Terahertz response of DL-alanine: experiment and theory

Abstract

The terahertz (THz) spectrum of DL-alanine has been measured for the first time at cryogenic temperatures and with a pure sample. Several sharp absorptions are observed, over a wide frequency range (0.8–4.8 THz), at 8 K. The sample structure and purity were confirmed with both Raman spectroscopy and X-ray diffraction. Temperature dependent spectra revealed redshifting, with increasing temperature, for all modes except one at 2.70 THz. This mode exhibits blueshifting until ≈120 K, where it starts to redshift. A Bose–Einstein distribution has been used to model the frequency shift with temperature for the four lowest energy modes. Strong correlations between the fits and data indicate that these modes are caused by phonon excitation in an anharmonic potential. Density functional theory has also been used to identify the origin of these low frequency modes. They are attributed to large scale molecular vibrations.

---

1 Introduction

Terahertz (THz) spectroscopy is a proven tool for studying intermolecular bonds, particularly those of biomolecules.^1–6 This is due to the energy of photons in the terahertz range, 0.1–3 THz, being equal to the energy of large scale molecular vibrations that are mediated by intermolecular bonds.¹ These bonds, which are prevalent in organic materials, have the potential to provide a spectral fingerprint once a data-base is established.

Amino acids are an important class of organic material that are the building blocks of proteins required for living tissue. The important biological functions of amino acids are achieved by strong intermolecular bonds. These are formed from the zwitterionic structure, where positive amine and negative carboxyl groups attract between neighbouring molecules.

All amino acids, excluding the simplest (glycine), have a mirror symmetry known as chirality. The second simplest amino acid, alanine (C₃H₇NO₂), has these chiral counterparts, as shown in Fig. 1, with the L-form being commonly found within living organisms. L-Alanine has been extensively studied using terahertz spectroscopy,^7–11 often in comparison to the D-enantiomer. Very few studies into the racemic compound DL-alanine have been undertaken,^4,12–14 all of which focus on the individual enantiomers. Interestingly, DL-alanine still forms the same head to tail amine–carboxyl bonds as its enantiomer constituents.

Fig. 1 Chirality of the α-alanine molecule, with the L-enantiomer on the left and D-enantiomer on the right. The dashed line represents a mirror plane, showing the symmetry of the enantiomers. Red represents oxygen, brown carbon, white hydrogen and blue nitrogen.

The molecular structure of DL-alanine is visualised in Fig. 2 which shows the unique crystal structure, where planes of each enantiomer can be seen parallel to the bc-plane. Intermolecular bonds in these planes are very similar to those in the pure enantiomer as they are composed of the same molecules in the same orientation with the same distance between molecules.¹⁵ However, intermolecular bonds along the a-axis are unique to the chiral form, as they are between D- and L-molecules.

Fig. 2 1.5 × 2 unit cells of DL-alanine, with the hydrogen bond threshold set to 2.5 Å. The box represents one unit cell. The unit vectors â and ĉ are shown, with the b̂ unit vector out of the page. Atomic positions and bond lengths, a = 12.0 Å, b = 6.0 Å, c = 5.8 Å, are taken from Nandhini et al.¹⁵

Previous terahertz spectra of DL-alanine^4,12–14 have only been reported at room temperature and within limited spectral ranges. Here, both the use of cryogenic temperatures and a wide frequency range of 0.8–4.8 THz have been employed. The temperature dependence of this spectrum and the absorptions within this broader range have been investigated for the first time.

