J. Phys. Chem. 1990, 94, 1807-1811
1807
An ab Initio Characterization of the Gaseous Diphosphorus Oxides P,O, ( x = 1-5) Lawrence L. Lohr, Jr. Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109 (Received: April 17, 1989; In Final Form: September 19, 1989)
The gaseous diphosphorus oxides P20, (x = 1-5) have been characterized by ab initio electronic structure calculations. A total of 20 stationary points have been located at the HF/3-21G* level, and 15 at the HF/6-31G* level, by using analytic gradients and the GAUSSIANE~ program. Vibrational frequencies were calculated from analytic second derivatives at these same levels for each stationary point. Ten of the points at each level were found to correspond to local minima. Also found is a transition state for the ring opening isomerization of cyclic P 2 0 (C,) to liner P20. The energetically preferred structures are the following: P20, linear (&), analogous to N20;P202,trans planar (C2*);P203,nonplanar oxo bridged (C2);P204, nonplanar oxo bridged (C, but nearly Cs);and P20,, nonplanar oxo bridged (C2). Isomerization energies were calculated at the MP2/6-3lG*//HF/6-3lC* and MP4SDTQ/6-31G*//HF/6-31G* levels; it is found that while correlation lowers the energies of P-P bonded isomers of P203and P204relative to the energies of their oxo-bridged isomers, the latter are nevertheless energetically preferred, by approximately 13 000 and 9500 cm-' for these two molecules, respectively. It is noted that the oxo-bridged structures of P203,P204,and P205closely resemble the local structures in the tetraphosphorus oxides P406and P4010,with the tetrahedral structures of P406and P40,0resolvable into a pair of C2-symmetry oxo-bridged P203 and P205 moieties, respectively.
Introduction The combustion of phosphorus and phosphorus-containing compounds is continuing to be an important area of research. Some recent developments include matrix isolation IR studies of the PH3-03 adduct,l of the products H3P0, H2POH, (HO),HPO, and HPO from the PH3 O3reaction,2 of the products P40, P20, , ~ of the products PO, PO, and PO2 from the P4 + 0 r e a ~ t i o nand HPO, PO2, PO3, HOPO, P205,H 2 P 0 , and HPOH from the PH3 0 r e a ~ t i o n . ~The related AsH3-03 adduct has been similarly c h a r a ~ t e r i z e d ,while ~ visible-UV absorption spectra have been obtained6 for matrix-isolated PO2 and PO3. The laser-induced fluorescence of gaseous PO2 has also been recently in~estigated.~ W e have presented8q9 two a b initio computational studies of phosphorus-oxygen systems, the first considering the species PO, PO-, HPO, PO2, and POT and the second considering HOPO, HPO,, H O P 0 2 , HOP, PO3, and PO3-. Key results included predictions of large electron affinities (EA'S) for PO2 and PO3, namely, 3.2 f 0.2 and 5.4 f 0.2 eV, respectively, and of strong acidity for HOP02, the results for the EA of PO3 and the acidity of H O P 0 2 being consistent with the observed gas-phase thermodynamic and kinetic properties of PO3-. A third studylo of ours has focused on the related NO3 molecule. Other recent computational studies of phosphorus compounds investigations of H3P0, of H2PXYH (X, Y = 0, s),and of HPPH and H2PP. Differences between phosphorus and nitrogen compounds abound, as strikingly shown in the bending potential energy curve we reportedI4 for HCP, with the isomer HPC, unlike HNC, corresponding to a local maximum instead of a minimum. In the present study we present a b initio results for the geometries, energies, vibrational frequencies, and vibrational intensities
+
+
Wlthnall, R.; Hawkins, M.; Andrews, L. J . Phys. Chem. 1986.90, 575. Withnall, R.; Andrews, L. J . Phys. Chem. 1987, 91, 784. Andrews, L.; Withnall, R. J . Am. Chem. SOC.1988, 110, 5605. Withnall, R.; Andrews, L. J . Phys. Chem. 1988, 92, 4610. ( 5 ) Andrews, L.; Withnall, R.; Mmres, B. W. J. Phys. Chem. 1989, 93, 1279. (6) Withnall, R.; McCluskey, M.; Andrews, L. J . Phys. Chem. 1989, 93, 126. (7) Hamilton, P. A. J . Chem. Phys. 1987, 86, 33. (8) Lohr, L. L. J . Phys. Chem. 1984,88, 5569. (9) Lohr, L. L.; Boehm, R. C. J . Phys. Chem. 1987, 91, 3203. (IO) Boehm, R. C.; Lohr, L. L. J . Phys. Chem. 1989, 93, 3430. ( 1 1 ) Boatz, J. A.; Schmidt, M. W.; Gordon, M. S. J . Phys. Chem. 1987, 91, 1743. (12) Boatz, J . A,; Gordon, M. S. J . Comput. Chem. 1986, 7 , 306. (13) Schmidt, M. W.; Gordon, M. S.Inorg. Chem. 1986, 25, 248. (14) Lehmann, K. K.; Ross, S. C.; Lohr, L. L. J . Chem. Phys. 1985,82, 4460. (I) (2) (3) (4)
0022-3654/90/2094- 1807$02.50/0
of the diphosphorus oxides P20, (x = 1-5). A total of 20 stationary points, including I O equilibrium structures, will be discussed from the standpoints of both structural chemistry and IR spectroscopy .
