The analysis of mixed-halide HMMCs is restricted to two main objectives. Firstly, the assignment of peaks that appear only in the spectra of mixed-halide HMMCs and an accurate description of the chain motion to which they relate. Secondly, an assessment of which model and set of force constants reproduces the observed spectra most closely. Only qualitative results can be derived because so many assumptions are made in producing the simulated plots. For instance, the relative intensities of the peaks in the simulated spectra will not be accurate. Raman intensities in the model are calculated from changes in bond distances. This is a reasonable approximation for a single-halide chain, but not for a system containing three different types of unit cell that do not have the same excitation profile.
Where possible, the force constants derived in the analysis of [Pt(en)2][Pt(en)2X2](CI0 4 ) 4
(X = Cl or Br) are retained in the modelling of the mixed-halide spectra, although three new forces have to be defined (see Figure 4.5.4). For simplicity, only cases where k2b and k2c are
equal are considered. The remaining force constants kpb and knc (n = 1, 3-6) take the values listed in Tables 4.5.4-5. Since knc = knb for n = 4, 5 or 6, k4m and kem are given the same
values as k4c and kgc respectively. The model was tested with kam equal to either ksc or ksb,
but the calculated spectra did not appear to differ significantly, so ksm is defined as the mean of k3c and ksb. The sets of force constants derived for each value of k2 are listed in Table 4.5.6.
'3 m ^4 m
--- M---
-BT'/wwwMiv w vw vvC I'/\/\/\/\/\/'M " v\/\/\/\/^B rvvvvvv w w w x ---
4--- ^ ---►
Figure 4 .5 .4 Diagram showing the three extra force constants defined for the mixed-halide model.
Three computer-generated HMMCs are investigated in this section. PtBro.s is modelled as a random (R) or an ordered (O) chain, while PtBro.25 is modelled only as a random chain.
The models are termed TZa, where T is the type (R, O or B), Z is the force constant data set (A, B or C) and a relates to the complex PtBr^ that is represented. The models of PtBro.5 are
using the unit cell probabilities determined in the solid-state NMR study; the models of RBro.2 5 contain just twenty-five chains. Each model was submitted to VibraGO to obtain the
vibrational frequencies and atomic displacements, which were processed by the program INTENS to give theoretical infrared or Raman spectra. The infrared spectra are not of great interest, because the experimental results are too poor to allow useful comparisons, and only the vi and V2 modes are evaluated in the Raman spectra.
Table 4.5.6 Force constants used in modelling the mixed-halide complexes
[P t(en)2][P t(en )2Cl2.2aBr2a](C I0 4)4
Force Previous Intemal Modelling run
constant label coordinate A / N m'^ B / N m'^ C / N m'^
K2 k2c m"-ci 0.2 0.4 0.6 K4 k2b M"-Br 0.2 0.4 0.6 Ki kic m'^'-ci 1.844 1.718 1.579 K3 kib M'^'-Br 1.303* 1.246* 1.166* K s ksc CI-M'^-CI 0.010 -0.038 -0.090 K y ksb Br-M'^-Br -0.075* -0.150* -0.240* K e ksm Br-M'^-CI -0.033 -0.104 -0.165 k^c ci-m"-ci K e k4b Br-M"-Br -0.035 -0.024 -0.002 k4m Br-M"-CI K g ks c M'^-CI-M" -0.02 -0.02 -0.02 ksb M'^-Br-M" K 1 0 kec» k e b i kem m'v.m'v 0.30 0.30 0.30
* the values o f k n j and a r e known to be incorrect (see text).