2 Modelling

2.1 Density functional theory

Density functional theory (DFT) modelling was performed with the Crystal17 package.¹⁶ Geometry optimisation was performed using the initial geometry from Nandhini et al.¹⁵ The B97-3c density functional was used, which has been well tested for molecular crystals.^17,18 It incorporates the dispersion, counter-poise and short-range basis set corrections. Modified def-TZVP basis sets¹⁹ are used with this functional, named mTZVP.^19,20 Very tight convergence criteria were used in the geometry optimisation. The energy convergence tolerance in self-consistent field cycles was 10⁻¹² hartree. The geometry convergence was achieved with the following criteria: RMS energy gradient lower than 10⁻⁶ hartree per bohr, maximum energy gradient 2 × 10⁻⁶ hartree per bohr, maximum atomic displacement 4 × 10⁻⁵ bohr and RMS displacement 10⁻⁶ bohr. The infrared absorption spectrum was calculated in the harmonic approximation. The intensity of the absorption bands was obtained within the Berry phase approach.^21,22

2.2 Temperature dependence

The temperature dependence of intermolecular absorptions is governed by the atomic potentials, which are anharmonic.¹¹ This means that, as the atoms involved in an intermolecular bond vibrate, their average displacement is proportional to their energy, and hence to the temperature. As temperature rises and atomic displacements increase, the elastic constant of the bonds is reduced. This lowers the frequency of modes resulting in lower energy photons being absorbed. The frequency of a mode shifting to lower values with increasing temperature will be referred to as redshift. This thermal expansion model is the usual explanation for the commonly observed redshift.²³

The shift in the absorption position with temperature can be fitted with a Bose–Einstein distribution,²⁴ assuming it is entirely mediated by phonons. In this quantum description of vibrational modes, the change in mode energy, ω, with temperature, T, is given by:

where ω₀ is the frequency of the mode at 0 K, A is a constant, and T_C is a characteristic temperature. In simple terms, this model predicts no shifting of the mode energy until a critical temperature proportional to T_C is reached. Above this temperature there is sufficient energy to significantly populate the excited phonon states, resulting in redshifting.²⁴

3 Experimental

3.1 Sample preparation

Powdered DL-alanine was purchased from Sigma Aldrich with a purity of ≥99%. This pure powder was compressed into an 0.8 mm thick, 13 mm diameter pellet under 48 MPa without a binding medium. Previous studies of DL-alanine have used binding media, of either polyethylene or magnesium oxide. The use of binding media for pellets of L-alanine has lead to additional features being reported in the terahertz spectrum,²⁵ so their use was avoided for its racemic partner studied here.

Single crystals were also investigated as a potential sample form; however only small needle-like crystals²⁶ of the order of 2.0 × 1.0 × 0.5 mm³ have been previously reported.²⁷ Crystals of this size are too small and fragile to be effectively mounted and positioned for temperature dependent measurements. Hence a pure pellet of powder was chosen as the most suitable sample form.

3.2 Raman spectroscopy

Raman spectroscopy was used to validate the purity of the bought powder. Measurements were taken using a LabRAM HR Evolution spectrometer (Horiba Scientific) in a backscattering configuration, at room temperature with 474 THz laser excitation. Low frequency Raman modes correspond to intermolecular bonds exactly, like infrared-active modes, but have different excitation requirements, according to the different quantum selection rules governing each. The low frequency spectrum seen in Fig. 3 identifies seven peaks between 1.85 and 6.00 THz. These low energy peaks match with the literature as seen in Table 1, as do the higher energy peaks shown in Fig. 4.

Fig. 3 Low frequency (1.85–6.00 THz) Raman spectra of powdered DL-alanine, with 474 THz laser excitation and a pump power of 17 mW incident on the sample. Peaks positions are labelled in units of THz.

Table 1 Observed Raman peaks of powdered DL-alanine compared to literature values. Uncertainty for all peaks is estimated to be 0.03 THz (1 cm⁻¹) or less

