ILYAS ABSARAND JOHN R. VANWAZER
1360
An A b Initio LCAO-MO-SCF Study of the Phosphoryl Fluoride Molecule, OPF, by Ilyas Absar and John R. Van Wazer* Department of Chemistry, Vanderbilt University, Nashville, Tennessee 37203 (Received December 31,1370) Publication costs borne completely by The Journal of Physical Chemistry
Ab initio LCAO-MO-SCP calculations have been carried out on the phosphoryl fluoride molecule, OPFs, using a Gaussian basis set consisting of eight s and four p atom-optimized exponents (with and without an added d exponent) to describe the phosphorus, with five s and two p atom-optimized exponents to describe the oxygen as well as each of the three fluorine atoms. I n addition, a CXDO calculation has also beell done for this molecule, and the resulting orbital energies have been compared to the a6 initio values. The effect of allowing d character in this molecule is examined in detail. Three-dimensional electron-density plots are presented for the valence orbitals in a plane containing the phosphorus, the oxygen, and one of the fluorine atoms.
I. Introduction The electronic structure of phosphoryl fluoride,’ OPF3, is particularly interesting in that both the fluorine and oxygen atoms are highly electronegative with respect to the phosphorus and both have unshared pairs of electrons which may feed into the unoccupied d orbitals of the phosphorus so as to prevent unduly large charge differences between the phosphorus and either the oxygen or the fluorine atoms. A preliminary ab initio study2of p,-d, bonding in the hypothetical molecule phosphine oxide, OPH3, has shown that, upon adding phosphorus d atomic orbitals to the (sp) wave function, there is a clearly observable transfer of charge from the lone-pair region of the oxygen to the P-0 bonding region. The main purpose of the study described herein is to discover whether or not a similar transfer occurs from the oxygen to the phosphorus as well as from the fluorine to the phosphorus when d character is allowed in the description of the phosphoryl fluoride molecule. It is also of interest to see whether or not p,-d, feedback is clearly recognizable in the Hartree-Focli representation of this molecule and whether it is confined to specific delocalized molecular orbitals for the P-0 bond and for the P-F bond.
11. Calculational Details The ab initio LCAO-NO-SCF calculations using uncontracted Gaussian orbitals were carried out with the program I\IOSES,3which is part of a package of computer programs for quantum-mechanical calculations put together in our group (primarily by Dr. J. H. Letcher and H. RIarsmann). With the (841/52/52) basis set,4 which was the larger of the two used t o describe the OPF, molecule, a linear combination of 70 atomic orbitals is employed to delineate the 25 filled molecular orbitals, thus necessitating the calculation of nearly 3 X IOetwoelectron integrals and nearly 2 X lo3 one-electron integrals. When d orbitals are employed with the version of The Journal of Physical Chemistry, Vol. 76,No. 10, 1371
MOSES we use, they are couched in terms of dX2,dug, dZ2,d,,, d,,, and due. When these are converted to the usual spherical-harmonic representation involving five d orbitals, a 3s orbital which exhibits the same exponent as those used for the d’s also results. This means that this 3s orbital should also be included in the atomic basis set when binding-energy calculations are carried out with the use of d functions. The exponents for the phosphorus atom in the (84) Gaussian basis set were obtained in our laboratory from an atom-optimizing program5 and were found to be the following: 5941.5, 920.30, 221.51, 68.164, 23.685, 5.1733, 1.9202, and 0.2141 for the s type; and 48.818, 10.6798, 2.7458 and 0.2478 for the p type. I n the calculation involving d character on the phosphorus, the d exponent was chosen to be 0.36 from the results of optimization in the phosphine6 and phosphine oxide2 molecules. The energy for the phosphorus atom in the (84) basis set was found to be -340.0926 au, whereas addition of the 3s orbital having an exponent of 0.36 lowered this energy to -340.1000 au. The exponents and energies for the oxygen and fluorine atoms were taken from the literature.'