A theoretical study on reactivity of singlet phosphinidene by itsreacting with polar water molecule

Ping Yin *, Zhi-Lin Wang, Zhi-Ping Bai, Chong-De Li, Xin-Quan Xin

State Key Laboratory of Coordination Chemistry, Department of Chemistry, Nanjing University, Nanjing 210093,

People's Republic of China

Received 14 September 2000

Abstract

The reaction mechanism of singlet phosphinidene with polar water molecule has been studied by ab initio molecular

orbital theory at the HF/6-31G(d), MP2(full)/6-31G(d) and G2 levels to better understand the reactivity of the singlet

phosphinidene. The results show that there are two parallel reaction channels: channel A is an addition reaction which

forms the three-membered ring transition state (TS) and obtains the product H2POH; channel B is a dehydrogenation

reaction taking place along a TS described by a four-membered ring and yielding (POH�H2). The general statistical

thermodynamics and Eyring TS theory with Wigner correction are also used to examine the thermodynamic and kinetic

properties of these two reaction channels during the range of 100±1100 K. It is concluded that channel A has ther-

modynamic advantage while channel B has dynamic advantage, especially at low temperatures, while at 1100 K channel

A is dominant for it has much larger equilibrium constant and the rate coe�cients of both reactions are almost

equal. Ó 2001 Elsevier Science B.V. All rights reserved.

Keywords: Singlet phosphinidene; Polar water molecule; Addition reaction; Dehydrogenation reaction; Thermodynamic and kinetic

properties

1. Introduction

Reaction characters of monovalent hydridesHX (X � C, Si, B) with some small molecules at-tracts much attention because they play an im-portant role in the chemical reactions involved inatmospheric chemistry, chemical catalysis, com-bustion and quantum chemistry [1±8]. Recently, asone of the key intermediates in the hydrogenationof phosphorus to PH3, the PH radical is being of

interest both experimentally and theoretically in®eld of interstellar chemistry, elemental chemistryand organic metal chemistry. For example, Pieriniand Duca [9] reported the proton a�nities ofphosphinidene by the AM1 and PM3 methods.The molecular properties and the valence stateenergies of PH were calculated by Park and Sun[10] using ab initio e�ective valence shell Hamil-tonian method. And Goto and Saito [11] observedthe lowest rational spectral lines of the PH radicalin its ground vibronic state by submillimeter-wavespectra. Gonbeau et al. have studied the reactionmechanism of alkene addition of complex (R±P±W(CO)5, R � H, ph, OCH3, NEt2) [12±15] and

Chemical Physics 264 (2001) 1±8

www.elsevier.nl/locate/chemphys

* Corresponding author. Fax: +86-25-3317761.

E-mail address: yinping426@263.net (P. Yin).

0301-0104/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved.

PII: S03 0 1-0 1 04 (0 0 )0 03 4 9- 9

have found their electrophilic carbene-like nature.So it is natural that people would like to knowwhether the uncomplexed parent phosphinidenealso could display carbene-like characters.

In view of electron con®guration, the singlet PHhas two r-electron pairs and one empty p-orbit inthe valence shell. Thus, 1PH is nucleophilic due tothe r-electrons and electrophilic due to the vacantp-orbit, and may yield r-complexes and p-com-plexes, respectively. The double properties lead toreactive complexity of 1PH while it reacts withionic compounds and polar covalence compounds,so we have selected polar water molecule to reactwith singlet phosphinidene in the present study.Until now, little is known about the reactionmechanism of monovalent phosphorus with smallmolecules such as H2O to our knowledge ex-cept that Sudhakar and Lammertsma [16] exam-ined theoretically the insertion reaction of singletphosphinidene in water at MP4(fc)/6-311g** andMP2(full)/6-31g* levels. Therefore a complemen-tary study with the aim to elucidate the reactionmechanism of singlet phosphinidene with watermolecule is of importance in order to have a pre-cise idea of the reactivity of 1PH.

