J. Phys. Chem. 1993,97, 6607-6615
6607
G2 ab Initio Calculations on the Thermochemistry of [P,N,H,,] (n = 0-2) and [P,N,H,,]+ (n = 0-3) Species and on the Potential Energy Surfaces of [P,N,H3]+ Singlet- and Triplet-State Cations M. Esseffar,?A. Luna, 0. M6, and M. Ytiiiez' Departamento de Quimica, C-14, Universidad Autbnoma de Madrid, Cantoblanco, 2%049-Madrid, Spain Received: January 5. 1993 Ab initio molecular orbital calculations at G1 and G2 levels of theory have been used to study the structures, relative stabilities, ionization potentials, heats of formation and proton affinities of neutral and cationic [P,N,H,] (n = 0-2) systems, for which there is a complete lack of experimental information. Some of the compounds investigated have been detected as products of the P+ NH3 reaction in the gas phase. Hence, the singlet and triplet potential energy surfaces for [P,N,Hs]+ have been also investigated. The global minimum corresponds to the HPNHz+(]Al) species, being the lowest triplet (PNH3+(3A1)) 18.5 kcal/mol aboveit. Since the calculated triplet-singlet energy gap for P+ is ca. 25.0 kcal/mol, the reactive channels on the singlet potential energy surface should be taken into account, at least for high-temperature gas-phase reactions. In this respect some possible mechanisms related to the formation of P N are discussed. A topological analysis of the electronic charge densities permits a systematization of the characteristics of the PN bonding along the series, as well as a quantification of bond activation effects upon ionization and protonation.
+
1. Introduction After the detection of phosphine, PH3, in Jupiter's atmosphere,* a certain attention was devoted to the study of the chemistry of phosphorus and in particular to the study of ion-molecule reactions involving PH,+ cationse2 The latter detection of PN in the Orion molecular cloud3v4has stimulated a renewed interest in the chemistry of these and other phosphorus containing compound^.^ In this respect, the experimental works of Thorne et a1.z and Smith et al.5 should be singled out, where the reactions of PH,+ (n = 0,4) with a considerable number of neutrals were envisaged, in an effort to provide kinetic data which would eventuallysubstantiate the quantitative ion-chemical models that describe the formation of a wide variety of molecules that nowadays have been detected in interstellar clouds. However, thermodynamic data on these species are very scarce. Hence, one of the aims of the present paper is to provide accurate theoretical estimations of the heats of formation, ionization potentials and proton affinities of different [P,N,H,] (n = 0, 3) neutral and cationic systems containing the P-N linkage. For this purpose we shall employ the G2 ab initio theory? which has been proved697 to yield values for these magnitudes which agree with the experimental ones to within *O.l eV. Some of the species studied were detected as products of the P+ NH3 reaction in the gas p h a ~ e ,so ~ .we ~ have considered it of interest to study also the potential energy surface of this system, since an understanding of the relevant phosphorus chemistry in these environments requires a knowledge of the thermodynamics of the individual processes. In this respect, the only theoretical study we are aware of regarding this system is that of Largo et a1.,8 but it was restricted to the triplet-state cations, while the information on the singlets is much scarcer and fragmentary.9-'3 On the other hand, it must be taken into account that the energy gap between P+(3P) and P+(lD)is only about 25 kcal/mol, hence, if as pointed out by Ziurys3 the most likely sources of PN are high-temperaturegas-phase reactions, reactive channels involving P+ in its singlet state should not be neglected. Actually, as we shall show in forthcoming sections, the global minimum, at the G2-level, of the [P,N,Hs]+ potential energy surface is not a triplet but a singlet state in contrast with the results obtained at the SCF level. In this respect, it should be emphasized that for some
+
t On leave from the University Cadi Ayyad, Marrakech, Morocco.
0022-3654/93/2091-6601$04.00/0
molecular cations the inclusion of electronic correlation effects is particularly significant when describing not only their relative stabilities but also their structures. As a consequence, some of our conclusions will be different from those obtained earlier in theoretical treatments based on SCF optimized structures. There is another additional interest associated to [P,N,H,] species which is related to the growing interest in compounds which feature double bonding to phosphoruslc17 and, in particular, in phosphazenes (-P=N-),lazo which can be Considered as analogous to diimines (-N=N-). The compounds considered in this work represent a suitable set to study the characteristics of the P-N linkage in different environments. This investigation will be carried out by means of a topological analysis of the electronic charge density, p, and its Laplacian, V p , for the different neutrals and cations under consideration. 2. Computational Details