^^ (1) A brief report of a Slater minimum-basis set SCF study of this molecule has been given by I. H. Hillier and V. R. Saunders, Chem. Comm., 1183 (1970). (2) H. Marsmann, L. C. D. Groenweghe, L. J. Schaad, and J. R . Van Wazer, J . Amer. Chem. SOC., 9 2 , 6107 (1970). (3) L. M. Sachs and M.Geller, Int. J . Quant. Chem., 15, 445 (1967). (4) The notation (abc/ef/gh) corresponds t o the assignment a Is, b 2p, c 3d atom-optimized Gaussian type orbital-exponents to the phosphorus, e 1s and f 2p t o each of the three identical fluorine atoms, Q 1s and h 2p to the oxygen atom. For the phosphorus atom alone, the notation is (ab), or (abc) when d orbitals are employed. (5) B. Roos, C. Salez, A . Veillard, and E. Clementi, “A General Program for Calculation of Atomic SCF Orbitals by the Expansion Method,” IBM Research Laboratory, San Jose, Calif. (6) J.-B. Robert, €1, Marsmann, L. J. Schaad, and J. R . Van Wazer, submitted for publication. (7) D. R. Whitman and C. J. Hornback, J . Chem. Phys., 51, 398 (1969). (8) C. 3 . Hornback, Ph.D. Thesis, Case Institute of Technology, Cleveland, Ohio, 1967.
LCAO-MO-SCF STUDY OF
THE
PHOSPHORYL FLUORIDE MOLECULE
The CNDO (complete neglect of differential overlap) program9 was obtained from the Quantum Chemistry Program Exchange. Planar electron-density maps were calculated by one programlo and these were converted to a three-dimensional representation by another." In accord with the literature,12 the C3, geometry of the OPFI molecule was chosen to correspond to a P-0 distance of 1.45 A and a P-F distance of 1.52 A, with the FPF angle equal to 102'30'.
111. Results and Discussion I n a recent study13 of the polarizing effects14 of d orbitals, it was shown that the total energy of silane was lowered by only 0.032 au when two reasonably selected d exponents were added to a contracted (129/ 51) Gaussian basis set (to give a total energy close to the Hartree-Fock limit) as compared with a lowering of 0.095 au when a molecularly optimized d function was added to a Slater minimum-basis set. We interpret these findings in terms of the d function, which was added to the minimum Slater set, partially serving in the place of an s or p function badly needed to give a proper description of the molecule. I n our study of phosphine oxide,2 where a very small Gauesian basis set was employed to describe the phosphorus, the effect of adding a molecularly optimized d function to convert a (73/52/2) to a (731/52/2) basis set was contrasted to the effect of adding another atom-optimized p function on the phosphorus to give a (74/52/2) basis set. Although the energy lowering on adding the p orbital was 1.67 au, as compared with 0.20 au for adding the d, the larger change was seen to be due mainly to improving the description of the phosphorus inner orbitals (primarily the 1s and three 2p), whereas the d addition led to considerably larger changes in the energies and calculated electronic populations of the valence orbitals (particularly the outermost one). Because of the fact that the added p and d orbitals played such different roles in a very small, unbalanced basis-set description of phosphine oxide, we believe that interpretation of d-orbital participation given herein for a larger, better-balanced Gaussian basis set ought to lead to a reasonably meaningful picture. The total energies calculated for phosphoryl fluoride in the (84/52/52) and (841/52/52) basis sets are presented in Table I along with the respective binding energies which have not been corrected for extra-correlation energy. The relatively large difference between the total energy in the two Gaussian basis sets reflects the fact that these basis sets are small and that (as will be shown later) the d character allowed to the phosphorus acts not only in polari~ing'~ the p orbitals but is also fundamentally involved in bonding. The values of the uncorrected binding energies derived from the ab initio calculations exhibit the correct sign for a stable compound but are very small, much
