6553
J. Phys. Chem. 1991, 95, 6553-6551
served when AVa < at 0.1 MPa, may be due to the difference in the pressure dependence of AVbt for the diffusion process and AV+t for the bond-breaking process in each solvent. This is supported by the shift of the maximum to lower pressure with increase in AV:. In conclusion, it has been shown in this work that the formation of pyrene excimer in six solvents is fully diffusion controlled, but the dissociation in nonaromatic solvents involves processes associated with solvent viscosity as well as the bond-breaking processes
in the solvent cage. This evidence may predict that the effect of pressure on k3/k4in nonaromatic hydrocarbons examined in this work cannot lead to the evaluation of the volume change for the excimer formation, which is shown clearly in Figure 5.
Acknowledgment. This work was partly supported by a Grant-in-Aid for Scientific Research from the Ministry of Education of Japan (No. 62540331). Registry No. Pyrene, 129-OO-0.
Theoretical Studies of Possible Processes for Interstellar Production of Phosphorus Compounds. Reaction of P+ with Methane Antonio Largo,**+Jesus R. Flores,f Carmen Barrientos: and Jesus M. Ugalde*y% Departamento de Quimica- Fisica y Analitica, Facultad de Quimica, Universidad de Oviedo, 33006 Oviedo, Spain, Departamento de Quimica- Fisica, Facultad de Ciencias, Universidad de Valladolid, 47005 Valladolid, Spain, and Kimika Fakultatea, Euskal Herriko Unibertsitatea, P.K.1072, 20080 Donostia, Euskadi, Spain (Received: December 5, 1990)
An ab initio study of the reaction of P+ with methane has been carried out. Two different channels leading to (H2CP)+ and (H3CP)+, respectively, have been considered. The geometries of the possible products have been optimized at the HartreeFock level and relative energies computed through fourth-order Mplller-Pletset theory. The stability order for triplet (H2CP)+is PCH2+> HPCH+ > H2PC+,whereas in the case of (H,CP)+ the relative energy ordering is PCH3+> HPCH2+ > H2PCH+> H3PC+. The reaction of P+ with methane has been estimated to be endothermic for the production of PCH3+, whereas it is slightly exothermic (with an estimated value of -4.4 kcal/mol) toward the production of PCH2+. A small energy harrier (about 2.5 kcal/mol) is estimated for the process leading to PCH2+. Therefore, the reaction of P+ with CH, is likely to proceed under interstellar conditions, but only toward the production of PCH2+.
Introduction The recent detection of PN in space,' the first interstellar phosphorus compound, has brought about a growing interest in the formation of phosphorus-bearing molecules in interstellar clouds. Grain disruption,' high-temperature gas-phase reactions? and low-temperature neutral-neutral reactions3have been invoked to account for the synthesis of PN. Also reactions of PH,+ ions with various molecules have been studied in terrestrial laboratories. Thus Thorne et a1.4 and Smith et concluded that P-O, P-N and P-C bonds are formed with relative ease in the reactions of pH,,+ ions with some neutral molecules (H20, NH3, or CHI). This clearly points to H,PO+, H,PN+ and H,PC+ ions to be likely precursors of neutral molecules, containing P-O, P-N, and P-C bonds, which are possible candidates to be found in the interstellar medium. Therefore, we have undertaken a series of theoretical studies focused on the ion-molecule chemistry of phosphorus. Previous papers6 have dealt with the P+ + NH3 and P+ + H 2 0 reactions. We have found that the reaction of P+ with ammonia is feasible under interstellar conditions toward production of PNH2+ and identified two different mechanisms for the formation of PNH2+; namely; hydrogen abstraction from the PNH3+ ion-molecule complex and isomerization of PNH3+ into HPNH2+and subsequent hydrogen abstraction. Both processes are calculated to be exothermic and to have no activation barrier. The reaction of P+ with water can occur in the interstellar medium through production of POH+, which is found to be exothermic. Our ab initio calculations have predicted that POH+ can be formed without an activation barrier through isomerization of the POH2+ ionmolecule complex into HPOH+ and subsequent hydrogen abstraction. These results suggest that reactions of P+ with neutral
molecules can be an effective source for phosphorus containing molecules in the interstellar medium. In the present work, we consider the reaction of P+ with CH, as a possible source of phosphorus-carbon interstellar compounds. In principle two different channels for this reaction are possible P+ + CH4 (H2CP)' + H2 (1) P+ + CHI (H&P)+ + H (2) But experiments4J detected (H2CP)+as the sole product of the reaction. In order to ascertain the feasibility of this reaction taking place under interstellar conditions (low temperature, low density), we have carried out a theoretical study of the possible reaction products, as well as of the relevant intermediates on the (H,CP)+ potential surface. Since the study of the (H,CP)+ and (H,CP)+ species is of general interest in phosphorus-carbon chemistry, we shall first discuss the structure of these compounds, and then we shall proceed to consider the viability of P+ reacting with CH, in the interstellar medium.