Ab initio molecular orbital calculations at the G12l and G26 levels of theory were carried out by using the Gaussian80 program package.22 G1 theoryz1 is a composite procedure based in Hartree-Fock (HF) and Moller-Plesset perturbation theory at second and forth orders (MP2 and MP4) and quadratic configuration interaction including single, double, and triple excitations (QCISD(T)) levels of theory. In the G1 procedure the initial equilibrium structures are optimized at the UHF/6-3 1G* level, in order to obtain the corresponding zero-point vibrational energies (ZPE) and to characterize the stationary points of the potential energy surface. These geometries are then refined at the MP2/6-3 lG* level. Assuming additivity of different basis set enhancements at the MP4 level, and additivity of basis set and correlation effects between MP4 and QCISD(T), relative energies are obtained at effectively the QCISD(T) level with the 6-311+G(2df,p) basis set. The final G1 energy is obtained after adding a high-level correction which accounts for the isogyric effect and the ZPE value obtained in the SCF/6-31G* calculation scaled by the empirical factor 0.893. G2 theory6 is a further refinement which corrects some shortcomings of the G1 theory which arise from the assumption of additivity of individual basis set improvements and from an overestimation of the isogyric effect. These corrections imply further calculations at the MP2/6-3 1l+G(3df,2p) level with the result thatfinalenergies areeffectivelyofa QCISD(T)/6-311+G(3df,2p) quality. 0 1993 American Chemical Society
6608 The Journal of Physical Chemistry, Vol. 97, No. 25, 1993
For some particular cases we have carried out additional calculations devoted to avoid possible shortcomings of the G1 and G2 theories which arise from the use of the 6-31G* basis set in the geometry optimization procedures. As we shall illustrate later, for some particular open-shell systems, a significant spin contamination from higher multiplicities was found in both the HF and the MP2/6-3 lG* calculations. More significantly,this contamination was found to be basis set dependent, due to accidental degeneracies at the 6-31G* level between states of different multiplicities, which disappear by enlarging the basis set. The characteristics of the P-N bonds and the nature of the interactions of the different neutrals with P+ were investigated by means of a topologicalanalysisof the electronic chargedensity, p, and its Laplacian, Vzp. As has been shown by Bader and co-workers,U-ZSV2pidentifiesregions of space where theelectronic charge is locally depleted (Vzp > 0) or built up (Vzp < 0). The former situation is typically associated to interactions between closed-shell systems (ionic bonds, hydrogen bonds and van der Waals molecules), while the latter characterizes covalent bonds, where the electronic charge concentrates between the nuclei. We have also located the relevant bond critical points (bcp), Le., points where the electronic charge density is minimum along the bond and maximum in the other two directions, because the values of p and Vzpat these points offer quantitative information on the strength and nature of the bonding. This topological analysis was carried out on the wave function correct to first order, to take explicitly into account electronic correlation effects. For this purpose we have employed the AIMPAC series of programs.26 3. Results and Discussion Some Geometry Considerations. The optimized geometries of the different species considered in this work have been schematized in Figure 1. As indicated in the Introduction, many of these structures have been reported previously in the literature, but the majority where obtained without taking into account electronic correlation effects. As a consequence,not always the bond lengths and bond angles shown in Figure 1 are in agreement with previously reported values. In general the most remarkable differences affect the P-N bond length, but not in a regular manner. Four particular cases deserve to be singled out for comment: ( i )The optimizedstructure found for HPN(ZA’)is quite similar to that reported earlier by Buenker et al.,9 but we have found significantdifferencesregarding that of PNH(2A’), in particular for the bond angle, which in our MP2/6-31G* optimization is found to be 15l0, i.e., 31° larger than that reported in ref 9. In this respect, it must be mentioned that at the HF level, the PNH angle (1 15O) is 36O smaller than at the MP2 level, and hence in better agreement with the value of Buenker et ale9 To check whether the origin of these differences lies on the level of theory used in the description of electronic correlation effects, we have refined the geometry of PNH species at the QCISD(T)/ 6-3 11G(d,p) level. At this level the bond angle found (see Figure 1) was quite close to that reported by Buenker et al.9 This sensitivity of the geometrical parameters to the level of theory employed was also observed by Ma et al.’ when investigatingthe structure of the methanol radical cation. (ii) HPN+(lC+) was found by Buenker et al.9 to be a linear moleculewith a very shallow potential minimum. More recently Maclagan” reported a similar structure for this species, although it was found to be a transition state at the HF/6-3 lG* level. We have found indeed that a geometry optimization of the HPN+ cation at the HF/6-31G* level, by forcing the molecule to be linear, leads to a stationary point, similar to that describe in ref 13, but of second order. If the linearity restriction is removed in the optimization process, the initial HPN+ system collapses to
Esseffar et al. the PNH+ stable isomer, without activation barrier. To check whether these results may be an artifact of the HF procedure, we have reoptimized the structure of the HPN+ species at the MP2/6-3 1lG(d,p) level. The vibrational frequencies obtained at this correlated level indicate that there exists indeed a minimum of the singlet potential energy surface with a HPN+ conformation which lies 85.4 kcal/mol above the PNH+ one, in fairly good agreement with the calculations of Buenker et al.9 (iii) HzPN+(2A1)was found by Largo et ala8to be pyramidal, in contrast with our findings when the geometry of this species is optimized at the MP2/6-31G* level. This disagreement seems to arise from the strong spin contamination of the doublet state of H2PN+ by quartet multiplicities, when small basis sets are used. Actually this spin contamination is significant at the HF/ 6-31G* (S2= 1.45)levelandprobablylargerat thelevelemployed in ref 8 (HF/3-21G*). However, when a larger 6-311G(d,p) basis set is used, the