Computational Method Molecular geometries were initially optimized at the S C F (HF) level by using analytic gradients with the GAUSSIANB~programI5 and the split-valence basis set 3-21G*, which contains polarization functions (all six second-order Gaussians were employed) for the second-row atom (P) only. This computation level is designated as HF/3-21G*. Vibrational frequencies were calculated at all HF/3-2 1G* stationary points from analytic second derivatives. Geometries were reoptimized and frequencies calculated at the HF/6-31G* level (polarization functions for both 0 and P) for 15 structures, the most significant change16 being the reduction in P-0-P bond angles in going from the 3-21G* basis to the 6-3lG* basis for P203,P204,and P2O5. Correlation energies were calculated at many of the stationary points at the MP2 and MP4SDTQ levels with frozen K-shells for 0 atoms and frozen K- and L-shells for P atoms; these computational levels are designated as MP2/6-3lG*//HF/6-3lG* and MP4SDTQ/631G*//HF/6-31G*, respectively. The 3-21G* and 6-31G* basis sets were selected in part because of their d e ~ n o n s t r a t e d ~ l - ~ ~ . ' ~ adequacy in describing phosphorus compounds and in part because of the practicality in using them for the larger molecules in our study, namely, P204 and P205. Some measure of the reliability of these computational levels may be made by a comparison of calculated and observed7J8 structural and vibrational parameters for the radical PO2. The HF/3-21G* bond length and bond angle are 1.456 8, and 131.9', as compared to the observed values of 1.4665 f 0.0041 8, and 135.3 f 0.8", respectively, while the HF/6-31G* values are 1.446 8, and 134.4'. Optimization at the MP2/3-21G* level (no frozen cores) gives similar parameters of 1.499 8, and 134.3', with, as (15) Frisch, M. J.; Binkley, J. S.; Schlegel, H. B.; Raghavachari, K.; Melius, C. F.; Martin, R. L.; Stewart, J. J. P.; Bobrowitz, F. W.; Rohlfing, C. M.; Kahn, L. R.; DeFrees, D. J.; Seeger, R.; Whiteside, R. A,; Fox, D. J.; Fluder, E. M.; Pople, J. A. GAUSSIAN86; Carnegie-Mellon Quantum Chemistry Publishing Unit: Pittsburgh, PA, 1986. (16) For similar computational conclusions see: Ewig, C. S.; Van Wazer, J . R. J . Am. Chem. SOC.1985, 107, 1965; 1986, 108, 4354; 1988, 110, 79. (17) (a) Schmidt, M. W.; Yabushita, S.; Gordon, M. S.J . Phys. Chem. 1984, 88, 382. (b) Gordon, M. S.;Boatz, J. A,; Schmidt, M . S. J . Phys. Chem. 1984, 88, 2998. (18) Kawaguchi, K.; Saito, S.;Hirota, E.; Ohashi, N. J . Chem. Phys. 1985, 82, 4893.
