2.5.1. Quantum Chemical Predictions
Methyl butanoate has three single bonds, which support several conformations. The C−O−C−C
α torsional angle can be either
trans (180°) or
cis (0°), while the other two, O−C−C
α−C
β and C−C
α−C
β−C
γ, can be
trans (180°) or
gauche (±60°), giving a total of 18 possible conformations. However, most of them can be disregarded. The
cis ester conformation adds an energy penalty of
mol
−1 on B3LYP/def2-QZVPP level; therefore, only the
trans C−O−C−C
α conformations need to be considered here [
38], in analogy to carboxylic acids [
39]. Additionally, in classical Raman spectroscopy, enantiomers can not be distinguished; therefore, only one member of the enantiomeric pairs will be considered. Lastly, the conformer with two heterochiral
gauche conformations for the C−C bonds is not a minimum structure at B3LYP/def2-QZVPP level. Hence, there are only four relevant conformers, as follows: The first letter denotes the conformation of C−O−C−C
α and is always t (
trans), the second and third letter denote the conformation of O−C−C
α−C
β and C−C
α−C
β−C
γ, respectively, and can be either t (
trans) or g (
gauche). Note that some angles deviate quite strongly from the ideal values of ±60° and ±180°, but we refrain from using a more differentiated nomenclature [
40].
A complete torsional scan of the B2PLYP-D3(BJ)/aug-cc-pVTZ PES has already been performed [
9]. In this work, only the stationary points were recalculated at the CCSD(F12*)(T*)//B3LYP level. Pictures of the conformers, their relative energies and barriers of interconversion are shown in
Figure 9 and in
Table 4, including a pioneering DFT study [
6]. The implications for the experiment shall be briefly discussed here.
At room temperature (i.e., prior to expansion), the population is Boltzmann distributed. Using the differences in Gibbs energies at 298.15 K (electronic energy from CCSD(T) and thermal enthalpy and entropy from B3LYP) and the twofold statistical advantage of the chiral enantiomeric pairs a population of ttt = 27%, ttg = 34%, tgt = 24%, tgg = 15% is found. These populations differ by less than four percentage points if the CCSD(T) correction is removed.
Downstream a supersonic expansion, the molecules are collisionally cooled and, therefore, try to relax into the global minimum, for which the barriers of interconversion need to be overcome. A typical estimate for our setup is that barriers mol−1 are easily overcome, whereas barriers mol−1 are largely insurmountable.
Our values suggest that the tgt minimum is higher than the barrier to ttt, once the ZPE (without imaginary contribution at the barrier) is added. Therefore, it is expected that, in a supersonic jet, it will fully interconvert into ttt. However, a small adiabatic barrier should not be ruled out [
9] and would still be consistent with easy relaxation. ttt and ttg will not interconvert significantly and will both be present, which can be described as conformational freezing, but is also supported by their very similar energy. No clear expectation for the probability of interconversion of tgg into ttg can be derived from the relative energies.
The effect of the ester group is very prominent: the adjacent C−C
α bond is much more flexible than the purely alkyl one. This effect is nullified if the alkanoate part of the ester is branched at the
position, which was shown in a recent microwave study on ethyl 2-methylpentanoate [
41]. There, the observed minimum structure has a O−C−C
α−C
β angle of 143.1°, which can be described as a slightly tilted ttt structure in our nomenclature. The barrier towards a conformer similar to tgt was predicted to be around 10
mol
−1 on various levels of theory. Additionally, the potential well around ttt was predicted to be rather flat and the O−C−C
α−C
β angle of the minimum structure differed by ±20°, depending on the method employed. At the MN15 hybrid density functional level, a double minimum was predicted, contradicting the experimental results.
2.5.2. Experimental Spectra
The
(C=O) fundamental (1750 to 1800 cm
−1) proved to be a useful clustering marker for methyl methanoate, and, therefore, an analogous variation in the ester concentration was found for methyl butanoate (
Figure 10). The signals at 1742 and 1753 cm
−1 show the most prominent changes w.r.t. ester concentration and can, therefore, be attributed to dimers and larger clusters on top of monomer signals. Monomeric
(C=O) shows remarkable splittings that might at first be attributed to the different conformers. However, the experimental splitting (1760, 1764, 1768 and 1772 cm
−1) is much larger than the harmonically predicted one (1785, 1786, 1787 and 1788 cm
−1); therefore, a splitting due to anharmonic coupling with combination modes seems more likely. It seems that such a splitting partially survives in the crystalline state [
6]. Interestingly, the position of the
(C=O) fundamental is a sensitive indicator of fatty acid chain length in the liquid state [
42], despite this gas phase complexity. A similar concentration series in the low-wavenumber region is provided in the ESI (
Figure S4). As no difference is observed between the lowest two traces, the settings with a relative concentration of 1.5 were used for further analysis.
