Mechanism and Kinetics of the Gas-Phase Stereoinversion in

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A: Kinetics, Dynamics, Photochemistry, and Excited States

Mechanism and Kinetics of the Gas-Phase Stereoinversion in Proteinogenic L-Threonine and Its Astrophysical Relevance Namrata Rani, and . Vikas J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b06659 • Publication Date (Web): 05 Sep 2018 Downloaded from http://pubs.acs.org on September 5, 2018

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The Journal of Physical Chemistry

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Mechanism and Kinetics of the Gas-phase Stereoinversion in Proteinogenic L-Threonine and its Astrophysical Relevance Namrata Rani and Vikas* Quantum Chemistry Group, Department of Chemistry & Centre of Advanced Studies in Chemistry, Panjab University, Chandigarh-160014, India. *Corresponding author e-mail: [email protected], Tel: +91-172-2534408

Abstract Quantum-mechanical computations are performed to trace the mechanistic pathways for the gasphase stereoinversion in proteinogenic L-Threonine, an amino acid with two stereocentres. The pathways are explored employing density functional and coupled cluster theories along with a global reaction route mapping strategy to locate various intermediates and transition states along the stereoinversion pathways on the complex potential energy surface of L-Threonine. A simultaneous intramolecular proton- and hydrogen atom transfer is observed to drive the stereoinversion in Threonine. The kinetics analysis of the stereoinversion pathways is also carried out using transition state theory while accounting for the quantum mechanical tunnelling, under conditions akin to various temperature regions of interstellar medium (ISM). The key step leading to stereoinversion through an achiral intermediate or transition state is predicted to involve a low energy barrier with high stereoinversion rates. The temperature region of 5001000K corresponding to protoplanetary disks was found to be an optimum region for stereoinversion to occur in L-Threonine with quite significant reaction rates. But in the cold molecular clouds of ISM, the stereoinversion is predicted to be a less likely event despite involving significant proton tunnelling. The stereoinversion pathways proposed in this work pay gainful insights, particularly, to the researchers looking for the complex organic molecules in outer space.

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1. Introduction The recent detection of propylene oxide in Sagittarius B2(N),1 as the first chiral molecule to be present in a star formation region, is quite stimulating for the researchers exploring chiral molecules in outer space, particularly the proteinogenic amino acids in the interstellar medium (ISM). Amino acids are much speculated to be present in the ISM or circumstellar medium, which in fact has been supported by their synthesis in the laboratories under experimental conditions mimicking the atmosphere of ISM,2-4 as well as by their presence in the extraterrestrial bodies such as comets and meteoritic samples of carbonaceous chondrites like Murchinson and Murray.5-7 Moreover, an appreciable excess of L-enantiomer of amino acids in these meteoritic samples further confirms the hypothesis that the source of bio-homochirality, in the living organisms, may belong to extraterrestrial processes.8-12 Hence, investigating the stereoinversion of amino acids under the conditions of ISM can help in unravelling the origin of life on early earth. In fact, the presence of complex organic molecules,13,14 in the ISM encourages one to explore the rich and diverse chemistry enveloped therein. The proteinogenic amino acid of interest in the present work is Threonine (2-amino-3hydroxy-butanecarboxylic acid) which is an essential hydroxyl-amino acid. Several studies had indicated its presence in meteoritic samples while speculating its existence in the outer space.6,7,15 Towards the synthesis of Threonine in ISM, the Miller and Urey experiment can be thought as a basis while following the Strecker’s mechanism,6,17 but that will result only in the racemic mixture of an amino acid. The mechanism for gas phase synthesis of Threonine can be hypothesised in three steps starting from the ISM’s ice analogues consisting of CO, CO2, CH4, CH3OH, NH3, H2O etc. As depicted in Figure 1, one of the key step is the synthesis of Glycine which in fact is speculated to be the most probable candidate to be present in the ISM.18 In an another step, the addition of formyl and methyl radicals on the surface of ice grains leads to the formation of acetaldehyde which has already been detected in the ISM.19,20 The final step


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involves a nucleophilic addition of acetaldehyde to Glycine zwitterionic isomer, followed by the migration of (N)-proton to carbonyl oxygen, finally leading to the formation of Threonine. Recently, Threonine and its stereoisomers have been experimentally synthesised from aldehyde and ammonia in a study by Koga et al.,6 supporting the above proposed mechanism. The feasibility of proposed mechanism depends on the energetics of the pathways leading to the formation of intermediate (I) in Figure 1, that resembles an ammonium ylide type species which had also been proposed in a computational study by Maeda et al.21 However, the stereochemistry of resulting Threonine, on the first chiral (carbon) centre will depend on the direction of migrating proton in the third step, whereas on the second chiral (carbon) centre, it will depend on the direction of nucleophilic attack on carbonyl carbon. Hence, there is an equal probability of formation of different stereoisomers (resulting in the racemic mixture), but still there is an abundance of L isomer observed in our biosphere. To pay insights into such bio-homochirality, it is necessary to explore the mechanism involved in the conversion of D and L stereoisomers. Thus, the main objective of the present work is to computationally explore the gas-phase stereochemical pathways of Threonine leading to its stereoinversion at the two chiral centres under condition similar to that in the ISM.

Figure 1. Probable routes towards the synthesis of Threonine in ISM.



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A successful exploration of the stereoinversion pathways in Alanine, Serine and 2aminopropionitrile (2-APN),22-25 had already been reported using quantum-mechanical computations, however, all these molecules are associated with only one chiral centre. To the best of our knowledge, stereoinversion pathways in a molecular species with two stereocentres have never been explored. Threonine is one of the two proteinogenic amino acids having two chiral centres, in fact, it is discovered as the last of the twenty common proteinogenic amino acids known so far.26 Moreover, it is quite interesting to explore the stereoinversion pathways in this molecule because of the fact that it cannot take the stereoinvesrion pathways involving swapping of substituents around chiral carbon substituent as proposed in the studies on previously explored molecules, rather it has to proceed through routes involving multi-migration of the substituents around asymmetric carbon(s) so as to pass through an achiral stationary point needed for the stereoinversion to occur (see later). Due to the presence of two chiral centres, Threonine can exist as four possible stereoisomers with the configurations: (2S,3R), (2R,3S), (2S,3S) and (2R,3R), as depicted in Figure 2. The (2S,3R), is the L-stereoisomer of Threonine (L-Thr). It is the only proteinogenically active form, all other stereoisomers are of little importance. Therefore, the present study mainly deals with the L-Thr, exploring the possible pathways for its conversion into its enantiomer D-Thr.

Figure 2. Stereoisomers of Threonine and inter-relations between them.


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Further, the ISM is a non-homogeneous medium distinguished on the basis of wide range of temperature distribution from as low as 10-20K in molecular clouds to as high as 8000-107 K in hot ionized medium27. Therefore, the stereoinversion pathways explored are also analysed on the basis of thermodynamic and kinetic feasibility in different regions of the ISM. Moreover, the role of quantum tunnelling is also gaining attention in reference to chemical processes in the ISM, in particular, to the chemistry in the lower temperature regions of ISM.28,29 The stereoinversion pathways proposed for Threonine involve the migration of proton or hydrogen atom (see later). Therefore, the role of quantum tunnelling in the feasibility of these pathways has also been explored through the reaction kinetics as discussed in the next section.

