Computational rotational–vibrational spectroscopic analysis of isomeric species in the interstellar gas-phase stereoinversion of amino acid threonine

Molecular Astrophysics 15 (2019) 8–16

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Research Paper

Computational rotational–vibrational spectroscopic analysis of isomeric species in the interstellar gas-phase stereoinversion of amino acid threonine Namrata Rani, Vikas

T

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Quantum Chemistry Group, Department of Chemistry & Centre of Advanced Studies in Chemistry, Panjab University, Chandigarh 160014, India

ARTICLE INFO

ABSTRACT

Keywords: Amino acids Rotational–vibrational spectra Anharmonic effects Astrochemistry Computational chemistry

The gas-phase stereoinversion of amino acid threonine under the condition of interstellar medium (ISM) has been predicted to proceed through isomeric species with diverse chemistry. These species including ammonium ylides, epoxides, contain a variety of functional groups such as geminal-diol, triol besides alkenyl, carboxy, keto, hydroxy, and amino groups. The detection of these species in ISM can help in unravelling the enantiomeric excess observed in meteoritic samples. Towards this, the present work reports rotational and vibrational spectroscopic data computed for the conformers and isomeric intermediates predicted along the stereoinversion pathways of proteinogenic threonine under conditions akin to ISM. The rotational parameters are computed using quantum mechanical methods employing Møller–Plesset perturbation theory whereas for the vibrational analysis, density functional computations are performed using dispersion corrected exchange-correlation functionals. The anharmonic corrections are also computed using vibrational second-order perturbation theory, which, however, fails to account for the hydrogen bonded interactions in the species investigated. The rotational and vibrational transitions predicted for the conformers of threonine are observed to be in good agreement with the available experimental data. The gas-phase spectroscopic data computed for other isomeric species of threonine is quite reliable and can be used to search threonine or other amino acids in ISM by resolving the astrophysical data observed in the microwave and mid-infrared regions.

1. Introduction A rapid increase in the number of space observatories, and an exponential rise in the interstellar spectroscopic data collected from these has propelled recent research in astrochemistry to unfold theories behind chemical evolution in interstellar medium (ISM) (Majumdar, 2018; Tanarro et al., 2018; Chaisson and McMillan, 2002). Great strides have been made towards this from the discovery of first interstellar molecule, methylene radical CH, via optical absorption spectroscopy to the latest finding of iso-cyanogen CNCN through rotational transitions (Swings and Rosenfeld, 1937; Agúndez et al., 2018). More than 240 molecules have been detected using different spectroscopic methods that are also helping to understand composite chemistry in the ISM (Endres et al., 2016). In fact, the presence of extra-terrestrial organic molecules has resulted into theories that the life on early earth originated from outer space. It is also hypothesised that the organic molecules detected in ISM may have acted as precursors to biological molecules (Koga and Naraoka, 2017; Kwok, 2016; McCollom, 2013). From the latest search of complex organic molecules (COM) in star forming regions to the discovery of first chiral molecule propylene oxide in

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molecular cloud Sgrb2(N) (Mcguire et al., 2016; Rivilla et al., 2017; Ohishi, 2016), the search for chiral molecules in outer space has been quite intensified. Moreover, strong speculations for the existence of simplest amino acids glycine in Orion and Sgrb2 nebula as well as in the low mass star forming region IRAS (Lattelais et al., 2011; Combes et al., 1996; Cazaux et al., 2003), had encouraged the scientists toward the quest for other amino acids in the ISM (Kwok, 2016), supported by the analysis of meteoritic samples, particularly the carbonaceous chondrites (Koga and Naraoka, 2017; Burton et al., 2012). Towards this, we had carried out quantum-mechanical investigations on the stereoinversion of some amino acids under the conditions of ISM (Kaur and Vikas, 2015; Kaur et al., 2018; Rani and Vikas, 2018). Recently, we had explored several species along the gas-phase stereoinversion pathways proposed for L-threonine, an amino acid with two chiral centres (Rani and Vikas, 2018). The pathways were predicted to proceed through simultaneous intramolecular proton and hydrogen atom transfer under the conditions of ISM. These multi-step pathways involve various isomeric intermediates and transition states, which can help in the detection of amino acids in outer space. In particular, the protoplanetary disks around young stars are widely

Corresponding author. E-mail address: [email protected] (Vikas).

https://doi.org/10.1016/j.molap.2019.04.002 Received 5 February 2019; Received in revised form 25 April 2019; Accepted 28 April 2019 Available online 30 April 2019 2405-6758/ © 2019 Elsevier B.V. All rights reserved.

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Fig. 1. Optimized equilibrium structures (EQs) of conformers and important isomeric intermediates explored along the stereoinversion pathways of L-Threonine [Ref. (Rani and Vikas, 2018)]. For the nomenclature adopted for various species in this article, see SI Table S1. The numerical values in parentheses are relative energies (in kcal/mol) including zero point energy of the molecular species relative to the energy of global conformer EQ0# at MP2/6–311+ +G(d,p) level of theory. The total energy (including zero point energy) of EQ0# is −437.125652 (0.143577) a.u. (for energetics predicted using other quantum-mechanical methods, see Ref. (Rani and Vikas, 2018)).

searched regions for COMs (Walsh et al., 2018; Garrod and Widicus Weaver, 2013; Aikawa et al., 2008). Notably, in threonine, this region was proposed to be the optimum region for its stereoinversion analysed in our study (Rani and Vikas, 2018). In the present work, a computational spectroscopic analysis is carried out for various species (EQs, depicted in Fig. 1) which are involved in the gas-phase stereoinversion of threonine. Among the molecular species depicted in Fig. 1, EQ0# is the global (minimum) energy conformer of L-threonine proposed in the stereoinversion study of L-threonine whereas EQ0 is a key conformer of threonine which has suitable orientation (of various substituents around the chiral centre) for the gas-phase stereoinversion to proceed (Rani and Vikas, 2018). Note that a total of seven conformers of threonine have been identified using rotational spectroscopy in a study by Alonso et al. (2009). Besides this, in a recent study by Dubey et al. (2019), characteristic peaks from matrix isolation IR spectroscopy have also been assigned to the four lowest conformers, though their computational study reports a total of 38 conformers. Notably, the two aforementioned conformers being discussed here were also reported to be among the lower energy conformers in the studies by both Alonso et al. (2009) and Dubey et al. (2019). The species, depicted in Fig. 1, show a rich chemistry, and includes triols (EQ1, EQ2), geminal-diols (EQ1, EQ5), epoxides (EQ3, EQ4), ammonium ylide (EQ6), besides having a variety of other functional groups. Notably, similar types of intermediate are either already known to be or can be significant in the synthesis of amino acids in the exotic environment of ISM. For example, the geminal-diol can act as an important precursor for the synthesis of aldehydes and ketones. These carbonyl compounds can then be converted into amino acids via Strecker reaction (Koga and Naraoka, 2017; Miller, 1957). Further, the epoxides investigated in this study are similar to the first chiral molecule propylene oxide recently detected in the ISM (Mcguire et al., 2016). In fact, epoxides are reactive species because of electrophilic as well as nucleophilic properties and ring strain, which can be involved in the synthesis of amino acids by first converting into diols. Besides these, the zwitterionic-type ammonium ylide intermediate had also been proposed to be an important intermediate in the formation of glycine in ISM (Maeda and Ohno, 2004). The detection of these species in outer space can provide important insights into the stereoinversion and synthesis of amino acids in ISM. This may also help in understanding the origin of enantiomeric-excess observed for several amino-acids including threonine in the meteoritic samples (Burton, 2018), and hence, the abiotic origin of bio-homochirality on pre-biotic earth. To explore the aforementioned chemical complexity of ISM, the rotational–vibrational spectroscopy has become an indispensable tool (Tanarro et al., 2018; Low et al., 2007). In fact, the protoplanetary disks

