# Quantum chemical computations of gas-phase glycolaldehyde deuteration and
constraints to its formation route

Fanny Vazart Univ. Grenoble Alpes, CNRS, Institut de Planétologie et
d’Astrophysique de Grenoble (IPAG), 38100 Grenoble, France  Cecilia Ceccarelli
Univ. Grenoble Alpes, CNRS, Institut de Planétologie et d’Astrophysique de
Grenoble (IPAG), 38100 Grenoble, France  Dimitrios Skouteris Master-Tec, Via
Sicilia 41, 06128 Perugia, Italy  Nadia Balucani Dipartimento di Chimica,
Biologia e Biotecnologie, Università degli Studi di Perugia, 06123 Perugia,
Italy

###### Abstract

Despite the detection of numerous interstellar complex organic molecules
(iCOMs) for decades, it is still a matter of debate whether they are
synthesized in the gas-phase or on the icy surface of interstellar grains. In
the past, molecular deuteration has been used to constrain the formation paths
of small and abundant hydrogenated interstellar species. More recently, the
deuteration degree of formamide, one of the most interesting iCOM, has also
been explained in the hypothesis that it is formed by the gas-phase reaction
NH2 \+ H2CO. In this article, we aim at using molecular deuteration to
constrain the formation of another iCOM, glycolaldehyde, which is an important
prebiotic species. More specifically, we have performed dedicated electronic
structure and kinetic calculations to establish the glycolaldehyde deuteration
degree in relation to that of ethanol, which is its possible parent species
according to the suggestion of Skouteris et al. (2018). We found that the
abundance ratio of the species containing one D-atom over the all-protium
counterpart depends on the produced D isotopomer and varies from 0.9 to 0.5.
These theoretical predictions compare extremely well with the monodeuterated
isotopomers of glycolaldehyde and that of ethanol measured towards the Solar-
like protostar IRAS 16293-2422, supporting the hypothesis that glycolaldehyde
could be produced in the gas-phase for this source. In addition, the present
work confirms that the deuterium fractionation of iCOMs cannot be simply
anticipated based on the deuterium fractionation of the parent species but
necessitates a specific study, as already shown for the case of formamide.

gas-phase chemistry, deuteration, glycolaldehyde, ethanol

##  1 Introduction

Among the more than 270 species that have been detected in the interstellar
medium (ISM) so far (McGuire, 2022), about 40% are composed of six atoms or
more and contain at least a carbon atom. They are referred as interstellar
Complex Organic Molecules (iCOMs: Herbst & van Dishoeck, 2009; Ceccarelli et
al., 2017), where the ”i” emphasizes that the ”complex” adjective only holds
in the ISM context. iCOMs are significant in prebiotic chemistry research,
whose goal is to understand how life could appear on an originally inorganic
Earth. iCOMs can be considered as precursors or intermediates in the formation
of the building blocks of life, such as amino acids or nucleobases for
instance. The question of their formation in the harsh ISM conditions is,
therefore, of paramount importance and far-reaching.

So far, two major processes responsible for the iCOMs synthesis have been
invoked in the literature: reactions occurring on the interstellar icy grain
surfaces or in the gas-phase (e.g. Garrod & Herbst, 2006; Balucani et al.,
2015; Ceccarelli et al., 2022). Which one dominates and where has been a
decades-long quarrel that started soon after the first detection of iCOMs in
massive hot cores (Rubin et al., 1971; Blake et al., 1987) and revived when
iCOMs were detected in hot corinos (Cazaux et al., 2003; Ceccarelli et al.,
2004). Traditionally, a major argument to distinguish the gas-phase versus
grain-surfaces origin of the gaseous species observed in hot cores/corinos has
been the molecular deuteration or deuterium fractionation, namely the
abundance ratio between the species containing D-atoms with respect to the
same containing H-atoms (e.g. Tielens, 1983; Charnley et al., 1992; Roberts &
Millar, 2000a, b; Ceccarelli et al., 2001, 2014). Indeed, since the D/H ratio
at the birth of the Universe is $A_{D}=2.4\times 10^{-5}$ (Planck
Collaboration et al., 2016; Cooke et al., 2016), the abundance of D-bearing
molecules would be extremely low without a chemistry-triggered deuterium
fractionation. Instead, since the 70s it has been known that many interstellar
di- and tri- atomic molecules do show an enhanced abundance of D-bearing
molecules with respect to the elemental D/H abundance (e.g. Hollis et al.,
1976; Penzias et al., 1977; Snyder et al., 1977). This is (mainly) caused by
the dense ISM low temperatures that enhance the H2D+/H${}_{3}^{+}$ abundance
ratio because of the different zero-point energy of the two species: then, all
other small deuterated molecules inherit the deuteration from H2D+ (Watson,
1974; Dalgarno & Lepp, 1984).

At the beginning of the 2000s, formaldehyde and methanol were the most complex
deuterated species detected in the ISM and the detection of doubly deuterated
formaldehyde and even triply deuterated methanol (Turner, 1990; Ceccarelli et
al., 1998; Parise et al., 2003) were used to assess their grain-surfaces
origin (e.g. Ceccarelli et al., 2001; Parise et al., 2006; Taquet et al.,
2013). Indeed, both molecules are (mostly) produced on the grain surfaces
thanks to the hydrogenation of frozen CO (Watanabe & Kouchi, 2002; Watanabe et
al., 2003; Rimola et al., 2014, e.g.), so the crucial parameter is the D/H
abundance ratio of atoms landing on the grain surfaces (Tielens, 1983), which
in turn depends on the H2D+/H${}_{3}^{+}$ abundance ratio in the gas (see e.g.
the review by Ceccarelli et al., 2014). In summary, until recently, the
deuteration of the observed molecules was only connected to the enhanced
H2D+/H${}_{3}^{+}$ in cold gas111Additionally and/or alternatively, CH2D+ and
OD can also enhance molecular deuteration in some species in somewhat warmer
gas ($\sim 30-100$ K; Roberts & Millar, 2000a; Thi et al., 2010). which, in
turn, is controlled by the so-called thermodynamic isotope effect (TIE, the
difference in the zero point energy is such that the isotopic variant
H${}_{3}^{+}$ \+ HD $\rightarrow$ H2D+ \+ H2 is slightly exothermic, while the
reverse process is slightly endothermic).

