Gas phase ion chemistry and ab initio theoretical study of phosphine. III. Reactions ofPH 2 + and PH 3 + with PH 3Paola Antoniotti, Lorenza Operti, Roberto Rabezzana, Glauco Tonachini, and Gian Angelo Vaglio Citation: The Journal of Chemical Physics 112, 1814 (2000); doi: 10.1063/1.480745 View online: http://dx.doi.org/10.1063/1.480745 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/112/4?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Experimental and ab initio studies of the reactive processes in gas phase i-C3H7Br and i-C3H7OH collisions withpotassium ions J. Chem. Phys. 141, 164310 (2014); 10.1063/1.4898377 A nine-dimensional ab initio global potential energy surface for the H2O+ + H2 → H3O+ + H reaction J. Chem. Phys. 140, 224313 (2014); 10.1063/1.4881943 Ab initio analytical potential energy surface and quasiclassical trajectory study of the O + ( 4 S)+ H 2 (X 1 Σ g +)→ OH + (X 3 Σ − )+ H ( 2 S) reaction and isotopic variants J. Chem. Phys. 120, 4705 (2004); 10.1063/1.1638735 Gas-phase ion chemistry and ab initio theoretical study of phosphine. II. Reactions of PH + with PH 3 J. Chem. Phys. 109, 10853 (1998); 10.1063/1.477782 Gas phase ion chemistry and ab initio theoretical study of phosphine. I J. Chem. Phys. 107, 1491 (1997); 10.1063/1.474502

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Gas phase ion chemistry and ab initio theoretical study of phosphine.III. Reactions of PH 2

1 and PH31 with PH 3

Paola Antoniotti,a) Lorenza Operti,a) Roberto Rabezzana, Glauco Tonachini,and Gian Angelo VaglioDipartimento di Chimica Generale ed Organica Applicata, Universita` degli Studi di Torino, CorsoMassimo d’Azeglio 48, 10125 Torino, Italy

~Received 19 July 1999; accepted 29 October 1999!

The gas phase ion chemistry of phosphine has been investigated byab initio theoretical calculationsand experimental techniques. Following previous studies dealing with3P1 and PH1 reacting withPH3, the quantum chemical study of these processes has been extended to the ion/molecule reactionsstarting from PH2

1 and PH3 ~reaction a! or PH31 and PH3 ~reaction b!, as observed by ion trapping.

In these experiments, PH21 reacts to give P2Hn

1 (n51,3) product ions, with loss of H2 throughdifferent pathways. These processes take place at quite different rates, their constants being 2.6 and7.6310210cm3 molecule21 s21, respectively. The geometrical structures and energies of transitionstructures, reaction intermediates, and final products have been determined byab initio theoreticalmethods. The initial step of the reaction of PH2

1 with PH3 is formation of the H2P–PH31 adduct.

Then, a hydrogen molecule can be directly lost either from tricoordinated or tetracoordinatedphosphorus, to give P–PH3

1 or HP5PH21, respectively. The shift of one H atom in HP5PH2

1

produces the bridged HP~H!PH1 ion, from which further dissociation of H2 yields PPH1. The initialstep of the reaction of PH3

1 with PH3 is formation of the H3P–PH31 adduct. Then inversion of the

H atoms in the PH3 group transforms the adduct in an electrostatic complex. This last species isrelated by a dissociation process to the PH2 and PH4

1 products. The heats of formation of the P2Hn1

(n51 – 6) ionic species have been computed and compared with the experimental data in theliterature. © 2000 American Institute of Physics.@S0021-9606~00!31204-1#

I. INTRODUCTION

The combined application of advanced experimentalmethods andab initio quantum chemical calculations haveimproved the understanding of processes of interest mainlyin research fields concerning atmospheric chemistry,1 theformation processes and reactivity of interstellar media,2 andthe preparation of solid materials by activation of volatilesystems.3–5 Understanding the nature of ion/molecule clus-tering reactions is an extremely important problem in thefield of cluster chemistry, in particular the investigation ofthe chain propagation and the consequent cluster nucleationand growth.

Recently, detailed investigations have been performedby mass spectrometric methods, on the germane/phosphine4

and silane/phosphine5 systems. These studies provided anunderstanding of the formation of ionic species containingnew Ge–P and Si–P bonds. In order to find the conditionsunder which preparation of germanium or silicon doped withphosphorus could be performed, it is important to know indetail the gas phase behavior of each of the reacting mol-ecules. We have recently reported the theoretical and experi-mental results on the reaction pathways of P1 with PH3,

6 andof PH1 with PH3.

