4318
J. Phys. Chem. 1991, 95,4318-4323
occupations for the niobium complex leads to the compromise angle of 126'.
Conclusions The low-spin-coupled rhodium atom (2D) inserts into the C-H bond of methane essentially without a barrier. For all the other first- and second-row transition-metal atoms studied so far the corresponding reaction has a barrier of more than 15 kcal/mol. One reason for the low barrier for the rhodium atom is that the ground state has the d"+'s' occupation, which means that the two bonds in the final, inserted, complex can easily be formed. Another reason is that the d'%tate and the low-spin-coupled d"+'s'-state are low lying. Both these states contribute to the lowering of the closed-shell repulsion in the initial stages of the reaction. The efficient mixing between the dnc2-stateand the low-spin-coupled dW-state is responsible for the formation of a precursor complex between a nearly undistorted methane and the rhodium atom. The formation of this bound precursor complex will not only be of importance for a low barrier but will also significantly increase the preexponential factor in the reaction rate expression. The binding in this cbmplex is due to an attraction between a partly unshielded rhodium core and the electrons of methane. The unshielding of the rhodium core occurs by the formation of two &hybrids, one pointing toward and one pointing perpendicularly away from methane. This type of sddhybrids can only be formed by the low-spin-coupled d'W-state. By populating the hybrid
pointing away from methane, the rhodium core becomes partly unshielded. The conclusion about the mechanism of this bonding is drawn based on two facts. First, there seems to be no other reason for the strong admixture of the excited d"+'s'-state. Second, the populations for complexes of this type do not show any significant charge transfer between the metal and methane which would otherwise be an alternative explanation for the bonding. It should here be stressed that the present conclusion about a low barrier for the insertion into methane of a low-spin rhodium atom does not contradict the experimental observationB that rhodium atoms do not activate methane. The high-spin ground state of rhodium is 14.5 kcal/mol (experimentally 8.1 kcal/mol) lower in energy than the lowest low-spin state and the ground state will therefore have a rather high barrier for the insertion reaction. However, for metal complexes with ligands, the low-spin state will be the important one. In contrast to rhodium, the niobium atom is found to have a potential energy surface similar to most other first- and second-row transition-metal atoms studied so far with a rather high barrier for the insertion reaction. The difference between rhodium and niQbiumcan be explained by the fact that for niobium the low-spin-coupled d'W-state is high in energy and that the dnc2state is of the wrong spin to mix with the ground state of the complex. R@try NO. CH4, 74-82-8; Rh, 7440-16-6; Nb,7440-03-1. (29) akin, M. R.; Cox, D. M.; Kaldor. A. J. Chem. Phys. 1988,89,1201.
A Theoretical Study of the Structures and Stabilities of (H2PO)+ Species and the Proton Affinities of HPO and POH Pilar Redondo, Laboratoire de Radioastronomie Millimetrique, Ecole Normale Superieure, 24 Rue Lhomond, 75231 Paris Cedex 05, France
Antonio Largo,* Carmen Barrieatos, Departamento de Quimica-Fisica y Analitica, Facultad de Quimica, Universidad de Oviedo, 33006 Oviedo. Spain and Jesus M. Ugalde* Kimika Fakultatea, Euskal Herriko Unibertsitatea. P.K. 1072, 20080 Donostia, Euskadi, Spain (Received: July 9, 1990; In Final Form: December 14, 1990)
An ab initio study of the structures and stabilities of the (HzOP)+isomers has been carried out. Geometries and harmonic vibrational frequencies have been obtained at the HartrecFock level, and Mollel-Plesset theory has been employed to predict the relative stabilities of the different (HzOP)+isomers. Both HPOH+ and H20P have singlet ground states, whereas a triplet ground state has been found for POH2+. Singlet tram-HPOH+is predicted to be the global minimum,, lying 2 kcal/mol below singlet cis-HPOH', 18 kcal/mol below triplet POHz+, and 22 kcal/mol below singlet HzOP+,at correlated levels. The proton affinities of POH and HPO, at both oxygen and phosporus atoms, are predicted to be relatively high, ranging from 154 kcal/mol (triplet POH) to 218 kcal/mol (singlet POH). 1. Introduction
processes are important.
Triatomic molecules containing second-row atoms have received renewed attention in recent years, due in part to the noticeable growth of the chemistry of molecules that have multiple bonds to second-row atoms. In particular, experimenta on ion-molecule have reactions of P+ and P H Z ions with some neutral molcculesl~ shown that P-O, P-N, and P-C bonds are formed with relative ease. This has stimulated the search for molecules containing such kinds of bonds in the interstellar media, where the ion-molecule Authors to whom corrmpondence should bc addressed.