2. Computational Methodology The pathways (comprising of stationary points for isomeric intermediates and transition states) leading to the steroinversion in L-Thr are traced using quantum mechanical methods while employing a Global Reaction Route Mapping (GRRM),30-33 computational strategy based on an anharmonic downward distortion following (ADDF) approach.33 Recently, the same strategy has been successfully employed for the conformational search of other proteinogenic amino acids by Kishimoto et al.34-36 Further, note that only the gas phase neutral Threonine has been investigated in this work. The importance of neutral form of amino acids, Glycine and Alanine, in the gas phase has been previously revealed by Iijima et al.37-38 For a preliminary investigation, the lowest energy pathways were first explored for the stereoinversion on the potential energy surface (PES) of L-Thr, using density functional theory (DFT) calculations employing M06-2X meta-hybrid Minnesota exchange-correlation (XC) functional with 6-31G Gaussian basis set.39 The M06-2X functional is known to be quite successful for the prediction of main group thermochemistry and kinetics, but note that the calculations were further refined with larger basis set as well as employing ab initio wave function methods (see later). Since the



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amino acids are quite flexible because of polar amino and acidic groups, therefore, the PES of Threonine is expected to be quite complex due to the presence of an extra polar hydroxyl group, thereby, making the search over its PES more challenging. Hence, a ‘First Only’ option of GRRM is utilized to restrict the search of stationary points on the PES, around the optimized equilibrium molecular structure of L-Thr. A total of 19 isomeric equilibrium structures (EQs) and equal number of transition states (TSs) were located. Out of the 19 EQs traced, 11 were found to be various conformers of L-Thr, however, no achiral stationary point could be located to trace the pathways leading to stereoinversion, which indicates that the stereoinversion in Threonine is associated with high energy barrier but these can be explored intuitively as in our recent studies on Serine and Aspartic Acid.23,25 Note that a full search with GRRM may also explore such pathways, which though depends on the calculation level, but it can be computationally quite expensive for the size of molecular species considered in the present work. Further, note that the gas-phase conformers of Threonine in neutral form had previously been explored computationally on its complex PES by several research groups,40-45 whereas Alonso et al., had investigated these through experimental rotational spectroscopy.44 The principle basis for the existence of a large number of conformers of amino acids is the various possibilities for the intramolecular hydrogen bonding, broadly categorised into three types, depending on the different H-donors [-N(H2),-COO(H)] and -acceptors [-(N)H2,-C(O)(O)H], as well as their relative orientation, as described by Alonso et al. In addition to this, a polar side chain [-CH(OH)CH3] is also present in Threonine, which further complicates its PES due to the presence of one more [-CH{O(H)}CH3] donor and [-CH{(O)H}CH3] acceptor for hydrogen bonding interaction. The 11 conformers searched using GRRM are further compared with this study of Alonso et al.,44 and also with the computational study of Xu and Lin,45 in the Supporting Information (SI). Note that not all the conformers reported in the literature could be


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traced during the ‘first only’ GRRM search as this option restricts the search around the initial equilibrium structure only. But the global minimum obtained from this preliminary investigation is ‘EQ0#’ depicted in Figure 3, which in fact was also reported as the global minimum (NR1) in the study by Xu and Lin as well as one of the lowest conformer (IIb) by Alonso et al. However, the position of various substituent groups in its geometry is not in a suitable orientation for appropriate migrations of groups to take place so that the stereoinversion can result as depicted in Figure 4 (for details, see later). Therefore, other conformers were also inspected and one of the suitable conformer ‘EQ0’ depicted in Figure 3, which has also been probed experimentally as conformer IIIβb by Alonso et al., and computationally reported as conformer NR6 by Xu and Lin, was further adopted for the intuitive exploration of stereoinversion pathways in L-Thr.

Figure 3. Optimized molecular structure of (a) Global minimum EQ0#, (b) conformer EQ0 of L-Thr, obtained through GRRM search at DFT/M06-2X/6-31G level of the theory, various H-bonding interactions are also shown in EQ0# and EQ0, (c) conformer EQ0 (with symmetry point group C1) at the DFT/M06-2X/aug-cc-pVTZ level of the theory, depicting the bond lengths (in Å), (d) depicting the bond angles (in degrees) in its enantiomer D-Thr. The geometrical parameters are exactly the same for both the enantiomers but are depicted in different isomers for the sake of clarity, The nomenclature in large parentheses is adapted from the study of Alonso et al.[Ref.44] whereas that in small parentheses is from the study of Xu and Lin [Ref. 45].



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Figure 4. General scheme depicting all possible migrations of various groups, for the stereoinversion to occur in a molecule with two stereocentre (C1 and C2). For Threonine, P= –COOH, Q= –NH2, R= –H, S= –OH, U= –H, and V= –CH3.

For the intuitive exploration of the stereoinversion pathways using GRRM strategy, computations using a 2-point scaled hypersphere search (2PSHS),33-36 and intrinsic reaction coordinates (IRC)46 were further carried out to locate the desired stationary points, particularly the achiral one, on the complex PES of Threonine. Initially, for this, the DFT calculations were performed using computationally less-expensive Becke three-parameterized Lee-Yang-Parr (B3LYP) hybrid exchange-correlation functional and 6-31G basis set.47-48 The refinement of the geometries of located EQs and TSs at the B3LYP/6-31G level, was performed using DFT/M062X/aug-cc-pVTZ method.39 Note that all the geometry refinements were followed by the harmonic vibrational frequency computations to obtain the zero-point energy (ZPE) correction besides ascertaining whether the stationary point is a minimum energy intermediate associated with no imaginary frequency or a transition state with one imaginary frequency. All the possible pathways (analysed later to be feasible or infeasible) for the stereoinversion in L-Thr are depicted in Figures 5-8.


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The energies of the intermediates and transition states along the ‘feasible pathways’ were further refined using ab-initio coupled-cluster (CC) calculations49 at the CCSD(T)/ccpVDZ//DFT/M06-2X/aug-cc-pVTZ level of the theory as well as using a computationally lessexpensive density fitting (DF) DF-CCSD(T)/cc-pVTZ//DFT/M06-2X/aug-cc-pVTZ method,50 but note that we could not utilize a more suitable aug-cc-pVTZ basis set with diffuse functions at the CCSD(T) level due to limited computational resources. Also note that the present work does not involve any radical species, for which a multi-reference approach will be more suitable. In fact, for the size of species considered in the present work, it is even difficult to employ single-reference CCSD(T) approach for the geometry optimization. However, energetics determined at the CCSD(T)//DFT level are known to be quite reliable for the species investigated in the present work. The refined energies of various stationary points and transition states along the pathways explored are further compared in Table 1 as well as through the potential energy profiles in Figure 9. To pay more insight into the mechanism of stereoinversion and to further confirm the migration of [–H] group as an atom, radical or proton along the explored pathways, the molecular orbital analysis (provided in Figure 10) and natural bond orbital (NBO) analysis51 (provided in Table 2) for important stationary points located along the stereoinversion pathways were also performed at the DFT/M06-2X/aug-cc-pVTZ level. The detailed analysis of the variations in the atomic charges of the species along the IRC of relevant pathways is also provided in SI Figure S2. The Gibbs free energy change associated with the pathways and its temperature dependence in various regions of ISM is further provided in Table 4. All these computations were carried out using GRRM 11,52 while performing quantum mechanical calculations through Gaussian 09 package.53 However, for the density fitting DFCCSD(T)//DFT calculations, PSI-4 quantum-mechanical code was utilized.54 To further analyze the kinetics of stereoinversion along the explored pathways, transition state theory was utilized. Each step along the proposed pathways is elementary in nature with