By varying the expansion conditions, spectra with differently pronounced collisional cooling can be obtained. In
Figure 11, the low-wavenumber range of methyl butanoate recorded in the gas phase as well as in five jet expansions with different conditions is shown alongside selected intense and separated lines of all four conformers taken from quantum chemical calculations. This spectral range was chosen because it has a pronounced conformational discrimination potential. In the room-temperature gas-phase spectrum (top trace), only some of the signals can be assigned in a straightforward way to conformers, such as 335 and 433 cm
−1 to ttt and 371 and 463 cm
−1 to ttg, but no reliable quantitative information can be obtained because of the overlap of the rotational branches. This underscores the need for supersonic expansions. In the hottest expansion (a) the rotational structure is much more narrow, and despite a nozzle temperature of 150
, the effective rotational temperature in this spectrum is substantially lower than room temperature. The two vanishing signals near 638 and 752 cm
−1 can be tentatively assigned to tgt, suggesting that even mild cooling effects completely funnel the initial tgt population to ttt.
If the expansion is probed further away from the nozzle, the collisional cooling process is more complete: The hot band structure at 463 cm
−1 is reduced from (a) to (b). If the nozzle is not heated during the expansion, even stronger cooling can be achieved (traces c and d). The partial relaxation of tgg into ttg can be tracked in the region around 600 cm
−1: the intensity of the tgg signal at 604 cm
−1 relative to the ttg signal at 585 cm
−1 decreases from (a) to (d), but does not vanish, even at larger nozzle distance (not shown). By substituting 20% helium carrier gas by argon (e), the cooling efficiency is increased due to the improved mass matching or transient attachment [
43]. Here, tgg is completely depleted and only the two most stable conformers ttt and ttg remain.
With 15% argon (not shown), a trace of tgg is still observable, while larger amounts of argon promote dimer formation. Trace (e) thus represents the simplest spectrum. The small surviving signal marked o? is possibly the (unusually strong) overtone of the ttt COC bending vibration near 310 cm−1, but other combinations, a ttg origin, or strongly Raman-active impurities cannot be ruled out. In the OH stretching range (3400 to 3850 cm−1), no other signals were observed, except for a small water signal at 3656 cm−1; therefore, impurities due to the direct dissociation products of methyl butanoate, methanol or butanoic acid, are not expected to contribute significantly to the low-frequency spectrum. This qualitative analysis shows how low barriers of interconversion are overcome in a supersonic expansion, and how high barriers lead to conformational freezing.
The coldest spectrum (
Figure 11e) will now be used to quantify the ratio of ttt and ttg. In
Figure 12 a section of the jet spectrum is shown along different simulated traces for these conformers. For comparison, the left part is the same as in
Figure 2. In the middle part the rovibrational simulation of ttt and ttg, as well as the sum of both (red), is shown. As was performed for methyl methanoate in
Figure 7, the simulated peak heights have to be multiplied by the factors shown above the corresponding signals in order to match the experimental spectrum. This can be done for the two main signals, but the harmonic calculation predicts that the two signals at
cm
−1 are too close to each other, so that their sum can not be properly fitted to the experiment. An improved simulation can be obtained if, instead of the harmonically calculated wavenumbers, the experimentally observed ones are used for the central wavenumber of the rovibrational simulation. This is shown in the right part. Here, the simulation becomes almost indistinguishable from the experimental spectrum, and the peak height factors for both ttg signals at 868 and 881 cm
−1 can be determined.
