382
J . Phys. Chem. 1984, 88, 382-389
Structure, Bonding, and Internal Rotation in H,PO, H,POH, and HFPOH Michael W. Schmidt, Satoshi Yabushita, and Mark S. Gordon* Department of Chemistry, North Dakota State University, Fargo, North Dakota 581 05 (Received: May 25, 1983)
The fundamental nature of the PO bond is reexamined by using ab initio (3-21G* and 6-31G*) wave functions and energy-localizedorbitals. The bond is best described as a dative single bond augmented by ?r back-donation from the oxygen lone pairs. The isomerization pathway from H3P0 to H2POH is followed by using the intrinsic reaction coordinate and localized orbitals. The latter, more stable, isomer has two forms, cis and trans, which are nearly equal in energy. The internal rotation barriers in this molecule and in HFPOH are examined with a Fourier analysis and compared with their nitrogen analogues. The major differences between the potential curves in phosphorus and nitrogen species are attributed to different dipole-dipole (DD) interactions between the HYX and OH moieties.
Introduction The oxides of substituted phosphines, Le., XYZPO, form a numerous class of hypervalent phosphorus compounds. The simplest molecule of this type is phosphine oxide itself; H3P0 is not known experimentally, but due to the simplicity of its ligands it is an obvious candidate for ab initio characterization of the PO bonding in these compounds. In the early 1970s several theoretical papers dealt with the nature of bonding in H3POI4 and some of its fluorine derivatives.>’ These SCF studies focused on the degree of participation of d orbitals centered on phosphorus in the molecular wave function, and the description of the PO bond. The earlier investigations led to the recent, more extensive calculations of Kutzelnigg and co-w~rkers,s~~ who concluded that, while d orbital participation is significant, it is much less than in a “true” hypervalent molecule (in the sense of full sp3d hybridization at P). In all these studies Mulliken population analyses indicate that the PO bonding is best described as a donation from the phosphine supplemented by some degree of back-donation from oxygen through the formation of p-d bonds. However, this consensus was muddled to some degree by the proposal of Kutzelnigg and c o - w o r k e r ~(based ~ ~ ~ on Boys-localized SCF orbitals) that PO be viewed as a triple bond. The present work reexamines the molecular electronic structure of the H3P0 molecule. The nature of the ”hypervalent” PO bond in this molecule is characterized via energy-localized SCF orbitals, and this bond is compared to the normal double bond in HPO and single bond in H2POH. As this latter molecule is slightly more stable than phosphine oxide, the isomerization surface connecting these isomers is presented. For comparison, the transition state for isomerization of HPO to POH is given. Finally, the surface for internal rotation in H2POH is described, together with the effect of fluoro substitution. Comparison of these phosphorus compounds to the analogous nitrogen systems is made wherever possible. Computational Approach It is well-known that adequate predictions of structural properties of hypervalent compounds (e.g., H3PO) require d orbitals To maintain consistency in the basis set of the central (1) Marsmann, H.; Groenmweghe, L. C. D.; Schaad, L. J.; VanWazer, J. R. J . A m . Chem. SOC.1970, 92, 6107. (2) Hillier, I. H.; Saunders, V. R. J . Chem. SOC.A 1970, 2475. (3) Demuynck, J.; Veillard, A. Chem. Commun. 1970, 873. (4) Guest, M. F.; Hillier, I H.; Saunders, V. R. J. Chem. SOC., Faraday Trans. 2 1972, 68, 867. (5) Bossett, P. J.; Lloyd, D. R.; Hillier, I. H.; Saunders, V. R. Chem. Phys. Leu. 1970, 6 , 253. (6) Serafini, A,; Labarre, J.-F.; Veillard, A,; Vinot, G. Chem. Commun. 1971, 996. (7) Absar, I.; Van Wazer, J. R. J . A m . Chem. SOC.1972, 94, 6294. (8) Kutzelnigg, W. Pure Appl. Chem. 1977, 49, 981. (9) Wallmeier, H.; Kutzelnigg, W. J . A m . Chem. SOC.1979, 101, 2804.
0022-3654/84/2088-0382$01 S O / O
in the current work, all basis sets use the same exponent (0.55)” for the phosphorus d orbital. For structural predictions both the STO-2G*Ioand 3-21G*I1 bases were used. Both of these bases include only the five true d orbitals on phosphorus, since the use of the x2 + y 2 z2 s contaminant present in the usual six Cartesion d orbitals exaggerates the importance of d orbitals in these basis sets. For single point calculations the larger 6-31G*I2(containing all six d components, on oxygen and fluorine as well as phosphorus) was used. The importance of the d orbitals in the wave functions can be monitored by a Mulliken population ana1y~is.I~ All stationary points (equilibrium geometries and transition states) were located at the SCF level. To improve the estimates of overall energy differences and barrier heights, the SCF calculations were supplemented by second- and third-order Moller-Plesset perturbation theoryI4J5(MP2 or MP3) or MCSCF calculations. The basic computer program used here is a slightly modified version of G A U S S I A N ~ ~ .This ~ ~ program features Schlegel’s method” for the location of stationary points and performs the perturbation theory corrections. Energy-localized orbitals were obtained by using the ALIS~*program system, while the MCSCF calculations, vibrational analysis, and determination of Boyslocalized orbitals were done by using the GAMESSI9 program.