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well-defined energy barriers, therefore, unimolecular rate coefficients were calculated using conventional transition state theory (CTST) while incorporating the quantum mechanical tunnelling effect as,

=

(1)

where χ(T) accounts for the tunnelling correction using an unsymmetrical Eckart potential at a temperature T, and is defined as,55,56

=

#

,

(2)

where p(E) is the probability of transmission through an associated energy barrier (E), kb is the Boltzmann’s constant, ∆H#f is the energy barrier in forward direction including zero point correction. In Eq.(1), kCTST(T) is the rate constant calculated using CTST at temperature T, and is defined as:

$#

=

! " !#

,

(3)

where σ is the reaction path degeneracy, h is the Planck’s constant, V# is the potential energy difference between transition state and the reactant excluding the zero point energy contribution but is included through the total partition function for transition state (QTS) and reactants (QR). The CTST rate coefficients along with tunnelling transmission factors provided in Table 3 were calculated using KISTHELP program, which can predict the reaction kinetics from electronic structure calculations.56 These kinetics along with aforementioned thermochemical data were utilized to unravel the mechanism for stereoinversion along the pathways explored on the PES of L-Thr as discussed in the next section.


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Table 1. Relative electronic energies (in kcal/mol) including the zero-point-energy (ZPE) correction of the relevant stationary point species (EQs and TSs), located along the feasible or infeasible pathways explored for the stereoinversion of L-Thr, with respect to the energy of conformer (2S,3R)-EQ0, at the specified levels of the theory. The ZPE values in the parenthesis are relative zero point energy of the species with respect to that of EQ0. Note that the refinement of energies at the CCSD(T) level of

the theory is carried out only for the species along the feasible pathways. Stationary point species

Symmetry Point Group

M06-2X/ aug-cc-pVTZ + ZPE (ZPE)

DF-CCSD(T)/cc-pVTZ// M06-2X/aug-cc-pVTZ + ZPE

P1

TS1 P1 EQ1

C1 C1

Pathway 1 (infeasible for stereoinversion) 37.34 (−0.40) 35.20 (0.04)

− −

P2

C1 C1 C1 C1 Cs

Pathway 2 (feasible for stereoinversion) 71.74 (−4.32) 23.86 (−1.10) 102.4 (−4.70) 19.19 (−0.75) 20.33 (−1.23)

73.74 27.30 97.80 21.66 22.69

TS1 P2 EQ1 P2 TS2 P2 EQ2 P2 TS P3a

TS1 P3a EQ1 P3a TS2 P3a EQ2 P3a TS3 P3 EQ3 P3 TS4 P3 EQ4 P3 TS P3b

P3c

TS1

EQ1

DC

TS1 DC1

DC

TS2 DC2

Pathway 3a (feasible for stereoinversion) 50.13 (−3.09) 54.03 29.86 (−0.74) 33.05 33.77 (−0.72) 36.85 29.38 (−0.55) 32.47 54.98 (−4.06) 58.96 11.73 (−0.8) 12.33 75.23 (−4.15) 79.59 46.99 (−0.8) 49.49 52.17 (−1.64) 56.24 Pathway 3b (feasible for stereoinversion) C1 62.21 (−4.87) 63.77 Pathway 3c (infeasible for stereoinversion) C1 22.06 (−0.65) − Dissociation Channel: EQ0 [CH4 + C3H5O3N] DC1 C1 102.07(−4.04) 104.54 C1 61.86 (−4.45) 59.98 Dissociation Channel: EQ0 [H2O + C4H7O2N] DC2 C1 79.52 (-4.64) 78.19 C1 76.44 (-2.47) 75.77 C1 C1 C1 C1 C1 C1 C1 C1 Cs

* The total energy including (ZPE) of EQ0 at the B3LYP/6-31G, M06-2X/aug-cc-pVTZ, CCSD(T)/cc-pVDZ//DFT/M062X/aug-cc-pVTZ and DF-CCSD(T)/cc-pVTZ//DFT/M06-2X/aug-cc-pVTZ levels of the theory is −437.9863 (0.1412), −438.1455 (0.1429), −437.0502 (0.1429) and −437.4882 (0.1429) a.u. respectively.



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Table 2. Natural atomic charges using NBO analysis at relevant sites of intermediates (EQs) and transition states (TSs) located along the stereoinversion pathways, at the DFT/M06-2X/aug-cc-pVTZ level of the theory. The values indicated in bold are discussed in the text.

Atom numbering used in NBO analysis Species

N(1)

H(2)

C(3)

H(4)

C(5)

C(6)

H(7)

O(8)

O(9)

H(10)

O(11)

-0.835

0.372

-0.155

0.215

0.122

0.817

0.169

-0.761

-0.631

0.492

-0.702

TS1

-0.664

0.425

-0.269

0.423

0.075

0.696

0.208

-0.784

-0.705

0.472

-0.790

EQ1

-0.681

0.416

-0.269

0.403

0.077

0.698

0.208

-0.789

-0.705

0.475

-0.795

TS1

-0.835

0.368

-0.253

0.466

0.117

0.716

0.173

-0.759

-0.712

0.465

-0.650

EQ1

-0.827

0.378

0.031

0.478

0.097

0.499

0.183

-0.752

-0.724

0.470

-0.727

TS2

-0.800

0.378

0.033

0.475

0.181

0.390

0.167

-0.714

-0.745

0.478

-0.734

EQ2

-0.877

0.373

-0.039

0.475

0.360

0.393

0.133

-0.704

-0.763

0.506

-0.738

P3a

TS1

-0.834

0.372

-0.161

0.210

0.407

0.686

0.065

-0.757

-0.730

0.512

-0.671

P3a

EQ1

-0.840

0.372

-0.167

0.132

0.619

0.412

0.216

-0.585

-0.768

0.500

-0.742

P3a

TS2

-0.830

0.372

0.346

0.154

0.107

0.353

0.160

-0.749

-0.580

0.493

-0.724

P3a

EQ2

-0.833

0.368

0.339

0.169

0.106

0.352

0.192

-0.737

-0.581

0.475

-0.726

P3a

TS3

-0.733

0.404

0.275

0.158

0.201

0.388

0.186

-0.810

-0.768

0.526

-0.755

P3

EQ3

-0.840

0.372

-0.167

0.132

0.619

0.412

0.216

-0.585

-0.768

0.500

-0.742

TS4

-0.852

0.432

-0.289

0.154

0.501

0.402

0.489

-0.662

-0.771

0.495

-0.758

EQ4

-0.675

0.447

-0.219

0.127

0.430

0.403

0.399

-0.739

-0.763

0.520

-0.804

-0.834

0.372

-0.161

0.210

0.407

0.686

0.065

-0.757

-0.730

0.512

-0.671

EQ0 P1

P1

P2

P2

P2

P2

P3

P3

P3b

TS1


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Figure 5. Pathway 1: A feasible migration of –H to –NH2 group but unable to result in stereoinversion. The values depicted are the relative energies (in kcal/mol) including the ZPE correction at the M062X/aug-cc-pVTZ level of the theory w.r.t. EQ0. The bond lengths depicted are in Å.



