Introduction:
When exposed to radiation the fate of molecules may differ upon how they may redistribute the impinging radiation. It is perfectly possible that the said molecule may dissociate although it is known that a lot of molecules have internal methods that allow them to redistribute this energy intramolecularly essentially allowing themselves to be ‘protected’ against radiation damage.
Being able to create a controlled environment of molecule-radiation interaction, one may be able to probe the effects of the radiation on the molecules and elucidate exactly how the energy becomes dispersed throughout the molecule. Benzene derivatives, in particular, are frequently occurring molecules in biology, particularly in amino acids such as tyrosine and phenylalanine. Benzene is a simple molecule which is fairly well understood hence is a good place to start when analysing radiation impact. Looking at each vibration individually and comparing the changes in the vibrational character and energy across a whole range of substituted benzene molecules makes it possible to see the effects of energy dispersal due to both electronic effects and reduced mass effects arising from substituting atoms across the ring.
The initial problem that must be overcome in the spectroscopic study is that there is no universal vibrational labelling scheme that currently applies to a large series of substituted benzenes. The ‘original’ labelling scheme, known as the Wilson scheme, provides a unique way to describe the 30 ring localized modes of vibration of Benzene itself. The labels each describe the movement and directionality of each atom in the vibrational motions. The importance of having a detailed vibrational labelling scheme is that, upon electronic excitation or ionization, one can apply a consistent label to the peaks which is related to a particular vibrational motion. Doing so allows us to relate geometry changes and other photo-physical properties, such as internal conversion, intersystem crossings etc, to a specific vibration.
The Wilson modes (Fig.1) themselves are perfectly useful for the benzene molecule. Problems begin to arise when atoms across the benzene becomes modified by substitution which causes the vibrational modes to change and become, in some cases, almost unrecognisable as pure benzene modes. When comparing the vibrations between multiple disubstituted benzenes it therefore becomes difficult to be certain that two vibrations are being compared ‘like for like’. These changes in vibrational character may be caused by (i) asymmetric substitution causing the lowering of the symmetry of the molecule i.e C2v to Cs, this allows the vibrations to mix in character; (ii) the substituted atom causing a change in the reduced mass and affects bond energy as a result; (iii) electronic effects which may cause the force constants of the bonds to change.
Fig 1. The 30 vibrational modes of Benzene labelled in the Wilson term nomenclature
An alternative approach to the Wilson labelling scheme is to use the Mulliken convention. This convention lists the vibrations of the molecule by symmetry and then by value in descending order. A Cs molecule would therefore list the A’ vibrations from highest to lowest starting from a label of 1 and working systematically through the numbers depending how many vibrations there are. The A’’ vibrations would then be listed highest to lowest where the label would continue on from where the A’ set of values left off. This method seems to be a better alternative to the Wilson scheme but also has its own disadvantages. The labels for identical vibrations may not be the same owing to the fact that the ordering of the vibrations may change upon substitution, therefore information about the actual motions of the atoms are lost from the label. Similarly depending on which axis the molecules are defined to be in, it is possible for labels to be interchanged i.e in C2v the b1 and b2 modes may swap depending on the way the x or y axis are employed. If the substituted groups comprise of multiple atoms they will contribute vibrations of their own which could also change the ordering of the vibrations. Finally, symmetry changes as a result of substitution would lead to a renumbering of the vibrations.
In this particular study we have started by showing why the vibrational labels of benzene are not appropriate for use in identifying substituted benzene vibrational motions. We have begun by calculating the benzene vibrational energies. We proceed by artificially modifying the mass of two hydrogen atoms on the ring that are adjacent to each other. This allows us to examine the behaviour of the benzene vibrations as a function of mass. We have chosen to vary the mass stepwise from the atomic mass value of hydrogen (1) up to the atomic mass value of fluorine (19) as this is the smallest stable substitution that can take place (barring o-deuterated benzene). Performing these calculations in a stepwise manner allows the details of the vibrational mixing to be elucidated in more detail than would be available by using the two extreme values only. We then follow on from this approach with a similar method in which we start with the explicitly calculated vibrations of fluorobenzene. We then artificially modify the mass of the hydrogen in the ortho position in the same manner as before until we reach an atomic mass of 19. We also try to express the vibrations of ortho disubstituted benzene rings with the same labels as we have used in the para and meta disubstituted rings using the same mass correlation approach as already described. What we will conclude from this is that we cannot use either the Wilson labels or any of the labels we have previously put forward for the monosubstituted benzenes (ref), para disubstituted benzenes or meta disubstiuteted benzenes and that there is no universal labelling scheme that may be used for different ring systems. We will put forward a scheme where we see if we can label vibrations consistently across all ortho-substitued benzenes using the vibrations of ortho difluorobenzene (oDFB) as a standard. This involves calculating the oDFB vibrational force constants and then subsequently increasing the mass of the fluorine atoms, both symmetrically and asymmetrically, to match those of the other halogens. This allows the modelling of any further change in vibrational character as a function of mass. What we will conclude from this is that the vibrations largely remain unchanged as a function of mass leading us to believe that we can label the vibrations of ortho disubstituted benzenes in a much more consistent manner.
