J . Phys. Chem. 1993,97, 13877-13886
13877
MNDO Model Structure for Poly(diphenoxyphosphazene) Derived from Clusters of Several Related Pbosphazenes Randall C. Boehmt Theory Project, Materials Chemistry, Idaho National Engineering Laboratory, EG&G of Idaho, Inc., P.O. Box 1625, Idaho Falls, Idaho 83415-2208 Received: June 4, 1993"
We have determined that the backbone of poly(diphenoxyph0sphazene) is not planar. Instead, significant evidence of a twisted T-ribbon like helix conformation is seen. The degree of twist is crudely estimated as 9 O (40 monomer units per revolution) making this compound one of the largest for which an approximate structure is first elucidated with the M N D O technique. The helix radius, neglecting extension of side groups, is 0.82 A. The phenyl groups remain approximately perpendicular to their nearest N P N backbone fragment. Several series of finite phosphazene clusters, including rings and oligomers, are characterized. It is found that many structural features are transferable to the polymer. The remaining features necessary to fill out the MNDO model of poly(diphen0xyphosphazene) are estimated by extrapolation of data originating from diphenoxyphosphazene oligomers (up to six monomer units).
Introduction
Method
It has been demonstratedthat magnetic coprocessing of epoxies and membrane filters can lead to significant enhancement of several mechanical properties.'J A number of hypotheses have been prop0~ed'Jto explain this curious result. Usually, the materials in question are composed of large closed-shell compounds which include aromatic side groups. The magnitude of the diamagnetic moment for a typical, single-ring aromatic compound (benzene, toluene, and phenol for example) is O(-10) hartrees/T2, which we recognize as being 5-6 orders of magnitude smaller than regular dispersion forces between any pair of simple aromatics. In this light it is curious that any effect should be demonstrated,as all of the mechanismswhich have been proposed thus far suggest that the magnetic forces are directly affecting the structure of the bulk materials. Some of our results suggest that paramagnetism could be a contributing factor in these observations, while other results strongly suggest that an appreciable gap between the valence and conduction bands at k = 0 (HOMO LUMO gap) persists regardless of polymer length. In this study our primary goal is to determine the structure of poly(diphenoxyph0sphazene)-a membrane filter which shows enhancement upon magnetic curing4-in order to provide a foundation for closer examination of its interactions with magnetic fields (staticor otherwise). The material is particularly ill-suited for conventional computational techniques, which have been developed for finite moleculesor infinite chains, in one case because their length is arbitrary, in the other case because too many atoms are contained within its unit cell (uncertain though this number is). The report is divided into four sections: Introduction, Method, Results, and Conclusion. The Results section is further divided into five subsections: series I-IV and Discussion. The series subsections are devoted to presentation and discussion of information which is gleaned individually and cumulatively from each of the four cluster types defined in the Method section. The discussionsubsection is devoted to discussion of data and problems which call for simultaneous comparisons between multiple data sets and some representativeHuckel band structure calculations.
The semiempirical modified-neglect-of-diatomic-overlap (MNDO) method, as implemented in the GAUSSIAN90 program suite? was used to model a number of molecular properties of four phosphazene cluster series. These properties are expected to converge toward the polymer (or bulk) limit as the number of (NP) linkages in the clusters is increased. In each case, valence orbitals were represented by the STO-3G valence basis. Local stationary points were located by following analytic first derivatives according to the Berny algorithm (NewtonRaphson steps). Frequency calculations (derived from analytic second derivatives) were performed on all clusters for which no user-imposed constraint was applied in order to verify that a local minimum had been found within the MNDO/STO-3G descrip tion. Some of the calculated frequencies may contribute to an understanding of the observed enhancements. As such, these frequencies are discussed under the Results section for series I1 clusters. Althoughwe recognize that MNDO frequencies deviate from observed values by as much as 40% for torsion about a C-C single bond, most values are within 10% of experiment and are essentially the same as Hartree-Fock frequencies? Equilibrium geometries' are described exceptionally well at this level provided the compound under study belongs to the same class of materials that was used to establish the MNDO parameters. (Structural parameters which typically require multicenter Coulomb and exchange terms, such as nonzero dihedral angles, in order to be reproduced consistently are admittedly less reliable). As several phosphazenes* were included as reference materials, we expect to obtain reliable structural data for the clusters under direct investigation here. The reliability of energy differencesbetween drastically different conformations of one empirical formula is questionable: while energy differences between conformations with like linkages are (for the most part) accurate.' The clusters we have characterized are included within the following series:
t Current address: The Department of Chemistry, Michigan State University, East Lansing, MI 48824. Abstract published in Advance ACS Abstracts, November 1, 1993.
0022-365419312097-13877$04.00/0
I.
chains EL-(NP(OPh),),-ER:
11.
rings (NPR,),:
E L and E R = H, NO, SNPCl,, etc.
m = 1-8, R = hydroxy or nothing
0 1993 American Chemical Society
Boehm
13878 The Journal of Physical Chemistry, Vol. 97, No. 51, 1993
111.
rings (NP(OPh),,,,),:
Y
m = 1-3
m = 1-6 chains H-(NP(OPh),),-H: IV. Trends in geometric parameters are enumerated for series II-IV, while relative energy differences are important for series I1 and IV. In addition to the variations which are evident from above, we have imposed severalvariationson geometric constraints.These range from a small set of constraints, which mandate that each phenyl ring possess a pseudo-bfold axis of symmetry with hydrogens lying in the same plane as the carbons and that each phenoxy group be identical to all other phenoxy groups, to a larger set of constraints, which mandate, additionally, that the NP backbone belong to a predetermined underlying structure, that each P-N, P-O, and C-O bond be equivalent to all other bonds of the same linkage, and that angles with common linkages maintain a common value as well. Most of these constraints are natural constraints in the limit of an infinite polymer. One exception to this, for example, is the (temporary) planarity condition on the backbone, which we know is not necessarily true.'O-12
X
X
Results Series I: EG(NP(OPb)&ER Cham. The general idea of breeding bulk (or polymer) properties from finite clusters has been used successfully by several research groups.l3-I8 In the case of oligomers breeding polymers, it is known that the choice of a chain terminating group can influence structural and other molecular properties in a very significant fashion.I9 This necessitates either of two options: the brute force option or the best-end-group option. In the brute force option, one simply increases the length of the chain until it becomes apparent that end group effects become relatively unimportant. In the bestend-group option, one selects a terminating group which mimics the truncated portion of the polymer from a list of promising candidates that have been tested on a few small clusters or one embeds the oligomer into a periodic host.20 Ultimately, a calculation is performed on the largest cluster which is practical within a host of other circumstances, regardless of which option is employed. In this study, the best-end-group option was particularly difficult to apply because we lacked the detailed experimental information about poly(diphenoxyphosphazene) which would allow the kind of bench-marking one needs to select a terminating group or an embedding scheme. With this in mind, several calculations were performed on EL-(NP(OPh)Z),-ER (EL and ER variable) clusters in order to shed some light on the severity of the end group effects in phenoxy-substituted phosphazene compounds. Tests were performed on the following (EL, ER) pairs: (H,ONP(OPh)Z), (HP(OPh)2, NH), (H, H), and (SNPC12, SNPCl2::spin doublet). The H, ONP(0Ph)Z) pair is chosen to illustrate (Figure 1) the simple point that end group effects are quite extreme in these compounds, making selection of a 'best" end group futile and complicating the brute force option to a point requiring external control of would-be symmetry. Note: since there is no end group which adequately mimics the purged ends of the polymer, we have chosen to use the smallest end group (H) for the brute force component of this study (series
IV).