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Figure 6. Same as Figure 5, but for Pathway 2 predicted to be feasible for stereoinversion.


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15

Figure 7. Same as Figure 5, but for Pathways 3a and 3b predicted to be feasible for stereoinversion.



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Figure 8. Same as figure 5, but for Pathway 3c predicted to be infeasible for stereoinversion.


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Figure 9. Potential energy profiles (with respect to energy of

EQ0), at the DF-CCSD(T)/cc-

pVTZ//DFT/M06-2X/aug-cc-pVTZ level of theory, for Pathways 2, 3a and 3b depicted in Figures 6 & 7, predicted to be feasible of stereoinversion in L-Thr. For energy profiles using other quantum mechanical methods employed, see SI Figure S1. (EQ: Equilibrium Structure and TS: Transition State).


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Figure 10. Surface plots (isovalue 0.02) of HOMO in transition states along the feasible stereoinversion Pathways 2, 3a, 3b, and that of HOMO-2 in transition state along pathway 3b, as specified in Figures 6 & 7, at the M06-2X/aug-cc-pVTZ level of theory.


Page 19 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47


19

Table 3. Rate constants (k), in sec-1, along with tunnelling transmission coefficient (χ) for each elementary step along the feasible stereoinversion Pathways 2, 3a and 3b depicted in Figures 6 and 7, in different temperature regions of ISM, at the DFT/M06-2X/aug-cc-pVTZ of the theory. T(in K)

100

200

298.15

500

1000

4000

8000

Pathway

Pathway 2 [(2S,3R)-EQ0→ (3R)-P2EQ1]

χ k1

1.948 x 1050 5.122 x 10-95

2.237 x 1017 2.916 x 10-49

8.160 x 1006 1.085 x 10-33

1.096 x 1001 4.674 x 10-18

1.540 7.053 x 10-03

1.030 7.826 x 1009

1.010 8.899 x 1011

3.554 x 1035 5.948 x 10-111

1.432 x 1010 3.310 x 10-57

3.727 x 1002 1.117 x 10-38

2.650 2.845 x 10-19

1.240 1.434 x 10-03

1.020 1.928 x 1009

1.030 2.264 x 1011

1.320 1.024 x 10+10

1.080 2.647 x 1011

1.040 8.379 x 1011

1.010 2.241 x 1012

1.040 5.022 x 1012

1.070 9.511 x 1012

1.000 9.808 x 1012

3.459 x 1035 3.419 x 10-121

1.415 x 1010 2.073 x 10-62

3.719 x 1002 3.226 x 10-42

2.650 2.048 x 10-21

1.240 1.220 x 10-04

1.020 1.110 x 1009

1.030 1.792 x 1011

1.971 x 1050 7.540 x 10-43

2.247 x 1017 3.162 x 10-23

8.175 x 1006 2.408 x 10-16 Pathway 3a

1.096 x 1001 5.726 x 10-8

1.540 2.856 x 1002

1.030 2.169 x 1010

1.010 5.056 x 1011

5.570 1.529 x 10-42

1.880 6.759 x 10-25

1.240 3.985 x 10-10

1.050 4.506 x 1001

1.030 1.354 x 1010

1.000 3.633 x 1011

1.020 6.986 x 1007

1.010 1.729 x 1009

9.900 x 10-01 2.346 x 1010

1.010 1.656 x 1011

1.010 7.064 x 1011

9.100 x 10-01 8.071 x 1011

6.490 3.705 x 10-15

1.950 2.709 x 10-06

1.250 9.857 x 1001

1.060 4.885 x 1007

1.000 1.345 x 1012

1.000 7.957 x 1012

2.412 x 1009

4.950 x 1002

3.360

1.300

1.020

1.020 5.169 x 1011

2.298 x 10-48

4.691 x 10-32

3.215 x 10-15

1.759 x 10-01

7.901 x 1009

[(3R)-P2EQ1→ (R)-P2EQ2]

χ k2 [(R)-P2EQ2→ (S)-P2EQ2]

χ k3 [(S)-P2EQ2→ (3S)-P2EQ1]

χ k4 [(3S)-P2EQ1→ (2R, 3S)-EQ0]

χ k5

[(2S,3R)-EQ0→ (1R,2R,3R)-P3aEQ1] χ 1.020 x 1009 k1 3.340 x 10-98 P3a [(1R,2R,3R)- EQ1→ (1R,2R,3R)-P3aEQ2] χ 1.070 3.696 x 1003 k2 [(1R,2R,3R)-P3aEQ2→ (2R)-P3EQ3] χ 1.394 x 1010 k3 3.755 x 10-34 P3 P3 [(2R)- EQ3→ (2R)- EQ4] χ 4.009 x 1033 k4 8.807 x 10-94

Table 2 continued...... ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

Page 20 of 43

20 T (in K)

100

200

298.15

500

1000

4000

8000

1.120 3.169 x 1001

1.030 3.838 x 1007

1.010 4.846 x 1009

1.000 3.138 x 1011

1.000 8.233 x 1012

9.100 x 10-01 9.184 x 1013

9.800 x 10-01 1.481 x 1014

2.213 x 1033 k6 4.944 x 10-17 P3 P3a [(2S)- EQ3→ (1S,2S,3S)- EQ2] χ 1.389 x 1010 k7 4.005 x 10-73 P3a [(1S,2S,3S)- EQ2→ (1S,2S,3S)-P3aEQ1] χ 1.070 k8 4.156 x 1002 [(1S,2S,3S)-P3aEQ1→ (2R, 3S)-EQ0] χ 1.060 x 1009 k9 9.404 x 10-24

2.107 x 1009 5.541 x 10-10

4.863 x 1002 2.654 x 10-06

3.360 7.314

1.300 9.339 x 1006

1.020 8.324 x 1011

1.020 6.030 x 1012

6.490 4.141 x 10-35

1.950 4.923 x 10-20

1.250 2.234 x 10-07

1.060 6.607 x 1002

1.000 1.295 x 1010

1.000 2.292 x 1011

1.020 3.108 x 1007

1.010 1.253 x 1009

9.900 x 10-01 2.577 x 1010

1.010 2.486 x 1011

1.010 1.350 x 1012

9.100 x 10-01 1.607 x 1012

5.570 1.091 x 10-9

1.880 8.747 x 10-03 Pathway 3b

1.240 6.972 x 1003

1.050 1.982 x 1008

1.030 6.005 x 1011

1.010 2.371 x 1012

1.168 x 1027 1.243 x 10-94

3.301 x 1007 4.155 x 10-49

3.750 x 1001 1.256 x 10-32

2.170 2.120 x 10-15

1.190 5.854 x 10-02

1.010 1.633 x 1009

1.000 1.031 x 1011

4.009 x 1033 8.807 x 10-94

2.412 x 1009 2.298 x 10-48

4.950 x 1002 4.691 x 10-32

3.360 3.215 x 10-15

1.300 1.759 x 10-01

1.020 7.904 x 1009

1.020 5.169 x 1011

1.120 3.164 x 1001

1.030 3.838 x 1007

1.010 4.846 x 1009

1.000 3.138 x 1011

1.000 8.231 x 1012

9.100 x 10-01 9.184 x 1013

9.800 x 10-01 1.481 x 1014

2.213 x 1033 4.944 x 10-17

2.107 x 1009 5.414 x 10-10

4.863 x 1002 2.651 x 10-06

3.360 7.314

1.300 9.339 x 1006

1.020 8.324 x 1011

1.020 6.030 x 1012

1.299 x 1030 4.423 x 10-69

3.280 x 1007 1.462 x 10-36

3.762 x 1001 2.148 x 10-24

2.170 9.232 x 10-11

1.190 5.231

1.010 1.333 x 1009

1.000 3.833 x 1010

Pathway

[(2R)-P3EQ4→ (2S)-P3EQ4]