7

In this paper we report the results ofab initio molecularorbital studies of the reaction pathways of PH2

1 and PH31

with PH3. In particular, the relevant intermediates and tran-

sition states have been characterized. Product distributions,reaction mechanisms, and rate constants of ion/molecule re-actions have been determined by the mass spectrometricmethod. Finally, heats of formation of ions containing twophosphorus atoms have been computed theoretically.

II. EXPERIMENTAL PROCEDURES

Phosphine was commercially supplied by Union CarbideIndustrial Gases N.V.~Belgium! at electronic grade degreeof purity. Prior to use, it was introduced into a flask, contain-ing anhydrous sodium sulfate as drier agent, which was con-nected to the gas inlet system of the instrument. Helium wasobtained commercially in extra-high purity and was usedwithout further purification. The manifold and the lines werebaked out frequently in order to reduce the water backgroundin the trap.

A Finnigan ITMS ion trap mass spectrometer was usedfor all experiments, which were run at 333 K. The theory,instrumentation, and methodology of ion trap mass spec-trometry have been discussed elsewhere.3–6 The pressureswere read by a Bayard-Alpert ionization gauge and weretypically 2 – 531027 Torr for phosphine and about 531024 Torr for helium. The real pressure in the trap wascalculated considering the relative sensitivity of the iongauge with respect to different gases8 and a calibration factorfor the geometry of the instrument.5 The scan modes forion/molecule reaction experiments, in which reaction mecha-nisms and rate constants are determined, have been previ-a!Authors to whom correspondence should be addressed.

JOURNAL OF CHEMICAL PHYSICS VOLUME 112, NUMBER 4 22 JANUARY 2000

18140021-9606/2000/112(4)/1814/9/$17.00 © 2000 American Institute of Physics

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ously described in detail together with the calculationprocedures.3–6 In kinetic experiments, isolation of the pre-cursor ions was generally obtained by a superimposition ofradio frequency~rf! and direct current~dc! voltages. In somecases, experiments were also performed in which ions wereselectively stored by resonance ejection, without any dc volt-age which could add energy to the ions under examination.The similarity of the rate constants determined by these twoisolation methods indicates that collisional cooling is effec-tive in removing most of the internal energy, as is also evi-denced by the single exponential behavior observed in cal-culating the rate constants. In all the experiments, ionizationwas obtained with an electron beam at about 35 eV and forionization times in the range 1–10 ms. Afterwards, reactionstake place during a time suitable to maximize the abundancesof ions to be collected. Isolation of the selected ion species,their reactions with neutral molecules present in the trap forconvenient reaction times, and acquisition are the successivesteps.

III. THEORETICAL METHODS

The study of the H atom rearrangement and H2 loss pro-cesses in the H2P2H3

1 singlet species and of therearrangement/dissociation process in the doublet H3P2H3

1

species, was carried out by determining, on the relevant en-ergy hypersurfaces, the critical points corresponding tostable and transition structures. This was accomplishedthrough unconstrained gradient optimization9 of the geo-metrical parameters at the complete active space~CAS! mul-ticonfiguration self-consistent field~MCSCF!10 and UMP211a

~second order unrestricted Mo” ller–Plesset perturbationtheory! levels of theory~MP2 for short in the singlet case!.For the doublet hypersurface, UMP2 energies were refinedby spin projection by using the method of Chen and Schlegel~PUMP2 values!.11b The UMP2 geometries were character-ized as energy minima or first order saddle points~transitionstructures! by diagonalization of the analytically computedHessian~vibrational frequencies calculations!.12 In the fig-ures, the interatomic distances are reported in A˚ ngstroms andangles in degrees. Atoms are connected by single lines, in-tended to identify distances, and not to provide informationon the bond order. The intrinsic reaction coordinate~IRC!13

procedure was applied, at the MP2 level of theory, in orderto unambiguously connect the transition structures to the rel-evant reactants and products. The polarized split-valenceshell 6-31G(d)14 basis set was used throughout this phase.The UMP2/6-31G(d) geometries were then used to recom-pute the relative energies by quadratic configuration interac-tion calculations at the QCISD~T! level,15 in conjunctionwith the more extended basis set 6-311G(3d f ,2p).14 Thebasis set superposition error~BSSE!16 was estimated at bothUMP2/6-31G(d) and QCISD~T!/6-311G(3d f ,2p) levels, inrelation with the first step in each reaction, in which theH2P–PH3

1 adduct is formed from H2P1 and PH3 ~reaction a!,

or the H3P–PH31 adduct is formed from H3P

1 and PH3 ~re-action b!. Thermal energies12,16 were computed at theUMP2/6-31G(d) level. The complete basis set method ofPetersson17 ~at the CBS-Q level! and the G2 method of

Pople18 have been used to compute thermochemical data.The GAUSSIAN94 andGAUSSIAN98 suites of programs19 wereused throughout.