Computational details
The majority of the harmonic vibrational frequencies calculated have been obtained via the Gaussian 09 software package using B3LYP/aug-cc-pVTZ. Excited state vibrational frequencies have been obtained using configuration interaction singles (CIS)/aug-cc-pVTZ. For bromine atoms, the fully relativistic effective core potentials ECP10MDF has been used, similarly with Iodine and ECP28MDF both used with aug-cc-pVTZ-PP valence basis sets. The calculated vibrational wavenumbers for the B3LYP based calculations have been scaled with the factor of 0.97, whereas the CIS based calculations have been scaled with a factor of 0.911 as the best approximation for anharmonicity. For the vast majority of cases, the values obtained via these calculations all seem to be in the same ‘ball pit’ as experimental values that have been obtained leadings us to be fairly confident in their accuracy.
Experimental section for REMPI
Results and Discussion
The idea behind the development of a universal vibrational labelling scheme stems from the idea that the character of the benzene motion does not remain the same as mass is added to the ring. Previous work reference Tim shows that a somewhat variation of the vibrational energies of benzene occurs as substitutions occur and the change in values can, sometimes, be very significant. We would expect this change to occur as the modes must take into account the motion of the ‘fluorine atom’ instead of hydrogen. Maybe change the order of this point group clarification? To provide a completely consistent comparison between both symmetric and asymmetrically disubstituted we have chosen to apply the Cs point group consistently across all molecules under study. We have therefore separated the vibrations into both the A’ and A’’ vibrations and they will be presented in this way from here onwards. The vibrations can be seen to be split into 21 A’ modes as well as 9 A’’ modes (Fig 2). This study goes into detail only about the changes occurring to the thirty ring localized modes standard to benzene. Other modes that may occur due to the substituted groups being polyatomic are treated separately and do not form part of the labelled vibrations. We begin with showing how the Wilson labels relate to the oDFB vibrations and to show why these are not particularly useful in consistent labelling of disubstituted rings.
Fig 2. The 30 vibrational modes of oDFB labelled by the Mulliken convention.
Wilson labelling
The change in vibrational wavenumber of benzene vibrations as a function of mass can be plotted as a mass correlation diagram (Fig 3). Two ortho hydrogens are picked and have their mass increased simultaneously and stepwise from 1 to 19 amu. The plot shows how each of the 30 vibrations change as the mass is increased. The vibrations are split by symmetry (A’ and A’’) and then ordered by wavenumber. In this case, we note that symmetric ortho disubstituted benzenes still have a point group of C2v. For clarity we have colour coded the lines where red depicts A1 or A2 vibrations and black depicts B1 or B2 vibrations. The force field constant is calculated as part of the benzene ground state vibrations and remains unchanged throughout the mass correlation plot. Each plot shows how the vibrations transition from those of the pure benzene modes, with their accompanying Wilson labels, (left) to the vibrations of oDFB (right), with their accompanying label from our scheme. In the mass correlation depicting the A’ modes it can be seen instantly that a few of the high-energy vibrations change drastically with mass. There is also a subtle change in wavenumber of a fair few vibrations at the intermediate-lower energy level where the mass dependence is not so extreme. There are also a number of vibrations both on the A’ and A’’ plots that seem to remain almost perfectly flat as mass is added to the ring. This signals that there are a fair number of vibrations that are not at all mass dependent. These vibrations tend to be those in which the substituents themselves are not moving therefore the overall motion seems to remain mostly very similar with only minor changes to take into account the changing centre of mass. Benzene itself has a D6h point group, as mass is added to the ring in the ortho positions the point group shifts towards a C2v point group. Due to this, vibrations close in energy are seen to interact. In these cases the lines on the mass correlation curve seem to move closer in energy and then ‘repel’ and move back away from each other, similar to how one would expect to see an avoided crossing on potential energy surfaces. Upon visualization of the vibrations we see that there is a significant amount of evolution in the vibrational character for many of the vibrations. A number of these vibrations seem to look as though they become superpositions of each other and essentially look like a ‘mixed’ version of two or more vibrations that were initially close in energy in benzene. Some vibrations that seem to undergo ‘avoided crossings’, similarly to the case of para-disubstituted benzenes, seem to swap over in energy where the vibrational motion seems to become somewhat mixed and then eventually move back to their original form with the vibrational motions of the atoms remaining unchanged. As a result of the somewhat significant levels of mixing, it is difficult to assign a single Wilson mode to many vibrations after mass is added. A possibility for labelling these vibrations would be to use a combination of Wilson modes ordered by which modes have the greatest contribution to the ‘new’ mode. A Duschinsky approach may be used as a way of visualising which Wilson labels contribute to each final mode of oDFB. This is done by using the FCLab software to compare the overlap of the vibrational wavefunctions of benzene with those of oDFB and , as a result, we may calculate a generalized Duschinsky matrix image (Fig 4). This data has also been drawn together (Table X) and we have expressed each vibration of oDFB in the form of Wilson labels as a result. Table X references the magnitude of the Duschinsky matrix elements. If there is a dominant contribution of a benzene vibration (>0.5) i.e the majority of the vibrational character of the benzene vibration is maintained
a bolt text is employed. If there is a contribution of a vibration falling between the range of 0.5 and 0.2 (a significant but not a majority contribution) plain text is employed. If the contribution of the benzene vibration to the oDFB vibration is between 0.2 and 0.05 (a somewhat small but noticeable contribution), the label is given in parentheses. Any contribution below 0.05 is ignored. In the case where there are multiple contributions, the labels have been listed in an order where the vibration that contributes the greatest to the final vibrational mode is displayed first, and the vibration that contributes the least is displayed at the end of the list.
