**6. Theoretical Vibrational Study of Pl _{3}, Pl_{2}H and PlH_{2}**

**Ben Said Ridha ,**

**Boughdiri Salima and**

**Tangour Bahoueddine**

Theoretical Chemistry Laboratory,

Science Faculty of Monastir.

Route de Kairaouane.

9000. Monastir.

Tunisia

Email: baha.tangour@fsm.rnu.tn

**Abstract
**

Ab-initio theoretical studies of the vibrational properties of Iodophosphines PI_{3}, PI_{2}H and PIH_{2} were performed at the SCF level. We obtained values which favorably compare with available experimental data.

**Keywords**

Iodophosphines / PI_{3} / PI_{2}H / PIH_{2} /ab-initio calculations

Introduction

The study of the halophosphines PX_{3}, PX_{2}H and PXH_{2} (X=F, Cl, Br, I) is topical because of their involvement in chemistry and in biochemistry [1]. Although some of them have been known for more than a century, in particular the trihalophosphines PX_{3}, the majority still resist synthesis or identification e.g. PFH_{2} [2] and PF_{2}H [3] were only formally identified after they had been trapped in a argon matrix at low temperature. At ambient temperatures, halophosphine compounds have a high tendency to polymerise.

Iodine presents more difficulties than do the other halogens. While information about the PI_{3} molecule is available for the gas state, the PIH_{2} and PI_{2}H molecules have only been detected in mixtures with PI_{3}, PH_{3}, I_{2} and P_{2}I_{4} in CS_{2}by Schmidt and coworkers [4]. Their presence was confirmed by the analysis of the NMR ^{31}P and H^{1} spectra. In particular, the NMR ^{31}P chemical shift and ^{1}JPH coupling constant of PIH_{2} and PI_{2}H are (-156, 168Hz) and (-9,145Hz) respectively. The PIH_{2} molecule was also detected by Beckers and coworkers[5] in a mixture of P_{2}H_{4} and HI. Experimental vibrational frequencies values are also available although they do not concern the isolated or synthesized molecule and were determined in situ.

*[Editor’s Note: those not familiar with ab initio calculations of molecular vibrational frequencies may find the article by W.O. George in the last edition of IJVS useful as an introduction – *www.irdg.org/ijvs*]*

This paper is aimed at a better understanding and description of the iodophosphines from physico-chemical vibrational properties.

**Computational details
**

Ab-intio calculations were supported by the PSHONDO algorithm[6], a modified version of the HONDO program [7], including the pseudo-potential suggested by Durand and Barthelat. Effective core potentials were used for each atom other than Hydrogen leaving five or seven electrons in the atomic valence space of the Phosphorus and Iodine atoms respectively. The valence electrons were described through a basic set of quadruple gaussian functions for both Phosphorus and Hydrogen and quintuple gaussian functions for Iodine. These functions were optimized in the ground state of each atom. We contracted the denoted DZ gaussian functions of double zeta by means of a 3+1 process for both Hydrogen and Phosphorus, and a 4+1 process for Iodine. The triples zeta denoted TZ, contraction was executed by means of a 2+1+1 process for the Hydrogen and Phosphorus, and a 3+1+1 process for the Iodine. We added to these basic sets, successively, the polarisation function 2p, 3d and 5d on Hydrogen, Phosphorus and Iodine atoms respectively. The exponents for these polarisation functions were optimized for each molecule. These basic sets will be described as DZP or TZP. We have shown in Table 1 the optimized values of the polarisation functions used.

Geometry optimization was performed using PSG[8] or MONSTERGAUSS[9] programs with a self-consistent-field (SCF) gradient technique. The convergence threshold on the gradient components was fixed at 10-4. The vibrational frequencies and corresponding normal modes of each state were determined under the same conditions.

**Results and Discussion
**

**Geometry Optimization **

We have optimized, at the SCF level, the geometries of the molecules studied vis. PIH_{2}, PI_{2}H and PI_{3} by using PSGRAD or MONSTERGAUSS programs. Bond length and bond angle values are shown in Tables 1a, 1b, 1c. The experimental and other theoretical calculations found in the literature are also included in this table. We have used several basic sets in order to study the influence of the basic set extension and the introduction of the polarisation function on our calculation accuracy.