IV. RESULTS AND DISCUSSION

A. Mass spectrometric determinations

Scheme 1 shows the ion/molecule reactions in phosphine

starting from the PHn1 (n52,3) primary ions. The dashed

arrows indicate processes already reported in previouspapers.6,7,20 The scheme was built by selecting and storingthe primary ions for times up to 500 ms. The secondary ionswere in turn isolated and reacted for the same reaction times;among these ions, the PH4

1 species did not display any reac-tivity in the time range considered here.

The PH21 ion yields the P2Hn

1 (n51,3) species by lossof two and one hydrogen molecules, respectively. PH3

1 sim-ply protonates or transfers a hydrogen atom from phosphine~pathways PT or HT! to originate the phosphonium ion.

On the basis of experimental thermochemical data avail-able in the literature,21,22 formation of P2H

1 from PH21 and

PH3 was endothermic by 26.7 kcal mol21 and that of P2H31

exothermic by 28.3 kcal mol21. It is worth noting that P2H1

formation occurs through loss of two hydrogen molecules.An analogous process has already been observed7 for P2

1

formation starting from PH1, and this reaction was endot-hermic as well.

In Table I the rate constants of the reactions reported in

TABLE I. Rate constants for reactions of PH21, PH3

1, and their product ionsin self-condensation of PH3.

a

Reaction kexp Skexp kADOb Efficiencyc

PH211PH3→P2H

112H2 2.6PH2

11PH3→P2H311H2 7.6 10.2 11.37 0.90

PH311PH3→PH4

11PH2d 12.4 12.4 11.28 1.10

P2H11PH3→PH4

11P2d 7.9

P2H11PH3→P3H2

1H2d 0.5 8.4 9.90 0.85

P2H311PH3→PH4

11P2H2 5.4 5.4 9.85 0.55

aRate constants are expressed as 10210 cm3 molcule21 s21; experimentswere run at 333 K; uncertainty is within 20%.

bRate constants have been calculated according to the ADO theory.cEfficiency has been calculated as the ratiokexp/kADO .dRate constants already published in Ref. 5 and reported here for sake ofcompleteness.

1815J. Chem. Phys., Vol. 112, No. 4, 22 January 2000 Reactions of PH3

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Scheme 1 are shown. Together with the experimental values,collisional rate constants calculated according to the averagedipole orientation~ADO! theory and reaction efficiencies arelisted. Reaction pathways already reported in previouspapers6,7 are written in italic. It is noticeable that the reactionof PH2

1 yielding P2H31 is almost three times faster than the

reaction leading to P2H1, in which two H2 molecules are

lost. This indicates that formation of P2H31 from PH2

1 is notonly more energetically favored than P2H

1 formation, but italso has the activation barrier relative to the loss of the sec-ond H2 higher than the first one.

B. Theoretical study of the reactions

In theab initio theoretical calculations, the two reactionsof H2P

1 ~reaction a! and H3P1 ~reaction b! with PH3 were

investigated. Several chemical processes, which can in prin-ciple take place, were examined. The steps considered arenumbered in the following list. The ensuing subsections willalso follow this order.~a1! In reaction a, the first process is the formation, fromH2P

1 and PH3, of the singlet H2P–PH31 adduct.

~a2! Then the hydrogen molecule dissociation fromH2P–PH3

1 is considered, which produces either P–PH31 or

HP5PH21.

~a3! The final steps are the shift of one H atom and a hydro-gen molecule dissociation from HP5PH2

1, giving two iso-meric P–PH1 species.~b1! Reaction b begins with the formation of the initial dou-blet H3P–PH3

1 adduct from H3P1 ion with PH3 molecule.

~b2! Then, the inversion of three hydrogen atoms in the ini-tial adduct gives an isomeric form of H3P–PH3

1, which has

the character of an electrostatic complex.~b3! The ensuing P–P bond cleavage process produces theH4P

1 and PH2 species.The first part of the study consisted of determining the

critical point geometries for the H2P1 with PH3 reaction at

the CAS-MCSCF/6-31G(d) level of theory, using an activespace defined by ten electrons in ten orbitals for a total of19 404 configurations23 ~Scheme 2!. Total and relative ener-

gies for reaction a are reported in Table II.An active space of nine electrons in eight orbitals has

instead been used24 ~Scheme 3! for the H3P1 with PH3 reac-

tion for a total of 2352 configurations. Total and relative

TABLE II. Total and relative energies~hartree and kcal mol21! for the reaction PH211PH3.