Similarly, we have provided a comparison between the Mi modes of fluorobenzene to the modes of oDFB. We have done this by employing the same technique as above. The force field for fluorobenzene has been taken and we have then calculated the wavenumbers for the vibrations as the mass of an ortho hydrogen has been modified from 1 to 19. These results have been presented in a mass correlation set in Fig X. Table X also shows a way in which we can express the vibrations of oDFB in the form of fluorobenzene (FBz) vibrations. A similar Duschinsky approach (Fig 4) is taken to allow visualization of the extent of vibrational ‘mixing’.
The following will discuss the variation of the vibrational wavenumbers and motions as Benzene is modified to oDFB as well as when FB is modified to oDFB. The vibrational mode diagrams calculated for oDFB (Fig 2) are also presented as a means of showing how the vibrations look upon visualization and as a comparison to show that they are not equivalent to the Benzene Notably, the extent of mixing of the normal modes of benzene to form the vibrational modes of oDFB seems to be much more significant than that of pDFB. There are a much larger range of contributions from each benzene mode that make up the final modes and therefore it becomes more difficult to see exactly how the vibrations of oDFB have come about after mixing. We will discuss which benzene vibrations contribute the majority of their character and what effect we would expect this to have on the energy of the corresponding oDFB mode.
A’ vibrations
In total there are 21 A’ vibrations. Before mass addition there are six vibrational modes (ν2, ν20a, ν20b, ν7a, ν7b, ν13) at high energy all corresponding to C-H stretch vibrations; these all transform as A’ symmetry. Table X shows calculated, as well as experimental, wavenumbers of each vibration for oDFB separated by symmetry and label. As one of the ortho H atoms become heavier it can be seen that one of the six vibrational modes drops significantly in energy, the others all stay relatively constant. Ref X (FB paper) showed that the 5 remaining high energy vibrations had dominant character from the 2, 20a, 13, 20b and 7b (with slight mixing) with the v7a losing it’s vibrational character as mono directed mass addition occurs. Upon making the other ortho H atom heavier, another of the 6 vibrational modes (20a) drops significantly in energy. In terms of the Mi labels applied to monosubstituted benzenes, we find that the M2 vibration gives way and mixes significantly as the ortho position hydrogen atom is substituted for a fluorine atom. The Duschinsky approach shows that the four remaining high energy vibrations D1-D4 maintain significant character from the 2, 20b, 7b and 13 benzene vibrations respectively. The remaining two high energy benzene vibrations appear to fall dramatically in energy with both the 7a and 20a vibrations not appearing as a dominant contribution in any of the final oDFB vibrations. With reference to Fig 2 (ortho cartoon), the D1 vibration is fairly clear cut and shares the same vibrational motion as the v2 albeit with the two ortho F atoms being stationary. This occurs due to mixing between v2 and the v20a (and v20b and v7b to a smaller extent) which causes the vibrations of the ipso and ortho position atoms to cancel each other out. Similarly, the D4 and the v13 also have very similar vibrational motions so it is clear why there is a strong correspondence between these two vibrations. The v20a and v20b seem to combine to give the D2 the stretching motion that we seem with small contributions from the 13 and 17a seeming to round off the vibration allowing full cancellation of the vibrations at the ipso and ortho position. An interesting aspect is that the 20a and 7a vibrations both have strong movement at the ipso and ortho H atom positions whereas the 20b and 7b only have H atom movement at one of those positions. This may well be the reason why the 20a and 7a vibrations seem to fall heavily in wavenumber as mass is incorporated into the ring. The v2 and v13 also have significant H atom motion at the ipso and ortho position suggesting that they also should fall in wavenumber but as the vibrational motions at the ipso and ortho positions seem to cancel, these particular vibrations seem to remain at a fairly constant energy with a significantly reduced mass dependancy.