0022-3654/91/2095-4318$02.50/0
Indeed,quite recently the first interstellar phosphoruscontaining compound has been found, Le., PN.' Since H 2 0 , 02,and COz are relatively abundant in space, molecules containing PO+ or HPO+ are the most likely candidates for interstellar phosphorus-containing species. Therefore, given the importance of protonation reactions in chemical reactivity theory (1) Thorne,L. R.; Anicich, V. G.; Huntress,W.T.Chem. Phys. Lrrr. 1983, 98, 162. ( 2 ) Smith, D.; McIntosh, B. J.; Adams, N. G. J. Chem. Phys. 1989,90,
6213. ( 3 ) Turner, B. E.; Bally, J. Asfrophys. J . 1987, 321, L75.
0 1991 American Chemical Society
Structures and Stabilities of (H2PO)+
The Journal of Physical Chemistry, Vol. 95, No. 1 1 , 1991 4319
and the astrophysical interest of both (HOP) and (H2P0)+ type of molecules, we present and discuss in this paper results from ab initio molecular orbital theory on the structures and vibrational frequencies of both system (HOP) and (H2PO)+. Also,the proton affinities of the HOP and POH are studied. HPO has been the subject of some experimenta_lwork. Thus, X’A’ the rotational and vibrational structure of the A‘A” transition was studied by Larzilliere et a1.4 Also, Larzilliere and Jacoxs obtained the vibrational spectrum of HPO in inert matrices. The spectrum of HPO, obtained as a product of the photolysis of phosphine peroxide in argon, has also been studied by Withnall and Andrews,6 obtaining the vibrational frequencies. The microwave spectrum and the molecular constants of HPO have been measured by Saito et al? Also, some results of theoretical studies on both HPO and POH are available from the literature. The ‘A’ ground state of HPO has been investigated by Tapia et ala,* who optimized the geometry and calculated some molecular properties at the SCF level. Schmidt et a1.9 studied by means of an ab initio method the isomerization of HPO to POH, on the ‘A’ potential energy surface, finding an isomerization barrier higher than the dissociation limit onto H + PO, using the 3-21G* basis set. Lohrlo has studied the ground state of HPO and the triplet ground state of POH” with the 6-31G* basis set. POH(3A’) was found to lie about 6 kcal/mol higher than HPO(’A’) at the MP3 level of theory. The HPO isomer has also been studied by Nguyen et a1.I2 with different basis sets, and they have as well computed the vibrational frequencies, force constants, and other molecular parameters at HF and correlated levels.
-
2. Computational Methods
Ab initio molecular orbital calculations have been carried out at the Hartree-Fock (HF) level (restricted for singlets and unrestricted for open-shell electronic states). Geometries have been optimized by using analytical gradient techniques, at the HF level with the split-valence plus polarization 6-31G** basis Harmonic vibrational frequencies have also been estimated at the HF level by using the 3-21G* basis set,I5for it is generally found that the HF/3-21G* and the HF/6-31G** vibrational frequencies are close while the computationalcost of the former is substantially lower. Electron correlation effects have been accounted for using fourth-order Moller-Plesset (MP4) perturbation the~ry,~’J* with the 6-31G** basis set, on the HF/6-31G** optimized geometries. The calculations reported herein have been carried out using both GAUSSIAN-8219 and GAUSSIAN-8620 packages. (4) Larzillierc, M.; Damany, N.; Lam Thanh, M.J. Chem. Phys. 1980, 46, 401. (5) La.rzilliere. M.;Jacox, M. E. J . Mol. Specrrosc. 1980, 79, 132. (6) Withnall, R.; Andrcws, L. J. Phys. Chem. 1987, 91. 784. (7) Saito, S.;Endo, Y.; Hirota, E. J . Chem. Phys. 1986, 84. 1157. (8) Tapia, 0.;Allavcna, M.; Larzillierc, M.Chem. Phys. Len. 1978,56, 25. (9) Schmidt, M. W.; Yabuschita, S.;Gordon, M. S. J . Phys. Chem. 1984, 88, 382. (10) Lohr. L. L. J . Phys. Chem. 1984,88, 5569. (11) Lohr, L. L.; Boehm. R. C. J . Phys. Chcm. 1987, 91, 3203. (12) Nguyen, M.T.; Hcgarty, A. F.; Ha, T. K.; Bruit, P. Chem. Phys. 1985. 98, 447. (13) Hariharan. P. C.; Pople, J. A. Theor. Chim. Acra 1973, 28, 213. (14) Francl, M. M.; Pietro, W. J.; Hehre, W. J.; Binkley, J. S.;Gordon, M.S.;DeFrees, D. J.; Poplc, J. A. J . Chem. Phys. 1982, 77, 3654. (15) Pictro, W. J.; Francl, M. M.; Hehrc, W. J.; DeFrees, D. J.; Pople, J. A.; Binkley, J. S.J. Am. Chem. Soc. 1982, 104, 5093. (16) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab lnitio Molecular Orbiral Theory; Wiley-Interscience: New York, 1986. (17) Pople, J. A.; Krishnan, R. Inr. J. Quanrum Chrm. 1978, 14, 91. (18) Krishnan, R.; Frisch, M.J.; Pople, J. A. J . Chem. Phys. 1980, 72, 4244.
