J. Phys. Chem. 1994,98, 6445-6451
6445
CloseBoranes, Xarboranes, and -Silaboranes: A Topographical Study Using Electron Density and Molecular Electrostatic Potential? Eluvathingal D. Jemmis' and G. Subramanian School of Chemistry, University of Hyderabad, Hyderabad 500 134, India
Indira H. Srivastava and Shridhar R. Gadre* Department of Chemistry, University of Poona, Pune 41 1 007, India Received: November 9, 1993; In Final Form: March 4, 1994"
A topographical study on a series of n-vertex (n = 5-7) closo-boranes, closo-carboranes, and closo-silaboranes using electron density (ED) and molecular electrostatic potential (MESP) reveals many interesting features on the molecular structure and reactivity. No B-B bond critical points exist in the equatorial plane for the five vertex cages. The charge density is found to be more on the exterior of the molecule than on the interior, However, all borane anions exhibit localization of ED in the centroid of the cage. The bond polarities are reversed while going from closo-carboranes to closo-silaboranes. But, the reactivity pattern toward electrophiles essentially parallels in both cases. Among borane anions, B5HsZ-is more prone toward electrophilic attack, Using MESP as a tool, the positional isomer stabilities of various closo-heteroboranes are predicted and found to agree well with experimental results and other theoretical models.
Introduction Understanding the molecular structure and the nature of bonding in boranes has always been a challenge to chemists since boranes generally exhibit an electron deficient character.lP2 It took a long time to establish the bonding pattern in the prototypical diborane.2 Styx formalism,3 Wade's rule: and Williams' classifications of boron hydrides were some of the concepts used in early days to assign structures in these unusual molecules. Later, tensor surface harmonics by Stone6and the six interstitial electron rules for nido- and closo-boranes and -heteroboranes7 led to the understanding on the type of interactions involved in these deltahedral clusters. The bonding topography of boranes and closo-boranes has been investigated via graph-theoretical analysis88 and a correlation made between delocalization,number of vertices, and skeleton electrons in the polyhedral molecules. Though all the above concepts provide a qualitative picture of the bonding patterns and the distribution of electrons and its topography, these molecules are not well understood in rigorous terms. Takano et a1.8b have used the concept of spherical charge analysis of Iwatascto provide a qualitative description of the electron density distribution in closo-boranes and closo-carboranes. A more detailed study on the structure and reactivity patterns of boranes and carboranes has recently been reported by Bader and Legarea by deriving the charge density ( p ( i ) ) topography using the theory of atoms in molecules. Such a theory has emerged to be a useful tool in determining the chemical properties of molecules.10a The molecular electrostatic potential (MESP), V ( i ) topography, on the other hand, has not been so extensively investigated, though a beginning has reecently been made by Gadre et al." This scalar field, by virtue of its attaining negative as well as positive features (due to negative electronic contribution and positive nuclear contribution) is capable of revealing more interesting topographical characteristics.Iz In the present work, we bring out the topographical characteristics of both p ( i ) and V ( i )on a series of n-vertex ( n = 5-7) closo-boranes and closoheteroboranes(closo-carboranesand closo-silaboranes). Possible reactive sites for all the molecules are studied, and V ( i )on the van der Waals (vdW) surface is employed to predict the positional isomer stabilities in closo-heteroboranes, f
0
Dedicated to Prof. C. N. R. Rao on his 60th birthday. Abstract published in Advance ACS Abstracts, May 15, 1994.
0022-3654/94/2098-6445%04.50/0
Method of Calculation All the structures considered in this study were optimized at the HF/6-31GS level13using the G a ~ s s i a n 9 program 0~~ package. Single point calculations employing better quality TZP basis15 were performred on these structures using the ab initio molecular package INDMOL16 on a parallel machine PARAM.17 The molecular wave functions thus generated were used for the study of the topographical features such as the critical points (CP's); viz., the point at which the gradient of the scalar field is zero."Jc A topographical analysis of both the charge density p ( i ) and V ( i ) of the moleculeshas been carried out using the program developed by Gadre et al." The molecules considered in our study are BsHs2-;B6Hs2-;B T H ~ ~1,-~; - A ~ B ~lr6-A2B4H6; Hs; and 1,7-AzBsH7 (A = C or Si), as shown in Figure 1.