At the intermediate level, (1700-1000 wavenumber range) there is a significant amount of mixing leading to a lot of the benzene modes having no correspondence to the motions of oDFB. What can be seen from the mass correlation curve is that there is also a noticeable mass dependence for a number of the vibrations which can be seen from the general tendency for a number of the lines to fall in energy as the mass increases. The D5 and D6 vibrations retain most of the vibrational character from the v9b and v9a vibration of benzene with a small amount of mixing. The motions of these vibrations seem to stay very similar and could confidently be assigned a pure benzene mode label each. Similarly with the D7 and D8, there is a significant amount of vibrational character that is maintained from the v18a and v18b. The vibrational motions are, again, replicated almost identically between oDFB and Benzene. The D9 and v15 vibrations can be seen to be almost indistinguishable in terms of their vibration. The vibrational energy also seems to remain almost equal suggesting that this vibration is not greatly affected by the change in mass. The D10 vibration appears to be fairly heavily mixed and becomes difficult to trace the original origin of this vibration via the mass correlation.
Table 1.
It has numerous contributions from the original benzene modes and doesn’t resemble any vibration particularly well. The D11 vibration has a strong connection with the v3 mode and remain fairly similar in motion, the energy change, and hence mass dependence, is not vast given the substitution of two H atoms and can be traced directly along the mass correlation curve. There is a contribution from the 19b vibration to the D11 which allows a near complete cancellation of the movement of the ipso and ortho position H atoms. This is a possible explanation as to why there is also not a significant mass dependence of this particular vibration. The v15 and the v3 do seem to have undergone an avoided crossing as the energy ordering has been swapped over in forming the D9 and D11 respectively. The D12 is another vibration which is formed through heavy amounts of mixing. It has no dominant contribution from any Benzene vibration. The Duschinsky matrix (Fig X) shows that none of the v8a, v8b, v19a, v19b, v12 and v1 vibrations appear as dominant contributions to any oDFB mode. These vibrations all become heavily mixed in forming a number of the D11-D21 vibrations. The D13 has a significant contribution from the v14 and retains the majority of its character. The v8b does mix with the v14 enough so that the ipso and ortho position H atom motions cancel each other out; this could be a reason why the energy remains fairly constant as a result of the mass change. This mode can be traced laterally along the mass correlation curve. It is also possible to confidently assign a pure benzene label to this particular vibration. The D14 does not have a heavy contribution from any pure benzene mode. The vibration itself appears to gain the majority of its character through the mixing of the v8a and v19b vibrations where the energy of the D14 seem to fall somewhat between the respective energies for 8a and 19b. The D15 vibration has contributions from the v19a and the v1 but with a more dominant contribution from the v19a. Some elements of the vibrational motion are retained although, again, it would be difficult to assign a Wilson label to this mode with any great level of certainty.
Finally, the lower energy level bracket (<1000 cm–1). The vibrations in this bracket appear to have a significant mass dependence. Each of the Di vibrations in this bracket retains significant motion at the atomic position where the mass is being varied. As a result of this, a change in mass is expected to affect the vibrational energy as a result of the reduced mass effect. This effect is observed in the mass correlation curve where, for each of these vibrations, the curves seem to fall significantly in energy. The D16 has a contribution of vibrational character attributed to the v12. Significant mixing does occur between other vibration motions, particularly the v6a. As a result the v12 does not resemble the motion of the D16 vibration. The D17 is related partially to the v1 in that the substituents seem to loosely follow a symmetric stretch motion. Where all of the H atoms in the v1 are undergoing an in-phase symmetric stretch, the H atoms in oDFB appear to simultaneously undergo a bending motion as a result of mixing between at least six other vibrational modes; this vibration is not similar enough to be identified by a Wilson label after mass addition. The D18 appears to have a near dominant contribution from the v6b. The ring motions comparing the D18 and v6b seem fairly similar in that there is a ‘ring stretching’ motion occurring but with some atoms moving in different directions as a result of mixing. The ipso and ortho position motions in the D18 are undergoing an in phase stretch where the motions of the other atoms seem to be moving to keep the centre of mass constant. The ring motion therefore seems to change quite significantly whereas the substituent vibration part looks identical. The D19-D21 vibrations all appear significantly mixed. The three vibrations do not have any dominant contributions from benzene vibrations and are almost completely unrecognisable in the oDFB vibrations.
Conclusively, some vibrations of oDFB can be expressed with a pure Wilson label. There are also some vibrations which are very uncharacteristic of any of the benzene vibrations; it would be misleading to apply a Wilson label to a significant number of these A’ vibrations.