The situation has changed in the last years with the detection of D-enriched
iCOMs (Coudert et al., 2013; Coutens et al., 2016; Jørgensen et al., 2018;
Manigand et al., 2019), because, whatever is their formation route, iCOMs
deuteration is not anymore directly connected to the enhanced (gaseous)
H2D+/H${}_{3}^{+}$ abundance ratio but to the deuteration of their parent
species. In this case, the question is whether the iCOM deuteration is
directly inherited from their parent species without any alteration or whether
the processes leading from the parent to the daughter species can induce an
enrichment or a decrease in the deuteration degree.

It is worth mentioning here that the rate coefficient of a chemical reaction
is expected to change when one of the atoms in the reactants is replaced by
one of its isotopes. This is the so-called kinetic isotope effect (KIE), not
to be confused with the TIE ruling the H2D+/H${}_{3}^{+}$ abundance. A further
distinction is made between primary kinetic isotope (in this case, a bond
involving the isotopically-labeled atom is being formed or broken) and
secondary kinetic isotope effect (when no bond to the isotopically-labeled
atom in the reactant is being broken or formed). Secondary kinetic isotope
effects are much smaller than primary kinetic isotope effects. Finally, and
perhaps more importantly, if there is competition between the formation of a
D-product or an H-product, it is very important to characterize the reaction
mechanism. As a matter of fact, if the reaction is an impulsive direct
reaction, H-products are favored while, if the reaction is an indirect
reaction featuring the formation of a reaction intermediate, since X-D bonds
are stronger that X-H bond (where X is an atomic species like carbon or
oxygen), D-products are favored. In other words, to assess the relationship
between the deuteration degree of one iCOM and its parent species, the
reaction mechanism has to be characterized.

Figure 1:  The genealogical tree of ethanol (adapted from Skouteris et al.,
2018) The numbers in the plot indicate the branching ratios. The present study
focuses only on the reactions leading to glycolaldehyde shown in the red
boxes.

For instance, in a recent example, Skouteris et al. (2017) showed that the
reaction mechanism of the gas-phase reaction NH2 \+ H2CO $\rightarrow$ NH2CHO
+ H is able to explain the measured D/H abundance ratios of formamide (NH2CHO)
towards IRAS16293 B. This is due to a combination of the D-/H-product
branching ratio and KIE.

To the best of our knowledge, the case of formamide is the only case reported
in the literature. The detection of its D isotopomers was first reported by
Coutens et al. (2016) towards the Solar-like protostar IRAS16293-2422 B
(hereinafter IRAS16293 B) hot corino. Skouteris et al. (2017) showed that, if
formamide is formed in the gas-phase by the NH2 \+ H2CO reaction, then: trans-
HCONHD/HCONH${}_{2}\sim 1/3$ NHD/NH2, cis-HCONHD/HCONH${}_{2}\sim 1/3$ NHD/NH2
and DCONH2/HCONH${}_{2}\sim 1/3$ = HDCO/H2C). In other words, (i) the singly-
deuterated formamide abundance will be a factor three lower than that
characterizing the parent species NH2 and H2CO, respectively, while (ii) the
relative abundance ratios will reflect those of the parent species (NH2 and
H2CO). Therefore, the strong message from the Skouteris et al. (2017) study is
that the deuterium fractionation of iCOMs from gas-phase reactions depends on
the specific characteristics of the formation reaction and cannot be
anticipated simply based on the mother species deuteration. Incidentally, the
Coutens et al. observations agree with these theoretical predictions,
supporting the case for a gas-phase formation of formamide in the IRAS16293 B
hot corino.

In this manuscript, following the Skouteris et al. (2017) study, we report on
the case of glycolaldehyde, the deuterated forms of which have been detected
in IRAS16293 B by Jørgensen et al. (2016). As for other iCOMs, two possible
formation routes are invoked in the literature: (i) in the gas-phase from
gaseous ethanol (CH3CH2OH) following the scheme by Skouteris et al. (2018),
reported in Fig. 1, or (ii) by the combination of radicals on the grain
surfaces as predicted by Garrod et al. (2008) (see also Simons et al., 2020,
and references herein). In the present work, we focus on the gas-phase route
only, and provide theoretical calculations to predict the deuteration of
glycolaldehyde when it is synthesized starting from monodeuterated ethanol.

To this end, we separately follow the effect on the deuteration degree of the
two steps shown in Fig. 1: first, the reactions of partially deuterated
ethanol with OH that leads to a combination of five isotopomers/rotamers of
CH2CH2OH, and, second, their reactions with atomic oxygen leading to the three
deuterated isotopomers of glycolaldehyde. While we discuss the consequences of
the first step starting from the data available in the literature, we have
calculated the rate coefficients and H-/D-product branching ratios associated
with the second step in this work. The studied reactions are listed in Table 1
and their scheme is shown in Fig. 2.

The article is organised as follows. In Section 2, we provide some
considerations on the first step, namely the hydrogen or deuterium abstraction
from deuterated ethanol. We then describe the theoretical methods used for
this study in Section 3, and show the results we obtained in Section 4.
Section 5 is dedicated to a discussion about the astronomical relevance of
this study and the comparison between our predictions and observations.
Section 6 concludes the article.

Table 1: List of isotopic variants of the OH + CH2CH2OH gas-phase reaction involved in the formation of deuterated of glycolaldehyde following the scheme in Skouteris et al. (2018) also shown in Fig. 1. The structural formula of each isotopomer is shown in Fig. 2. The reaction numbers follow the sequence of reactions shown in Fig. 2. Note that the radical CHDCH2OH can be generated by both reactions 3 and 4 and, therefore, reaction 9 accounts for both. Note that reactions 6 and 7 produce the same isotopomer of glycolaldehyde, as well as reactions 8 and 9. No. | Reactants |  | Products
---|---|---|---
Step 1
1 | CH3CH2OD + OH | $\rightarrow$ | CH2CH2OD + H2O
2a | CH3CHDOH + OH | $\rightarrow$ | CH2CHDOH + H2O
2b |  | $\rightarrow$ | CH2CDHOH + H2O
3a | a-a-CH2DCH2OH + OH | $\rightarrow$ | CHDCH2OH + H2O
3b |  | $\rightarrow$ | CDHCH2OH + H2O
4 | a-s-CH2DCH2OH + OH | $\rightarrow$ | CHDCH2OH + H2O
Step 2
5 | CH2CH2OD + O | $\rightarrow$ | CH2ODCHO + H
6 | CH2CHDOH + O | $\rightarrow$ | CHDOHCHO + H
7 | CH2CDHOH + O | $\rightarrow$ | CHDOHCHO + H
8a | CHDCH2OH + O | $\rightarrow$ | CH2OHCDO + H
8b |  | $\rightarrow$ | CH2OHCHO + D
9a | CDHCH2OH + O | $\rightarrow$ | CH2OHCDO + H
9b |  | $\rightarrow$ | CH2OHCHO + D

Figure 2: Summary of the multi-step reactions with their respective major
products. Reactions are numbered as in Tab. 1. The colored boxes show the
parent-daughter relationship. The magenta boxes show the channels that lead to
undeuterated glycolaldehyde products (8b and 9b).