Results and Discussion Our analysis is divided into three parts. First we explain the topographical features of p ( i ) and V ( i ) exhibited by five-, six-, and seven-vertex closo-boranes and closo-heteroboranes. Next we study the reactivity pattern. Finally, we use V(i)to predict the positional isomer stabilities in closo-heteroboranes and compare it with various models reported previously. TopographicalCharacteristics of p ( r ) and V(r)for Five-Vertex Polyhedra. The topographical features exhibited by BsHs*-, 1,5CZB~HS, and 1,5-SizB3H~are considered among the five-vertex polyhedra possessing a trigonal bipyramidal (tbp) arrangement (Figure 1). In this series,only 1,5-CzB~Hshas been characterized by electron diffraction,ls and the molecule is said to be electron precise with no bonding between B-B in the equatorial plane.9 The p ( i ) topography for all three molecules shows a (3, -1) bond CP between the A-E bond (throughout the discussion A and E represent the axial and equatorial atoms, respectively), whereas the E-E bonds show a (3, +1) CP, indicating that they are not bonded.l o This general feature observed for the five-vertex cage is in agreement with that reported by Bader et ala9for 1,5-C2B3H5 and to that of Takano et al.,8b who observe a very small electron density between the E-E bonds in B5Hs2-. The p ( i ) value at the (3, -1) bond CP (Table l), is 0.169 au for 1,5-C2B3H~,which is higher than the corresponding values in either BsHs2- (0.137 au) or 1,5-Si2B3Hs (0.102 au). This indicates a higher charge concentration between A (C) and E (B) and hence a stronger 0 1994 American Chemical Society
6446 The Journal of Physical Chemistry. Vol. 98. No. 26, 1994
B,H+
1.5
- c2BsHs
1.5 - Si2BsHs
1.6 - C2BJls
1.7 - CZBSH?
1.6 - SizBsls
Structures of closo-boranes, closo-carboranes, and clososilaboranes. Hydrogens are omitted for clarity.
Figure 1.
TABLE 1: Topogrnpbical Features in p ( i ) (nu) for Five-Vertex Deltahedmn
Q d Pb A BsH~'-(TotalEnergy = -126.106 50 au) A-E (3,-l) 3.177 0.254 0.137 0.0 E-E (3.+1) 3.541 0.0 0.080 0.0 A-H (3,-1) 2.308 0.0 0.139 0.342 E-H (3,-l) 2.319 0.0 0.151 -0.005 1,5-CzB3Hs (Total Energy = -152.728 08 au) A-E (3,-l) 2.939 0.150 0.169 -0.523 E-E (3,+1) 3.564 -0.187 0.101 0.0 A-H (3,-1) 2.020 0.0 0.294 -0.277 E-H (3,-1) 2.232 0.0 0.182 0.169 I J - S ~ B ~ H(Total J Energy = 454.716 50 au) A-E (3.~1) 3.799 0.514 0.102 0.116 L E (3,+1) 4.783 -0.275 0.048 0.0 A-H (3,-1) 2.778 0.0 0.117 0.048 0.0 0.181 0.171 E-H (3,-l) 2.236 a A, axial atom; E, quatorial atom; H, exo-hydrogenbonded to A, E. Q,quilibrium bond distancc; d, deviation of CP from R. (positive value indicates the convex nature of the bond, and negative value, the concave nature); pb. functionvalue at the density critical point; A, shift of the CP from the geometrical center of two nuclei (positive value indicates the CP to be shifted toward A or E far A-H and E H bonds and toward A for A-E bonds; the density values of the (3,+3) cage critical point for BJHS~-, CzBlH~,andSizB3H5are0.068.0.091, and 0.039 au, respectively). bonds
type
A-E bond in 1,5-C2B3Hsthan the corresponding A-E bonds in B5HSz-or 1,5-Si2B3Hs(Table I). The shift in the bond CP (A in Table 1) from the midpoint of the line joining the two nuclei provides a quantitative measure of the bond polarity.l".b The larger the shift, the more polar is the bond. The (3, -1) bond CP of the A-H bond is closer to A in BrHs" and 1,5-SizB3HS, whereas, in I,5-C2B3H5,the CP is closer to H, indicating a hydridic nature of the H in the former two cases (Table I). The E-H bonds also have a polarity in WCzB3H~and1,5-Si2B1Hs,withtheH bearingaslight negative charge (Table I). On the other hand, the E-H bonds in B5H5zare seen to he homopolar, in agreement with Takano et aLSbThe A-EbondCPin I,5-C2B3H5isshiftedtowardE(boron)andthat in 1,5-SizB3Hs toward A (silicon), indicating a transfer of