-
Computational Methods The geometrical parameters for the different species studied in this work were optimized at the Hartree-Fock (HF) level. Restricted HF theory was employed for closed-shell states, whereas open-shell states were studied at the unrestricted H F level. In (1) Turner, B. E.; Bally, J. Asrrophys. J . 1987, 321, L75. (2) Ziurys, L. M.Astrophys. J . 1987, 321, L81. (3) Millar, T. J.; Bennet, A.; Herbst, E. Mon. Nor. Roy. Astron. Soc. 1987, 229, 41p. (4) Thorme, L. R.; Anicich, V. G.; Huntress, W. T. Chem. Phys. krr. 1983, 98, 162. (5) Smith, D.; McIntosh, B. J.; Adams, N. G. J . Chem. Phys. 1989, 90,
6213. (6) Largo, A,; Flora, J. R.; Barrientas, C.; Ugalde, J. M.J . Phys. Chem. 1991, 95, 170. Largo, A,; Redondo, P.; Barrienos, C.; Ugalde, J. M.J . Phys. Chem. 1991,95, 5443.
'Universidad de Oviedo.
*IUniversidad de Valladolid. Euskal Herriko Unibertsitatea. 0022-3654/91/2095-6553502.50/0 , I
,
0 1991 American Chemical Society
6554 The Journal of Physical Chemistry, Vol. 95, No. 17, 1991
Largo et al.
TABLE I: Harmollrc Vibntioarl Frequencies (em-’)at the HF/3-21G* Level for tbe Various (HzCP)+ Speciesu HPCH+(3A”) PCHz+(’AI) PCHZ’(’A2) CH2 rock (b2) out-of-plane bend (b,) P-C str (al) CH2 sym bend (al) CH2 sym str (al) CH2 asym str (b2) 4P-C)
607 1064 1 I39 1479 3186 3260 1.160
898 982 932 1569 3253 3357 1.750
asym bend (a’) out-plane bend (a”) P-C str (a’) sym bend (a’) P-H str (a’) C-H str (a”)
667 692 982 1031 2615 3363 1.403
H2PC+(’A’’)
wag (a‘) asym bend (a”) P C str (a’) sym bend (a’) PHI sym str (a’) PH2 asym str (a”)
624 812 1038 1165 2713 2758 1.675
‘P-C distances (in A) are at the HF/6-31GS level. TABLE 11: Total (hirtree) a d Relative (kcal/mol) Energies of the (H2CP+) Species at Different Levels of Tbeory with the 6-31C** Basis Set PCH,+(’A, PCH,+PA,I HPCHt(’A’’) H,PCt(’A”) -379.300 19 (58.7) -379.385 51 (5.2) -379.333 28 (37.9) HF -379.393 73 (0.0) -379.45060 (102.8) -379.57004 (27.8) -379.51071 (65.1) MP2 -379.61440 (0.0) -379.53899 (62.0) -379.475 37 (101.9) -379.59704 (25.6) MP3 -379.637 80 (0.0) -379.544 54 (62.7) -379.481 31 (102.4) -379.601 91 (26.7) MP4SDQ -379.644 50 (0.0) -379.549 36 (65.2) -379.485 16 (105.5) MP4 -379.653 31 (0.0) -379.606 82 (29.2)
the optimizationsthe split-valence plus polarization 6-31G** basis set7,*was employed. This basis set includes d functions for heavy atoms and p functions for hydrogen. Harmonic vibrational energies have been computed at the HF level with the 3-21G* basis set? which includes d functions only for second-row atoms. The HF/3-21G* vibrational frequencies were also used to estimate zero-point vibrational energies (ZPVE). Electron correlation effects were included through complete fourth-order Moller-Plesset (MP4) perturbation with the 6-31G** basis set, at the HF/6-31G** geometries. Second-order (MP2), third-order (MP3), and partial fourth-order (MPaDQ, which neglects the contribution of triple substitutions) Maller-Plesset results are reported. All calculations were carried out by using the GAUSSIAN 8212 and GAUSSIAN 8613 program packages.