+
Results and Discussion Structures. Optimized equilibrium geometries for all molecules considered here are presented in Figure 1. Transition-state structures are given in Figure 2. For the most part, the chemical significance of the computed geometries will be discussed where appropriate below. Here we are concerned primarily with comparison of the geometries predicted by both the STO-2G* and 3-21G* bases. The most interesting coordinates are, of course, the PO bond lengths. STO-2G* consistently predicts shorter PO distances than (10) Collins, J. B.; Schleyer, P. v. R.; Binkley, J. S.; Pople, J . A. J . Chem. Phys. 1976, 64, 5142. (1 1) Pietro, W. J.; Francl, M. M.; Hehre, W. J.; DeFrees, D. J.; Pople, J. A.; Binkley, J. S. J. A m . Chem. SOC.1982, 104, 3039. (12) Francl, M. M.; Pietro, W. J.; Hehre, W. J.; Binkley, J. S.;Gordon, M. S . ; DeFrees, D. J.; Pople, J. A. J . Chem. Phys. 1982, 77, 3654. (13) Mulliken, R. S. J . Chem. Phys. 1955, 23, 1833, 1841. (14) Moller, C.; Plesset, M . S. Phys. Rev. 1934, 46, 618. (15) Pople, J. A.; Binkley, J. S.; Seeger, R. Inr. J . Quanrum Chem.,Symp. 1976, JO, 1. (16) Binkley, J. S.; Whiteside, R. A.; Krishnan, R.; Seeger, R.; DeFrees, D. J.; Schlegel, H . B.; Topiol, S.;Kahn, L. R.; Pople, J. A. QCPE 1981, 138 406. (17) Schlegel, H. B. J . Compur. Chem. 1982, 3, 214. (18) Elbert, S. T.; Cheung, L. M. Ruedenberg, K. NRCC Software Catalog 1980, 1, Program QMO1. (19) Dupuis, M.; Spangler, D.; Wendoloski, J. J . NRCC Software Catalog 1980, 1. Program QGOl.
0 1984 American Chemical Society
The Journal of Physical Chemistry, Vol. 88, No. 3, 1984 383
Structure of H3P0, H,POH, and HFPOH
an encouraging result in view of the computational savings of this basis vs. 3-21G*. Since S C F geometry optimizations are dominated by integral and integral derivative computation, STO-2G and STO-2G* are to be preferred over the more commonly used STO-3G or STO-3G* bases, which contain 50% more Guassian primatives. Bonding in Phosphine Oxide. The phosphorus-oxygen linkage in molecules such as H 3 P 0has been described variously as single, double, or triple in nature. The PO group is customarily written as a double bondz2
105 3
\
,;iP=o
I597 I518 ( I 5881,
962
,P-
o
L H
H
(95 91 b H P O = 9 2 8 (9551
a H P 0 = 9 8 3 (10001
4 FPO =IO1 8
Z$FP0=102I 1 l O l O l
(10191
Figure 1. Equilibrium geometries: STO-2G*, 3-21G* (in parentheses), and experiment (underlined).
a H p P 0 = 9 88 ( 9 8 9 )
w H,POH=26 6 1367)
&
HPO- 9 5 6 (976)
b H P 0 = 9 7 1 (1000)
FPO=1006 (998)
bFPO.989
wHOPH=1215 (12721
(974)
wHOPH = - 3 2 7 ( - 5 8 61
Figure 2. Transition states: STO-2G*, 3-21G* (in parentheses).
does 3-21G*. Perhaps the most severe test of the STO-2G* predictions is H3P0, the only hypervalent molecule considered here. As this molecule is presently unknown, the true PO distance is unavailable. However, the PO distance in trimethylphosphine so the 3-21G* result of 1.470 8, for H 3 P 0 is oxide is 1.48 probably accurate. Thus, the STO-2G* basis underestimates the PO bond length in hypervalent compounds by about 0.05 A. In hydroxy phosphines, STO-2G* underestimates the POH angles by about loo compared to 3-21G*. On the basis of calculations on the geometry of water," the smaller basis set is more likely to be correct here. The STO-2G basis set has previously been found to be surprisingly accurate for estimating stable structures and transition states for normal-valent compounds.21 The current work suggests that the STO-2G* basis works as well for hypervalent systems, (20) Wang, H. K. Acta Chem. Scand. 1965, 19, 879. (21) Gordon, M. S.; Holme, T. A,; Stone, C., unpublished results.