CASSCFa DE UMP2a DE ZPEg QCISD~T!h DE

PH211PH3 2687.159 352 87.7 26.7 2684.370 382 86.0

~82.5d! ~84.2d!1a H2P2H3

1 2684.154 360 0.0 2684.299 139 0.0 30.0 2684.507 465 0.02a P2H3

1 2684.039 755 77.45b 2683.020 638 84.3e 18.0 2683.204 790 82.7i

TS1a-3a H2P2H~H2!1 ~H2 dissociation TS! 2682.884 603 71.9 2684.199 139 62.7 26.6 2684.420 980 54.3

3a HP2H21 2682.939 543 43.0b 2683.091 712 39.7e 17.4 2683.269 095 42.3i

TS3a-4a HP~H!PH1 ~H migration TS! 2682.843 654 103.1b 2682.996 949 99.2e 15.3 2683.186 040 94.5i

4a HPHPH1 2682.850 795 98.7b 2683.007 969 92.3e 15.5 2682.199 193 86.3i

TS4a-5a ~H2!P2H1 ~H2 dissociation TS! 2682.836 174 107.8b 2682.998 666 98.1e 13.9 2683.194 194 89.4i

5a P2H1 2681.746 255 72.4c 2681.895 156 72.6f 4.9 2682.032 244 83.8j

TS5a-6a P~H!P1 ~H migration TS! 2681.729 844 82.7c 2681.878 476 83.1f 4.4 2682.031 347 84.4j

6a PHP1 2681.737 853 77.7c 2681.899 601 69.8f 5.5 2682.048 114 73.9j

aCalculated using a basis set 6-31G(d).bE(H2)521.146 338 added in.cE(H2) added twice.dWith counterpoise correction of the basis set superposition error.eE(H2)521.144 141 added in.fE(H2) added twice.gZero-point energies~kcal mol21! at the MP2/6-31G(d) level of theory.hCalculated using a basis set 6-311G(3d f ,2p) and UMP2/6-31G(d) optimized geometries.iE(H2)521.170 809 added in.jE(H2) added in twice.

1816 J. Chem. Phys., Vol. 112, No. 4, 22 January 2000 Antoniotti et al.

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energies for reaction b are reported in Table III. This firstphase of the study had the purpose of ascertaining the natureof the wave function in the different processes, in order todecide if a single reference wave function provides a quali-tatively acceptable description of the potential energy hyper-surface.

For all critical points in both reactions, the CAS-MCSCFwave function is characterized by the dominance of one con-figuration, with coefficient 0.94–0.98 in most cases~only theHP~H!PH1 species presents a lower coefficient: 0.92!.

Thus, a single configuration seems to provide, for allstructures of interest but the last one,25 a rather adequatereference in perturbative calculations. In a second phase, thecritical point geometries were redetermined by perturbativeUMP2 optimizations, in conjunction with the same basis setsused in the previous calculations. Finally, the energetics wasbetter assessed by QCISD~T! calculations with a more ex-tended basis set~Tables II and III for reactions a and b,respectively!. The results of these three sets of calculationswill be presented in the following for each reaction pathwayof the two reactions.

1. (a1) Formation of singlet H2P–PH31

The initial step is the reaction of a singlet H2P1 ion with

phosphine, which brings about the formation of a singletH2P–PH3

1 adduct ofCS symmetry, whose structure,1a, isshown in Fig. 1.

The P–P bond length is close to that found for a singlePP bond.7 The CAS-MCSCF and MP2 optimizations pro-T

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1817J. Chem. Phys., Vol. 112, No. 4, 22 January 2000 Reactions of PH3

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duced similar geometries~bond lengths differ by 0.04 Å, andangles by 1.1° at most!.

It is important to consider the energy gain of the systemin proceeding from the two separate reactants to the adduct1a, because all the subsequent processes are feasible if therelevant energy barriers are lower than the quantity of kineticenergy acquired by the system in this first step. As regardsthe energy of this process, the MP2/6-31G(d) is estimated tobe 87.7 kcal mol21, while the QCISD~T!/6-311G(3d f ,2p)gives 86.0 kcal mol21 ~Table II!. These estimates can beaffected to some extent by a basis set superposition error. Anassessment of this error gives the values of 5.2 kcal mol21, atthe MP2 level, and 1.8 kcal mol21, at the QCISD~T! level.This estimate provides a limiting energy value of 82.5 kcalmol21 ~for the MP2 barriers!, or 84.2 kcal mol21 ~for theQCI estimate of the same barriers!, for ideal collisions tend-ing to zero kinetic energy.