1361
Table I : Energies Calculated for Phosphoryl Fluoride, OPF, ---ab
Energies
initio (82/62/52)
Total, au -710.0193 Binding," eV -1.99 (experimentalb 21.1 eV) Orbital, eV lal (P Is) -2185.9 l e (F Is)' -720.3 2al (F Is) -720.3 3al (0 1s) -560.5 4al (P 2s) -213.9 5a1 (P 2p) -155.0 2e (P 2 ~ ) -155.0 681 -47.2 3e -45.1 7a1 -36.9 8a1 -23.1 4e -19.9 9a1 -18.6 5e -16.6 6e -16.0 1a2 -16.0 loal -13.0 7e -11.3 +8.3 l l a l (virtual)
Gaussian--(821/52/52)
-710.5867 -1.25
-2182.5 -722.0 -722.0 -561.8 -210.3 - 151.4 -151.4 -46.9 -43.7 -36.0 -23.1 -20.0 -19.0 -17.8 -16.6 -16.0 -13.7 -11.7 $9.7
CNDO (with d)
-14.40
-47.5 -46.8 -39.7 -25.4 -24.7 -24.6 -23.5 -21.6 -20.8 -18.4 -18.4 -1.1
a The value of the (uncorrected) binding energy was obtained by simply subtracting the sum of the calculated total energies of the constituent atoms from that of the molecule, using the same basis sets in the atomic and molecular calculations. b From AH" = -476 kcal/mol [D. D. Wagman, W. H. Evans, V. B. Parker, I. Halow, S. M. Bailey, R. H. Schum, Nut. Bur. Stand. (U.8 . ) Tech. Note, No. 270-3 (1968)] at 0°K for the formation of OPFp(g) from the ground-state gaseous atoms, the binding energy was calculated using a correction of 9.1 kcal/mol for the zero-point energy [H. S. Gutowsky and A. D. Liehr, J . Chem. Phys., 20, 1652 (1952)l. There is a degenerate pair of orbitals for each e symmetry.
smaller than the experimental value. This low value is probably attributable to the fact that there are three covalently bonded fluorine atoms in the molecule. For the NF3 molecule,15the uncorrected binding energy is positive, but this is converted to the appropriate value when the molecular extra-correlation energy16is added. (9) P. A. Dohosh, Program CINDO, Program 142 of the Quantum Chemistry Program Exchange, Chemistry Department, Room 204, Indiana University, Bloomington, Ind. (10) W. E. Palke, an electron-density program modified by T . H. Dunning at the California Institute of Technology and later improved by H. Marsmann. (11) D. L. Nelson, "Perspective Plotting of Two Dimensional AsS ~ ~ S - P L O T ~ D , ' 'a computer program for a digital plotter, University of Maryland, Department of Physics and Astronomy, College Park, Md. (12) Q. Williams, J. Sheridan, and W. Gordy, J . Chem. Phys., 20, 164 (1952). (13) S. Rothenberg, R. H. Young, and H. F. Schaefer, J . Amer. Chem. soc., 92, 3243 (1970). (14) C. A. Coulson, Nature, 221, 1106 (1969). (15) M. L. Unland, J. H. Letcher, and J. R . Van Wazer, J . Chem. Phys., 50,3214 (1969). The Journal of Physical Chemktry, Vol. 76, No. 10, 1971
1362 Even a t the Hartree-Fock limit, the F2 molecule is seen also to exhibit a positive binding energy, with stabilization of the molecule being closely accounted for by pair correlations.16 For the semiempirical CNDO calculations, l7 the uncorrected binding energy is much larger than the values obtained from the ab initio computations. This difference must surely be attributable to the approximations involved in avoiding evaluation of the integrals rather than to differences between the basis sets used (a minimum Slater plus a single fivefold set of Slater d atomic orbitals on the phosphorus for the CNDO). Inspection of the orbital energies shows that inclusion of the d atomic orbitals in the ab initio calculations has an appreciable effect on the inner-shell molecular orbitals, raising the energy of the orbital corresponding to the phosphorus r r l ~by” 3.4 eV while lowering the fluorine and oxygen “1s” orbital energies by 1.7 and 1.3 eV, respectively. Similarly, the energies of the phosphorus “2s” and “2p” electrons are each raised by 3.6 eV. We can interpret these results in terms of the idea developed in the study of photoelectron spect r o s ~ o p y ’ ~that, ~ ’ ~when electrons are withdrawn from a given atom, the inner-orbital binding energies increase (so that the respective orbital energies should decrease) by about the same amount for each of the inner-shell orbitals of that atom. Application of this rule to the calculated results given above indicates that, upon