’7.
lA,
1.610
P-G\H 121.9
1 081
3A
/
1.750
2
P - c
L \
121.8
H
H
H
Results and Discussion (H2CP)+. Singlet (H2CP)+structures have been obtained at the MNDO level in a general study of the fragments derived from methylph~sphines,’~ as well as at various ab initio levels in the study of the roton affinities of some phosphorus-containing m 0 1 e c u l e s . l ~However, ~~~ we are interested in triplet (H2CP)+, since the reaction of P+(’P) with CH4 should lead in principle to triplet (H2CP)+. The HF/6-31G** optimized geometries for the lowest-lying triplet states of PCH2+, HPCH+, and H2PC+are given in Figure 1, along with the optimized structure of the global minimum on the singlet surface, PCH2+(’AI),for comparison. The ‘A, state corresponds to the following electronic configuration: 5a126a122b227a122b12 (IA!), which can be represented by the following valence-bond picture. H 1 .P =c,
.+
H
(7) Harriharan, P. C.; Poplc, J. A. Theor. Chim. Acra 1973, 28, 213. (8) Francl, M. M.; Pietro, W. J.; Hahre, W. J.; Binkley, J. S.;Gordon, M. S.; DcFrees, D. J.; Pople, J. A. J. Chrm. Phys. 1982, 77, 3654. (9) Pietro, W. J.; Francl, M. M.; Hehre, W. J.; DcFrecs, D. J.; Pople, J. A.; Binkley, J. S. J . Am. Chem. SOC.1982, 104, 5039. (IO) Pople, J. A.; Krishnan, R. Inr. J . Quanrum Chem. 1978, 14, 91. (1 I ) Krishman, R.; Frish, M. J.; Pople, J. A. J . Chrm. Phys. 1980, 72, 4244. (12) Binkky, J. S.; Frisch, M. J.; DeFrees, D. J.; Roghavachari, K.; Whiteside, R. A.; Schlegel, H. B.; Fluder, E. M.; Pople, J. A. GAUSSIAN 82; Carnegie-Mellon University: Pittsburgh, PA, 1983. (13) Frisch, M. J.; Binkley, J. S.;Schlegel, H. B.; Raghavachari, K.; Melins, C. F.; Martin, R. L.; Stewart, J. J. P.; Bobrowicz, F. W.; Rohlfing, C. M.; Kahn, L. R.; DeFrees, Seeger, R.; Whiteaide, R. A.; Fox, D. J.; Fluder, E. M.; Pople, J. A. GAUSSIAN 86; CarnegieMellon University: Pittsburgh, PA, 1984. (14) &ws, J. R.; Glidewell, C. THEUCHEM 1983, 104, 105. (15) Lohr, L. L.; Schlegel, H. 6.;Morokuma. K. J. Phys. Chem. 1984,88, 1981. (16) Maclagan, R. G . A. R. J . Phys. Chem. 1990, 94, 3373.
. P-c 1 . 6 7 5 -/1.385 H
Figure 1. Optimized geometries at the HF/6-31G** level for (H,CP)+ structures. Distances are in angstroms, and angles in degrees.