0 1990 American Chemical Society
1808 The Journal of Physical Chemistry, Vol. 94, No. 5, 1990
TABLE I: Ab Initio Energies and Energy Differences for P20, (X
Lohr
m
a)
= 1-5)
imag molecule structure' P20 TS P2OZ
symmetry CS
I II 111
c2,
C,,
O-h
1V
C2'
v
c2c c2,
VI
2PO VI1
P20,
c 2h
PO + PO2
Vlll IX X XI XI1
P204
cs
c, c2 h
c2, c 2
XI11
PO + PO, 2P02
O2h
XIV
O2h
xv
O2d
c,
XVI XVll
P205
PO2+ PO, XVIll XIX
CS
O2h O2d
E"
-752.53210 -752.56542 -752.573 16 -826.88965 -826.91832 -826.96999 -827.02149 -827.023 82 -827.035 31 -90 1.48444 -901.52597 -901.52625 -901.62591 -901.62663 -901.628 59 -975.88087 -975.92091 -975.945 06 -976.00405 -976.00493 -976.09278 -976,095 59 -1050.381 53 -1050,54926 -1050.553 90
A E ~ fred
9012 1699 0
31 969 25676 14336 3033 2 522
1
0 0 2 0 0 1
0
0
3 I 640 22520 22462 585 426
1 0 1
0
0
47126 38338 33 038 20091 19897 617
5
0
m
1
1
0 1 0
37834 1020
2
0
0
e)
m
(2.304) 7 4 7 8 P- 2.282 p (1.4671 p 9(101.6)
"Energies in au at the HF/3-21G* level. bEnergy differences in cm". CStructure number from Figures 1-5. dNumber of imaginary
vibrational frequencies. 0) & $: (
Figure 2. As in Figure 1, but for P202.
P
1.483 (1.478) TS
(1,852) (1.446) Figure 1. Stationary-point geometries at the HF/3-21G* and (in parentheses) HF/6-31G* levels for PzO. Bond distances in angstroms and angles in degrees. The structures are in the order of decreasing energy
d
(increasing stability). expected, a bond length that is too long rather than too short. The HF/6-31G* vibrational frequencies (all in cm-I) of 1207 for u,(a,), 456 for v2(al),and 1452 for v3(b2) are characteristically higher than the experimental value^^,^* of 1090 (estimated from centrifugal distortions), 387 f 20, and 1319.1. Thus, these computational levels appear to be satisfactory for the exploration of molecular geometries and the approximation of vibrational frequencies for P-O systems. This level is, as indicated, augmented by correlation corrections for calculating isomerization and transition-state energies. Results and Discussion A. General. The results will be discussed in the order of increasing number of oxygen atoms. Table I contains the H F / 3-21G* energies for the 20 stationary point structures shown in Figures 1-5, together with the energies of fragments (combinations of PO, PO2, and PO3 as appropriate for comparison). Table I also gives the number of HF/3-21G* imaginary vibrational frequencies for each structure. Table I1 contains the HF/6-31G* and MPn/6-31G*//HF/6-31G* energies, as well as HF/6-31G* ZPE (zero-point energies), for reoptimized structures also shown
D.81 2 (713 ) Figure 3. As in Figure I , but for P,O,.