Figures 1 and 2 illustrate clearly that the orientation of the phenoxy groups is strongly dependent on end group effects; in both clusters there is at least one phenoxy group which infringes upon that space which would be occupied by another monomer unit were the chain not truncated. Further, this infringement into its neighbor's space is seen to propagate through the chain and varies with respect to choice of end group and user-imposed constraints. A closer inspection of the data reveals that similar variations exist with respect to other important structural features as well. In order to circumvent these problems, it is clear that
Figure 1. Result of the test of H and 0terminating groups. In the sketch the central phenyl groups have been removed in order to emphasize the orientations of the terminal phenyl groups, and the backbone has been highlighted in order to distinguish it from the remainder of the cluster.
\
,
-d:
Figure 2. Impact of chain trunctation on structure.
externally applied structural constraints on the H-NP(OPh)2 and NP(0Ph)Z-H end groups are required in order to better mimic those portions of the chain which have been severed. The details of these constraints will be addressed under series IV. Series I1 and I11 are devoted to the elucidation of structural properties which are insensitive to the shape of the model cluster. Series 11: (NPRz), Rings. The idea of using the molecular orbitals of rings to imitate the band structure of infinite chains is well established for simple systems.21 We, however, cannot apply this logic directly to this polymer for several reasons. First, we do not know apriori how many PN units are contained within a primitivecell of poly(diphen0xyphosphazene) (apriori we know there are at least two). Second, we have no way of knowing a priori how to orient the [(NP(OPh)2Jn(n 2 2) groups relative to one another as we make larger and larger rings. Finally, the number of orbitals that must be involved in the calculatiorisscales as 148nm, where n is the number of N P units and m is thenumber of cells contained in the ring, so that even moderately large rings are computationally prohibitive. We have therefore used an alternative logic-one which does not necessarily blend an MO
MNDO Model Structure for Poly(diphenoxyphosphazene)
The Journal of Physical Chemistry, Vol. 97, No. 51, 1993 13879
TABLE I: MDNO Properties as a Function of (NP).Ring Size N 1 2 3 4 5 6 I 8 0
energy/ unit (au)
point group C-"
charge (e)
length (A)
av NPN bond angle (deg)
av PNP bond angle (deg)
planarity deviation (A)
gap" (au)
0.40 0.69 0.95
1.398 1.628f 0.090 1.558 f 0 1.538 f 0.037 1.524f 0.002 1.521 f 5E-Sb 1.520f 0.002 1.520f 0.002
84.9 f 0 104.2f 0 111.5fO 107.7f 2.0 106.9 f 0 108.3f 1.5 108.3f 0.8
95.1 f 0 135.8 f 0 154.4 f 0 168.5 f 4.0 172.7 f 0 173.8f 3.1 173.5 f 3.9
0.0 0.0 1.07 1.66 1.37 1.80 2.95
0.44 0.30 0.33 0.29 0.30 0.30 0.31 0.30
0.055 0.046 -0.013 -0.014 -0.019 -0.022 -0.021 -0.021
021
D3h
C2u
9 9" C, C S
av bond
av
1.11
1.14 1.15 1.14 1.14
The orbital energy difference between the highest occupied MO and the lowest unoccupied MO. Read as 5
X
HL
lW5.
2
\
Y
N
Figure 4. Lewis dot structure of the phosphazene skeleton. X
13 y
Y I
2
X Y
Y
z
X
X
Figure 3. Phosphazene rings. The two best perspectives of each cluster are shown. The point group for each cluster is given in Table I.