based primarily on the short length of this bond. Computed PO distances, using a 3-21G* basis set, are 1.470 8, in H,PO, compared to 1.469 8, in the doubly bound, normal-valent HPO, and 1.641 8, in the singly bound H2POH. Formally, however, the doubly bonded picture for H 3 P 0 requires the expansion of the octet about the phosphorus to 10 electrons, indicating that the low-lying atomic d orbitals are involved in the hybridization at P. A naive picture of the PO bond is that of a single dative bond,,* formed by the u donation of the phosphine lone pair to a vacant p orbital on the oxygen. This viewpoint is simpler in that all atoms possess normal octets. It explains the tetrahedral arrangement of the atoms about phosphorus but does not account for the shortened PO distance. This shortened bond length was explained by ab initio calculations in the early 1970s.'-' The S C F configuration is ...(7a1)2(3e)4,where 7al is the strong u bond, and the 3e shell primarily two lone pairs localized on the oxygen atom. However, these lone pairs are aligned such that they can form p,-d, bonds with certain of the low-lying d orbitals present on phosphorus. It is this partial x back-donation in addition to the strong u donation that accounts for the strength, and shortness, of the bond. This is readily proven by calculations with and without a set of d basis functions on phosphorus. Adding these functions shortens the bond by about 0.13 A9 and leads to appreciable population of these orbitals. Upon isoelectronic replacement of oxygen by the poor x donor BH3, the importance of the d orbitals on phosphorus is much dimini~hed.~ A standard device for analysis of quantum-mechanical wave functions is the determination of localized orbitals. Perhaps the most widely applied method for the determination of such orbitals, because of its speed, is that of Foster and Boys.24 H 3 P 0 orbitals localized by the Boys procedure were first obtained by Guest, Hillier, and S a ~ n d e r s .They ~ consist of three P H bonds, three equivalent "banana" bonds betweem the phosphorus and oxygen atoms, and one long pair on the oxygen atom, directed away from the phosphine group along the PO axis. On the basis of such localized orbitals Kutzelnigg*and Wallmeir and Kutzelnigg9have suggested that the PO linkage is best viewed as a triple bond, since there are six electrons between P and 0. Contour plots of the Boys-localized orbitals for phosphine oxide have never been published and accordingly are presented in Figure 3. An alternative, slightly more time-consuming localization procedure is the energy localization scheme of Edmiston and RuedenbergSz5The energy-localized orbitals of phosphine oxide are also shown in Figure 3. They consist of three equivalent P H bonds, one strong PO u bond, and three equivalent orbitals on oxygen whose character is principally lone pair. However, it may be seen that each of these oxygen lone pairs possesses some tendency to back-donate electron density to the phosphorus. These (22) Hudson, R. F. "Structure and Mechanism in Organophosphorus Chemistry"; Academic Press: New York, 1965. (23) Jenson, K. A. Z. Anorg. Allg. Chem. 1943, 250, 268. (24) Foster, J. M.; Boys, S. F. Reu. Mod. Phys. 1960, 32, 300. (25) Edmiston, C.; Ruedenberg, K . Reu. Mod. Phys. 1963, 35,457. Edmiston, C.; Ruedenberg, K . J. Chem. Phys. 1965, 43, 597. (26) Trinquier, G.; Malrieu, J.-P. J . Am. Chem. Soc. 1979, 101, 7169. See also: Mitchell, D. J.; Wolfe, S.;Schlegel, H . B. Can. J . Chem. 1981, 59, 3280. (27) von Burkart, W. D.; Hohn, E.-G.; Goubeau, J. Z . Anorg. Allg. Chem. 1978, 442, 19. (28) Selig, H.; Claasen, H . H. J . Chem. Phys. 1966, 44, 1404.
384 The Journal of Physical Chemistry, Vol. 88, No. 3, 1984
Schmidt et al.
I
I
I
I
Enemy
c
/
t
t
3
'
r
-
L
-
1
-
-
!
Figure 3. Contour plots of the 3-21G*Boys-localized and energy-localizc:d orbitals. Increment between all contours is 0.05 bohi3i2.
back-donating lone pairs are staggered with respect to the P H bonds. The energy- and Boys-localized MOs shown in Figure 3 are quite dissimilar. Usually the two procedures lead to similar results, and thus the same interpretation of chemical binding, as is the case here for the PH bonds. That the remaining orbitals represent distinct rather than multiple solutions to the localization equations was demonstrated by starting each localization process with the localized orbitals from the other method. Both procedures reverted to their original solution. The localization sums for the 3-21G* basis, which are maximal for the most localized orbitals, are 455, 1006, and 995 D2in the Boys method, and 3.691,5.025, and 5.079 hartree in the energy localization, for the canonical, Boys-localized, and energy-localized MOs, respectively. Thus, the two localization methods do yield distinct solutions and thus differing interpretations of the binding. The energy-localized orbitals are clearly in accord with the picture of the PO bond as arising from strong u donation enhanced by some degrees of a back-bonding. The extent of this backdonation may be gauged by a Mulliken population analysis. When a 3-21G* basis is used, a total of 0.408 electron is present in the phosphorus d orbitals in phosphine oxide, compared to just 0.126 in phosphine. Clearly the d orbitals are much more important in the oxide. Each P H bond contributes 0.0604 to the oxide's d population, the PO u bond contributes 0.0573, and each oxygen lone pair contributes 0.0565 electron. For comparison, the d population in each energy-localized P H bond of phosphine is 0.0421, with just 0.00006 in the phosphine lone pair. While the total population in the d orbitals clearly shows their greater importance in the oxide, this importance is not isolated in any
particular type of localized orbital. The back-bonding seen in the oxygen lone pairs in Figure 3 is directly responsible for 60% of the increased d population in the oxide. A Mulliken breakdown of one such oxygen lone pair is informative: the bulk of the pair, 1.805 e-, is situated on oxygen, with 0.195 e- on phosphorus, and only traces on the hydrogens. The 0.195 e- population on phosphorus breaks down as follows: s basis functions, -0.0056; p basis functions, 0.1439; and d basis functions, 0.0565. Thus, the a back-donation evident in these lone pairs is primarily into p rather than d orbitals! Since phosphorus p orbitals participate in back-bonding in the oxide, their role in the other valence MOs is necessarily reduced, thereby producing the secondary effect of increasing the d orbital population in the other valence MOs. Of the three bonding schemes discussed, namely single, double, or triple bonding, the picture of a single u bond reinforced by some a back-bonding is best supported by the energy-localized orbitals presented here. There is no quantum-mechanical justification in the form of the canonical or either type of localized SCF orbitals for a double bond, in the sense of four binding electrons. Triple bonding is supported by the Boys-localized orbitals, but this interpretation seems overly complicated compared to the enhanced single-bond interpretation afforded by the energy-localizedorbitals. Therefore, we favor the energy-localization procedure in hypervalent compounds containing the PO moiety. Consequently, this functional group is better represented by the Lewis structure \P+
"I than by the conventionally written double linkage or a triple bond.