This work [THz]	This work [cm^−1]	Ref. 28 [cm^−1]	Ref. 29 [cm^−1]	Ref. 30 [cm^−1]
a Peak positions extracted from graphs. Spectral range from 1200–1350 cm^−1 not reported.
2.22	74			72
2.69	90	90		89
2.99	100	99		98
3.51	117	117	119	115
4.43	148	147		149
4.82	161	160	159	160
5.58	186	186		180
6.84	228	229		259
8.47	282	283	286
10.05	335			337
12.21	407	408	412	408
16.26	543	542	547	543
19.33	645	645	645	644
23.07	770	772	771	770
25.51	851	852	854	852
27.62	921	926	921	918
30.40	1014	1016	1015	1014
30.76	1026	1027	1030	1030
33.41	1114	1115	1115	1115
34.23	1141	1143	1141	1143
34.89	1164	1158	1155
37.21	1241			1237
39.20	1308		1308	1307
40.68	1357		1359	1356
41.38	1380	1381	1380
42.35	1413	1410	1413	1412
43.75	1459	1461	1461	1460
44.40	1481	1481	1483
45.57	1520	1518	1526	1520
47.79	1594	1592	1595	1593
		1618		1621
49.57	1654		1648	1653

---

Fig. 4 High frequency (6–60 THz) Raman spectra of powdered DL-alanine, with 474 THz laser excitation and a pump power of 8.5 mW incident on the sample.

The low frequency limit of the reported spectra is restricted by the instrumentation used. Lower frequency data still has been previously reported by Aviv et al.,³¹ who report the same peaks below 6.00 THz as seen here with the addition of another, even lower energy peak at 1.2 THz (40 cm⁻¹). This peak, along with the next two lowest energy features at 2.22 and 2.69 THz, are also visible in the optical terahertz spectrum of DL-alanine, as will be shown in the Results and discussion section.

3.3 X-ray diffraction

To complement the Raman spectroscopy and further confirm the purity of the powder, X-ray diffraction (XRD) was performed using Cu K-α radiation from a first generation Empyrean diffractometer by Malvern Panalytical. The results are shown in Fig. 5 where room temperature measurements are compared to a calculated model based on the structure from Nandhini et al.¹⁵ There are no spurious features in the experimental results. This confirms the sample purity. Good agreement is seen between the peaks observed and the model. By a direct comparison between the calculated XRD-pattern from the known structure and the experimental results, the Miller indices of the observed peaks have been assigned.

Fig. 5 Powder X-ray diffraction of DL-alanine measured at room temperature and the VESTA³² calculated model, constructed using atomic parameters from Nandhini et al.¹⁵ Miller indices have been labelled vertically above prominent peaks.

Temperature dependent measurements were also obtained to investigate if and how the crystal structure changes with temperature. A temperature range of 13–296 K was used, spanning the same range as the THz spectra, giving further insight into the changing intermolecular bonds. The results are presented in Fig. 6 where all planes are observed to increase in interplanar spacing with increasing temperature. This shifting is quantified in Table 2. Pairs of parallel planes are observed to shift by a comparable amount, validating the assignment of Miller indices. The largest change is seen in the 131, 331 and 620 planes with 1.12% difference in spacing from cryogenic to room temperature, while the 122̄ plane undergoes the least shifting with only 0.28% expansion over the temperature range studied. Along with 122̄, the 112 and 113 planes also undergo a comparable minimal increase of 0.29%. These three planes are additionally the closest to being parallel with the ab plane. The planes closer to parallel with either the ac or bc planes then show the larger percentage increases in interplanar spacing with temperature. This indicates that the a and b axes are more affected by thermal expansion, as opposed to the c axis of the crystal. Head to tail intermolecular bonds between neighbouring amine and carboxyl groups along the c axis, seen in Fig. 2, may be responsible for the least shifting in this direction.

Fig. 6 Temperature dependence of the XRD pattern for DL-alanine powder, over the range of 13–296 K. All observed interplanar spacings are seen to increase with increasing temperature. The inset gives an example of the detail available throughout the pattern.