of the finite system into a band in its corresponding infinite system-in order to ascertain important structural data. The method employsonly (locally) minimum energy structures, counts each PN group as one unit, and omits most of the orbitals that are expected to define the bulk electronic (and magnetic) properties of the polymer. The behavior of several electronic properties of the ring compounds is recorded here, although a discussion of these properties in relation to similar properties of the infinite system is relegated to the Discussion section. It is immediately clear from Table I that many properties (PN bond length and its deviation,PNP bond angles, NPN bond angles,
and several electronic properties) have converged. The deviation from planarity increases linearly from n = 2 to n = 8, and no pattern is apparent for the deviation in bond angles. The deviation in bond distances, of 0.002 A, is consistent with what is known about the structure of related compounds, as determined from X-ray diffraction data.zz-24Likewise, the average bond distance (1.52 A) and the average NPN bond angle are well within the bounds of experimental determinations. The average PNP bond angle is well outside similar bounds. The conuenienf source of the error in PNP bond angles is the condition that the ends of the (NP)" moiety be tied together. (After all, the external angle of a regular planar polygon is given by 180° (1 - 2 / m ) , where m is the number of sides of the polygon, and approaches 180° as the number of edges tends toward infinity.) The problem with this logic is that no condition of planarity is imposed upon the phosphazene, and beyond that, no symmetry constraint whatsoever is imposed. Thus, the external angles of the phosphazene polygons (NPN and PNP) are allowed to distort in any fashion (best illustrated by (NP)s in Figure 3), including closure of all bond angles to values which are less than their regular polygon counterparts. Another potential source of the error in PNP bond angles is an artificially high degree of charge polarization (ioniccharacter) across the P-N bonds. If this were indeed true, then an accompanyingincreasein P-P and (N-N) repulsionswould occur. Such an increase might be sufficientto push the PNP bond angles apart, to superfluousvalues. In fact, the frequencieswhich involve primarily bends across PNP angles are quite small, and either source could be sufficient to cause the observed error. In the Discussion subsection we will revisit this topic in order to clarity the factors which lead to this error. The average charge density on P (or N), in combination with the HOMO-LUMO gap, offers an interesting breakdown of Othorder electronic structure principles. If the data shown in Table I are to be taken literally,then the average localized charge density would suggest that N gains approximately one electron, for n * 3 or greater, while P loscs an equal amount of charge density. Hence, the best Lewis dot structure would be drawn as shown in Figure 4. This, in turn, suggests that two valence electrons on P would be distributed between two nearly generate P valence orbitals, suggestinga small energy differencebetweenthe HOMO and the LUMO. However, the data indicate that such an energy difference is quite large (-7 eV). In fact, the errors in each of these approximations probably add to produce the observed contradiction. That is, more polarization is predicted by the (MNDO/STO-3G) Mulliken population analysis than is actually present; the Lewis dot structure does not account for relative
13880 The Journal of Physical Chemistry, Vol. 97, No. 51. 1993
Boehm
TABLE Ik MDNO Properties as a Function of INP(0H)zL Ring! Size DroDerty N=l N=2 N=3 . . 1.534 1.679 f l E 4 1.634 0.003 R-NP (A)b 93.6 f 0 122.6 0 A-NPN (deg) 86.4 f 0 117.3 f 0 A-PNP (deg) 1.602 1.598 f 1E-4 1.605 f 0 R-PO (A) 0.944 f 1E-6 0.943 0.944 f 5E-5 R-OH (A) 103.2 0 102.3 102.9 f 9E-3 A-OPO (deg) 115.5 f 6E-3 112.3 115.0f9E3 A-POH (deg)
* *
~
HL g a p (a4
-0.069 0.3 1 0.67 -0.28
N=6 1.603 f 0.006 119.8 1.0 133.4 f 3.0 1.606 0 0.943 0 102.7 0.2 116.5 0 1.29 -0.165 0.32 1.43 -0.96
0.0
3E-4
-0.141 0.35 1.01 -0.61
-0.165 0.36 1.21 -0.79
-0.164 0.31 1.35 -0.92
* *
*
off-planar (A) energy/unit (au)
N=4 1.611 f 0.003 126.0 0 129.6 1 . 1 1.605 f 0.001 0.943 0.001 102.4 f 0 116.2 f 0.6 1.13
* ** *
charge on P (e) charge on N (e) a The orbital energy differencebetween the highest occupied MO and the lowest unoccupied MO. Note that if a parameter is not converged outright, its difference with the corresponding parameter of the (NP), clusters is converged. Read as 1 X 1od. shifts in orbital energies which originate from the asymmetric environmentthey are placed into; and the 1e- energy of the LUMO is not variationally optimized, so the calculated HOMO-LUMO gap will tend to be somewhat too high. In spite of their flaws, the fact that these properties are essentially converged at n = 4 will allow us to draw interesting conclusions from subsequent data. The convergenceof relativeenergy,for n = 6 or greater, suggests that no benefit is observed, at 0 K, by increasing ring sizes beyond six monomer units. On the other hand, there is no benefit observed by shrinking rings either. Hence, at equilibrium and 0 K, an equal amount of every isomer with the maximum stabilization per monomer unit will be present. Presumably, this leads to an increase in high molecular weight phosphazenes, as the number of isomers, with like energy, is expected to increase rapidly as n increases. Table I1 is a compilation of results pertaining to (NP(OH)z),, n 5 6. As was the case for the unsubstituted phosphazenes, the HOMO-LUMO gap quickly converges to a value of 0.3 hartree, while the energy per monomer unit converges to -0.165 hartree. Thus, a pair of hydroxy groups is shown to stabilize its host monomer unit by approximately 0.15 hartree. Likewise, the structural properties undergo a shift upon changing from (NP), to (NP(OH)*),, but show similar behaviors with respect to changing values of n. The average P-N bond distance, for example, increases by approximately 0.075 A upon addition of hydroxy groups to the unsubstituted phosphazenes. This result is expected to carry over to the phenoxy-substitutedphosphazenes because the PN bond distance is believed to be influenced principally by the electron-withdrawing (or electron-donating) properties of the side groups rather than by their steric presence. Other structural parameters, such as the PNP bond angle, are expected to depend strongly on steric factors. These parameters, therefore, will not transfer readily onto the poly(diphenoxyph0sphazene). The most dramatic differences in the (NP), and [NP(OH)z], data sets are with respect to the NPN and PNP bond angles. The former increases by approximately 13O regardless ofcluster size, while thelatter shows noconsistentrelation between the two cluster types. In the limit of infinitely large clusters the PNP bond angle decreases by approximately 40° upon hydroxy addition at the P sites. The localized chargedensity, as expected, shifts in order to accommodate the electron-withdrawinghydroxy groups. The remainder of Table I1 is a compilation of structural data pertaining to the side groups. Of these data, only the P-O bond distance is expected to carry over to the phenoxy-substituted phosphazenes. Others, such as the OPO and POH bond angles, are expected to be crude estimates of their phenoxy counterparts, as steric interference is expected to push the phenyl groups apart. The convergence behavior of the 0-H bond lengths is expected to parallel that of C-O bond lengths in the phenoxy-substituted phosphazenes, while the relative orientation of the side groups is as shown in Figure 5. Although the degree of this trans-like shift
Figure 5. Relative orientations of side groups.