(19) Binldcy, J. S.; Frisch, M. J.; DeFrees, D. J.; Raghavachari K.; Whiteside. R. A.; Schlegcl, H. B.; Fluder, E. M.;Poplc, J. A. GAUSSfAk82; Carncgic-Mcllon University: Pittsburgh, 1983. (20) Frisch, M. J.; Binkley. J. S.;Schlegel, H. B.; Raghavachari, K.; Melius. C. F.; Martin, R. L.; Stewart, J. J. P.; Bobrowitz, F. W.; Rohlfing, C. M.;Kahn, L. R.; DeFrces. D. J.; Seegcr, R.; Whiteside, R. A.; Fox, D. J.; Fluder, E. M.; Pople, J. A. GAUSSfAN8R Carnegie-Mcllon University: Pittsburgh, 1986.
x -P
1.610
1.461
0
Figure 1. Optimized structures at the HF/6-31G** level for the lowest lying singlet and triplet states of POH and HPO.
TABLE I: Harmonic Vibrational Frequencies ( c d ) at the HF/IU;* Lvel for the S i t a d Triplet States of POH md HOP POH(’A’) HPO(’A’) POH(’A”) HPO(’A”) bend v2 1017 1143 (998.0)’ 892 866 PO str vi 1163 1375 (1185.2)” 1007 915 OH, PH str v3 3825 2412 (2088.8)” 3885 2564
’Experimental values (see ref 6). 3. Results and Discussion 3.1. HPO and POH Isomers. Before discussing the structures of the (H2PO)+species, it is necessary to carry out a complete study of HPO and POH molecules at the same level of theory. Besides, it is worth noting that, though there are theoretical studies on singlet HPO and singlet and triplet POH, there is not theoretical prediction at the same level of theory about the molecular structure and properties of the lowest lying HPO triplet state. The electronic configuration of the singlet state of both HPO and POH molecules is ...6a‘27a‘28a’29a’22a‘1210a’2 ’A’ The 2a” is obviously a u-type molecular orbital, whereas the loa’ is a px-type orbital centered on the atom not bonded to hydrogen. A qualitative valence-bond description of both isomers is
H, p
=e:
:P-0:
/H
which shows that, whereas in the HPO isomer the 2a” orbital gives rise to a ?r bond, the 2a” orbital is esentially a 2p,(O) orbital. Triplet states originate from a loa’ 3a” electron promotion. In both cases the H F wave functions are nearly spin pure ( (S2) = 2.026 for both triplet HPO and POH states), and therefore spin contamination is not a problem in these molecules. The HF/631G** optimized geometries are given in Figure 1. It is readly seen that the P-O bond distances in the ‘A’ states of both isomers are in close agreement with the qualitative VB picture, for the P-O bond length is 0.15 A shorter in HPO than in POH. In the case of HPO there is a great difference in the P-O bond distance between singlet and triplet states. This is attributed to the fact that in HP0(3A”) one of the electrons originally occupying the 10 a’ MO (essentially a 2px(0)) is promoted to a 3a” orbital which is substantially centered on phosphorus. Therefore, the 2a” MO, which forms the u bond, is displaced toward the oxygen atom, weakening the P-O bond. The presence of a 3a” electron, in addition to the phosphorus lone pair, results in a bond angle much closer to u/2, which is the bond angle usually found for normal trivalent phosphorus. For the POH isomer the situation is quite different. Both loa’ and 3a” orbitals are mainly centered on phosphorus; therefore, the P-O bond distance and the rest of the geometrical parameters are slightly modified with respect to the singlet state. The quality of the HF/6-31G** results can be put into perspective by comparison of calculated molecular properties with the available experimental data. In particular, from the microwave spectrum of HPO( 1A’) the following rotational constants have been obtained (in GHz): A = 265.307, B = 21.0746, and C = 19.4648, which compare well with the calculated HF/6-31G** ones, namely, A = 271.635, B = 21.662, and C = 20.094. The discrepancy for A is 4.6% and for B and C less than 3%. Also, we have found that our calculated HF/6-31G** dipole moment
-
4320 The Journal of Physical Chemistry, Vol. 95, No. I I, I991
Redondo et al.
