Article pubs.acs.org/JPCA
Using Density Functional Theory To Interpret the Infrared Spectra of Flexible Cyclic Phosphazenes Adrian K. King,* David F. Plant, and Peter Golding AWE Aldermaston, Reading, Berkshire RG7 4PR, United Kingdom
Michael A. Lawson and Paul B. Davies Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom S Supporting Information *
ABSTRACT: The cyclic phosphazene trimer P3N3(OCH2CF3)6 and the related cyclic tetramer P4N4(OCH2CF3)8 have been synthesized, isolated and their vapor-phase absorption spectra recorded at moderate resolution using an FTIR spectrometer. The interpretation of these spectra is achieved primarily by comparison with the results of high-precision density functional calculations, which enable the principal absorption features to be assigned and conclusions to be drawn regarding the geometries and conformations adopted by both molecules. These in turn allow interesting comparisons to be made with analogous cyclic halo-phosphazenes (such as P3N3Cl6) and other related ring compounds. The highly flexible nature of the two cyclic phosphazenes precludes a complete theoretical study of their potential energy hypersurfaces and a novel alternative approach involving the analysis of a carefully selected subset of the possible molecular conformations has been shown to produce satisfactory results. The two cyclic phosphazene oligomers have been proposed as the major low-to-medium temperature pyrolysis products of the parent polyphosphazene (PN(OCH2CF3)2)n, and the identification of vibrational absorption features characteristic of each molecule will enable future studies to test the validity of this proposition.
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proposed that below ∼500 °C the pyrolysis products of PPZ-T are the cyclic oligomers, primarily the trimer and tetramer, P3N3(OCH2CF3)6 and P4N4(OCH2CF3)8.5,6 In this work we report the infrared spectra of the cyclic trimer (PZ-T3) and tetramer (PZ-T4), recorded in the gas and condensed phases, and their vibrational assignment. The latter was achieved with the aid of complementary density-functional theory (DFT) calculations of their molecular structure and harmonic vibrational frequencies. Both molecules can be synthesized from the cyclic precursors P3N3Cl6 and P4N4Cl8. P3N3Cl6 has been shown to have a planar ring structure (of D3h symmetry) in the gas phase,7,8 and the infrared and Raman spectra of cyclic P4N4Cl8 have been comprehensively assigned by Varma and coworkers.9 It has a “skew-tub” (S4) conformation at low temperatures and a “skew-chair” (Ci) conformation at higher temperatures.
INTRODUCTION The polyphosphazenes comprise an extensive family of polymers built on a −[PN]n− backbone. A wide range of side chains (R1 and R2, Figure 1a) may be attached to this
Figure 1. (a) General structure of polyphosphazene molecule and (b) structure of PPZ-T.