TABLE III: MNDO Frequencies of (NP),, Clusters range(cm-I) N = 1 N - 2 N = 3 N = 4 N = 5 N = 6 N = 7 N = 8 0-50 50-100 100-150 150-200 200-250 250-300 300-350 350400 400450 450-500 500-600 600-700 700-800 800-900 900-1000 1000-1250 1250-1500 >1500
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
0 0 0 0 1 0 0 0 0 0 1 0 0 1 1 2 0 0
0 0 0 0 2 0 0 2 0 1 0 1 0 4 0 0 2 0
0 0 2 2 2 0 0 0 0 3 0 2 2 1 0 1 0 3
1 3 1 1 2 0 1 1 0 2 2 0 3 3 0 0 0 4
2 2 4 0 4 0 0 0 0 5 1 0 5 1 1 0 0 5
4 2 3 3 2 1 0 1 2 2 2 0 5 2 1 0 0 6
4 4 4 3 3 0 0 0 4 1 3 0 5 3 1 0 0 7
is expected tochangesignificantlyupon replacement of OH groups with OPh groups, it is later argued that its direction (trans-like rather than cis-like) will not change. Finally, we have compiled frequencies (Table 111) for each of the structures that we know corresponds to a local energy minimum. As the clusters grow, it becomes apparent that frequencies pack into four distinct bands: 0-250,400-600,700950, and 1500-1700 cm-I. The low-energy band obviously includes puckering (or torsional) deformations, while the highenergy band includes bond stretches. As we are concerned with deformationswhich may lead to subtle differences in the geometry of the backbone, our primary concern is with the low-energy (puckering) deformations; but these are precisely the frequencies which are most uncertain. For this reason we are not exploring thedeterminationof related frequencies, for theinfinite polymer. Series IIk [NP(OP€I)Z,/PL:.m = 1-3. Now that we have established that some properties of phosphazene rings are transferable to polyphosphazenes, it is constructive to perform a series of calculations on phenoxy-substituted phosphazene rings so that we may determine important structural data concerning the side groups. In each case the (NP)3 backbone was required to remain invariant to each symmetry operation of the D3h point group (similar to the (NP)3 molecule shown in Figure 3), while the cluster as a whole was not so required. The data, compiled in Table IV, indicate that several structural parameters are insensitiveto the number of phenoxy groups present, while others are quite sensitive to this change.
MNDO Model Structure for Poly(diphenoxyph0sphazene)
TABLE I V MDNO Properties of [NP(OPL)2,/3]3 Cyclophosphazenes’ property M =0 M =1 M=2 hf= 3 R-PN (A) 1.558 1.561 1.587 1.631 1.617 1.618 1.619 R-PO (A) R-CC (A) 1.411 1.411 1.411 R-CH (A) 1.090 1.090 1.090 R-CO (A) 1.362 1.363 1.363 A-NPN(deg) 104.2 109.0f0.5 1 1 5 . O f O . 4 1 2 1 . 7 f 0 . 1 A-PNP (deg) 135.8 131.0 f 0.5 125.0 f 0.4 118.3 f 0.1 A-OPO (deg) 102.3 102.6 101.8 A-POC (deg) 124.0 124.5 124.8 DH-COPN (deg) 138.7 147.5 152.7 DH--CCOP (deg) 85.2 83.9 83.5 0.28 0.27 0.33 0.28 HL gapb(au) +0.95 +1.11 f 0.21 +1.20 f 0.24 +1.25 charge on P (e) charge on N (e) -0.95 -0.97 f 0.03 -0.90 f 0.05 -0.79 Each cluster contains three (NP) units but may contain 0, 2,4, or 6 (OPh) groups. None of the clusters contain a 3-coordinate P atom. The orbital energy difference between the highest occupied MO and the lowest unoccupied MO. @
Figure 6. Quick sketch of the (RO)P(OR) moieties. The open circles represent phenyl groups, while the shaded ellipses represent the phosphazene ring.
Those parameters which show variance with respect to phenoxy group additions (R-PN, A-NPN, A-PNP, and DH-COPN) are thus known to be significantly influenced by the degree of electron-withdrawing (or electron-donating) character of the side groups. Either those parameters which show little or novariance with respect to phenoxy group additions are completely internal to the side groups (R-CC, R-CH, and R-CO) or they are influenced primarily by the bulkiness of the side group (R-PO, A-POC, A-OPO, and DH-CCOP). (For further support of these claims, see Table 11, column N = 3.) Interestingly, A-OPO in [NP(OPh)2]3is smaller than in [NP(OH)2]3. A quick sketch of the respective P(OR)2 moieties (Figure 6) makes it clear that sinceA-OPOis primarily influenced by steric factors, it should decrease upon replacement of R = H with R = Ph (in [NP(OR)2]3), as the phenyl groups are seen to infringe upon the backbone rather than adjacent phenyl groups. Note: neither infringement is expected to be important in pseudolinear phosphazenes. Every cluster in this series (as well as those in series I and IV) can be thought of, alternatively, as a phenoxy group with various bulky phosphazene groups attached to it. Since the electrondonating (or electron-withdrawing) character of each of these phosphazene groups is essentially identical, we expect to see no change in those parameters (R-CC and R-CH) which depend dominantly (although weakly) on that property and very little change in those parameters (R-CO) which depend primarily (although not exclusively) on that property. The data in Table 1V verify these statements.
The Journal of Physical Chemistry, Vol. 97, No. 51, 1993 13881
Before proceeding, let us collect what we learned about the structure of poly(diphenoxyph0sphazene) so far. Series I1 gives us the important value of R-PN = 1.595 A, while supporting what is gleaned from series 111 concerning R-PO, R-CO, A-OPO, and A-POC. Series I11 further allows one todetermine thevaluesofR-PO= 1.62A,E-CO= 1.36A,R-CC= 1.411 A, R-CH = 1.090 A, A-OPO = 102’, and A-POC = 125O. It indicates that the value of the CCOP dihedral angle may be close to 90°, while the COPN dihedral angle is shown to depend on electronic factors in addition to its presumed dependence on steric factors. Finally, limited support is provided for A-NPN and A-PNP, where it is clear that the nature of the rings (ends being tied together) has some influence on the value of these parameters. Series IV: H-[NP(OPh)21m-H Chains: m = 1-6. Now we are ready to discuss the “brute force” component of this study, where H has been chosen for each of the terminating groups. Thechains here naturally introduce several more variables into the picture: R-PH, R-NH, A-NPH, and A-PNH. Further, the PNPN and PNPN dihedral angles (and the A-PNP and A-NPN bond angles) take on additional flexibility, which effectively renders these variables unrelated to their counterparts in the cyclic clusters. In order to determine these variables and refine those already determined, we have characterized H-[HP(OPh)l],-H clusters under three distinct sets of constraints. In one set of constraints a cis-trans planar configwation for the backbone was imposed in addition to several constraints common to all three sets. The common constraints are as follows: Only seven unique bond lengths (R-CH, R-CC, R-CO, R-PO, R-PN, R-PH, and R-NH) and seven unique bond angles (A-NPN, A-PNP, A-POC, A-OPO [or OPN], A-PNH, A-NPH and 120’ = A-CCC, A-CCH, and A-CCO) are allowed. The phenoxy groups are planar, while all of their orientations relative to the plane of the backbone (or the plane of that portion of the backbone NPN to which the relevant side group is attached) are given by the dihedral angles CCOP and COPN. The C”C’0P dihedral angles define the extent to which the P atom is lifted out of the plane of the phenyl groups (*90° maximizes this lift). Note: the periodicity of CCOP is 180° rather than 360’ because .he (central) CO bond coincides with the C2 symmetry axis of the respective phenoxy group. Whether the P atom is shifted toward the right or left of its apex position depends upon the choice of C”. In this study, CCOP = 90 A implies that P is shifted to the left of the CO bond, while CCOP = 90 - A implies a shift toward the right. The tilts (A # 0) of the phenyl groups on opposite sides of the backbone (or backbone segment) are oriented in opposite directions so their relative tilt (to each other) is 2A. The COPN dihedral angles are not defined consistently. In thecaseof the planar backbone, the pertinent N atoms (sometimes H instead of N) always falls to the right of the PO bond, while looking down the PO bond from 0. This definition results in a problem (perhaps inconsequential) that is immediately apparent from Figure 7, lower left. The root of the problem is in a natural dissimilarity between A-NPN and A-NPH parameters, which alters the meaning of COPN with respect to exactly one phenoxy group (shaded in Figure 7). For nonplanar oligomers, either COPN is redefined to eliminate any involvement with EL or it is broken into a set of dihedral angles so that variation at the ends will not necessarily affect each member of the set. Table V is a numeric compilation of structural parameters associated with the structures shown in Figure 7. The PO, CC, CH, and N H bond lengths, as well as the CCOP dihedral angle, remain nearly constant as the size of the cluster is increased. The data for R-CC, R-CH, and R-PO further support our earlier assertions about the value of each in the infinite chain limit, while the R-NH value is estimated here (0.996 A) for the first time.