allowing d character to the phosphorus, the fluorine and oxygen atoms lose electrons and the phosphorus gains electrons. Note that the CKDO optimization does not involve the inner-shell orbitals. For the valence-shell molecular orbitals, the ab initio calculations show essentially no change in the energies of the four orbitals Sa1, the 4e pair, and la2upon allowing d character to the phosphorus. The valence orbitals having the higher energies (i.e. loal, Ge, 5e, and gal) are stabilized by allowing d character, whereas the other orbitals, except for the four which were not affected appreciably, are destabilized. The orbital energies calculated from the CSDO approximation are consistently large, with the difference between them and the comparable ab initio calculation in which a d orbital is involved [i.e., the (841/52/52) basis set] being greatest for the orbitals of lesser stability. Indeed for the pair of 7e molecular orbitals (i.e., those related to the first ionization energy of the molecule), the absolute numerical value obtained from the CNDO calculation is nearly twice as large as that from the ab initio computations. Another interesting result of this particular CNDO calculation is that the first virtual (i.e., unfilled) orbital is computed to be slightly stable. These results again emphasize the fact that numerical values of energies of the valence-shell filled orbitals as well as those of the virtual orbitals are usually poor if they are basedz0on the CXDO approximation. The Journal of Physical Chemistry, Vol. 76,No. 10,1971
ILYAS ABSARAND JOHN R. VAN WAZER The calculated dipole moments and the atomic charges, obtained by subtracting the gross population for each atom (as obtained from a Mulliken population analysis2’) from its atomic number, are shown in Table 11. The dipole moment from the CNDO calculation Table I1 : Calculated Dipole Moment and Atomic Changes for Phosphoryl Fluoride, OPFI --ab
Property
Dipole moment, D (experimental 1.77 D ) On P On 0 On each F
initio Gaussian--
(82/52/52)
2.05
(841/52/52)
CNDO (with d)
2.00
2.29
Atomic Charges (Electrons) $1.616 +0.628 -0.658 -0.344 -0.320 -0.095
+0.826 -0.277 -0.183
Total Overlap Populations (Electrons) P-0 0.67 1.34 P-F (per bond) 0.37 0.67
was the farthest from the experimental value with the ab initio calculation including d atomic orbitals being the closest. I n accord with the prediction made from the changes in inner-orbital energies, it is seen that, upon allowing d character, the calculated positive charge on the phosphorus atom is decreased by nearly a full electron whereas the negative charge on the oxygen and the fluorine is simultaneously decreased by nearly ‘/a and ‘/4 of an electron, respectively. In all three calculations, it is clear that the oxygen is assigned a more negative charge than each of the fluorine atoms. Furthermore, the CSDO and (841/52/52) calculations, both of which realistically include d orbitals, are in agreement in assigning a formal charge of around f0.7 electron to the phosphorus atom and around -0.1 to -0.2 electron to each fluorine atom. Since fluorine is the most electronegative of all elements, the higher negative charge on oxygen as compared with fluorine in the phosphoryl fluoride molecule as calculated without phosphorus d character must be attributable to the (16) C. Hollister and 0. Sinanoglu, J . Amer. Chem. SOC.,88, 13 (1966). Also see G. Das and A. C. Wahl, Phys. Rev. Lett., 24, 440 (1970) for a related treatment. (17) J. A. Pople, D. P. Santry, and G. A. Segal, J. Chem. Phys., 43, 5129 (1965). (18) K. Siegbahn, et al., “ESCA-Atomic, Molecular and Solid State Structure Studied by Means of Electron Spectroscopy,” Almquist and Wiksels, Roktryckeri, Uppsala, 1967; also see “ESCA Applied to Free Molecules,” North-Holland Publishing Co., Amsterdam, 1959. (19) R. Kordberg, H. Brecht, R . G. Albridge, A. Fahlman, and J. R. Van Wazer, I n o r g . Chem., 9, 2469 (1970). (20) M. L. Unland, J. H. Letcher, I. Absar, and J. R. Van Wazer, J . Chem. SOC.London, in press. (21) R. S. Mulliken, J. Chem. Phys., 23, 1833, 1841, 2338, 2343 (1955).