are under the influence of radiation from their parent star and therefore, are heated continuously. Due to the temperature gradient, different chemical layers in protoplanetary disks are formed. Hence, different wavelength regions are required to probe the complete range of protoplanetary disks (Henning and Semenov, 2013; Pontoppidan et al., 2010; Dishoeck, 2004; Hardy et al., 2015). Several molecules have been detected in the protoplanetary disks so far, from the detection of simpler hydrocarbons such as C2H2 to hydrogen cyanide HCN using vibrational spectroscopy to the detection of some complex organic molecules like methanol, formaldehyde and the discovery of formic acid via their millimetre and sub-millimetre signatures (Walsh et al., 2018; Pontoppidan et al., 2014; Favre et al., 2018). The temperature trait of warmer star-forming region is such that the most of spectroscopic information received is in the range of mid-infrared (IR) and far-IR wavelengths (Pontoppidan et al., 2010; Dishoeck, 2004; Avenue et al., 2013). Notably, the C60 and C70 fullerenes were detected around the planetary nebula using their infrared lines. Hence, infrared lines can be helpful to search more complex molecules around the protoplanetary disks (Cami, 2010). For stereoinversion to be observed in threonine, we had proposed a temperature range of 500–1000 K to be optimum, which corresponds to the inner mid planes (∼ 1 astronomical units) of the disks. Therefore, the present work provides the vibrational characteristics of various isomeric intermediates involved in the stereoinversion of threonine at 298 K. In fact, an advantage of IR spectroscopy is that it can be used to detect gas phase molecules without permanent dipole moment, and hence is also acting as a great probe in the study of complex organic molecules in the outer space (Herbst and van Dishoeck, 2009), though most of the infrared region is not transparent to the ground-based telescopes. However, with access to a large number of highly efficient space observatories/telescopes such as Hubble, ISO, spritzer and the most futuristic, James Webb Space telescopes (JWST) by NASA and ESA, the discovery of new interstellar molecules via infrared spectroscopy can be expected (Pontoppidan et al., 2010; Dishoeck, 2004; Ieke et al., 2015; Benedict et al., 2017). Besides the IR spectroscopic data collected from the space observatories, the greater sensitivity and high resolution of modern radio telescopes such as Atacama Large Millimeter/submillimeter Array (ALMA), has extended the scope of rotational spectroscopy in the detection of molecules in ISM (Hardy et al., 2015; Baudry et al., 2016; Wootten and Thompson, 2009). In fact, most of the interstellar molecules have been identified by their characteristics rotational lines that are capable of differentiating even between the conformers of the same molecule. The inspection of the bulk of rotational lines in colder region (10–50 K) and other denser region of the ISM, can help in search of 9

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Table 1 Equilibrium rotational constants Ae, Be & Ce, (in MHz), of threonine conformers EQ0# and EQ0, computed using different quantum-mechanical methods. These are compared with available experimental values as well as ab initio values at MP2/6–311++G(d,p) level (indicated in italics) from Ref. (Alonso et al., 2009). The notation of conformers in parentheses is taken from the experimental study. The values in parenthesis are absolute deviation from the corresponding experimental values. The best computed values are highlighted in bold. Method

Experimental (Alonso et al., 2009) MP2/6–31+G(d,p) MP2/6–311++G(d,p)* B3LYP-D3(BJ)/cc-pVTZ B2PLYP-D3(BJ)/cc-pVTZ B3LYP-D3(BJ)/aug-cc-pVTZ B3LYP-D3(BJ)/SNSD ⁎

EQ0# (I1b)

EQ0(IIIβb)

Ae

Be

Ce

Ae

Be

Ce

3232.48 3226.3 (6.16) 3232.6 (0.1) 3237.2 (4.7) 3247.3 (14.8) 3222.9 (9.6) 3210.3 (22.2)

1533.72 1539.0 (5.32) 1542.7 (9.0) 1533.5 (0.2) 1544.2 (10.5) 1526.4 (7.3) 1520.3 (13.4)

1267.89 1267.6 (0.30) 1271.8 (3.9) 1266.3 (1.6) 1270.0 (2.1) 1265.5 (2.4) 1260.8 (7.1)

3379.84 3370.4 (9.49) 3382.6 (2.8) 3393.1 (13.3) 3401.8 (22.0) 3377.3 (2.6) 3360.9 (18.9)

1482.05 1482.00 (0.05) 1487.7 (5.6) 1470.3 (11.7) 1479.5 (2.5) 1467.8 (14.4) 1461.8 (20.3)

1237.59 1237.2 (0.40) 1239.5 (2.0) 1247.1 (9.5) 1248.5 (10.9) 1244.5 (6.9) 1239.7 (2.1)

The MP2/6–311++G(d,p) values (rounded-off) has also been reported in Ref. (Alonso et al., 2009) along with the experimental study.

threonine and other species related to its stereoinversion in ISM. Though the stereoinversion pathways in threonine are proposed to be more feasible in hot regions of protoplanetary disks but there is continuous outflow of matter (gas and dust) in the ISM from different evolutionary stages of star and planet formation (Cox, 2005; Zinnecker and Yorke, 2007). Thus, ISM can be thought of chemically enriched with trace amounts of complex molecules via small eruptions or catastrophic supernovae explosions that distribute the mass in ISM (Olivier and Hennebelle, 2015). Thus, it is also of worth to provide the rotational characteristics of different species involved in the stereoinversion of threonine for their search in the cold regions of ISM. However, to resolve the complex spectroscopic data collected from radio telescopes and space observatories, the computational spectroscopic analysis using quantum mechanical methods has become an integral part of the research on the detection of molecules in outer space. In the present work, the gas-phase rotational and vibrational spectrum of various species explored for the stereoinversion of threonine is computed using appropriate quantum-mechanical methods. The choice of the method is based on the best estimation of rotational–vibrational characteristics of the two well-known conformers of threonine, EQ0 and EQ0# depicted in Fig. 1 (Rani and Vikas, 2018). As discussed in the subsequent sections, the computed spectroscopic parameters for the two conformers match quite well with the various theoretical and experimental studies already reported in the literature (Alonso et al., 2009; Dubey et al., 2019; Xu and Lin, 2010). The rotational spectra of these conformers is compared with the experimental study by Alonso et al. (2009), whereas the vibrational traits are matched with a very recent gas phase vibrational study by Dubey et al. (2019). Further, the potential energy distribution analysis of each fundamental vibrational mode of various species has also been carried out including the effect of anharmonicity in the frequency calculations using vibrational second-order perturbation theory (VPT2) (Bloino and Barone, 2012). Note that for the characterisation of interstellar molecular species, laboratory data is essential, usually aided by computational calculations. The computations performed in the present study are discussed in details in the next section.