+
Boehm
13882 The Journal of Physical Chemistry, Vol. 97, No. 51, 1993 z
Y
TABLE VI:
Oligomers
X
X
Y
Y
Y
.z
X
Figure 7. Planar oligomers. Looking on the face of the backbone, it is apparent that the phenyl groups are very nearly perpendicular to it. TABLE V:
Clusters
MNDO Properties of Planar H-[NP(OPh)&-H
property
N= 1
N=2
N=3
R-PN (A) R-PO (A) R-CC (8) R-CH (A) R-CO (A) R-PH (A) R-NH (A) A-NPN (deg) A-PNP (deg) A-OPO (deg) A-POC (deg) A-NPH (deg) A-PNH (deg) DH-COPN (deg) DH-CCOP(deg)
1.591 1.629 1.41 1 1.090 1.358 1.365 0.996
1.583 1.621 1.411 1.090 1.349 1.375 0.995 110.4 143.9 91.2 134.2 104.0 114.5 67.0 89.6 0.006 0.22 1.40 -0.89
1.614 1.621 1.41 1 1.090 1.349 1.376 0.997 117.8 136.4 91.4 137.0 102.9 112.4 56.8 91.2
total energy (au) HL gapu(au) charge on P (e) charge on N (e)
99.8 124.4 107.4 114.1 137.6 91.8 0.006 0.27 1.05 -0.66
0.023 0.19 1.41 -0.85
The orbital energy differencebetween the highest occupied MO and the lowest unoccupied MO.
In the case of DH-CCOP, however, we see a significant shift toward higher values compared to the similar parameters inherent to the clusters of series 111;in series IV this value is approximately goo*
The change in DH-CCOP could result from the effective removal of steric factors,brought about by the decrease in A-OPO and the increase in A-POC (see Figure 6), or a change in the electronic character at the P site (compare Tables IV and V). In either case one should expect to see a large difference in the value of DH-CCOP between the N = 1 and N = 2 clusters followed by a relatively small difference between the N = 2 and N = 3 clusters. This is not observed. An alternative explanation is free of the above inconsistency. This explanation attributes the
MDNO Properties of H-[NP(OPh)zL-H
property
N= 1
N=2
R-PN (A) R-PO (A) R-CC (A) R-CH (A) R-CO (A) R-PH (A) R-NH (A) A-NPN (deg) A-PNP (deg) A-OPO (deg) A-POC (deg) A-NPH (deg) A-PNH (deg) DH-COPN (deg) DH-COP0 (deg) DH-CCOP (deg) DH-HPNXU (deg) DH-PNPN (deg) DH-NPNX(deg) DH-PNPN (deg) DH-NPNX(deg) DH-PNPN (deg) DH-NPNH(deg) off-planar (A)
1.592 1.629 1.411 1.090
0.224
0.489
0.841
105/25 89/15 303 -159 254 -121 233 119 310 1.203
total energy (au) HLgape(au) charge on P (e) charge on N (e)
0.006 0.27 1.05 -0.66
-0.028 0.22 1.26 -0.80
-0.065 0.20 1.32 -0.80
-0.040 0.19 1.48 -0.88
113.8
1.600 1.625 1.411 1.090 1.359 1.372 0.996 113.9 132.0 106.4/99.46 125.7 107.8
108.2
113.1
138.3
148.4
92.0 165.8
90.3 140.3 56.4 155.5
1.358
1.365 0.996 100.2 124.2
N=3 1.601 1.625 1.411 1.090 1.360 1.377 0.997 115.4 132.5 102.9/102.7 125.8 113.0 115.2 -25.4 89.1 383.2 -125.2 241.2 -75.9 214.9
N=4 1.590 1.613 1.411 1.090 1.358 1.378
0.996 113.2 141.1 106.4/111.0 134.4 117.2 112.4
X is a wild card that can represent H or P. The slash between values implies bivalue variables. The orbital energy difference between the highest occupied MO and the lowest unoccupied MO.