optimized structure corresponds to a Cb planar conformation and the spin contamination dramatically decreases (S2 = 0.78). Furthermore, we have also found that when the structure is forced to be planar the corresponding stationary point found at the 6-31G* level, corresponds to a transition state, which would connect the two nonplanar minima. To understand this finding, we have optimized also the geometry of the lowest quadruplet state of HzPN+ at both HF/6-3 lG* and HF/6-3 1lG(d,p) levels of theory. At both levels, this state is not planar, but more importantly, it was found to be the global minimum. Furthermore, while the former basis set predicts that the doublet and quartet states are almost degenerate (the quartet is only 0.6 kcal/mol lower than the doublet) the larger basis yields 1.9 kcal/mol for this difference at the H F level and 13.0 kcal/mol at the MP2 level. Hence, we must conclude that the lack of planarity found for the lowest doublet state of HzPN+ at the HF/3-2lG* and HF/6-31G* levels is an artifact, due to the strong mixture with the corresponding quartet state, which, at the aforementioned levels, appears almost degenerate with the doublet. (iu) The fourth case where our geometries disagree more strongly with previous ones corresponds to the HPNHz+ ()A”) species. Our results show a markedly shorter P-N bond (1.63 A) than that found in ref 8. It must be indicated, that our HF/ 6-31G* value does not differ significantly from that reported before* what is an indication that this significant shortening is a somewhat unexpected electroniccorrelation effect. As we shall discuss later, this geometrical change will also be mirrored in the relative stabilities of the different PNHa+ triplets. Finally, it should also be noticed that Figure 1 does not contain the HpPN+ singlet state cation, because although at the HF/ 6-3 1G* level a stationary point with these characteristics and no imaginary frequencies is found, it evolves without activation barrier to yield the HNPHz+stable species, when theoptimization is carried out at the correlated level. Thermodynamic Data. The G 1 and G2 total energiesof neutral and cationic [P,N,Hn] ( n = 1-3) species have been summarized in Table I. It must be observed that this table contains also information on other species as NH(’A), NHz(*AI),N H z ~ B I ) , etc., because they have not been reported before at the same level of accuracy, and their total energies will be necessary when discussingthe possible dissociationproducts of [P,N,H,,]+ cations. Table I shows that, for all the systems considered there are no significant discrepancies between G1 and G2 predictions. Relative Stabilities. One of the problems inherent to the study of [P,N,Hn] systems is the relative stabilities of the different isomers and, for each isomer, therelativestabilities of thedifferent states. Since the stabilities of PN and the different PH,+ cations have been already described at the G2 level in ref 6 we shall start our exploration with the [P,N,H] systems. [P,N,HI and [P,N,HI+. Our results indicate that the neutral PNH(2A’) is 18.7 kcal/mol more stable than HPN (*A’). This
Thermochemistry of [P,N,Hn] and [P,N,Hn]+ 1.031 N-H
N-H 1.064
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The Journal of Physical Chemistry, Vol. 97, No. 25, 1993 6609
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TS4T T4 T S 51 T5 Figure 1. Optimized geometric9of the systems included in this study. Bond lengths are in angstroms and bond angles in degrees. The structures shown were optimized at the MP2/6-31G* level, with the exception of HPN(ZA')and HPN+('Z+) which were optimized at the QCISD(T)/6-31 lG(d,p) and MP2/6-31lG(d,p) levels, respectively.
energy difference, which is slightly smaller than that obtained in the MRD-CI calculations of Buenker et al.? increases dramatically upon ionization and the PNH+(lZ+)state is 85.4 kcal/mol more stable than HPN+(lZ+),again in good agreement with the results of ref 9. The same trend is observed for the triplets. PNH+('A') is predicted to be 30.0 kcal/mol more stable than HPN+(3A"), although our estimation is 20 kcal/mol smaller than
previously reported values.* It must be also observed that for PNH+ the singlet (12+)state is 92.6kcal/mol more stable than the triplet ('A'), while for the HPN+ isomers this difference reduces to 37.1 kcal/mol. [P,N,H2] and [P,N,H2]+. In qualitative agreement with previous theoretical studies,1+12 our results show that among the [P,N,Hz] neutrals the iminophosphane (HPNH) is the global
6610
Esseffar et al.
The Journal of Physical Chemistry, Vol. 97, No. 25, 1993
TABLE I: G1 and C2 Total Energies (in au) of the Mfferent Systems Included in This Study
compound N-H(’A) N-H+(’II) P-H( ‘A) NHz+(’Ad NHz+(~BI) PHz+(’Bi 1 PN(’Z+) PN+(Q) PNH(2A1) HPN(zA’) PNH+(IZ+) PNH+(’A’) HPN+(’Z+) HPN+(’A’) HzPN(’Ai ) HzPN(’A”) HzPN+(ZAl) HzPN+(‘A’’) PNHz(’Ad PNHz(’A”) PNHz+(ZBz) HPNH(’A’) HPNH(’A) HPNH+(2A’) PNH,+(’A’) Sl’ PNH3+(3A~)T1 HPNHz+(lA’) S2 HPNHz+(~A”)T2 HzPNH+(‘A’) 53 t-HzPNH+(’A’’) T3 c-HzPNH+(~A”) T4 H3PN+(3A~)TS TSlSC TS2s
TS3s Ts4s
E(G1) -55.017 05 -54.648 21 -341.388 82 -55.332 03 -55.316 22 -341.657 81 -395.568 58“ -395.151 I6 -396.124 50 -396.095 70 -395.861 56 -395.120 08 -395.732 50 -395.61 1 95 -396.680 21 -396.649 64 -396.231 34 -396.258 53 -396.118 81 -396.115 32 -396.443 84 -396.141 66 -396.610 81 -396.394 43 -396.988 51 -391.038 59 -391.068 13 -396.991 54 -391.01 1 10 -396.959 31 -396.941 19 -396.931 94 -396.940 85 -396.991 95 -396.942 99 -391.003 01 -396.963 69 -396.913 94 -396.936 19 -396.811 18
TABLE II: Ionization Potentials (in eV) and Estimated Heats of Formation (in kcal/mol)
E(G2)
compound
-55.011 65
PN(lZ+) PNH(zA’) HPN(2A’) PNH+(’Z+) PNH+(3A’) HPN+(‘Z+) HPN+(3A’) HzPN(’Ai) HzPN(~A”) HzPN+(’Ai) PNHd’ AI) PNHz(~A”) PNHZ+(~B~) HPNH( ‘A’) HPNH(3A) HPNH+(ZA’) PNH,+(’A’) S1“ PNH3+(3A~)T1 HPNHz+(‘A’) S2 HPNHz+(’A’‘) T2 HzPNH+(’A’) S3 t-HzPNH+(3A”) T3 H3PN+(3A1)T5