Note that the two types of CH2DCH2OH (a-a and a-s) are characterized by
different spectroscopic properties which make them observationally
distinguishable. They are characterized, however, by very similar chemical
behavior. Branching ratios are also indicated (see text).

##  2 The first abstraction step and implications for the deuteration degree

Following the suggestion by Skouteris et al. (2018), the first step of the
envisaged reaction sequence consists of an H-atom abstraction from ethanol by
OH. The all-protium reaction OH + C2H5OH has been investigated from an
experimental and theoretical point of view (Galano et al., 2002; Xu & Lin,
2007; Elm et al., 2013; Sivaramakrishnan et al., 2010). The rate coefficients
as a function of the temperature (encompassing the range of temperature of
interest in the ISM) was determined in two different CRESU (Cinétique de
Réaction en Ecoulement Supersonique Uniforme) experiments (Caravan et al.,
2015; Ocaña et al., 2018). However, this technique is not able to give
information on the branching ratios of the different products (Cooke & Sims,
2019). Theoretical calculations and experimental work have pointed out that
both CH3CHOH and CH2CH2OH can be formed (Marinov, 1999; Carr et al., 2011),
while the formation of CH3CH2O has been ruled out (Caravan et al., 2015).
Given the uncertainty on the product branching ratios at low temperatures,
Skouteris et al. (2018) have adopted two sets of branching ratios, that is,
0.9/0.7 for CH3CHOH and 0.1/0.3 for CH2CH2OH, respectively (see the two
scenarios in Skouteris et al.). Here, we have adopted an intermediate value
using a yield of 0.8 for CH3CHOH and of 0.2 for CH2CH2OH.

In this work, we are interested only in the formation of deuterated
glycolaldehyde and, therefore, we will consider the part of the ethanol tree
that leads to it, i.e. the H-abstraction from the methyl group with the
formation of the 2-hydroxyethyl radical (the red boxes of Fig. 1). To be noted
that abstraction reactions are impulsive direct processes.

Figure 3: Different types of deuterated ethanol (left) and deuterated
2-hydroxyethyl radical (CH2CH2OH: right).

Ethanol and the 2-hydroxyethyl radical exist under the form of three rotamers
regarding the CO bond: the anti-, +gauche\- and -gauche\- isomers (see Fig.
3). The two gauche isomers are chemically indistinguishable. In the case of
ethanol, the anti\- rotamer is the one with the lowest energy content, while
in the case of CH2CH2OH the most stable rotamer is the gauche-2-hydroxyethyl
radical.

If we consider the monodeuterated species of ethanol, because of its four
distinct types of hydrogen atoms we have four isotopomers (Fig. 3, panels a
and b): CH3CH2OD (D1), CH3CHDOH (D2), a-s-CH2DCH2OH (D3) and a-a-CDH2CH2OH
(D4). Note that a-s-CH2DCH2OH and a-a-CDH2CH2OH have different spectroscopic
properties and, therefore, are distinguishable when observed in the ISM.
However, they are characterized by a very similar chemical behaviour.

Let us now consider the relation between the four isotopomers of ethanol and
the isotopomers of the 2-hydroxyethyl radical that can be formed by H- (or
D-)abstraction. In all cases, we are considering only the abstraction from the
methyl group of ethanol because this is the step that leads later to
glycolaldehyde. Also, since the gauche-2-hydroxyethyl radical is the most
stable rotamer and the calculations have been done starting from this species
(see below), the relation will be shown for this species only. Similar
reasoning can be applied also to the case of the anti rotamers.

If we start from CH3CH2OD, the degree of deuteration remains unchanged in this
first step because the D atom is not directly involved in the process and the
mechanism is of the direct type (impulsive reaction). If compared to the all-
protium reaction, the rate coefficient could be slightly affected by secondary
KIE, but the effect is expected to be minor.

If we start from CH3CHDOH, the H-abstraction from the terminal methyl group
leads to the formation of two isotopomeric radicals (Fig. 3, panel c):
CH2CHDOH (D2’) and CH2CDHOH (D2”). In this case, there is no direct
competition between the H- or D- abstraction and the deuteration degree is not
going to be affected. Given the chemical equivalence of the D2 position, we
assign a branching ratio of 0.1 to both CH2CHDOH and CH2CDHOH. Also in this
case, secondary KIE are expected to be negligible.

Finally, in the case of the CH2DCH2OH isotopomers, there is a competition
between D-abstraction and H-abstraction. However, the H/D-abstraction in the
reaction OH + ethanol is characterized by a significant entrance barrier and,
while the H-abstraction process is made possible at low temperature by quantum
tunneling through that barrier (Ocaña et al., 2018; Caravan et al., 2015), the
same is not valid for the D-abstraction. The tunneling probability shows
exponential dependency on the mass of the particle and doubling the mass of a
tunneling H atom by replacing it with deuterium drastically reduces the rate.
Therefore, only the H-atom will be abstracted by OH since the same process
involving D will not benefit from the tunneling effect (primary KIE). In this
case, as well, the original deuteration degree of ethanol will be retained in
the 2-hydroxyethyl radical.

In conclusion, we can say that, for different reasons, the first step does not
alter the deuteration degree or the position of the deuterium atom in the
2-hydroxyethyl radical with respect to its parent ethanol molecule. Secondary
KIE are expected to be negligible in all cases and we can assume that
reactions (1-4) are characterized by the same rate coefficients as the all-
protium reaction.