2. (a2) H2 dissociation from H2P–PH31

The initial adduct can undergo a hydrogen molecule lossin two different ways. If, on one hand, H2 dissociates from

the P atom bearing two hydrogen atoms, then singlet P–PH31

is obtained, whoseC3v structure is shown in Fig. 1,2a. Thisdissociation requires overcoming a barrier of 84.3 kcalmol21 at the MP2 level of theory, or 82.7 kcal mol21, at theQCISD~T! level of theory ~Table II!. This process takesplace without formation of a transition structure~the reverseprocess has no barrier to overcome!. On the other hand, H2can be lost by the PH3 group. The relevant transition struc-ture is shown in Fig. 1 as structureTS1a-3a. Some of thegeometrical parameters calculated at the CAS-MCSCF level,in particular those relevant to the farthest H atom in thedetaching H2 moiety, depart significantly from those ob-tained at the MP2 level, even though one single configura-tion in the CAS-MCSCF wave function is dominant, its co-efficient being 0.964. This could be due to some looseness ofthis portion of the transition structure, related at both levelsto some flatness of the energy surface, in correspondence ofthe motion of that hydrogen. This dissociation requires over-coming a barrier of 62.7 kcal mol21, at the MP2 level, or54.3 kcal mol21, at the QCISD~T! level. At the CAS-MCSCF level the barrier results are 71.9 kcal mol21. Thedissociation product is the singlet ion HP5PH2

1. Its planarstructure,3a, was already discussed in the previous paper,7

and is not reported in Fig. 1.

3. (a3) H2 dissociations from HP5PH21 yielding HPP1

An isomer of the HP5PH21 ion, characterized by a pla-

nar geometry, with a H atom bridging the P–P bond, can beobtained through the H migration transition structureTS3a-4a, shown in Fig. 2. Its energy is 59.5 kcal mol21 above3a,at the MP2 level, or 52.2 kcal mol21, at the QCISD~T! level.The resulting isomer,4a ~Fig. 2!, is higher in energy than3aby 52.6 kcal mol21 at the MP2 level, or 44.0 kcal mol21 atthe QCISD~T! level.

H2 dissociation from this species leads to HPP1. Thisprocess requires 5.9 kcal mol21, at the MP2 level, and 3.1kcal mol21 at the QCISD~T! level, i.e., 3–10 kcal mol21

above the thresholds of the reagents H2P1 and PH3. In cor-

respondence of this barrier, the transition structureTS4a-5ais found ~Fig. 2!. An IRC calculation carried out on thistransition structure shows its connection with4a.

The HPP1 ion exists in two geometries,5a and 6a. Ofthe two isomeric ions, one is shown to be linear from theMP2 optimization, and is 2.8 kcal mol21 less stable than theother isomer~Table II!. The linear ion,5a, was already dis-cussed in the previous paper.7 At the CAS-MCSCF level,this linear structure results in a second order saddle point.The minimum is not linear and its geometry is shown in Fig.2, below the linear MP2 structure. Its energy is lower by 5.3kcal mol21, when compared with that of the other isomer~Table II!. The PP bond length, together with the orbitaloccupations, suggests that this ion, even if not linear, has atriple PP bond. The other isomer,6a ~Fig. 2!, has a geometri-cal structure with an H atom bridging the PP bond. Theenergy difference between the two isomers, 2.8 kcal mol21 atthe MP2 level, becomes 9.9 kcal mol21 at the QCISD~T!level,6a being the most stable isomer in both cases. The twoisomers are connected by the transition structureTS5a-6a,

FIG. 1. Intermediates and transition structures for the initial part of theH2P

11PH3 reaction~reaction a!. Bond distances are in Ångstro¨m, and bondangles in degrees. Dihedral angles~in parentheses! are defined as HPPH,where the referenceH lies on the sheet plane. CAS-MCSCF/6-31G(d)~bold! and MP2/6-31G(d) ~plain! values are shown.

1818 J. Chem. Phys., Vol. 112, No. 4, 22 January 2000 Antoniotti et al.

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also displayed in Fig. 2. This process is described as requir-ing 10.5 kcal mol21 at the MP2 level, but only 0.6 kcalmol21 at the QCISD~T! level.

4. (b1) Formation of doublet H3P–PH31

The initial step is the formation of a doublet H3PPH31

adduct,1b, of CS symmetry, from the reaction of doubletH3P

1 with phosphine. The geometrical parameters are shownin Fig. 3. The CAS-MCSCF wave function for this species

has one dominant configuration, corresponding to a singleoccupancy of the antibonding orbital pertinent to the P–Pbond. This is in agreement with the P–P bond length, sig-

FIG. 2. Intermediates and transition structures for the final part of theH2P

11PH3 reaction~reaction a!. Bond distances are in Ångstro¨m, and bondangles in degrees. CAS-MCSCF/6-31G(d) ~bold! and MP2/6-31G(d)~plain! values are shown.