-54.649 21 -341.389 53 -55.333 92 -55.318 34 -341.659 41 -395.567 12 -395.128 46 -396.126 48 -396.096 64 -395.868 88 -395.121 32 -395.132 10 -395.613 55 -396.683 01 -396.651 33 -396.239 16 -396.260 30 -396.120 13 -396.711 53 -396.445 68 -396.143 61 -396.613 54 -396.397 00 -396.990 60 -397.041 28 -397.010 81 -391.000 85 -397.015 19 -396.962 65 -396.950 52 -396.940 36 -396.942 58 -396.994 90 -396.945 41 -391.001 43 -396.966 12 -396.911 06 -396.939 81 -396.819 91
TSlT TS2T TSJT TSllT a Taken from ref 6. These symbols correspond to those employed in Figures 2 and 3. Transition states of the singlet and triplet [P,N,H3]+ potential energy surfaces. See Figures 2 and 3. minimum, while PNH2 and H2PN lie 14.3 and 28.0 kcal/mol, respectively, above it. Thesevaluesslightlycorrectthosepublished by Trinquier.10 However, we have found significant discrepancies with previously reported results regarding the singlet-triplet energy gaps. For HPNH the G2 separation between the (IA’) and the (3A’) states is considerably larger (44.0 kcal/mol) than previous estimations”JJ1(28.0 kcal/mol and 36.1 kcal/mol). The same applies to H2PN, for which our results predict a singlettriplet energy gap of 19.9 kcal/mol, which is ca. 12 kcal/mol larger than the values given in refs 10 and 11 (6.0 and 7.0 kcal/ mol, respectively). Nevertheless,the most significantdiscrepancy corresponds to PNH2. Previous theoretical treatments10.11 indicate, contrarily to the other two isomers, that the ground state of this species was a triplet 3A” rather than a singlet ‘AI. Our results show however that the singlet state, both at the G1 and G2 levels, is about 2 kcal/mol more stable than the triplet. Quite interestingly,the relative stabilities of the corresponding cations are reversed with respect to those of the neutrals. The most stable [P,N,Hz]+ isomer is now the PNHz+(2B2), while HPNH+ and HzPN+ species lie 31.1 and 129.2 kcal/mol, respectively, above it. It should also be noticed that for the latter system, the quartet (4A”) is found to be 12.9 kcal/mol more stable than the doublet (ZA1). [P,N,H3]+.One of the most significant results regarding the [P,N,H# cations is the fact that the global minimum, at both the G1 and G2 levels, is the singlet HPNH2+(lA1) species, while at the H F level the global minimum corresponds to the PNH3+
a
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46.2 58.1 73.1 218.9 311.5 300.8 331.9 10.9 90.8 348.5 50.6 52.5 222.8 36.3 80.2 253.5 248.7 211.1 196.5 239.8 221.5 260.8 214.1
These symbols correspond to those employed in Figures 2 and 3.
triplet state cation. This clearly illustrates that a proper description of electronic correlation effects is unavoidable to achieve a reliable energy ordering for these kinds of systems. On the other hand, as we shall show in forthcoming sections, this finding might have a considerable importance when discussing the reactivity of P+(3P) or P+(lD) with NH3 in the gas-phase. This global minimum (HPNH~+(’AI))is 43.9 kcal/mol more stable than the corresponding triplet (3A”), while this difference reduces to 33.0 kcal/mol for the HzPNH+ species. Quite on the contrary the PNH3+ triplet state cation (3Al) is 31.8 kcal/mol more stable than the singlet (lA’). Also HsPN+ cation, as indicated above, exists only as a triplet, since the corresponding singlet collapses to H2PNH+ species. Ionization Potentials and Heats of Formation. The calculated ionization potentials for thedifferent neutrals under consideration have been summarized in Table 11. Unfortunately we have not found experimental values to compare with. Something similar can be said regarding the corresponding heats of formation of the different neutral and cationic species. Nevertheless it must be mentioned that our estimated ionization energy for the process PHz(2B1)-PH2+(3B~)+ e-is 10.60eV, infairlygoodagreement with the best experimental estimate2’ of 110.534 eV. To obtain the heats of formation we have used the total G2 energies reported in Table I as well as those of H2, NH3, PH3, P, P+, N, and N+ taken from ref 6. These theoretical values were then combined with the experimental heats of formation2*of NH3, PH3, P, and N and their experimental ionization potentialsz9 in adequate reactions which permit to define the heat of formation of a given system. For instance, the heat of formation of PNH3+(3Al) may be obtained from the following process:
+
P+(3P) NH,(’A,)
-
PNH3+(3A1)
TheG2 enthalpy change for this reaction is -92.1 kcal/mol. Since the experimental heats of formation of P+ and NH3 are 320.2 and -1 1.0 kcal/mol, respectively, one can obtain as a reasonable estimation for the heat of formation of PNH3+ the value of 217.1 kcal/mol. Analogous processes were defined to obtain the remaining heats of formation. Since the experimental heats of formation and ionization potentials are usually given at 298.1 5 K, for the sake of consistency the enthalpies of the different reactions employed in our estimations include the corresponding thermal corrections. Thermal contributions to the enthalpies
The Journal of Physical Chemistry, Vol. 97, No. 25, I993 6611
Thermochemistry of [P,N,H,] and [P,N,H,]+
TABLE IIk
ProtonationEnergies (in kcrl/mol) for Different [Paw(a = 0-2) species
+ -
+
PN(lZ+) H+ PNH+(lE+) PN(’Z+) + H+ -.,HPN+(lZ+) PNH(2A’) + H+ P N H Z + ( ~ B ~ ) PNH(2A‘) H+ HPNH+(2A’) PNHz(’A1) + H+ HPNHz+(’A‘) PNHz(’A1) + H+ PNH>+(’A’) HSN(’A1) + H++HzPNH+(’A’) HzPN(3A”) H+ H3PN+CAi) HZPN(~A”)+ H+ HsPNH+(~A”) PNHz(3A”) + H+ PNH3+(’Ai) PNHzCA”)+ H+-HPNHz+(’A’’) HPNH(1A‘) + H+ -.,HPNHz+(’A’) HPNH(1A’) + H+ HzPNH+(’A’) HPNH(3A) H+ HPNH2+(3A”) HPNH(3A) H+ HzPNH+()A”) 4
+
+
+
+ -+
+ +
a Experimental
-
+
+
189.4. 103.9 200.3 169.7 219.7 169.3 208.4 181.4 195.4 203.1 177.8 205.3 170.4 205.4 181.4
value taken from ref 13, 190.0 kcal/mol.