In spite of the use of relatively large dimension basis sets and of polarisation function optimization, we obtain for the molecule PI_{3} 2.489 Å for the P-I bond length which is larger by 2.4% than the experimental value of 2.43Å. This could have as its origin the influence of relativistic effects which are completely ignored in the pseudopotentials determinations.

We note a substantial decrease of the bond lengths when the basic set dimension increases. The P-I bond length decreases, when we pass from the DZ basis sets to the TZP by 5.9%, 4.8% and 4.3%, for PIH_{2}, PI_{2}H and PI_{3} respectively. The P-H bond length decreases only in this series by 1.3% and 1.5% for PIH_{2} and PI_{2}H respectively.

We also note that the introduction of the polarisation function has a more important effect than the basis set relaxation on the decrease of the bond length. For example, for the PIH_{2} molecule, the former effect decreases the P-I bond length by 5.9% and the latter only by 1.3%.

As usually observed, the basis set dimension is less significant on changes in the bond angles than it is on the bond lengths. So the HPH angle increases only by 1.1% in passing from the TZP basis set to the DZ. Similar results are observed on HPI and IPI bond angles.

**Vibrational Frequencies And Normal Modes**

We have calculated vibrational frequencies and normal modes for the molecules PIH_{2}, PI_{2}H and PI_{3} using different basis sets. Experimental results are also available (Tables 2a,2b and 2c). The molecules PI_{2}H and PIH_{2 }as we have noted have not been effectively synthesized. They have rather been detected and characterized in mixtures. Schmidt and coworkers have chosen experimental values among the frequencies of a mixture of PI_{3}, PH_{3}, I_{2} and P_{2}I_{4} in CS_{2}. Those suggested by Beckers and coworkers concern only the molecule PIH_{2}detected in a mixture of P_{2}H_{4} and HI. Despite the fact that the experimental available values do not concern the isolated or synthesized molecule, they appear reliable. PI_{3}, whose symmetry group is C_{3v}, has 6 vibrational normal modes.

The experimental values (Table 2c) are 325cm^{-1}, 303cm^{-1}, 111cm^{-1} and 79cm^{-1}attributed to the modes ν _{3}(e), ν _{1}(a1), ν _{2}(a1) and ν _{4}(e).

We begin by noting that our calculated values are basis set independent and they are in excellent agreement with the experimental values in spite of the fact that the basic sets used do not contain polarisation functions. The largest error of 14% is for the modes

ν _{3} the assymetric PI stretch.

For PHI_{2}, whose symmetry classification is Cs , Schmidt and coworkers [4] suggest the following values: 2260-2270 cm^{-1} for ν (PH), 781-782 cm^{-1} for δ(PHI),

327-329 cm^{-1} for the ν _{as}(PI_{2}) mode and for ν _{s}(PI_{2}) 320-322 cm^{-1}. They indicate that ν _{as}(PI_{2}) might also have a value of 336 cm^{-1}.

For PIH_{2} molecule, whose point group is Cs, Schmidt et al suggest the following values: 2360 cm^{-1} for ν (PH),750 cm^{-1} for δ (PH_{2}). The valence stretching n (PI) mode was not assigned with precision. The authors indicate simply that it is in the domain 337 – 320 cm^{-1} “common to all PI vibrations”.

However, Beckers and coworkers suggest for this molecule P the following values: 2306 cm^{-1} for ν (PH), 1030 cm^{-1}, one band of C type, for δ (PH_{2}), 752 cm^{-1}, one band with the A type*, for δ (PHI) and 338 cm^{-1}, one band of the A type, for ν (PI).

For the PI_{2}H molecule, we think that the assignment by Schmidt and coworkers of the two valence modes ν _{as}(PI) and ν _{s}(PI) as two very close frequencies is hazardous considering the large number of compounds in the mixture#. The value of 337 cm^{-1}, in spite of the fact that it also exists in PI_{3}, is more probable.

