J. Phys. Chem. 1995, 99, 2267-2277
2267
Ab Initio Conformational and Stereopermutational Analyses of Phosphoranyl Radicals HP(OR)3 and P(OR)4 [R = H or CH31 Susan M. Gustafsont and Christopher J. Cramer” Department of Chemistry and Supercomputer Institute, University of Minnesota, 207 Pleasant St. SE, Minneapolis, Minnesota 55455-0431 Received: June 24. 1994@
The potential energy hypersurfaces for HnP(OH)4-, and HnP(OCH3)4-n3 n = 0 or 1, have been explored at correlated levels using polarized valence double-5 and triple-5 basis sets. Numerous local minima and several distinct types of stereopemutational transition states interconnecting them have been identified. These transition states correspond to (i) bond rotation, (ii) pseudorotation, (iii) double pseudorotation, and (iv) pseudoinversion. The stereochemical consequences of these processes are analyzed in detail as is the nature of the singly occupied molecular orbital throughout. Geometric and natural bond orbital analyses indicate the importance of stabilizing hyperconjugative interactions in these systems. The latter effect is maximized for interactions between equatorial substituents in trigonal bipyramidal (TBP) phosphoranyl structures. Unlike the TBP local minima of the mono- and dihydroxyphosphoranyls, where the unpaired electron always localizes in an equatorial site, tri- and tetrahydroxyphosphoranyl minima localize their unpaired electrons in both equatorial and apical positions.
Introduction In prior studies, we have examined the effects of various substituents on the structure and energetics of tetrasubstituted phosphoranyl radicals. 1-5 The five most important idealized phosphoranyl radical geometries which we will use in later discussion are illwtrated in Chart 1. If one views the unpaired electron as a fifth “substituent”, then the trigonal bipyramidal (TBP) and square pyramidal (SP) stereostructures are familiar from phosphorane chemistry. Because of the unique nature of the unpaired electron, each of these two geometries is further defined by the localization of this electron, either equatorial (TBPe) or axial (TBP,) in the trigonal bipyramid, or apical (SP,) or basal (Spb) in the square pyramid. Finally, there is clearly no requirement that the unpaired electron really resemble a substituent. If it is instead predominantly localized in some antibonding molecular orbital (MO), the phosphoranyl radical may adopt what amounts to a distorted tetrahedral (DT) geometry, sometimes called a u* geometry by reference to the MO picture. Considerable theoretical work has appeared assessing the relative energies of these different structures for selected phosphoranyl radicals.’-22 Experimentally, electron spin resonance (ESR)spectroscopy suggests that the majority of phosphoranyl radicals exist as TBPe ~ t r u c t u r e s .However, ~ ~ ~ ~ ~ phosphoranyl radicals of TBP, structure have been implicated in a few controversial case^.^,^^ Numerous theoretical studies support the contention that the unpaired electron is particularly apicophobic. However, it is possible that certain combinations of substituents may lend stability to TBP, structure^.^ We present here an exhaustive search of the potential energy surface for HP(OH)3, focusing on all local minima and stereopermutational transition state structures (TSs) interconverting them. It is generally accepted that ligand substitution processes at tetrahedral phosphorus that involve TBP intermediates proceed via apical addition and e l i m i n a t i ~ n ;it~ ~ is thus of t Present address: Cray Research, Inc., 655E Lone Oak Dr., Eagan,MN 55121. LS Abstract published in Advance ACS Abstracts, February 1, 1995.
considerable interest to examine stereopermutations which exchange axial and equatorial ligands. The P(OH)4 potential surface is qualitatively similar to that of HP(OH)3; we will thus discuss only the lowest energy minima and transition state structures. Geometrical and natural bond orbital (NB0)26 analyses are employed to interpret the importance of hyperconjugation in these radicals. In addition to being of increased biological relevance, polyhydroxy- and polyalkoxyphosphoranyl radicals are experimentally a c c e ~ s i b l e . ~ ~ Thus, * ~ ~we - ~examine ~ the lowest energy TBP, and TBP, minima for HP(OCH3)3, CH3P(OCH3)3, and P(OCH3)4. Comparison of calculated and experimental ESR hyperfine coupling constants for these systems will be reported separately; we have found such comparison to be generally useful for other phosphoranyl radicals.30
Theoretical Methods All calculations employed either the GAUSSIAN 923! or suites. Most of the calculations use the 6-31G* basis set.33 In certain instances, the 6-311G**34,35 and C C - ~ V D Zbasis ~ ~ ~sets ~ ’ were used in order to examine any basis set dependencies in the results. Open-shell geometries were fully optimized at the UHF and UMP2 levels of theory while closed-shell geometries used the corresponding restricted leve l ~ . ~Spin * contamination was negligible in all instances, with values of (p)ranging from 0.75 to 0.77 for doublets. The effects of correlation were examined via single point calculations at the MP4 level with excitations of core electrons included using the MP2 (frozen core) geometries. In specific instances, we have also calculated single point energies at the CCSD39-41 and CCSD(T)42 levels of theory in order to calculate as accurately as possible specific TBP,-TBP, energy differences. Vibrational frequencies were calculated using the rigid-rotor harmonic oscillator approximation at the HF level for all stationary points;38local minima and transition state structures were c o n f i i e d to have exactly zero and one imaginary frequencies, respectively. Infrared frequenices for global minima are provided as supplementary material. For each transition state giving rise to a stereopermutation, the intrinsic GAMESS~* program
QQ22-3654/95/2Q99-2267$09.QQIQ 0 1995 American Chemical Society
2268 J. Phys. Chem., Vol. 99, No. 8, 1995
Gustafson and Cramer
CHART 1
TBP,
TBPa
spb
TABLE 1: Relative Energies (kcaYmol) for HP(OH)J Isomers at Various Levels of Theory structure
symmetry UHF/6-31G* MP2/6-31G* MP4/6-31G* 0.0 ( 0 . 0 ) C 1.4 6.1 8.5
0.0 2.2 8.1 8.2
0.0 2.2 6.0 8.0
2.3 2.4 2.5 4.5
2.0 1.7 2.3 4.2
1.8 2.2 2.6 4.3
4.7 5.4 8.5 13.4
0.9 2.3 6.0 11.6
1.5 3.1 7.0 12.8
7.7 8.8 11.3
6.0 7.8 9.4
6.3 8.4 10.1
36.7 41.1
30.8 35.2
30.5 34.8
15.4 20.7 21.4
12.5 17.2 19.0
12.9 17.5 19.6
7.9 9.3 13.9 7.0 10.2 6.0 11.9 9.3 8.4 16.1 10.9 8.3 10.5
7.1 9.6 13.8 4.8 8.7 4.2 11.7 8.2 6.9 15.1 9.6 6.3 9.0
7.1 9.6 13.8 5.0 9.3 4.5 12.3 8.5 7.3 15.9 10.0 6.5 9.5
5.9 8.4 9.8 12.0 11.1 11.5
5.0 8.6 9.2 12.2
5.1 8.6 9.2 12.0
b
b
9.7
9.7
-5.1 (-6.5)' 5.2 (-6.7)' 14.3 (-4.1)c
-4.5 6.7 43.0
-1.9 7.1 37.0
a Single point energies at the MP2 optimized geometries. Not stationary at the MP2 level. Correction for zero point energies.