Promotion of an electron from the HOMO, the P-C *-bond orbital, to the vacant 3b2 orbital results in the ’A2 state: 5a126a122b227a122bl’3b2~ It is then clear that the P-C bond distance must be increased for the triplet state, as can be seen in Figure 1 where a lengthening of 0.14 A is observed on going from singlet to triplet PCH2+. Since the remaining electron in the 2bl orbital is now mainly located at the carbon atom, the P-C bond is essentially a single bond, and therefore the valence bond picture for the triplet state is best described by
Although one should expect PCH2+to be the lowest lying triplet state, we have also searched for triplet states of HPCH+ and H2PC+. Despite the fact that apparently there exists no true minimum for singlet HPCH+,’s*’6since it collapses without an activation barrier to singlet PCH2+,we were able to find a minimum for triplet HPCH+. Its geometrical parameters indicate a situation intermediate between a single and double P-C bond, corresponding to a valence bond description close to H
..Ped, H
\ +
where the unpaired T electron appears t o be largely polarized toward the carbon atom.
The Journal of Physical Chemistry, Vol. 95, NO. 17, 1991 6555
Reaction of P+ with Methane TABLE 111: Net Atomic Charges from Mulliken Population Analysis at the HF/6-31C** Level PCH3' HPCHZ' HzPCH' H3PC' OIPI 0.932 0.735 0.703 0.73 1 sic) -0.716 -0.406 -0.172 0.033 Q(H,) 0.256 0.1 12 0.089 0.083 Q(H2) 0.264 0.281 0.094 0.076 Q(Hd 0.279 0.285
PCHIHz = 115.7
Finally, triplet H2PC+shows a relatively short P-C bond, which can be considered to correspond to a weak PC double bond. Both unpaired electrons are located on carbon,and the molecule is found to be pyramidal. The valence bond picture is typical of a triplet carbene. c
HI PCH3 = 42.8 HIPCH,
Harmonic vibrational frequencies at the HF/3-21G* level are given in Table I. All frequencies are real, thus confirming that the four structures are true minima on the corresponding potential surfaces. It is worth noting that P-C stretching frequencies increase as the P-C bond length decreases as expected. The absolute electronic energies at different levels of theory with the 6-31G** basis set are given in Table 11, with relative energies given in parentheses. It is clearly seen that singlet PCH2+ lies lower in energy than the triplets at all levels, with triplet PCH2' lying just 5.2 kcal/mol higher in energy at the H F level. As expected, this energy difference increases when correlation effects are included. It is also clear that PCH2+(3A2)is the lowest lying triplet state, with HPCH' and H2PC+lying 36 and 76 kcal/mol, respectively, higher in energy at the MP4 level. The MP results should be quite reliable for triplet PCH2+and HPCH+, since their wave functions are nearly spin pure ((S2) = 2.019 and 2.014, respectively). On the other hand H2PC+exhibits a certain degree of spin contamination ((9) = 2.653), but the energy differences with respect to the other structures are large enough to consider the stability order PCH2+ > HPCH' > H2PC+definitive on the triplet surface. (H3CP)+. The (H3CP) isomers have been studied, both in their singlet and triplet states, with ab initio methods by Nguyen et alei7 Several other theoretical studies have been devoted to the ground state, namely phosphaethene HPCH2i8-2i However, to the best of our knowledge the only theoretical study for the cation is the MNDO study carried out by Bews and Glidewell for the PCH3+and HPCH2+isomers." We have considered four isomers: PCH3+,HPCH2+,H2PCH+, and CPH3+. The optimized HF/6-31G** geometries are shown in Figure 2. Atomic charges are given in Table 111, and harmonic vibrational frequencies are shown in Table IV. The PCH3+(C,) isomer is a 2A" state whose electronic structure can be described by the following valence structure: H +
:P
-c
/
\iH
Although a word of caution is needed when discussing Mulliken atomic charges quantitatively, it is clear from Table 111 that the partial negative charge of the carbon atom is due to the polarization of the C-H bond rather than of the P-C bond. This 2A'' state, state is one of the Jahn-Teller components of the 2E (C3") ~
~~
~
(17) Nguyen, M. T.; McGinn, M. A.; Hegarty, A. F. Inorg. Chem. 1986, 25, 2185. (18) Thsomson, C. J . Chem. Soc., Chem. Commun. 1977, 322. (19) Gonbeau, D.;Pfister-Guillouzo,G.; Banans, J. Can. J. Chem. 1983, 61, 1371. (20) Schoeller, W. W.; Niecke, E. J . Chem. Soc., Chem. Commun. 1982,
569. (21) Van der Knaap, T. A.; Klebach, T. C.; Visser, F.; Bickelhaupt, F.; Ros, P.; Baerends, E. J.; Stam. C. H.; Konigen, M. Terrahedron 1984, 40, 165.