Jemmis et al. electronic charge density from boron to carbon in the former9 and from silicon to boron in the latter. Yet another parameter (d)that has been derived via the p(i) topographyshedslighton thebent natureofthe A-Ebonds.This is equal to the deviation (Table I ) of the bond CP from the interatomic connection line.1° As seen in Table I, the deviation ismaximum for the A-Ebondin 1,5-SizB3H5,followed by B5Hs2-, and is the least in 1,S-CzB3H5. The larger convexity of 0.5 I4 au may be attributed to the more diffuse nature of the p-orbital of Si as compared to the p.-orbital of B lying in the equatorial plane. Further, such a bent bond is highly strained (this can he compared with the bent bond of cycl~propane)'~ and is expected to be less stable. This is in agreement with the lower stability of the 1,s isomer as compared to the 2.3- and I,Z-SizB,H5 isomers." On the other hand, carbon with a low d value (0.15 au,-Table 1) hasstrain freeA-Ebonds (thep-orbitalsoncarbon are less diffuse), which accounts for the preference of the 1,s isomer over 1,2- and 2,3-C2B3Hsisomers." Thus this parameter is seen to correlate well with the overlap argument given by Jemmis"Jo for the reversal in trends in the relative stabilities of the positional isomers of carboranes and silaboranes based on five-vertex cages. Thep(i) topographicalstudydoesnotdirectlyrevealanyregion of localization of the charge density, whereas the MESP topographical investigation reveals more transparently the region of electron localization in terms of the (3. +3) CP's (minima). Parts a< of Figure 2 show the V(i) characteristics on the vdW surface21 in the fivevertex cage. The program used to visualize this MESP on the vdW surface was developed by Gadre and Taspa:2 on a Silicon Graphics Iris4D/ZO workstation. In all the figures, thedeep bluecolorrepresents the more negativepotential, which progressively changes through green to red as the MESP value increases. BsHsz-,being an anion,23is enclosed in a sheath of negative potential (Figure Za). However, the apical region has more negative potential than the equatorial plane (Figure Za), indicating localization of charge on the apex rather than in the equatorial plane. This observation is in accord with that pointed out by Takano et a l j b and the classical representation of diaxial borate anions. The MESP value is 4 . 3 9 8 au (Table 2) for the minima lying in the exterior of the A-E bond (edge) and slightly less (-0.389 au) for the minima lying in the exterior of the E-A-E bond (face). These minima on the cap surface, inB5HS2-,areconnectedbyagirdleof (3,+l)and(3,-1)saddles in the equatorial plane. In 1,5-Si2B3H5(Figure Zc) and 1.5C2B3Hs(Figure Zb), the (3, +3) CP are found to he localized in the exterior of the edge and not on the exterior of the face, a distinguishing feature between the anion and neutral molecules. The V(i) values at the minima are considerably less for 1.5Si2B3H5(4.013 au) and I,S-CZB~H~ (4.008 au) as compared to those for B5H52-(Table 2). Further, from the MESP plot on the vdW surface of 1,S-CzB3H5and 1,5-SizB3H5(Figure Zb,c), it is observed that the blue region of the more negative potential is seen to be closer to the equatorial plane than to the apical region. These localized regions (minima) serve as potential sites for electrophilic attack. Accordingly, the preferred direction of electrophilic attack would be along the A-E bond in BsHs2-, 1.S-C2B3H5. and 1,5-SizB3H5. Moreover, since the negative potential is seen to he localized in the basins of boron rather than on carbon or silicon in 1,S-CzB3H5and 1,5-Si2B3H5,the electrophilic attack should be more prone in this site. This observation for 1,5-C2B3Hsisnotinagreementwith that reported by Bader and L e g a ~ e who , ~ predict the electrophilic attack to occur at carbon and in the facial direction in 1,5-CzB3H5. Our results can be correlated with experimental observation, in that the hydrogen bonded to boron is replaced by deuterium when treated with BZDsJ4 Further evidence can also be obtained from the dehydrocoupling reaction of 1.5-C2B3H5 which gives 22'[Ir5-C2B3H5]z, the coupled cage product, in excellent yields.25
The Journal of Physical Chemistry, Vol. 98. No. 26, 1994 6441
Topographical Study of Various Boranes
TABLE 2: V(FJValues (nu) at the (3,+3) CP iu the Exterior of the Edge and Cage Centroid for ,Vertex Cages0
3 . 1 B"H"2.
4.398 (4.389) [4).102] 4.007 10.4521
CzB*zHa SizB-zH.
n=6
n=5
3.013'
[0.27 I ]'
n=7 4.355
-X-
(4.377) [4.0621
-X-
[4).071] 4,017 10.4I9lc
-X-
10.4481 a.020' (0.3621
* Valuer m parentheses arc V ( i )O ~ S C N M J on the exterior of the face
Values in squarc brackets arc the (3.+31 cage critical points -a- doer noi correspond to a minimum. e Corrcdpsondr io a (3.-Il CP.
