J. Phys. Chem. 1993,97, 4078-4079
4078
Ab Initio Characterization of Gaseous PzOz Xabier Lopez,? Cecilia Sarasola,t B. Lecea,+Antonio Largo,'9$ Carmen Barrientoqi: and Jesus M. Uga1de.J Kimika Fakultatea, Euskal Herriko Unibertsitatea, P. K. 1072, 20080 Donostia, Euskadi, Spain, and Departmento de Quimica Fisica y Analitica, Universidad de Ouiedo, 33006 Ouiedo, Spain Received: November 17, 1992 Ab initio electronic structure calculations demonstrate that a singlet planar cyclic isomer of P202 with D2h symmetry is more stable than all the previously characterized P202 isomers. A proper description of the electronic structure wavefunction is found to be essential to predict correctly the multiplicity of the ground state. This singlet D2h symmetry isomer is found to have no central P-P bond and a large biradical character.
In a recent paper, Lohrl revised some of his previous work on the characterization of gaseous diphosphorus oxides P20, ( x = 1, 5), by ab initio electronic structure calculations, to include a nonplanar bicyclic isomer of PZOZand trigonal-bipyramidal isomers of P203, P2O4, and PzO5. It is remarkable that the bicyclic ("butterfly") isomer of C2" symmetry was found to be 10.39 kcal/ mol lower in energy at the MP4SDTQ/6-3lG*//HF/6-3lG* level of theory with HF/6-31G* ZPVE corrections, than the previously reported lowest energy structure, namely, the planar C2h isomer having a P-P bond and two terminal oxygem2 In this report we describe a new isomer of P202 having a planar cyclic structure with D2h symmetry, which is calculated to be more stable than all previously characterized P202 isomers.'12 Throughout this paper the 6-31G* basis set3 has been used. Geometry optimizations and subsequent frequency analysis were carried out with the H F and the multiconfigurational SCF (CASSCF) approximations. We found it important to use at least a minimal active space including two electrons and two orbitals. This level of theory is customarily denoted as two configuration SCF (TCSCF).4 Indeed, TCSCF is the minimal treatment needed for a proper description of singlet biradicaloids. Also it was long ago recognized5 that TCSCF is the simplest wavefunction permitting a qualitative comparison of singlet and triplet energy levels. The importance of the antibonding orbitals will be assessed by means of the natural orbital occupation numbers. For the triplet state both orbitals are singly occupied but for the TCSCF singlet the occupation numbers N ( 4 ) and N(4*),which sum to exactly 2, are in general different and provide a direct quantitative measure of how close the wavefunction is to complete biradical character, Le., N ( 4 ) = N(4*) = 1. All calculations were performed with use of the electronic structure code GAUSSIAN 90.6 A planar P202 isomer of D2h symmetry has been found to be a stationary structure at 5.17 kcal/mol lower in energy than the previously lowest energy' CZuisomer at the HF/6-31G* level of theory, as shown in Table I. Although this DZh symmetry isomer is a real minimum on the potential energy surface, it has a mode with a small vibrational frequency of 39 cm-I (see Table 11).This might be an indication that this structure is not described correctly by a singledeterminant wavef~nction.~ This is further confirmed by a TCSCF/6-31G* calculation on the HF/6-31G* geometry which shows already a large biradical character. At thisgeometry, the electron occupation numbers of the orbitals are N ( 4 ) = 1.64 and N(4*) = 0.36 and thecorresponding hessian matrix is positive definite. The TCSCF/6-31G* energy at this H F structure is 27.6 kcal/mol lower than the H F energy. Full geometry optimizationwith TCSCF wavefunction leads to a further energy +
t
Euskal Herriko Unibertsitatea. Universidad de Oviedo.