reaction coordinate was calculated at the UHF level of theory in order to determine the corresponding reactants and products and the minimum energy path connecting them.43 Hyperconjugative delocalization was examined by secondorder perturbation analysis of the off-diagonal Fock matrix elements in the NBO basis. Hyperconjugation is measured in terms of bond or lone pair delocalizations into antibonding
-
DT
-
orbitals (Le., u u* or n o*)and their energetic contribution to the overall electronic structure relative to the idealized Lewis structure. Application of NBO analysis to hyperconjugation in TBP systems has been described p r e v i ~ u s l y . ~ ~ ~ . ~ ~ Molecular orbital depictions of the singly occupied molecular orbital (SOMO) are presented as planar slices taken from the appropriate UHF a eigenvector. Nomenclature. For ease of notation, we will identify HP(OH)3 structures in the following manner. The gross structures of the local minima are all either TBP, or TBP,; TBP, is indicated by an "e" prefix and TBP, by an "a" prefix. A positional identifier is then used to indicate whether the hydroxyl substituents are in the axial or equatorial positions (e.g., e-aae would indicate a TBP, local minimum with two hydroxyl groups axial and one equatorial). The prefixes will be followed by a number, reflecting the order in which each member of a particular class of structures is presented in the text. Stereopermutation transition state structures will be uniquely identified by the following prefixes: qrolfor pseudorotation, for double-pseudorotation, and qlnY for pseudoinversion. The pseudorotation transition states occur with the unpaired electron in either the apical or basal position. These two possibilities are distinguished by the extension -a or -b (qrot., or qr0t.b). Again, the prefixes will be followed by a number reflecting the ordinal occurrence of the particular TS in the discussion. In gross structure, $+of., TSs have SP, geometries, yjr0t.b and TSs have SPb geometries (which may closely resemble TBP,), and TSs have geometries roughly intermediate between square planar and DT. Numerous figures are provided to assist in visualization. Finally, similar conventions will be used for the other phosphoranyl radicals, but to avoid confusion they will additionally be distinguished by the attachment of their molecular formulas.
&:
v:t:
Results As is typical for phosphoranyl radicals, the local minima of the tri- and tetrahydroxy-substituted isomers are trigonal bipyramidal in nature. However, in both cases the unpaired electron may reside in either equatorial (TBPe) or apical (TBP,) positions. This is in dramatic contrast with the mono- and dihydroxyphosphoranyl radicals where all equilibrium geometries were TBPe and all stationary TBP, structures were transition state struct~res.'.~Similar to the situation for the mono- and dihydroxy isomers, pseudorotation, double-pseudorotation, and pseudoinversion pathways interconvert the various TBP, and TBP, minima. The relative energies and selected geometric data for all minima and stereopermutational transition state structures on the HP(OH)3 potential surface are collected in Table 1 and Figures 1-5. Figure 6 plots the SOMOs for each type of minimum and stereopermutational transition state structure. Absolute energies and complete
J. Phys. Chem., Vol. 99, No. 8, 1995 2269
HP(OR)3 and P(OR)4 [R = H or CH3] A
W
0 a-eee1
a-eee2
A
U
e-eeal
e-eea2
A
e-eea3
a-eee3 n
a-eee4 n
.706 .679
e-me1
e-eea4
31.414
e-aae2
1.404 n
a-eeal
a-eea2
a-eea3
1.684
e-me3
1.670
I 1.637
e-aae4
Figure 1. Selected geometrical data for the TBP, local minima of HP(OH)3optimized at the UMp2 and UHF (italics) levels; bond lengths are in angstroms and bond angles in degrees.
geometries are included in the supplementary material. Unless otherwise noted, all energies refer to MP4/6-31G*//MP2/6-31G* calculations. We do not discuss processes which interconvert various local minima exclusively via hydroxyl rotation; such pathways have been examined in detail for the mono- and dihydroxy phosphoranyls, and few differences are expected to arise for the present subject HP(OH)3 Local Minima. The unpaired electron and the three hydroxyl groups generate two possible TBPe substitution patterns, e-eea and e-aae (Figure l), and two possible TBP, substitution patterns, a-eee and a-eea (Figure 2). In TBP, HsPOH, the hydroxyl group prefers the apical position by 5.8 kcallmol.' Consistent with this hydroxyl apicophilicity, the TBP, global minimum structure for H2P(OH)2 also has both hydroxyl substituents in axial position^.^ With trihydroxy substitution, the C, global minimum e-eeal is also TBPe, however, it has two hydroxy groups equatorial and only one in an axial position. Infrared frequencies for e-eeal are provided in the supplementary material. The equatorial hydroxyl groups in e-eeal eclipse the axial P-0 bond in part in order to take advantage of favorable electrostatic interactions between the eclipsing protons and the axial oxygen. Similarly, the three hydroxyl groups in e-eea2 are oriented sequentially to take advantage of such nonideal hydrogen bonding. An alternative C,structure, e-eea3, where the hydrogen bonding interaction between the axial and equatorial hydroxyl groups is essentially opposite to that in the global minimum, is significantly higher in energy. Slightly higher in energy is the related rotational isomer e-eea4.