TABLE 3 Topographical Features in p(FJ (nu) for Six-Vertex Deltabedra' bonds type R. d Pb BsHk (Total Energy = -151.491 30 au) A-E
&I)
E-E A-H
(?.-I)
E-H
A-E E-E A-H
E-H
L
A-E E-E
A-H E-H
(3,-l) @-I)
3.286 3.286 2.304 2.304
0.0 0.0 0.0
0.126 0.126 0.150
0.0
0.150
A 0.0
0.0 0.192 0.192
I,6-CzB.H6 (Total Energy = -177.992 54 au) 3.059 0.050 0.144 3.229 0.0 0.129 2.024 0.0 0.298 (3,-1) 2.221 0.0 0.182 1.6-SizBB6 (Total Energy = 480.032 40 au) @-I) 3.742 0.190 0.096 0.0 0.107 &I) 3.568 2.750 0.0 0.122 (&I) 0.0 0.179 (3,-l) 2.232 (3,-1)
(%+I) (3,-i)
4.551 0.0
4.293 0. I69 0.449 0.0
0.042 0.167
a A, axial atom; E, equatorial atom; H, ex+hydrogen bonded to A, E. R.,equilibrinmbonddistance;d, deviationofCPfromQ(positiveva1ue indicates the convex nature of the bond, and negative value, the wncave nature);pb function value at the density critical point; A,shift of the CP from the geometrical center of two nuclei (positive value indicatev the CP to be shifted toward A or E for A-H and E-H bonds and toward A for A-E bonds. The density values of the (3,+3) cage critical p i n t for BsHs", CzB& and SizB4H6are 0.063.0.080. and 0.046, respectively).
I . . ..
.-,..
l l
\",top). I.S-CzB,Hs (b, middle), and I.S-SizB,Hs (c, bottom). The orientation of the molecules are as shown in Figure I . The MESP values, color coded, are given adjacent to each figure. Dccp blue wlor indicates the region of more negative potential, and red, the least negative (positive MESP value in the case of neutral molecules). L 1
* r."."
"
This reaction, mediated througha metalcatalyst (PtBrz), involves the electrophilic attack of the metal on boron and not on carbon, clearly supporting our result and not that of Bader and Legare.9 The reason why carbon is not subject to electrophilic attack has already been pointed out clearly by Onak.'6 The MESP value at the (3, +3) CP (Table 2) suggests that BrHsz-and 1,5-CzB3Hr
are respectively the most and the least susceptible to electrophilic attack among the five-vertex deltahedra studied here. In V(i) topography, a negative valued ( 4 , 1 0 1 au) minimum (Table 2 ) is observed in the cage centroid for B5HrL, indicating a "percolation" of charge inside the cage. This is a rather rare phenomenon and has been noticed to occur in the cage center of decavanadate anion.z7 This feature could not be Observed by the spherical charge analysis which showedsb "the centroid of the cagetobeelectronically empty". In 1,5-CzB3H~,thereisapositive valued (0.452au) (3,+3) CPin thecagecentroidandinSizB3Hs a (3, -1) CP in the cage centroid with the V(i) value of 0.271 au (Table 2). The V(i) values at the (3, +3) CP and in the cage centroid (Table 2). indicate that the electronic contribution to V(i) is higher on the exterior of the.cage than on the inside. Topographical Characteristics of p(FJ.and V(FJin Six-Vertex Polyhedra. The six-vertex polyhedra studied in the present work includeB6H62,z81,6-C2B4H6,'*and 1,6-SizB4H6.z9Among these, only 1,6-SizB4H6has not been observed experimentally. Due to theoctahedralsymmetry in BsHsz-, theEEbondsareequivalent to the A-E bonds. In the p(i) topography, a (3, -1) bond CP is observed between the A-H, E-H, and A-E bonds in all three structures (Table 3). The E E b o n d in 1.6-CzB4Haexhibitsa (3, + 1 ) CP, indicating a lack of bonding between E B , whereas, in 1,6-SizB4H6,the same bond shows the bonding signature of a (3, -1) CP (Table 3). On the other hand, Bader and Legare have characterized the E-E bonds in 1.6-CzB4H6 by a (3, -1) bond CP.9 Though the results obtained by us should be more reliable because of the TZP quality of our basis set, they fall in a grey area, warranting a closer examination of the correlation of (3, -1) CP with the existence of a chemical bond for molecular
6448
The Journal of Physical Chemistry. Vol. 98, No. 26. 1994