χ k5 [(2S)-P3EQ4→ (2S)-P3EQ3]

χ

[(2S,3R)-EQ0→ (2R)-P3EQ3]

χ k1 [(2R)-P3EQ3→ (2R)-P3EQ4]

χ k2 [(2R)-P3EQ4→ (2S)-P3EQ4]

χ k3 [(2S)-P3EQ4→ (2R)-P3EQ3]

χ k4 [(2R)-P3EQ3→ (2R,3S)-EQ0]

χ k5


Page 21 of 43


21 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Table 4. Gibbs free-energy change (∆G), in kcal/mol, in different temperature regions of ISM, along the feasible stereoinversion pathways of L-Thr depicted in Figures 6 and 7, at the DFT/M06-2X/augcc-pVTZ of the theory.

T (in K)

10

50

100

298.15

500

1000

4000

8000

Pathway (2S,3R)-EQ0→(3R)-P2TS1

71.74

71.76

71.79

71.86

71.81

71.65

73.93

83.33

(3R)-P2TS1→(3R)-P2EQ1

-47.88

-47.90

-47.92

-48.19

-48.73

-50.60

-65.83

-92.31

(3R)-P2EQ1→(R)-P2TS2 (R)-P2TS2→(R)-P2EQ2

78.58

78.60

78.67

79.12

79.66

81.14

93.61

116.57

-83.25

-83.26

-83.35

-83.95

-84.56

-86.03

-97.99

-120.29

(R)-P2EQ2→P2TS

1.63

1.63

1.64

1.74

2.03

3.35

18.07

44.99

∆GPathway 2

20.32

20.32

20.29

20.05

19.71

19.09

21.54

32.35

(2S,3R)-EQ0→(3R)-P3aTS1

50.13

50.16

50.24

50.80

51.50

53.48

69.58

97.48

(3R)- TS1→(1R,2R,3R)-P3aEQ1 (1R,2R,3R)P3aEQ1→(1R,2R,3R)P3aTS2

-20.27

-20.27

-20.31

-20.64

-21.20

-23.08

-39.44

-67.76

3.91

3.92

4.02

4.86

6.05

9.63

38.03

83.22

(1R,2R,3R)P3aTS2→(1R,2R,3R)P3aEQ2 (1R,2R,3R)-P3aEQ2→(R)-P3aTS3

-4.39

-4.39

-4.46

-5.05

-5.96

-8.83

-32.89

-72.27

P3a

25.60

25.60

25.57

25.45

25.45

25.87

32.84

48.29

(R)-P3aTS3→(2R)-P3EQ3 (2R)-P3EQ3→(R)-P3TS4

-43.25

-43.29

-43.40

-44.19

-45.22

-48.15

-69.74

-104.69

63.50

63.53

63.59

63.87

64.14

64.92

73.76

92.09

(R)-P3TS4→(2R)-P3EQ4 (2R)-P3EQ4→P3TS

-28.24

-28.27

-28.35

-28.73

-29.01

-29.57

-36.73

-53.08

5.18

5.11

4.97

4.25

3.49

1.84

-1.54

1.62

∆GPathway 3a

52.16

52.08

51.88

50.62

49.23

46.12

33.87

24.91

(2S,3R)-EQ0→(2R)-P3bTS1 (2R)-P3bTS1→(2R)-P3EQ3

62.21

62.25

62.36

63.12

64.13

66.94

86.22

117.44

-50.48

-50.53

-50.70

-51.89

-53.51

-58.01

-87.83

-133.17

(2R)-P3EQ3→(R)-P3TS4 (R)-P3TS4→(2R)-P3EQ4

63.50

63.53

63.59

63.87

64.14

64.92

73.76

92.09

-28.24

-28.27

-28.35

-28.73

-29.01

-29.57

-36.73

-53.08

(2R)-P3EQ4→P3TS

5.18

5.11

4.97

4.25

3.49

1.84

-1.54

1.62

∆GPathway 3b

52.16

52.08

51.88

50.62

49.23

46.12

33.87

24.91



Page 22 of 43

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3. Results and Discussions It is well known that for stereoinversion to occur in molecules with one chiral (for example, an asymmetric carbon) centre under uncatalyzed gas phase conditions, a migration of one of the four substituent groups on to another one around the chiral centre should take place resulting in swapping of the two groups via an achiral intermediate or transition state (with Cs point group), though there can be exceptions involving species with helical and axial chirality. However, in the present work, Threonine is associated with two chiral centres, and the swapping of two groups around one chiral centre is not sufficient enough to result into an achiral stationary species with Cs symmetry. This is due to the fact that the second stereocentre with four different groups drive the geometry of resulting species (after swapping) to be of C1 symmetry instead of the required Cs symmetry. Thus, locating an achiral stationary point species on the PES of a molecule with two stereocentres is a challenging task. It certainly requires a multi-migration of groups around both the stereocentres, may be simultaneously, so as to break the tetrahedral configuration at these centres. However, the basic scheme of stereoinversion via achiral species will essentially be the same as proposed in previous studies on species with one chiral centre.23,24 But the necessary conditions for the migrations of groups to take place can be summarised in four basic criteria: (a) proper orientation of groups around the stereocentres, (b) chemical feasibility for the formation of species upon migration, (c) sterically unhindered movement of the groups, (d) low dissociation probability of species with respect to the migrating groups. Hence, all the migrations following these four basic criteria along with the requirement of corresponding achiral stationary point species, together forms the necessary and sufficient conditions for the search of a pathway along which stereoinversion can become feasible. In order to trace the possible stereoinversion pathways of L-Thr, the species with Cs symmetry obtained after allowed migrations of relevant groups around the two chiral centres,