Table 2 Peak positions [Å] for XRD data at 13 K and 296 K and their percentage increase with temperature over this range

Miller index	13 K	296 K	% increase
1 2 0	5.827	5.877	0.87
1 1 0	5.269	5.316	0.88
2 1 0	4.166	4.212	1.11
2 0 1̄	4.091	4.111	0.48
2 1 1̄	3.387	3.407	0.59
3 1 0	3.273	3.305	0.96
4 0 0	2.948	2.978	1.03
4 1 0	2.649	2.677	1.07
1 1 2	2.536	2.544	0.29
2 2 1̄	2.408	2.430	0.91
2 1 2̄	2.372	2.396	1.03
3 2 1	2.197	2.219	0.99
4 2 0	2.098	2.121	1.09
4 0 2	2.066	2.077	0.53
1 2 2̄	2.050	2.056	0.28
4 2 1̄	1.971	1.990	0.96
4 1 2	1.958	1.971	0.68
6 0 1	1.869	1.889	1.06
1 3 1	1.850	1.871	1.12
1 1 3	1.819	1.824	0.29
5 1 2̄	1.763	1.772	0.49
3 3 1	1.693	1.711	1.12
6 2 0	1.647	1.665	1.12

---

3.4 THz instrumentation

Fourier transform spectroscopy (FTS) and terahertz time domain spectroscopy (THz-TDS) have both been employed here. The specifications of both systems along with the helium flow cryostat used for temperature dependence measurements have already been reported.²⁴ Preliminary TDS measurements in the range of 50–300 K have also been previously reported,³³ with a focus on the fundamental mode. That report was limited to a frequency range below 2.5 THz and also limited in the temperatures used. Here a broader temperature range of 8–295 K has been explored for DL-alanine within the spectral range of 0.8–4.8 THz using the FTS system.

4 Results and discussion

4.1 Terahertz spectra

A comparison of the spectra from the FTS and TDS systems taken at cryogenic temperatures, as given in Fig. 7, shows the same four absorptions between 0.8–3 THz. Previous work³³ confirms no absorptions below 0.8 THz. This comparison between experimental systems shows that the background is much smoother in the FTS system, which has the added effect of making the absorptions more symmetric, hence its use here.

Fig. 7 Comparison of FTS and TDS experimental DL-alanine spectrum at cryogenic temperatures. TDS spectrum vertically offset for clarity.

The THz spectra of DL-alanine were taken using the FTS system over a wide temperature range, 8–295 K, and are shown in Fig. 8. A resolution of 0.5 cm⁻¹ was used to record spectra while the sample slowly cooled to base temperature. The THz spectra have been analysed with zero-padding applied, to appear smoother, extending the initial interferograms from 4729 up to 65 536 points. No adopisation has been used.

Fig. 8 Temperature dependent terahertz transmittance spectra of DL-alanine using FTS. Numerical labels represent the frequency of each mode at 8 K.

The high quality spectra are a feature of the cryogenic temperatures, where thermal vibrations are greatly reduced and the material becomes less absorbing and more transmissive. Spectra on a more transmissive sample will have more signal while background fluctuations remain constant, leading to a larger signal to noise ratio and thus higher quality spectra.

In Fig. 8, four distinct absorptions are identified below 3 THz. The fundamental mode at 1.35 THz is observed to be highly absorbing in comparison to the following three modes. Additionally, there are three modes observed between 3–4.8 THz; however, these are too absorbing for the sample thickness employed and consequently the absorption features hit the noise floor. These three features will not be analysed to the same extent as those below 3 THz due to poor signal to noise ratio, making fitting less reliable. For all absorptions observed, a Gaussian fit has been used to determine the peak position at each temperature. The peak positions are shown in Fig. 9. All features here are observed to redshift with increasing temperature as expected, apart from the mode at 2.70 THz, which blueshifts.

Fig. 9 All absorption bands determined using FTS system for DL-alanine. Data is from Table 3. Positions were calculated by Gaussian fits to the spectral data. Statistical fitting uncertainties are too small to be shown on this scale.

4.2 Temperature dependence of frequency

For the four lowest energy absorptions, the peak position against temperature has been fitted using Bose–Einstein statistics in Fig. 10. The first two modes, at 1.35 THz and 2.24 THz, redshift by 0.095 THz and 0.023 THz, respectively, over the full temperature range. The mode at 2.89 THz redshifts by 0.044 THz from 8–190 K. The Bose–Einstein fits are in very good agreement with the three redshifting absorption bands. This indicates that the model is sufficient here, and that these absorptions are entirely mediated by phonons.