E
179.9
< CPHlHp = 118.9
Figure 2. Optimized geometries at the HF/6-31G** level for the lowest lying states of (H3CP)+. Distances are in angstroms, and angles in degrees.
and corresponds to the minimum of the Jahn-Teller potential surface. The other component, 2A' (not included in this study), which corresponds to the transition state, presents a very similar geometry and is very close in energy to the 2A" state, the difference being less than 1 kcal/mol. This is due to the fact that the unpaired electron interacts very weakly with the -CH3 group. The HCP angles are quite close to those found for singlet PCH3,I7the main difference being the P-C bond len th of 1.835 A for the neutral molecule, compared with 1.777 for the cation. HPCH2+has a 2A' ground state that may be described by the following valence structure
w
where the unpaired electron and positive charge are located at the phosphorus atom. The ?r-type bond is strong enough to prevent pyramidalization of the carbon atom, even though it appears somewhat polarized in the UHF wave functions. It is worth mentioning that singlet HPCHz is also found to be planar with geometrical parameters quite close to those of the cation,17except for the HPC angle (98.9' for the neutral molecule), but triplet HPCH2 adopts a pyramid-like ~onformati0n.I~ The H,PCH+ isomer is a nonplanar molecular cation whose electronic structure can be depicted as follows
The carbon atom presents an unpaired electron, essentially in the H,PC plane, and there is a very spin-polarized P-C non-u bond located approximately in the plane perpendicular to the H,PC plane. In other words, at the level of theory employed to optimize the geometries (HF/6-3 1G**) the P-C ?r-type bond is not strong enough to prevent pyramidalization of the P atom. However, pyramidalization in this case might be due to the spin polarization of the ?r bond or even to basis set effects, so higher level calculations are necessary to ascertain the nonplanarity of this molecular cation. We have found, however, that the torsion motion between the optimized and planar geometries has very little effect on the total energies, so there is no need to refine the optimized geometry
6556 The Journal of Physical Chemistry, Vol. 95, No. 17, 1991
Largo et al.