In the present paper, considerable interest isgiven to the investigation of the reaction channelsof 1PH�H2O at the HF/6-31G(d), MP2(full)/6-31G(d) and G2 levels. Moreover, it is unsuitable tojudge the reactivity only by the total electronicenergy and the barrier calculated by a quantumchemistry method [17]. So further calculations ofthermodynamic and kinetic properties have beenintroduced in this work during the range of 100±1100 K to obtain better understanding of thereaction mechanism of 1PH with polar watermolecule.

2. Computational methods

Ab initio molecular orbital calculations havebeen performed with the GAUSSIAN 94GAUSSIAN 94 [18] pro-gram. The optimized geometries and Millikenpopulation of all species were obtained at the HF/6-31G(d) and MP2(full)/6-31G(d) levels, and thefrequencies for all required structures were evalu-ated at HF/6-31G(d) level to ascertain the nature

of stationary points. Moreover, the intrinsic reac-tion coordinate (IRC) method [19] at the HF/6-31G(d) level was also used to further analyze thecharacters of the channels. On the other hand, byusing general statistical thermodynamics and Ey-ring transition state (TS) theory with Wigner cor-rection, we examined the in¯uence of temperatureon the two reaction paths during the range of 100±1100 K, in steps of 200 K. All computations ofthe thermodynamic and kinetic parameters wereachieved by use of a locally developed program[20], the required geometrical parameters and fre-quencies were obtained at the MP2(full)/6-31G(d)and HF/6-31G(d) level, respectively. And the (G2-ZPE) energies were used as the electronic energycontribution, in which ZPE was obtained at HF/6-31G(d) level and scaled by 0.8929.

3. Results and discussion

Milliken electronic population diagrams of allspecies are displayed in Fig. 1. The 6-31G(d)structures for the stable molecules and TSs areshown in Table 1. The calculated HF/6-31G(d)harmonic vibrational frequencies of the optimizedstructures are displayed in Table 2. TS1 and TS2each has only one imaginary frequency 2154.2i and2007.4i, respectively, which con®rms the saddlepoint characters and corresponds to their localmaximum stationary structures, i.e. TS. The othersare of real frequencies which correspond to theirlocal minimum stationary structures.

We have only obtained one initial complexHPOH2, which has Cs symmetry and is a charge-accepting complex. In HPOH2, the 0.157 e (at theHF/6-31G(d) level) goes to the diatomic PH fromthe H2O, and its bond angle Ha±O±Hb (108.7°) isslightly larger than the angle of H±O±H (105.5°) inan H2O molecule at the HF/6-31G(d) level. Thetotal energies for all species and their relativeenergies are shown in Table 3. The complex-ation energy of HPOH2 is 63.3 kJ molÿ1 at theG2 (0 K) level. These results suggest that HPOH2

is formed by insertion of the O atom of H2Ointo the P empty p-orbital and 1PH displays verystrong eletrophilic behavior in its interaction with

2 P. Yin et al. / Chemical Physics 264 (2001) 1±8

strongly polar water molecule, so the complexHPOH2 could be called p-complex.

Two transition states (TS1 and TS2) for(PH�H2O) system have been found. The fact thatthe Hb±P distance and its bond order of TS1 are1.5706 and 0.254 �A (at the HF/6-31G(d) level)leads to the conclusion that TS1 is a three-mem-bered ring structure and is formed by insertion ofthe O atom of H2O into the P atom empty p-orbitand attack of the H atom of H2O to the P lone pair.Similarly, at the HF/6-31G(d) level the Hc±Hb

distance is 0.9485 �A and its bond order is 0.222 forTS2, which suggests that TS2 is a four-memberedring structure which is formed by insertion of theO atom of H2O into the P atom empty p-orbitaland the simultaneous coulombic attraction of twoH atoms. In order to con®rm the reactants and theproducts connecting the obtained TSs, the IRCcalculations have been carried out at the HF/6-31G(d) level. The total energies and bond dis-tances along the reaction paths (reactions A andreaction B) of the (PH�H2O) system are shown inFigs. 2±5, respectively.