0022-3654/93/2097-4078%04.00/0
0
.P Figure 1. Optimizedgeometriesat theHF/6-31G*andTCSCF/6-31G8, in parentheses, levels of theory for P202. Distances are in angstroms and angles in degrees.
lowering of 0.7 kcal/mol and consideration of zero point vibrational energies fixes the energy difference at 27.3 kcal/mol. The optimum TCSCF structure, which is shown in Figure 1, has electron occupation numbers of N ( 4 ) = 1.63 and N(4*) = 0.37. We have also characterized a triplet PZOZ D z symmetry ~ species (see Figure 1) which is 22.0 kcal/mol lower in energy than the
0 1993 American Chemical Society
Gaseous P202
The Journal of Physical Chemistry, Vol. 97, No. 16, 1993 4079
TABLE I: Ab Initio Energies, in hartrees, for P202
HF TCSCF ZPVE a
p202 (C2J
singlet
triplet
-831.11622"
-83 1.12446 -83 1.16956 0.01 025
-83 1.15969
0.00890
0.009 16
From ref 1.
TABLE Ik Vibrational Frequencies, in cm-I, for P202
a
P
0
now two molecules can combine breaking the PO ?r bond P
0
n
n
0
P
singlet
p202 (C20 H Fa
HF
TCSCF
triplet HF
432 43 3 575 73 1 880 982
39 499 638 807 850 1022
422 663 738 833 874 965
122 602 65 1 826 897 920
From ref 1.
singlet HF structure but lies 5.5 kcal/mol higher in energy than thesinglet TCSCF, at the UHFlevel with ZPVE effects included. Thereforeit is seen that use of the appropriate level of electronic structure theory to describe these compounds is very important. Notice that a single determinant approximation to the wavefunction dues not correctly predict the multiplicity of the ground state. All structures mentioned in the research are depicted in Figure 1, whose inspection reveals that the TCSCF optimum geometry of singlet D2h symmetry is very similar to that obtained at the HF level of theory (see Figure 1B). Also it is worth mentioning that the P-0-P angle is wider for both the singlet and triplet D2h symmetry isomers relative to the C b symmetry isomer. This allows for a large P-P distance, i.e. 1.99 A at the HF/6-31G* in the CZ,form and 2.46 A in the singlet D2h and 2.47 A in the triplet D2h forms, respectively. A detailed inspection of the Mulliken population analysis shows a negligible P-P overlap population in both D2h symmetry singlet and triplet species, as expected. A qualitative description of these results may be given reasoning on the following schematicrepresentationof the 2II ground state of PO:
which localizes an electron on each of the phosphorus atom. Whether these electrons have their spins paired or unpaired leads to the above discussed triplet or singlet states, respectively. In summary we have found that the minimum energy structure of the Pz02species is the singlet D2h symmetry isomer shown in Figure 1B. A proper description of its electronic wavefunction reveals that this species has a large biradical character. Thus its experimental isolation seems unlikely.
Acknowledgment. Support by the Basque Country University (Euskal HerrikoUnibertsitatea),GrantNo. UPV/203.215-E171/ 9 1, and the Provincial Government of Gipuzkoa (Gipuzkoako Foru Aldundia) is gratefully acknowledged. References and Notes (1) Lohr, L. L. J. Phys. Chem. 1992, 96,
119. (2) Lohr, L. L. J. Phys. Chem. 1990, 94, 1807. (3) Hehre, W.J.; Ditchfield, R.; Pople, J. A. J. Chem. Phys. 1972, 56, 2257. (4) For complete description of the basis sets and the methods used see:
Hehre, W.J.; Radom, L.;Scheleyer, P. v. R.; Pople, J. A. Ab initio Molecular Orbital Theory; Wiley: New York, 1986. (5) Bender, C. F.; Scheafer, H. F., 111; Franceschetti, D. R.; Allen, L. C . J. Am. Chem. Soc. 1972, 94,6888. (6) Frisch, M. J.; Head-Gordon, M.;Trucks, G. W.;Foresman, J. B.; Schlegel, H. B.; Raghavachari, K.; Robb, M.; Binkley, J. S.; Gonzalez, C.; Defrees, D. J.; Fox, D. J.; Whiteside, R. A.; Seeger, R.; Melius, C.F.; Baker, J.; Martin, R. L.; Kahn, L. R.; Stewart, J. J. P.; Topiol, S.; Pople, J. A. Gaussian 90, Revision J; Gaussian, Inc.: Pittsburgh, PA, 1990. (7) Schmidt, M. W.;Nguyen, K. A.; Gordon, M. S.;Montgomery, J. A. J. Am. Chem. Soc. 1991, 113, 5998.