A’’ vibrations
For the A’’ vibrations there seems to be a ‘mixed’ correspondence between the benzene and oDFB. Similar to para disubstituted benzenes, there are a few vibrations that are very clear cut and may easily be assigned a Wilson label. There are also vibrations that are heavily mixed and not at all recognisable. The D22 and the v5 are very similar in both energy and motion and can be traced directly along the mass correlation curve. What one sees is that this particular vibration undergoes a significant amount of mixing with the 17a and 17b vibrations which leads to the motions at the ipso and ortho position substituents being cancelled out and, hence, a mass independent vibration. One could apply a pure benzene mode to this vibration. On a similar note, the D23 largely resembles the v17a with contributions from the 17b and 10b which also cancel out the vibrational movements at the substituent atom positions. Although the D23 and v17a are very similar, the mixing that occurs seems to ‘shuffle’ the vibrations around. Comparing the mode diagrams (Fig X and Fig Y) one will see that the D23 and v17a both have an alternating C-H bending motions; the vibrations at the ortho and para position seem to have ‘switched positions’ but with the overall vibrational motions remaining the same. The changes between the D24 and v10a vibration are similar to those above in that if one was to ‘swap’ the motions of the ortho and para atoms in oDFB around, the motion of benzene is replicated perfectly. This occurs for similar reasons in that the major contribution (from the v10a) as well as contributions from the v10b, v17b and v5 cause there to be an additive bending motion at the para position, whereas the vibrations at the ortho position seem to cancel out completely. This gives the effect that the vibrations have ‘swapped’ position. A dominant contribution of vibrational motion is evident but significant mixing occurs to form the final vibration. It should be straightforward to assign a Wilson label to the D23 and D24 as the vibrational motions themselves are identical but localised to different atoms. What is noted from Table X and Fig X is that the energy ordering between the corresponding benzene and oDFB vibrations becomes slightly ‘confused’. The D22 and D23 both correspond to the v5 and v17a, but from this point it becomes difficult to trace any vibrations along the mass correlation curve. An explanation is that number of avoided crossings occur which largely mixes the character of each of the vibrations from the D24-D29. The D25 and v11 look fairly identical in that all H atoms are bending out of plane and in phase. The difference is that the F atoms appear stationary. This is also due to a significant amount of mixing with modes that cancel out that particular part of the vibration. One could assign a pure benzene vibrational mode to the D25. The D26 is almost identical in motion to the v4. The D27 and D28 have a noticeable change in wavenumber as mass is incorporated. The D27 appears to be a product of both the v16b and the v4 with a small, but noticeable, contribution from the 16a. There is some cancellation of the motion at the substituent atom positions but some remains in the oDFB vibration so there does remain a dependence of mass on the vibrational energy. The D28 has a major contribution from the 16a with small contributions from the v16b and v11. Lastly, the D29 and D30 are fairly well mixed and don’t retain a majority of character from any original Benzene mode.
Conclusively, the A’’ vibrations seem to be mostly very mixed. There are, perhaps, a few vibrations that look very similar between Benzene and oDFB but it is questionable whether or not the two corresponding vibrations could be attributed with a Wilson label. The energy ordering seems to become fairly muddled as a result of the mixing which makes it difficult to trace along the mass correlation curves to see which initial Benzene vibration corresponds to each oDFB vibration.
Ortho vibrations expressed as fluorobenzene vibrations
Ortho vibrations expressed as meta and para vibrations
We have undertaken a comparison between the labels put forward for ortho disubstituted benzenes and compared them to both the meta and para disubstituted vibrations and labels (Ref Tim) to see if a universal labelling system can be put forward. Both a mass correlation (Fig X) and a Duschinsky approach (Fig Y) has been taken. Each mass correlation curve starts with the vibrations of FB in the middle and extends out to the para (Fig 1) and the meta (Fig 2) on the left with the ortho vibrations on the right of each cirve. Each oDFB vibration (oDi) has also been expressed as well as possible in terms of both the meta (MDi) and para disubstiuted (PDi) vibrations which has been collated in Table X.
Upon comparing the vibrations between mDFB and oDFB, what is immediately noticed in the Duchinsky matrix (Fig X) is that there appears to be significant differences between the vibrations. Similarly, the pDFB to oDFB Duschsinky matrix shows that the vibrational character is largely very different between these two species. By using the matrices independently one would expect that the vibrations would not appear in any way similar. The mass correlation curves show a significant level of mixing in both directions; tracing the lines across can be misleading due to the number of curves which appear to undergo avoided crossings with each other, particularly in the 1600-400 cm-1 region. Some of the lower energy vibrations i.e D21 and D30 seem to stay fairly constant in energy as the oDFB is shifted to either the m- or pDFB. Table X lists the oDFB vibrations and shows which vibrations of m or pDFB correspond to each of those vibrations. What can be seen in the mDFB->oDFB case is that the amount of mixing that occurs is significant enough so that the ordering of the vibrations appear to be ‘mixed up’ i.e the oD1 does not correspond with the MD1, oD2 with the MD2 etc. This can be seen all the way through the A’ vibrations and also in a lot of the A’’ vibrations. This means that if one traces along the mass correlation curve, the label at the start and end of each curve do not necessarily correspond to each other, the vibrations do not always have the same motion. In the case of the D21 where the line is largely very flat, what is seen is that the vibration can be traced directly and the vibration appears nearly identical at both sides of the curve. However, upon visualization of some other modes what is seen is that some parts of the vibration remain the same whereas other parts may change. An example of this is the D20 vibration shown in Fig X. What is seen is that the two F atoms in oDFB and mDFB can be seen to be undergoing similar motions. The positions of the F atoms are obviously different so when motions involving these atoms are proceeding, the vibrations of the other atoms must change in order to keep the centre of mass constant. What is seen in this case is that the ring vibrations change quite significantly and it becomes difficult to assign a label consistently between such cases.