observed change to an effective removal of steric interference between the phenyl group@)and the phosphazene backbone upon (phosphazene) ring opening. As this is true regardless of the number of monomer units (N) in the chain, and DH-CCOP is shown to be invariant with respect to N as well, we view this as the probable cause of the noted difference between the two data sets. The behavior of the remaining parameters is erratic. Next, the planarity constraint was lifted, and the energy was reoptimized. Table VI (N = 1-3) is a compilation of minimum energy structural parameters under these (relaxed) conditions. Here we see that most of the erratic behavior has been eliminated. For example, now we learn additionally that R-CO, R-PN, A-OPO, and A-POC in the “unconstrained” oligomers are essentially identical to similar parameters in the ring compounds. We are able now to make reasonable estimates of R-PH (1.38 A), A-PNH (1 15O), and A-NPH (1 13O) as well. In the N = 4 column of the Table VI we see the effect of relaxation of the “uniquely valued” constraint on DH-CCOP and DH-COPO, where the replacement of DH-COPN with DH-COP0 effectively unties this parameter from the end group (H). Immediately we see behavior that is similar to that exhibited by the [NP(OH)21n rings. That is, given sufficient flexibility, the Ph (or H) portion of side groups on opposite sides of the cluster will not point in the same direction. Although we accept that the bulky ends of the side groups should point in opposing directions,we are cautiousabout our interpretationof the complete break in symmetry that is implied by the observedvalues(specific values available on request) of DH-COPN (rings) and DH-COPN (oligomers). We doubt this property transfers to poly(diphenoxyphosphazene), as X-ray diffraction studies of several related polyphosphazenes fail to show any evidence of this behavior.9-1 We believe that independent factors effect this break in symmetry for each of the two cluster types. End group effects are blamed in the case of pseudolinear clusters, and improper symmetry control is blamed for the [NP(OH)21nclusters. Since most of the structural parameters depend on DH-COP0 either directly or indirectly, and the constrained clusters are
MNDO Model Structure for Poly(diphenoxyphosphazene)
The Journal of Physical Chemistry, Vol. 97, No. 51, 1993 13883
TABLE VIII: MNDO Properties of Twisted H-[NP(OPh)&-H Clusters property N= 1 N=2 N=3 N=4 N=5 N=6 ma A-PNP (deg) 134.7 135.3 135.6 135.6 135.5 135.55 155.1 155.3 155.7 DH-COPN (deg) 143.7 149.0 153.7 154.7 DH-XNPXb (deg) 156.3 53.5 60.0 68.4 72.4 74.8 81.7 103.8 93.0 88.1 85.2 79.8 DH-NPNP(deg) 140.7 off-planar (A) 0.25 0.73 1.08 1.1 1 1.21 1.13 1.64 0.007 -0.029 total energy (au) -0.055 -0.089 -0.125 -0.162 -0.032Nd 0.23 0.20 0.18 0.17 0.16 0.13 HL gape ( a 4 0.27 1.07 1.28 1.36 charge on P (e) 1.40 1.42 1.45 1.51 -0.66 -0.79 charge on N (e) -0.86 -0.89 -0.91 -0.92 -0.96 The data in this column are the result of an extrapolation of the data in the previous columns. X is a wild card that can represent N, P, or H. For example, if N = 3, then XNPX includes HNPN, PNPN, and PNPH. The orbital energy difference between the highest occupied MO and the lowest unoccupied MO. dThis value means -0.032 hartrees/monomer unit and is crudely estimated from E/N for 6 1 N 1 3. 0.05
-,
1
- 0 . 2 5 ! . ,
1
2
. , . , 3
4
. , 5
. ,
6
. I
. , 1
8 N Figure 8. MNDO energy as a function of cluster size. Circles represent nonplanar H-[NP(0Ph)2ln-H chains. The + sign represents planar H-[NP(OPh)z-H chains. The X sign represents the twisted H-[NP(OPh)2].-H chains.
TABLE VII: Summary of MNDO Structural Parameters for the H-[NP(O~)IL-HPolymer distance (A) anale (dea) R-PN = 1.595 A-NPN = 115 A-OPO = 102 R-PO = 1.62 A-POC = 125 R-CC = 1.4106 A-NPH = 115 R-CH = 1.090 A-PNH = 113 R-CO = 1.359 DH-CCOP = 90 R-PH = 1.38 R-NH = 0.9961 ~
believed to represent a (frozen) chunk of the polymer more accurately than the relaxed cluster, the structure given by the final column ( N = 4) in Table VI should have little significance attached to it. An exception to this is with regard to the A-NPH parameter, which is now independent of the orientation of the side groups. On the basis of the above considerations (series 11, 111, and IV), we feel the data compiled in Table VI1 provide a reasonable estimate for similar structural parameters of poly(diphenoxyphosphazene). It is also reasonable to conclude from the above data that such polymers are not planar. Several structure determinations (from X-ray diffraction data) of related compounds verify this result.l@-l* With this in mind, we have performed a series of calculations under the following external constraints. One, the parameters listed in Table VI1 are fixed a t these values (A-OPO is fixed directly), while A-PNP is treated as before and the pseudosymmetry constraint on the side groups is maintained. Two, only one value is allowed for DH-COPN, where interference from H is not relevant because A-NPN = A-NPH. Three, exactly one unique value for each of the PNPN (including HNPN and PNPH) dihedral angles is allowed. Four, exactly one unique value for each of the NPNP dihedral angles is allowed. We thus are hypothesizing a helical chain structure, consistent with some experimental data.’“ This hypothesis is then supported by showing
that the helicalclusters consistently yield lower or similar energies than those of series IVa and IVb in spite of the fact that they are subject to greater user-imposed constraints (see Figure 8). Data from thesecalculations arecollected in Table VIII. While each of the structural parameters are approaching their respective asymptotic limits, the A-PNP parameter shows little variance with cluster size, holding steady at approximately 135.5’. In principle, the asymptotic limits of the remaining parameters can be determined by a simple fit to vi versus 1/ N curves, where 6 is the relevant parameter and N is the number of monomer units in thechain. In practice we have found that more data are required in order to extrapolate confidently to the infinite chain limit. To a large degree this need is offset by doubling the data set by employing the following trick. Suppose Q is a point that is R-NH/2 8, to the left of one terminating group H and R-PH/2 8, to the right of the other terminating group. Let us assign N to be one unit length and equivalent to the length of any one monomer unit. This unit is then negative if a monomer unit is inserted to the end of Q and positive for insertions to the right of Q. Since these two cases necessarily refer to the same physical situation, any function of 1/N F(l/N), must equal F(-l/N). Thus, the parameter value a t 1/N = 0 is found by interpolation rather than extrapolation, affording greater confidence in the fit. The “trick” is really just a justification for fitting to an even polynomial, which could be defended on other grounds as well. For example, we have already imposed the condition that {dF(1 / N)/d(l/N) = 0 at the origin) by presuming that sufficiently large clusters will breed bulk properties. The loss of the first odd power ( 1 / N ) is a consequence of this condition. Figure 9 is a plot of each of the parameters DH-PNPN, DH-NPNP, and DH-COPN versus 1/N. The fits to these curves suggest that DH-PNPN = 82O, DH-NPNP = 80°, and DH-COPN = 155.7’ in the limit of an infinite chain. The extrapolated value for ‘off-planar” in Table VI11 is derived from the extrapolated values of DH-NPNP and DH-PNPN. Now we may sketch a frozen segment of the infinite polymer. Figure 10 contains three views on the polymer backbone. View A is an imagined overview of the “ribbon” in the absence of helical twist. The remaining views are authentic and are derived from end-on and side-on perspectives. Lines are drawn between every fourth atom in order to bring out the rope-like quadruple helix character in the model. In this way it is clear that, although a complete revolution about the helix axis contains 40 monomer units, one strand of a given atom type (P or N ) is simply shifted by approximately 180’ relative to its partner of the same atom type. This renders an effective repeat unit that contains half of a pitch, instead of a whole pitch. It is a t least interesting to note that, although one unit pitch contains 40 monomer units, the radii of the (outer) P helices are 0.82 8, each. This is quite different from that of, say, a transtrans coil, whose radius would be approximately 1 order of magnitude larger. We feel this is an important difference because the twisted ribbon structure holds the (bulky) side groups in close proximity to one another, while the side groups may be free to
Boehm
The Journal of Physical Chemistry, Vol. 97, No. 51, 1993
13004
-
-
y = 155.71 12.108~"2 5 8 . 8 9 8 ~ 4R"2 = 1.OW
'
7
5
1
147 -0.5
-0.3
0.1
-0.1
0.3
0.5
l/N
-
y = 81.6% 2 5 6 . 7 3 ~ ~ +25 7 4 . 7 6 ~ 4R"2 = 0.999
Figure 11. Six-monomer-unit twisted cluster. Every other phenyl group pair has been delected in order to reduce clutter.
