 R(Cr-F,), au 01 a3 6.7 7.3 R(Cr-F1), au 100 (99) 103 (103) 120 107 90 94 B(F,-Cr-F,), deg 103 (103) 100 (99) 90 90 95 90 el(F,-Cr-F,), deg Energies and distances in atomic units. The geometricparameters optimized at the MCPF level are given in parentheses. RHF energies obtained by using the Cr[9s,6p,2d] and F[4s,3p] basis sets. MCPF energies obtained by using the AN0 basis and evaluated at the RHF geometries. MCPF energies obtained at the MCPF-optimized geometries (except at TS). Q)
CrF;
CrF;
TABLE 2 RHF and MCPF Relative Energies (kcal/mol) of the Different Relevant Entities, with the Zero of Energy at the Most Stable Structure (3A2’ of the TBP, plus One Isolated F-)* RHF MCPF MCPF (RHF) (RHF) (MCPF)b CrF$ (’Td 24.6 29.8 30.2 transition states (’A2) 64.5 67.5 68.0 CrFj- + F-
(W
TBP(3A2’;(e”)2) SP(3A2;e2) SP(3E;e1b21)
66.0 0.0 10.0 11.2
67.0 0.0 11.0 8.7
67.4
0.0 10.4 8.8
ThefirstsymboloftheTable headingshowsthelevelofthecalculation, the second symbol (in parentheses) indicates the level at which the optimization was carried out. Except at the transition state.
Figure 1. Qualitative correlation diagram for the different dissociation
paths leading to CrFs- SP and TBP. Symmetry labels refer to the Cb and D3h symmetry, respectively; the labels in parentheses are those for the CZ,symmetry group for which the coordinate systems are denoted at the bottom of the figure. F1 is the leaving ligand; Fa and Fb are the two ligands in the x z plane, F, and Fd are the two ligands in t h e y plane. When the CrF6- entity (in its octahedral Z T ~ground g state) is optimized at the MCPF level, the bond distance is found to be 3.38 au, and the energy is 30.3 kcal/mol higher than the CrF6’ground state. The so-obtained value of the electron affinity of CrF6- can be compared with the previously reported value of 56 kcal/mol.6 While the value obtained at the MCPF level is significantly smaller than in the earlier report, the large positive electron affinity of the octahedral CrF6- entity is confirmed. As for the five-coordinate CrF5- fragment, two possible geometries should be considered: the square pyramid (SP) and the trigonal bipyramid (TBP). There is general agreement in the literature on the ordering of the valence orbitals for ML5 complexes characterized by the latter conformation,21and it is safe to assume that the ground configuration is (e”)2, leading to a 3Az’ground state. At the R H F level, geometry optimization of this state leads to the following bond distances: R,, = 3.41 au and R , = 3.28 au (Table 1). These bonds are shorter than those obtained for the CrF$ molecule as could be expected from the smaller negative charge on CrFs-. The fact that the axial bonds (along t h e y axis in Figure 1) are found to be longer than the equatorial bonds in the xz plane is accounted for by the fact that both occupied antibonding e” orbitals (d, and dyz)are directed toward the axial ligands. Table 1 shows that the MCPF optimization tends to lengthen the bond distances somewhat, especially for the axial bonds.