1.380
Wnvl
6 KnJ 1.714 1.625
Figure 3. Selected geometrical data for the pseudoinversion and SP, pseudorotation transition state structures of HP(OH)3 optimized at the UMP2 and UHF (italics) levels; bond lengths are in angstroms and bond angles in degrees.
In the axial monohydroxyphosphoranyl' and diaxial dihydroxypho~phoranyl~ radicals, the hydroxyl groups prefer orientations where the 0-H bond is staggered between an equatorial P-H bond and the axis of the orbital containing the unpaired electron. In all but one of the axial-axial-equatorial (aae) substituted structures shown in Figure 1, this arrangement is favored. For the most stable of these, e-aael, which lies about 2 kcal/mol above the global minimum, the two axial hydroxyl groups are eclipsed (projected along the OPO axis) just as is observed for H2P(OH)2. Slightly higher in energy is e-aae2, where the eclipsed hydroxyl group rotates to the other orientation gauche to the orbital containing the unpaired electron. Rotation of one axial hydroxyl group so that it eclipses the equatorial P-0 bond (Le., creating sequential nonideal hydrogen bonding)
2270 J. Phys. Chem., Vol. 99, No. 8, 1995
Gustafson and Cramer
1.451 145.2
1.470
vrot-b
1.672
vrot-b4
Yrot-b3
Yrot-b2
n
143.8
1.683 1.664
152.6
1.670
152.8
148.1
148.5
yrot-b9
v.ot-b1O
Yrot-bll
vrot-b12
~ ~ t - b l 3
Figure 4. Selected geometrical data for the SPb pseudorotation transition state structures of HP(OH)3 optimized at the UMP2 and UHF (italics) levels; bond lengths are in angstroms and bond angles in degrees.
149.2
Figure 5. Selected geometrical data for the SPb double-pseudorotation transition states of HP(OH)3 optimized at the UMP2 and UHF (italics) levels; bond lengths are in angstroms and bond angles in degrees. gives rise to the higher-energy isomer e-aae3 while rotation in the opposite direction yields the highest energy aae isomer e-aae4. Seven local minima were found to have overall TBPa structure, four having all three hydroxyl substituents equatorial, and three having two equatorial and one axial (Figure 2). (The latter three were not found until after a prior communication of this work.)4 The most stable TBPa structure, a-eeel, places all three hydroxyl groups equatorial with their 0-H bonds antiperiplanar to the apical P-H bond. This C3" symmetric isomer is 1.5 kcdmol higher in energy than the TBP, global minimum,
e-eeal. Sequential rotation of each hydroxyl group through 180" (Le., eclipsing the apical P-H bond) generates three additional stereoisomers, a-eee2-4. During this process, the isomeric relative energies increase geometrically. Of the three TBPa minima having one hydroxyl group axial, C, a-eeal is lowest in energy. Again the equatorial hydroxyl groups prefer to orient anti to the apical bond and the apical hydroxyl proton maximizes its electrostatic interactions with the equatorial oxygens. The equatorial hydroxyl bonds in the remaining two higher-energy isomers, a-eea2 and a-eea3, both eclipse the apical hydroxyl grOUP. HP(OH)3 Pseudoinversions. Pseudoinversion converts both axial substituents to equatorial and vice versa; concomitantly, the unpaired electron inverts through phosphorus, remaining equatorial in the TBP. Transition state structures for pseudoinversion are intermediate between square planar and tetrahedral about phosphorus, with the unpaired electron localized in a p orbital approximately perpendicular to the mean plane of the four ligands (Figure 3). The 0-H bonds prefer to remain roughly in the plane of the ligands and -90° to the inverting unpaired electron. Two pseudoinversion TS structures have been located lying more than 30 kcdmol above the global minimum. The lowest energy TS structure (2238i cm-I), vinvl, displays the electrostatically favorable sequential hydrogen bonding observed for the minima. Figure 6 plots the SOMO for v i n v l and illustrates the unpaired electron to reside in a p-like orbital. Figure 7a illustrates the intrinsic reaction coordinate (IRC) for pseudoinversion through vinvl, which is a transition state linking e-eea2 and e-aae3. Within the constraints of the hydroxyl group orientations being in the approximate plane of the substituents, there are three other possible stereoisomeric TS structures. One is illustrated by vinv2 (2333i cm-I), which
HP(OR)3 and P(OR)4 [R = H or CH31
I
I1
II
I
I
1
I
1.1
J. Phys. Chem., Vol. 99, No. 8, 1995 2271
I
1,
I
II
I’
I
I
1 I1 1
1
I
U
I
I
I
Figure 6. Contour diagrams (0.05 au) of planar slices through the SOMO for various HP(OH)3 stationary points. Upper left: e-eeal, TBP, minimum. Lower left: a-eeel, TBP, minimum. Upper center: Vin.l, flattened DT pseudoinversion TS structure. Lower center: Vrot-,l, SP, pseudorotation TS structure. Upper right: Vrot.& SPb pseudorotation TS structure. Lower right: &:l, SPb double-pseudorotationTS structure.
rotates one of the two hydroxyl groups anti to each other about phosphorus so that it no longer eclipses the remaining hydroxyl group. In principle, two additional related isomers might be available after a rotation of the other hydroxyl, Le., a switch from eclipsing P-H to eclipsing P-0. Careful searching, however, did not locate such TS structures. This is probably because of unfavorable steric interactions that would arise between the protons for the two hydroxyl groups eclipsing each other in such putative structures. Pseudorotationand Double Pseudorotation. The transition state structures for Berry p~eudorotation~-~* in phosphoranyl radicals are square pyramidal in structure, with the unpaired electron occupying either the apical, Spa, or the basal, SPb, position. SP, pseudorotation interchanges both axial substituents with both equatorial in TBP, structures (Le., the unpaired electron remains localized equatorially). Pseudorotation via an SPb transition state interconverts one axial and one equatorial ligand and converts TBP, to TBP, structures since one of the remaining “ligands” undergoing an equatorial-axial interconversion is the unpaired electron. There is a third unique type of pseudorotation possible when TBP, geometries are not stable minima. In cases where the TBP, endpoint is not stable, a double pseudorotation characterized by a single barrier is observed. In this situation, the reaction path proceeds through the TBP, geometry, which may itself be the double-pseudorotation TS, and on to a stable TBP, minima. For monohydroxy’ and dihydroxy5 substituted phosphoranyls, there are no minimum energy TBP, geometries. Therefore, all SPb transition states for H3POH and H2P(OH)2 corresponded to double pseudorotations. As presented above, however, many minimum energy TBP, structures exist for HP(OH)3, and thus both types of SPb pseudorotation are computationally predicted in addition to SP, pseudorotation.