include l/zRT for each translational and rotational degree of freedom, plus changes in the vibrational energy due to thermal population of the excited vibrational modes evaluated at the HF/ 6-31G2 level. Proton Affiiitles. The calculated proton affinities (at 0 K)of [P,N,H,] (n = 0, 2) are presented in Table 111. At present no experimental data are available for comparison with the only exception of PN. The agreement between our calculated value for this species and the experimental outcome’f is very good. All systems, with the only exception of PNHz(*Al), behave as nitrogen bases in the gas phase. It must be mentioned however that, once more, elcctronic correlation effects are crucial when describing these protonation processes. Actually, we have found that at the HF level, PNHz(lA1) is predicted to be a nitrogen rather than a phosphorus base. Quite importantly, this phosphorus base is predicted to be about 17 kcal/mol more basic than ammonia, while its isomer HzPN protonates exclusively on nitrogen since the phosphorous protonated species is not stable. Only PN and PNH(*A’) systems are predicted to be weaker bases than ammonia. The latter finding has some relevance
t
regarding the reactivity of P+ and ammonia in the gas phase. In fact, Thome et al.2 have found that the dominant reactive channel for the reaction P+ + NH3 products PNH2+,but they have also observed the proton-transfer reaction:
PNH;
+ NH,
-
NH;
+ PNH
in the NHJPH3 mixture. Our theoretical results sustain this finding since the proton affinity of PNH should be 2.0 kcal/mol smaller than that of ammonia favoringthe aforementionedprotontransfer process. [P,N,H# Potential bray Surfaces. The relevant stationary points of the potential energy surfaces of singlet and triplet [P,N,H3]+ systems are schematized in Figures 2 and 3, respectively. This information is complemented with that summarized in Table IV which corresponds to the dissociation energies of both (singletand triplet) global minima to yield different products, in processes which involve only one bond fission. It may be observed that the binding energy of P+,in its first excitedstate (‘D), toNH3isconsiderably higher thaninitsground state (3P) due to the ability of the former to insert in the N-H bonds of the base. This result may be of some significance for P+ + NH3 reactions at high temperature, since as we have mentioned before the triplet-singlet energy gap for P+is only of 25.0 kcal/mol. Quite surprisingly,N+ association to PH3 occurs only in theN+ ground state, with a binding energy of 172.8 kcal/ mol, while the adduct N+(’D)-PH, is not stable and evolves without activation barrier to yield HNPH2+. It should benoticed that HPNHz+ and H2PNH+singlet systems are planar and therefore the two possible conformers (S2 and S2’; S3 and S3’)are identical. This is not the case for the triplet HzPNH+ for which the trans conformer is about 8 kcal/mol more stable than the cis one. The transition states corresponding to the possible isomerizationswere also identified. It is interesting to observe that the interconversion between T3 and T4 occurs via a nitrogen inversionprocess, while T2 -T2’ isomerizationimplies an intemal rotation of the -NH2 group rather than a phosphorus inversion.
SINGLET
5I
(2)
\
0
.
5 I’( 0.0
1
r
Reaction Coordinate
Figure 2. Energy profile for the potential energy surface of singlet (P,N,H3]+ system calculated at the G2 level of theory.
Esseffar et al.
6612 The Journal of Physical Chemistry, Yol. 97, No. 25, 1993
*-/p m
TRIPLET
01
(14&4)
REACTION COORDfNATE
Figwe 3. Energy profile for the potential energy surface of triplet [P,N,H# system calculated at the G2 level of theory. Values referred to the HPNHz+ singlet global minimum.
