J . Phys. Chem. 1985,89, 2304-2309
2304
scope for further development. Our study represents a first step in this direction. In view of the experimental simplicity of collecting far-IR metal cluster vibrational data, its application to a multitude of longstanding and new problem involving supported metal clusters is likely to grow rapidly in the near future.
Acknowledgment. The financial assistance of the Natural
Sciences and Engineering Research Council of Canada's Strategic Grants Programme and the Connaught Foundation of the University of Toronto is gratefully appreciated. We are also indebted to Drs. Edith Flanigen (Union Carbide) and Paul Kasai (IBM) for supplying various ultrahigh-purity zeolites. Registry No. Ag, 7440-22-4.
Ab Initio Molecular Orbital Calculations on Phosphates: Comparison with Silicates M. O'Keeffe,* B. DomengL, Department of Chemistry, Arizona State University, Tempe, Arizona 85287
and G. V. Gibbs Department of Geological Sciences, Virginia Polytechnic Institute, Blacksburg, Virginia 24061 (Received: October 26, 1984)
The results of molecular orbital calculations using several different basis sets are reported for a number of phosphate and silicate molecules. In order to reproduce equilibrium P-O bond lengths correctly, d orbitals are necessary on P. d orbitals are necessary on 0 also to reproduce observed T-0-T bond angles (T = P or Si) at atoms bridging two tetrahedra. Energies are derived for hydrolysis of T-0-T linkages (-23 kJ mol-' for T = P and -20 kJ mol-' for T = Si), for hydrolysis of the monomeric metaphosphate ion (-150 kJ mol-') and a number of other hydrolysis reactions, for the difference in energy between a P=O double bond and two P-O single bonds (-238 kJ mol-'), and for deprotonation of phosphoric and silicic acids. Bond length-bond angle relationships are derived that closely mimic behavior observed in crystalline silicates and phosphates.
Introduction Molecular orbital calculations on suitably chosen molecules have provided valuable insights into the factors determining local geometries in crystals; a prime example is provided by recent studies of silicates and related materials.' In this paper we are concerned mainly with phosphates, although we will be particularly interested in comparing and contrasting their behavior with that of silicates. As for silicates, a striking feature of phosphates containing P207 groups (and more-condensed groups) is the large and characteristic angle at the bridging 0 atom which results in an almost constant d(P-P) in the same configurations.* Phosphates differ from silicates in one important way however, in that they exhibit a wider range of bond orders (and hence a wider range of bond lengths3) than the analogous silicates. This results in PO4and PzO, groups in crystals being more adaptive to the bonding requirements of other groups in ternary, etc. crystals than are the analogous silicates. A striking example, which interests us, is the large number and variety of tungsten phosphates4 in contrast to the apparent nonexistence of tungsten silicates. Calculations have been made with the GAUSSIAN-80 computer program5 using the STO-3G minimal basis set and the 6-31G split-valence basis sets6 It was found necessary to use polarization functions (ad = 0.55) on phosphorus to reproduce known geometries accurately. We identify basis sets employing such functions by adding a suffix of one of two asterisks according to whether there are polarization functions on phosphorus only or on phosphorus and the other atoms (excluding hydrogen). Unless otherwise stated, the basis set used for a particular calculation was 6-31G*. Care was taken to optimize the geometry of the mole(1) G. V. Gibbs, Amer. Mineral., 67,421 (1982), and references therein. (2) M. O'Keeffe and B. G. Hyde, Trans. Am. Crystallogr. Assoc., 15, 65 (1979).
(3) G. A. Lager and G. V. Gibbs, Amer. Mineral., 58, 756 (1973). (4) B. Domengts, Thtse, Universite de Caen, 1983. (5) J. S . Binkley, R. A. Whiteside, R. Krishnan, H. B. Schlegel, R. Seeger, D.J. DeFrees, and J. A. Pople, Quantum Chemistry Program Exchange, Indiana University, Bloomington, IN. (6) W. J. Pietro, W. H. Hehre, J. S. Binkley, M. S. Gordon, D.J. DeFrees, and J. A. Pople, J . Chem. Phys., 77, 3654 (1982), and references therein.
0022-3654/85/2089-2304$01.50/0
TABLE I: P-0 Bond Lengths (A) and Stretching Force Constants (N m-') and SCF Energies (in hartrees) at the Optimized Geometries for PO4* as a Function of Basis Set basis set bond length force constant SCF energy STO-3G STO-3G* 6-31G 6-31G* 6-3 1G**
1.713 1.547 1.653 1.574 1.572
372 1055 670 821 840
-630.835 28 -631.30637 -639.479 98 -639.649 38 -639.681 47
cules, a procedure that is efficiently implemented in GAUSSIAN-80' (although it might be mentioned that large stretch-bend force constants (in the phosphates particularly) make these molecules unusually difficult to optimize). Structures thus found often differ significantly from those assumed in some earlier studies. In what follows we first present the results of the calculations for each molecule individually; we then assess the significance of these data collectively. Some of the species have been studied before; however, we report our results even when the previous work has employed larger basis sets as it is useful to have a set of data (particularly total energies) all calculated at the same level of approximation. Where possible, we compare local geometries calculated for molecules with those observed in crystals, as we are concerned to establish the extent to which molecular calculations can be used to predict conformations to be expected in the solid state. The work here complements to some extent recent ab initio c a l c ~ l a t i o n son ~ ~other phosphorus-containing molecules.