A further problem is that, although rare, there are instances where a vibration of the mDFB is the most significant contributor to multiple oDFB vibrations. The oD30 and oD29 both have their most significant contributions from the MD29. The idea of the labelling scheme is that we can assign each vibration a clear, consistent label that can be attributed easily. At this point it becomes difficult to say which of those ortho vibrations could be expressed as the MD29 which casts doubt on the use of a universal vibrational labelling scheme.
Both the para and meta vibrations, when compared to the ortho vibrations, appear very different as a result of the reasons mentioned above. It is therefore impossible to use a universal labelling scheme with any certainty.
Trends in vibrational wavenumber of symmetrically ortho disubstituted benzene (oPhX2)
We show in Fig X and Fig Y the trends in vibrational wavenumber for symmetric ortho disubstituted benzene (Two ortho substituents are the same) as the mass of the two substituents, X (where X=CH3, OH, F, Cl, Br, I), are both varied from a mass of 15 amu through to 127 at the same time. The mass correlation itself is calculated by taking the ground state vibrational energies and force field of oDFB and artificially changing the mass of the F atoms to match those of other species varying from a methyl group up to an iodine atom; the calculated data is given by the line. Experimental data is also displayed against the mass correlation line and appears in the form of the symbols. An important note is that symmetric disubstituted benzenes actually have C2v symmetry as opposed to Cs. For clarity, each data set that has A1 or A2 symmetry has been drawn in red; the B1 and B2 data sets have been drawn in black. Due to the C2v symmetry, curves that are the same symmetry are not allowed to cross, but curves of different symmetries may cross.
With regards to the trends, similarities to the para disubstituted benzenes (Ref X) can be spotted in that, although some variation with mass is seen, the lines actually remain fairly flat. There are no points where it appear two vibrations approach each other and repel i.e like an avoided crossing. There is no obvious evidence for any mixing of vibrations and no stand out vibrations which change significantly in energy, unlike what is found on the Benzene-oDFB mass correlation curve (Fig X). Experimental data collected from the literature (Ref X) has been displayed in Table X as well as the explicitly calculated data for comparison. All vibrational data was collected by Green from IR and Raman sources. For consistency the IR data has been used where possible; where there is no IR value a Raman data point has been used instead. A “-“ denotes where an experimental value that was not present in the literature data. This may be due to some of the peaks being very small/not noticeable or they are simply not IR or Raman active. All experimental data is either in the liquid or solution phase, stated in the tables. The experimental values have each been paired with a calculated vibrational energy where the correspondence between these data seems to be fairly good. There does appear to be some differences between a few vibrational energies, particularly at the very highest energy and lowest energy levels. The intermediate values seem to be in better agreement. Fig X shows the mass correlated curve with experimental data for each species plotted on top in the form of symbols. The data is also contained in Table X. Fig Y shows the exact same mass correlation curve but instead with calculated data for the species as opposed to experimental data. Duschsinky matrices comparing the vibrations of oDFB to each of oXyl, oDClB, oDBrB, oDIB are presented Fig X as a visual means of comparison showing how the vibrational motions change as the mass of the ortho substituents are varied. Each Duschsinyk matrix shows a strong correspondence between the vibrations of oDFB and each oDXB albeit with a slight amount of mixing in the intermediate range of A’ vibrations. Visualisation of these vibrations shows that, for the most part, these vibrations do indeed look very similar in their motions so application of the Di labels to each vibration is reliable. Below, we will compare the trends shown in Fig X and Y and discuss the reliability of using the mass correlation curves as a predictive tool for ground state vibrational energies of other ortho disubstituted rings. We will also discuss any discrepancies between the predicted and experimental vibrational energies for the oDXB systems.
o-Xylene
Catechol
oDFB
The experimental vibrational data for oDFB was interpreted and tabulated by Green (Ref X). The calculated energies for D1-D4 vibrations, i.e the high energy vibrations, are perhaps slightly too high compared to the experimental data shown in Table X. A few of the lower energy vibrations also appear slightly higher in energy. A reason for this may be that the 0.97 correction does not take into account more extreme anharmonic effects. A number of the intermediate A’ vibrations also seem to have experimental values that deviate quite significantly from those of the calculated values by wavenumbers up to 50. These differences may be due to solvent effects on the vibrations as these spectra were obtained in the liquid or solution phase. An alternative explanation is that some of the assignments may, in fact, be incorrect and the wrong vibration has been attributed to a peak which could be due to combinations, overtones or Fermi resonance etc. The majority of the values, however, seem to be in the correct ‘ball park’ to match those of the calculated wavenumbers. The A’’ vibrations seem to be a lot closer in magnitude with the least accurate experimental-calculated pair having a difference of only 9 wavenumbers. The experimental points therefore seem to mostly fit on the mass correlation curve fairly well showing a distinguished agreement between theory and experiment.