Structure of H3P0, H2POH, and HFPOH
The Journal of Physical Chemistry, Vol. 88, No. 3, 1984 385
TABLE I: Vibrational Frequencies"
open H,POH OH torsion PO stretch PH, n.ag-OH defd HPH bend PH, wag-OH detP HPH bend PH stretch PH stretch OH stretch
a"
a' a'
a" a' a' a"
a' a'
H,PO
-244 91 1 1007 1024 1206 1299 25 94 26 12 390 I
HPO bend HPH bend PO stretch HPH bend PH stretch PH stretch
HPOC
e
e a, a, C
a,
a'
HPO bend PO stretch PH stretch
976 I238 1 287b 1437 2644 2687
I'
a'
1152 1498 25 14
"
SCF harmonic frequenciea calculated by using a 3-21G* basis in c i i i - ' . Harmunic Lero-point encrgics are 21.1. 21.6. and 7.4 kcal/nlol for H,POH, H,PO, and HPO, respectively. This frequency is 1160 c i ~ i r 'for (CH,) PO.?' 1284 c i i i - ' for (OCH,),PO.*' and 1418 C I I I - ' tor I.',PO.zs The experimental frcquencies are 9 8 5 , 2 9 1 188,29and 2IOO3' c m - l . 3 Syminctric combination. e Antisymmetric combination TABLE 11: Energies of H,PO Isomersa
This interpretation is also supported by the large charge separation in the PO bond. The above Lewis structure has formal charges P'O-, and the computed 6-3 lG* Mulliken charges are as follows: P, 0.912+; 0,0.688-; H, 0.075-. This charge separation produces a large electric dipole moment of 3.73 D. The PO single bond in phosphine oxide can be viewed as forming in an acid-base reaction, where oxygen serves as the acid. This interpretation is confirmed by viewing oxygen as the ultimate member of an isoelectronic sequence of acids: BH3, CH,, NH, 0. Compounds of substituted phosphines with each of these are known experimentally. The borane adduct lacks any lone pairs on boron to back-donate; thus, the PB bond consists purely of u donation to BH3. Trinquier and Malrieu26have shown that singlet methylene tilts during attack of phosphine, enabling donation of the phosphine lone pair into methylene's vacant p orbital during formation of the ylide methylene phosphorane. As the number of lone pairs present on the acid increases, the amount of a back-donation should increase, presumably in proportion to the number of such pairs. Thus, the ylide and phosphine imide are also better viewed as containing PC or PN single bonds, reinforced by back-donation from one or two lone pairs, in preference to their usual representation as double bonds. One might justify the description of the PO bond as double, based on its strength, even though one cannot point to a set of four binding electrons. One measure of a bond's strength is its length. As already mentioned, phosphine oxide's bond length is close to that of the double bond in HPO. Another measure is the PO stretching frequencies, which are calculated to be 91 1, 1287, and 1498 cm-I for H2POH, H3P0, and HPO. This would indicate that the a back-donation in H 3 P 0 has substantially strengthened the bond compared to a normal PO single bond. Nonetheless, the H3P0 stretching frequency falls significantly short of that of the normal double bond in HPO. The remaining frequencies of these molecules are given in Table I. Finally, we summarize Wallmeir and Kutzelnigg's results for H3N0.9 These workers find that d orbitals on N are energetically less important than in the phosphorus analogue but that these functions must be used for correct computation of the rather short NO bond distance. Thus, while back-bonding to d orbitals is more important in H3P0 than H 3 N 0 , the two compounds are more similar than not in that the primary binding effect is u donation. It is interesting to note that these authors find the Boys-localized MOs in H 3 N 0 to resemble the energy-localized set for H 3 P 0 presented here. 1-2 Hydrogen Shifis. In view of the above interpretation of the PO bond in phosphine oxide as a single bond, albeit strengthened through appreciable back-bonding, a comparison of this bond to a "normal" PO single bond is of interest. The simplest possible compound containing such a bond is phosphinous acid, H2POH, an isomer of H3P0. The total and relative energies for these isomers and the transition state separating them are given in Table 11. At the best level of calculation the "normal" isomer
lies 5.6 kcal/mol below the hypervalent compound. The structure of the transition state for the isomerization of H 3 P 0 to the open form of HzPOH is given in Figure 2. At the transition state the PO bond length has become intermediate between H 3 P 0 and H2POH. The latter species are separated by a sizable barrier of 70 kcal/mol, again at the best level of calculation. While the large isomerization barrier makes such an isomerization unlikely to occur, the reaction path connecting these stationary points is still of interest for it connects the hypervalent "single" and normal-valent single PO bonds. We have used the intrinsic reaction coordination (IRC) method of Fukui3' and M o r o k ~ m ato~proceed ~ from the transition state toward both products and reactants. Energy-localized orbitals have been obtained at representative points along the IRC and are shown in Figures 4 and 5. It is apparent that, apart from lengthening, the PO u bond changes very little during the isomerization. Of particular interest is the region in which the loss of a back-bonding occurs. This clearly happens before H 3 P 0 reaches the transition
(29) Larzilliere, M.; Danamy, N.; Lam Thanh, M. Can. J . Phys. 1979, 57, 539. (30) Larzilliere, M.; Jacox, M . E. J . Mol. Specrrosc. 1980, 79,132.