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backbone, leading to products with a similarly diverse range of physical and chemical properties.1 One polyphosphazene in particular −[NP(OCH2CF3)2]n−, Figure 1b (hereafter referred to as PPZ-T), has proven to be a useful synthetic intermediate and has been used both by ourselves2 and by others3 as a precursor to a wide variety of product polymers. As part of an ongoing study into polymer degradation mechanisms for certain random copolymers derived from this material,4 we have examined the thermal decomposition of this material as a benchmark for polyphosphazene pyrolysis. Earlier studies have Published 2012 by the American Chemical Society
EXPERIMENTAL METHODS a. Oligomer Synthesis. PZ-T3 was synthesized by substitution from P3N3Cl6 using the method of Carriedo et al.10 P3N3Cl6 was supplied by Sigma-Aldrich and purified by Received: October 2, 2011 Revised: December 15, 2011 Published: January 19, 2012 2080
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Hessian matrix. No empirical scaling factor was applied to these predictions. All calculations were undertaken using the “Gaussian 03” computational software package14 running on a multiprocessor SGI-Altix supercomputer, each run typically taking 96 h to complete. Predicting the vibrational spectrum of even a relatively small phosphazene oligomer is a nontrivial task for several reasons. First, because there are many atoms and hence many electrons to consider, the calculations are computationally expensive, even when using a relatively modest basis set. Second, the molecules are flexible and able to adopt a large number of stable conformations; a simple steric analysis of PZ-T3 suggests 312 (greater than half a million) stable conformations, though not all would be spectroscopically distinguishable. These conformers correspond to local minima on the potential energy surface and a complete analysis of a molecule would involve systematically identifying all these minima in conformation space and performing geometry optimizations within each to deduce the structure of each conformer. A prediction of the vibrational frequencies of each conformer would then be required and the final prediction of the vibrational spectrum would be a weighted average (based on Boltzmann populations of each conformer at the temperature of interest) of all the different conformations. Clearly such a methodology is not practicable in terms of time and computational resources, so a more pragmatic approach was adopted. This involved, for each oligomer, the careful selection and detailed analysis of a small number of conformations considered most likely to be at or near the “ground” conformational state based on steric arguments, comparison with analogous ring compounds and an appropriate amount of chemical intuition. To the best of our knowledge, the detailed conformational analysis (albeit selective, rather than exhaustive) of a molecule exhibiting this level of flexibility in unprecedented. Although Furer et al.15,16 have used DFT methods to model the spectra of various dendritic macromolecules based on cyclic triphosphazene rings, their analysis has generally been limited to the identification of the global minimum conformer for each system studied and little consideration appears to have been given to the influence of higher energy conformations on the observed spectra.
recrystallization from cyclohexane before use. Reaction with CF3CH2OH and CsCO3 was carried out in acetone at 70 °C for 24 h and the product separated by evaporation and two recrystallizations from acetone. Product purity was confirmed by 31P and 19F NMR spectroscopy (characteristic resonances were observed at +18.79 and −75.04 ppm, respectively). PZ-T4 was also synthesized by the Carriedo method, with suitable adjustments made to the reaction stoichiometry to account for the additional PNCl2 unit. The P4N4Cl8 precursor was synthesized and isolated using the method of Lund et al.11 The purity of the resulting PZ-T4 product was confirmed by 31 P and 19F NMR spectroscopy, with characteristic resonances at −0.31 and −75.11 ppm. b. Infrared Spectroscopy. All infrared spectra were recorded using a Perkin-Elmer “Spectrum 100” FTIR spectrometer fitted with a KBr beamsplitter, KBr windows, and a liquid nitrogen-cooled mercury cadmium telluride (MCT) detector. Spectra were recorded at a resolution of 0.5 cm−1 and an interferometer scan rate of 1 cm s−1. A total of 64 individual scans were coadded to produce each spectrum, the coaddition process taking approximately 5 min. Analysis of the cyclic oligomers was undertaken using a commercial heated cell (SPECAC Storm 10H) mounted inside the sample compartment of the spectrometer. The cell, which was 47 mm in (internal) diameter and had a path length of 10 cm, could be evacuated, and was fitted with an internal K-type thermocouple. It was fitted with KBr, ZnSe, or CaF2 windows when in use and was operated at temperatures up to either 150 °C (KBr) or 250 °C (ZnSe, CaF2), respectively. Each experiment used around 100 mg of sample, which was placed within a small, open glass vial, laid lengthwise on the bottom of the cell. The cell was then heated to 50 °C and pumped overnight to remove residual solvent. Each experiment was conducted “cyclically”, i.e., by first raising the temperature incrementally from 50 °C to the target maximum temperature and then decreasing it back to ambient, recording a spectrum at each stage. Increments of 20 °C were made and equilibration at each new temperature typically took approximately 5 min. After the cell had cooled, a final spectrum was recorded and the cell