FIG. 3. Intermediates and transition structures for the initial part of theH2P

11PH3 reaction~reaction a!. Bond distances are in Ångstro¨m, and bondangles in degrees. Dihedral angles~in parentheses! are defined as HPPH,making reference to the rightmostH lying on the sheet plane.CAS-MCSCF/6-31G(d) ~bold! and MP2/6-31G(d) ~plain! values areshown.

1819J. Chem. Phys., Vol. 112, No. 4, 22 January 2000 Reactions of PH3

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nificantly larger than in a typical single P–P bond.26 TheUMP2 calculation produced a similar geometry. This kind ofcomputation can be affected by a contamination of spin mul-tiplicities higher than the doublet. In this case the total spineigenvalue S2& appears to be rather close to 0.75~Table III!.Projected MP2 energy values are also reported inTable III.

The energy gain achieved in proceeding from the two

reactants to the adduct is228.2 kcal mol21 at the PUMP2level, and229.1 at the QCISD~T! level. It can be affected bya basis set superposition error. Its magnitude is estimated tobe 2.8 kcal mol21, at the UMP2 level, and 1.3 kcal mol21 atthe QCISD~T! level ~Table III!.

Any H2 loss process from this adduct would lead to spe-cies~HPPH3

1 or H2PPH21! whose structure, energy, and evo-

lution have been the subject of the preceding paper.7

FIG. 4. QCISD~T! energy profiles for reaction a~energy values are reported as integers; reference can be made to Table II!.

FIG. 5. QCISD~T! energy profiles for reaction b~energy values are reported as integers; reference can be made to Table VIII!.

1820 J. Chem. Phys., Vol. 112, No. 4, 22 January 2000 Antoniotti et al.

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5. (b2) Inversion of a H3P group in H3P–PH31

The initial adduct can also transform to an electrostaticcomplex, by umbrella inversion of the hydrogen atoms ofone PH3 group. The transition structure is shown in Fig. 3 asTS1b-2b. The already long P–P bond of1b is cleaved by theinversion process, as witnessed by the 3 Å P–P distance inthe transition structure. This process requires only 13.6 kcalmol21 at the PUMP2 level, or 14.4 kcal mol21 at theQCISD~T! level. The contamination of the total spin eigen-value is not very large~Table III!.

The electrostatic complex,2b ~Fig. 3!, has a P–P dis-tance significantly larger than that in1b. The two moietiesheld together are basically a PH3

1 and a phosphine. It is just11.7 kcal mol21 ~PUMP2!, or 11.1 kcal mol21 @QCISD~T!#above the adduct. Also for this minimum, the^S2& eigen-value is close to 0.75 and consequently contamination is notlarge.

6. (b3) Complete dissociation of PH3PH31

The decomposition of PH3PH31, yielding doublet PH2

and the PH41 ion, takes place by passing through a transition

structure, indicated asTS2b-3b in Fig. 3. The geometricalparameters calculated at the CAS-MCSCF level differ tosome extent from those calculated at the UMP2 level. Inparticular, the two P–H distances relevant to the hydrogenatom migrating from one PH3 to the other differ by;0.2 Å.The activation energy of this decomposition process is com-puted as 6.7 kcal mol21 at the CAS-MCSCF level and be-comes 5.0 kcal mol21 at the UMP2 level, or 4.9 kcal mol21

at the QCISD~T! level. As expected, the IRC pathway fromthe transition structure leads in one direction to the decom-position products PH2 and PH4

1, and, in the reverse direction,back to the electrostatic complex2b.

C. Thermochemistry

For all ions studied, the formation enthalpies (DH f0) at

298 K were calculated at the CBS-Q17 and G218 levels oftheory. The results are shown in Table IV, together withexperimental values reported in literature.22

The method used relies on tabulated experimental for-mation enthalpies21 of 3P(g) , 2P~g!

1 , and H(g) . These are com-bined, as exemplified in Scheme 4 for PPH1, with the theo-retically computed atomization enthalpy relevant to the ion

P2Hn1 , and provide an estimate of itsDH f

0 . The atomizationprocess is

P2Hn1→P1P11nH.

The enthalpies of formation of the P2Hn1 ions previously

obtained by experimental methods22 are also reported forcomparative purposes. In considering these data, it must beremembered that Fehlner and Callen determined theDH f

0

values from the appearance potentials of ions generated fromP2H4.