(31) Fukui, K . J . Phys. Chem. 1970, 74, 4161. (32) Ishida, K.; Morokuma, K.; Kornornicki, A. J . Chem. Phys. 1977, 66, 2153.
T S ~
H3POb RH1'/3-21G*
-415 2 0 7 0 1
(0.0) RHb/6-3 IC"
-41 7.306 6 9
MP213-21G"
-415.435 6 1
MP216-31G"
-417 594 0 9
(0.0)
(0.0) (0.0) MP3/3-21GX - 4 1 5 . 4 3 9 9 3
(0.0) MP3/6-31G*
-417.602 86
-415.068 22 (87.1) -417.173 16 (83.8) -415.320 1 1 (72.5) -4 17.487 90 (66.6) -4 15.3 19 65 (75.5) -417.491 34
(70.0)
(0.0)
open H , P O H ~ -415.21665 (-6.0) -417.313 32 (-4.2) -415.431 81 (-2.4) -4 17.594 6 4 (-0.3) -415.446 6 0 (-4.2) -417.61173 (-5.6)
a In hartrces. with relative energies in kcal/lnol in parenrhdscs. TS = tranyition s t a t e . At 3-21G* geometry.
TABLE Ill: Energies of 'A' HPO Isomers' HPO RHI' MP2 MP3
MCSCI'
-414.09453
TS
-413.95291 (0.0) (88.9) - 4 1 4 . 3 2 2 3 6 -414.206 1 2 (0.0) (72.9) - - 4 1 4 . 3 2 2 9 6 -414.196 16 (0.0) (79.6) -414.206 77 -414.081 3 2 (0.0) (78.7)
POH
H A POo
-414.054 10 - 4 1 4 . 0 1 0 7 3 (25.4) (52.6) -414.26446 (36.3) -414.27299 (3 1.3) -414.152 28 - 4 1 4 . 0 9 8 4 1 (34.2) (68.0)
" Using a 3-21G* + basis. containing a s a n d p shell with a dii'fusc exponent 10.039) o n pho\phoru\. and all si\ d components. Total cnergics in hart recs, with relative cncrgics, i n parcnthcses. in kcal/mol. Transition stale. In ground * S and * T rtates. The KIII, a n d l'ORS-hlCSCI: cncrgy of hydrogen i n this basis is -0.496 20.
386
The Journal of Physical Chemistry, Vol. 88, No. 3, 1984
Schmidt et al. 1,s.
Hpo
--
.
...
.
\
.
-
w - 00 Cd
)o.
0-
. . ..
27.0 Q4Q
7a7 0.358
OXI
am
Figure 4. 3-21G* energy-localized orbitals along the IRC from H3P0 to the isomerization transition state.
state. Another measure of this loss of hypervalence is the phosphorus d orbital Mulliken population, which decreases from 0.408 for H,PO to 0.299 at the transition state to 0.191 for H,POH. Clearly, the change in the orbitals is more in keeping with the view of a meinforced single bond gradually becoming a single bond than a double or triple bond becoming single. Finally, we have examined the isomerization of oxophosphine to hydroxyphosphinidene, HPO to POH, on the ‘A’ surface. Energy results from a variety of calculational levels are given in Table-111. The geometry of the transition state is presented in Figure 2. The MCSCF calculations are based on the fully optimized reaction space (FORS) model of Ruedenberg et al.33and include 1316 configurationscorrelating all valence electrons within the nine valence MOs. The hydrogen shift in this system has a large barrier, 79 kcal/mol, quite comparable to the barrier to isomerization of H3P0. This type of shift, despite being symmetry allowed, has a barrier of nearly insurmountable size. In view of this large barrier to direct isomerization, we have explored hydrogen dissociation followed by recombination. H PO is calculated to lie 68 kcal/mol above HPO, lower than the transition state for direct isomerization. However, this channel involves greater changes in correlation energy than the direct pathway, since bonds are completely broken. FORS-MCSCF calculations underestimate AH bond strengths for first-row atoms A by 15-25 so that the direct isomerization is probably a lower kcal/m01,~~ energy pathway than dissociative recombination. The ‘A’ surface of HPO is quite analogous to that for HNO. Unpublished FORS-MCSCF calculations for HN035predict an
+
(33) Ruedenberg, K.; Schmidt, M. W.; Gilbert, M. M.; Elbert, D. T. Chem. Phys. 1982, 71, 48. (34) Schmidt, M. W., unpublished results.