oDClB
This case is very similar to oDFB in that the experimental values at the highest and lowest energy seem to be a fair way off the calculated values due to reasons stated previously. Using both mass correlation curves (Fig X and Fig Y) it is noticeable that the experimental and calculated data points for the D5-D15 bracket appear to fall below the lines quite significantly. A number of the data points seem to shift around as the mass of the substituents increase from 19 to 35. If we treid to use the mass correlation curve as a predictive tool in this case i.e if we did not have the data points and we estimated the vibrational energies using only the curve, it would be fairly misleading and would product vibrational energies that are, in some cases, over 60 wavenumbers away from their true values. Some of the other data points on both the calculated and experimental mass correlation curves also fall south of the line by a significant amount, particularly the D16-D20 vibrations. This discrepancy may be due to significant electronic effects as these particular vibrations have significant vibrational motions at the C-Cl positions. The fact that the calculated and experimental data points both seem to fall south of the line and agree with each other suggests that they are indeed the same vibration and were assigned correctly by Green however. The A’’ vibrations appear to follow the mass correlation curve quite well. The majority calculated data points are replicated almost identically by the mass correlation curves; the D27 and D29 points, in particular, seem to fall to a lower energy value. Although slightly off, the mass correlation seems to be a reliable tool in being able to predict ground state vibrational energies for the A’’ vibrations this far. For the A’ vibrations it seems as though the predictive nature of the mass correlation curve becomes more tenuous.
oDBrB and oDIB
The set of vibrations for both oDBrB and oDIB are both very similar again to how the oDClB changes from the oDFB. The A’ vibrational energies between the D1-D15 and D21 all remain fairly constant as predicted by the mass correlation curve. The experimental data plots for D16-D20 appear to fall further south of the lines going from oDBrB to oDClB to oDIB. This trend is, again, matched by the computational plots shown on Fig Y. These particular modes all involve a stretch of bending mode involving the C-X substituents and we would therefore expect them to have an electronic dependancy. There is, for oDIB, also what appears to be an outlying result at for the experimental value of D18. This appears to be about 100 wavenumbers lower than expected which may be due to a misassigned peak. The D18 and D19 are two vibrations that seem to be worst affected as the mass of the substituents increases as they can be seen to fall further from the predicted mass correlation line the greater the mass becomes. This appears not to be modelled by the mass correlation particularly well. What can be seen on the Duschinsky matrix is that the D14 and D16, D17 and D18 well as the D19 and D20 all appear to mix slightly which effects the vibrational character and energies enough so that there is a deviation from the correlation curve. The vibrations themselves remain largely similar however.
A’’ vibrations seem to fall mostly on or very close to the plotted curves. The D22-D26 experimental and calculated data points match the curves almost perfectly. There does lie a problem with the D27-D30 data points in both oDBrB and oDIB as they appear to move further from the line as the mass difference increases. There is no significant mixing that occurs between these vibrational modes so and each of those vibrations have out of plane bending motions at the halogen atom position. As a result of this, these particular data points falling below the line are most likely due to electronic effects again. There does, however seem to be no doubt as to which energy value should match each curve meaning that the predictive properties still apply here.
Trends in vibrational wavenumber of asymmetrically substituted rings (oPhFX)
We show in Fig X and Fig Y the trends in vibrational wavenumber for asymmetric ortho disubstituted benzene rings (Two ortho substituents are both different) as the mass of the one substituent remains as a F atom and the other substituent is varied from a mass of 15 amu through to 127. These lines, as before, are calculated by taking the ground state vibrational energies and force field of oDFB and artificially changing the mass of a single F atom to match the other species that we are testing. In this case, the Cs symmetry point group is the real point group, the lines are therefore not colour codes as there is potential for every curve to repel and ‘mix’.