In the C4”square pyramid, there are two possible configurations for the ground state. Indeed, removal of F1- (leaving atom) along the z axis stabilizes e(dx,,dy,) with respect to bz(dxy), but simultaneous out-of-plane bending of the equatorial ligands destabilizes (dxz,dyz)with respect to d,. Out-of-plane bending tends to reduce the ligand-ligand repulsion, but it also changes the nature of the ligand-(d,,,d,,) interaction from a* into u*. The balance between these different effects will determine the orbital occupation numbers of the ground state of the square pyramid and the extent of out-of-plane bending. As a consequence, in the SP structure, we have two possible ground-state candidates: either e2,3A2;or elbzl,3E.Table 1 shows the results of the geometry optimization for both states. Both structures turn out to be characterized by equatorial out-of-plane bending: for ’A2(e2),the angle Fap-Cr-Fbas equals looo, for 3E(e1b21)the angleequals 103’. In both cases, the equatorial bonds are longer than the apical bond because of the partial u* antibonding character of the former ones. A comparison of the total R H F energies for the different CrFSentities in Table 1 or 2 indicates the TBP to be the most stable conformation by about 10 kcal/mol. The difference between both SP conformations amounts to about 1 kcal/mol. Table 1 shows that the introduction of valence correlation by means of MCPF calculations confirms these conclusions. The MCPF optimizations do not alter the picture to any significant extent. A possible (dynamic) Jahn-Teller effect can be expected to induce only very small energy stabilizations as was verified numerically for the parent hexacoordinated compound. The R H F energy for the F- ground state was calculated at -99.438 079 au; the MCPF energy for F- is -99.609 152 au. Combining these results with the appropriate numbers in Table 1 thus indicates that-at the MCPF as well as at the H a r t r e e F o c k l e ~ e l - c r F 6 ~is-situated higher in energy than all equilibrium geometries of CrFS- F-. More specifically at the H a r t r e e Fock level, CrFs2- is found at 24.6 kcal/mol above the lowest configuration of CrFS-+ F-. It is well-known that theintroduction of electron correlation will tend to stabilize the united entity AB
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The Journal of Physical Chemistry, Vol. 98, No. 4, 1994 1119
CrFs2-: A Stable Dianion in the Gas Phase?
TABLE 3 Correlation Table of the Different States along Two Dissociation Paths from the Octahedron to the TBP and to the S P Symmetry of the Intermediate Structures Was Kept at CzVSymmetry
B
( y z ) bending
I
-
-
i x z ) bending B
9"
%2(xy)ixz 1
~ B , ( Xy ) i y z
Figure 2. Schematic t2, orbital energy (upper part) and 'TI, state energy (lower part) diagrams for the two equivalent dissociation paths, corresponding to F- loss along the z axis (Figure I), accompanied by FaxCr-F, bending in the xz plane (right) or the yz plane (left).
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with respect to the separated entities A B. In the present case however, the introduction of correlation on the bond energy can be expected to be attenuated. Indeed, the AB entity, being a negative dianion, is characterized by a larger bond length and a more diffuse wave function than the separated entities. Therefore, the differential correlation may be expected to be less significant than for neutral entities. By way of comparison, in the BeFd2case, the introduction of correlation did not change the R H F results to any significant extent. In the present case, Tables 1 and 2 show that the MCPF results even increase somewhat the relative stability of the separated entities (from 24.6 kcal/mole a t the R H F level to 29.8 or 30.2 kcal/mol at the MCPF level). We therefore suggest that the dianion is thermodynamically unstable with respect to the loss of one fluoride ligand. This conclusion does not necessarily mean that CrFs2- cannot exist as a stable entity in the gas phase. If it is separated from the dissociation products CrF5- F- by an activation barrier that is sufficiently high and wide, CrFs2- may very well exist as a (meta)-stable species. To verify this, an investigation of reaction paths leading to CrF5- in both conformations was undertaken. (B) Dissociation Path. The dissociation process was studied by using the coordinate driven approach: for several Cr-FI distances the remaining CrF5 entity was optimized. At all stages of the reaction, the equatorial ligands were held in two perpendicular planes, ensuring CzOsymmetry. This restriction does of course not prevent the resulting CrF5- moiety from obtaining either the SP or the TBP structure: a C2" dissociation path incorporates all desired internal degrees of freedom. Within this symmetry the octahedral 3T1, ground state is split in three components 3A2,3 B ~and , 3B2. For symmetry reasons the loss of an F- ligand will give rise to equivalent energy profiles for the )BI and 3B2states. Figure 2 shows how the energy splitting occurs, depending on whether the predominant out-of-plane bending takes place in the xz or in the y z plane. In Table 1, only one of these two equivalent dissociations needs to be taken into account. Table 3 shows the correlation table of the different states along the here-considered dissociation paths. For all states the transition states (TS) are found to be characterized by rather long Cr-FI distances (Table 1). Beyond the TS the energy only very slowly decreases toward the dissociation limit. In this region of the