Fig. 10 Bose–Einstein fits to absorption band shifting in the four lowest energy absorptions. Statistical fitting parameters are shown, with ω₀ in THz, A in THz K⁻¹, and T_C in K. Vertical error bars of 0.001 THz were determined from fitting.

A prominent feature of the Bose–Einstein fitting is the constant frequency of the mode at low temperatures. The extent of this region, as seen in Fig. 10, is governed by the fitting parameter T_C which is related to the ground state energy of the phonons in a particular mode. The modes at 2.24 and 2.89 THz have T_C values of ≈300 K, indicating that these modes may share a common phonon bath. The observation of this constant frequency region in all four low energy modes supports the theory of these modes being mediated by phonons.

Contrary to what thermal expansion predicts, the absorption at 2.70 THz blueshifts, by 0.015 THz from 8–116 K, while only initially following a Bose–Einstein fit. The rate of shifting appears to decrease after ≈80 K, before changing to redshifting. Unfortunately, above 125 K this mode is no longer observable. As this behaviour is not well described by either the thermal expansion or phonon model its origin remains undetermined.

An assumption of the Bose–Einstein fitting is that the potential energy surface for the atoms is constant at all temperatures. This assumption is not entirely accurate, yet for the redshifting modes this effect must be negligible due to the accuracy of the fits. However, the absorption at 2.70 THz demonstrates a mode where the potential energy surface may change enough that the Bose–Einstein model no longer fits. This could be due to thermal expansion, where the separation of the molecules with increasing temperature starts to dominate the shifting of the mode. So, initially, we observe blueshifting; but, as the potential energy surface changes due to thermal expansion, it leads to redshifting at higher temperatures. This behaviour is similar to observed shifting in sucrose,³⁴ where deuteration of the hydrogen atoms produced a stronger shifting indicating the importance of hydrogen bonds in this absorption. A precursor to the explosive TNT has also shown this unusual blueshifting behaviour below 100 K,⁵ with DFT modelling showing a complex interplay of inter- and intra-molecular hydrogen bonds leading to the observed blueshifting. Temperature dependent modelling for DL-alanine is thus desirable to verify the mechanism for the observed blueshifting.

4.3 Temperature dependence of linewidth

The full width at half the maximum height (FWHM) has been determined using a Gaussian fit for the four absorptions below 3 THz, and is shown in Fig. 11. As the temperature decreases, absorptions become deeper and narrower. This is explained by the anharmonic potential where successive energy states are not uniformly separated, but the spacing decreases with increasing energy. At low temperatures the phonon population is restricted to a narrow band of allowed states, as the energy gap to excited states is large. However, as the temperature rises and phonons populate higher and higher energy states, the energy gap to neighbouring states keeps reducing, allowing the phonon population to spread out. As each energy state corresponds to a distinct frequency, absorptions are observed to broaden with increasing temperature.

Fig. 11 Linewidth of the four lowest energy absorptions in DL-alanine's terahertz spectra.

In Fig. 11, quadratic fits have been used, of the form Γ₀ + Γ₁T + Γ₂T², and the fit parameters are recorded in Table 4. As the quadratic fit shows good agreement, a T² dependence on the linewidth is implied. Additionally as the number of phonons, n, is proportional to temperature, the broadening has an n² dependence, as has been shown for α-glycine²⁴ another molecular amino acid crystal.