Page 23 of 43


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were further considered. As depicted in the Figure 4, there are twelve distinct migrations possible around each chiral carbon in the case of Threonine. The groups around the first chiral carbon (C1) are –H, –NH2, –COOH and –CH(OH)CH3 polar side chain {–SC(1)}. Therefore, probable migrations include: the movement of –H onto other three groups i.e., {– NH2, –COOH, –SC(1)}, the –NH2 group can migrate onto {–H, –COOH, –SC(1)}, –COOH group can move to {–H, –NH2, –SC(1)}, and SC(1) onto {–H, –NH2, –COOH}. However, all these possibilities are unlikely to occur. The migrations: –H onto –SC(1); –NH2 onto –H & – SC(1); –COOH onto –H & –SC(1); and –SC(1) onto –H, are chemically not feasible because these lead to an attack either on the sp3 carbon atom or on the hydrogen atom, both of these are unlikely to extend their valence. The migration of –SC(1) onto –NH2 and –COOH is though chemically allowed but is sterically hindered. Similarly, the migration of –NH2 and – COOH onto each other is also not achievable due to unsuitable orientation. Therefore, only two possibilities are left: the migration of –H onto –NH2 as along Pathway 1 (depicted in Figure 5) and onto –COOH as along Pathways 2 and 3 (depicted in Figures 6-8). Note that there are two attacking site on the –COOH, one the electrophilic carbon and other the nucleophilic carbonyl oxygen, both these possibilities are investigated through Pathways 2 and 3 (see later). Similarly, twelve possibilities also emerge around the second chiral centre (C2) with – H, –OH, –CH3, and –CH(NH2)COOH {–SC(2)} as four different substituent groups around it. But the migration of –CH3 onto –H; –OH onto –H, –CH3; –SC(2) onto –H and –CH3 are chemically not workable. Also, the transfer of –H onto –OH, –CH3; and of –CH3 onto –OH are prone to dissociation resulting in H2O, CH4 and CH3OH (see discussions later), whereas the migration of –CH3 onto –SC(2), and of –SC(2) onto –NH2 are sterically hindered. So overall, only two migrations are likely to occur, i.e., of –H onto –SC(2), and of –OH onto – SC(2). Further, there are three attacking site on the –SC(2): nucleophilic nitrogen, carbonyl



Page 24 of 43

24 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

oxygen and electrophilic carbon. The possibility of migration of –H onto the nitrogen can be ruled out due to orientation factors, however, the migrations associated with its movement onto the carbon and oxygen are traced out as depicted along Pathways 2 and 3, respectively, in Figures 6 and 7. Similarly, –OH group being nucleophilic in nature is expected to only attack electrophilic carbon of –SC(2) but the corresponding pathway could not be traced because of improper orientation. But as depicted in Figure 7 along Pathway 3, the hydrogen of –OH group can migrate to carbonyl oxygen of –SC(2) because of intramolecular Hbonding interactions (depicted in Figure 3). The aforementioned migrations around the two chiral centres along Pathways 1-3 can help in driving the geometry of L-Thr towards the achiral structure required for stereoinversion to occur. The thermodynamic and kinetics feasibility of these pathways is further discussed below. 3.1 Pathway 1 The migration of –H, on first chiral centre of (2S,3R)-EQ0, onto –NH2 is predicted to result into a zwitterionic-like carbanion intermediate

P1

EQ1 as depicted in Figure 5, with

positive charge on nitrogen but negative charge on the carbon. This migration occurs via transition state

P1

TS1 with an activation barrier of 37.34 kcal/mol. Moreover, the –H is

migrating as proton as can be inferred from the NBO analysis in Table 2, with increased negative charge on C(3) but increased positive charge on –H(4) in

P1

EQ1 compared to NBO

charges in EQ0. This pathway is similar to one of the feasible stereoinversion pathways predicted previously in the case of Alanine, Serine and Aspartic acid.22,23,25 But in the case of Threonine, resulting intermediate from this single migration could not approach towards an achiral stationary point due to the tetrahedral nature of the adjacent carbon. Moreover the movement of other groups from the resulting intermediate

P1

EQ1 is also not chemically

viable, hence, this pathway is considered to be infeasible for stereoinversion in L-Thr.


Page 25 of 43


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3.2 Pathway 2 As depicted in Figure 6, the first step of this pathway involves a migration of –H, via chiral transition state

P2

TS1, from the first chiral carbon in (2S,3R)-EQ0 to the carbonyl

oxygen (of –COOH group) that are initially 3.13 Å apart. This step is associated with very high activation energy barrier of 71.74 kcal/mol, resulting in a less stable intermediate (3R)P2

EQ1 compared to EQ0 but with disrupted chirality at first chiral centre. From NBO analysis,

it is examined that –H is migrating as a proton as indicated by the increased negative charge on the C(3) from -0.15 (in EQ0) to -0.25e (in transition state

P2

TS1) with an increased

positive charge on –H(4) from 0.22 (in EQ0) to 0.47e in P2TS1. But there is also an increase in the negative charge on the recipient carbonyl oxygen O(9) in EQ0. This is further looked into while analysing HOMO of

P2

P2

TS1 as compared to that in

TS1 in Figure 10 which reveals

an overlapping charge density on C(3)-C(6)-O(9) along with proton being migrated from C(3) to O(9) via C(6). This indicates a probable proton coupled electron transfer (PCET) mechanism.57 Moreover, this step is similar to a keto-enol type tautomerism, however, the enol type intermediate

P2

EQ1 is 23.86 kcal/mol less stable than the ketone type initial

equilibrium structure EQ0. This is obvious in such tautomerism of carboxylic acid due to more stability of carbon-oxygen double bond than the carbon-carbon double bond. Therefore, though the equilibrium lies more towards EQ0 than formation of intermediate

P2

P2

EQ1, but still the possibility of

EQ1 cannot be ruled out provided the activation energy of the

reaction is achieved under the conditions of ISM. In the subsequent step along this pathways, intermediate

P2

EQ1 undergoes a [1,3]-H

atom transfer around the one chiral centre. The recipient sp2 hybridised carbon is 2.56 Å away from migrating hydrogen, and conversion occurs via a four membered ring transition



Page 26 of 43

26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

state

P2

TS2 having an activation energy barrier of 78.58 kcal/mol. This migration is observed

with a decreased positive charge on the migrating –H(7) from 0.17e in P2

P2

EQ1 to 0.13e in

EQ2, indicating –H is migrating as an atom in this step. Moreover, from HOMO of P2TS2 in

Figure 10, it is clear that there is a shift of charge density from C(6)-C(3) double bond to C(3)-C(5) bond. Thus, this step can be simply characterised as hydrogen atom transfer. The resulting axially chiral intermediate (R)-P2EQ2 can now easily flip to its counterpart of opposite chirality via achiral transition state

P2

TS with Cs symmetry. Interestingly, this

conversion involves activation barrier of only 1 kcal/mol. Thus, overall two migrations, one each from two chiral carbons, resulted into an achiral transition state that can facilitate stereoinversion in L-Thr. Though the activation barrier along the initial step is quite high but due to proton and hydrogen atom transfer taking place along this pathway, the probability of quantum tunnelling is quite high. Therefore, the kinetics analysis of this pathway can pay more insight into the stereoinversion (see later). Besides this, note that there is also a possibility of [1,4] migration of hydrogen from hydroxyl group of second chiral centre in intermediate (R)-P2EQ1 on to the sp2 carbon, but orientation factor restrict such migration. 3.3 Pathway 3a Along Pathway 3a depicted in Figure 6, the –H on first chiral carbon of (2S,3R)-EQ0 migrates to carboxy carbon, with an activation barrier of 50 kcal/mol, resulting in the formation of an epoxide (1R,2R,3R)-P3aEQ1 with the generation of one more chiral centre at first carbon (of previously -COOH). The migrating H seems to be moving as an atom via transition state

P3a

TS1 as inferred from NBO analysis (in Table 2) indicating decreased

positive charge on departing –H(4) and recipient C(6) carbon atom compared to EQ0. Also, note that though there is migration of an atom from C(3) but NBO analysis indicate increased negative charge on this carbon. This can be due to an interaction with nitrogen as evident from overlapping of charge density on nitrogen and C(3) in HOMO of