TABLE II: Total (hrtrees) and Relative (kcal/mol) Energies of the Different (HPO) (Relative Energies Are in Parentbeses) POH(’A’) HPO(’A’) HF -416.090 I5 (23.1) -416.12700 (0.0) MP2 -416.36500 (34.1) -416.41938 (0.0) MP3 -416.37702 129.5) -416.42403 (0.0) -416.43496 (o.oj MP4SDQ -416.38541 (31.1j MP4 -416.39295 (33.1) -416.445 65 (0.0)
of 2.075 D agrees well with previous estimates (see ref 8) and is large enough as to favor radio astronomical detection. The dipole moment of triplet HPO, p = 1.549 D, is smaller than that of the singlet as should expected on the basis of the charge redistribution caused by the loa’ 3a” promotion. As discussed earlier, this charge redistribution is no so severe in the POH isomer, and accordingly the dipoles of the triplet and singlet states are rather similar, 1.742 and 1.669 D, respectively. The HF/3-21G* harmonic vibrational frequencies for HPO and POH are given in Table I. It is of interest to compare the theoretical vibtrational frequencies for HPO(’A’) with the experimental results, obtained from the photolysis of phosphineozone complex in solid argon.6 The HF/3-21G* frequencies exceed the experimental data by a constant amount of 15%. It is well established that the H F methods overestimate vibrational frequencies by 10-20%;16therefore, our estimates should be regarded as normal. It is worth noting that expanding the basis set does not necessarily improve the theoretical prediction. Thus, the HF/6-31G** vibrational frequencies of the HPO(’A’), Le., uI = 1376 cm-I, uq = 11 10 cm-I, and u3 = 2327 cm-I, reported by Nguyen et al.,I2 lie within a 2% deviation bandwidth with respect to our HF/3-21G* estimates. The P-0 stretching frequencies for the different species reflect the differences in P-0 bond lengths. The absolute and relative energies for the lowest lying singlet and triplet states of HPO and POH are shown in Table 11. MP2, MP3, and MP4 denote second-, third-, and fourth-order Moller-Plesset (MP) results, respectively, whereas MP4SDQ refers to partial fourth-order (neglecting triple substitutions) MP theory. Inspection of Table I1 reveals that the triplet state of the POH is the most stable at the H F level, but when correlation effects are included HPO(’A’) appears to be the most stable species. However, in the case of POH, even at correlated levels, the 3A” state is more stable than the ‘A’ state. Inclusion of correlation effects is Seen to decrease the energy difference between these two states from 34 kcal/mol at the HF level to 20 kcal/mols at the MP4 level. This clearly points to singlet POH as a two-configuration state as revealed by the dramatic effect that inclusion of electron correlation effects has in lowering the energy of this state relative to the triplet. Also, we would like to point out that HPO(’A’3 lies the highest in energy at correlated levels, though it is found to be more stable’ than POH(’A’) at the H F level. therefore, our calculated energy order for HPO(’A’), POH(’A’’), and POH(’A’) is the same as found by Lohr and Boehm” at the MP3 level. However, it is worth noting that their MP3/6-31+G+(d,p) calculation predicts HPO(IA’) to be 6.08 kcal/mol more stable than POH(3A’’), while we found energy differences of 7 kcal/mol at MP3/6-31G** and 13.3 kcal/mol at the MP4/631G** levels. Finally, we would like to point out that the energy order of the (HPO) system and that of its isovalent (HNO) system are the same. Bruna2’found that at the CI level HNO(IA’) is more stable than the 3A” ground state of its NOH isomer. 3.2. (HzPO)+ Isomers. The protonated species of the POH and HPO molecules appear as products in some of the reactions of the PH,+ with various oxygen-containing neutral m~lecules.~*~ The structures and molecular properties of these cations are highly valuable to gain insight into the gas-phase chemistry of POH and HFQ, and in particular into their proton affinity (seesection 3.3),
Species at Several Levels, with the 6-31C** Basis Set POH(3A”) -416.14477 (-11.2) -416.40048 (11.9) -416.41235 (7.3) -416.41879 (10.1) -416.42453 (13.3)
HPO(3A”) -416.10371 (14.6) -416.337 18 (51.6) -416.358 38 (41.2) -416.366 15 (43.2) -416.371 75 (46.4) 1Q.L
-
1.787
O\ pT
JAZ
\H DIH-101 .I
H
\
117.5
1.401
1208
H
H
\ 122.2
/A:=”
H
Figure 2. Optimized structures at the HF/6-31GL* level for the lowest lying singlet and triplet states of the (HzPO)+ isomers. TABLE 111: Net Atomic Charges and Dipole Moments (debye) at the HF/6-31C** Level for the (H2PO)+ Isomers POHZ’ t-HPOH* C-HPOH’ HZPO+
‘AI 3Az ‘A’ )A ‘A’ ‘AI ’A,
Q(p) +0.676 +0.736 t1.079 +0.989 +1.122 +1.199 +1.012
Q(0) -0,610 -0.650 -0.542 -0.558 -0.546 -0.363 -0.200
Q(WP Q W o +0.016 +0.121 +0.022 +0.082 +0.094
+0.467 +0.457 +0.447 +0.428 +0.446
P 3.172 2.694 1.234 2.338 2.493 5.255 3.431
which is a key property in interstellar chemistry. Although the neutral (H,OP) species have been the subject of several theoretical studies,z4to the best of our knowledge there are no previous ab initio studies on their corresponding cations. The HF/6-3 1G** optimized geometries for the lowest lying singlet and triplet states of POH2+,cis- and truns-HPOH+,and H2PO+ are shown in Figure 2, and their net atomic charges and dipole moments are given in Table 111. 3.2.1. POH2+. This molecule can be formally considered as the oxygen-protonated derivative of POH. The electronic configuration found for its singlet state is ...5a126a122bz22b127a123b22‘Al The orbital 2bl is the out-of-plane 2p(O) orbital and therefore
(21) Bruna, P. J . Chem. Phys. 1980, 49, 39. (22) Magnuason. E. Tetrahedron 1985,4I,5235. (23) Yabuschita, S.; Gordon, M. S.Chem. Phys. Lerr. 1985, 117, 321.