isomerization barrier of 76.0 kcal/mol, with singlet NOH 42.3 kcal/mol above HNO. While the barriers for the two systems are similar, XOH is lowered (relative to HXO) by about 10 kcal/mol when X = P. Preliminary calculations suggest that POH has a triplet ground state in analogy with the ground state for NOH.~~ Internal Rotation in H,NOH, H,POH, HFNOH, and HFPOH. Though there are several e~perimental~’-~l and the~retical~*-~O
(35) Feller, D. F. Ph.D. Thesis, Iowa State University, Ames, IA, 1979. (36) Bruna, P. J.; Marian, C. M. Chem. Phys. Lett. 1979, 67, 109. (37) Giguere, P. A,; Lie, I. D. Can. J . Chem. 1952, 30, 948. (38) Tsunekawa, S. J . Phys. SOC.Jpn. 1976, 41, 2077. (39) Riddell, F. G.; Turner, E. S.; Rankin, D. W. H.; Todd, M. R. J . Chem. Soc., Chem. Commun. 1979, 72. (40) Rankin, D. W. H.; Todd, M. R.; Riddell, F. G.; Turner, E. S. J . Mol. Struct. 1981, 71, 171. (41) Riddell, F. G. Tetrahedron 1981, 37, 849. (42) Fink, W. H.; Pan, D. C.; Allen, L. C. J . Chem. Phys. 1967,47, 895. (43) Veillard, A. Theor. Chim. Acta 1966, 5, 413. (44) Pederson, L.; Morokuma, K. J . Chem. Phys. 1967, 46, 3941. (45) Wolfe, S.; Rauk, A,; Tel, L. M.; Csizmadia, I. G. J. Chem. SOC.B 1971, 136. (46) Radom, L.; Hehre, W. 5.; Pople, J. A. J . Am. Chem. SOC.1972, 94, 2371. (47) Pakiari, A. H.; Semkov, A. M.; Linnett, J. W. J. Chem. SOC.,Faraday Trans. 2 1976, 72, 1298. (48) Brunck, T. K.; Weinhold, F. J . A m . Chem. SOC.1979, 101, 1700. (49) Olsen, J. F.; Howell, J. M. J. Fluorine Chem. 1979, 12, 123. (50) Olsen, J. F.; O’Connor, D.; Howell, J. M. J . Fluorine Chem. 1978, 12, 179. (51) For a review see, e&: Payne, P. W.; Allene, L. C. In “Applications of Electronic Structure Theory”; Schaefer, H. F., Ed.; Plenum Press: New York, 1977; pp 29-108.
Structure of H3P0, H2POH, and HFPOH
The Journal of Physical Chemistry, Vol. 88, No. 3, 1984 387
TABLE IV: Calculated Relative Energies (in kcal/mol) of H , X O H and HFXOH, X = N or P'zb molecule
LM
TS
LM
ti = 0'
8 = 121.2"
e = 180"
10.14 8.69 8.68 12.0 1126.5") 9.9 ( 1 2 0 . 0 " ) 11.7 ( I 10.0") 10.2 (125.0") 0 = 96.1' 3.62 4.14 4.31 8 = 134.1' 5.20 6.49 8.25 (1 15.0') 0 = 102.4' 3.50 4.30
8.09 5.72 6.15 10.8C3d 7.4c>e 8.OCsp 6.4'~~ 0 = 180" -0.93 0.15 0.39 8 = 157.0" 5.08 4.62 5.04 (175.0") e = 183.6" -1.26 -0.30 0.06
method
H,NOH energy HF/3-21G HF/6-3 1G* MP3/6-3lG* previous work
H,POH energy H1:/3-21G* HI'/6-3 l G * MP3/6-31G* HI:NOH energy HI:/3-2 IG HI'/6-3 IG* previous work HFPOH energy €€1'/3-21G* HI'/6-3 1G* MP3/6-3 IG"
0.0 0.0 0.0 0.0 0.0 0.0 0.0 8 = 0" 0.0 0.0 0.0 0 = 36.0" 0.0
0.0 0.0 (25.0") 0 = 3 1.6" 0.0 0.0 0.0
TS
-
e = 260.6" 12.68 11.36 14.79 (270.0")C,f 8 = 288.1' 6.10 6.30
a LM means local minimum. T S tramition state (local maximum). The rotation angle 8 is defined as thc dihedral angle between thc OH bond and the lone pair on X atoni; see t e s t for details. Values in parcntheses reprevent 0 deterrnincd in previous calculation^. Reference 39. e Reference 41. Reference 4 3 . Ret'erencc 4 4 ,
studies concerning the internal rotations of H2NOH and derivatives, little attention has been paid to the phosphorus analogues. In order to investigate the nature of the PO single bond, as well as the different effects caused by phosphorus and nitrogen atoms, an analysis of internal rotation potential functions in these compounds was carried out. There are a number of approaches for treating internal rotation barriers.51 In the present work, the Fourier analysis method, which was first applied with ab initio wave functions by VeillardS2and Pople et a1.$6 has been used to facilitate the interpretation of the origin of the rotation barriers. Accordingly, the potential functions for H2NOH and H2POH are approximately expanded in a truncated series as follows:
v(e)= 1/zv,(1 - COS e) + Y2v2(1- COS 28) + 1/2V3(1 - COS 38) (1)
For HFNOH and HFPOH, owing to the lack of symmetry about 8 = 180°, additional parameters cy, are introduced as follows:
V(8)= f/zvl{cosa1 - cos (e - CYJ) + f/~V,(COS2az cos 2(8 - "2)) + '/ZV,(cos3"3 - cos 3(8 - 4)(2) Though this expression is somewhat different from the original it makes it possible to compare the potential constants 6 in eq 1 and 2 directly as well as to discuss the physical origins of the cyi. Here a Oo rotation angle 8 is defined so that the O H bond is antiperiplanar to the bisector of, e.g., the PF and PH bonds. The conformation with 8 between 0' and 180' means that the O H bond is closer to the P F bond than the P H bond:
For the local minima and maxima, shown in Figures 1 and 2, respectively, full geometry optimizations were performed, while for some midpoint geometries partial optimizations fixing the dihedral angle were carried out. Calculated relative energies of these molecules are listed in Table IV, and previous calculations (where available) are also included. H2NOH. The potential curve (HF/6-31G*//3-21G) for internal rotation in hydroxylamine is given in Figure 6a along with the Fourier decomposition according to eq 1 and the dipole moment function. The potential constants V, from eq l and total (52) Veillard, A. Chem. Phys. Left. 1969, 4, 51.