Table 3 Absorption band peak positions for DL-alanine THz spectra from the FTS system at temperatures 8–295 K. Positions were calculated by Gaussian fits to the spectral data. Uncertainty in temperatures is ±0.1 K, and statistical uncertainty in band fitting is ±0.001 THz for all peaks

Temp. [K]	1.35 [THz]	2.24 [THz]	2.70 [THz]	2.89 [THz]	3.22 [THz]	3.77 [THz]	3.91 [THz]
8	1.352	2.244	2.699	2.885	3.222	3.774	3.914
12	1.352	2.244	2.700	2.885	3.223	3.774	3.915
13	1.351	2.244	2.700	2.885	3.222	3.774	3.914
29	1.351	2.244	2.700	2.885	3.219	3.773	3.914
42	1.349	2.244	2.702	2.885	3.218	3.772	3.898
52	1.348	2.243	2.703	2.885	3.216	3.769	3.894
63	1.345	2.243	2.706	2.883	3.213	3.767	3.886
71	1.342	2.243	2.708	2.880	3.208	3.765	3.884
79	1.340	2.243	2.709	2.879	3.201	3.758	3.882
87	1.338	2.242	2.711	2.878	3.198	3.746	3.878
97	1.335	2.242	2.712	2.876	3.197
105	1.331	2.241	2.713	2.874	3.196
116	1.328	2.241	2.714	2.871	3.189
125	1.326	2.240	2.713	2.868	3.176
135	1.321	2.239		2.864	3.169
145	1.317	2.239		2.859	3.163
155	1.314	2.237		2.857	3.159
166	1.310	2.236		2.850	3.151
178	1.304	2.236		2.845	3.145
190	1.300	2.235		2.841	3.137
203	1.294	2.233
218	1.288	2.232
232	1.281	2.230
250	1.274	2.229
264	1.269	2.227
280	1.261	2.225
295	1.257	2.221

---

Table 4 Fitting parameters to linewidth data in Fig. 11. A quadratic fit of the form Γ₀ + Γ₁T + Γ₂T² has been used, with Γ₀ in THz, Γ₁ in THz K⁻¹ and Γ₂ in THz K⁻²

Absorptions [THz]	Γ 0	Γ 1	Γ 2
1.35	0.04493	1.011 × 10^−4	6.585 × 10^−9
2.24	0.02445	8.665 × 10^−6	4.087 × 10^−7
2.70	0.02857	<1 × 10^−9	5.147 × 10^−7
2.89	0.04528	2.352× 10^−5	9.737 × 10^−7

---

4.4 DFT modelling

Numerical modelling has calculated four modes with non-zero intensity below 3.1 THz, which have been assigned to the four observed peaks in Table 5 (for details see the ESI†). A comparison of the experimental and theoretical peaks is seen in Fig. 12. There is very close agreement between the two lowest energy modes. A shift of ≈0.2 THz is seen in the next two low energy absorptions between the observed and calculated spectra. These higher energy modes are assigned with less confidence due to the shifting present. From the experimental results we see that the mode at 2.70 THz blueshifts and the mode at 2.89 THz redshifts. Hence temperature dependent modelling may help to further validate this assignment. Experimentally, if large single crystals of DL-alanine could be grown, polarisation measurements would add further constraints to the mode assignment.

Table 5 Assignment of calculated vibrational modes of DL-alanine. A brief description of the modes is given, with each mode visualised in Fig. 13

Experimental peaks [THz]	Calculated peaks [THz]	Mode description
1.35	1.33	Gliding of molecular planes, in the b-axis direction
2.24	2.19	Gliding of molecular planes, in the c-axis direction
2.70	2.95	Rotation of individual molecules around the c-axis
2.89	3.06	Rocking of molecules, with twisting of the COO^− groups

---

Fig. 12 Calculated absorbances (vertical lines) of DL-alanine compared to the experimental transmittance spectrum (full curve) at cryogenic temperatures.

Fig. 13 Calculated THz vibrations of DL-alanine using the B97-3c functional. Solid rectangles represent one unit cell and the dashed boxes represent a region with a generally collective motion indicated by the arrows. Animated media files of these four modes are available in the ESI.†

The two lowest energy modes observed in DL-alanine are attributed to the gliding of molecular planes. For the 1.35 THz mode, molecular planes parallel to the bc plane oscillate in the b-axis direction. Similarly for the 2.24 THz mode, molecular planes parallel to the bc plane oscillate in the c-axis direction. Previous DFT modelling of DL-alanine by Fu et al.,¹⁴ using the RPBE functional, only investigated the fundamental mode. They found a similar gliding mechanism to be the origin. Here we have experimental results that observe the next three absorptions, which further validates our model, as these are also calculated.