The net result of Spa pseudorotation is the same as for pseudoinversion. The key difference is that the unpaired electron does not invert through the central phosphorus atom in the former process. As in pseudoinversion, the 0-H bonds prefer to lie roughly in the plane of the ligands (Figure 3). As discussed above for pseudoinversion, there are thus four potential orientations of the hydroxyl groups, and three such structures are observed lying roughly 13-20 kcal/mol above the global minimum (vrot.al, 3 0 5 cm-I; qrot-a2, 361i cm-’; vrot-a3, 323i cm-I). The missing permutation would maintain the sterically unfavorable double eclipsing interaction of hydroxyl groups found in lyrat.,2but would not have the nonideal hydrogen bond involving the remaining hydroxyl group. Figure 6 includes a SOMO slice illustrating the SP, nature of the unpaired electron in vrot.,l. Finally, the SP, pseudorotation process is illustrated in Figure 7b using the IRC interconverting e-aae3 and e-eea2 through V r o t - a l . Note that the interconversion is identical to that for the pseudoinversion in Figure 7a, only the nature of the transition state (and the height of the barrier) has changed. An SPb pseudorotation converts between TBP, and TBP, ground states with one axial-equatorial ligand exchange. Analogous to pseudoinversion and SP, pseudorotation, the 0-H bonds of the basal hydroxyls prefer to lie in the approximate plane of the basal ligands. A hydroxyl ligand in the apical position, on the other hand, can take on a variety of orientations, as discussed below. This contrasts somewhat with HzP(OH)~,~ where the apical hydroxyl group prefers exclusively to either eclipse or be antiperiplanar to the unpaired electron. In terms of axial or basal ligand position, there are three possible combinations for the three hydroxyl substituents: (i) one apical and two basal (syn and anti to the unpaired electron);
Gustafson and Cramer
2272 J. Phys. Chem., Vol. 99, No. 8,1995
t-b4
4.0
3 .O E 2.0
S
S
8 8‘ 8
E
.
8 8
8
8
8
2.0
8
.
88
.’
8
8
#
1.o
#
.
8 8
0.0 S
m ‘
#8
8 8’
ea2 S
Figure 7. Intrinsic reaction coordinates (in mass scaled internal coordinates) (a) linking minima e-eea2 and e-aae3 via pseudoinversion transition state lyinVl,(b) linking minima e-aae3 and e-eea2 via Spa pseudorotation transition state lyrot-al, (c) linking minima a-eeel and e-aae2 via Spb pseudorotation transition state ?/4,,teb4, (d) linking minima e-eea2 and e-aae3 via SPb double-pseudorotation transition state ?+9:::1. Energetic scaling is not uniform on the four ordinates. In each figure, the sphere representing the central phosphorus atom is kept fixed with respect to rotation, so changes in ligand positions only reflect motion along the reaction coordinate.
(ii) one apical and two basal (both syn to the unpaired electron); and (iii) all three basal. For case i, when the orientations of only the basal hydroxyl groups are considered, there are four possible orientational isomers. Additionally, the apical hydroxyl group tends to either eclipse or be antiperiplanar to the unpaired electron, analogous to the situation found for H2P(OH)2. Thus, accounting for all possible permutations leads to eight possible transition state structures all of which have been located and correspond to vrot-bf-vrot-b3 in Figure 4 and - 74::s in Figure 5. At the MP2 level, however, vd,b,’Sis no longer stationary. For case ii, there are only three unique sets of orientations available to the basal hydroxyls-both, one, or neither eclipsing the basal P-H bond. The apical 0-H bond, in contrast with earlier precedent, tends to be staggered between adjacent pairs of the three basal ligands and the unpaired electron. Within this case, then, 12 possible isomers can be generated; however, there are 4 pairs related as enantiomers, so 8 unique diastereomers exist. Again, all have been located and they are TS structures ‘?#rot-b4-?)rot-bll. Case iii has all three hydroxyls in the basal position, leading to four unique diastereomers. Only three of these could be located, however, namely, ‘&ot-b12,vrot-bl3, and v::6. It is
interesting to note that the “missing” TS is the one which would have a sequential arrangement of hydrogen bonds, as is seen for vinvl; moreover, one of the missing pseudoinversion TS structures is the one with the hydroxyl ligand arrangement observed for v::6. It may be, given the overall structural similarities between the two kinds of TS structure, that there is no barrier on the hypersurface separating these pairs, so that only the lower energy one is observed. While this seems reasonable in the latter instance, the relative energies required for the two processes make it seem less likely for the former. Of course, the same argument may hold for there being no barrier between the missing double pseudorotation and the structurally similar minimum e-aae3. The IRC for one of the SPb pseudorotations, interconverting a-eeel and e-aae2 via vrot-b4>is illustrated in Figure 7c. In addition, as observed for less substituted phosphoranyls? when intervening TBP, structures are not stable, an SPb double pseudorotation can interconvert two different TBP, isomers. We have found no general formula for distinguishing between single- and double-pseudorotation transition state structures other than by following the appropriate IRC: in other respects they are indistinguishable (see, for instance, the SOMO slices in The IRC for a double Figure 6 for v r o t - 9 and .1):$(
J. Phys. Chem., Vol. 99, No. 8, 1995 2273
,708
,681
1.373
OP(OH)2H
P(OW3 1.482 1.450
W
v r of- CP(OH)4 vrot-b-P(OH)4 Figure 8. Selected geometrical data for the lowest energy stationary points of P(OH)4 optimized at the UMP2 and UHF (italics) levels; bond lengths are in angstroms and bond angles in degrees. TABLE 2: Relative Energies (kcdmol) for P(OH)4 at Various Levels of Theorp structure symmetry UHF MP2 MP4(FU)b e-eeaa c 2 0.0 (0.0)" 0.0 0.0 a-eeea cs 4.6 2.6 2.9 Win"
s 4
vrot-a
c 4
vrot-b
+ +
OP(OH)3 H P(OH)3 OH
CI
53.6 13.1 5.7 -6.5 (-7.3)" 14.7 (-5.3)"
41.8 9.4 4.7 -3.9 42.3
41.5 9.9 4.7 -1.8 36.4
a All calculations used the 6-3 1G*basis set. Single point energies at the MP2 optimized geometries. Correction for zero point energies.