(24) Boatz, J. A.; Schmidt, M. W.; Gordon, M. S.J . Phys. Chem. 1987,
91, 1743.
The Journal of Physical Chemistry, Vol. 95, No. 11, 1991 4321
Structures and Stabilities of (HzPO)+ is essentially a nonbonding orbital. On the other hand, the 3b2 is centered on the phosphorus atoms as well as the 3bl orbital which is the LUMO. Therefore, the electronic configuration can be represented by 3b9
HF/IZIC* Level of Theory of the Different (H20P)+ Isomers
POH'7 ~~~
825 677 934 181 1 3764 3762
out-of-plane bend PO str
A small T backdonation from the oxygen lone pair into the vacant phosphorus 3d orbitals is observed (-0.06 e-), which is to be compared with the relative large amount of T back-donation reported by TrinquierZ5for the isoelectronic (HzNP) series. In particular, he found that 0.32 e- migrates from nitrogen to phosphorus due to delocalization of the 2bl nitrogen lone pair in the singlet HzNP. Undoubtedly, the higher electronegativity of oxygen compared with that of nitrogen reduces the extent of delocalization. It is also interesting to note that 3d (P) 2p(O) back-donation is nearly absent in the singlet state of POHz+,as reflected by the negligible population of phosphorus orbitals. All these effects result in a relatively weak P-O bond, with a bond length of 1.787 A. Comparison with the P-O bond distance in singlet POH (1 -610 A) shows a lengthening of more than 0.15 A upon protonation on the oxygen atom. Promotion of a 3bz electron to the vacant 3b, orbital gives rise to the lowest lying triplet state, 3Az. In contrast with triplet PNHz,25which was shown to be pyramidal when nitrogen d functions are included in the basis set, triplet POHz+is found to be planar. The FQH bond angle is nearly the same found for the singlet, but the P-O bond length is increased substantially. This is due to the fact that a small amount of delocalization present in the singlet POHz+is entirely eliminated in the triplet state by the 3bl electron; therefore, the P-O bond is weakened relative to the singlet state. The very long P-O bond distance as well as the very small P-O overlap population of the triplet state of POHz+ suggests that it should be described better as an ion-molecule complex (P+(3P) HZ0('A1)),rather than the triplet state of the oxygen-protonated POH. This is further confirmed by the calculated P-O stretching frequencies shown in Table 1V. It is worth noting that P-O stretching frequencies of both singlet and triplet POHz+ are approximately half of those calculated for HPOH+ and HzPO+species. Therefore, one should conclude that the P-O bond is going to be weak in POHz+,especially in its triplet state, Finally, it would be interesting to point out that in the singlet/triplet energy splitting in P+ mimics that of the POHz+ molecule. Thus, if one uses the 6-31G** basis set at the HF, MP2, MP3, MP4SQD, and MP4 levels of theory, the differences between the energy of singlet P+ relative to triplet P+ are 50.8,43.9, 42.1, 41.0, and 40.9 kcal/mol, respectively, which are to be compared with the comsponding calculated values for the POHz+ molecule, namely, 40.4, 30.1, 32.9, 28.1, and 27.5 kcal/mol, respectively. 3.22 HPOH+. Singlet cis- and trans-HFQH+ can be obtained by the protonation of either POH or HPO and have the following electronic configuration ...6a'27a'28ar29a'22a''zlOa'2 !A'
-
+
The 2a" orbital corresponds to a P - 0 ?r bond, which is strongly polarized toward the oxygen, and the 9a' and loa' MOs have appreciable contributions only from the 2p(O) and the 3p(P) atomic lone-pair orbitals, respectively. Therefore, the electronic structure of both cis- and rrans-HPOH+ is well represented by H
'H The P-O bond length is much shorter than in singlet POHz+(see Figure 2) and is intermediate between the bond distances found for singlet POH and HPO. Therefore, it represents roughly an (25) Trinquier. G. J . Am. Chcm. Soc. 1982, 104, 6969.