P3a

TS1 depicted in

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Figure 10. However, this overlap of charge density extends to C(6) indicating an hydrogen atom transfer from C(3) to C(6). It is quite interesting to note that the aforementioned epoxide intermediates

P3a

EQ1 and

P3a

EQ2 are very similar to the first chiral molecule ‘propylene

oxide’ recently confirmed in the outer space.1 Further, in the second step along this pathway, stable rotational conformer

P3a

P3a

EQ1 gets converted to its more

EQ2 through a small energy barrier of 4 kcal/mol so as to get

appropriately oriented for the next migration to take place. Subsequently, in different migrations of –H take place simultaneously, via the –H on the third chiral centre in

P3a

P3a

P3a

EQ2, two

TS3 to form (2R)-P3EQ3. One of

EQ2, at a distance of 2.12 Å from the second chiral

centre, migrates as an hydrogen atom as indicated by the decreased NBO positive charge on migrating H(7) in P3aTS3 than that in

P3a

EQ2. The other –H (of –OH group) on the third chiral

carbon migrates as a proton to the epoxy oxygen with increased positive charge on migrating H(10) from 0.48 to 0.53e via transition state

P3a

TS3 while the negative charge increases on

oxygen O(8) from which it departs. Overall in this step, a simultaneous movement of proton and hydrogen atom transfer is inferred from the NBO analysis, and the same can be observed from the HOMO of P3aTS3 in Figure 10. The resulting intermediate

P3

EQ3 from the aforementioned migration still have C1

point group symmetry but there is a further possibility of another migration of H from the only chiral centre of this intermediate onto the –NH2 group, thereby, driving the geometry towards Cs symmetry. This final migration of –H takes place as a proton on the NH2 substituent, that are initially 2.07 Å distance apart, resulting into a zwitterionic-like intermediate

P3

EQ4 similar to that along the infeasible Pathway 1. The migration of –H is

inferred as proton from NBO analysis in Table 2, with increased positive charge from 0.22 to 0.40e on H(7) in

P3

EQ4. The zwitterionic character is also verified by the decreased negative

charge on nitrogen and increased negative charge on C(3) carbon in


P3

EQ4 compared to the


Page 28 of 43

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NBO charge in

P3

EQ3 as highlighted in Table 2.. However, in this case

P3

EQ4 can now flip

into its equivalent intermediate of opposite chirality via achiral transition state

P3

TS through

only a small energy barrier of 6 kcal/mol. Such zwitterionic-type intermediates were also predicted to be responsible for inverting the chirality of species investigated in previous studies.22-25 Moreover, the achiral P3TS transition state having a plane of symmetry resembles an achiral ammonium ylide type species encountered in Strecker synthesis, which was also proposed by Maeda et al., in a study on the formation of Glycine under conditions akin to ISM.21 Overall, Pathway 3a is a probable route for stereoinversion though it requires four –H migrations to approach towards the desired achiral species. 3.4 Pathway 3b Similar to the aforementioned Pathway 3a, a simultaneous migration of –H at the second chiral centre of EQ0 and another -H of hydroxyl group at the same chiral centre C(5), respectively, onto the carbonyl carbon and oxygen (of –COOH) is also detected via transition state P3bTS1 as depicted along Pathway 3b in Figure 6. In the first step of this pathway, the –H migrates as an atom on to the carbonyl carbon as indicated by the decreased NBO positive charge on both the departing hydrogen H(7) as well carbonyl carbon C(6) being attacked, compared to the NBO charges in EQ0 to that of

P3b

TS1 as indicated in Table 2, and the same

can also be observed from HOMO of P3bTS1 in Figure 10. Besides this, simultaneously, H(10) of hydroxy group at the same chiral carbon seems to migrate but as a proton through the PCET mechanism. As evident from the HOMO-2 of P3bTS1 in Figure 10, there is a significant overlap of charge densities on C(6) and O(9), indicating a charge migration to O(9) besides a synchronous movement of the proton H(10). Overall, the two simultaneous –H migrations results in an intermediate

P3

EQ3 (as in Pathway 3a), the subsequent stereoinversion of which

is the same as discussed along the Pathway 3a. Thus, there are two different ways of H-


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migrations through Pathways 3a and 3b leading to stereoinversion in L-Thr, their thermodynamic and kinetic feasibility is discussed later. 3.4 Pathway 3c Furthermore, there is also a possibility that the –H on third chiral carbon depart on to epoxy oxygen instead of hydroxyl hydrogen (as observed in step 3 along Pathway 3a). This is predicted to result into an intermediate

P3c

EQ2 as shown in Figure 7. This migration is

chemically as well as sterically allowed besides having proper orientation in Although the resulting intermediate

P3c

P3a

EQ1.

EQ2 was located but we were unable to find any

transition state connecting these two intermediates, thereby ruling out any feasibility of stereoinversion through this route. 3.5 Feasibility of the stereoinversion pathways All the aforementioned pathways predicted to be feasible for stereoinversion in L-Thr involves an initial step with high activation barrier as can also be inferred from the potential energy profiles of these pathways depicted in Figure 9. Therefore, it is prudent to consider their viability under conditions akin to ISM. The kinetic and thermodynamic feasibility of the proposed pathways was analysed in different temperature regions of ISM through rate coefficients and Gibbs free-energy analysis presented in Tables 3 and 4, respectively. The temperature in ISM ranges from 10-50 K in dense cold molecular clouds to 8000 -107 K in hot ionized medium. As the proposed stereoinversion pathways proceed via intramolecular H-transfer, either as proton or hydrogen atom, therefore, significant quantum tunnelling can be expected. Thus, the CTST rate constants estimated in Table 3 incorporates quantum tunnelling through the transmission coefficient (χ) calculated using an unsymmetrical Eckart tunnelling potential as discussed in the previous section.



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As evident in Table 3, significant tunnelling is predicted at low temperatures. Note that the tunnelling coefficient is estimated through Equation (2) for unsymmetrical Eckart potential, which involves an inverse dependence on the temperature. Though a high value is expected for the proton transfer pathways at lower temperatures as listed in Table 3 at 100K but a value as high as 1050 may be an overestimation by the Eckart potential. However, even such high tunnelling probability is found to be inadequate to drive the stereoinversion with moderate rates. Thus, it can be deduced that the proposed stereoinversion pathways are dominated by thermal effects rather than the quantum effects alone. Further, the rate constant for each step along Pathways 2 and 3 reveal that the rate of formation of intermediates for stereoinversion varies significantly in different region of ISM. For example, the rate constant k1 along Pathway 2 ranges from a negligible value of 10-95 s-1 in cold neutral medium of molecular clouds to a rate as high as 1011 s-1 in the warm neutral and hot ionized medium. Similar variation in the rates is predicted for other steps of the pathways associated with high energy barrier. However, quite low energy barrier (of the order of 5 kcal/mol) was predicted for steps leading to either the inversion of chirality (as along Pathways 2, 3a and 3b) or the conformational changes (as along Pathway 3a). Hence, the corresponding rate constants (k3, k5 and k3 along Pathway 2, 3a and 3b; and k2 along Pathway 3a) are quite high irrespective of the regions of ISM. This indicates that once the appropriate intermediate required for stereoinversion is created, the reversal of chirality through Cs transition state may become feasible and that too in every region of ISM. Similarly, from the Gibbs free energy analysis in Table 4, it is observed that the proposed pathways are thermodynamically more feasible at high temperature compared to their feasibility in molecular clouds. However, along Pathway 2, there is an increase in Gibbs free-energy change from 19.09 to 32.35 kcal/mol while moving from temperature region of 1000 to 8000K, due to high positive enthalpy change that suppress the effect of increased temperature. Pathways 3a and 3b, though involve different


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mechanistic steps, but the overall Gibbs free energy change along the two is exactly same, so these are equally feasible.