stereoisomers are exactly the same, therefore, the present work deals with only proteinogenic L-threonine. Table 1 compares the computed rotational parameters of both the conformers with their experimental values available from the study by Alonso et al. (2009). The computed rotational constants are in good agreement with the experimental ones but the value of principal rotational constant A is found to be more accurate using MP2/6–311++G(d,p) than MP2/6–31+G(d,p) method. The same method was also successfully employed for threonine and other amino acids to resolve their experimental rotational data (Alonso et al., 2009; Pen et al., 2012; Cocinero et al., 2007; Sanz et al., 2010). Therefore, MP2/6–311++G(d,p) method was further employed to compute the rotational constants of various species involved in the stereoinversion of threonine, as provided in Table 2. However, as depicted in Fig. 1, the conformations of various species are highly influenced by the hydrogen bonding interactions between the substituents within the molecule. Besides this, the anharmonic effects can further complicate the vibrational analysis of such species. In the present work, to account for the anharmonic effects, densityTable 2 Equilibrium rotational constants Ae, Be & Ce (in MHz), vibrationally corrected ground state rotational constants A0, B0 & C0 (in MHz)*, Ray's asymmetry parameter, κ = (2Βe−Αe−Ce)/(Αe−Ce), 14N nuclear quadrupole coupling constants χaa χbb & χcc (in MHz), electric dipole moment components μa, μb & μc (in Debye), the quartic centrifugal distortion constants ΔJ, ΔK, ΔJK, δJ & δK (in kHz)*, and barrier to methyl rotation V3 (in cm−1), for the L-threonine conformers EQ0# & EQ0 and the isomeric intermediates EQ1–EQ6 depicted in Fig. 1.

Αe Βe Ce Α0 Β0 C0 κ ΔJ ΔK ΔJK δJ δK χaa χbb χcc μa μb μc V3

2. Computational details First, the two important conformers, EQ0# and EQ0 (depicted in Fig. 1), which are involved in the stereoinversion of L-threonine, were optimized using 2nd order Møller-Plesset perturbation theory (MP2) (Møller and Plesset, 1934; Krishnan et al., 1980). The computations were performed employing Pople's gaussian basis sets 6–31+G(d,p) with 319 basis function as well as 6–311++G(d,p) with 369 basis function while using frozen core approximation. The geometry of the conformers was further verified using frequency calculations. Note that except for the optical rotation and the reaction with chiral compounds, the geometrical parameters and properties of both D- and L-

EQ0#

EQ0

EQ1

EQ2

EQ3

EQ4

EQ5

EQ6

3232.6 1542.7 1271.8 3190.9 1506.4 1269.4 −0.72 0.29 0.10 0.28 0.08 0.55 −3.71 1.88 1.83 3.36 3.32 1.11 1185

3382.6 1487.7 1239.5 3351.4 1475.9 1225.6 −0.77 0.15 0.60 0.16 0.02 0.83 −2.31 −0.12 2.43 2.31 −1.13 −1.08 1043

3144.4 1370.4 1185.9 3113.8 1362.6 1177.0 −0.81 0.07 −0.59 1.01 0.01 −2.24 1.20 2.52 −3.72 2.54 −0.95 −0.72 1141

3146.4 1374.9 1169.2 3116.3 1367.4 1161.1 −0.79 0.06 −0.42 0.87 0.00 −2.12 −3.46 1.74 1.71 0.99 −1.87 1.08 441

3645.7 1431.6 1337.6 3613.0 1416.5 1326.2 −0.92 0.09 0.38 0.54 0.00 −2.20 1.18 −3.87 2.69 1.57 0.03 −1.57 1137

3562.4 1600.4 1294.0 3527.3 1582.5 1281.8 −0.73 0.01 0.36 0.20 0.01 0.19 1.31 2.42 −3.73 −0.82 0.47 0.82 1341

3378.1 1485.8 1235.4 3345.9 1474.6 1220.0 −0.77 0.13 0.47 0.13 0.02 0.55 −3.34 0.85 2.49 −0.38 −1.10 −1.51 145

2884.4 1738.7 1188.3 2878.8 1722.8 1172.6 −0.35 0.20 0.59 −0.11 0.03 0.28 −0.11 0.01 0.11 1.88 8.89 0.31 125

⁎ Calculated using B3LYP-D3(BJ)/cc-pVTZ method, while the rest of the parameters are computed using MP2/6–311++G(d,p) method (see text for explanation).

10

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functional theory (DFT) computations were performed employing a hybrid B3LYP-D3(BJ) as well as a double-hybrid B2PLYP-D3(BJ) exchange-correlation parameterized functionals of Becke (B) exchange and Lee-Yang-Parr (LYP) correlation corrected with Grimme's D3 dispersion and Becke-Johnson (BJ) damping to account for the dispersion interactions as well (Grimme et al., 2011). For the DFT computations, Dunning's correlation consistent basis sets, cc-pVTZ as well as diffusion function (aug)umented, aug-cc-pVTZ, were employed. The efficacy of these cost-effective D3 corrected B3LYP-D3(BJ) functional is quite wellknown, for example, in a study on the nucleobases and their dimers by Fornaro et al. (2014), though in a recent study by Goerigk and Bauer (2017), the B2PLYP-D3(BJ) method is observed to outperform B3LYP-D3(BJ) when dispersion is included. Further, as analysed in Table 1, the rotational constants computed for the aforementioned conformers of threonine, the B3LYP-D3(BJ)/cc-pVTZ shows much less deviation from the experimental data than the B2PLYP-D3(BJ). Moreover, cc-pVTZ computed rotational constants are found to be more accurate than the computationally more expensive aug-cc-pVTZ basis set indicating a lesser role of diffuse functions here. Besides this, a medium sized basis set, SNSD as suggested by Fornaro et al. (2014), was also tested but as evident in Table 1, no satisfactory results for our system could be obtained. Moreover, B3LYP-D3(BJ) is observed to be computationally more cost-effective and time-economical over the B2PLYP-D3(BJ). Thus, for the present work, B3LYP-D3(BJ)/cc-pVTZ method is employed to estimate anharmonic vibrational frequencies utilizing vibrational second-order perturbation theory (VPT2). In VPT2, anharmonicity is added as a perturbation to the zeroth order Hamiltonian (Ĥ) of harmonic oscillator:[46]

^ ^ ^ H VPT2 = Hharmonic + Hanh

Table 3a Comparison of experimental vibrational frequencies (vexp) from Ref. (Dubey et al., 2019) observed for L-threonine conformer EQ0#, with the computed harmonic (vharm) and anharmonic (vanharm) frequencies (all in cm−1) and their intensity (I, in km/mol−1) at B3LYP-D3(BJ)/cc-pVTZ level of the theory. The assignment in bold depicts the characteristic vibrations. vexp

vharm (unscaled)

Iharm

vanharm

Ianharm

Vibrational assignment*

3623 3432 1784 1357

3796 3449 1831 1423

44.0 244.4 284.0 430.1

3646 3165 1797 1370

34.8 230.7 193.7 83.6

1201

1281

1.8

1271

70.2

1044

1056

54.2

1035

32.4

v [O8-H10] v [O11-H12] v [C6]O9] β [H12-O11-C16] + v [C6O11] β [H7-C5-C14] + τ [(H4-C3CO11)] v [C5-C14] + β [H10-O8-C5]

v: stretching, β: bending, τ: torsional, γ: out of plane vibrations, a: asymmetric, s: symmetric; (for atom numbering, see Fig. 1). ⁎

for transition states located along the stereoinversion pathways are also provided in SI Table S4. Besides these, the characteristic vibrational frequencies (harmonic as well as anharmonic) computed in mid-IR region are provided in Table 4. Note that the conformers of threonine and all the related intermediates are non-linear with seventeen atoms and hence, are associated with 45 fundamental modes of vibration. Each fundamental mode for every intermediate is further analysed using ‘potential energy distribution (PED)’ analysis provided in Table 3a and b and SI Table S5. The PED analysis was performed through Vibrational Energy Distribution Analysis (VEDA4) program of Jamróz (2013). The characteristic fundamental frequencies for conformers EQ0 and EQ0#, are compared with the available experimental values in Table 3a and b. The next section discusses the computed rotational and vibrational spectroscopic data for the conformers and isomeric intermediates observed along the stereoinversion pathways of L-threonine.