pseudorotation, the interconversion of e-eea2 and e-aae3 via &:l, is illustrated in Figure 7d; again, this is exactly the same conversion as that depicted for pseudoinversion and Spa pseudorotation in Figure 7 parts a and b, respectively. Thus, there are (at least) three stereochemically distinct ways to interconvert these two minima with descending barrier heights of 30.5, 12.9, and 5.1 kcaVmo1, respectively (see Figure 7). Finally, much as was found for the TBPa minima, it proves energetically favorable in these TS structures for appropriately positioned hydroxyl groups, especially basal ones, to eclipse the singly occupied orbital. The five lowest energy pseudorotation TSs, vrot-b6, vrot-b4, ly;:1, lyrot-bl2, and lyrot-bl, all follow this rule. Tetrahydroxyphosphoranyl Minima and Stereopermutational Transition State Structures. The P(OH)4 hypersurface is qualitatively similar to that of HP(OH)3 and therefore we limit our discussion to the lowest energy stationary point for each structural type (TBPe, TBPa, vinv, lyrot-a, and vrot-b). These structures are illustrated in Figure 8, and the corresponding relative energies are povided in Table 2. The C2 global minimum on the P(OH)4 hypersurface has a TBPe structure with the hydroxyl groups oriented in an Indian swastiska-like fashion to take maximum advantage of proton-oxygen electrostatic interactions. The C,lowest energy TBPa structure orients the equatorial hydroxyls relative to the apical bond eclipsing-antianti. The latter structure is similar to that calculated by TureEek et al.49 These authors found the TBPa conformer to be the local
HP(OH)2 OP(OH)3 Figure 9. Selected geometrical data for OP(OH)2H, P(OH)3, HP(OH)2, and OP(OH)3 optimized at the UMP2 and UHF (italics) levels; bond lengths are in angstroms and bond angles in degrees. minimum first reached upon relaxation of a structure corresponding to the global minimum of the tetrahydroxyphosphonium cation, i.e., following vertical electron capture by P(OH)4+. This is an interesting example of how FranckCondon effects can be used to experimentally generate higherenergy local minima by neutralization-reionization mass spectrometry.50-52 The lowest energy transition state structure for pseudoinversion, vin"-P(OH)4, has S4 symmetry. This structure lies 41.5 kcaVmo1 above the global minimum. The lowest energy Spa and SPb pseudorotational transition state structures, vrot-a-P(OHk and lyrot-b-P(OH)4, have C4 and C1 symmetry, respectively. Pseudorotations proceed at much lower energy than does pseudoinversion for P(OH)4. Bond Homolysis Products. In order to assess the energetic stability of HP(OH)3 and P(OH)4 we have considered several structures which would result from the dissociation of an H or OH radical from the HP(OH)3 and P(OH)4 global minima, and they are shown in eqs 1-5. The energies of the global minima of the possible products (Figure 9) relative to the hydroxyphosphoranyl global minima are given in Tables 1 and 2. HP(OH), HP(OH), HP(OH), P(OH), P(OH),
-
+
OPH(OH),
+H
+H PH(OH), + OH P(OH),
+H P(OH), + OH OP(OH),
(1)
(2)
(3) (4)
(5)
As was found for H2P(OH)2,5breaking the 0-H bond is the most energetically favorable process, breaking a P-H bond is approximately energetically neutral, and breaking a P-0 bond is highly endoergic. Relative zero point energies at the UHF/6-3lG* level are also given in Tables 1 and 2. Inclusion of zero point energies inevitably favors homolysis. Breaking an 0-H bond becomes exothermic by -8.4 kcaVmol for HP(OH)3 and -9.1 kcaVmol for P(OH)4. Breaking the P-H bond of HP(OH)3, eq 2, is approximately thermoneutral. Breaking a P-0 bond, on the
2274 J. Phys. Chem., Vol. 99, No. 8, 1995
Gustafson and Cramer
TABLE 3: Relative Energies (kcavmol) for Several Phosphoranyl Radicals at Various Levels of Theory structure H3POMe e-a e-e HP(OH)? e-eeal a-eeel P(OH)J e-eeaa a-eeea HP(OMe)3 e-aae e-eea a-eee MeP(OMe)3 e-aae e-aae a-eee P(0Meh e-aaee a-aeee
symmetry
UHF
MP2(fc)
MP2(f~ll)~
MP4(full)'
CCSD'
CCSD(T)'
ZPVEd
0.0 5.5
0.0 6.5
0.0 6.5
0.0 4.7
0.0 0.9
0.0 1.2 (0.9)'
0.0 1.5
0.0 (0.0Y 2.3 (3.4)'
0.0 1.9
0.0 1.1
0.0 4.6
0.0 2.6
0.0 2.8
0.0 2.9
0.0 3.5
0.0 3.3
0.0 0.1
0.0 0.1 3.3
0.0 2.0 1.3
0.0 1 .o 2.3
0.0
0.0
2.7 4.1
4.2 1.6
0.0 4.2 3.3
0.0 4.6
0.0 2.9
0.0 3.8
0.0
0.0
2.4
0.0 0.3
0.0 0.0 3.9
0.3 0.0
Unless otherwise indicated, all calculations used the 6-31G* basis set. Calculations employed the 6-31 1G** basis set. Single point energies at the MP2(fc)/6-31G* optimized geometries. Relative zero point energies scaled by 0.89. e Calculations using the cc-pVDZ basis set at MPZ(fu)/cc-pVDZ optimized geometries.