**Conclusion
**

In this work, we have obtained results in good agreement with the available experimental data. We have proposed theoretical values for the several vibrational modes of PI_{3}, PI_{2}H and PIH_{2} molecules.

We hope that our investigations give chemists useful information leading to a better characterisation and identification for the as yet unsynthetised molecules PI_{2}H and PIH_{2}.

*[Editor’s Notes:* * *Vapour phase band contours in infrared absorptioon. The subject will be covered in future editions.*

# *But this is normal in a molecule Ab _{n} where the mass of B>A. An example is the sulphur and selenium molecule X_{2}Y_{2}. Where X = and Y = the sym and assym XY stretching…………by only cm^{-1}].*

BASEP I H |
r_{(P-I)}(Å) |
r_{(P-H)}(Å) |
∠HPH(degree) |
∠HPI(degree) |

DZ/DZ/DZ |
2.629 | 1.439 | 95.4 | 93.7 |

TZ/DZ/DZ |
2.634 | 1.420 | 95.8 | 93.2 |

TZ/TZ/DZ |
2.595 | 1.419 | 95.8 | 96.3 |

TZ/DZ/TZ |
2.633 | 1.418 | 95.6 | 93.0 |

DZ/TZ/TZ |
2.579 | 1.435 | 95.2 | 96.6 |

TZ/TZ/TZ |
2.594 | 1.417 | 95.6 | 96.1 |

TZ/TZ/TZP |
2.589 | 1.410 | 93.8 | 94.8 |

TZ/TZP/TZ |
2.529 | 1.420 | 96.0 | 96.6 |

TZP/TZ/TZ |
2.490 | 1.415 | 95.6 | 93.9 |

TZP/TZP/TZP |
2.482 | 1.417 | 94.3 | 96.0 |

Théor.[33] |
2.466 | 1.401 | 94.6 | 96.6 |

**Table 1a**. PIH_{2} geometry parameters in the different basis sets.

BASEP I H |
r_{(P-I)}(Å) |
r_{(P-H)}(Å) |
∠HPI(degree) |
∠IPI(degree) |

DZ/DZ/DZ |
2.600 | 1.442 | 93.0 | 102.8 |

DZ/DZ/TZ |
2.600 | 1.440 | 93.0 | 102.8 |

DZ/TZ/DZ |
2.575 | 1.440 | 95.7 | 104.8 |

TZ/TZ/DZ |
2.585 | 1.418 | 95.4 | 104.4 |

DZ/TZ/TZ |
2.575 | 1.437 | 95.5 | 104.8 |

TZ/TZ/TZ |
2.585 | 1.416 | 95.4 | 104.4 |

TZ/TZ/TZP |
2.581 | 1.409 | 94.2 | 104.3 |

TZP/TZ/TZ |
2.485 | 1.420 | 95.04 | 103.9 |

TZ/TZP/TZ |
2.528 | 1.418 | 96.1 | 103.9 |

TZP/TZP/TZP |
2.481 | 1.420 | 95.2 | 104.0 |

**Table 1b**. PI_{2}H geometry parameters in the different basis sets.

BASEP I H |
r_{(P-I)}(Å) |
∠IPI(degree) |

DZ/DZ |
2.597 | 101.5 |

TZ/DZ |
2.600 | 101.4 |

TZ/TZ |
2.584 | 102.7 |

TZ/TZP |
2.531 | 103.1 |

TZP/TZ |
2.492 | 102.7 |

TZP/TZP |
2.489 | 102.7 |

Exp. |
2.43± 0.04 | 102± 2 |

Théor. [11] |
2.597 | 104.4 |

**Table 1c**. PI_{3} geometry parameters in the different basis sets

ModeSym. P / I / H |
ν(PI)a’ |
_{δas}(HPI)a’’ |
_{δs}(HPI)a’ |
_{δs} (HPH)a’ |
_{νs} (HPH)a’ |
_{νas}(HPH)a’’ |