LCAO-MO-SCF STUDY OF
THE
PHOSPHORYL FLUORIDE MOLECULE
Figure 1. Eleotron-density maps for the plane passing through the oxygen, the phosphorus, and one of the fluorine atoms of phosphoryl fluoride, OPF3. The basal plane of these plots shows the molecular geometry in the F-P-0 plane, with the electron density in this plane being shown vertically to this plane. (A) Total electron density for the (841/52/52) basis set and (B) an electron-density-difference map for the (841/ 52/52) minus the (84/52/52) basis set. The electron density (vertical scale) in (B) is magnified five times over that in (A).
dative (coordinate-covalent) bonding between the oxygen and the phosphorus. Furthermore, since the drop in negative charge due to allowing d character is large for the oxygen as well as for each of the fluorine atoms, electronic feedback from the unshared pairs to the bond with phosphorus is indicated for both fluorine and oxygen. This conclusion is supported by the approximate doubling of the substantial P-0 and P-F overlap populations upon allowing d character to the phosphorus. I n Figure lA, a relief map of the electron density of the phosphoryl fluoride molecule is shown for the plane passing through the phosphorus, the oxygen, and one of the three fluorine atoms. I n the representations given in Figures 1 and 2, the electron density at any point on the plane is plotted perpendicular to that point. The unshared pairs of electrons around the fluorine and oxygen atoms are readily apparent in Figure 1A. This plot corresponds to the (841/52/52) basis set, and when d character is forbidden to the phosphorus [i.e., for the (84/52/52) basis set], the resulting plot has the same general appearance. However, the relatively subtle differences in the electron density brought about by allowing d character to the phospho-
1363
rus can be seen from a difference map such as the one shown as Figure lB, in which the vertically plotted electron-density differences are magnified fivefold as compared to the electron densities of Figure 1A. From Figure lB, as well as from similar plots made for different viewing angles, it is apparent that addition of d character to the phosphorus causes a concentration of electronic charge in the neighborhood of each of the nuclei. I n addition, a ring of charge is removed from around the oxygen and each of the fluorine atoms. These rings of charge deletion, the centers of which lie on the respective bond axis, represent the transfer of charge corresponding to unshared pairs on the oxygen and fluorine atoms to other parts of the molecule. These are predominantly the regions near the nuclei mentioned above, as well as a ring of increased charge around the phosphorus atom. This ring is a wobbly shaped (with a threefold axis) annulus, as indicated by the two mammilar humps on either side of the phosphorus atom in Figure 1B. Without question, the charge transfer from the oxygen to the phosphorus can be interpreted as p,-d, bonding. However, for the charge transfer from the fluorine to the phosphorus, the placement of the humps on either side of the phosphorus is such that it appears that some of the electrons taken from the fluorine lone-pair region by allowing d character on the phosphorus would have to be considered in terms of