TABLE IV: Harmonic Vibrational Frequencies (cm-') at tbe
OH2 rock OHz sym bend OH2 sym str OH, asym str
615 614 848 1802 3712 3806
HPOH' c-'Af
t-'A'
t-'A
813 76 1 1236 1147 2609 3164
857 840 1210 1135 2862 3765 H,PO'
438 768 1161 876 2527 3712
out-of-planebend asym ben PO str sym bend PH str OH str
IAl 843 892 1255 1485 275 1 2812
out-of-planebend PHI asym bend PO str PH2 sym bend PHI sym str PHI asym str
3AIf
74 1 880 1002 1111 2690 2746
intermediate situation between a single and a double P-O bond. The *-bond electron pair is strongly polarized toward oxygen, but it is not yet centered on it, as in the case of HPO. Also, it is worth noting that the P-0 bond length for cis- and truns-HPOH+ is shorter than for the neutral molecule,24by approximately 0.1 A. The main difference between cis- and rruns-HPOH+ geometries is the bond angle widening for the cis isomer (4-7O) with respect to the trans, whereas no appreciable differences were found for the bond distances. We have found two different structures for triplet trans-HPOH', which are close in energy. One of them originated by promoting a 2p(O) electron to the vacant 3a" orbital (essentially a 3p(P)), giving rise to a 3A" state. As a consequence of this electron promotion, the 2a" orbital, which makes a r-type P-0 bond in the singlet, is pushed over the oxygen and its main contribution comes now from the 2p,(O) atomic orbital. Therefore, the chief characteristics of the resulting electronic structure can be depicted by loa'
This state has a P-0 bond length remarkably increased with respect to singlet HPOH+, namely, 1.864 A at the HF/6-3 1G** level. The other triplet trans-HPOH+ structure is originated from the unpairing of phosphorus lone pair and therefore is adequately described by the following valence-bond structure H
'id; H
Its P-0 bond length is much shorter than the former (1.549 A at the HF/6-31G** level). Although the A bond is polarized toward oxygen, the 3d(P) 2p(O) back-donation is relatively high, with a population of 3d(P) orbitals of 0.23 e-. Both triplet HPOH' structures were found to be nonplanar, and since the former is 17 and 25.8 kcal/mol at the H F and MP4 levels, respectively, more unstable than the latter, we will disregard it and consider only the more stable of the two. It should also be mentioned that all attempts to optimize triplet cis-HPOH+ structure collapsed to trans-HPOH+. From the electronic configuration of HPOH' it is clear that a substantial electron re-
-
4322 The Journal of Physical Chemistry, Vol. 95, No. 11, 1991
Redondo et al.
TABLE V: Rehtlve Energies ( k u l / d ) of tbe Different (HsOP)’ Isomers at Different Levels with tbe 6-31G** Basis SeC HF/6-3 1G** MP2 MP3 MP4SQD M P4
POHz+(’Ai) 39.1 46.7 43.5 44.3 45.7
POH2+?A2) -1.3 16.6 10.6 16.2 18.2
c-HPOH+(’A’) 1.3 1.7 1.5 1.6 1.7
t-HPOH+(’A’) 0.0 0.0 0.0 0.0 0.0
t-HPOH’CA) 27.8 42.0 43.1 44.1 45.0
HzPO+(’AI) 30.1 19.9 26.5 24.5 22.3
H$0+(3A”) 43.8 75.6 69.7 71.0 72.6
OThe following energies for r-HPOH+(’A’) are taken as reference values: HF, -416.437 95; MP2, -416.71847; MP3, -416.7314; MP4SDQ, -416.740 17; MP4, -416.74805. pulsion between the 2a” and the 3a” electrons will likely occur. In fact, it is found that the ’A” state has one negative force constant, indicating the existence of a more stable nonplanar structure. A nonrestricted optimization of the HPOH+ triplet state converges to a structure with a dihedral angle of 101.5O. On the other hand, optimization of the triplet cis-HPOH+ collapses to trans-HPOH+. 3.2.3. H2PO+. The electronic configuration of the singlet H2PO+ is
...5al26a122b227a122b, 23bz2
IAl where Sal through 7al are the 20 P-H bonds, the u P-O bond, and the nonbonded oxygen lone pair, respectively. The 2bl molecular orbital is of r type between phosphorus and oxygen, and the 3b2is essentially a 2py(0). Therefore, its electronic structure is depicted as 3b2
H >P
=
0 8:
H Singlet H2PO+exhibits the shortest P-O bond distance of all the electronic states considered in this paper and is also much shorter than the P-O bond length in neutral H2P0, namely, 1.613 A at the HF/3-21G* leveL2‘ This is a consequence of the significant amount of 3d(P) 2p(O) back-donation encountered for the singlet H2PO+,as revealed by the population of the phosphorus d orbitals, namely 0.31 e-, which is even greater than the corresponding population of the phosphorus d orbitals in the H2PN system.25 The end result is a strong P-O bond with overlap population from a Mulliken analysis of 1.194. Triplet H2PO+is obtained when a 3b2electron is promoted to the vacant 3bl orbital, which is essentially a 3p(P) orbital. However, a full optimization of the geometry shows that triplet H2PO+ is in fact pyramidal, and its electronic state is ’A’’. The same was found for triplet H2PN,25but there is a difference in the electronic structure since in H2PO+ both unpaired electrons are located in different atoms, and the resulting electronic structure can be represented as
-
-