Further, the kinetics of the proposed stereoinversion pathways can be inferred from the rate constants of the slowest step associated with highest activation barrier. For Pathways 2 and 3a, the fourth step is the slowest step whereas for Pathway 3b, first step is the slowest one. Comparing the rate constants of these steps in temperature region of 500-1000K, Pathway 3a is kinetically most favourable followed by Pathway 3b whereas Pathway 2 is the slowest. Similarly, from Gibbs free energy analysis, the Pathway 2 is speculated to be thermodynamically more feasible than Pathway 3. However, note that the above analysis of rate constants and Gibbs free energy analysis does not take into account the molecular density of ISM which ranges from a maximum density of 103-106 molecules per cm3 in cold molecular clouds to only few molecules per cm3 in warmer regions. This must be considered for more accurate quantitative analysis because under the conditions of ISM, a gas-phase unimolecular isomerization is more likely than a collisional event. Based on the aforementioned thermo-kinetic analysis, the ISM region with temperature more than 500K may be an appropriate place for the stereoinversion in L-Thr except in the hot ionized medium where ionization and dissociation of L-Thr and its intermediates explored becomes more likely. Overall, the temperature zone of 500-1000K can be suitable for inverting the chirality in the gas-phase neutral L-Thr. Moreover, no lowlying dissociation channel could be found in the GRRM search indicating the dissociation of L-Thr to be a high barrier process. Further, the dissociation channels (DCs) of EQ0 (listed in Table 1) were intuitively explored, but only two DCs, Pathways 4 and 5 (provided in SI Figure S3) resulting into methane and water, respectively, could be found. The dissociation



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into methane is associated with a very high energy barrier of 104.54 kcal/mol as predicted at the CCD(T)//DFT level of the theory, and thus is less likely to occur than the stereoinversion proposed in this work. Pathway 5 leading to its dissociation into water molecule though also requires a high activation barrier of 78.19 kcal/mol but the barrier is comparable to those along the proposed stereoinversion Pathway 2, however, much higher than those along Pathway 3b involving simultaneous proton- and hydrogen-atom transfer. Moreover, both the DCs lead to thermodynamically less stable dissociation products. Therefore, the stereoinversion in L-Thr may be a more likely event than its dissociation, particularly, in the less warmer regions of the ISM. Nevertheless, considering the kinetics and thermodynamic feasibility of the stereoinversion pathways, it can be inferred that the temperature zone of 500-1000K is more suitable for inverting the chirality of gas-phase L-Thr. Such temperature zone actually corresponds to protoplanetary disk around young stars, and only simple elementary molecules have been detected in this region so far.58 Although the presence of complex organic molecules (COMs) in space have been detected in hot cores of protostars,59-60 but the temperature here ranges between 100-500K, at which the proposed stereoinversion pathways are predicted to be less likely than that in the protoplanetary disk. However, during last few years, the search of COMs in protoplanetary disks is becoming an intensive research area among astrochemists.14,61 The intermediates located along stereoinversion pathways are though less stable than the Threonine, and their formation may be a questioned as far as terrestrial chemistry is concerned but ISM is always seen as a site of such exotic chemistry to be observed. For example, the formation of less stable HNC with abundance more than that of HCN, and that too in cold molecular clouds, has been observed in interstellar environment.62 Though such unusual ratio of HNC/HCN in the interstellar space is explained -

by considering the dissociative recombination reaction of HCNH++e ,63 however, the


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formation of intermediates and transitions states through the unimolecular isomerisation pathways similar to those proposed in this work may also be possible under the conditions of ISM. It is possible because of the fact that the transition state species along the explored pathways resemble the intermediates involved along the synthetic routes of amino acids, in particular, those leading to the achiral species. 4. Conclusions In the present study, through quantum mechanical computations, we have explored three pathways feasible for stereoinversion in L-Threonine (L-Thr) under the gas-phase conditions akin to interstellar medium (ISM), perhaps for the first-time in a species with two stereocentres. All the pathways are observed to proceed via intramolecular hydrogen atom and proton transfer. In fact, a simultaneous proton-hydrogen atom transfer was observed along a few pathways. The thermodynamic and kinetic analysis of the pathways in different regions of ISM indicates that the temperature region of 500-1000K corresponding to protoplanetary disk can be an optimum region for stereoinversion to occur in L-Thr. In the cold molecular clouds, however, despite significant quantum tunnelling involved along the proton transfer pathways, the stereoinversion is observed to be infeasible due to quite high energy barrier. Therefore, the present case of Threonine suggests that unless the amino acids are exposed to warm regions of ISM without being dissociated there, the stereoinversion is a less likely event in the ISM, any racemisation of amino acids in ISM is likely to occur only during their synthesis. Therefore, in the event that the synthesis of only one enantiomer of amino acids occurs, for example in the cold molecular clouds, then to explain the enantiomeric excess observed in the meteoritic samples, the hypothesis for the destruction of the other enantiomer by an external agencies such as circularly polarised light from a neutron star may be ruled out.64,65 Nevertheless, the intermediates and transition states located along the proposed stereoinversion pathways in this work can help the researchers searching for the



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presence of amino acids in the ISM as well as those exploring the extraterrestrial origin of bio-homochirality. Supporting Information Supporting Information SI includes Figure S1 to S3, Cartesian coordinates of all the conformers of L-Threonine searched using GRRM along with their comparison from the literature, and Cartesian coordinates of the stationary points located along the proposed stereoinversion pathways using GRRM. ACKNOWLEDGMENTS The authors gratefully acknowledge the financial assistance received for this work under a research project sanctioned by Science & Engineering Research Board (SERB), India (Project Sanction No. EMR/2016/002074). Namrata Rani thanks University Grants Commission (UGC), New Delhi (India) for providing JRF(NET) fellowship. The authors are also grateful to Prof. K. Ohno for providing the GRRM program, and to the Department of Chemistry, Panjab University, Chandigarh, for providing other computational software and resources. Notes The authors declare no conflict in the interests. REFERENCES (1) Mcguire, B. A.; Carroll, P. B.; Loomis, R. A.; Finneran, I. A.; Jewell, P. R.; Remijan, A. J.; Blake, G. A. Discovery of the Interstellar Chiral Molecule Propylene Oxide (CH3CHCH2O). Science 2016, 352, 1449-1455. (2) Smith, I. W. M. Laboratory strochemistry Gas-Phase Processes. Annu. Rev. Astron. Astrophys. 2011, 49, 29–66. (3) Muñoz Caro, G.M.; Meierhenrich, U.J.; Schutte, W.A.; Barbier, B.; Arcones


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