5 Conclusions

A pure pellet of DL-alanine has been used to study its terahertz spectrum. Raman spectroscopy and powder X-ray diffraction have been used to confirm the sample structure and purity. Temperature dependent XRD results also confirmed that the crystal expands in all directions with increasing temperature.

The terahertz spectrum of DL-alanine has been explored for the first time over a wide temperature range (8–295 K). Seven unique spectral absorptions have been identified at cryogenic temperatures. Only the first four absorptions are completely resolved with the others being too strong and hitting the noise floor. The temperature dependence of these first four modes has been studied further. Three of these modes redshift and are well described by Bose–Einstein statistics indicating their phonon origin. The other mode blueshifts, a phenomenon seen in molecular crystals with intricate hydrogen bonding. The precise mechanism remains to be determined and will be investigated further.

DFT calculations have been used to identify the vibrations that lead to the first four absorptions. Close correlation between the predicted theoretical modes and the experimental spectra validates these calculations. The modelling shows that large scale molecular vibrations are indeed the cause for the observed low frequency terahertz modes. These are mediated by the intermolecular bonds, some of which are shared with the enantiopure forms of alanine. In the future, a comparison of the intermolecular modes and the molecular vibrations they cause in these various forms of alanine will be investigated, both experimentally and theoretically.

Credit authorship contribution statement

T. J. Sanders: conceptualisation, methodology, formal analysis, data curation, investigation, writing – original draft, writing – review & editing, visualisation. J. L. Allen: conceptualisation, methodology, formal analysis, data curation, investigation, writing – review & editing, visualisation. J. Horvat: conceptualisation, investigation, resources, software, writing – review & editing, visualisation, supervision, project administration. R. A. Lewis: conceptualisation, investigation, resources, writing – review & editing, visualisation, supervision, project administration.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

We thank J. Lang of the University of Wollongong for providing the Raman spectroscopic results. We also thank Y. Wang from the University of New South Wales for the XRD data. This work was supported by the Australian Research Council through the Linkage Infrastructure, Equipment and Facilities scheme, grant number LE170100020. Numerical modelling was undertaken with the assistance of resources and services from the National Computational Infrastructure (NCI), which is supported by the Australian Government.