DZ / DZ / DZ |
323.36 | 765.54 | 803.44 | 1208.5 | 2428.2 | 2455.4 |

TZ / DZ / DZ |
337.76 | 794.6 | 830.3 | 1243.4 | 2432.5 | 2446.8 |

DZ / TZ / TZ |
321.6 | 778.11 | 817.1 | 1215.1 | 2426.5 | 2454.0 |

TZ / TZ / DZ |
318.0 | 781.2 | 827.9 | 1232.8 | 2465.4 | 2474.5 |

TZ / TZ / TZ |
318.3 | 784.5 | 829.5 | 1244.9 | 2478.5 | 2487.7 |

TZ / TZ / TZP |
323.1 | 789.7 | 831.7 | 1273.0 | 2593.2 | 2605.3 |

TZ / TZP / TZ |
333.2 | 801.2 | 849.4 | 1238.7 | 2462.6 | 2465.0 |

TZP / TZ / TZ |
345.7 | 845.6 | 879.8 | 1224.0 | 2561.5 | 2568.8 |

TZP / TZP / TZP |
344.8 | 829.4 | 872.9 | 1214.1 | 2558.2 | 2662.2 |

Exp. [5] |
338 | 752 | 1030 | 2306 | ||

[4] |
750 | 2360 | ||||

Théor.[5] |
314 | 737 | 761 | 1100 | 2339 | 2345 |

% errors |
2.0 | 10.310.6 | 17.9 | 8.410.9 |

**Table 2a**. Normal modes PIH2 vibrationnal frequencies , expressed in cm^{-1}.

ModeSym P / I / H |
_{δs}(PI)a’ |
_{νs}(PI)a’’ |
_{νas}(PI)a’ |
_{δs} (HPI)a’’ |
_{δas}(HPI)a’ |
ν(PH)a’ |

DZ / DZ / DZ |
82.29 | 315.03 | 368.51 | 784.81 | 868.05 | 2428.8 |

DZ/DZ/TZ |
82.67 | 311.21 | 362.98 | 755.66 | 840.40 | 2428.3 |

DZ/TZ/DZ |
87.39 | 304.29 | 343.60 | 748.46 | 862.78 | 2445.4 |

DZ/TZ/TZ |
87.56 | 304.46 | 343.60 | 751.24 | 866.40 | 2446.00 |

TZ/TZ/DZ |
86.84 | 303.37 | 341.30 | 763.30 | 868.4 | 2476.5 |

TZ/TZ/TZ |
88.88 | 349.97 | 405.10 | 856.38 | 966.00 | 2422.90 |

Exp.[4] |
320-322 | 327-329or 337 | 781 | 782 | 2260-2270 | |

% errors |
8.7 / 9.4 | 23.9 / 23.1 /20.2 | 9.6 | 23.5 | 7.2 / 6.7 |

**Table 2b**. Normal modes PI2H vibrationnal frequencies, expressed in cm^{-1}.

ModeSym. P / I |
_{δas}(P-I)e |
_{δs}(P-I) |
_{νas}(P-I) |
_{νas} (PI)e |
||

a_{1} |
||||||

DZ/DZ |
76.30 | 77.96 | 116.38 | 296.09 | 355.67 | 358.59 |

TZ/DZ |
70.03 | 75.49 | 107.51 | 300.67 | 350.88 | 352.82 |

DZ/TZ |
80.90 | 82.58 | 118.22 | 289.82 | 339.44 | 343.69 |

TZ/TZ |
82.11 | 83.60 | 119.40 | 290.43 | 340.83 | 344.44 |

Exp. [20] |
85.00 | 113.00 | ||||

79.00 | 110.00 | 303 | 25 | |||

-1.7 | 5.7 | |||||

% errors |
5.8 | 8.5 | -4.2 | 4.9 |

**Table 2c**. Normal modes PI3 vibrationnal frequencies in cm^{-1}.

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**

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*Received in original format 27th May 1999, accepted 7th June 1999*