The appearance of the lines remains to be as expected. They are mostly very flat, perhaps flatter than those shown in the symmetric mass variation case. The most notable change is that where there was a line crossing in the symmetric mass correlation curves at D18 and D19, there appears to be an avoided crossing in which the lines approach each other and repel. Interestingly, where the vibrations seem to switch over in energy in the symmetric mass variation it would appear that in the asymmetric mass variation the two vibrations in question appear to begin to mix between at an intermediate mass in the middle of oDFB and oFIB but appear to then separate and appear as they were initially by the time the mass of oFIB is reached. Similarly as before experimental data collected from the literature (Ref X) has been displayed in Table X as well as the explicitly calculated data. All vibrational data was collected by the same source (Ref). The energy correspondence between the experimental and calculated data, again, seems fairly good with most vibrations being within a difference of 20 wavenumbers. The experimental data is mostly complete with a few high energy vibrations missing. As before, the experimental data is plotted on the lines of Fig X and calculated data points on Fig Y both on top of the same modelled curve. Duschsinky matrices have also been provided in Fig X to visualise the mixing that occurs as the mass changes. The matrices all bear a strong diagonal trend showing that the modelling of the multiple substituted rings match those of oDFB very well. There is slight amounts of mixing at certain points for the intermediate energy values of the A’ vibrations. As in the symmetric mass variation, the motions themselves do not change significantly so we are happy to consistently apply the Di reliably. Similarly to before we will compare the trends shown in Fig X and Y and discuss how reliable the curves are as a predictive tool and will discuss any notable difference between the predicted energies and the experimental and calculated 
energies.
oClFB
The experimental data points for oClFB on the mass correlation plot match the lines extremely well as well as the computed values. The A’ vibrations all seem in very good agreement. What can be seen at oClFB is that the D17 seems to begin to move south of the line. The D17 seems to begin mixing with the D16 – the D17 in particular seems to mix more than the other vibrations in the ‘lower intermediate’ range that are close in energy (i.e D15-D21) as seen in the Duschinsky matrix. The D14 and D12 are two other vibrations that seem to undergo more significant mixing compared to the other A’ vibrations. These particular motions also have vibrational motion at the C-X and C-Y position so are expected to have a degree of electronic dependence. The experimental values for the A’’ vibrations match the mass correlation curve excellently. There doesn’t appear to be any mass dependence on these vibrations and there doesn’t appear to be any significant differences between the plotted data of oDFB and oClFB suggesting that the vibrational character remains largely the same. Similarly, the Duschinsky plot for this molecule is almost perfectly linear allowing us to accurately use the same labels between oDFB and oClFB.
oBrFB
Similarly to the data for oClFB it is noticeable that the majority of experimental data points match both the curve as well as the computed values. For the A’ vibrations a similar pattern is seen as before where the gap between the exerpimental data and the mass correlation curve seems to be opening up for the D20 and the D17 as well as the gap between the line and the D14 and D12 increasing. What is noticeable from the Duschinsky matrix is that the extent of mixing I perhaps more noticeable with the bracket of vibrations between the D14 and D20 inheriting a lot of character from each other. The D18 seems to mix slightly with the D19 and D20. As a result of this, the motion of the C-Br seems to become almost stationary whereas the C-F bending motion remains as it was. As a result, there seems to be very small dependency of mass and electronic properties contributed from the I. The D18 therefore seems to remain fairly constant in energy and the experimental data seems to agree with this. Similarly, the D19 appears to mix with the D20 and D21 meaning that the C-Br vibration comes to a standstill. The energy of this vibration also seems to remain constant as the substituent is varied. The D21, D20 and D17, unlike the previous cases have experimental data that falls south of the line quite noticeably. The D21 appears almost identical between oDFB and oClFB. The discrepancies between the mass correlation and experimental could be down to electronic effects once again as the C-Br bends are quite prominent in this particular vibration. Similarly the D20 has quite prominent C-Br stretches so the discrepancies may be due to the same reason. The D17 has partial contributions from the D16-D20 vibrations and as a result the experimental data seem to fall short of the calculated line. The A’’ vibrations appear mostly as already noted. There are no significant changes occurring as a result of mass change. The experimental data and mass correlation curve agree excellently, there is no apparent amounts of mixing shown in the Duschinsky matrix that is worth commenting on.
oFIB
The experimental data for oFIB follows exactly the same trends that oClIB showed. The gaps between the mass correlation curve and the D21, D20, and D17 seem to open up further due to reasons stated before. The vibrations where the C-I motion is cancelled out remain largely the same and do not deviate from the lines and the agreement between experimental and calculated is very good. The A’’ vibrations, again, remain almost diagonal as shown by the Duschinsky matrix and no noticeable mixing occurs. What is perhaps noticeable is that, while all of the other vibrations are recognisable and a label can be applied, the D12 becomes significantly mixed by oFIB. It is not particularly noticeable at this point and attributing the label to it is somewhat misleading. The label has only been applied here as a result of the other vibrations being used. However, oFIB is an extreme case of mass where each I is in fact larger than the rest of the ring altogether. We are happy that the labelling system is otherwise applicable to asymmetric ortho disubstituted rings.
Conclusively for the asymmetrically disubstituted rings, what we see is that there is small amounts of mixing occurring in the A’ vibrations where all vibrations apart form the D12 are noticeable by oFIB. The A’’ vibrations are modelled very well by the mass correlation and the character of the vibrations remains identical across all of the applied mass changes. This labelling system can therefore be applied consistently across the board for these particular systems.