TABLE Iv: Possible Mssociation Products of the hwest Siqplet and Triplet P,N,Hd+ Systems8 dissociation mniucts E(G2) ( a d Des (kcal/mol) DeT (kcal/mol) 136.8 *FD)+ NH~(’AI) -396.852 85 93.0 P+(’P) + NH~(’AI) -396.893 02 87.2 P(4S) + NH3+(zA1) -396.902 32 105.0 123.5 P(2P) + NH3+(2A~) -396.873 93 122.1 140.6 PH+(’ll) + NHz(2Bi) -396.846 67 147.2 PH(’Z-) + NHz+(’Bl) -396.806 77 175.0 PH(’Z-) + NHz+(’A1) -396.762 35 165.3 PH(’A) + NH2+(3Bi) -396.777 86 218.0 PH(’A) + NH2+(’A1) -396.723 34 130.1 PHz+(’Ai) + NHOZ-) -396.834 01 150.4 PHz+(~BI) + NHOZ-) -396.801 64 189.1 PH2+(’Al)+ NH(’A) -396.769 49 191.0 PHz+(3B1) + NH(’A) -396.737 12 129.8 PH~+(’AI)+ N(%) -396.834 38 186.0 204.5 PH3+(2Al)+ N(2P) -396.744 90 236.1 PH,(’Ai) + N+(3P) -396.665 01 300.9 PH,(’Al) + N+(’D) -396.591 24 60.0 78.5 PNHz’(’B2) + H(’S) -396.945 68 189.2 NPHz+(’Ai) + H(%) -396.739 76 207.7 219.7 PNHz(’Ai)+ H+ -396.720 73 243.3 NPHz(’A1) + H+ -396.683 01 203.2 PNH2(’At’) + H+ -396.717 53 244.7 NPH&A”)+ H+ -396.651 33 HPNH(’A’) + H+ -396.743 61 205.3 230.8 HPNH(3A) + H+ -396.673 54 90.5 109.1 HPNH’(2A’) + H(%) -396.897 00 The sccond column gives the sum of the total G2 energies of both fragments. Third and fourth columns present the dissociationenergies with respect to the global singlet (Des) and triplet (De? minima, respectively. According to our results, the experimentallyobserved reaction
P+ + NH3 .-,PNH:
+H
(3) is exothermic by 33.0 kcal/mol. However, as shown in Figure 3, the reaction P+(3P) + NH3 yields the PNH3+ adduct, and its isomerization to yield the HPNH2+ conformer impkies an
activation barrier of 47.2 kcal/mol, that although smaller than that reported in ref 8 ($3.9 kcal/mol) is still quite large. Hence, even though the hydrogen loss is energetically more favourable for the HPNH2+ species than for PNH3+ one, very unlikely reaction 3 is preceded by the PNH3+-HPNH2+ isomerization. Then the alternative mechanism to produce PNH2+ would be a direct dissociation of the PNH,+ adduct. The corresponding transition states have been described at the HF/6-31G** level in ref 8 and for the process PNHs+ PNH2+ + H it was found to be 16.0 kcal/mol above the dissociation products. However, when its geometry is refined at the MP2/6-31G* level, we have found it to be below the dissociation products. Similar findings were obtained also for the transition state corresponding to the hydrogen loss of HPNH*+ system. This is not surprising since HF theory is not suitable to describe dissociation processes, and the existence of these TS seems to be an artifact of this theory. We may then conclude that the hydrogen loss of the PNH~+(’AI) global minimum is thermodynamically controlled and not kinetically controlled. In this respect, it must be noticed (see Table IV) that the dissociation products are 60.0 kcal/mol above this minimum. Our results alsoshowthat thecharge transfer processesolxewed in P+ + NH3 reactions5 are also exothermic for both P+(’D) and P+(3P). As mentioned in the Introduction,it is also interestingto explore the possible routes for the production of PN. One possible mechanism would imply the formation of HPN+, as an intermediate, which after neutralization would eventually evolve to yield PN. However, the two possible channels of the reaction of P+(3P) with ammonia to yield PNH+ or HPN+, are endothermic. Quite on the contrary, if the reaction involves excited P+(’D) the production of PNH+(’A’) is, according to our calculations,highly exothermic (AH= -1 14.4 kcal/mol). Hence, this might be a likely mechanism, provided the production of PN implies hightemperature gas-phase reactions, as proposed by Ziurys.3 There are, of course, other alternative ways to produce PN. In this
-
The Journal of Physical Chemistry, Vol. 97. No. 25, 1993 6613
Thermochemistry of [P,N,H,] and [P,N,H,]+
respect,it must be taken into account that if the reaction OCCUR via P+ in its excited ID state, the stable ion formed corresponds to a HPNH2+ species, that may dissociate according to the following exothermic process:
-
+ NH,('A,)
P+('D)
-
+H
PNH:(IB,)
AH = -58.2 kcal/mol (4)
Then, a further endothermic hydrogen loss reaction: PNH;('B2)
PNH+('Z+)
+H
AH = 48.2 kcal/mol (5)
would yield PNH+. The important thing is that this two-step mechanism would be still exothermic by 10.0 kcal/mol. HPN+ can be produced by reaction of N+(3P) or N+('D) with PH3 in the gas phase. The direct processes:
-
+ PH,('A,)
N+('P)
HPN+(3A')
+ PH3('Al)
N+('D)
+ H,
AH = -109.7 kcal/mol HPN+('Z+)
(6)
+ H2
AH = -146.9 kcal/mol (7)
are clearly exothermic. On the other hand, if the mechanism implies two steps: (a)
N+(3P)
+ PH,('A,)
H,PN+('A')
(b)
-
-
+
H,PN+('A,) H AH = -46.9 kcal/mol (8)
+
HPN+('Z+) H AH = +4.4 kcal/mol (9)
the overall process will be still highly exothermic. Other possible pathways would involve PH and PHz or alternatively N H and NH2 species. Reaction of N+ with PH to produce HPN+ is highly exothermic: N+cP)
+ PH('Z3
-
HPN+('A')
AH = -162.6 kcal/mol (10)
Similarly, the mechanism involving PH2 as reactant would be also clearly exothermic: N+('P)
-
+ PH2(2Bl)
H,PN+('A,)
-
H,PN+(2A,)
AH = -128.4 kcal/mol
HPN+('Z+)
(11)
+H
AH = +4.4 kcal/mol (12) An analogous behavior is predicted for reactions involving P+ and NH or NH2: P'(3P) P+('P)
+ NH('Z3 + NH,('B,)
PNH;(2B,)
-
-
PNH+('A')
AH = -90.8 lccal/mol (1 3) PNH;(IB2)
PNH+('Z+)
AH = -139.5 kcal/mol (14)
+H AH = +48.2 kcal/mol (1 5)
Both ways of producing PN, either from PNH+ or HPN+ are thermodynamically feasable since although both hydrogen loss processes are endothermic: PNH
-
+H PN + H PN
AH = +37.2 kcal/mol
(16)
HPN -.c AH = +18.5 kcal/mol (17) electron capture processes by PNH+ or HPN+ are strongly exothermic.