After the first step, therefore, we have five possible monodeuterated species
of 2-hydroxyethyl radical (there is no symmetry in this case): CH2CH2OD (D1),
CH2CHDOH (D2’), CH2CDHOH (D2”), CHDCH2OH (D3), CDHCH2OH (D4).

In the ISM, only the anti ethanol rotamer has been observed so far, but the
gauche-ethanol is expected to be more abundant because of its degeneracy and
little energy difference. Considering also that the gauche-2-hydroxyethyl
radical is the more stable rotamer, our theoretical study was performed
starting from it. This is also motivated by the fact that the H-abstraction is
an exothermic reaction that will liberate a large excess energy allowing all
possible rotations to occur. In any case, we have verified that, if we
consider anti-2-hydroxyethyl radical as a starting reactant, the global
outcome is not changing (see Fig. 4). The addition of atomic oxygen to
anti-2-hydroxyethyl radical leads indeed to the addition intermediate RI2 (RI
stand for Reaction Intermediate) rather than to the addition intermediate RI1,
but RI1 and RI2 easily interconvert through the transition state TS1 (TS
stands for Transition State) and are expected to be in equilibrium. Therefore,
no changes are expected whether we start from the anti or the gauche radical.

##  3 Methods

All the computations were carried out using the Gaussian16 suite of programs
(Frisch et al., 2016). Geometry optimizations were performed for every
involved species employing the B2PLYP double hybrid functional (Grimme, 2006),
in conjunction to the aug-cc-pVTZ triple-$\zeta$ basis set (Kendall et al.,
1992; Woon & Dunning, 1993). Semi-empirical dispersion effects were included
by means of the D3BJ model of Grimme (Grimme et al., 2011), leading to the so-
called B2PLYP-D3/aug-cc-pVTZ level of theory. These optimizations were
followed by harmonic vibrational calculations adopting the same method, in
order to verify that all intermediates were true minima of the potential
energy surface (PES) and that all transition states exhibited a single
imaginary frequency. The electronic energies were then reevaluated via the
coupled-cluster singles and doubles approximation augmented by a perturbative
treatment of triple excitations (CCSD(T), Raghavachari et al., 1989) in
conjunction to the same basis set. This composite method will be hereafter
named CCSD(T)/aug-cc-pVTZ//B2PLYP-D3/aug-cc-pVTZ.

As in previous works (Balucani et al., 2012; Leonori et al., 2013; Skouteris
et al., 2015; Vazart et al., 2015; Skouteris et al., 2018), a combination of
capture theory and the Rice-Ramsperger-Kassel-Marcus (RRKM) calculations was
used to determine the relevant rate coefficients and branching ratios
regarding the reactions following the oxygen addition to the radicals. We have
used capture theory for the addition of the O(3P) atom to the various forms of
deuterated hydroxyethyl radicals, whereas for the subsequent steps
(isomerizations or bond fissions) energy-dependent rate constants were
calculated using the RRKM scheme. We used an in-house code to solve the master
equation in the zero pressure limit. The quantum tunneling effects were
computed following the symmetric Eckart potential treatment, which provides
results that do not deviate much from the more accurate instanton method (e.g.
Senevirathne et al., 2017).

Given the critical role of the long range interaction in the capture model, we
decided to employ a higher accuracy theoretical method based on CASSCF and
CASPT2 calculations (OpenMolcas 18.09). However, we met with considerable
difficulty to identify the van der Waals minima in the entrance valley and
possible transition states from the van der Waals complex(es) to the first
covalently bound intermediate. Therefore, as a guide to locate the position of
the van der Waals energy minimum we resorted to a semiempirical method
developed by Pirani et al. (2008), as recently done for other systems by de
Aragão et al. (2021) and Marchione et al. (2022). This treatment of the
entrance channel leads to some variation in the rate coefficient values with
respect to those reported in Skouteris et al. (2018). Since the focus of this
manuscript is on the deuteration degree of the reaction products, which is not
affected by the long-range potential, the details of these calculations and
the effect on the global rate coefficients will be the subject of a future
publication.

Finally, to obtain the product branching fractions, the master equation was
solved at all relevant energies for all systems (to consider the overall
reaction scheme), Boltzmann averaging was carried out to obtain temperature-
dependent values.

##  4 Results

###  4.1 Electronic structure: Potential Energy Surfaces (PESs)

Figure 4: Proposed full reaction path, starting from CH2CH2OH + O(3P), at the
CCSD(T)/aug-cc-pVTZ//B2PLYP-D3/aug-cc-pVTZ level of theory. The relative
energies are the electronic ones, as they remain equal for every deuterated
and undeuterated reactions. RI = reaction intermediate; TS = transition state.
The detailed energies are given in the Appendix.

Figure 4 shows the minimum energy path following the addition of atomic oxygen
O(3P) on the 2-hydroxyethyl radical CH2CH2OH, already proposed by Skouteris et
al. (2018). All the energies and the coordinates of the involved species are
reported in the Appendix.

As both fragments approach each other, the barrierless addition of oxygen on
the gauche-2-hydroxyethyl radical leads to the RI1, which is ca. 370 kJ/mol
more stable than the reactants. Its trans counterpart, the slightly less
stable (by 5 kJ/mol) compounds RI2, can easily be reached from the cis,
through a transition state (TS1) reflecting a 15 kJ/mol barrier. It is also
possible to start from the anti\- conformer of the radical (ca. 2 kJ/mol less
stable than the gauche) that would lead to RI2. Both RI1 and RI2 species are
then able to undergo a dissociation into formaldehyde and the CH2OH radical,
through the transition states TS5 and TS6. These dissociation channels exhibit
barriers of around 50 kJ/mol. Other dissociations can also be observed from
both RI1 and RI2, leading this time to cis- or trans-glycolaldehyde and H,
through TS2 and TS3, respectively, that are about 95 kJ/mol higher in energy
than their corresponding reaction intermediates.