Therefore, a two-step analysis of the full spectrum is employed: First, the rovibrational simulation with harmonically predicted wavenumbers is used to assign all relevant signals in the experimental spectrum, then the simulation is redone using the experimental wavenumbers, and finally the peak heights for each assigned signal are fitted. The results are shown in
Figure 13. We note that the ttt signal at 338 cm
−1 is at the edge of the poorly illuminated part of the CCD (vide supra) and, because of that, its experimental intensity might be slightly underestimated. This datapoint is still included in the analysis, because it does not seem to be strongly distorted. From these 7 (ttg) +4 (ttt) numbers the mean value and the population standard deviation (
) are formed: ttg = 1.09 ± 0.39, ttt = 0.92 ± 0.09. These are normalised to give 100 in sum, and the uncertainty is propagated, giving: ttg = 54 ± 9, ttt = 46 ± 9.
For comparison, those 5 + 3 signals that were spectrally separated enough were integrated, and the integrals were divided by calculated Raman cross sections, which are shown as bold numbers in
Figure 13. The individual errors were determined similar to methyl methanoate (vide supra). The integration error was estimated from statistical noise analysis (see
Section 3) and propagated in the normalisation step to the ttg signal at 466 cm
−1. Then, the relative temperature error and 3% of the intensity due to non-uniform illumination and uncertainty in the polarisation selectivity were added, and finally 1% of the most intense signal (ttg at 868 cm
−1) was added uniformly, due to reproducibility and (dimer) impurity issues. Again, from the mean and population standard deviation (excluding the ttg signal at 868 cm
−1), the final ratio for ttg:ttt of 57:43 is obtained. The error bar is ±5 without and ±8 with inclusion of the individual integration errors.
Both of our methods for the determination of conformational ratios agree with each other, and, as expected, the peak height method provides a higher level of uncertainty than the integral method. This ratio has also been determined by microwave spectroscopy in supersonic expansions, where a similar conformational freezing was observed and a ratio of ttg:ttt of (59 ± 6):(41 ± 4) was found [
9]. Both of our results agree with the reference values. Hence, our Raman setup is capable of distinguishing different ester conformers and semi-quantifying their abundance.
With a similar procedure, the peak heights of the coldest, argon-free spectrum from
Figure 11 (trace d) were analysed as well, yielding the relative abundance: ttg = 53 ± 9, ttt = 45 ± 9, tgg = 2.0 ± 0.4.
The main conformers ttt and ttg were previously identified by a combination of quantum chemical calculations and Raman spectroscopy of solid methyl butanoate [
6]. There, a strong connection between basis set size and quality of the theoretical prediction was observed. Already the gas phase B3LYP/6-31G(d) approach, which is superseded by far more accurate methods at present, was sufficient for a reliable signal assignment based on the vibrational wavenumbers, despite the difference in phase state. However, the corresponding Raman intensities were insufficient for conformer quantification. Reasonable intensities that qualitatively matched the experimental spectrum were obtained with the larger Sadlej pVTZ basis set [
44]. Our calculations with the even larger def2-QZVPP basis set are also in reasonable agreement for most of the fundamentals, but quantitative matching is only obtained if a favourable anharmonicity effect of up to 20% is assumed (see ESI,
Table S7).
Table 5 compares the experimental isomer ratios with theoretical models which all assume that the torsional angle around the C−C
α bond relaxes completely to its global minimum (t) value, consistent with the experimental observation under cold jet conditions. The outer torsional angle distribution is assumed to either freeze at the nozzle (300 K) or to relax to a conformational temperature of 200 or 100 K. 100 K is not very likely given the height of the barrier, but is still included for comparison. One might further assume that the rotational and vibrational partition functions are the same in both surviving conformations (simple Boltzmann model,
) or include those partition functions explicitly into the population calculation before relaxation (entropy-inclusive
model in the harmonic/rigid rotor approximation). In Reference [
9],
values are actually used in the model, whereas
values were intended [
45]. We also tabulated the
values obtained from the authors [
45], for convenience. Both models based on MP2 energies disagree with all three experimental estimates. The
model based on CCSD(T)-edited B3LYP calculations gives the same prediction as the one based on B2PLYP energies, and it still disagrees with two experimental evaluations. The other models agree with two or three experimental values within their error bars, and we cannot decide between them.
In summary, the separation of the Cα−Cβ torsional families (tgt, ttt) and (tgg, ttg) in the jet expansion is either complete (no transfer between them, corresponding to , neglecting partition function differences) or partial ((<300 K), with some Cα−Cβ torsional relaxation despite the significant barrier and small energetical driving force).