evacuated for 10 min before recording a post-evacuation spectrum. This corresponded to the transmission spectrum of those volatized products that had condensed upon the cell windows. The difference between the final spectrum and the post-evacuation spectrum corresponded to the spectrum of any gaseous products present at ambient temperatures. A solid-state transmission spectrum of each oligomer was also recorded. This was achieved by solvent-casting a sample in acetone onto a KBr disk. c. Density Functional Theory (DFT) Calculations. All the calculations employed the well-known B3LYP hybrid exchange−correlation functional to calculate the electron density.12 The basis set chosen was the “6-31G” set of splitvalence Gaussian functions,13 augmented by a single set of diffuse functions and a single set of d-type polarization functions on each heavy (non-hydrogen) atom and by a set of p-type polarization functions on the hydrogen atoms. The overall calculation was therefore B3LYP/6-31+G(d,p). Each calculation involved a molecular geometry optimization, where the potential energy was minimized by stepwise adjustment of the internal molecular coordinates, followed by prediction of the harmonic vibrational frequencies and fundamental transition intensities, based on the evaluation of the corresponding
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RESULTS a. PZ-T3 Trimer Calculations. The conformation of the PZ-T3 molecule is defined by hindered rotation about its six P−O bonds and six O−C bonds. Figures 2 and 3 show Walden
Figure 2. Walden projections for the P−O bond conformations of PZT3 and PZ-T4.
projections for these two types of bond. The P−O bond conformations are defined by the relative positions of the CH2CF3 and OCH2CF3 groups, viewed along the P−O bond (from O to P) and with the P3N3 ring oriented uppermost. Similarly, the O−C bond conformations are defined by the 2081
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The starting structures for the remaining six geometry optimizations performed were all derived from this initial, symmetrical conformation. Two of these (structures 2 and 3a, Figure 4) were obtained simply by changing the conformation of one P−O bond to each of its two other possible conformations (“anti” and “left”, Figure 2). Similar variation of the conformation of one of the O−C bonds (“left” and “right”, Figure 3) produced a further two (structures 4 and 5). The remaining two starting points were obtained by adjusting two of the P−O bond conformations to the “anti” form. The two bonds chosen were located on different faces of the P3N3 ring, and involved either the same (structure 7, Figure 4) or different (structure 6, Figure 4) P atoms. Table 1 shows the results of these seven calculations along with energies, rotational constants, and dipole moment components for the corresponding optimized conformations. Figure 4 shows the stable conformations found. Several points may be made regarding these results. First, it appears that structure 1 (the most symmetrical of the initial structures), though a stable conformation, is not the most energetically favorable. Structure 2, where one P−O bond conformation is altered (“anti”) so as to allow one of the CH2CF3 side groups to partially overhang the P3N3 ring, is also stable and has the lowest energy, presumably the change in P−O bond conformation reduces the steric strain between the bulky side groups. In contrast, structure 3a, where a single P−O bond conformation is changed (“left”) so as to have the side group facing in the “opposite” direction to the other five, is energetically unstable. Interestingly, the conformation into which the molecule relaxes (structure 3, Figure 4) retains the “left” conformation of one P−O bond and, instead, changes the conformation of two other bonds to accommodate it, both within the side group that shares a P-atom with the group in which the P−O bond was initially altered. Within this side group the P−O bond converts to the “anti” conformation, moving the associated OCH2CF3 moiety over the P3N3 ring and reducing the overlap between this side group and its counterpart on the other face of the ring. The O−C bond converts to an “ eclipsed” conformation, where the P−O bond and one of the C−H bonds are very nearly coplanar. The fact that structure 3 is a stable one (albeit one significantly disfavored in energy relative to the ground state) highlights an interesting phenomenon: the conformation adopted by a given side group may be influenced more strongly by the need to minimize steric strain between it and its neighboring groups than by the need to adopt a conformation that minimizes strain internally. Structures 4 and 5 were initially identical to structure 1, save that one O−C bond was adjusted to each of the two other conformations it could adopt (“right” and “left” respectively). In both cases the optimization procedure produced a structure virtually identical to the optimized form of structure 1. This sheds further light on the behavior of the O−C bond conformations. It would appear that the energy barriers to their interconversion are either very low or nonexistent and the O−C bonds are essentially “free” to rotate to minimize their energy in response to any changes in the P−O bond conformations, even to the extent of adopting “eclipsed” conformations that are usually considered to correspond to energy maxima, as seen in the aforementioned behavior of structure 3a. The final two structures, 6 and 7, constitute an extension of the conformational variation that produced structure 2. By
Figure 3. Walden projections for the O−C bond conformations of PZT3 and PZ-T4.