TABLE I V Harmonic V i b n t i d Frequencies (cm-I) Calculated at the HF/3-21CS Level for the (H&P)+ Iso” PCH,+ HPCH2’ H,PCH+ H\PC+ CH, deform 664 (a”) torsion 464 (a”) torsion 468 deform 381 (a”) CH, rock 724 (a’) rock 598 (a’) wag 557 rock 702 (a’) rock 662 PC str 635 (a’) PC str 845 (a’) wag 912 (a”) HCP bend 8 18 PH, deform 1111 (a’) CH, deform 1344 (a”) PC stret 971 (a’) PC stret 1026 PH deform 1163 (a”) HPC bend 1038 (a’) CH, deform 1493 (a’) PHI bend 1171 PH, deform 1201 (a’) CH2 s-bend 1514 (a’) CH, deform 1554 (a’) PH2 s-str 2718 PH, str 2708 (a’) PH strt 2670 (a’) CH, str 3025 (a’) PH, str 2743 (a’) CH, s-str 3256 (a’) PH2 a-str 2770 CH, str 3169 (a’) PHI str 2751 (a”) CH, a-str 3381 (a’) CH str 3403 CH, str 3176 (a”) TABLE V Total (hartme) and Relative (kcrl/mol) Energies of the (H3CP)+Isomers Calculated at Different Levels of Tbeory with the 6-31C** Basis s e t level PCH3+(2A”) HPCH2+(,A’) H,PCH+(~A) H3PC+(2A”) -379.883 64 (68) -379.975 62 (10.3) -379.95492 (23.3) -379.99201 (0.0) HF -379.88403 (69.6) -379.991 08 (2.4) -379.97344 (13.5) PHF -379.99493 (0.0) -380.057 79 (93.9) -380.17674 (19.2) -380.141 60 (41.3) -380.207 35 (0.0) MP2 -380.15908 (31.6) -380.058 18 (94.8) -380.191 23 (11.4) -380.209 38 (0.0) PMP2 -380.169 56 (40.6) -380.08920 (91.1) -380.202 37 (20.0) -380.234 32 (0.0) MP3 -380.185 32 (31.6) -380.08959 (91.7) -380.215 14 (12.9) PMP3 -380.235 65 (0.0) -380.17596 (40.1) -380.095 96 (90.3) -380.208 83 (19.5) MP4SOQ -380.239 86 (0.0) -380.180 82 (40.8) -380.09971 (91.7) -380.21480 (19.4) MP4 -380.245 79 (0.0)
in order to calculate absolute and relative energies for this isomer. The H3PC+(CJ isomer is a 2A” state, which can be represented by the following valence structure H
:c -P.
+/
bH‘H
This electronic state is completely analogous to the PCH3+ground state; both states result from Jahn-Teller distortion of the (degenerate) 2E ((2%)state. Carbon is not negatively charged in this species, be!cause no inductive effect over hydrogen atoms is possible here. Note that the P-C bond is extremely polar in PCH3+and also much shorter than in H3PC+. The P-C bond may be considered single in PCH3+and H3PC+ isomers and double in HPCH2+and H2PCH+. Note that despite the pyramidalization of phosphorus in H2PCH+,the P-C bond is even shorter than in HPCH2+(planar) and the P-C stretching frequency is also slightly higher. A possible explanation for this fact is that pyramidalization of phosphorus permits a stronger u P-C bond because electrostatic repulsion between hydrogen atoms is weaker than in HPCH2+. Table V shows the absolute electronic energies and the relative energies for the (H3CP)+species. The PCH3+ isomer appears at all computational levels as the most stable, HPCHf being quite close in energy. Note that inclusion of correlation energy is clearly favorable to PCH3+. The relative energies corresponding to projected HF, MP2, and MP3 wave functions are quite different from the nonprojected values for HPCH2and H2PCH+,in which the UHF/6-3 1G** wave functions are highly spin contaminated ((9) values are 1.338 for H2PCH+and 1.247 for HPCH2+). The projected wave functions, however, are almost spin pure, so we believe the corresponding energies to be quite reliable. Note in this respect that, since MP3 and MP4 results are very similar, the PMP3 values may suffice to discuss relative energy orderings for this system, giving H3PC+> H2PCH+ > HPCH2+> PCH3+. The relative energy ordering contrasts to the one corresponding to the isovalent (H3CN)+ s y ~ t e m , ~where ~ , ~ ’ the sequence is H2NCH+ > HNCH2+ > CNH3+, and H3CN+ is not even a minimum in the potential surface; but it is in some way equivalent to the sequence observed in the isoelectronic (H3SiN)+ system” (SiNH3+ > HSiNH2+> H2SiNH+> H3SiN+) where hydrogen atoms ‘prefer” to be bonded to the first-row atom. This can be (22) Frisch, M. J.; Raghavachan, K.; Pople, J. A.; Bouma, W. J.; Radom,
L. Chcm. Phys. 1983, 75, 323.
(23) Koch, W.; Heinrich, N.; Schwartz, H. J . Am. Chcm. Soe. 1986,108, 5400. (24) Flora, J. R.; Gomez, Crespo, F.; Largo-Cabrerizo. J. Chem. Phys. ha.1988, 147, 84.