TABLE V:
HF/6-31G* Potential Constants for Internal
Rotation of HYX-OH a n d Component Analysis of HYX-H Dipole Momenta
H,NOH 6 . 4 9 H,POH 0.87 HFNOH 6 . 7 9 HI:POH 2.70
5.15 3.95 6.58 5.21
-0.77 -0.72 -1.27 -0.70
0.0 0.0 64.7 112.7
0.0 0.0 0.0 0.0 14.3 2.2 16.3 -14.1
1.81 0.83 2.17 1.41
0.0 0.0 77.2 103.2
a V , in kcal/mol, iui and O 1 in degrees, /JL in debye. 'See text for definitions of constants.
TABLE VI: Total Atomic Charges from the Mulliken Populations for the Most Stable Trans Conformation of HYXOH' n1olcculcs H,NOH H,POH H1:NOH HI.'POH
qXb
-0.537 -0.486 0.072 0.905
qHC
qYd 40 ____-________
0.359 -0.058 0.400 -0.090
0.359 -0.058 -0.348 -0.473
qHP
-0.636 -0.840 -0.596 -0.821
0.456 0.471 0.472 0.480
a 6-3 1G* basi\ $et was used throughout. X = N or P. H atom bonded to X atom. Y = H or I:. e H atom bonded to 0 a t 0111,
atomic charges from a Mulliken population analysis for the most stable trans (open) form (e = 0') are listed in Tables V and VI, respectively. It is clear that there is a large internal rotation barrier and a large energy difference between the two local minima, trans (8 = 0 ') and cis (8 = 180°).53 Geometry optimization seems to be responsible for making these values slightly smaller than those from previous calculations. Following Pople et al.,43it is reasonable to relate the VI term to a dipole-dipole (DD) interaction between the N H 2 and OH groups, the V2term to charge transfer (CT) of the nitrogen lone-pair electrons into the OH antibonding orbital, and the V, term to bond-bond repulsions, as illustrated in 1-111, respectively. Variation of the dipole moment H
(53) Riddell et al.'9,40recently predicted a much smaller free energy difference (0.6 kcal/mol) for trimethylhydroxylamine from their electron diffraction studies. Our ab initio calculation (HF/6-31G*//ST02G) for this molecule gives 7.4 kcal/rnol.
388 The Journal of Physical Chemistry, Vol. 88, No. 3, 1984
Schmidt et al. ypon
T.S.
\
-
80.8
Ewrgy9 87.1 Pd pop.
0.234
0.299
n.r am
-a0 0.m
Figure 5. 3-21G* energy-localized orbitals along the IRC from the isomerization transition state to H2POH.
dipole moment function, confirming the DD interpretation of the VI term. Comparing total atomic charges for HzPOH with those for HzNOH in Table VI, one finds the P-H bonds to be weakly polarized in the opposite direction relative to the corresponding N-H bonds, as shown in I and IV. Kutzelnigg et aL9 have
n
Iv
ROTATION
ANGLE
e
(DEG)
Figure 6. HF/6-31G* potential energy function (v),its Fourier decomposition (Vl-V3),and dipole moment function ( k ) for HzNOH (a) and HzPOH (b). The scale of the coordinate is common to energy (kcal/mol) and dipole moment (D).