relative positions of the CF3 group and the P atom, viewed along the O−C bond (from C to O) with the P atom oriented uppermost. Seven different conformations of the PZ-T3 molecule were investigated. Their structures were closely inter-related and derive from the one (structure 1, Figure 4) that was initially
Figure 4. Structures of the stable conformations found for PZ-T3.
judged (on grounds of minimized steric hindrance) to be the most plausible candidate for the molecular ground-state conformation. This structure has two notable features. The first is the planar P3N3 ring, a feature shared with analogous molecules like P3N3Cl67 and P3N3Br6.8 The second is the highly symmetrical nature of the molecule; the conformations of all six P−O bonds are identical (all “right”, Figure 2), as are the conformations of all six O−C bonds (all “anti”, Figure 3). 2082
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Table 1. Structures, Relative Energies, Rotational Constants, and Dipole Moment Components for the Seven PZ-T3 Trimer Structures Investigated structure 1 2
3
4
5
6
7
initial conformation all PO = “right”, all OC = “anti” five PO = “right” one PO = “anti” all OC = “anti” five PO = “right” one PO = “left” all OC = “anti”
E/Ha
ERel/cm−1
A/GHz
B/GHz
C/GHz
μa/D
μb/D
μc/D
same as initial
−3901.6653885
+279.6099
0.0511502
0.0509071
0.0425668
−0.0957
−0.0572
−0.0134
same as initial
−3901.6666625
0
0.0539144
0.0479592
0.0470165
−0.3785
−1.0257
−0.3780
+421.6315
0.0594927
0.0499312
0.0472245
−2.6450
0.8938
2.3397
+264.7954
0.0521133
0.0509977
0.0432733
−0.4041
−0.4038
−0.4950
+265.3221
0.0524154
0.0507514
0.0433540
0.2871
0.3471
−0.1966
+100.3435
0.0506832
0.0503775
0.0491723
0.1105
0.0837
2.1016
+661.6044
0.0532734
0.0506792
0.0476871
−0.4326
−1.3535
3.4793
final conformation
four PO = “right” −3901.6647414 one PO = “left” one PO = “anti” five OC = “anti” one OC = “eclipsed” converted to structure 1 −3901.6654560
all PO = “right”, five OC = “anti” one OC = “left” all PO = “right”, converted to structure 1 −3901.6654536 five OC = “anti” one OC = “right” four PO = “right” same as initial −3901.6662053 two PO = anti all OC = “anti” (different P atoms, different faces) four PO = “right” same as initial −3901.6636480 two PO = anti all OC = “anti” (same P atom, different faces)
allowing one side group to adopt the “anti” P−O bond conformation on each side of the P3N3 ring, one might postulate that further reductions in the energy of the system may result. The choice of which two groups to alter is therefore restricted to those attached to the same (structure 7) or dif ferent (structure 6) P atoms. The results are slightly surprising, in that whereas, as expected, both correspond to stable conformations, their energies are, respectively, 661 and 100 cm−1 higher than that of structure 2. This appears to suggest that although the relief of steric strain between the side groups acts to reduce the energy of the system (as per structure 2), there must be some additional “through-ring” interaction between the two “anti” side groups that counteracts this effect. This is supported by the observation that structure 7, where the two “anti” groups share a P-atom and therefore occupy “mirror image” positions on either side of the ring, is significantly disfavored in energy. A couple of final structural observations may be made. First, in some cases (structures 2, 3, and 6), a small deviation from a completely planar ring was observed in the optimized structures. In the case of halophosphazene analogues such as P3N3Cl6, such small deviations would be expected to have significant effects upon the observed spectra as they lead to a reduction in the overall symmetry of the molecule. For PZ-T3 this is not the case as, with the exception of structures 1 and 7 (which are of D3 and C2 symmetry, respectively), all the conformations studied are of the C1 point group and reduction of symmetry cannot occur. Nevertheless, these small deviations are an indication that the conformations adopted by the side groups may have a small influence upon the ring structure. Second, although structures 1, 4, and 5 all optimized to the