Calculated Properties of Molecules ( a ) PO:-. Table I lists the P-0 bond lengths, stretching force constants, and S C F energies at the optimized geometry of this species ( Td symmetry assumed). The bond length calculated by using polarization functions is reasonably close (see below) to that found in orthophosphates; however omitting these functions results in dramatically longer bonds and smaller stretching force constants. (7) M. O'Keeffe and G.V. Gibbs, J . Chem. Phys., 81, 876 (1984).
0 1985 American Chemical Society
A b Initio Molecular Orbital Calculations on Phosphates h
Figure 1. Sketches (at the 6-31G*optimized geometry) of molecules. Large circles are P or Si, intermediate ones are 0, and small ones are H: (a) H3P04,(b) HSPOS,(c) H6Si2O7,an (d) H4P207(note that an 0 atom is obscured by the P atom on the left).
In contrast to our earlier experience7 with silicates, we conclude therefore, that, to obtain reliable results for phosphates, polarization functions on phosphorus are essential. On the other hand, the addition of polarization functions on oxygen appears to make little difference [but see (i) and (k) below]-this time in accord with experience with silicates-so that in the interest of economy these have normally been omitted in subsequent work; thus the preferred basis set is 6-3 1G*. (b) H$04+. The geometry of this species was optimized subject to the constraints that all P-O and all 0-H bonds were of equal length and that there were only two independent 0-P-0 angles (symmetry DZd).The bond lengths found are d(P-0) = 1.524 A and d(0-H) = 0.953 A. Relevant angles are 0-P-O = 103' and 112' and P-0-H = 136.9'. The total energy, E = -642.26492 hartree. The P-O stretching force constant is 1000 N m-I. It is interesting that H4P04' mimics the situation in orthophosphate crystals much more closely than does PO4'. In AlP04, for example d(P-0) = 1.522 Thus it appears to be important to use neutral or nearly neutral fragments to predict the dimensions expected in such crystals. Using experimental correlationsi0 of bond valence, u, with bond length, u = (1.607 A/d)4329,we calculate u = 1.255 for the P-0 bond in H4P04'. The valence is thus 5/4 and not 1.O as might be expected from the analogy with the isoelectronic molecule H4Si04. (c) H3Po4. The constraints used in optimizing the geometry of the phosphoric acid molecule (shown in Figure 1) were as follows: all P-OH and all 0-H were kept of equal length; angles of the type 0-P-O were kept equal (optimized value 102.8'), as were angles of the type 0-P=O (optimized value 115.5') and P-O-H (optimized value 123.5'). The bond lengths are d(P-0) = 1.573 A, d(P=O) = 1.457 A, and d(OH) = 0.951 A. The energy is E = -641.93376 hartree. The bond valence-bond strength correlation quoted above corresponds to bond lengths of 1.61 and 1.37 A for single and double bonds, respectively-compare the observed values of 1.60 However, in P205-II113 the corresponding and 1.40 A in P4010.11*12 lengths are 1.56 and 1.49 A, and in crystalline H3P04itselfI4 1.57 (8) H. B. Schlegel, J . Chem. Phys., 77,3676 (1982); J . Comput. Chem., 3, 214 (1982). (9) H. N. Ng and C. Calvo, Can. J. Phys., 54, 638 (1976). (10) B. Domengb, N. K. McGuire, and M. O'Keeffe, J . Solid State Chem., 56, 94 (1985). (11) D. W. J. Cruickshank, Acta Crystallogr., 17, 677 (1964). (12) P. A. Akisin, L.V. Vilkov, E. 2.Zasorin, N. G . Rambidi, and V. P. Spiridonov, Zh. Strukt. Khim, 3, 267 (1962). [Engl. Trans. in J . Struct. Chem. 3, 267 (1962).] (13) D. W. J. Cruickshank, Acta Crystallogr., 17, 677 (1964).
The Journal of Physical Chemistry, Vol. 89, No. 11, 1985 2305
A (mean) and 1.52 A (although in this last instance the situation is complicated by strong hydrogen bonding). (6)HP03. This molecule was found to be planar with d(P-OH) = 1.559 A and d(P==O) = 1.441 A, close to the results for H3P04. The angle 0-P-0 is 133.0°, the angle P-0-H is 124.2O, and E = -565.85070 hartree. (e) PO