(1)

^ where the anharmonic term H anh includes the cubic and quartic force constants. Note that, in addition to the calculation of vibrational frequencies and corresponding intensity at both the harmonic and anharmonic levels, this also helps in the estimation of vibrational correction to the ground state rotational constants and quartic centrifugal distortion constants, as provided in Table 2. All the computations were performed using GAUSSIAN 09 quantum-mechanical software package (Frisch et al., 2009). Note that the rotational parameters provided in Table 2 are obtained from anharmonic calculations performed using Watson's A-reduced Hamiltonian in Ir representation (Gordy and Cook, 1984). Using the aforementioned rotational parameters, significant rotational transition lines were predicted for conformers EQ0 and EQ0# as well as other molecular species being investigated, through PGOPHER program (Western, 2017), for simulating rotational and vibrational spectra. The computationally predicted line list is provided in SI Tables S2, S3 and S6. As evident in SI Table S2, the location of predicted lines for the conformers is in good agreement with those observed in the experimental study of Alonso et al. (2009). Notably, the agreement with the experimental values is within 50 MHz. Moreover, the equilibrium rotational constants calculated with the MP2/6–311++G(d,p) method were found to be closer to the experimental values than those computed using B3LYP-D3(BJ)/cc-pVTZ, with a deviation of < 3 MHz for principal rotational constant A, and < 9 MHz for B and C. Therefore, MP2 method was used for the computation of rotational constants of other molecular species in the present work. However, note that the vibrational correction to the ground state rotational constants and centrifugal distortion constant were evaluated using anharmonic calculations performed at the B3LYP-D3(BJ)/cc-pVTZ level of the theory. Besides these, due to the presence of nitrogen atom in the threonine, the effect of nuclear hyperfine coupling constant (14N) was also included in the rotational transitions. Using the computed rotational parameters, the rotational spectra simulated for isomeric intermediates explored along the stereoinversion of threonine are further depicted in Fig. S1. The rotational parameters

3. Results and discussion 3.1. Rotational analysis The interaction of microwave radiation with a molecule possessing a permanent electric dipole moment results in a rotational spectrum (Puzzarini et al., 2010). All the species located along the stereoinversion pathways of L-threonine exhibit a non-zero dipole moment (at least along one direction), on the three principal rotational axes: a, b and c; hence, all are microwave active. Moreover, these species possess significant and unequal values of moment of inertia (Ia ≠ Ib ≠ Ic) along the principal axes. Therefore, all the species are associated with three different rotational constants and are asymmetric tops. In addition to the computed equilibrium rotational constants (Ae, Be, Ce), the respective vibrational corrections leading to the vibrationally-corrected ground-state rotational constants A0, B0, C0, are also provided in Table 2. Further, asymmetric tops possess very low degree of symmetry that often complicates their spectra due to complex rotational energy levels. Their rotational levels are characterised by three rotational quantum numbers J, K-1 and K+1 where J is associated with total angular momentum of the molecule, and K−1, K+1 are pseudo-quantum numbers because of the absence of a symmetry axis in the asymmetric species. Furthermore, the Ray's asymmetry parameter κ = (2Βe−Αe−Ce)/(Αe−Ce), governs the quantitative deviation of asymmetric top molecules from symmetry limits i.e., symmetric prolate (κ = −1) and symmetric oblate (κ =+1). The Ray's asymmetry parameter for species of our interest ranges between −0.35 and −0.92. This clearly indicates that the isomeric intermediates are near-prolate asymmetric tops except EQ6 which is a prolate asymmetric top molecule. The ammonium-ylide type EQ6 with κ = −0.35 exhibits least extended configuration, whereas EQ3, an epoxide, is found to be the most extended with κ = −0.92. 11

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Table 3b Same as Table 3(a) but for L-threonine conformer EQ0 . vexp

vharm (unscaled)

Iharm

vanharm

Ianharm

Vibrational assignment

3570 3534 1770 1402 1284 1149 1106

3740 3729 1786 1446 1309 1177 1146

69.3 84.3 260.3 40.7 68.3 106.4 214.6

3566 3525 1754 1410 1288 1142 1105

138.5 18.9 90.4 27.1 48.4 53.4 196.6

v [O8-H10] v [O11-H12] va [C6]O9] β [H10-O8-C5] + β [H7-C5-C14] β [H7-C5-C14] + β [H10-O8-C5] τa [(H15-C14-C5-C3) - (H16-C14-C5-C3)] + va [(C5-O8) - (C5-C14)] + v [(C5-O8) - (C6-O11) - (C6-C3)] v [(C6-O11) + (C3-N1) + (C5-C14) - (C3-C5) - (C5-O8)] + β [H12-O11-C16]

while in EQ0# (with ĸ = −0.72) the transitions are most deviated. Furthermore, for isomeric intermediates, EQ2 and EQ5, a-type transitions are dominated by b- and c-type transitions. These intermediates can be distinguished by the position of a characteristic doublet in b-type transitions: J′2J’−1←J′′1J’’−1 and J′2J’−2←J′′1J’’, centred at [3Ae+Ce+(Be-Ce)/2]+(Be+Ce)(J′′−1) MHz and separated by [(BeCe)/2]J′J′′ MHz as shown in Fig. S1. The location of b-type J′1J’ ←J′′0J” transition is predicted at (Ae+Ce+2CeJ′′) MHz. For EQ2, these b-type transitions are more intense than c-type transitions and can be used to locate EQ2 which is a triol. However, for ammonium ylide type EQ6, these b-type transitions are distinctly intense due to an extremely high magnitude of μb, and can particularly be used to search EQ6 through the predicted values. Further, to locate EQ5, a geminal-diol with a keto group, the c-type doublet, arising from transitions: J′2J’−1←J′′1J’’−1 and J′2J’−2←J′′1J’’, which is observed closer to the b-type doublet, can be searched. Moreover, c-type transition: J′1J’−1←J′′0J” is predicted to be at (Ae+Be+2BeJ′′) MHz, so that the difference between the successive transition is equal to 2Be as shown in the spectrum of EQ5 in Fig. S1. Further, the two epoxide isomers, EQ3 and EQ4, can be differentiated with the help of characteristic rotational transitions due to difference in their rotational parameters (note that the two isomers cannot be distinguished on the basis of vibrational spectrum as discussed in next section). For EQ4, the intensity of all types of transitions is quite low due to extremely low magnitude of dipole moment along all the principal axes, whereas as discussed before, EQ3 exhibits strong atype transitions that can be easily located, thus, differentiating it from EQ4. The line list for the molecular species EQ1-EQ6 is further provided in SI Table S3, with J′<5 and K-1 ≤ 1, in accordance with the rotational transitions observed for the conformers of threonine in the experimental study of Alonso et al. (2009).Besides this, the line list in high frequency range of 84–116 GHz corresponding to the band 3 of ALMA (Wootten and Thompson, 2009), is also provided in SI Table S6 but with J’≤20, for the conformers EQ0#, EQ0 and species EQ1-EQ6. Further, note that the location of rotational lines predicted from the aforementioned formulae strictly depends on the value of Ray's parameter and principal rotational quantum number. A large deviation/ separation of rotational lines may be expected with high deviation in Ray's parameter from the near prolate limit and for states with higher principal rotational quantum number (Cooke and Ohring, 2013). Furthermore, due to the presence of nitrogen (with nonzero nuclear spin) in molecular species being investigated, there exists a significant value of quadrupole moment in these species (Gordy and Cook, 1984; Puzzarini et al., 2010). From the interaction of nuclear spin angular momentum with the rotational angular momentum, a nuclear hyperfine structure in the rotational spectrum can be expected, as predicted for 202 ← 101 transition in EQ0# as depicted in Fig. S1. The hyperfine transitions in rotational spectra follow the selection rule ΔF = −1,0, and +1, where F = J + I with I being the nuclear spin quantum number. The value of quadrupole coupling constants and their effect on the rotational spectrum is also an important way to characterize, identify and differentiate between the molecular species, particularly if the values of rotational constants are similar. Therefore, computed 14N nuclear quadrupole coupling constants provided in Table 2, can further help in the identification of species investigated in this study. The