systems. This is more so baause lr6-CzB4H6has been characterized by electron diffraction studies, and the structure assigned apparently has a 5 B bond. Further, the B-B distance (3.229 au-Table 3) in I,6-CzB4H6 falls within the range of normal single bond distance. The important aspect to note is that for a classical 2-2e bond a (3, -1) CP will always be obtained. In practice, one could have bonds of varying strengths. Thus the criterion based on CP should be used carefully, especially in the case of atom pairs bound weakly or involved in highly delocalized structures. A similar situation exists also in 1,7-C2B5H7,which is discussed in the next section. The polarity of the A-H and E-H bonds (Table 3) follows the same pattern as their five vertex counterparts (Table 1). But, the A values are correspondingly smaller in the six-vertex cages, indicating lower bond polarities. The A-E bonds in B6H62-are homopolar, while in 1,6-CzB4H6and 1,6-Si2B4H6they are polar similar to those in their five-vertex cages. The convexities of the A-E bonds (Table 3) are also less, thereby reducing the strain in the six-vertex cage. The six-vertex borane anions exhibit localization of electron density. From the V ( i ) plots textured on the vdW surface (cf. Figure 3a-c) for B6H62-, 1,6-C2B4H6,and 1,6-SizB4H6,respectively, the negative potential is seen to be in the equatorial plane for the latter two (Figure 3h,c), though it does extend slightly aboveand below theequatorial planealso. Theminimain B6H62are seen to be above the face center (Figure 3a) with V ( i )equal to 4.377 au (Table 2). On the other hand, in lr6-Si2B4H6the minima lie in the equatorial plane (Figure 3c), with a relatively less negative potential (4.02 au-Table 2). In 1,6-CzB4H6no negative valued minima could be located, though there are (3, + I ) CP’s both in the equatorial plane and on the exterior of the edges. The blueregion in Figure 3b indicates the (3, + I ) saddle with the V ( i )value of 4.009 au. As in the case of 1,5-C2B3HS, 1,6-C2B4H6also undergoesexchange reaction with the hydrogen bonded to boron being replaced by deuterium.10 The dehydrccoupling reaction leading to 22‘-[1,6-CzB4H5]zandthegeneration of diborane-coupled species [1,6-C2B4Hs]B2Hs31 take place at boron rather than at carbon, offering supportiveevidence for the localization of the electronic charge density. On the basis of the above observation of the negative valued minima, we predict the facial region of B&2- to be the most likely direction of electrophilic attack. In 1,6-SizB4H6the equatorial plane serves as the potentialsite for electrophilicattack. From the V ( i )values, at the (3, +3) CP’s,(cf. Table 2), B6Hs2-is expected to be the most susceptible to electrophilic attack, among the six vertex deltahedra studied here, and C2B4H6,the least. In V ( i )topography, the centroidofthecage exhibitsa positive valued (3, +3) CPin 1.6-c2B4H6and I,6-SizB4H6(Table 2). In B6H6’- the cage centroid shows a negative valued minimum, similar to that in BsH,*-,onceagain indicatingcharge localization in the cage centroid. To~pbie.ICh.mfteristi*lolp(q and V(i)inseven-Vertex Polyhedra. The molecules studied in this category are B7H,zand I,~-CZBJH,.Among these, the borane anion is observed as asalt.12 Theanionshowsa (3,-l) bondCPin thep(i) topography for A-E, E-E, A-H, and E-H bonds (Table 4). There are (3, + I ) CP‘s at the centroid of each face in B7HTZ-,and the density value is 0.108 au, close to that of the (3, - I ) CP characterized along the edges (Table 4). Such a density distribution along the edge and face accounts for the three-dimensionallydelocalized bonding anticipated for the polyhedral boranes. This observation should be contrasted with B5Hr2- which does not exhibit such a topography, and hence the description in terms of localized bondingfor B5H5”secmsappropriate.’6 The A-E bonds in B,H72are slightly concave (Table 4). The A-H bond polarity is higher than that of A-E and E-H in B7H12-. In 1,7-CzBsH7,the A-E nuclei are not bonded, while the E-E, A-H, and E-H bonds show a (3, -I) bond CP. The trends in the polarities of the various
Jemmis et al.
‘I
-2.m.-
L L -,.“,r*
It:::: 4.U.l
I,S-Cz&H6 (b, middle), and I,S-SizB.H6 (c, bottom). The orientati of the molecules are as shown in Figure 1. The MFSP values, ca coded, are given adjacent to each figure. Dcep blue color indicatest region of more negative potential, and red, the least negative (posit) MESP value in the case of neutral molecules). boudsaresimilar to thatobservedin I,5-C2BlH5and 1,6-CzB4H6. The A-E bonds are seen to be more concave and hence highly strained. This arises because the five-membered ring in the sevenvertex cage is large and the CH acting as the capping group is smaller is size with less diffuse p-orbitals. A BH, acting as a capping group, is larger in size with a more diffuse p-orbital. This
The JOurMl of Physical Chemistry, Vol. 98. No. 26. 1994 6449
Topographical Study of Various Boranes TABLE 4: T o ~ p b i uFentuns l in ~ ( F (au) J for Seven-Vertex Deltahedn’ bonds tvm R d .DL_ B7Hlb (Total Energy = -176.785 81 au) 0-1) 3.474 -0.072 0.108 A-E
,.