in Figures 1-5. Table 111 contains the HF/6-31G* frequencies together with IR and Raman intensities for each of the 10 HF/6-3 lG* equilibrium structures from Table 11. All structures numbered with Roman numerals (I-XX) are energy minima subject to the designated symmetry constraint, although many of these are unstable with respect to one or more symmetry breaking displacements. The P 2 0 structure labeled TS (transition state) is the only structure unstable with respect to a totally symmetric displacement. Figure 6 is a composite of IR intensities vs frequency (600-1800-cm-' range only) for a number of the equilibrium structures. B. P 2 0 . For P 2 0 we find (Tables I and 11; Figure 1) not surprisingly the favored structure (structure 11) to be collinear
An ab Initio Characterization of P20, (x = 1-5)
The Journal of Physical Chemistry, Vol. 94, No. 5, 1990 1809
TABLE 11: Ab Initio Isomerization Energies and Energy Differences for P20,(x = 1-5)
molecule P20 P202 P20, P2O4 P205
structureC
symmetry
TS I
c,
I1 IV V
C,"
VI1 IX Vlll XI1 XV XVIl XVlla XVlll XIX
c2 h
c2u
c2u c 2 u
xx
c,
CS
c2 D2d
cs Cl D2h D2d
C2
H Fa -756. I99 52 -756.223 28 -756.231 83 -830.96681 -831.02204 -831.10612 -906.002 71 -906.003 54 -906.074 90 -980.88581 -980.94503 -980.94508 -1055.79491 -1055.800 10 -1055.80631
~ ~ 2 -756.575 24 -756.62671 -756.64081 -831.55787 -831.60435 -831.67878 -906.766 28 -906.764 89 -906.827 00 -981.83408 -981.876 54 -981.87642 -1056.90345 -1056.90783 -1056.91781
MP4SDTQ' 9 -756.622 36 -756.665 49 -756.678 06 -831.60196 -831.653 14 -831.725 11 -906.81 2 70 -906.81 1 37 -906.873 42
ZPEd 0.004 I9 0.004 39 0.005 88 0.00894 0.01020 0.00850 0.013 76 0.01 3 74 0.013 07 0.01956 0.018 78 0.018 79 0.02386 0.02407 0.024 56
AHFb 7 091 1 876
AMP2b AMP4SDTQb AZPEb I4 391 12 225 -371 3 094 2 759 -327
0
0
0
0
30575 18453
26537 16335
27028 15796
97 373
0
0
0
0
15 844 15 662
13 326 13 632
13 326 13 618
151 147
0
0
0
13008
9319
0
I69 -2
imag freqC 1 0 0 0 0 0 1 0 0 0 1 0
11
0
0
2052 1363
26 3152 2 190
-1 54
-108
2 2
0
0
0
0
0
a Energies in au at designated level with 6-31G* basis and HF/6-31G* optimized geometries. bEnergy differences in cm-I. CStructurenumber from Table I and Figures 1-5. dZero-point energy at the HF/6-31G* level.
ai
n
L"'
d
b
U
b
C) (I 592) (1427)
E ( 1 3 63)\
(1316 ) 81120)
81429)
D=(4551 Figure 5. As in Figure I , but for P205. V
e)
f)
D(P,~-05-P2-06)= (12.6) Figure 4. As in Figure I , but for P204.
PPO analogous to NNO. What is somewhat surprising is the small excitation energy of only 1876 cm-l at the HF/6-31G* level (referred to below as simply HF) to the cyclic isomer (structure I ) . However, this difference increases somewhat (Table 11) to 2759 cm-' at the MP4SDTQ/6-3lG*//HF/6-31G* level (referred to below as simply MP4). In addition, we have located a transition state (structure TS) for the cyclic to collinear transformation. It is characterized (Fi ure 1) by a bond angle of 94.1' and a P-P bond longer (2.109 ) than that in either the cyclic (1.939 A) or the collinear (1.852 A) form. While its H F energy is 7091 cm-I above that of the collinear form, this increases (Table 11) to 12 225 cm-I at the MP4 level. The collinear structure thus has correlation stabilizations of approximately 900 and 5100 cm-' relative to the cyclic and TS structures, respectively. C. P,02. For P 2 0 2the preferred structure is the trans planar P-P bonded form (structure VII) with C2, symmetry (Tables I
w
and 11; Figure 2). The cis rotomer lies 3033 cm-' higher at the HF/3-21G* level. We located two other local minima, cyclic , symmetry, lying 30 575 and structures IV and V, each with C 18 453 cm-l higher, respectively, at the HF/6-31G* level (Table 11). These energies are somewhat affected by correlation, becoming (Table ll) 27 028 and 15 796 cm-', respectively, at the MP4 level. A collinear OPPO form (structure 111) is found to be unstable at the HF/3-21G* level with respect to bending. D . P2O3. Whereas for P 2 0 and P 2 0 2 there is no feasible oxo-bridged form, such a structure feature dominates for P 2 0 3 and the higher diphosphorus oxides. Perhaps our most interesting structural result is the preferred nonplanr oxo-bridged P2O3 structure XI1 (Tables 1 and 11; Figure 3), with C2symmetry and a dihedral angle of 71.3". The trans and cis planar rotomers (X and XI) are both unstable at the HF/3-21G1 level with respect to internal rotation, reminiscent of H 2 0 2 ,although the energy differences are only of the order of 500 cm-'. The P-P bonded forms, both nonplanar (VIII) and planar (IX), lie significantly higher in energy than the oxo-bridged forms, the stable planar form (IX) lying higher than the C2 structure (XII) by 15844 and 13 326 cm-l (Table 11) at the H F and MP4 levels, respectively. Although the planar form (IX) is unstable with respect to a twisting deformation at the HF/6-31G* level, it is stable at the HF/3-21G* and MP4/6-3lC*//HF/6-3lC* levels with respect to the nonplanar form (VIII). Thus, despite correlation effects, the oxo-bridged form is significantly favored over the P-P bonded form. We note that the well-known tetrahedral structure of P,O,, with all oxygens bridging, is resolvable (Figure 7a) into a pair of C2symmetry P2O3 moieties, although the observed19 P-0-P bridging angle in P4OlOof 1 2 6 O is somewhat smaller than our computed angle of 138.8' for P203. (19) Beagley, B.;Cruickshank, D.W. J.; Hewitt, T.G.;Jost, K.H.Trans. Faraday SOC.1969, 65, 1219.