The position of rotational transition lines depends on the value of rotational constants associated with the molecule, whereas the most important factor affecting the intensity of a transition is the value of the dipole moment of the molecular species. The selection rule in terms of quantum number J is ΔJ = −1,0, and +1 that corresponds to the P, Q and R branches, respectively (but note that these are different from the well-known P,Q,R branches in a ro-vibrational spectrum). Three different types of transitions a-type, b-type and c-type further complicate the rotational spectrum of an asymmetry top. These different types of transitions are based on the selection rule for pseudo-quantum numbers. The latter depends on different symmetry requirements of the wavefunction associated with upper and lower energy levels needed for the molecular rotation along different principal axes (Gordy and Cook, 1984). Thus, the limiting selection rule in term of quantum number K is ΔK-1 = 0, ± 2, ± 4,…, and ΔK+1 = ± 1, ± 3, ± 5,…, which corresponds to the a-type transitions and will be active if molecule possesses non-zero dipole moment (μa) along the principal axis ‘a’. Similarly, ΔK-1 = ± 1, ± 3, ± 5,…, and ΔK+1 = ± 1, ± 3, ± 5,…, corresponds to the family of b-type transitions, whereas, ΔK−1 = ± 1, ± 3, ± 5,…and ΔK+1 = 0, ± 2, ± 4,…, is the limiting selection rule for c-type transition. If a molecule has significant value of dipole moment along all the three principal axes, the rotational spectrum is expected to have all the three different types of lines present in it. A simplified pure rotational spectra of all the isomeric intermediates of threonine, exhibiting ‘R’ branch transition between rotational energy level J = 1 to J = 2, is simulated using PGOPHER program, and are depicted in SI Fig. S1 (significant a, b and c type transitions for J:2←1 are explicitly depicted). The simulated spectra are depicted in the low frequency region where the experimental results for the conformers of threonine have been analyzed (Alonso et al., 2009). Also note that the transitions with value >1 for ΔK−1 and ΔK+1 are of extremely low intensity, dominated by strong lines with values ≤ 1. For example, as shown for spectra EQ0# in Figure S1, the intensity of 202 ←110 and 220 ←101 transitions is negligible in comparison to other lines arising via ΔK ± 1 = 0 or 1. Therefore, the search of intense transition lines corresponding to ΔK ± 1 = 0 or 1 can be of more importance than the weaker rotational lines. Further, the conformer EQ0# exhibits significant value of dipole moment along all the three directions, hence, its spectrum is quiet complex and involves all the three types of transitions but with weak ctype transition due to a low μc value. The a-type transitions are identifiable via a group of transitions together with the most intense characteristic, J′0J′ ← J′′0J′′ transitions occurring at (Be+Ce)J′ MHz, as shown for EQ0# (prime and double prime refer to upper and lower states, respectively) (Cooke and Ohring, 2013). A similar group of atype transitions with notable intensity is also exhibited by EQ0, EQ1, and EQ3. The spectra simulated with J′≤ 6 for EQ0#, EQ0, EQ1 and EQ3, distinctly identifying the characteristic J′0J′ ← J′′0J′′ transition, are further provided in SI Figure S3. Note that in these, the successive transitions are separated by a frequency of (Be+Ce) MHz. However, as evident in SI Fig. S3, the more far away a species is from the prolate limit, more is the deviation observed from the predicted value (Cooke and Ohring, 2013), which deviates even further with increasing J value. For example, EQ3 (with ĸ = −0.91) exhibits least deviation 12

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Table 4 Characteristic anharmonic frequencies (in cm−1) and corresponding unscaled harmonic values (in italics) calculated at B3LYP-D3(BJ)/cc-pVTZ level of theory, for important conformers and isomeric intermediates along the stereoinversion pathways of threonine. The values in parenthesis are corresponding intensity (in km/ mol−1). For a complete list of all the computed frequencies, see SI Table S5. (v: stretching, β: bending, τ: torsional, γ: out of plane vibrations, a: asymmetric, s: symmetric, + and – sign represents the relative direction of vibration in a mode). EQ0#

EQ0

EQ1

EQ2

3796 (44.0), 3646 (34.8) v [O8-H10] 3590 (11.5), 3423 (7.1) va [NH2] 3490 (8.2), 3333 (45.2) vs [NH2] 3449 (244.4), 3165 (230.7) v [O11-H12] 3116 (18.5), 2974 (21.7) v [C14-H16] 3100 (29.5), 2956 (33.1) va [(C14-H15) + (C14-H17)] 3051 (15.2), 2926 (9.7) v [(C5-H7] 3041 (9.1), 2917 (1821.5) vs [(C3-H4) + (C14-H15)] 3036 (11.0), 2945 (771.1) v [(C3-H4) - (C14-H15) - (C14-H17)] 1831 (284.0), 1797 (193.7) v [C6]O9] 1652 (28.6), 1583 (1.6) β [H2-N1-H13] 1423 (430.1), 1370 (83.6) β [H12-O11-C16]

3740 (69.3), 3566 (138.5) v [O8-H10] 3729 (84.3), 3525 (18.9) v [O11-H12] 3590 (8.8), 3416 (5.2) va [NH2] 3499 (3.8), 3343 (2.3) vs [NH2] 3129 (14.5), 2980 (16.1) v [(C14H15) - (C14-H16) - (C14-H17)] 3110 (23.6), 2965 (26.7) va [C14-H16) - (C14-H17)] 3056 (21.8), 2914 (54.3) v [C3-H4] 3046 (13.1), 2941 (10.5) vs [(C14-H15) + (C14-H16) + (C14-H17)] 2986 (43.1), 2863 (26.6) v [(C5-H7] 1786 (260.3), 1754 (90.4) va [C6]O9] 1637 (39.3), 1620 (19.5) β [H2-N1-H13] 1309 (68.3), 1288 (48.4) β [H10-O8-C5]