It is very obvious that the position of TS1 onthe reaction path is near the product region andthat of TS2 is near the reactant region in Figs. 2and 3, so the former is a early barrier and the latteris a later barrier. The total energy of reactionA decreases sharply after the TS1, while that ofreaction B decreases relatively slowly, which cor-responds to what is predicted by imaginary fre-quencies of transition states (TS1: 2154.2i cmÿ1,TS2: 2007.4i cmÿ1). Furthermore, the total ener-gies of the reactants and the products corre-sponding to TS1 are ÿ417.23 and ÿ417.31 a.u.Similarly, those corresponding to TS2 are ÿ417.23and ÿ417.21 a.u. From Table 3, we could ®nd thatthey are equal to the total energies of HPOH2,H2POH, HPOH2 and (POH�H2), respectively.From Fig. 4, it is very clear that the P±Hc andO±Ha distances are almost constant along thereaction path, whereas the P±O bond distancedecreases monotonically until it reaches 1.6 �Awhich is just equal to the bond distance of P±Oin H2POH, and P±Hb bond distance decreasessharply in the reactant region, however it decreases

-0.113(-0.131)

H P(0.248)0.247

-0.038 0.038(-0.039) (0.039)

O

H H

(-0.864)-0.869

0.434(0.432)

0.268(0.263)

1 2 3

P

H

HbHc

O(0.211)0.2160.481

(0.488)

0.314(0.315)-0.056

(-0.054)

-0.836(-0.842)

0.268(0.262)

0.467(0.463)

4 5 6

P O

Hb

HcHa

TS1

0.254(0.176)

0.261(0.253)

-0.055(-0.058)

-0.108(-0.094)

0.475(0.480)

0.244(0.243)

-0.865(-0.856)

0.003(0.078)

(0.430)0.382

0.062(0.004)

0.046(-0.090)

0.147(-0.043)

0.069(0.271)

-0.106(-0.017)

0.222(-0.009)

0.360(0.433)

0.051(0.084)

-0.884(-0.854)

0.254(0.244)

0.482(0.481)

Hc

P O

H

Hba

(-0.012)-0.008 0.266

(0.260)

0.500(0.506)

-0.844(-0.837)

0.258(0.262)

-0.044(-0.045)

O

PH

(-0.765)-0.750

0.171(0.169)

0.259(0.254)

0.266(0.283)

0.485(0.482)

H H(0.405)0.406

P O

Hc Hb

Ha

TS2

Fig. 1. Milliken electronic population diagrams of the reactants, initial complex, TSs and products for 1HP�H2O at the HF/6-31G(d)

and MP2(full)/6-31G(d) (in parentheses) levels.

P. Yin et al. / Chemical Physics 264 (2001) 1±8 3

Table 2

Harmonic vibrational frequencies for all required stable species and transition states at the HF/6-31G(d) level

Molecules Frequencies (cmÿ1)