22 Therefore, heats of formation are typically overesti-mated, due to a significant kinetic shift.27

Of course, the computations have some limitations ontheir own, but the experimental values suffer from some un-certainty too: both estimates are contributions to a better as-sessment of theDH f

° values. Moreover, the overall consis-tency of the computed values must be noted, whichever themethod used.

V. CONCLUSIONS

Two different reactions have been investigated in thisstudy by experimental techniques and theoretical methods.They originate from collision of H2P

1 or H3P1 with phos-

phine ~reactions a and b, respectively!. The initial adductsH2PPH3

1 ~1a! and H3PPH31 ~1b! can evolve through different

reaction pathways. The different processes involved~hydro-gen molecule dissociations, H atom migrations, fragmenta-tion via P–P bond cleavage! have been studied by correlatedab initio methods.

Figures 4 and 5 provide an overall picture of the calcu-lated reaction energy profiles. The potential energy releasedin the adducts formation is estimated to be;86 kcal mol21

for reaction a and 29 kcal mol21 for reaction b. These valuesset a reference value for determining which rearrangementand cleavage products are attainable, in the limit of zerokinetic energy.

TABLE IV. Heats of formation at 298 K (DH f0) of the P2Hn

1 ions ~kcalmol21!.

Structure CBS-Q G2 Experimentala

1a H2P2H31 181 177

4a HPHPH1 261 257 2342a P2H3

1 259 257 2345a P2H

1 255 254 2896a PHP1 245 245 2891b H3P2H3

1 209 205

aFehlner and Callen, Ref. 22.

1821J. Chem. Phys., Vol. 112, No. 4, 22 January 2000 Reactions of PH3

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Two different H2 dissociations can take place in reactiona, yielding from H2PPH3

1 ~1a! the two isomers P–PH31 ~2a!

and HP5PH21 ~3a!. The former process presents a very high

barrier ~;83 kcal mol21!. The latter is easier, and3a canrearrange to give the significantly less stable H-bridged iso-mer HP~H!PH1 ~4a!. From this intermediate, a further H2

dissociation can take place, with a slightly endothermic bar-rier, to give the two isomeric PPH1 ions. The features of thereaction profiles displayed in Fig. 4 are in agreement with theexperimentally determined rate constants of the formationprocesses of the ions P2H

1 and P2H31, the latter being three

times the former.In reaction b, the initial umbrella inversion of one H3P

group in H3PPH31 ~1b! appears to be quite viable. The P–P

bond in the initial adduct is already longer than a single P–Pbond and is cleaved by this process. The two moieties arestill held together in an electrostatic complex~2b!. A follow-ing H migration leads to the formation of the two completelyseparated fragments H2P and PH4

1. The overall process ap-pears to be particularly viable, consistent with the experi-mental kinetic constant.

Finally, the enthalpies of formation of the P2Hn1 ions

have been calculated theoretically. The obtained estimatesare subject to known limitations. However, they can be con-sidered a useful contribution, because also the experimen-tally determined values present some uncertainties.

ACKNOWLEDGMENTS

The authors thank MURST and University of Torino forfinancial support.

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4P. Benzi, L. Operti, R. Rabezzana, M. Splendore, and P. Volpe, Int. J.Mass Spectrom. Ion Processes152, 61 ~1996!.

5P. Antoniotti, L. Operti, R. Rabezzana, G. A. Vaglio, P. Volpe, J. F. Gal,R. Grover, and P. C. Maria, J. Phys. Chem.100, 155 ~1996!.

6P. Antoniotti, L. Operti, R. Rabezzana, M. Splendore, G. Tonachini, andG. A. Vaglio, J. Chem. Phys.107, 1491~1997!.

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8M. Decouzon, J. F. Gal, P. C. Maria, and A. S. Tchinianga, personalcommunication.

9H. B. Schlegel, inComputational Theoretical Organic Chemistry, editedby I. G. Csizsmadia and R. Daudel~Reidel, Dordrecht, The Netherlands,

1981!, p. 129; J. Chem. Phys.77, 3676 ~1982!; H. B. Schlegel, J. S.Binkley, and J. A. Pople,ibid. 80, 1976~1984!; H. B. Schlegel, J. Comput.Chem.3, 214 ~1982!.

10M. A. Robb and R. H. A. Eade, NATO Adv. Studt Inst. Ser., Ser. C67, 21~1981!.

11 a!C. Mo” ller and M. S. Plesset, Phys. Rev.46, 618~1934!; J. S. Binkley andJ. A. Pople, Int. J. Quantum Chem.9, 229~1975!. The computations werecarried out without the ‘‘frozen core’’ approximation.b!W. Chen and H.B. Schlegel, J. Chem. Phys.101, 5957~1994!, and references therein.