TABLE V Electronic Cha e Densities, pe (e/&) and Their Laplacians, V p , (ehu7), Evaluated at the PN Bond Critical Points compound PC QZPC PN('Z+) PN+(2Z) PNH(2A') HPN(zA') PNH+('Z+) PNH+(3A') HPN+('E+) HPN+()A') HzPN('Ad HzPN()A") HZPN+(~A 1) PNHz('Ad PNHz(3A") PNHZ+(~B~) HPNH(' A') HPNH('A) HPNH+(2A') PNHa+('A') Sl0 PNH~+CAI)T1 HPNHz+('A') S2 HPNHz+("") T2 HzPNH+('A') S3 t-HzPNH+CA")T3 c-H~PNH+(~A") T4 HaPN'('A1) T5
0.214 0.218 0.216 0.210 0.211 0.176 0.196 0.179 0.218 0.159 0.203 0.158 0.150 0.185 0.189 0.161 0.207 0.110 0.107 0.175 0.174 0.210 0.170 0.171 0.168
1.318 1.839 1.664 1.257 1.627 0.909 0.805 0.980 1.230 0.341 0.647 0.837 0.491 0.987 0.885 0.542 1.445 0.099 0.07 1 0.897 0.727 1.139 0.602 0.843 0.156
* These symbols correspond to thosc employed in Figures 2 and 3. Alternative reaction paths involving N+ in its 'Dexcited state might be discarded because the triplet-singlet energy gap for N+ is much larger (46.3 kcal/mol) than for P+. Clnuacteristics of thePN Bond. Table V presents the electronic chargedensity and its Laplacian evaluated at the PN bond critical points of the different neutral and ionic [P,N,H,] (n = 0-3) systemsinvestigated. Thevalues of pc (and V2p,)for thesesystems may be classified in three different sets: those which are around 0.21 au(and lSau),thosearound0,18au(andO,9au)andthose around 0.16 au (and 0.5 au), respectively. The former should correspond to typical PN triple bonds, as it is expected in the PN molecule (see Table V) and the following ones to double and single PN linkages. More significantly, thesevaluesare practically identical to those reported by Bachrach'o for PEC, M, and P-C bonds in a series of phosphines, phosphaalkanes, and phosphaalkynes. Some significant features should be emphasized. Protonation of PN either at nitrogen or phosphorus has a quite small effect on the PN bonding characteristics. Something similar can be said for the phosphorus protonation of HPN. As shown in Table IV, the triple-bond character of the PN linkage of this neutral is practicallyretained in the H2PN+species. However, in general, one may observe that when protonation takes place at the more electronegative nitrogen atom there is a significant activation of the PN bond. For instance, protonation of PNH to yield PNH2+, implies a change from a triple to a double-bondlinkage. Similarly, protonation of PNH2 to yield PNH3+ implies a significant weakening of the P-N bond. On the contrary, protonation at the less electronegative phosphorus atom is accompanied by a reinforcement of the PN linkage, which becomes evident by comparing the values of pcfor HPNH and H2PNH+or for PNH2 and HPNH2+. This general behavior was already reported and explained for other bidentate bases?' and those arguments will not be repeated here. Our results also confirm the conclusion of Trinquier'O in the sense that phosphonitrene presents a pentacoordinated phosphorous atom (HI"). It must be observed that its ionization to yield the corresponding doublet state cation does not affect significantly to the PN bonding, which becomes slightly weaker. However, ionization of PNH2 or HPNH is followed by a reinforcement of the corresponding PN linkage.
Esseffar et al.
6614 The Journal of Physical Chemistry, Vol. 97, No. 25, 1993
interaction between closed-shellsubunits. Consistentlywith this topological description of the PNHs+(’Al), the two unpaired electrons in this system are localized at the phosphorus atom. We can then conclude that the association of P+,either in its triplet ground state or in its singlet D excited state, to ammonia is essentially electrostatic. In agreement with this, the corresponding association energy evaluated at the SCF level is about equal in both cases. However, as mentioned above, electronic correlation effects favor the triplet and at the G2 level the P(3P) binding energy to ammonia (93.1 kcal/mol) is 6.6 kcal/mol greater than that of P+(lD) (86.5 kcal/mol). Quite on the contrary, in NPH3+ species the PN bond is clearly covalent (see Figure 4c),and the value of pc at the corresponding bond critihl point is typica1 of a P=N bond. Hence, we conclude that, also in this compound, phosphorous appears pentacoordinated.
a
4. Conclusions
L 1 /’ Figure 4. Contour maps of the Laplacian of the charge density of (a) Pmitive values of PNH,+(IA’); (b) PNHs+(’A,), and (c) HSPN+(~A~). V2paredenotd bysolidlinsaandnegativeval~~bydarhdlines.Contour valuca in au are f0.05, f0.25, f0.50, f0.75, and f0.95.