HPOH2 268.8 340.4 577.7 707.6 857.6 1799.4 2571.0 4044.6 4156.9

H2POH 296.1 878.3 1003.1 1006.4 1251.4 1280.0 2598.1 2609.6 4128.6

H2O 1826.5 4070.7 4189.0

POH 966.8 1201.1 4059.8

H2 4644.1

PH 2566.8

TS1 2154.2i 517.3 591.3 866.2 1056.3 1333.0 2103.2 2561.5 4070.6

TS2 2007.4i 665.2 694.4 1034.0 1101.0 1237.2 2013.7 2077.0 4084.3

Table 3

Total energies E and relative energies Erel for required speciesa

Structure HF/6-31G(d) MP2(full)/6-31G(d) G2 (0 K) ZPE(HF/6-31G(d))b Erelc

PH�H2O ÿ417.200486 ÿ417.479744 ÿ417.721575 0.025739 0.0

HPOH2 ÿ417.231605 ÿ417.524953 ÿ417.745721 0.031172 ÿ63.3

H2POH ÿ417.314237 ÿ417.610722 ÿ417.833345 0.030618 ÿ293.2

POH�H2 ÿ417.210399 ÿ417.513349 ÿ417.739325 0.022117 ÿ46.6

TS1 ÿ417.180024 ÿ417.500033 ÿ417.728882 0.026647 ÿ19.2

TS2 ÿ417.140575 ÿ417.502518 ÿ417.730517 0.026255 ÿ23.5

a Total energies and ZPE in hartree (Eh), reactive energies in kJ molÿ1.b Scaled by 0.8929.c Erel is calculated by G2 (0 K) energies.

Table 1

Structure parameters of all stable species and TSs were optimized by HF/6-31G(d) and MP2 (full)/6-31G(d)a

Structure Bond HF/6-31G(d)

(�A)

MP2(full)/6-

31G(d) (�A)

Angle HF/6-31G(d)

(deg)

MP2(full)/6-

31G(d) (deg)

HPOH2 O±Ha(Hb) 0.9506 0.9747 HaOHb 108.7 107.4

P±O 2.0545 2.0130 POHa(Hb) 111.3 107.6

P±Hc 1.4067 1.4186 HcPO 87.7 87.9

HcPOHa ÿ119.2 ÿ122.3

H2POH P±Hb(Hc) 1.4014 1.4160 HbPHc 94.3 93.4

P±O 1.6504 1.6808 OPHb(Hc) 99.4 99.1

O±Ha 0.9468 0.9703 HaOP 110.9 108.0

HaOPHb ÿ132.0 ÿ132.5

POH O±H 0.9505 0.9776 POH 113.3 110.8

P±O 1.6120 1.6423

H2 H±H 0.7301 0.7375

PH P±H 1.4109 1.4243

H2O O±H 0.9473 0.9686 HOH 105.5 104.0

TS1 P±O 1.9192 1.9914 HbPO 39.7 36.1

Hb±P 1.5706 1.6535 HcPO 92.7 91.7

Hc±P 1.4075 1.4227 HaOP 111.7 107.0

Ha±O 0.9522 0.9800 HcPOHb 91.6 91.5

Hb±O 1.2296 1.1755 HaOPHb ÿ101.3 ÿ98.6

TS2 P±O 1.8286 1.9890 HcPO 78.9 88.9

Hc±P 1.5851 1.4146 HbOP 61.3 56.2

Hb±O 1.3518 1.1734 HaOHb 109.5 105.3

Ha±O 0.9504 0.9809 HbOPHc ÿ0.4 ÿ96.7

Hc±Hb 0.9485 2.2341 HaOHbP 102.8 97.1

a The subscript of H atoms is consistent with that in Fig. 1.

4 P. Yin et al. / Chemical Physics 264 (2001) 1±8

slowly to 1.4 �A through the TS to the productregion. So in the reactant region, the changes ofbond distances show that the Hb atom attracted bythe r-electron pair of P atom in HPOH2 shift fromthe O atom to the P atom which is the process toform three-membered ring. And in the productregion, the changes of the bond distances corre-spond to the process opening the three-memberedring to produce H2POH. These facts all clearlyshow that the reactant corresponding to TS1 isHPOH2 and the product is H2POH. From Fig. 5 itcan be seen that the O±Hb and P±Hc bond dis-tances are almost constant before the TS and in-crease monotonically after the TS. And the P±Obond distance rises gently before the point ±1.5,then decreases slowly to the point 1.5 and becomesa constant (1.6 �A) which is equal to the P±O bonddistance of POH. The Hb±Hc bond distance de-creases sharply in the reactant region, while it al-

most keep constant and to be 0.7 �A (which is equalto H±H bond distance in H2) in the product re-gion. These results indicate that the reactant cor-responding to TS2 is HPOH2 and the products arePOH�H2. So reaction B is a dehydrogenationreaction which can be considered as a hydrogenatom rotating around the P±O axis before the TS.The reaction region between points 0.0 and 0.5 onthe IRC path is a region of H2 formation, and theregion after point 0.5 is the H2-o� region. There-fore TS1 can be considered to be related to theproduct (H2POH) and TS2 is related to products(POH�H2).