3806 (19.2), 3614 (13.2) v [O8-H10] 3760 (34.7), 3554 (20.5) v [O11-H12] 3729 (23.6), 3514 (15.7) v [O9-H4] 3622 (16.1), 3450 (9.4) va [NH2] 3519 (5.8), 3363 (2.8) vs [NH2] 3123 (21.1), 2978 (22.7) va [(C14-H15) - (C14-H17)] 3110 (24.8), 2962 (29.4) va [C14-H17) - (C14-H16)] 3062 (13.3), 2929 (15.0) v [C5-H7] 3044 (17.9), 2942 (22.1) vs [(C14-H15) + (C14-H16)] 1800 (36.2), 1750 (8.1) v [C6]C3] 1632 (53.3), 1608 (2.5) β [H2-N1-H13] 1388 (6.4), 1354 (4.9) β [H7-C5-O8] 1266 (116.4,) 1216 (76.1) βa [(H4-O9-C6) - (H12-O11-C6)] 1220 (137.9), 1187 (132.0) va [(C6-O9) - (C6-O11)] 1167 (109.3), 1141 (58.5) βs [(H4-O9-C6) + (H12-O11-C6) - (H13-N1-C3)]

3810 (24.3), 3614 (22.3) v [O9-H4] 3798, (36.7), 3635 (32.6) v [O11-H12] 3550 (102.7), 3303 (93.8) v [O8-H10] 3534 (9.6), 3356 (6.1) va [NH2] 3478 (4.7), 3325 (4.0) vs [NH2] 3146 (15.3), 2996 (3.7) v [C14-H17]{89} 3082 (10.6), 2936 (12.2) va [(C14-H15) - (C14-H16)] 3038 (26.3), 2939 (23.7) vs [C14-H15) + (C14-H16)] 3000 (58.9), 2895 (57.7) v [C6-H7] 1754 (146.2), 1712 (81.9) v [C5]C3] 1647 (6.6), 1586 (8.6) β [H2-N1-H13] 1461 (21.7), 1415 (20.3) β [H12-O11-C6] + β [H7-C6-O11] 1391 (63.2), 1332 (48.1) β [H10-O8-C5] 1241 (183.1), 1203 (127.8) β [H4-O9-C6] + β [H12-O11-C6] 1218 (11.1), 1178 (55.3) β [H13-N1-C3] 1033 (134.4), 992 (92.9) v [C6-O11] 973 (141.4), 944 (125.5) v [C6-O9]

EQ3

EQ4

EQ5

EQ6

3808 (50.6), 3631 (37.7) v [O11-H12] 3791 (28.0), 3621 (21.1) v [O8-H10] 3625 (22.1), 3459 (17.7) va [NH2] 3530 (8.0), 3378 (4.5) vs [NH2] 3129 (16.7), 2979 (19.9) va [(C14-H15) - (C14-H17)] 3111 (21.9), 2969 (23.7) va [(C14-H15) - (C14-H17)] + va [C14-H17) (C14-H16)] 3076 (44.2), 2916 (48.5) v [C6-H4] 3047 (13.9), 2948 (15.0) vs [C14-H15) + (C14-H16)] 3007 (34.2), 2886 (27.9) v [C5-H7]

3814 (54.5), 3657 (43.2) v [O11-H12] 3749 (37.2), 3543 (28.4) v [O8-H10] 3613 (16.1), 3438 (12.6) va [NH2] 3528 (8.1), 3373 (4.1) vs [NH2] 3123 (20.5), 3001 (26.8) v [C6-H4] 3116 (16.8), 2972 (22.0) v [C14-H16]

3807 (44.0), 3602 (35.6) v [O11-H12] 3712 (105.8), 3518 (83.3) v [O9-H10] 3560 (8.0), 3378 (4.0) va [NH2] 3483 (2.6), 3330 (0.9) vs [NH2] 3148 (6.7), 2999 (5.0) va [(C14-H16) - (C14-H15)] 3101 (4.2), 2959 (3.1) v [(C14-H17) - (C14-H16) - (C14-H15)]

3774 (37.4), 3574 (33.4) v [O11-H12] 3505 (52.0), 3311 (35.6) v [N1-H13] 3341 (34.0), 3106 (43.1) v [N1-H7] 3216 (171.0,) 2957 (170.5) v [N1-H2] 3107 (8.2), 2952 (26.9) v [C14-H17] 3081 (73.7), 2919 (2376.0) va [(C14-H15) - (C14H16)]

3097 (30.0), 2967 (31.7) va [(C14-H15) - (C14-H17)] 3060 (11.8), 2923 (22.9) v [C5-H7] 3031 (13.6), 2868 (12.1) v [C14-H16] + vs [(C14-H15) + (C14-H17)] 1655 (59.9), 1626 (25.1) β [H2-N1-H13] 1431 (37.0), 1382 (4.0) β [H10-O8-C5] 1179 (173.1), 1153 (50.0) β [(H13-N1-C3] 1115 (40.3), 1081 (3.0) v [(C5-C14) + (C6-O11) - (C5-O8)]

3042 (20.5), 2902 (12.3) v [C3-H7] 3032 (0.1), 2916 (2864.4) v [(C14-H15) + (C14-H16) + (C14-H17)] 2952 (77.3), 2874 (68.0) v [C6-H4]

3052 (469.3), 2617 (496.5) v [O9-H10] 3010 (63.9), 2880 (809.1) vs [(C14-H15) + (C14H16)] 2932 (182.3), 2779 (367.3) v [C6-H4]

1767 (154.8), 1734 (88.9) v [C5]O8] 1672 (27.1), 1604 (6.3) β [H2-N1-H13] 1302 (92.1), 1247 (73.1) β [H10-O9-C6] + β [H4-C6-O9] 1267 (42.2), 1234 (30.9) β [H12-O11-C6] + β [H4-C6-O9] 1204 (34.3), 1171 (26.4) v [C5-C14] + β [H13-N1-C3] 1107 (57.8), 1080 (60.9) v [C3-N1]

1685(39.1), 1602 (5.9) β [H2-N1-H7] 1634 (13.6), 1565 (5.8) βa [(H2-N1-H13) - (H7-N1-H13] 1621 (236.9), 1579 (9.2) va [(C5-O8) - (C5-C3)] 1592 (229.5), 1537 (87.6) β [H10-O9-C6] 1460 (12.9), 1427 (1.4) βa [H15-C14-H17) − (H15-C14-H16)] 1423 (67.5), 1374 (53.4) β [(H2-N1-H7) + (H2-N1-H13) + (H7N1-H13)

1638 (63.5), 1614 (55.5) β [H2-N1-H13] 1166 (161.0), 1128 (119.0) β [H13-N1-C3] 1074 (37.2), 1043 (72.8) vs [(C6-O9) + (C6-O11)] 1039 (102.8), 1011 (71.5) va [(C14-C5) - (C5-O8)]