0.07-
0.060.05-0.5 150
-0.3
-0.1
lm
0.1
0.3
0.5
0.04-
y = 79.815 + 195.53~~2 + 1 9 1 . 7 7 ~ 4R"2 = 1.OW
4
-
1
0.03
0.02:. 0
I
.
20
I
40
.
.
,
60
I
80
.
I
100
.
I
120
.
. , . I
,
140
160
180
DH CCOP (degrees)
-0.5
-0.3
-0.1
im
0.1
0.3
Figure 12. Barrier for concerted rotation about CO bonds. The rotation is about each of the CO bonds in planar H-[NP(OPh)&-H and is concerted. Several variables are allowed to flex with this rotation including A-PNH, A-NPH, A-NPN, A-PNP, A-OPO, A-POC, R-PN, P-PO, R-CO, R-NH, and E-PH. There is a drastic change in several of these parameters in the neighborhood of the secondary well, but the continuous and periodic nature of the data is preserved.
0.5
Figure 9. Structural parameters as functions of cluster size. '
2
h . c) a
$
a
0
End On View 0.0
0.2
0.6
0.4
OS
1.o
1/N Side View
Figure 10. Underlying structure of the polymer backbone. In view A, the unshaded plane contains P atoms exclusively, while the shaded plane contains N atoms exclusively. Likewise, the outer circle of the end-on view and the outer strands of the side view contain P atoms exclusively, while the inner circle and strands contain N atoms exclusively.
rotate if the underlying structure were a coil. Figure 11 is one perspective of the six-monomer-unit cluster, which reveals that, indeed, the phenyl groups are held together close enough to hinder free rotation about either of the PO or CO bonds. Figure 12 is an energy surface corresponding to a concerted rotation of each
Figure 13. Partial atomic charges as a function of cluster size. The charge densityis averaged over P atoms (positive) and N atoms (negative). Data from the twisted chains are represented by X, while and o represent the (NP), and [NP(OH)& rings, respectively.
+
of the phenyl groups in planar H-[NP(OPh)2]3-H about the CO bond. The barrier shown here (already supportive of the above observation) can be taken as a lower limit to the MNDO barrier of similar rotations in the twisted polymer, as the phenyl groups are somewhat closer together in the twisted clusters than they are in the planar cluster. Although torsions about the PO and CO bonds are hindered for vibrationally hot conformers, it is easily imagined that nearly free rotation could occur about any one of the PN bonds in the backbone, which reinforces our earlier
MNDO Model Structure for Poly(diphenoxyphosphazene)
The Journal of Physical Chemistry, Vol. 97, No. 51, 1993 13885
DH O P N = 155.7'
C'
y
o,ao * A O P O = 102'
1.359A DH CC'OP = 90.d
,, , ,
i3
I
I
:
...-
*.--
/--* /---
;k.*
, ,, , , , ,, ,, I
d
DH NP'N'P = 79.8' DH P N P N = 81.7' Figure 14. MNDO model structure of poly(diphenoxyphosphazene). The primed symbols represent atoms that appear in multiple locations. presumption that conformational changes would involve lowenergy backbone deformations rather than side group deformations. Disclmsioa. Under series I1it was noted that each of theskeleton bond angles is well outside the bounds of a range of experimentally determined values of similar angles in similar compounds, while the values derived from series IV are consistent with e ~ p e r i m e n t . ~ ~ In this light, it becomes clear that whatever causes the discrepancy with respect to cyclic compounds is not relevant for pseudolinear compounds. For example, if PN bond polarization, as given by the MNDO method, is at the root of the problem with the cyclic clusters, then it must somehow diminish upon ring opening. In fact, the charge on P in the pseudolinearclusters is approximately 0.1 e greater than it is in cyclic compounds (Figure 13), where half of this differencecan be attributed to the differencebetween OH and OPh sidegroups. The greater charge on Pimplies greater P-P repulsions for adjacent P atoms and thus implies greater PNP angles, not smaller. On the other hand, if ring closure were the cause of exaggerated bond angles, then we should see similar behavior for real compounds. Although the experimental data necessary to check this idea is limited, it does suggest that large cyclic phosphazenes have somewhat larger PNP angles than pseudolinear phosphazenes; only the extent of this exaggeration of bond angles is overestimated by the MNDO method. Apparently, the forced ring closure, together with effects from P-P repulsions other than those from adjacent pairs, is enough to induce the obseved discrepancy. The band gap is also shown to be quite sensitive to the shape of the cluster. We have performed a series of Huckel band structure calculationsin order to further explore this dependence. Two artificial polymers with two monomer units per unit cell were employed: the cis-trans planar polymer and a helix with all N atoms in a plane perpendicular to the plane of all P atoms. In each case, the bond distances and angles were fixed according to Table VII. The COPO (and thus the COPN) dihedral angle was varied within each polymer type. For the cis-trans planar polymer, the minimum energy configuration occurs at COPO = 180°, and the representative polymer is clearly an insulator with a bandgapofmorethan2eV. For thehelixpolymer,theminimum energy configuration occurs at approximately COPO = 140' (trans phenyl groups), and this structure is approximately6.5 eV per unit cell more stable than the cis-trans planar structure. The
center (spanning 1.5 eV), the shape, and the dispersion (ranging from 0.1 to 1 eV) of the valence and conduction bands are all very sensitive to the COPO geometric parameter. We view this dependence as a reinforcement of our claim that a clear determination of polymer structure is necessary before band structures and investigations into the magnetic propertiesof this material can be taken literally. The band gap that we report in Table VI11 does not account for dispersion and is therefore likely to be an overestimate. On the other hand, it carefully accounts for structural data and should therefore provide a better estimate than ad hoc band structure calculations. Given the possible relationship between the band gap of this polymer and its magnetic properties, further investigations should be tailored to determine this quantity.