Fig. 2. Total energy along the reaction path of HPOH2 !TS1 ! H2POH (reaction A). R, TS and P stand for reactant

region, TS and product region, respectively, which are same

with that in Figs. 3±5.

Fig. 3. Total energy along the reaction path of HPOH2 !TS2 ! POH�H2 (reaction B).

Fig. 4. Bond distances along the reaction path of reaction A,

the subscript of H atoms is consistent with that in TS1 (Fig. 1).

Fig. 5. Bond distances along the reaction path of reaction B,

the subscript of H atoms is consistent with that in TS2 (Fig. 1).

P. Yin et al. / Chemical Physics 264 (2001) 1±8 5

We sum up the analysis of IRC starting fromthe initial complex (HPOH2), there are two par-allel reaction channels in the system of PH�H2O:

HPOH2 ! TS1! H2POH �reaction A�

HPOH2 ! TS2! POH�H2 �reaction B�The four-membered ring structure of TS and thereaction channel B were not found in the studiesby Sudhakar and Lammertsma [16].

It is well known that the change of electronicdistribution has good correlation with barrierheight of TS. We got the results at the HF/6-31G(d) level that the charges of P atom increase0.175 and 0.260 e from the initial complex HPOH2

to TS1 and TS2, respectively (see Fig. 1). On theother hand, the negative charges of O atom in-crease 0.021 and 0.040 e during the same process.Then the result that the change of electronic dis-tribution in forming TS2 is larger than that of TS1suggests that reaction B is more di�cult to go on.

The above-mentioned analysis of ab initio cal-culations provided the conclusion that in the re-action of 1PH with polar water molecule, there aremainly two parallel reaction channels. The G2(0K) energies described in Table 3 display that theexoenergic energy DE of channel A is 246.6kJ molÿ1 larger than that of channel B, showingthat channel A is thermodynamically favored overchannel B. Contradictorily, the barrier of chan-nel A is 4.3 kJ molÿ1 higher than that of chan-

nel B, indicating that channel B is kineticallyfavored over channel A. So it is di�cult to predictwhich channel will be virtually dominant only byab initio calculations even at 0 K. For this reason,a further examination of the thermodynamic andkinetic properties have been made by using ahome-made program [20] based on the generalstatistical thermodynamics and Eyring TS theorywith Wigner correction.

The variation of the thermodynamic and kineticparameters with temperature is given in Table 4.For channel A, the enthalpy changes DH0, theGibbs free energy changes DG0 and the en-tropy changes DS0 are all negative in the rangeof 100±1100 K. So channel A is an exothermicand spontaneous process in which its entropy in-creases. While both the enthalpy changes DH0 andthe entropy changes DS0 of channel B are positiveand its Gibbs free energy changes DG0 is negativeabove 300 K, which means that it is endothermaland spontaneous and its entropy decreases. Theequilibrium constants (K(T )) are very large in thetemperature range 100±1100 K and fall quicklywith the ascend of the temperature for the channelA. However, K(T )s of channel B have smallervalues and gradually rise with the temperature.Then the thermodynamic parameters give therelative thermodynamic probability for variouschannels at various temperatures in the system of(1PH�H2O). As can be seen from Table 4, betweenthe parallel channels A and B, channel A is ther-

Table 4

The thermodynamic and kinetic data for reactions during the range of 100±1100 K

Reaction type T (K) DH0

(kJ molÿ1)