TABLE VI: W e s (kcal/d) of t k Products rad Tnaritioa State (TS)for the Readon of P+ with Mctbw, Relative to Reacbats. P+ + PCH#A2) PCH,+(*A”) CH, +H, +H TS 0.0 -1.7 (-2.8)b (-5.l)c 14.4 10.5 (8.0)b(6.5)’ HF 10.2 8.3 (5.3)b (3.7)’ MP2 0.0 -1.9 (-3.0Ib (-3.6)‘ MP3 0.0 -2.0 (-3.2jb . . 14.8 8.8 (5.8jb 15.4 8.4 (5.4)b MP4SDQ 0.0 -1.9 (-3.1)b 0.0 -2.7 (-3.8)b 13.9 7.1 (4.1)b MP4
‘Electronic energies were computed at different levels of theory with the 6-3 IG** basis set, whereas zero-point vibrational energy differences were estimated at the HF/3-21G* level. bObtained with the MC-31 IG** basis set. (Obtained with the MC-311G (2d,2p) basis set.
rationalized if one takes into account that X-H bonds are stronger for first-row atoms than for their second-row analogues, and that T bonds between first- and second-row atoms are usually weak. It is also of interest to compare the ionic system with the neutral system. In this respect, the relative energy ordering for the cations is similar to that found for triplet (H3CP),I7 namely PCH3 > HPCH, > HzPCH (H3PCwas not investigated by Nguyen et aLi7 and contrasts with that of singlet (H3CP,) i.e. HPCH2 > PCH3 > H2PCH.17 Closed-shell HPCH2 was found to be the global minimum, with triplet PCHSlying close in energy (- 10 kcal/mol higher at correlated levelsI7).
P+with Methane In this section we discuss the reaction between P+ and CH4. Two different reaction channels, (1) and (2), are possible in principle. The first requirement for a gas-phase reaction to take place under interstellar conditions is that it be ex other mi^.^^ Therefore we have computed the energies at different levels of theory for the products obtained in both processes, (1) and (2), relative to the reactants and collected them in Table VI. (Zero-point vibrational energy differences, computed at the HF/3-21G* level, are included.) It is readily seen in Table VI that process 2 is endothermic by 14 kcal/mol at the highest level of theory employed, namely MP4, even for the production of the ground state PCH3+(2A”),which is not spin allowed. The production of other isomers would be highly endothermic. It is worth noting that correlation effects favor only slightly the products of reaction, so no dramatic changes are to be expected at higher levels of theory. On the other hand, the products of process 1 lie below the reactants, although by a very small value, less than 3 kcal/mol at the MP4/6-31G** level. This is true only for the lowest lying Reaction of
-
(25) Duley, W. W.; Williams, D. A. Interstellar Chemistry; Academic Press: New York, 1984.
The Journal of Physical Chemistry, Vol. 95, No. 17, 1991 6557
Reaction of P+ with Methane
Figure 3. Optimized geometry at the HF/6-31G** level for the transition state leading to PCH2+()A2) H2. Distances are in angstroms, and angles in degrees.