same conformation, their resulting energies and rotational constants were not identical, the differences being generally on the order of 2−3%. The dipole moments, it should be noted, displayed significantly greater variation. This behavior is indicative of a very “flat” potential energy minimum, where significant changes in the molecular geometry produce only a small change in the energy. It is possible that this observation is related to the apparently unhindered rotation about the O−C bonds and that, taken together, they may be considered indicative of a generally very flexible molecule. Having completed the structural calculations, predicted infrared absorption spectra were obtained for each stable conformer. These were produced by representing each harmonic mode with a Lorentzian function, centered at the appropriate wavenumber and scaled in proportion to the mode intensity. The full width half-maximum (fwhm) of these Lorentzians was kept the same for all modes and was set at an empirical value of 6 cm−1 as this gave peak widths broadly consistent with those observed in the infrared spectra. A Boltzmann-weighted sum of the individual conformer spectra was then produced. b. PZ-T4 Tetramer Calculations. The conformation of the PZ-T4 is defined by hindered rotation about the eight P−O bonds, the eight O−C bonds and, in addition, by the conformation of the P4N4 ring. The PZ-T3 Walden projections shown in Figures 2 and 3 are also applicable to the P−O and O−C bonds within PZ-T4. A brief consideration of analogous 8-membered ring compounds, such as 1,3,5,7-cyclooctatetraene17 and P4N4Cl8,9 suggests several possible ring structures, the six judged the most likely to be stable are shown in Figure 5. Briefly, they consist of (a) a D4h planar ring structure, 2083
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perhaps unsurprising that, during optimization, structure 6 relaxes to the ground-state form. Clearly, in this case the energy barrier to pseudorotation is sufficiently low that the “skew-tub” form is not a stable conformer. Contrasting behavior is observed with structures 12 and 5, where an “N-planar boat” pseudorotates to a “skew-tub”. Further rotation to a “P-planar boat” does not occur, either due to a high barrier or due to the “skew-tub” being the lower energy form. This section concludes with two general observations. First, having predicted that, in contrast to both P4N4Cl8 and 1,3,5,7cyclooctatetraene, for PZT-4 the “P-planar boat” is the lowest energy ring conformation, it is interesting to consider the energy ordering of the remaining ring forms. Three forms (“planar”, “crown”, and “N-planar boat”) are best considered “high” in energy as the only stable examples are at least 900 cm−1 above the ground state (structures 1, 3, and 10). The energetic “middle ground” seems to be occupied by the various “skew-tub” and “skew-chair” forms though their ordering appears random. Second, as alluded to above, the barriers to ring interconversion appear generally lower than to P−O bond conformational change, though still higher than those to O−C bond rotation, which (as with the trimer) appear to be essentially nonexistent, leaving the O−C bonds free to adopt near-eclipsed conformations (structures 2 and 14) to minimize the energy of the system. c. PZ-T3 Trimer Spectroscopy. Figure 7 shows the infrared spectrum of PZ-T3. The uppermost trace shows the solid-phase transmission spectrum of a PZ-T3 sample recrystallized from acetone. The middle trace shows the corresponding vapor spectrum, recorded at 100 °C using the heated cell apparatus described above. The bottom trace shows the DFTbased prediction of the vapor-phase spectrum. All three spectra are characterized by a dozen absorption features in the range 500−1500 cm−1, and the positions of these features are listed in Table 3, together with their assignment based on the DFT predictions. It should be noted that each of the absorption features corresponds to several vibrational modes (for each constituent conformer); therefore, the assignment for each absorption feature is intended to give an indication of the type of vibrational motion responsible, rather than a precise identification of the individual modes. d. PZ-T4 Tetramer Spectroscopy. Figure 8 shows the infrared spectrum of PZ-T4. As with the trimer, the upper trace corresponds to the solid phase, the middle trace to the vapor phase (in this case at 80 °C), and the lower trace to the DFT-based prediction. As with the trimer spectra, there are a dozen absorption features present in the 500−1500 cm−1, range and these are listed in Table 4, along with assignments based on the DFT predictions.