an increase in P-F u as well as P-F a character. It should be noted that the terms u and ?r used in this discussion refer to the charge-density maxima lying along the respective bond axis for the u bond or on either side of the bond axis for the a bond. Of course, the usual precise mathematical definition of u and a applies only to planar molecules. A population analysis for the 16 valence-shell molecular orbitals is given in Table 111. These values should be compared with the electron-density plots shown for these orbitals (with d character being allowed) in Figure 2 . Most of these delocalized Hartree-Fock orbitals are dominated by one or two bonding functions as defined in the classical valence-bond sense. These dominant contributions are listed in the second column of Table 11. Note that the electronic populat,ions of orbitals, 6a1, 7al, 4e, 6e, and laz are not greatly affected by allowing d character on the phosphorus. However, in the pair of 3e orbitals, there is some increase in the overlap of each P-F bond along with a transfer of a total of about 0.2 electron from the three fluorine atoms to the phosphorus. The most notable change in molecular orbital 8al upon allowing d character to the phosphorus is an increase in the overlap of each P-F bond from nothing to about 0.3 electron. For orbital gal, there is also a small increase in P-F overlap accompanied by a transfer of a small amount of charge from the fluorine to the phosphorus. Upon allowing d character to the phosphorus atom, the pair of 5e orbitals is The Journal of Physical Chemistry, Vol. '76,N o . IO, 1971
1364
ILYAS ABSARAND JOHN R. VANWAZER ~~
Table 111: Electronic Populations21 of the Valence Orbitals" Orbital
Dominant contribution
6a1
P-F u
3eb
F lp, P-F u
7al
P-0
U, 0
lp
8a1
P-F
U, 0
lp
4e 9%
P-F u P-F
T , '
F lp
---Overlap
P-0
0.01 0.01 0.00 0.00 0.59 0.64 -0.01 -0.04 -0.04 -0.08 -0.04 -0.31
5e
F lp, P-F
6e
F 1P
la2
F 1P
1Oal
7e
v
0 IP, F 1P P-0 F 1P
77,
0 lp
0.02 0.00 0.02 0.00 0.00 0.00 0.05 0.07 0.66 0.34
population------Eaoh P-F
0.15 0.16 0.24 (0.24)c O.IS(0.16) 0.00 -0.01 0.34
_-_-____ P
Gross population------0 Each F
0.39 0.46 0.50 0.34 0.50 0.44 0.47
0.01 0.01 0.00 0.00 1.45 1.49 0.11
0.00
0.63
0.12
0.15 (0.06)
0.84 0.96
0.18
0.12 (0.09)
0.06
0.10
0.35
0.17
0.08
0.30 0.40 0.00 0.18 0.00 0.00 0.00
0.17
0.16 0.00 0.06 (0.05) 0.00 ( -0.01 ) 0.00 0.00 -0.01
0.04 0.02
-0.03
0.14
-0.05 ( -0.04) -0.11 (-0.09)
0.56
0.04 0.00 0.00 0.00 1.44 1.36 3.00
0.22
3.32
0.20
7
0.53 0.61 1.17 (1.17) 1.21 (1.21)
0.02 0.02
0.47 0.46 1.03 (0.69) 0.98(0.33) 0.49 0.48 l.lg(O.65) 1 .33 (0.70) 1.26 (1.01) 1 ,33(1.08) 0.67 0.67 0.12 0.17 0.14 (0.12) 0.16(0.11)
a The values in regular type correspond to the (841/52/52) basis set, whereas the values in italics correspond to the (84/52/52) basis. Hence the italicized numbers give the respective numbers of electrons when d character is disallowed. * The charges in electron units Values are given in parentheses shown for each set of e orbitals correspond to the sum of the constituent pairs of a1 and a2 orbitals. for the a1 orbital of each e pair (when the charge is unequally distributed between the a1 and a2 orbitals) for the fluorine atom appearing in the electron-density plots of the figures. d See text for this usage of the "T" notation.