+
triplet state, since other isomers would lie higher in energy and lead to endothermic values. We also found that inclusion of correlation energy favors the products, PCH2+('A2) + H2, by just 1 kcal/mol when the 6-31G9* basis set is employed. Also we like to point out that calculated HF/3-21G* stretching vibrational frequencies are well-known to be generally 3-696 t? high. This would decrease a bit the ZPVE of the products and transition states, resulting in a small but net lowering of the activation barriers. In addition to the exothermicity, it is also important to know whether the process has an activation barrier, since gas-phase reactions having nonnegligible barriers cannot take place under interstellar conditiomZS We have characterized the transition state for the production of PCH2+()A2). Its geometrical parameters are given in Figure 3, and its relative energy with respect to the reactants is also given in Table VI. We found that this transition state lies -7 kcal/mol higher in energy than the reactants at the MP4 level with the 6-31G** basis set. Given the crucial importance of the relative energies of the products and transition state with respect to the reactants, and the smallness of these values for process 1, we have computed them with a somewhat larger basis set, namely the one usually denoted MC31 lG**. This set is constructed from the 6-31 1G** basis setZ6 for carbon and hydrogen (which has triple-j' character for the valence orbitals) and the McLean and Chandler (12,9)/(6,5) basis set2' (with triple-{ character for the 3p orbitals), supplemented with a set of d functions for phosphorus. As it can be seen in Table VI, extension of the basis set favors exothermicity of process 1 by just 1 kcal/mol, with a value at the MP4 level of 3.8 kcal/mol. The activation energy is also reduced with the MC-31 lG** basis set by some 3 kcal/mol, and at the MP4 level is only 4.1 kcal/mol. In addition, MP2 calculations were also carried out with the MC-311G (2d,2p) basis set that is, including a second set of d orbitals for heavy atoms and an additional set of p orbitals, for hydrogen. The effect of these additional sets of polarization functions is to lower substantially (2.3 kcal/mol) the HF enthalpy
-
(26) Kriahman, R.; Binkley, J. S.;Seeger, R.; Pople, J. A. J. Chem. Phys.
1980, 72,650.
( 2 7 ) McLean, A. D.; Chandler, G. S. J . Chem. Phys. 1980, 72, 5639.
of process 1, probably because a second set of d functions favors the PC bond in PCH2+()A2)and to a minor extent the activation energy. Since a constant difference of -0.8 k d / d between MP4 and MP2 results is found for the enthalpy with both basis sets, 6-31G** and MC-311G**, a good estimate of the enthalpy is -4.4 kcal/mol for the MC-311G (2d,2p) basis set. With the same assumption, and noting that the difference in the energy barrier obtained at MP4 and MP2 levels is also a constant value (1.2 kcal/mol) for both basis sets, we can expect a value of 2.5 kcal/mol for the activation energy with the MC-311G (2d,2p) basis set at higher correlated levels. Therefore on the basis of the results collected in Table VI, we may conclude that process 2 is endothermic and most likely would not take place in the interstellar medium. On the other hand, the small exothermicity and barrier found for process 1 make difficult a definitive conclusion about the feasibility of production of PCH2+ under interstellar conditions. It is clear that at thermal energies this small barrier can be easily overcome, and reaction proceeds toward the production of PCH2+. In fact, measurements at 300 K5found that P+ reacts with CH4, with a relatively high rate constant, leading exclusively to PCH2+. However, at low temperatures the reactions should be much slower, but the barrier found in our calculations is too low for the reaction to be ruled out altogether.
Conclusions A theoretical study of the possible products of the reaction of P+ with methane has been camed out. The (H2CP)+lowest lying triplet state corresponds to a PCH2+conformation, with HPCH+ and H2PC+ lying 36 and 76 kcal/mol, respectively, higher in energy at correlated levels. Singlet-triplet separation for PCH2+ is estimated to be around 29 kcal/mol. The relative energy ordering for the (H3CP)+ system is found to be PCH3+ > HFCH2+ > H2PCH+> H3PC+,which is similar to those found for the neutral system on the triplet surface and for its isoelectronic (H3SiN)+system. We have found that the reaction of P+ with CH4 is endothermic toward the production of PCH3+but is slightly exothermic (with an enthalpy of - 4 . 4 kcal/mol according to our calculations) for the production of PCH2+. In addition, a small energy barrier (-2.5 kcal/mol) is expected for the second of these processes. Both basis set extension and correlation effects tend to diminish the energy barrier, so they are expected to be even lower at higher levels of theory. Therefore, on the basis of our results, the reaction of P+ with CH4 cannot not be ruled out as a possible interstellar process. Nevertheless it should be pointed out that it is predicted to proceed at a slow rate and only toward the production of PCH2+. Acknowledgment. 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 No. UPV/203.215-107/89), and by Gipuzkoako Foru Diputazioa.