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potential energy surface the 1/R[(CrFs--F-)] Coulombic repulsion between the two fragments is dominant. The wide barrier which results form this slow decrease, effectively prevents any tunneling from taking place. As shown in Figure 1 and Table 3 the 3A2(b~'b21)transition state correlates with the 3A2(e2)ground state of the square pyramid, but with an excited configuration (e')l"'')l of theTBP. It is therefore not surprising that the CrFs moiety in its 3A2 TS resembles quite well a square pyramid (see Table l ) , with four nearly equatorial bond lengths and bond angles. The 3Bl(a21b21) transition state, on the other hand, correlates directly with the ground state of the TBP, which has been found as the most stable conformation of the CrF5- molecule. Although in the TS for this state the leaving fluoride anion is at a slightly shorter distance from the chromium ion, the remaining CrF5- moiety resembles very well the optimum geometry of the TBP with three nearly equal equatorial bonds and two longer axial bonds. The same results will be obtained for 3B2,but in this case the two axial ligands of the TBP-like structure will be on the x axis (Figure 1). At the R H F level the energies of the TS differ by less than 2 kcal/mol,i.e., 39.9and41.4 kcal/mol(Table2). Thetworelevant dissociation modes are therefore almost equally likely-or unlikely-to occur: in the present case the potential barrier can be expected to be sufficiently high to prevent the dissociation from taking place. Indeed, the calculated activation barrier at this level of approximation amounts to about 40 kcal/mol, which is more than twice the value calculated for the BeFd2- dianion.2 Since the transition states are found at rather large metalligand distances, it is conceivable in principle that the basis set used was not sufficiently diffuse to cover the TS geometries adequately. To check this point, we minimized the geometry of both CrFs2- and the different transition states with a larger basis set: we added a diffuse s function (a = 0.09) and p function (a = 0.04) for the F atoms and a diffuse p function (a = 0.04) and d function (a= 0.08) for the Cr atom. The results were not very different from what we obtained with the standard basis set: the geometrical parameters changed by at most 0.01 au, and the activation barrier for the 3A2reaction path dropped from 39.9 to 39.0 kcal/mol. Similarly, the introduction of electron correlation does not lead to a modification of the picture. From Table 1, we find that the MCPF energies of both CrF& and the transition states are stabilized to approximately the same extent (with respect to the R H F results); the resulting kinetic energy barrier is 37 kcal/mol. Also the position of the TS was found to be rather insensitive to the method of optimization: along several points along the H F reaction path the energies were recalculated at the MCPF level, and the R(Cr-F1) distance of the TS was found to vary by at most 0.1 au. A similar observation was made for the BeF42molecular ions2 From Figure 3, it is clear that the two dissociation paths are energetically very close to each other. Depending on the finer details of the computational method and probably on the amount of correlation included, either 3B1of 3A2may become slightly higher or lower than theother one. Relaxationof the C2"constraint did not lead to a further lowering of the activation energy.
1120 The Journal of Physical Chemistry, Vol. 98, No. 4, 1994
energy barrier-quite similar to the closed-shell structures studied by Cederbaum.24 For CrFb2-, the activation energy at the R H F level amounts to about 40 kcal/mol. The introduction of the valence correlation energy by means of MCPF calculations only slightly affects the activation energy. All these observations indicate that CrF6*- in its open-shell ground state should be regarded as a likely candidate to form a stable dianion in the gas phase.
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Hendrickx et al.
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Acknowledgment. The authors are indebted to L. Cederbaum (University of Heidelberg) for helpful discussions and to the Belgian Government (DPWB) for financial support.
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[Z"
oh
References and Notes
2"
Figure 3. M C P F dissociation energy paths (schematic). The dotted lines show the Coulombic repulsion between two negative point charges.