E-E A-H
E-H A-E E-E A-H E-H
&-I) (3,-l) (&I) 1.7-CzB,H,
(%+I) (GI) &I) @-I)
3.137 0.008 0.149 0.0 0.155 2.301 0.0 O.IS0 2.300 (Total Energy = -203.169 62 au) 3.281 -0.159 0.124 3.069 0.0 0.152 2.029 0.0 0.301 2.228 0.0 0.178
A 0.063 0.0 0. I92 0. I89 -0.582 0.0 4.305
0.167
‘A,axialatom;E,equatorialatom;H,ex~hydrogenbonded1oA.E: &.equilibrium bonddistanee;d,deviationofCPfrom &(positivevalue indicates the convex nature of the bond, and negative value. the concave nature); pb function value at the density critical point; A. shift of the CP
from the geometrical center of two nuclei (positive value indicates the CP to be shifted toward A or E for A-H and E-H bonds and toward A for A-E bonds; the density values of the (3,+3) cage critical point for B,H?- and C~BJH,are 0.047 and 0.065. rspcctively).
enhance the overlap of the p.-orbitals involving the cap and the ring. Thus the exchange of the C H group from the apical to the equatorial position increases the stability of the molecule. In other words. as the bent nature of the bond increases (convex, I,5-SizBIHs;concave, 1.7-CzBsH7).the stability of the molecule decreasesJ0.” The V ( i )textured on the vdW surface for B,H7z- (Figure 4a) and I.7-CzBsH7 (Figure 4b) indicates an extensive negative potential in the equatorial plane which diminishes progressively as it goes toward the apical region. The V(i) values are -0.355, and 4 . 0 1 7 au, respectively (Table 2). The regions of negative potential are reverse to that observed for the five-vertex cage. These observations are in agreement with that of Takano et a l j b and Bader and Legare9 for B7H,l-. B7HIZ-is seen to be more susceptible toward electrophilic attack compared to 1.7-CzB~H7 (Table 2). The cage exhibits a (3, +3) CP which is negative valued but of a very small magnitude for B ~ H I ~ - . The potential values at the (3, +3) minimum in the five-, six-, and seven-vertex deltahedral anions indicate that B5Hsz- is most susceptibleto electrophilic attack followed by B6H6”and B,H7” (Table 2). Similarly, 1,5-CzBIHs and I,5-Si2B3Hsare expected to be the least susceptible ones for electrophilic attack. Isomer Stabilities in mVertex Heteroborams. Three a p proaches have been formulated in literature to predict the positional isomer stabilities in rloso-heteroboranes. According to Williams.13 electronegative atoms prefer the site of lower coordination so that it can have minimum electron sharing with its neighboring atoms. Moreover, electronegative atoms tend to be far apart so that the repulsion between them is minimized. The ruleof topographical charge stabilization by Gimarc3‘states that electronegative atoms prefer electron rich sites. The pattern of relative electron densities has been determined by calculations fora homonuclear, isostructural reference framework. The third qualitative approach by Jemmis’ says that a cap (apex) with morediffuseorbitalsprefersa larger ringandsmallerringsprefer less diffuse orbitals such that the overlap between the cap and the ring is maximized. All the three models worked well in predicting the positional isomer stabilities of rloso-carboranes.” While the approach due to Williams” was not extended beyond closo-carboranes, the charge model proposed by Gimarc” is not successful in explaining the isomer stabilities calculated for 1.6SilB4H6,z9isovalent to I,6-C2B4H6. We use V(i) to predict the positional isomer stabilities, in order to overcome the known drawbacks of the charge model, to quantify the observed trends in positional isomerstabilitiesreported in literature,and toassess the reliability of this model in predicting the same. The electrostatic potential for a homonuclear, isostructural molecule like B.H.2- ( n = 5-7) which acts as a reference
and I.l.C?B,H. (b. b t i m l . ‘The oiient3iion of the molecules are r h w n tn Figure I . The MLSP i a l w s a r e given adjacent locach figure. Drcp gray indicaio the region of more negaiivc picntial.