12J. A. Pople, A. P. Scott, M. W. Wong, and L. Radom, Isr. J. Chem.33,345 ~1993!.

13C. Gonzalez and H. B. Schlegel, J. Chem. Phys.90, 2154~1989!; J. Phys.Chem.94, 5523~1990!.

14R. Ditchfield, W. J. Hehre, and J. A. Pople, J. Chem. Phys.56, 2252~1972!; P. C. Hariharan and J. A. Pople, Theor. Chim. Acta28, 213~1973!; M. M. Francl, W. J. Pietro, W. J. Here, J. S. Binkley, M. S.Gordon, D. J. Defrees, and J. A. Pople, J. Chem. Phys.77, 3654~1982!;K. Raghavachari, J. S. Binkley, R. Seeger, and J. A. Pople,ibid. 72, 650~1980!; A. D. Mc Lean and G. S. Chandler,ibid. 72, 5639~1980!.

15J. A. Pople, M. Head-Gordon, and K. Raghavachari, J. Chem. Phys.87,5968 ~1987!.

16See, for instance, W. J. Hehre, L. Radom, P. v. R. Schleyer, and J. A.Pople, inAb Initio Molecular Orbital Theory~Wiley, New York, 1985!; S.M. Bachrach and A. Streitwieser, Jr., J. Am. Chem. Soc.106, 2283~1984!; see also the discussion in, J. H. van Lenthe, C. C. M. vanDuijneveldt-van de Rijdt, and F. B. van Duijneveldt, inAb Initio Methodsin Quantum Chemistry II, edited by K. P. Lawley~Wiley, New York,1987!, p. 521, and references therein.

17G. A. Petersson, T. G. Tensfeldt, and J. A. Montgomery, Jr., J. Chem.Phys.94, 6091~1991!.

18L. A. Curtiss, K. Raghavachari, G. W. Trucks, and J. A. Pople, J. Chem.Phys.94, 7221~1991!.

19M. J. Frisch, G. W. Trucks, H. B. Schlegel, P. M. W. Gill, B. G. Johnson,M. A. Robb, J. R. Cheeseman, T. Keith, G. A. Petersson, J. A. Montgom-ery, K. Raghavachari, M. A. Al-Laham, V. G. Zakrzewski, J. V. Ortiz, J.B. Foresman, J. Cioslowski, B. B. Stefanov, A. Nanayakkara, M. Challa-combe, C. Y. Peng, P. Y. Ayala, W. Chen, M. W. Wong, J. L. Andres, E.S. Replogle, R. Gomperts, R. L. Martin, D. J. Fox, J. S. Binkley, D. J.Defrees, J. Baker, J. P. Stewart, M. Head-Gordon, C. Gonzalez, and J. A.Pople, Gaussian Inc., Pittsburgh, PA, 1995.

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21S. G. Lias, J. E. Bartmess, J. F. Liebman, J. L. Holmes, R. D. Levin, andW. G. Mallard, J. Phys. Chem. Ref. Data Suppl.17, 639 ~1988!; 17, 616~1988!.

22T. P. Fehlner and R. B. Callen, Adv. Chem. Ser.72, 181 ~1968!.23The ten active orbitals chosen are, in the H2P–PH3

1 adduct: thes, p, andp8 of the PH3 group, carrying six electrons in the aufbau configuration, aswell as their antibonding counterparts,s* , p* , andp8* ; thes andp of thePH2 group carrying four electrons, as well as their antibonding counter-parts, s* and p* . In this space a full configuration interaction~CI! isperformed and the molecular orbitals are allowed to relax. When somenuclear rearrangement occurs, these starting orbitals mix consistently toprovide other combinations. Compare, for instance, T. A. Albright, J. K.Burdett, and Myung-Hwan Whangbo, inOrbital Interactions in Chemistry~Wiley, New York, 1985!, pp. 55, 133–137, 171–179.

24The eight active orbitals chosen are, in the H3P–PH31 adduct: thes ands*

orbitals pertinent to the P–P bond; thes, p, and p8 of one of the PH3group, carrying six electrons in the aufbau configuration, as well as theirantibonding counterparts,s* , p* , andp8* . See Ref. 23, pp. 152–154.

25The one-electron density matrix diagonal elements which deviate moresignificantly from 2 and 0~values relevant to the configuration with CIcoefficient of 0.92! are of 1.83 and 0.17.

26H. B. Schlegel, J. Chem. Phys.84, 4530~1986!.27D. H. Williams, in Mass Spectrometry. A Specialist Periodical Report

~The Chemical Society, London, 1971!, Vol. 1.

1822 J. Chem. Phys., Vol. 112, No. 4, 22 January 2000 Antoniotti et al.

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