Cis- and trans-glycolaldehyde are connected by TS4 and require a 30 kJ/mol
energy to go from one to the other. The cis conformer is the marginally most
stable one, by 13 kJ/mol. Two epoxidations can also be envisaged. The first
one, starting from RI1, leads to the epoxide CH2OCHOH + H and exhibits a
barrier (represented by TS13) of ca. 220 kJ/mol. The second one starts from
RI2, leads to ethylene oxide and OH and has to go through a ca. 200 kJ/mol
barrier, represented by TS14. Again starting from both RI1 and RI2 species,
one can observe hydrogen migrations from carbon atoms to the oxygen atom
bearing the lone electron. Both TS7 and TS8 correspond to hydrogen migrations
from the carbon atom linked to the oxygen atom bearing the lone electron and
are around 120 kJ/mol more energetic than their corresponding intermediates.

The TS9 transition state can be reached from both RI1 and RI2 and consists in
a hydrogen migration from the carbon that is not linked to the oxygen atom
bearing the lone electron. It is ca. 115 kJ/mol energetically higher than RI1
and RI2. TS7 and TS8 lead to RI3 and RI4, respectively, while TS9 leads to
RI4. These intermediates are found to be more than 400 kJ/mol more stable than
the precursors and can be linked to each other thanks to the TS10 transition
state with a small barrier of around 20 kJ/mol. Starting from both RI3 and RI4
compounds, an epoxidation leading to the epoxide CH2OCHOH and H can be
envisaged and exhibits ca. 250 kJ/mol barriers (TS15). The other possible
reaction is a dissociation from both RI3 and RI4 into Z\- and
E-ethene-1,2-diol isomers and H, respectively. The step from RI3 to
Z-ethene-1,2-diol + H and the one from RI4 to E-ethene-1,2-diol + H exhibit
barriers of about 150 kJ/mol (through the TS11 and TS12 transition states,
respectively), both isomers being found around 260 kJ/mol more stable than the
precursors and the Z one slightly more stable (by 20 kJ/mol) than its E
counterpart.

If we look more carefully at the products that can be obtained via this path,
one can see that the most stable ones are formaldehyde + H2COH. The following
ones, in decreasing order of stability, are glycolaldehyde + H, Z\- and
E-ethene-1,2-diol + H, ethylene oxide + OH and CH2OCHOH + H.

Figure 5: Unimolecular rate coefficients from RI1 to $cis$-glycoaldehyde via
TS2. Red: all-protium reaction. Green: CH2ODCHO from reaction 5. Blue:
CHDOHCHO from reaction 6. Magenta: CHDOHCHO from reaction 7. Light blue:
CH2OHCDO from reaction 8a. Purple: CH2OHCDO from reaction 9a.

When the deuteration of a species is considered, only Zero-Point Energies
(ZPEs) are affected as the electronic energy remains identical. Indeed,
isotopomers carry the same amount of electron(s) and this is the reason why
the reaction path of Fig. 4 is valid for all isotopic variants, since the
electronic energies remain identical for all five reactions that involve one
of the monodeuterated 2-hydroxyethyl radicals. The energetic distinction
between the five paths is then made thanks to zero-point corrections
originating from frequencies computations that take into account the masses of
the atoms. These differences of zero-point corrected energies are reported in
Appendix for each case.

The only difference originates from to the presence of a loop between RI1/RI2
and RI3/RI4 through TS7, TS8 and TS9. Indeed, for each stage of a reaction,
one has to consider the backward and forward steps and if in the all-protium
reaction TS9 and TS7/TS8 link the same intermediates, it is not the case
anymore when deuterated species are involved. An example of this loop
regarding reaction (1) is described in Appendix, together with figures
representing all the cases, and were all taken into account for the kinetics
calculations. The deuteration propagation between hydroxyethyl radical and
glycolaldehyde in every case is also given in Appendix. We have verified that
these loops are not affecting the final outcome, as the dominant channels are
those leading from RI1 and RI2 to cis- and trans-glycolaldehyde.

###  4.2 Kinetics

Figure 6: The structures of the various isotopomers of 2-hydroxylethyl
radical, of the relative addition intermediate RI1, of the TS2 connecting RI1
and the products, of the resulting isotopomers of glycolaldehyde for the
reactions (5)(9). The D atoms are marked orange.

The main goal of these new calculations is to evaluate the variation of the
rate coefficients due to KIE and the D-product branching ratios. In Fig. 5, we
have reported the decomposition rate coefficients of the different
monodeuterated RI1 into monodeuterated glycolaldehyde (+H) for the reactions
(5)-(7), (8a) and 9(a). A first aspect to be noted is that the decomposition
rate coefficient of RI1 is not very different when the all-protium reaction is
compared to the reaction (5) and (6). A rather small difference is visible in
the case of reaction (7) and (9a) while a more pronounced difference is
visible for the reaction (8a). An inspection of Fig. 6 can help to clarify
this trend. Reactions (5)-(7) can only form one isotopomer of glycolaldehyde
without competition. Furthermore, the C-H bond which is going to be broken
does not involve the deuterium atom. The similarity with the rate coefficient
of the all-protium reaction clearly indicates a very minor contribution from
secondary KIE as expected, with the exception of reaction (7) where a small
effect can be noted.

The situation is different for the reactions (8) and (9) as in this case we
expect competition between the fission of a C-H bond and that of a C-D bond.
As expected for an indirect reaction, this competition favors the C-H bond
breaking over that of C-D. Having said that, however, there is a significant
difference between the case of reaction (8) and (9). In the case of reaction
(9), the fission of the C-H bond is so favored that the rate coefficient of
the (9a) channel is almost the same as the other rate coefficients of Fig. 5.
Instead, the rate coefficient for reaction (8a) is significantly smaller. An
inspection of the characteristics of the transition states reported in Fig. 6
can help in understanding the reason: in order for the H atom to reach the
appropriate geometry of the TS2-8a, a significant amount of internal rotation
must also occur simultaneously with the bond breaking, increasing the height
of the barrier and the rate of its surmounting. As a consequence, the yield of
the undeuterated glycolaldehyde + D, is significant for reaction (8). In the
case of reaction (9), instead, the opposite is true because it is the
mechanism leading to undeuterated glycolaldehyde + D that features a
reorientation of the RI1 intermediate to reach the critical configuration of
TS2-9a. Indeed, the yield of HOCH2CHO + D is much smaller than in the case of
reaction (8).

In conclusion, the effect of secondary KIE is small in all the cases
considered, while primary KIE affecting reaction (8) and (9) has a rather
different outcome depending on the details of the potential energy surface
and, more specifically in this case, on the difference in the geometry of the
intermediates with respect to that of the transition states connecting the
intermediates to the products.