1810 The Journal of Physical Chemistry, Vol. 94, No. 5 , 1990
TABLE 111: Vibrational Frequencies for P20,(x = 1-5) molecule structureb symmetry mode Y" IRc I
c2u
b, al al
11
C ,,
?r
u+ u+
IV
C,"
b, b2
a, b, a,
V
c2r:
a, b, b2
a,
VI1
C2h
b2 al al a, b, a8
ag VI11
XI1
xv
cs
c2
D2d
b, ag a" a" a' a' a' a' a' a' a" a b a b a a b b a bl e
a,
e b2
a,
XVIla
CI
b, a, e a a a a
a a
a a a a a
P205
xx
a
c2
b a
a a b a b b
a a b b a b a
270 55.3 734 29.1 924 41.0 201 18.4 749 0.2 1429 274.4 148 2.7 244 3.3 608 33.9 792 4.1 899 36.0 1242 228.9 374 0 533 1.2 5.1 694 834 56.3 876 100.0 10.0 1166 39 24.0 163 28.6 293 0 542 0 1334 272.5 1359 0 33 8.4 146 3.6 199 28.8 323 88.3 455 114.0 604 12.6 1284 138.3 1396 109.7 1593 264.6 84 1.7 95 10.2 109 4.2 435 87.8 556 17.7 639 13.0 933 1172.3 1433 92.2 1452 164.3 45 0 170 38.5 311 0 420 100.0 300.1 498 671 0 1273 202.8 1322 0 1642 462.0 7 0.4 90 0.7 128 7.7 411 25.6 442 174.8 491 52.8 577 25.4 716 76.0 1009 775.4 1302 202.6 1455 125.4 1617 273.1 54 3.8 68 0.6 110 2.1 352 10.5 391 23.4 450 32.1 499 239.2 514 136.0 574 6.1 776 78.0 1104 553.8 1287 389.9 1322 32.6 1636 241.4 1644 281.4
Lohr 1
8.6 129.5 24.6 20.8 57.0 3.2 15.6 14.8 35.3 5.0 30.8 5.3 1.4 9.3 71.0 0.0 20.4 7.4 0 0 28.7 75.8 0 53.7
i
1
i
6 -
Ramand
;P-o-P:
;p-o-p:
1
I1
0
11
0" 1
1
Frequency (cm-') Figure 6. Infrared intensities in km mol-' calculated at the HF/6-31G* level vs frequency in cm-' (Table 11) for equilibrium geometries of P20x
Frequencies below 600 cm-' are not shown. The frequencies here and in Table I 1 should be multipled by a scale factor of approximately 0.9 to approximate better the observed frequencies.
(x = 1-5).
1.1
3.9 3.5 14.0 4.9 18.3 15.1 23.9 7.8 0.9 0.4 0.7 1.8 1.2 14.1 0.1 11.7 18.6 2.0 3.0 10.2 0.2 0.7 9.0 9.3 28.5 13.5 0.9 0.6 0.8 0.7 4.3 1.0 1.2 7.7 5.9 13.1 15.4 3.2 0.5 1.3
0.4 4.0 0.8 0.3 2.1 0.8 1.8 9.7 0.8 5.5 28.7 2.5 3.7
"Frequencies in cm'l at the HF/6-31G* level. *Structure number from Table I and Figures 1-5.