The former a-bonding orbital is now basically an oxygen lone pair, and although the 3d(P) 2p(O) back-donation is still noticeable (the population of phosphorus d orbitals is 0.21 e-), the P-O bond distance is considerably lengthened (more than 0.17 A compared with singlet H2PO+). Net atomic charges (obtained from the Mulliken population analysis) and dipole moments for the different (H2P0+)species are given in Table 111. In most cases the phosphorus atom shows a net positive charge of more than 1 e-. The only exceptions are both singlet and triplet POH2+,where oxygen is able to extract charge from the hydrogen atoms. Dipole moments (taking the center of mass as origin) are large enough for all the molecules. However, it is noticeable that POH2+has a smaller dipole than H2PO+. Harmonic vibrational frequencies computed at the HF/3-21G* level are given in Table IV. Their most remarkable feature is that all species are true minima on their corresponding
singlet or triplet surface, since all their force constants are positive. It should be pointed out that the P-O stretching frequencies for the different species are consistent with the P-O bond distances and electronic structure pictures discussed above. In the cases of singlet and triplet POH2+the P-O stretching frequencies are nearly half the value of the strongest P-O bond, namely, that of singlet H2PO+. Relative energies for all the electronic states considered in this work are given in Table V. These values have been obtained with the 6-31G** basis set at different levels of theory. HF/6-31G** wave functions for triplet are nearly spin pure (POH2+, (S2) = 2.027; r-HPOH+, (S2) = 2.009; H2PO+, (9) = 2.016). Therefore, the MP series should exhibit in principle a reasonable convergence, for spin contamination is almost negligible in this case. HPOH+ and H2PO+isomers have singlet ground states, whereas in the case of the POH2+ isomer a triplet ground state is found. This is not surprising, since triplet POH has been found to lie below singlet POH at all levels of theory (see Table II), the energy difference being close to 20 kcal/mol at correlated levels. This value increases by some 7 kcal/mol upon protonation of the oxygen. (The energy difference is 27.5 kcal/mol at the MP4 level.) In fact, triplet POH2+lies the lowest of all species at the H F level. Inclusion of correlation effects via Moller-Plesset theory, as expected, favors singlet states in all cases and has the important effect of placing singlet HPOH+ below triplet POH2+by 18 kcal/mol at the highest level of theory. Therefore, singlet f-HPOH+ is found to be the lowest lying state, with the cis isomer lying less than 2 kcal/mol higher in energy. It is also interesting to note that POH2+is the least stable of all singlet isomers, lying 9 kcal/mol above singlet H2PO+ at the H F level. Correlation effects favor H2PO+ by a considerable amount, with a multiple-bonding electronic structure, and POH2+ is more than 20 kcal/mol higher in energy than H2PO+at the MP4 level of theory. On the other hand, POH2+ is much lower in energy than both HPOH+ and H2PO+ on the triplet surface (by more than 50 kcal/mol). The stability order at correlated levels is r-HPOH+(’A’) c-HPOH+(’A’) < POH2+(’A2) < H2PO+(’AI) C POH2+(’AI) f-HPOH+(’A) < H2PO+(’A”) (< means more stable). The small energy difference between cis- and rrans-HPOH+(’A’) is nearly the same as found for the neutral molecule, 1.6 kcal/mol, at the MP3 level.” Also,these authors found H2P023.1 kcal/mol higher in energy than t-HPOH at the same level of theory, a value which closely matches our calculated differences of 26.5 and 22.3 kcal/mol at MP3/6-31G** and MP4/6-31G** levels, respectively, between singlet H2PO+and r-HPOH+. It is also of interest to compare the stability order of the different (H2PO)+species with that obtained for its isoelectronic system (H2NP). T r i n q ~ i eobtained r~~ the following stability order at the PNH2(’A”) c-HPNHCI level of theory: r-HPNH(lA’) (‘A’) < PNHZ(’A1) < t-HPNH(’A) < H,PN(’Ai) < H,PN(’A’’). Remarkable differences between both systems are the destabilization of POH2+relative to PNH2 and the stabilization of singlet H2PO+relative to H2PN; whereas triplet PNH2 is found to be nearly isoenergetic with the ground state (singlet t-HPNH) in the case of the (H2PO)+system, triplet POH2+ is more than 18 kcal/mol higher in energy than the ground\state. In addition, singlet PNH2 was just 7.2 kcal/mol above t-HPNH at the CI level,25but singlet POH2+ is more than 45 kcal/mol higher in energy than singlet t-HPOH+, partially due to the fact that in the POH2+conformation oxygen is formally positively charged
-
-
-
-
Structures and Stabilities of (H2PO)+ TABLE VI: Rota Aflwtka for the S h g h rad Tripkt Statea of HPO at Merent k e l a of Tkory with the 6-31C** B M Set ~ HPO( IA') HPO('A") HZPO' C-HPOH' I-HPOH' H2PO' t-HPOH' 160.5 175.9 187.6 188.7 HF/6-31G** 159.2 158.2 191.3 181.2 161.9 179.7 MP2 158.9 185.0 186.4 160.5 185.1 MP3 184.6 185.1 158.2 MP4SDQ 161.2 183.7 158.1 185.1 181.8 183.3 MP4 161.7 TABLE VII: Proton Affinities for the Singlet and Triplet States of POH at Different L.evels of Theory with the C31C** Basis Set POH('A') POHCA") C-HPOH' t-HPOH' POH?' t-HPOH' POH2' 152.2 178.7 213.3 181.5 HF/6-31G** 212.3 216.9 195.2 153.6 176.4 MP2 215.4 179.2 189.2 153.2 217.4 MP3 216.2 191.5 153.6 179.0 216.3 217.7 MP4SDQ 193.9 154.0 178.3 216.4 217.9 MP4