In order to be able to compare our new computations with astronomical
observations, it is necessary to figure out the amount of every type of
deuterated glycolaldehyde that is formed starting from each radical of
deuterated ethanol. Therefore, we have considered the effect of the first step
and multiplied the global rates obtained from each reaction (5-9) by their
respective branching ratios resulting from the first step, according to the
scheme depicted in Fig. 2. In the cases where the same isotopomer of
glycolaldehyde has more than one formation reaction, the contributions have
been summed up.

##  5 Discussion

###  5.1 How to compare the theoretical values with astronomical observations

In this section, we aim to provide guidelines to compare the results of our
new computations with astronomical observations. As mentioned in Section 2,
ethanol exists under the form of 3 rotamers: the anti-, the +gauche\- and
-gauche-. However, in the ISM, so far the only detected deuterated conformer
is the anti- one. To derive the total abundance of deuterated ethanol (i.e.
including the gauche rotamers), Jørgensen et al. (2018) suggested to apply a
factor of 2.69 to the measured anti rotamers abundance (see also Manigand et
al., 2020). This practically means that having (so far) only the abundance of
the anti deuterated conformers, it is necessary to multiply by 2.69 to account
for the entire abundance of monodeuterated ethanol. Indeed, since we want to
compare the abundances of monodeuterated glycolaldehyde and monodeuterated
ethanol, we have to keep in mind that all three starting rotamers of ethanol
can lead to glycolaldehyde. If a total abundance of the various ethanol
isotopologues is ever measured, the factor is not needed anymore.

Given the very close energies of the rotamers of both ethanol and
2-hydroxyethyl radical, we can say that the proposed chemical schemes hold for
all rotamers. In particular, the very low energy of TS1 warrants an
equilibrium population between RI1 and RI2, which are the intermediates formed
by either the addition of the O atom to the gauche- or anti- rotamers of
2-hydroxyethyl radical. To address the astrophysical implications, the rate
coefficients obtained for reactions (5)-(9) will be divided by the rate
coefficient derived for the all-protium reaction. Any correction factor
necessary to recover the global abundance from the anti rotamer is therefore
simplified.

###  5.2 Application to IRAS16293 B

As mentioned in the Introduction, molecular deuteration has proven to be an
efficient way to discriminate among the possible different routes of formation
of interstellar molecules. Until very recently, this could only be done for
small ($\leq 5$ atoms) molecules and methanol, in which the molecular
deuteration is basically set by the H2D+/H${}_{3}^{+}$ abundance ratio, which,
in turn, is due to thermodynamic isotope effect, TIE. In large molecules, such
as the iCOMs, instead, the deuteration is governed by the kinetic isotope
effect, KIE.

The new calculations reported in the present work allow us to test whether the
observed deuteration of glycolaldehyde is compatible with its formation in the
gas phase from ethanol, following the chain of reactions suggested by
Skouteris et al. (2018) and schematically shown in Fig. 1. This is also
possible thanks to the very sensitive ALMA observations towards the Solar-like
protostar IRAS16293 B hot corino obtained by the PILS project (Jørgensen et
al., 2016), which detected various isotopomers of deuterated ethanol and
glycolaldehyde (Jørgensen et al., 2016, 2018).

Table 2: Comparison of the computed D/H ratios with respect to the
observations towards IRAS 16293-2422 by Jørgensen et al. (2016)
(glycolaldehyde) and Jørgensen et al. (2018) (ethanol). The first two columns
report the observed ratio of the measured column densities of the three
D-bearing isotopomers of ethanol (D-ethanol) with respect to the H-bearing
ethanol (CH3CH2OH). Columns 3 and 4 report the observed ratio of the measured
column densities of the three D-bearing isotopomers of glycolaldehyde
(D-glycolaldehyde) with respect to the H-bearing glycolaldehyde (CH2OHCHO).
Following the scheme of Fig. 2, we then compared the observed and predicted
ratios of (CH2ODCHO/CH2OHCHO)/(CH3CH2OD/CH3CH2OH),
(CHDOHCHO/CH2OHCHO)/(CH3CHDOH/CH3CH2OH) and (CH2OHCDO/CH2OHCHO)/(CH2DCH2OH/
CH3CH2OH

).  Observed D-ethanol Observed D-glycolaldehyde D-glycol/D-ethanol
Isotopomers obs. D/Ha Isomer obs. D/Ha Observed Predicted CH3CH2OD 0.05
CH2ODCHO 0.05 1.0$\pm$0.8 0.90 CH3CHDOH 0.10 CHDOHCHO 0.10 1.0$\pm$0.8 0.95
CH2DCH2OH 0.17 CH2OHCDO 0.05 0.30$\pm$0.24 0.54

Note. — a) Jørgensen et al. (2018) report an uncertainty of 20% on the
estimates of the ethanol isotopologues column densities, which translates into
40% on their column density ratio. We assumed the same for glycolaldehyde.
When then propagating to the ratio of the ratios in the penultimate column
gives an approximate uncertainty of 80% on each quoted value.

Table 2 summarises the measured D/H abundance ratios of the three deuterated
ethanol isotopomers and the three isotopomers of deuterated glycolaldehyde
that would originate from them according to the scheme illustrated in Fig. 2.
Please note that the abundance of a-a and a-s CH2DCH2OH have been added
because, even if they can be spectroscopically identified, they are chemically
indistinguishable. In the same table, we report the abundance ratios of the
measured and computed (CH2ODCHO/CH2OHCHO)/ (CH3CH2OD/CH3CH2OH), (CHDOHCHO/
CH2OHCHO)/(CH3CHDOH/CH3CH2OH) and (CH2OHCDO/CH2OHCHO)/(CH2DCH2OH/ CH3CH2OH),
respectively. Please note that by ”measured D/H abundance ratios” we mean the
ratios of the measured column densities of each D-bearing isotopomer with
respect to the H-bearing species. Likewise, the computed abundance ratios are
obtained considering the rate coefficients of all reactions leading to each
deuterated glycolaldehyde isotopomer from the relevant deuterated ethanol one
(scheme in Fig. 2). Also note that the computed ratios actually do not depend
on the temperature in the 10–300 K range.