As should be expected, the PN bond for the triplet states of NPH2, PNH2, HPNH, PNH+, and HPN+ are weaker than for the singlets. Furthermore, two of these species (HPNH and PNH+) have one of their unpaired electronslocalized at nitrogen, whereas the other is at phosphorus. In HPN+ and HzPN both unpaired electrons are on the nitrogen atom while in PNH2 are both on the phoephorous. Among the doublets, NPH2+, HPNH+ and HPN are nitrogen radicals, while PNHz+ and PNH have the unpaired electron localized at phosphorous. On the other hand, isomerization is accompaniad by significant changes in the PN bond. Onemayo~rve,takingtheseriesofthe[P,N,H3]+singlet state cations as a suitable example, that while PNH3+S 1 presents a P-N single bond, its isomer HPNHz+ S2 has a P - N linkage and the HzPNH+ cation has a practically pentacoordinated phosphorous atom. Table V also shows that there are significant differences in the bonding between PNH3+ and NPH3+ species. As illustrated in Figure 4a.b in both singlet and triplet PNH3+ systems the Laplacian in the P-N region is positive as it corresponds to an
We have found that for neutral and cationic [P,N,H.] (n = 0-3) species a theoretical treatment at the HF level of theory would yield a quite incorrect energy ordering for the different isomers. Besides, for some particular species for which the optimized structures are sensible to electronic correlation effects, the explicit consideration of correlation corrections at HF optimized geometries does not solve the problem. We have provided accurate theoretical estimationsfor different thermochemical data that can guide future experimental studies on these species for which there is an almost complete lack of experimental information. Regarding the reactivity of P+with ammonia in the gas phase, one of the most relevant conclusions of this workis that the global minimum of the singlet and triplet potential energy surfaces is the HPNHz+(lA’) species. This can be rationalized in terms of the topological characteristics of these cations since, as we have mentioned above, the global minimum of the triplet potential energy surface correspondsto an electrostaticinteraction between P+(3P) and NH3, while in the global minimum of the singlet potential energysurfacethe P atom appearscovalently coordinated to nitrogen and hydrogen. Hence, taking also into account that the triplet-singlet energy gap for P+ is not significantly large (25.0 kcal/mol), the singlet potential energy surface cannot be disregarded when confronting P+ + NH3 reactivity. In this respect, our results suggest that if, as pointed out by Ziurys,) PN molecule is produced in high-temperature gas-phase reactions, one possible channel for the production of PNH+ species would be the reaction of P+(lD) with ammonia. Some other possible mechanisms are also examined. Our topological analysis of the electronic charge densities of the different species investigated allow us to conclude that [P,N,H,] (n = 0-3) constitute a set which clearly illustrates the ability of phosphorous to yield multiple bonds. In particular PN, PNH+, HzPN and H*PN+ present typical PN triple bonds. Acknowledgment. This work has been partially supported by the DGICYT Project No. PB90-0228-(202-01. M.E. gratefully acknowledges a postdoctoral grant from the Ministerio de Educaci6n y Ciencia. Refereucea and Notes (1) Ridgeway, S. T.;Wallace, L.; Smith, G. R. Asrrophys. J. 1976,207, 1002. (2) Thome, L.R.; Anicich, V. G.; Huntress, W. T. C h m . Phys. Lrrr. 1983, 98. 162. (3) Ziurys, L. M. Astrophys. J. 1987, 321, L81. (4) Turner, B. E.; Bally, J. Asrrophys. J. 1987, 321, L75. (5) Smith, D.;McIntosh, B. J.; Adam, N. G. J. Chem. Phys. 1989.90, 6213. (6) Curtis, L. A.; Raghavachari, K.; Trucks, G. W.; Poplc, J. A. J . Chem. Phys. 1991, 94, 7221. (7) Ma, N.L.;Smith, B. J.; Radom, L. J. Phys. Chem. 1992,96,5804. ( 8 ) Largo, A.; Flora, J. R.; Barrientos, C.; Ugaldc, J. M. J. Phys. Chem. 1991, 95, 170.
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The Journal of Physical Chemistry, Vol. 97, No. 25, 1993 6615 J. S.;Gondlez, C.; Defrtcs, D. J.; Fox, D. J.; Whiteside, R. A.; Secger, R.; Meliua, C. F.; Baker, J.; Martin, R. L.; Kahn, L. R.; Stewart, J. J. P.; Topiol, S.;Poplc, J. A. Gaussian Inc.: Pittsburgh, PA, 1996. (23) Bader, R. F. W.;E&n, H. J. Chew. Phys. lW, 80, 1943. (24) Bader, R. F. W.; MacDougall, P. J.; Lau, C. D. H. J . Am. Chem. Soc. 1984,106, 1594. (25) Bader, R. F. W. Atoms in Molecules. A Quontum Theory; Oxford University Press: New York, 1990. (26) AIMPAC programs package has been provided by J. Cheeseman and R. F. W. Bader. (27) Berkowitz, J.; Curtis, L. A.; Gibson, S.T.; Greene, J. P.; Hillhouse, G. L.; Poplc, J. A. J. Chem. Phys. 1986, 84, 375. (28) Pedley, J. B.; Rylancc, J. CATCH Tables, University of Sussex, 1977; Beneon, S.W.; Cruickshank, F. R.; Golden, D. M.; Haugen, G. R.;O”ea1, H. E.; Rogers, A. S.;Shaw, R.; Walsh, R. Chem. Ref. 1%9,69,279. (29) (a) Moore, C. Natl. Bur. Stand. Cfrc.1969,467. (b) Martin, W. C. J. Opt. Soc. Am. 1959,49, 1071. (30) Bachrach, S.M. J . Comput. Chem. 1989, 10, 392. (31) Alcaml,M.;M6,O.;YgnCz,M.;Abboud,J.L.-M.;Elguero,J.Chem. Phys. Lett. 1990, 172, 471.