function b(0) is consistent with the above interpretation of the Vl term, as can be seen in Figure 6a. Therefore, it is clear that the rotation barrier can be attributed to the C T and DD interactions, while the trans-cis energy difference originates from the DD interaction. H2POH. Figure 6b shows the potential curve (HF/6-31G*// 3-21G*) for internal rotation in H2POH with the Fourier decomposition according to eq l and the dipole moment function. Compared with H2NOH, the barrier is reduced by one-half, moves to about 0 = 90°,and becomes symmetric about 0 = 90° in its shape. In fact, the cis and trans forms were found to be nearly identical in energy as shown in Table IV. These characteristics of the surface for internal rotation reflect a smaller Vl value in Table V. This is consistent with the diminished variation of the
V
observed the same trends in total atomic charges for H2NOH and H2POH. The reversed polarization in the P-H bonds is probably responsible for the smaller change of the dipole moment function, as is easily seen in IV and V, although the point charges are not the only contribution to the net dipole moment. The main difference in the characteristics of the potential surface between H2POH and HINOH can therefore apparently be explained by the difference in the electronegativities of P and N atoms. Moreover, the difference between the P-0 and the N-O bond distances causes additional changes in both Vl and V,, because these interaction energies should be affected by the bond length. Figure 6b shows that the CT interaction (V,) is the predominant contribution to the H2POH rotational potential. HFNOH. As shown in Figure l a and Table IV the potential curve (HF/6-31G*//3-21G) for internal rotation in HFNOH has two barriers, at about 0 = 120' and at 0 = 270°, giving a shallow minimum at a cis form (0 = 180'). Similar results were obtained by Radom et The Fourier decomposition indicates that the potential curve is dominated by the Vl and V2components as in H2NOH. Figure 7 also shows a close relationship between the Vl and the dipole moment function. By use of the total atomic
The Journal of Physical Chemistry, Vol. 88, No. 3, 1984 389
Structure of H 3 P 0 , H2POH, and HFPOH
the potential constant V , for HFPOH is smaller than that for HFNOH. The origin of this as well as the larger V , value is illustrated in structure VII, depicted by using the results in P‘
I -”
H
F‘
’
VI1
HFPOH in Table VI. Again, it is noteworthy that the direction
I
0
60
120
ROTATION
180 ANGLE
240
e
300
3
(DEG)
Figure 7. HF/6-31G* potential energy function (V), its Fourier decomposition (Vl-V3),and dipole moment function ( p ) for HFNOH (a) and HFPOH (b). The scale of the coordinate is common to energy (kcal/ mol) and dipole moment (D).
charges of Table VI, the variation of this dipole moment function can be explained schematically as follows:
where the local dipole moment of the O H group is represented with a dashed arrow, while that of the N H F moiety is represented with a thick arrow. The latter is a vector combination of the moments of the N H , N F bonds and the lone pair on the nitrogen atom. From this one would anticipate that the DD interaction between these two and the dipole moment function have their minimum and maximum at common 8 values. Therefore, the close relationship between the Vl term and the dipole moment function suggests that the same physical significance can be attributed to the VI term even in nonsymmetric molecules. The V, component in Figure 7a shows almost the same behavior as in Figure 6a for H,NOH, in both the height and the position (a2= 14.3O). This is reasonable because fluoro substitution seems to have a minor effect on the C T from the lone-pair orbital on nitrogen into the O H antibonding orbital. HFPOH. As in H,POH, the cis and trans forms of HFPOH have almost the same energy. As shown in Table IV, MP3/631G* predicts the trans form to be slightly lower than the cis form. The potential curve (HF/6-31G*//3-21G*) for internal rotation in HFPOH is given in Figure 7b along with the Fourier decomposition according to eq 2 and the dipole moment function. This analysis shows that the potential barriers are dominated by the V, term as is the case for H2POH. Table V indicates that
of the charge polarization in the P-H bond is reversed relative to the N-H bond (cf. structure VI). According to Table V, one can say in general that the potential parameter VI for HYXOH is greater for X = N than for X = P. These trends can be explained through the bond moment analysis of structures I, IV, VI, and VII. Finally, in order to simulate realistic local dipole moments for the HYX fragments in the HYX-OH molecules, dipole moment components of HYX-H molecules were calculated by using 3-21G* X-H bond lengthses4 We define pI as that component of the molecular dipole moment which is perpendicular to the X-H bond, since pL is the critical value for evaluating dipole-dipole interactions. The results are shown in Table V, where O1 is the rotation angle of the pL component. There are g o d correlations between Vl and pLI and between a1and 81. This supports the simple bond moment analysis described above.
Conclusion The present paper has examined the electronic structure of the hypervalent PO bond in H3P0. This bond is found to consist of a strong B donation of the phosphine lone pair to the oxygen atom, augmented by a back-bonding of oxygen lone pairs to the phosphine. This interpretation of the PO bond is based on energy-localized S C F orbitals and a Mulliken population analysis. The role of d orbitals in H 3 P 0is intermediate between polarization (d population near zero, d’s having little effect on geometry) and true valence participation (d population 11). The viewpoint that H 3 P 0 contains an enhanced PO single bond is confirmed by PO stretching frequencies and by following the small, gradual changes in localized orbital shapes along the intrinsic reaction coordinate connecting H3P0 to H2POH. The potential curves for internal rotation in HYXOH molecules are described as a combination of the charge-transfer (CT) interaction from the lone-pair orbital on the X atom to the antibonding O H orbital and the dipole-dipole (DD) interaction between the HYX group and the O H group. Since the former is almost independent of the X and Y atoms, the differences in the shapes of the internal rotational potentials must inevitably be ascribed to the latter. The dependence of the DD interaction on the nature of the X and Y atoms is explained by a simple bond moment analysis. This is supported by the model calculations for the corresponding HYX-H molecules. Acknowledgment. This work was supported by the AFOSR grant 82-0190. The computer time made available by the North Dakota State University computer Center is gratefully acknowledged, as are the illuminating discussions with Professor Patrick Hoggard. Registry No. H 3 P 0 , 13840-40-9; H2POH, 25756-87-0; HFPOH, 14616-32-1; P, 7723-14-0; oxygen, 7782-44-7. (54) 1.003 A for N-H and 1.402 A for P-H. The remainder of the geometry was taken from the trans HXYOH structures.