While the measured (CH2ODCHO/CH2OHCHO)/ (CH3CH2OD/CH3CH2OH) and (CHDOHCHO/
CH2OHCHO)/(CH3CHDOH/CH3CH2OH) are about 1, the (CHDOHCHO/ CH2OHCHO)/
(CH3CHDOH/CH3CH2OH) is a factor 3 lower. The computed abundance ratios follow
exactly this trend, with the first two ratios being also around unity, and the
last one a factor of two lower. When considering the error bars associated
with the observations (around 20% for each column density, which translates
into a 40% for two column densities ratios and, finally, to 80% for the ratio
of two ratios) the agreement between the measured and computed abundance
ratios is very good. We notice that Skouteris et al. (2018) already showed
that the measured gaseous abundances of ethanol and glycolaldehyde observed in
low-mass warm objects are also consistent with the gas-phase formation of
glycolaldehyde from ethanol according the scheme of Fig. 1 (see their Figure
4). The present results support the suggestion by Skouteris et al (2018)
because they show that the observed deuteration of ethanol and glycolaldehyde
are compatible with a gas-phase synthesis of glycolaldehyde from ethanol.
However, since at present and to our best knowledge, no similar computations
on the molecular deuteration for the grain-surface formation routes of iCOMs
are available, we cannot exclude that pathway. It would be extremely
important, if not essential, to have also those computations so as to be able
to really understand if the two pathways lead to different molecular
deuteration and, consequently, if iCOMs deuteration can be used to
discriminate their formation route.

Finally, an important result of our new calculations is that, in gas-phase
reactions, the molecular deuteration of the parent species is not ”just”
passed to the daughter one, as already found by Skouteris et al. (2017) for
formamide. What more, it is impossible to predict a priori the molecular
deuteration of different isomers, only specific calculations can provide the
correct values. For example, for the NH2 \+ H2CO $\rightarrow$ NH2CHO + H2
reaction, the rate coefficients to form NH2CDO from HDCO is about a factor
three smaller than that to form NH2CHO, whereas the formation of CH3OHCDO from
CH2DCH2OH is a factor two smaller. Therefore, specific calculations need to be
carried out for the systems where deuterated iCOMs isomers are detected, both
to have the deuterium fractionation from gas-phase and grain-surface
reactions.

##  6 Conclusions

In this work, we present a theoretical study of the gas-phase formation of the
deuterated glycolaldehyde isotopomers using the deuterated ethanol isotopomers
as mother species. This work is based on the original scheme proposed by
Skouteris et al. (2018) (see Fig. 1). The list of the reactions between the
deuterated isotopomers of ethanol and glycolaldehyde is summarised in Tab. 1
and their scheme is shown in Fig. 2. It involves two steps which lead first
from ethanol to the 2-hydroxyethyl radical (CH2CH2OH) and then from the latter
to glycolaldehyde. Here we report new computations of the second step, which
allow to provide theoretical predictions of the abundance ratios of the
different D isotopomers of glycolaldehyde with respect to those of ethanol.

We have found a significant primary KIE (kinetic isotope effect) for the case
of the reaction CHDCH2OH + O, while in the cases of the other reactions the
KIE is modest. Starting from CH3CH2OH, CH3CH2OD or CH3CHDOH, similar rates for
the formation of the major monodeuterated glycolaldehyde products are
obtained, due to the deuterium atom being only an onlooker in these reaction
paths. On the contrary, starting from CH2DCH2OH, a competition between
hydrogen and deuterium loss leads to a depletion of the corresponding
deuterated glycolaldehyde, but with a significant difference in the case of
reactions CHDCH2OH + O, where the yield of undeuterated glycolaldehyde is not
negligible.

This new study confirms that the molecular deuteration of the parent species
is not ”just” passed to the daughter one, as also found in the case of the
formamide when formed in the the NH2 \+ H2CO gas-phase reaction (Skouteris et
al., 2017)).

Finally, the comparison of the new predicted deuterated glycolaldehyde over
ethanol isotopomers with those measured towards the Solar-like protostar
IRAS16293 B suggests a gas-phase origin for the glycolaldehyde. However,
lacking similar computations for the glycolaldehyde grain-surface formation
route, the latter cannot be excluded.

We conclude emphasizing that the new facilities like ALMA and IRAM/NOEMA are
now so sensitive that the deuterated iCOMs isomers can be detected. Their
observed ratios can potentially be used to discriminate their formation routes
if, and only if, computations similar to those reported here are carried out
both for the gas-phase and grain-surface reactions.

We warmly thank Dr. Joan Enrique-Romero, Luca Mancini, Prof. Fernando Pirani
and Prof. Marzio Rosi for very helpful discussions. This project has received
funding from the European Research Council (ERC) under the European Union’s
Horizon 2020 research and innovation programme, for the Project “The Dawn of
Organic Chemistry” (DOC), grant agreement No 741002. Most of the computations
presented in this paper were performed using the GRICAD infrastructure
(https://gricad.univ-grenoble-alpes.fr), which is partly supported by the
Equip@Meso project (reference ANR-10-EQPX-29-01) of the programme
Investissements d’Avenir supervised by the Agence Nationale pour la Recherche
NB and DS thank the Italian Space Agency for co-funding the Life in Space
Project (ASI N. 2019-3-U.O).