DG0

(kJ molÿ1)

DS0

(J Kÿ1 molÿ1)

K(T ) k (sÿ1) A (sÿ1)

A HPOH2 !H2 POH

100 ÿ230.3 ÿ230.0 ÿ3.7 0:12� 10121 0:29� 10ÿ8 0:39� 1013

300 ÿ231.8 ÿ228.5 ÿ11.2 0:60� 1040 0:59� 106 0:39� 1013

500 ÿ233.6 ÿ225.7 ÿ15.8 0:38� 1024 0:29� 109 0:36� 1013

700 ÿ234.6 ÿ222.3 ÿ17.5 0:39� 1017 0:39� 1010 0:37� 1013

900 ÿ234.9 ÿ218.8 ÿ17.9 0:50� 1013 0:17� 1011 0:40� 1013

1100 ÿ234.9 ÿ215.2 ÿ17.9 0:17� 1011 0:45� 1011 0:44� 1013

B HPOH2 !POH�H2

100 16.7 8.3 84.5 0:57� 10ÿ5 0:52� 10ÿ6 0:38� 1013

300 19.7 ÿ11.1 102.5 3.4 0:28� 107 0:30� 1013

500 20.5 ÿ31.8 104.8 51.7 0:64� 109 0:24� 1013

700 20.6 ÿ52.8 105.0 152.4 0:61� 1010 0:24� 1013

900 20.2 ÿ73.8 104.4 259.2 0:22� 1011 0:27� 1013

1100 19.3 ÿ94.6 103.5 343.2 0:51� 1011 0:30� 1013

6 P. Yin et al. / Chemical Physics 264 (2001) 1±8

modynamically favored over B especially at lowtemperature. In addition, we computated kineticparameters which can be calculated by Eyring TStheory with Wigner correction to reveal the prob-abilities of the parallel channels to occur. Bothreactions present that all their logA values arenearly equal to 12, which indicates that they bothbelong to the Arrhenius-typed reactions. In thesystem of (1PH�H2O), the barrier height associ-ating with channel B (via TS2) presents lowervalue than that of channel A. These reactions keepkB > kA in the whole temperature range, So reac-tion B is kinetically favored over reaction A es-pecially at low temperature (with rate coe�cientsof 0:52� 10ÿ6 sÿ1 for reaction B vs. 0:29� 10ÿ8 sÿ1

for reaction A at 100 K), but at 1100 K the kvalues of both channels are almost equal (with ratecoe�cients of 0:51� 1011 sÿ1 for reaction B vs.0:45� 1011 sÿ1 for reaction A). So at high tem-perature, channel A is dominant for K(T ) ofchannel A is much larger than that of channel Band their k values are almost equal.

4. Conclusions

From the detailed theoretical studies reportedin this paper, the following conclusions can bedrawn:

(1) The initial association between 1PH andH2O can give a stable intermediate. Starting fromthe initial complexes HPOH2, there are two par-allel reaction channels: one is an addition reactionvia the three-membered ring TS1 to give H2POHand the other is a dehydrogenation reaction via thefour-membered ring TS2 to give (POH�H2).

(2) The thermodynamic and kinetic calculationsshow that: at low temperature, channel A hasthermodynamic advantage while channel B hasdynamic advantage; at high temperature, channelA is dominant for K(T) of channel A is muchlarger than that of channel B and their k values arealmost equal.

At present the direct experimental measure-ments of thermodynamic and kinetic properties for

reaction of 1PH and H2O are insu�cient, so wethink that the results based on quantum chemistry,the general statistical thermodynamics and EyringTS theory with Wigner correction in this work willprovide some useful predictions for experimentalresearch.

Acknowledgements

This work was supported by the National Sci-ence Foundation of China and the DoctoralFoundation of State Education Commission ofChina, and it also bene®tted from valuable com-ments of Professor Guan-Zhi Ju.

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