The Raman spectra calculated for the three models are displayed over the range 150-400 cm'^ in Figures 4.5.6-8. They have some general features in common with each other. There are large signals in only four areas, significantly fewer than in real spectra. The resonances at 165-175 cm'^ and 305-315 cm’^ correspond to the vib and vic modes respectively. The atomic displacements associated with the peaks in the other two regions show that they involve vibrations of the mixed-halide unit, [CIPt'^Br]. The signals at
ca. 200 cm*^ result from the breathing mode, while the asymmetric vibration V2m gives the
Vibra90; the subscripts denote the vibration (1 for vi, 2 for V2) and the atom (c = Cl, b = Br and
m = metal), vim mostly involves motion of bromine atoms. dib is roughly 1.8-2.0 times the size of die when k2 = 0.2 N m "\ and a further 10 % bigger when k2 = 0.6 N m "\ By contrast
the V2m mode involves almost no movement of the bromine atom since d2b is about a tenth of
d2c, and only a third of d2m- The movements of the atoms account for the isotopic structure of
the two resonances. The V2m signal consists of two peaks that relate directly to the two chlorine
isotopes: the v2[^^CI-Pt'^-Br] peak is roughly three times more intense than the v2[^^CI-Pt'^-Br]
peak, and is at more than 6 cm'^ higher wavenumber. v i^ shows no more isotopic structure than vib does in [Pt(en)2][Pt(en)2Br2](CI0 4 ) 4 since it involves relatively little movement of the
chlorine atoms.
^1m Yzm
Br--- ---a ---Br--- M>v---Cl---
Ab Am Ac Ab Am Ac
Figure 4 .5 .5 Exam ples o f vim and V2m m odes for single units o f [BrPf^C IJ. The dashed arrowheads represent approximate relative atomic displacem ents an d are not to scale with the bond lengths.
The influence of the force constant k2 on the structure or wavenumber of a given peak
depends on which atoms have the greatest amplitude in the vibration to which it relates. Modes in which chlorine atoms are the more mobile are largely unaffected by k2, so neither vic
nor V2m varies much when the force constant set is changed. In contrast, vib and vim separate
into two or even three peaks as k2 is increased. For instance, when k2 = 0.6 N m '\ the
approximate positions of the zone centre vib modes for segments of one, two or three units are 173, 170 and 167 cm "\ respectively. These wavenumbers differ sufficiently for individual peaks to be distinguished in the simulated spectra.
There are so few differences between the spectra calculated for RZq.sand OZq.sfor all Z
that it is hard to favour one model over the other. The vic resonance has more of its intensity in the high energy region in OZq.sthan it does in RZq.s, but the distinctions between their vib modes are more significant, particularly when k2 = 0.4 or 0.6 N m "\ RCq.s has two prominent
only a weak signal at ca. 173 c m '\ This pattern is repeated for RBq.s and OBq.s, although the highest energy peak is at ca. 170 cm'^ because of the smaller dispersion.
The influence of the bromine content on the calculated spectra can be seen by comparing the results for R2 ^ .5 and RZ0.2 5. Neither vim nor V2m changes much in profile as the
proportion of bromine is increased, but vic and v^b are significantly different. v«ic for R Z 0 . 2 5 has
similar shape to v^c for PtCI (or RZq.q for that matter), but the isotopic pattern for v<ic in RZq.s is closer to the 9 :6 :1 associated with Pt'^ complexes. RZ0.2S contains few [BrPt'^Br] units, so
long segments of PtBr are rare and the most intense peak in the v^b region is that at highest wavenumber for k2 = 0.4 or 0.6 N m '\
All four of the major resonances seen in the theoretical spectra of the mixed-halide HMMCs are observed in real Raman spectra, although the wavenumbers of some peaks do not match up precisely, mainly because of the effects of dispersion (see section 4.5.7). However, the wavenumbers predicted for vim are too low while those for V2m are too high, even when
dispersion is taken into account. The energy of vim can be raised by increasing the value of k3m, but it is more difficult to adjust the energy of V2m as it requires the ki and k2 terms to be
reworked from first principles. The experimental spectra contain other peaks for which the models fail to account. The majority of these are overtone or combination modes, but three of the peaks in the range 100-350 cm'^ result from fundamentals. They are labelled v^b, v^c and Vg in the tables in section 4.4.
(a) Model RAg 5
w
(b) Model RBgg c (c) Model RCq 5 250 200 300 350 400 Wavenumber/cm'Figure 4 .5 .6 Theoretical Ram an spectra for PtBrp.s using the models (a ) R Aq.s, (b) R Bq.s and (c) R Cq.s.
(b) Model OB05