(continued on next page) 13

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Table 4 (continued) EQ3

EQ4

predicted nuclear hyperfine splitting is further simulated in SI Fig. S2, for one of the characteristic a-type transition 202 ← 101 in all the intermediate species except for EQ6 for which the intensity of a-type transitions was observed to be quite low. The magnitude of hyperfine splitting depends on the value of nuclear quadrupole coupling tensor elements that further depends on the orientation of –NH2 group with respect to the remaining fragment of the molecule, and hence it can reveal characteristic molecular features. Besides these, the effect of methyl torsion can also be observed in the rotational signal from threonine and its related isomeric intermediates, which depends on the potential barrier for the rotation of methyl group with respect to the rest of the molecule. This splits the rotational lines into two torsional components, A and E (Lin, 1959). Though these are not included in the simulated spectra (depicted in Figure S1), but to account for its effect in rotational spectra, the barrier height (V3) for the methyl rotation, is calculated by performing relaxed potential energy scan at MP2/ 6–311++G(d,p) level of theory, and the values calculated are provided in Table 2. Notably, barrier is predicted to be quite low in ammonium ylide type intermediate EQ6 and geminal diol EQ5. Thus, the aforementioned computed rotational constants, dipole moment, quadrupole moment and the barrier for methyl internal rotation besides the simulated rotational spectra of the conformers and isomeric intermediates located along the stereoinversion pathways of threonine can be helpful in resolving the experimental transitions observed in the specified frequency region, particularly those received from the cold molecular clouds in the ISM. This is further augmented by the vibrational analysis presented next.

EQ5

EQ6

1095 (51.0), 1063 (23.5) v [C6-O9] 1072 (100.6), 1034 (93.8) v [C6-O11]

1081 (43.4), 1047 (25.3) v [C3-N1]

calculations. Among the 45 vibrational modes associated with threonine and its related isomers, most can be considered as the characteristics of these species. For example, for conformers EQ0# and EQ0, the most significant mode is the intense stretching vibrational motion associated with carboxyl group [C6]O9]. As provided in Table 4, its harmonic frequency is at 1831 cm−1 and 1786 cm−1, respectively, for EQ0# and EQ0 with an anharmonic correction of ca.33 cm−1. As evident in Fig. 1, the interaction of carboxyl's oxygen with the hydrogen of polar side chain in EQ0 lowers down its stretching frequency compared to that in EQ0#. Besides this, the O-H stretching can also be used to differentiate between the two conformers. The frequency difference (of ca. 200 cm−1) between the two different –OH stretching frequencies in EQ0# is quite large compared to a difference of 40 cm−1 in EQ0. This is probably due to trans and cis orientation of NH2 group with respect to –COOH group in EQ0# and EQ0, respectively. This can be used as important characteristic frequencies to distinguish between the two conformers. Further, the region of 2850–2900 cm−1 corresponds to the –CH stretch in both the conformers but this is unlikely to differentiate the two isomers. Besides these, the bending vibration, β [H2-N1-H13], appears at 1583 cm−1 in EQ0# and at 1620 cm−1 in EQ0 with a moderate intensity though in EQ0# it is quite weak. However, the moderately intense bending of the hydroxyl group involved in the H-bonding, i.e., β [H10-O8-C5] in EQ0# and β [H12-O11-C5] in EQ0, can be used to differentiate the two conformers. Further, the intermediate EQ1, a geminal diol as well as a triol, can easily be differentiated from EQ0 due to the absence of –C]O stretch as H(4) migrates to O(9) along the stereoinversion pathways (Rani and Vikas, 2018). This results into an additional transition due to [O9-H4] stretch at 3614 cm−1. This transition is at highest frequency value perhaps due to the absence of any non-covalent interactions around this –OH group. Moreover, a new intense transition due to the stretching corresponding to [(C6-O9) – (C6-O11)] arises in EQ1 at 1187 cm−1 which was absent in EQ0. Besides this, the bending of [H4-O9-C6] couples with the neighbouring [H12-O11-C6] resulting in asymmetric and symmetric bending modes of strong intensity. The symmetric mode (v22 in SI Table S5) matches with that in EQ0, but the asymmetric stretch is unique both in terms of position as well as intensity. Further, the presence of carbon–carbon double bond [C6=C3] also result into a new transition at 1750 cm−1 but is of rare importance because of quite low intensity. The other isomeric intermediate EQ2 can be identified by an intense, high frequency [O8-H10] stretch appearing at 3303 cm−1. The orientation of [O8-H10] is such that the H-bonding interaction of H(10) with the nitrogen of amino group shifts the frequency from 3614 cm−1 in EQ1 to 3303 cm−1 in EQ2. However, NH2 bending, -OH bending and –C-H stretch are not helpful in differentiating this isomer despite of being significantly intense. Though there is a change of peak position of [C6-H7] and [C5-H7] stretch from EQ1 to EQ2, but the frequency region corresponding to these vibrations are very close and complex. However, the intensity of [C5]C3] stretch is very high compared to that of [C6]C3] stretch in EQ1, probably due to greater change in dipole moment accompanying this vibration in EQ2. Besides these, the intense low frequency transitions are also important characteristics of this isomer, which are predicted at 992 and 944 cm−1, corresponding to [C6-O11] and [C6-O9] stretch, respectively. Further, the epoxide EQ3 can be distinguished based on the absence

3.2. Vibrational analysis Table 3b compares the computed vibrational frequencies of Lthreonine conformers, EQ0# and EQ0, with those observed in a gas phase experimental study by Dubey et al. (2019). As evident, except for the O-H stretching frequency in EQ0#, the computed anharmonic frequencies at B3LYP-D3(BJ)/cc-pVTZ level of theory are in good agreement with the experimentally observed transitions. For example, the observed [O8-H10]-stretching frequency in EQ0# and EQ0 is at 3623 cm−1 and 3570 cm−1, respectively, which are closely predicted by the computed anharmonic frequency of 3646 cm−1 and 3566 cm−1, respectively. Similarly, [O11-H12] stretching frequency is predicted to be at 3449 cm−1 and 3525 cm−1 in EQ0# and EQ0, respectively, which are observed at 3432 and 3534 cm−1, respectively. Note that in EQ0#, the experimentally observed vibrational frequency of [O11-H12] stretch is in a better agreement with its computed harmonic frequency value rather than one computed with an anharmonic correction (under VPT2). As evident in Fig. 1, H(12) is involved in the hydrogen-bonding interaction with nitrogen N(1), thereby affecting the vibrations of O11H12. This clearly conveys that the VPT2 fails to account for it. However, excluding this vibrational mode, all other experimental transitions, whether corresponding to the important –C]O stretch or peaks related to –OH bending as well as the complex C-C and C-N stretches and distortions, are best predicted by the anharmonic frequencies as evident in Table 3(a). Thus, anharmonic corrections computed in this study can be taken to be reliable for predicting the vibrational frequencies of the important conformers and isomeric intermediates along the stereoinversion pathways of threonine. Moreover, this avoid the use of ad-hoc scaling factors commonly employed in harmonic frequency 14