Figure 5. Possible P4N4 ring structures for PZ-T4: (a) planar; (b) crown; (c) skew-chair; (d) P-planar boat; (e) skew-tub; (f) N-planar boat.
(b) a C4v “crown” structure with P−N bonds alternating upward and downward, (c) the Ci “skew-chair” form, (d) a D2d “boat” form in which all four nitrogen atoms adopt a planar arrangement, (e) the S4 “skew-tub form (generally accepted as the ground-state structure for both the aforementioned cyclocompounds), and (f) another D2d “boat” form, in this case one in which all four phosphorus atoms adopt a planar arrangement. Structures d−f may interconvert by pseudorotation. The selection of starting structures for the PZ-T4 calculations reflected this extra degree of molecular flexibility; either two or three structures were chosen for each of the six ring conformations. The P−O and O−C bond conformations of these structures were adjusted to produce either the conformation judged the least sterically hindered or a closely related conformation, usually obtained by adjustment of one or more P−O bond conformations. Table 2 lists the fourteen structures studied, the results of the associated calculations and their relative energies, rotational constants, and dipole moment components. As with the trimer calculations, predicted infrared absorption spectra were generated for each stable conformation and a Boltzmann-weighted sum of these taken to produce the final predicted spectrum. Figure 6 shows the structures of a representative selection of the stable conformations found. As might be expected, the results of the tetramer calculations present a somewhat more complex picture than the trimer. Starting with the structures of the ring, it is notable that the ground-state conformation appears to be one of the “P-planar boat” forms (structure 8, Figure 6), with all P−O bonds in the “right” conformation and all O−C bonds “anti”. In contrast to the trimer, moving one of the P−O bonds to the “anti” conformation (structure 9, Figure 6) does not lower the energy of the system, though the resulting structure is still the third lowest in energy. Structure 2, which was second lowest in energy, underwent a change in ring conformation during the optimization process, relaxing from a planar ring to a somewhat distorted “P-planar boat” form with all P−O and O−C bond conformations unaltered. This suggests that the potential energy barriers to ring conformational change may be lower than those corresponding to changes in the P−O bonds. As six of the fourteen initial structures underwent a change of ring conformation during optimization, it would appear that this idea has some merit. Structure 6 is also of interest in this respect. It corresponds to the ground-state form except that the ring is in the “skew-tub” conformation rather than the “P-planar boat”. As these two may interconvert by pseudorotation, it is
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DISCUSSION We begin this section by making some general points about the observed spectra and their correlation with the calculated spectra. In general, the match between the two is very good, especially when the size and complexity of the molecules under investigation is taken into account. The match between theory and experiment is, understandably, slightly better for the trimer than for the tetramer. The positions of the absorption features are generally predicted to within a few cm−1, the percentage error for a given feature being, on average, around 0.9% for a trimer peak and around 1.1% for a tetramer peak. The error distribution is similar for the two species: the peak errors are low (