other hand, remains quite endothermic with a cost of 33 kcal/mol for HP(OH)3 and 31.1 kcal/mol for P(OH)4. TureEek et have also calculated the energetics associated with eqs 4 and 5 starting from the TBP, conformer of P(OH)4; at the MP4SDQ/ 6-3 1+G**//MP2(fu11)/6-3 1+G* level (including zero point energies) they find the reaction energies to be -8.8 and 23.9 kcdmol, respectively. Differences in the two calculations arise in part from the different reactant conformers (TureEek et al. used the TBP, isomer which is about 3 kcal/mol higher in energy at this level) and from the relative importance of triple excitations in the MP4 calculations (favoring the reactants by 1.O and 2.1 kcal/mol for eqs 4 and 5, respectively). Remaining differences reflect different basis sets and levels of theory for geometry optimization and calculation of zero point energies. Since eqs 2 and 4 are reasonably exothermic, it is apparent that observation of HP(OH)3 and P(OH)4 in condensed phases will require temperatures low enough to eliminate the additional entropic factors favoring dissociation and also require that there be a reasonable kinetic barrier to homolysis following creation of the radical.53 TureEek et al.49have generated P(OH)4 in the gas phase using neutralization-reionization mass spectrometry and have found it to have a lifetime of no more than 4.5 ,us under their experimental conditions. They have further calculated the lowest barrier to 0-H bond homolysis in TBP, P(OH)4 at the MP4SDQ/6-3 1+G*//MP2(f~11)/6-31G* level (including zero point energies) and found it to be 21.5 kcal/mol. This activation barrier is sufficiently low that excess internal energy accumulated in the neutralization-reionization process permits rapid 0 - H bond dissociation. However, assuming that TBP, conformers do not permit significantly lower-energy 0-H bond homolyses, it is sufficiently high to suggest that P(OH)4 will be kinetically stable in very low temperature inert matrices, for example. Moreover, pseudorotation in P(OH)4 is calculated to occur with less than half of the homolysis activation energy, so that stereopermutation might in principle be observed under such conditions. Pseudoinversion, on the other hand, appears to be out of the question. Finally, while these calculations and earlier indicate that the thermal stability of polyhydroxylated phosphoranyl radicals decreases with increasing hydroxyl substitution, it is certainly worth noting that the synthesis of metastable alkoxy
substituted phosphoranyl radicals has been accomplished by addition of alkoxy1 radicals to phosphines and p h o s p i t e ~ , * ~ , * ~ - ~ ~ so prospects for the hydroxyl congeners bear further study. Methoxy-Substituted Phosphoranyl Radicals. In order to compare to available experimental data, we have examined the structures of several methoxy-substituted phosphoranyl radicals. In particular, we have calculated the structures of TBP, and TBP, H3P(OCH3), HP(OCH3)3, CH3P(OCH3)3, and P(OCH3)4. Using the hydroxylated congeners as guides, appropriate structures for these isomers were first optimized at the UHF/3-21G* level, and then the lowest energy TBP, and TBP, isomers were reoptimized at the UHF/6-3 1G* level and finally at the MP2/6-31G* level. Multiple isomers were surveyed at the higher levels of theory only when the relative energies at lower levels remained similar. Single point energies were then calculated at the MP2(fu11)/6-311G**, MP4SDQ/6-31G*, and CCSD/6-31G* levels (the latter both with and without perturbative triples) using the MP2/6-31G* geometries. In certain instances, methoxyl group apicophilicity was also explored. A summary of the relative energies of the TBP, and TBP, isomers for all of these cases is given in Table 3 and selected geometrical details are given in Figure 10. Absolute energies and complete geometries are included in the supplementary material. In every case where both are minima, the TBP, isomer is somewhat lower in energy than the TBP,. We found the methoxyl group apicophilicity, based on comparison of e-a-H3P(OMe) to e-e-HsP(OMe), to be 5.5 and 6.5 kcaVmol at the UHF and MP2 levels, respectively. This compares to 4.9 and 5.9 kcal/mol at the same respective levels for the hydroxyl group,' Le., methoxyl is slightly more apicophilic than hydroxyl. Although the difference is small, it is enough to lower the energy of diaxially substituted e-aaeHP(OMe)3 to the point of being the global minimum; this is in contrast to the trihydroxy case, where the slightly preferred substitution is e-eea. For trimethoxymethylphosphoranyl, e-aaeMeP(OMe)3 is also the lowest energy isomer. As expected from the increased apicophilicity of one methoxyl group at the MP2 level relative to the UHF, in both of the trimethoxy systems correlation decreases the energy of e-aae relative to e-eea. Similarly, correlation stabilizes TBP, structures relative to TBP,, however, this effect is overestimated at the MP2 level. In no case is correlation sufficient to render the TBP, isomer the most
HP(OR)3 and P(OR)4 [R = H or CH3]
J. Phys. Chem., Vol. 99, No. 8, I995 2275
n
Figure 10. Selected geometrical data for lowest energy TBP, and TBP, minima for H3POCH3, HP(OCH3)3, CH3P(OCH3)3, and P(OCH3)4 optimized at the UHF and UMP2 (italics) levels; bond lengths are in angstroms and bond angles in degrees.
stable. Moreover, replacement of the apical hydrogen in HP(OCH3)3 with either a methyl or a methoxyl group further destabilizes the TBPa structure. Comparison of different basis sets suggests that the relative energies are converged to no better than about 1-2 kcal/mol, and the trend appears to be for larger basis sets to further destabilize the TBPa isomer. Finally, except for HP(OH)3, differences in UHF zero point energies tend to be quite small between TBP, and TBP, isomers.