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of intense –C]O stretch and the shift of [O8-H10] stretch above the frequencies observed in all other isomers. However, the transition due to bending β [H13-N1-C3] at around 1128 cm−1, is relatively more intense than the similar bending in other isomers. Besides this, the transition due to [C6-H4] stretch is also predicted to appear in EQ3 though it is difficult to locate in nearby peaks of similar energy and intensities. Similar transitions are predicted for another epoxide isomer EQ4 which is a conformational isomer of EQ3. Therefore, the two epoxide isomers are difficult to differentiate solely using the IR spectroscopy, and hence, the rotational spectroscopy is the main tool to uniquely identify these isomers as discussed in previous section. For the keto intermediate EQ5, an intense –C]O stretch between C5 and O8 at 1734 cm−1 is predicted besides a high intensity [O9-H10] stretch appearing at 3518 cm−1. However, the characteristic [C-N] stretch predicted to appear at 1050 cm−1 can be used to identify this isomer. Finally, for the ammonium ylide type intermediate, EQ6, many noteworthy features are predicted in its vibrational spectrum, which includes three different N-H stretch at 3311, 3106 and 2957 cm−1. The first two are predicted to be moderately intense and can also be intermixed with the –O-H stretch and –C-H stretch of similar peak positions. But the highly intense –N-H stretch at 2957 cm−1 can be uniquely identified for this isomer. Similarly, due to large changes in the dipole moment associated with the stretching vibration corresponding to [C6H4], it is also predicted to be exceptionally intense when compared to other –C-H stretch in this isomer as well in other isomers in similar region. In addition to this, bending [H10-O9-C6] predicted to be at 1537 cm−1 can also be used as characteristic of EQ6. It is to be noted that due to the zwitterionic character of EQ6, negative charge present on the carbon atom C(3) is in resonance with O(8). Therefore, C5]O8 bond also exhibits partial single bond character, therefore, no characteristic –C]O stretch is predicted for EQ6. Moreover, the –O-H stretching frequency in 3600 cm−1 region is also predicted to be absent in this isomer. However, the two –O-H frequency corresponding to moderately intense [O11-H12] stretch and a strong [O9-H10] stretch are computed to be at 3574 cm−1 and 2617 cm−1, respectively. The latter transition due to OH stretch at relatively less crowded frequency is complicated by the hydrogen-bonding interactions. However, it can be regarded as an inadequacy of VPT2 similar to that observed for highly intense [O11-H12] stretch in EQ0#. Such erroneous anharmonic corrections, however, are also believed to be due to coupling of large amplitude vibrations which can be tackled using approaches based on diffusion Monte Carlo, for example, as utilized in the case of water clusters (Biczysko et al., 2017; Dzugan et al., 2018). Nevertheless, for such hydrogen bonded modes, harmonic values may be more trustworthy. Besides this, as evident in SI Table S5, it is also important to point out that the anharmonic correction also shows some discreteness in intensity value of some lower frequency fundamental bands for example, v38, v39 in EQ0 and v38, v41in EQ1. However, except for these couple of discrepancies, the anharmonically corrected vibrational transitions can reliably be used to resolve and aid the experimental astronomical observations. Apart from the fundamental vibrations discussed in this section, all other low frequency mode, up-to the range of 1000 cm−1, can also be significant for the identification of different isomeric species, using the potential energy distribution provided in SI Table S5.

parameters predicted for the conformers of threonine are observed to be in good agreement with the available experimental data. The rotational transitions predicted for other isomeric species will also help in understanding their rotational features in association with nuclear-quadrupole moment and barrier to methyl internal rotation. The rotational parameters for the isomeric species computed in this work can be used to generate low temperature rotational database, which may be helpful in their detection in cold interstellar clouds. Moreover, the anharmonically corrected vibrational frequencies of the conformers are found to be in a close agreement with the experimental ones. However, the present work suggests that for the hydrogen-bonded vibrational modes, harmonic frequency values should be followed since the anharmonic corrections computed through VPT2 are found to be unreliable. The vibrational frequencies provided for the isomers can be helpful for their search in warm star-forming region in the ISM. Acknowledgements The authors gratefully acknowledge the financial assistance from Science & Engineering Research Board (SERB), India, under a research project (sanction order no. EMR/2016/002074). Namrata Rani thanks University Grants Commission (UGC), New Delhi (India) for providing SRF(NET) fellowship. The authors are also grateful to the Department of Chemistry, Panjab University, Chandigarh, for providing other computational software and resources. Conflict of interest The authors declare no conflict in the interests. Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.molap.2019.04.002. References Agúndez, M., Marcelino, N., Cernicharo, J., 2018. Discovery of interstellar isocyanogen (CNCN): further evidence that dicyanopolyynes are abundant in space. Astrophys. J. Lett. 861, 1–5. Aikawa, Y., Wakelam, V., Garrod, R.T., Herbst, E, 2008. Molecular evolution and star formation: from prestellar cores to protostellar cores. Astrophys. J. 674, 984–996. Alonso, J.L., Pérez, C., Eugenia Sanz, M., López, J.C., Blanco, S., 2009. Seven conformers of L-threonine in the gas phase: a LA-MB-FTMW study. Phys. Chem. Chem. Phys. 11, 617–627. Avenue, B., View, M., Ricca, A., Bauschlicher, C.W., Allamandola, L.J., 2013. The infrared spectroscopy of neutral polycyclic aromatic hydrocarbon clusters. Astrophys. J. 31, 1–9. Baudry, A., Brouillet, N., Despois, D., 2016. Comptes rendus physique star formation and chemical complexity in the orion nebula : a new view with the IRAM and ALMA interferometers. C. R. Phys. 17, 976–984. Benedict, G.F., Mcarthur, B.E., Nelan, E.P., Harrison, T.E., 2017. Astrometry with hubble space telescope fine guidance sensors-a review. In: The Astronomical Society of the Pacific. 129. IOP Publishing, pp. 1–16. Biczysko, M., Bloino, J., Puzzarini, C., 2017. Computational challenges in astrochemistry. WIREs Comput. Mol. Sci. e1349, 1–38. Bloino, J., Barone, V., 2012. A second-order perturbation theory route to vibrational averages and ttransition properties of molecules: general formulation and application to infrared and vibrational circular dichroism spectroscopies. J. Chem. Phys. 136, 1–15. Burton, A.S., 2018. Insights into abiotically-generated amino acid enantiomeric excesses found in meteorites. Life 8, 1–21. Burton, A.S., Stern, J.C., Elsila, J.E., Glavin, D.P., Dworkin, J.P., 2012. Understanding Prebiotic chemistry through the analysis of extraterrestrial amino acids and nucleobases in meteorites. Chem. Soc. Rev. 41, 5459–5472. Cami, J., 2010. Detection of C60 and C70 in a young planetary nebula. Science 329, 1180–1182. Cazaux, S., Tielens, A.G.G.M., Ceccarelli, C., Castets, A., Wakelam, V., Caux, E., Parise, B., Teyssier, D., 2003. The hot core around the low-mass protostar IRAS 16293-2422: scoundrels rule!. Astrophys. J. 593, L51–L55. Chaisson, Eric, McMillan, S., 2002. Astronomy Today, fourth ed. Prentice Hall, New Jersey, United States. Cocinero, E.J., Lesarri, A., Grabow, J., López, J.C., Alonso, J.L., 2007. The shape of leucine in the gas phase. ChemPhysChem 8, 599–604.

4. Conclusions In this computational quantum-mechanical work, reliable rotational–vibrational spectroscopic data, including the vibrational correction to rotational constants, nuclear hyperfine coupling and anharmonic corrections, have been computed for the conformers and isomeric intermediates predicted along the interstellar stereoinversion pathways of threonine, an amino acid with two stereocentres. The isomeric species investigated include epoxide, geminal-diol, ammonium ylide, triol, besides having other diverse functional groups. The rotational 15

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