The general picture emerging from these calculations corresponds to a barrier height of approximately 40 kcal/mol, due to the removal of the leaving ligand, and essentially independent of the two possible concomitant distortions, which are very nearly equivalent in reducing the activation energy. The maxima in Figure 3 do not necessarily have to be seen as the result of an avoided crossing and the concomitant configurational mixing between a repulsive curve (CrF5- F-) and an attractive curve (CrFs2- + F), as suggested in ref 2. Indeed, the predominant configuration of the potential surfaces in Figure 3 remains essentially unchanged along the entire path (both for 3A2and 3B1). The reason the energy drops when F- approaches CrFS- beyond the TS conformation is not so much a configurational changeas the onset ofchemical bonding within theorbitals of the predominant configuration.
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Conclusion In this contribution we have studied the possible existence of stable open-shell dianionic structures. We analyzed the equilibrium structures for the CrFb2- and CrF5- molecules. For the latter ion a TBP structure was found to represent the most stable conformation. A comparison of the total energies showed CrF6*to be less stable than the CrFS- F- system. For the dissociation reaction, the different investigated path ways are found to be characterized by a wide and rather high
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(1) Schauer, S.; Williams, P.; Compton, R. Phys. Rev. Lett. 1990, 65, 625. (2) Weikert, H.-G.; Cederbaum, L.; Tarantelli, F.; Boldyrev, A. Z . Phys. D 1991, 18, 299. (3) Scheller, M. K.; Cederbaum, L. S. J . Phys. B 1992, 25, 2257. (4) Scheller, M. K.; Cederbaum, L. S. J . Chem. Phys., in press. ( 5 ) Sakai, Y.; Miyoshi, E. J. Chem. Phys. 1987,87, 2885. (6) Miyoshi, E.; Sakai, Y.; Murakami, A.; Iwaki, H.; Terashima, H.; Shoda, T.; Kawaguchi, T. J. Chem. Phys. 1988,89,4193. (7) Wachters, A. J. H. J . Chem. Phys. 1970, 53, 1033. (8) Hendrickx, M.; Berghmans, E.; Ceulemans, A.; Vanquickenborne, L. J. Chem. SOC.,Dalton Trans. 1992, 281. (9) Vanquickenborne, L.; Verhulst, J.; Coussens, B.; Hendrickx, M. J . Mol. Struct. (THEOCHEM) 1987, 153, 227. (10) TURBOMOLE, Ahlrichs, R.; Bar, M.; Ehrig, M.; Haser, M.; Horn,
H.; Kolmel, C.; Quantum Chemistry Group, University of Karlsruhe,Gennany. (1 1) Pierloot, K.; Dumez, B.; Widmark, P.-0.; Roos,B. O., unpublished results. (12) Widmark, P.-0.; Malmqvist, P.-A.; Roos, B. Theor. Chim. Acta 1990, 77, 291. (13) Sodupe, M.; Bauschlicher, C. Jr.; Langhoff, S.;Partridge, H. J. Phys. Chem. 1992, 96, 21 18. (14) MOLCAS-2, Anderson, K.; Fulscher, M.; Lindh, R.; Malmqvist,
P.-A.; Olsen, J.; Roos,B.; Sadlej, A. Department of Theoretical Chemistry, University of Lund, Sweden. (15) Kent, R. A,; Margrave, J. L. J . Am. Chem. SOC.1965, 87, 3582. (16) Partridge, H.; Bauschlicher, C. W.; Sodupe, M.; Langhoff, S. R. Chem. Phys. Lettt. 1992, 195, 200. (17) Bauschlicher, C. W.; Partridge, H.; Sodupe, M.; Langhoff, S. R. J. Phys. Chem. 1992, 96, 9259. (18) Bode, H.; Voss, E. Z. Anorg. Chem. 1956, 286, 36. (19) Ceulemans, A.; Vanquickenborne, L. Strucr. Bonding 1989,71,125. (20) Frey, R. F.; Davidson, E. R. In Advances in Molecular Electronic Structure Theory; JAI Press: London, 1990; Vol. I, 213-262. (21) Jarid, A,; Aaid, M.; Legoux, Y.; Merini, J.; Loudet, M.; Gonbeau, D.; Pfister-Guillouzo, G. Chem. Phys. 1991, 150, 53.