Discussion Stereoelectronic Effects in TBP, Structures. One common approach to identifying lone-pair hyperconjugation, sometimes called the generalized anomeric e f f e ~ t , ~ * ~isl ~toy analyze ~~-~~ bond lengths with respect to the orientation of the delocalizing lone pair. As a rule, delocalization is maximized when the lone pair is antiperiplanar to the X-Y acceptor bond. Such an orientation enjoys a parallel alignment of orbitals and simultaneously minimizes 4e destabilizing interactions between the lone pair and the filled OXY while maximizing overlap with the empty O*XY which may have large amplitude outside the bonding region. Since the delocalization is occurring into an antibonding orbital, the bond in question tends to lengthen with increasing hyperconjugation. In our prior investigation of H2P(OH)2? we demonstrated that these hyperconjugative interactions dictated the local orientation of the hydroxyl ligands. Moreover, we found interactions occurring between two equatorial ligands to inevitably be significantly stronger than between the same two ligands when either or both were axial. Similar results have been observed in polyfluorinated phosphoranyl radicals.* Such a situation necessarily generates a competition between apicophilicity and hyperconjugation in determining the relative stability of different polysubstituted stereoisomers. Wang et al. have investigated apicophilicity in closed-shell phosphoranes for a large number of ligands.60.6*They calculated the apicophilicity of OH to be only 0.5 kcal/mol at the MP2/6-3 1G*//HF/6-31G* level of theory. This is much smaller
than that found in phosphoranyl radicals at the same level of theory (vide supra). Evidently, the residence of the unpaired electron in the equatorial position serves to considerably increase the apicophilicity of the hydroxyl ligand. For closed-shell H3P(OH)2, Wang et al. found diequatorial substitution to be the global minimum. This observation, together with other analyses, makes it apparent that the stronger equatorial-equatorial hyperconjugative interactions discussed above are operative in th phosphorane series as well and that they are sufficient to overcome the weak apicophilicity of OH in this system. The stronger apicophilicity of hydroxyl in the phosphoranyls favors the diaxial conformation in the dihydroxyphosphoranyl radicals. However, in the trihydroxy system discussed here, the large equatorial-equatorial hyperconjugative interactions result in a global minima, e-eeal, where the substitution pattern is diequatorial-monoaxial. NBO analysis provides semiquantitative support for this contention, insofar as the sum of all no O*PO interactions is greater for the eea isomer than for the aae, with the ee interaction being largest, the ae still of moderate importance, and the aa very small. Stereoelectronic Effects in TBP, Structures. The largest hyperconjugative stabilization in TBPa systems remains associated with the delocalization of equatorial oxygen lone pair density into other equatorial P-X antibonding orbitals. There being three possible equatorial-equatorial interactions available in the TBPa systems, the structure can remain stable even in the face of the pronounced apicophobicity of the unpaired electron. Interestingly, in the series of all equatorial trihydroxy TBP, structures, the highest doubly occupied orbital (HOMO) switches with the next lowest orbital (NHOMO) on going from the all anti system a-eeel to the anti-anti-eclipsed a-eee2. In a-eeel the HOMO is the fully antibonding combination of the three oxygen p orbitals in the equatorial plane and the NHOMO is composed of the apical hydrogen s orbital interacting in an antibonding fashion with the oxygen and phosphorus p orbitals parallel to the symmetry axis. This latter orbital continues to
-
Gustafson and Cramer
2276 J. Phys. Chem., Vol. 99, No. 8, 1995 increase in energy with successive hydroxyl rotations, giving rise to the observed stability ordering in the a-eee TBP, series. Put more succinctly, it appears to be the avoidance of destabilizing 4-electron interactions between the 0-H and P-H bonds which drives the preference for anti vs eclipsed hydroxyl orientations relative to the apical P-H bond, and it is the maximization of hyperconjugative stabilization which drives the preference for hydroxyl groups to align themselves parallel with the apical axis. Finally, TureEek et al.49 have suggested a stereoelectronic component in accessible 0-H bond dissociation pathways in P(OH)4 that resembles anchimeric assistance. Stereoelectronic Effects in Transition State Structures. Hyperconjugative delocalization of basal oxygen lone pairs into apical antibonding (or half-filled) orbitals appears to be in part responsible for the hydroxyl orientations in the pseudoinversion, spa pseudorotation, and SPb pseudorotation transition state structures. In each case, the basal hydroxyls prefer to orient themselves perpendicular to the apical bond (or the p orbital containing the unpaired electron in the case of pseudoinversion). When available, of course, this orientation also maximizes electrostatic interactions available from nonideal hydrogen bonding. Hyperconjugative delocalization of apical lone pairs into basal antibonding (or half-filled) orbitals is moderate to large depending on the orientation of the 0,-H bond. Stabilization is maximized when the H-O,-P-Ob dihedral is -45", Le., a typical (for a square pyramid) gauche orientation is preferred. The relative p-01, bond lengths for the transition state structures discussed above as case ii for HP(OH)3 illustrate this effect: in every case, the P-ob bond to which the apical hydroxyl is gauche is longer than the one to which it is not. NBO results are in excellent accord with this geometrical analysis. Finally, NBO analysis identifies moderate to large stabilizations from delocalization of basal oxygen lone pair density into anti basal u*po orbitals. Anti arrangement of the two basal hydroxyl groups appears to generate better overlap than does syn, insofar as NBO analysis indicates interactions in the latter instance to be uniformly less stabilizing than the former. PseudoinversionBarriers. Previously, we observed that the barrier to pseudoinversion increased from roughly 13 to 20 kcaVmol going from mono- to dihydroxypho~phoranyl.~ The activation energy required for the pseudoinversion process continues to increase with tri- and tetrahydroxy substitution (30 and 42 kcaumol, respectively). This is, of course, entirely consistent with the general trend observed for atoms substituted with an increasing number of electron withdrawing groups, e.g., NF3 has a much higher inversion barrier than NH3. This is generally rationalized by noting that the central atom is forced to remove all s character from the orbital containing the nonbonding electron(s) in the approximately planar transition state and instead must distribute it among the bonds to its more electron-withdrawing substituents.62 It appears unlikely that pseudoinversion could be observed for HP(OH)3 and P(OH)4, since the activation energies are above those required for 0-H bond d i s s o ~ i a t i o n . ~ ~ Conversion Pathways. For a given SPb pseudorotation transition state structure, it is essentially impossible to predict the corresponding reactants and products without following the intrinsic reaction coordinate. In addition to the two IRCs of Figure 7 parts c and d, Figure 11 illustrates the connectivity between reactants, products, and transition state structures for all 19 SPb single and double pseudorotations (except for ?)rot. b 6 , for which the IRC proved technically problematic). We note again that single pseudorotations interconvert TBP, and TBP,
e-eeal
/
dbl yror
\
e-aael e-aae2
e-aae3
e-eea4
% .