frameworkin predicting the positional isomerstabilitiesinn-vertex heteroboranes was calculated. The locations of the minima ((3, +3) CP) serves as the regions of electron localization in the n-vertex cage (n = 5-7). Such localized regions are expected to be the preferred position for more electronegative atoms. In B,H,’-, the apical region i s found to be more negative (Figure 2a), and hence moreelectronegative atoms should prefer the 1.5position compared to the 1.2 and 2.3 positions. This is in agreement with the positional isomer stabilities calculated for the five-vertex closo-carboranes.m azaboranes.Mand phosphab rancs.16 and the fact that the 1.5 isomer has been synthesized in carboranes’s and phosphaboranes” supports our results further. Electropositive elements, on the other hand. should prefer the equatorial positionswhichare not electron rich. Thisisinaceord with the positional isomer stabilities reported forSi2B]H,. where the 2.3 isomer is calculated to be the most stable.*0 For a six-vertex cage, all sites are equivalent due to the octahedral symmetry. Hence. perturbation of the cage with one heteroatom was considered. This would lower the symmetry of thecage but offena distinction bctween thequatorial andapical positions. closo- I -NBIH6I8and rloso- 1-SiBJH61-were considered as the reference frame for electronegative and electropositive perturbation. The MESP textured on the vdW surface for the above two are shown in Figure 5a,b. It can be clearly seen that thenegativepotential (gray region) liesclose to thevertexopposite to nitrogen and silicon, indicating the 1.6 isomer to be preferred forcarboranes and a7aborane~’~and the I .2 isomer for Si2B4H6.m These predictions are in agreement with the reported positional
Jemmis et al.
6450 The Journal of Physical Chemistry. Vol. 98. No. 26. 1994
charge density is localized on the exterior of all the faces (and not delocalized over the entire skeleton, as expected. due lo its high symmetry), a feature that went unnoticed in all previous studies. The trends observed in the polarities of the bonds are reversed in silaboranes as compared to that of carboranes. But. the reactivity pattern parallels that of carboranes. The suscep tibility forelectrophilicattack isseen tobemore for boraneanions followed by silaboranes and then by carboranes. The five-vertex cages are expected to be more prone for electrophiles, and the seven-vertex ones, the least in borane anions, while the reverse is observed for carboranes and silaboranes. Among all the molecules studied, I,6-CzB4H6 alone does not exhibit any minimum in V(i) topography. Another interesting feature is the shift of the (3, +3) CP in V ( i ) topography from apical to the equatorial region as we go from five- to seven-vertex boranes. We also have pinpointed the grey areas in p(i) topography, where caution may be exercised while choosing the basis set and the interpretation of the (3, -1) CP for two nuclei to be bonded together. The MFSP has been shown to offer a qualitative explanation fortheobservedtrendsinisomerstabilitiesandproved to be successful where the charge model failed.
Acknowledgment. The authors thank the C-DAC, Pune, for computational facilities. I.H.S. thanks the DST, New Delhi, for financial assistance. E.D.J. andG.S. thanktheCSIR, New Delhi, for financial support.
Reference and Notes ( I ) (a) Stock. A. Hydrides of Boron and Silicon: Cornell University Ras: Ithaca.New York. 1933. (b) Liebman. J. F.,Gretnbcrg. A.. William.
R. E .Ed% A d u n ~ ~ r i n B o r o n ~ n d r h r B o r o n r ~ : VNew C H : York. 1988.1~) Grimk, R. N.Corboronrs; Academic Pias: New Y a k . 1970. 12) Bell. R. P.: Laneuet-Himins. H. C . Nofvre 1945. ISS. 328. fbl Langud-Higgi& H. C.J.C6m.Phy~Chim.Biol.1949,46.268. (cjL0ng;CiHiggins. H. C.;Phil. M.A. D.Q. Chcm.Sm. Rev. 1957. 11, 121. (d) Prim, W. C. J . Chem. Phys. 1947, I S . 614: 1948. 16. 894. (e) H d k r g . K.; Schomakcr. V. J . Am. Chem.Sm.1951.73.1482. 1nSmith. H. W.:Limmb. . . W : N : J ~ ~ C h c & . P h1y%5 ~, 43. 1060. ' (3) Lipscomb. W. N.Boron Hydrides: Benjamin: New York. 1963. (4) (a) Wade. K. 1.Chem.Soe.,Chem. Commun. 1971.792. (b) Wade, .gure5. ~ ~ ~ ~ p i o t ~ n t h e vwaana di se~i r a c eror I - B ~ N H ~ ( ~ , ~ o ~ ) K. Narurc Phys. Sci. 1972.240.71. (c) Wade. K. Ad". 1nor.q. Radimhem. and I-SiBrHal- (b. bottom). Thc MESP values are given adjacent to 1976, 18. 1. each figure. Deep gray color indicates the region of more negative ( 5 ) Williams, R. E. Inorg. Chem. 1971. IO, 210. potential. (6) (a) Stone. A. J. Mol. Phys. 19W. 41. 1339. (b) Stone. A. J. lnorz.