References

1. A. Matei, N. Dricho, B. Gompf and M. Dressel, Chem. Phys., 2005, 316, 61–71.
2. M. R. C. Williams, A. B. True, A. F. Izmaylov, T. A. French, K. Schroeck and C. A. Schmuttenmaer, Phys. Chem. Chem. Phys., 2011, 13, 11719–11730.
3. P. U. Jepsen and S. J. Clark, Chem. Phys. Lett., 2007, 442, 275–280.
4. Y. Liu, T. Zhou and J.-C. Cao, Infrared Phys. Technol., 2019, 96, 17–21.
5. L. M. Lepodise, J. Horvat and R. A. Lewis, J. Phys. Chem. A, 2015, 119, 263–270.
6. A. D. Squires, A. J. Zaczek, R. A. Lewis and T. M. Korter, Phys. Chem. Chem. Phys., 2020, 22, 19672–19679.
7. Z.-P. Zheng and W.-H. Fan, J. Biol. Phys., 2012, 38, 405–413.
8. S. C. Shen, L. Santo and L. Genzel, Can. J. Spectrosc., 1981, 26, 126–133.
9. J.-P. Yu, C. Li, W.-T. Yi, B.-B. Jin, Y.-F. Liu and L. Jiang, Spectrosc. Spectral Anal., 2018, 38, 386–393.
10. Z. Mita, H. Watanabe and S.-I. Kimura, Infrared Phys. Technol., 2019, 96, 7–9.
11. N. Laman, S. S. Harsha, D. Grischkowsky and J. S. Melinger, Biophys. J., 2008, 94, 1010–1020.
12. T. Sakamoto, T. Tanabe, T. Sasaki, Y. Oyama, J.-I. Nishizawa, T. Kawanishi and Y. Hiyama, Malays. J. Biochem. Mol. Biol., 2009, 11, 88–93.
13. M. Yamaguchi, F. Miyamaru, K. Yamamoto, M. Tani and M. Hangyo, Appl. Phys. Lett., 2005, 86, 053903.
14. R. Fu, Z. Li, B. Jin, C. Zhang, H. Dai, Y. Xue and J. Chen, Spectrosc. Spectral Anal., 2010, 30, 2023–2026.
15. M. S. Nandhini, R. V. Krishnakumar and S. Natarajan, Acta Crystallogr., 2001, C57, 614–615.
16. R. Dovesi, A. Erba, R. Orlando, C. M. Zicovich-Wilson, B. Civalleri, L. Maschio, M. Rérat, S. Casassa, J. Baima, S. Salustro and B. Kirtman, Wiley Interdiscip. Rev.: Comput. Mol. Sci., 2018, 8, e1360.
17. J. G. Brandenburg, C. Bannwarth, A. Hansen and S. Grimme, J. Chem. Phys., 2018, 148, 064104.
18. S. Grimme, J. Antony, S. Ehrlich and H. Krieg, J. Chem. Phys., 2010, 132, 154104.
19. F. Weigend and R. Ahlrichs, Phys. Chem. Chem. Phys., 2005, 7, 3297–3305.
20. S. Grimme, J. G. Brandenburg, C. Bannwarth and A. Hansen, J. Chem. Phys., 2015, 143, 054107.
21. F. Pascale, C. M. Zicovich-Wilson, F. López Gejo, B. Civalleri, R. Orlando and R. Dovesi, J. Comput. Chem., 2004, 25, 888–897.
22. C. Zicovich-Wilson, F. Pascale, C. Roetti, V. Saunders, R. Orlando and R. Dovesi, J. Comput. Chem., 2004, 25, 1873–1881.
23. Terahertz Spectroscopy, ed. S. L. Dexheimer, CRC Press, Boca Raton, FL, 2008.
24. J. L. Allen, T. J. Sanders, J. Horvat and R. A. Lewis, Spectrochim. Acta, Part A, 2021, 244, 118635.
25. T. J. Sanders, J. L. Allen, M. Large, J. Horvat and R. A. Lewis, 44th International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz), 2019, pp. 1–2.
26. X. Li, K. Xu, H. Li, S. Yao, Y. Li and B. Liang, RSC Adv., 2016, 6, 8395–8405.
27. S. A. M. B. Dhas and S. Natarajan, Mater. Lett., 2008, 62, 2633–2636.
28. E. A. Belo, J. A. Lima Jr., P. T. C. Freire, F. E. A. Melo, J. M. Filho, H. N. Bordallo and A. Polian, Vib. Spectrosc., 2010, 54, 107–111.
29. Y. Gong and W.-Q. Wen, Spectrosc. Spectral Anal., 2005, 26, 90–93.
30. K. Machida, A. Kagayama and Y. Saito, J. Raman Spectrosc., 1978, 7, 188–193.
31. H. Aviv, I. Nemtsov, Y. Mastai and Y. R. Tischler, J. Phys. Chem. A, 2017, 121, 7882–7888.
32. K. Momma and F. Izumi, J. Appl. Crystallogr., 2011, 44, 1272–1276.
33. T. J. Sanders, J. L. Allen, M. Large, J. Horvat and R. A. Lewis, 45th International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz), 2020, pp. 1–2.
34. M. Walther, B. M. Fischer and P. Uhd Jepsen, Chem. Phys., 2003, 288, 261–268.

---

Footnote

† Electronic supplementary information (ESI) available: Overview document, numerical calculation output file and videos of the four lowest modes. See DOI: 10.1039/d0cp05432a

---