seen to evidence P-F overlap accompanied by an increase of the charge on the phosphorus from zero to about 0.4 electron, with this increase in charge having come from the three fluorine atoms. The same situation holds for the pair of 6e orbitals, but to a lesser extent. The effect on orbital loal is also small, corresponding to charge transfer from the fluorines to both the oxygen and the phosphorus. In the case of the pair of 7e orbitals, there is an appreciable increase in the P-0 overlap accompanied by the transfer of about 0.3 electron from the oxygen to the phosphorus. From inspection of the data given in Tables I and I11 as well as Figure 2, it is clear that P-0 ?r bonding is associated with the orbital of least negative energy whereas the electronic feedback from the fluorine atoms to the phosphorus upon allowing d character to the latter shows up in orbitals which are considerably more stable (sal, 5e, and 3e). Likewise, as expected, the orbitals associated with the fluorine lone-pair character are somewhat more stable than those associated with the oxygen lone pair, with both of these being less stable than the orbital which accounts for much of the P-0 u bonding. Further, in spite of the fact that the P-F u bonding is delocalized among a number of orbitals, this bond appears to involve more energy per bond than does the P-0 u bond. From the geometries shown in Figure 2, only molecular orbital 9al is seen to have a t all the proper shape to The Journal of Phvsical Chemistry, Vol. 76, N o . 10,1971
correspond to a P-F ?r bond. However, upon allowing d character to the phosphorus, there was only a small increase in the P-F overlap population for this orbital. The orbital (sal), which shows the greatest increase in P-F overlap on allowing d character to the phosphorus, clearly involves P-F u bonding as can be seen from Figure 2. These results on the various individual orbitals are, of course, consistent with the overall electrondensity-difference map of Figure 1B which shows that the ring of charge increase lying around the phosphorus atom appears to pretty much block the P-F bond axis. In Figure 2, molecular orbitals 6a1 and 3e in the case of the fluorine atom and orbitals 7al, Sal, and 9al for the oxygen clearly exhibit a central spike of charge surrounded by a ring of charge. This observed charge geometry is clearly a distortion of the 2s atomic orbitalsZ2of these atoms. Likewise, the split electrondensity maxima (sal, 4e, gal, 5e, 6e, and 7e for the fluorine and 4e, loal, and 7e for the oxygen) represent distortions of the 2p orbitals of these atoms.22 Figure 2 shows for the phosphorus central maxima surrounded by two more or less annular rings of charge (with the outer ring being very flat and diffuse) in orbitals 6a1 and Sal. These represent distortions of the 3s atomic orbital of phosphorus.20 Likewise, the split central (22) W. T. Bordass and J. W. Linnett, J . Chem. Edue., 47, 672 (1970).
LCAO-MOSCF SRTDYOF
THE
PHOSPHORYL FLUORIDE MOLECULE
1365
0
I
"..,
. I .
"4- ... ... .. . .,. .. ..e--.,::;& ~
._ ,.. .
.
.-:. .
..
:
,,i
~
. .. ... .
Figure 2. Electrondensity maps of the valence orbitals of phosphoryl fluoride, OPFa, in the (841/52/52) basis set as observed in the plane determined by the oxygen, the phosphorus, and one of the fluorine atoms. The electron-density scale is the same as that used in part A of Figure 1.
hump surrounded on either side by flat diffuse humps, aa seen in orbitals 3e, 7e, and particularly 4e'are similar to a 3p phosphorus atomic orbital.22 As was pointed out in a previous paper,13electron-density plots, such as shown in Figure 2, clearly relate the shape of the molecular orbitals of the main contributing atomic orbitals of the respective atoms, and this occurs in even as complex a molecular structure as O W a .
Acknowledgment. We wish to thank the National Science Foundation for support of this study, and Drs. J. H. Letcher, M. 1,. Unland, and H. Marsmann for some preliminary studies of phosphoryl fluoride in a localized description.
~
(23) J.-B. Robert. H. Mamrnann, I. Absar, and J. R. Van Waeer. J . Amw. Chem. Soc.. in press.
The Journal of Physicol Chemiatru. Vol. 76, No. 10, 1971