-acre4
Figure 11. The interconnectivity of the HP(OH)3 local minima through the SPb pseudorotation and double-pseudorotation transition state as determined from IRC calculations. Single-headed arrows are in the direction of decreasing energy.
minima while double pseudorotations interconvert two TBP, minima. Because double pseudorotations may be thought of as first interchanging two pairs of equatorial and axial ligands and then interchanging another (not necessarily identical) two pairs of each prior to returning to a minimum, it is possible for multiple \:?) TS structures to connect the same two minima; thus, there are three unique double pseudorotations interconverting e-aae3 to e-eea2. In addition, it is possible that paths leading downward from some of the transition states bifurcate;63 we have not searched carefully for such situations, and that may explain why not all minima are shown connecting to a pseudorotation TS structure. Conclusions. We emphasize five points illuminated from studies of the polyhydroxylated phosphoranyl radicals. (i) A subtle interplay of electrostatic interactions, intrinsic apicophilicity, and hyperconjugative stabilizations dictates the relative energies of minimum energy stationary points. With three or four hydroxyl groups, hyperconjugative stabilization between substituents can overcome the intrinsic apicophobicity of the unpaired electron and render TBP, stationary points minima. (ii) The magnitude of the hyperconjugative stabilization between any two equatorial substituents is always significantly greater than the equivalent interaction for any other substitution pattern.
HP(OR)3 and P(OR)4
[R = H or CH31
(iii) For mono- and dihydroxyphosphoranyl radicals, normal pseudorotation between TBP, and TBP, minima is not possible since TBP, stationary points are not minima; double pseudorotation is observed for these systems. However, since tri- and tetrahydroxy substitution stabilizes the TBPa geometry, pseudorotation proceeds in both the single and double modes. (iv) In general, pseudorotations in which the unpaired electron is basal in the TS structure (both single and double) are the lowest energy stereopermutational processes. Pseudoinversions are lower in energy than pseudorotations in which the unpaired electron is apical in the TS structure (single only) when only one hydroxyl group is present, they are roughly equal in energy when two hydroxyl groups are present, and pseudoinversions become quite high in energy when either three or four hydroxyl groups are substituted. (v) Although our present efforts have not yet identified a system in which a TBP, isomer is the global minimum, we have certainly established that TBP, isomers can be minima and indeed that they are not significantly higher in energy than TBP, isomers in select instances. It is intriguing to speculate that the realization of the former goal requires only a more judicious choice of phosphoranyl substituents.
Acknowledgment. It is a pleasure to acknowledge support from the U.S.Army Research Office (DAAH04-93-G-0036). We thank Professor Frantisek TureEek for sharing with us his experimental and theoretical results on P(OH)4 prior to publication. Lastly, we are grateful to Dr. Mike Miller for assistance in molecular visualization. Supplementary Material Available: Listings and one table giving predicted IR spectral data for the lowest energy TBP, and TBP, minima of HP(OH)3 and P(OH)4 and Gaussian 92 archive information for all structures (23 pages). Ordering information is given on any current masthead page. References and Notes (1) Cramer, C. J. J . Am. Chem. SOC.1990, 112, 7965. (2) Cramer, C. J. J . Am. Chem. SOC. 1991, 113, 2439. (3) Cramer, C. J. Chem. Phys. Lett. 1993, 202, 7034. (4) Cramer, C. J.; Gustafson, S. M. J. Am. Chem. SOC. 1993,115,9315. ( 5 ) Cramer, C. J.; Gustafson, S. M. J. Am. Chem. SOC. 1994, 116,723. (6) Gillbro, T.; Williams, F. J . Am. Chem. SOC. 1974, 96, 5032. (7) Gorlov, Y. I.; Penkovsky, V. V. Chem. Phys. Lett. 1975, 35, 25. (8) Howell, J. M.; Olsen, J. F. J . Am. Chem. SOC.1976, 98, 7119. (9) Roberts, B. P. Tetrahedron Lett. 1983, 24, 3377. (10) Janssen. R. A. J.: Visser. G. J.: Buck. H. M. J . Am. Chem. SOC. 1984, i06, 3429. i l l ) Janssen, R. A. J.: Buck, H. M. J . Mol. Struct. (THEOCHEM) 1984, 110, 139. (12) Janssen, R. A. J.; Buck, H. M. Chem. Phys. Lett. 1986, 132,459. (13) Janssen. R. A. J.: Sonnemans. M. H. W.: Buck, H. M. J. Am. Chem. So;. 1986, 108, 6145. (141 Gonbeau. D.: Guimon, M.-F.; Ollivier, J.; Pfkter-Guillouzo, G. J. Am: Chem. SOC. 1986, 108, 4760. (15) Janssen, R. A. J.; Kingma, J. A. J. M.; Buck, H. M. J. Am. Chem. SOC.1988, 110, 3018. (16) Nguyen, M. T.; Ha, T.-K. Chem. Phys. 1989, 131, 245. (17) Demolliens, A.; Eisenstein, 0.; Hiberty, P. C.; Lefour, J. M.; Ohanessian, G.; Shaik, S. S.; Volatron, F. J . Am. Chem. SOC. 1989, 111, 5623. (18) Geoffroy, M.; Rao, G.; TanEic, Z.; Bemardinelli, G. J. Am. Chem. SOC.1990, 112, 2826. (19) Janssen, R. A. J.; Aagaard, 0. M.; van der Woerd, M. J.; Buck, H. M. Chem. Phys. Lett. 1990, 171, 127. (20) Aagaard, 0. M. Ph.D. Thesis, Technische Universiteit Eindhoven, 1991.
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