.,.,
._
.
isomer stabilities for closo-CzB4H6,cIoso-N2B4H4.and dosoSi2B4H6.36 While the charge model by G i m a r ~ ' ~was not successful in predicting the correct order of isomer stabilities in SizB4H6,our model rationalizes the observed experimental and theoretical trends. Fortheseven-vertex cage, the reference frame B1Hl2-showsregionsofmorenegativepotentialin theequatorial plane (Figure4a). This explains the preferenceofthe 2,4-CzBsH1 and 1,7-Si2BsHlisomers amongtheseven-vertex closo-carboranes and clo~o-silaboranes.~~ The good correlation we obtain with reported experimentaland theoreticalstudies indicatesthe success ofthismodel in predicting the positionalisomenfordoso-boranes. Conclusions The topographical study using p(i) and V(i) reveals many interesting features on the molecular structure and reactivity in n-vertex boranes and heteroboranes ( n = 5-7). The five-vertex cages do not exhibit any bond CP's in the equatorial plane. They seem to obey the conventional description of bonding (they are electron precise molecules) and no longer can be classified as electron deficient molecules. The exocyclic B-H bonds in borane anions are not homopolar, and the centroid of the cage is not electronicallyempty in contrast to that reported by Takanoet al. The V(i) topography indicatessomeperwlationof chargedensity in the centroid of the cage. In agreement with Takano et al., the the electron density is localized on the exterior surrounding the apex for B5Hsz- and equatorial atoms in BIH,~-. In B6HaZ-.the
Chrm. 9. R.,I ~20. . ....... 1.. .., S63. .... (7) (a) Jcmmis, E.D.J. Am. Chrm. Soe. 1982.104.7071. (b) Jcmmis. E. D.: Schleycr. P. Y. R. 1. Am. Chem. Sm.1982. 104,4781. (8) (a) King. R. B.: Rouvray. D. H. J. Am. Chcm. Soe. 1911.99.7834. (b) Takano, K.; Izuho. M.;Hmoya. H. J. Phys. Chem. 1992.96.6962, (e)
Iwala. S.Chem. Phvr. Lcfl. 1980.69. . . 305. (9) Bade?. R. F. W.: Legare, D. A. Can. J . Chem. 199t70.657. ( I O ) (a) Bade,. R. F. W. Afom in Molemlrs:Clarcndon: Oxford. U.K.. 1990 (b) Kraka. E.:Cmmsr.D. I n T h ~ o r r r r ~ ~ l M ~ ~ l r o f C h ~ m i ~ ~ l B ~ ~ d Pan 2 Mahic. 2 E.. Ed:. Snrincer: ~ . Berlin. 1990. lcl The critical minls ~~~
(CP)p of three-dimensional sca& fields arcdcfind
'aithose where ?& =
0. The nondegencrate CP's in thc three-dimensional case are (3, +3), a minimum;(3.-3)a marimum:and (3,-l) and(3, + I ) saddlw. Adassilication oftheCPs is given in termsofthe eigenvalues AI, A?, and Xlof the wncsponding Hssian matrix HI,= J2f/Jxj Jxh. Here. the notation (r, o) stands for thc rank, r, and signature (ciesr of positive cigenvaluw over the negative onw). 0 , For B lucid introduction to topographical wneepls. refer Stewart. 1. Sei. Am. 1991.264,89.
(1 I ) Cadre, S.R.; Bapat. S. V.: Shrivaslava. 1. H. Compuf. Chem. 1991.
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(13) (a)Ha~haran.P.C.:Poplc.J.A.Thror.Chim.Aoo.l971.28,213. (b) For details of the baris e t . see: Hehre. W. J.: Radam. L.: Sehleyer. P. Y . R ; Poplc. J A Ab initio Moltmlor Orbird Theory. Wiley: New York. 1986. (14) Frisch. M. J.: Trucks. G W.; Foraman. J. B.: Schlcgcl. H. B.; Raghavachari. K.. Robb. M. A.: Binkky. J. S.:Gonzalcz. C.: DcfrCa. D. J.; For. D . J., Whitcsidc. R .A,: h g e r . R ;Mcliu. C . F.; Baker. J.; Martin. R. L.. Kahn. L. R..Stewan. J. J. P.:Tapial.S.:Poplc. J. A.GausrionW:Cauuian c '~Pitwbumh. PA. 1990 .I n~ .. ~ ..... (IS) Ahlrichs. R.; 8Hr. M.: Hger, M.: Kalmcl, C . Chcm. P h p . Lcff. 1989.162. 165. The basis sct was taken from the package TURBOMOLE. developed by Alriehs and coworkers. ~~
~
L 1 ~ ~ . ~
~
~. ~~
~
~
Topographical Study of Various Boranes (16) Shirsat, R. N.; Limaye, A. C.; Gadre, S.R. J. Compur. Chem. 1993, 14, 445. (17) PARAM, a 64-node parallel machine developed by C-DAC, Pune,
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