for this state originating from a protonation of POH on oxygen lone pair. In the case of singlet POH2+ there is an additional destabilization with respect to PNH2, since the delocalization of the 2b, oxygen lone pair into the 3bl vacant orbital (3p(P)) is quite small relative to that of singlet PNH2 The higher electronegativity of oxygen with respect to phosphorus prevents the delocalization, and therefore the P-O bond is comparatively weakened with respect to the P-N bond. Finally, singlet H2PO+is comparatively more stable than singlet HIPN (the former is 22 kcal/mol higher in energy than singlet HPOH+, whereas the energy difference between the latter and singlet HPNH is more than 40 k c a l / m ~ l ~and ~ ) exhibits a very strong P-O bond. 3.3. Proton Affinities of HPO and POH. An estimation of the proton affinities for possible interstellar molecules is highly valuable since proton-exchange reactions are very frequent in space. Proton affinities (PA's) for the HPO and POH isomers in both of their singlet and triplet states were computed by means of PA(7') = -Me- AEv - AEr + 5RT/2 where Meis the electronic difference, AEvthe vibrational energy difference (which can be taken approximately as the zero-point vibrational energy difference AZPVE), and AEr the rotational energy difference. The PA values, for T = 298.15 K, are shown in Table VI (HPO) and Table VI1 (POH). In both isomers protonation could take place, in principle, either on oxygen or on phosphorus, and therefore we have included the proton affinities for the different protonation processes possible on their singlet and triplet surfaces. Usually there are not big differences between PA's computed at the H F and correlated levels, perhaps with the exception of protonation of singlet POH to give POH2+,where a difference of more than 12 kcal/mol between H F and MP4 proton affinities is found. It is generally observable that correlation effects tend to increase the PA of singlet POH, whereas in the cases of singlet
The Journal of Physical Chemistry, Vol. 95, No. 11, 1991 4323 and triplet HPO and triplet POH the electron correlation effects tend to lower the PA (with the exception of protonation on P, where it is increased by 2.5 kcal/mol) or have almost no effect at all. The highest PA is found for protonation of singlet POH at phosphorus (218 kcal/mol), and the lowest PA corresponds to protonation of triplet POH at the phosphorus atom (1 54 kcal/ mol), a fact that clearly reflects the unstability of triplet HPOH' compared with that of singlet HPOH+. Therefore, it is seen that the preferred protonation sites are phosphorus for singlet POH and oxygen for triplet POH. In the case of both singlet and triplet HPO protonation at oxygen is favored over protonation at phosphorus from the energetic point of view. It is interesting to note that the PA values obtained are higher than those of neutral precursors of some of the most important interstellar protonated species, such as H,+ and HCO+ (PAH,(300 K) = 101.3 kcal/mol, P&0(300 K) = 141.9 kcal/mol to give HC0+.26 4. Conclusions
A theoretical study of the structures and stabilities of the (H,PO)+ isomers has been carried out. Whereas HPOH+ and H2PO+have singlet ground states, a triplet state has been found to be the lowest lying state corresponding to POH2+conformation. The global minimum has been shown to be singlet rranr-HPOH+, which is the (H2PO)+species with the smallest dipole moment (1.234 D). The proton affinities of POH and HPO, at both oxygen and phosphorus atoms, have been estimated to be relatively high, varying from 154 kcal/mol for protonation of triplet POH on the phosphorus atom to 218 kcal/mol for protonation of singlet POH on phosphorus. The estimate for errors in the proton affinity calculations is usually around 5-7 kcal/mol, although in some cases errors as high as 10 kcal/mol have been encountered.16 This means that in our case errors around 8% should be expected. However, due to the high values of the PA's reported in this paper, one may conclude that HPO and POH,if present in interstellar medium, would experience protonation with relative ease. Preliminary calculations from our group suggest that the reaction of P with water can lead to phosphorus-xygen compounds under interstellar conditions." In fact, we have found that only POH+ cations (and not HPO+ cations) can be obtained as primary compounds. Therefore, the most likely (HPO) compound to be found in space should be POH, and consequently HPOH+ and POH2+cations are probably the preferred protonated species to be searched for in the interstellar medium.
Acknowledgmenr. This research has been partially supported by the Spanish Ministerio de Educacion y Ciencia (DGICYT PB88-0343), by the Basque Country University (Euskal Herriko Unibertsitatea) Grant UPV/203.215-107/89, and by the Basque Foru Aldundia. P.R. is also grateful to the Spanish Ministerio de Educacion y Ciencia for a Postdoctoral Fellowship. (26) Duon, D. A.; Komomicki, A,; Kraemer, W. P. J. Chrm. Phys. 1984, 81, 3603. (21) Largo, A.; Redondo, P.; Barrientos, C.; Ugalde, J. M. J. Phys. Chrm., submitted for publication.