Conclusion We have shown that several structural features of phosphazene rings (R-PN, R-PO, R-CO, R-CC, R-CH, A-OPO, and A-POC) are transferable to poly(diphenoxyph0sphazene). Further, we have shown that small phenoxy-substituted phosphazenes do not possess a planar (NP) backbone, and we believe this is certainly true of the polymers as well. The pseudolinear clusters, with H end groups, reveal sufficient data to allow an estimate of R-NH, R-PH, A-PNH, A-NPH, and DH-CCOP. At this pointwemadeanassumption,baseduponx-ray diffraction studies of similar species, that the backbone forms a helix with a radius that is approximately one-half the width of a cis-trans planar backbone. This helix is allowed to twist by deviation of the DH-NPNP and DH-PNPN sets of dihedral angles away from their initial values 0 and 180°, respectively. Such clusters (up to six monomer units) then provide us with the remainder of the structural data for our MNDO model of poly(diphenoxyphosphazene). All of these data are summarized by Figure 14. As several of the parameters (especially the dihedral angles) are difficult to reproduce by deployment of computational techniques, the final MNDO model should be viewed as a selfconsistent model which qualitatively reproduces all properties of the real polymer. For example, the model suggests that 4 0 monomer units are contained in one unit pitch of the infinite helix. In reality this number may be 20 or 80 (etc.), but the qualitative picture of four strands of helices, chemically bound,
13886 The Journal of Physical Chemistry, Vol. 97, No. 51, 1993
that share a single very long pitch should be expected. A more serious potential shortcoming of the model regards the relative placement of the phenyl groups which share, through an oxygen atom, a common linkage to P. In our model, the important DH-COPN parameter is defined so that each phenyl group will fall onto opposite sides of the OPO plane whenever DH-COPN # f90. Although it seems like a reasonable position to take so that steric hindrance between all of the phenyl groups can be avoided, we have limited evidence to convince us that some other means cannot be employed to avoid steric hindrance between side groups in the real polymer. On the basis of the calculations we have performed, there is little doubt that dramatic changes in the orientation of the side groups will cause significant variations in several structural parameters of our MNDO model. Acknowledgment. The author would like to thank the INEL Supercomputing Center for its generous allocation of time on its Cray XMP. He would also like to extend a special degree of gratitude to Drs. Eric S. Peterson, Dennis C. Kunnerth, and Randall A. LaViolette, who went out of their way to make this work possible and provided many helpful scientific discussions concerning the phenomona which led to this work. The work was supported by the US.Department of Energy Office of Industrial Technologies, Advanced Industrial Concepts Division, under contract DOE Idaho Field Office DE-AC07-76ID01570. References and Notes (1) Gerzeski, R. H. Masters Thesis, University of Dayton, 1989, UMI 1339289. (2) Donaldson, A. D.; Epstein, M. M. Materials Production, In Energy Applications of High- Temperature Superconductivity; Dale, S. J., Wolf, S. M., and Schneider, T. R., Eds.; Electric Power Research Institute: Palo Alto, CA, 1990 Vol. 2, Chapter 9.
Boehm (3) Rodin, Y. P.; Molchanov, Y. M. Mekh. Kompoz. Mater. 1982, 4. 671. (4) Peterson, E. S.; Kunnerth, D. C. Private communications. (5) Frisch, M. J.; Head-Gordon, M.; Trucks, G. W.; Foreman, 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. GAUSSIAN90, Revision H; Gaussian, Inc.: Pittsburgh, PA, 1990. (6) Dewar, M. J. S.; Ford, G. P.; McKee, M. L.; Rzepa. H. S.; Thiel, W.; Yamaguchi, Y. J . Mol. Srrucr. 1978, 43, 135. (7) Dewar, M. J. S.; Thiel, W. J . Am. Chem. SOC.1977, 99, 4907. (8) Dewar, M. J. S.; McKee, M. L.; Rzepa, H. S. J . Am. Chem. Soc. 1978, 100, 3607. (9) Take the nitrate radical as an example, MNDO (a) compared to ab initio (b). (a) Dewar, M. J. S.; Rzepa, H. S. J . Am. Chem. SOC.1978, 100, 784. (b) Boehm, R. C. Ph.D. Thesis, University of Michigan, 1991, UMI DA9 123979. (10) Bishop, S. H.; Hall, 1. H. Er. Polym. J . 1974, 6, 193. (11) Allcock, H. R.; Kugel, R. L.; Stroh, E. G. Inorg. Chem. 1972.11, 1120. (12) Allcock, H. R.; Kugel, R. L.; Valan, K. J. Inorg. Chem. 1966, 5, 1709. (13) Cox, B. N.; Bauschlicher, C. W., Jr. Surf.Sci. 1981, 108, 483. (14) Boehm, R. C.; Banerjee, A. J . Chem. Phys. 1992, 96, 1150. (15) Cui, C. X.;Kertesz, M.; Jiang, Y. J. Phys. Chem. 1990, 94, 5172. (16) LaFemina, J. P.; Duke, C. B.; Paton, A. J. Chem. Phys. 1988,89, 2668. (17) Kirtman, B.; Nilsson, W. B.; Palke, W. E. Solid State Commun. 1983, 46, 79 1. (18) Duke, C. B.; Lipari, N. 0.;Salaneck, W. R.; Schein, L. B. J. Chem. Phys. 1975,63, 1758. (19) Ferris, K. F.; Risser, S. M. Chem. Phys. Lett. 1990, 174, 333. (20) Zunger, A. Phys. Rev. E 1978, 17, 642. (21) Hoffman, R. Solids and Surfaces: A Chemist's View of Bonding in Extended Structures; VCH: New York, 1988. (22) Wagner, A. J.; Vos, A. Acta Crystallogra. 1971, 827, 51. (23) Marsh, W. C.; Trotter, J. J . Chem. SOC.A 1971, 169. (24) Allcock, H. R.; Tollefson, N. M.; Arcus, R. A.; Whittle, R. R. J . Am. Chem. SOC.1985, 107, 5166.