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##  Appendix A ENERGIES

Table 3: Involved energies Part 1, in Hartrees. | Electronic energies | undeuterated | D1
---|---|---|---
| CCSD(T)/ | B2PLYPD3/ | ZPE B2 | ZPE-corr | ZPE-corr | ZPE B2 | ZPE-corr | ZPE-corr
| aug-cc-pVTZ | aug-cc-pVTZ |  | B2PLYPD3 | B2//CCSD(T) |  | B2PLYPD3 | B2//CCSD(T)
CH2CH2OH | -154.13636 | -154.3101518 | 0.065377849 | -154.244774 | -154.0709822 | 0.0620758 | -154.2480760 | -154.0742842
O | -74.97895233 | -75.05099966 | 0 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$
RI1 | -229.2627622 | -229.511562 | 0.071620018 | -229.439942 | -229.1911422 | 0.0682610 | -229.4433010 | -229.1945012
RI2 | -229.2596686 | -229.5087096 | 0.070337589 | -229.438372 | -229.189331 | 0.0670636 | -229.4416460 | -229.1926050
TS1 | -229.2555932 | -229.5047613 | 0.070431348 | -229.43433 | -229.1851619 | 0.0671333 | -229.4376280 | -229.1884599
RI3 | -229.280304 | -229.5300827 | 0.072307655 | -229.457775 | -229.2079963 | 0.0689597 | -229.4611230 | -229.2113443
RI4 | -229.2752895 | -229.5252501 | 0.071691112 | -229.453559 | -229.2035984 | 0.0683771 | -229.456873 | -229.2069124
TS10 | -229.2714876 | -229.5214045 | 0.070910492 | -229.450494 | -229.2005771 | 0.0676605 | -229.453744 | -229.2038271
cis-glycol. | -228.7283987 | -228.9792354 | 0.061282384 | -228.917953 | -228.6671163 | 0.0579184 | -228.9213170 | -228.6704803
trans-glycol. | -228.7230381 | -228.9737467 | 0.060606706 | -228.91314 | -228.6624314 | 0.0573357 | -228.9164110 | -228.6657024
TS4 | -228.7157718 | -228.9662472 | 0.060708204 | -228.905539 | -228.6550636 | 0.0574292 | -228.9088180 | -228.6583426
TS2 | -229.218992 | -229.4698015 | 0.06338652 | -229.406415 | -229.1556054 | 0.0600095 | -229.4097920 | -229.1589824
TS3 | -229.2147955 | -229.4655661 | 0.062653149 | -229.402913 | -229.1521423 | 0.0593911 | -229.4061750 | -229.1554043
TS6 | -229.2418373 | -229.4951938 | 0.068737806 | -229.426456 | -229.1730995 | 0.0653728 | -229.4298210 | -229.1764645
TS5 | -229.2388407 | -229.4922154 | 0.068636375 | -229.423579 | -229.1702044 | 0.0652584 | -229.4269570 | -229.1735824
TS13 | -229.1709749 | -229.4211155 | 0.064329474 | -229.356786 | -229.1066454 | 0.0610465 | -229.3600690 | -229.1099284
TS14 | -229.1823514 | -229.4323995 | 0.068804454 | -229.363595 | -229.113547 | 0.0658265 | -229.3665730 | -229.1165250
TS7 | -229.2134739 | -229.4629519 | 0.066841945 | -229.39611 | -229.1466319 | 0.0634669 | -229.3994850 | -229.1500069
TS8 | -229.2097829 | -229.4594576 | 0.066667631 | -229.39279 | -229.1431152 | 0.0633656 | -229.3960920 | -229.1464172
TS9 | -229.2156562 | -229.4659675 | 0.067715499 | -229.398252 | -229.1479407 | 0.0643525 | -229.401615 | -229.1513037
TS15 | -229.1728045 | -229.4255038 | 0.063381787 | -229.362122 | -229.1094227 | 0.0600308 | -229.3654730 | -229.1127737
TS11 | -229.2141893 | -229.4659948 | 0.063609818 | -229.402385 | -229.1505795 | 0.0603338 | -229.4056610 | -229.1538555
TS12 | -229.2062338 | -229.4579936 | 0.062820588 | -229.395173 | -229.1434132 | 0.0595416 | -229.3984520 | -229.1466922
ep-CH2OCHOH | -228.6992322 | -228.9483692 | 0.062141192 | -228.886228 | -228.637091 | 0.0588422 | -228.8895270 | -228.6403900
E-ethen-1,2-diol | -228.7083621 | -228.9595503 | 0.061060253 | -228.89849 | -228.6473018 | 0.0577773 | -228.9017730 | -228.6505848
Z-ethen-1,2-diol | -228.7159011 | -228.9669892 | 0.061556193 | -228.905433 | -228.6543449 | 0.0581452 | -228.9088440 | -228.6577559
H | -0.499821176 | -0.498668238 | 0 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$
ethylene oxide | -153.5565781 | -153.7306824 | 0.057680359 | -153.673002 | -153.4988978 | 0.0543794 | -153.6763030 | -153.5021988
OH | -75.64558477 | -75.7193689 | 0.008511898 | -75.710857 | -75.63707287 | 0.0061969 | -75.7131720 | -75.6393879
formaldehyde | -114.34288 | -114.4688577 | 0.026675717 | -114.442182 | -114.3162043 | 0.0238247 | -114.4450330 | -114.3190553
H2COH | -114.8988513 | -115.0245879 | 0.037422909 | -114.987165 | -114.8614284 | 0.0341269 | -114.9904610 | -114.8647244
Table 4: Involved energies Part 2, in Hartrees. | D2 | D3 | D4
---|---|---|---
| ZPE B2 | ZPE-corr | ZPE-corr | ZPE B2 | ZPE-corr | ZPE-corr | ZPE B2 | ZPE-corr | ZPE-corr
|  | B2PLYPD3 | B2//CCSD(T) |  | B2PLYPD3 | B2//CCSD(T) |  | B2PLYPD3 | B2//CCSD(T)
CH2CH2OH | 0.0620798 | -154.2480720 | -154.0742802 | 0.0620478 | -154.2481040 | -154.0743122 | 0.0625128 | -154.2476390 | -154.0738472
O |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$
RI1 | 0.0682290 | -229.4433330 | -229.1945332 | 0.0682630 | -229.4432990 | -229.1944992 | 0.0685320 | -229.4430300 | -229.1942302
RI2 | 0.0669806 | -229.4417290 | -229.1926880 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 0.0672716 | -229.4414380 | -229.1923970
TS1 | 0.0670293 | -229.4377320 | -229.1885639 | 0.0670753 | -229.4376860 | -229.1885179 | 0.0674133 | -229.4373480 | -229.1881799
RI3 | 0.0689817 | -229.4611010 | -229.2113223 | 0.0689457 | -229.4611370 | -229.2113583 | 0.0692487 | -229.4608340 | -229.2110553
RI4 | 0.0683701 | -229.4568800 | -229.2069194 | 0.0683451 | -229.4569050 | -229.2069444 | 0.0686521 | -229.4565980 | -229.2066374
TS10 | 0.0675495 | -229.4538550 | -229.2039381 | 0.0676015 | -229.4538030 | -229.2038861 | 0.0679515 | -229.4534530 | -229.2035361
cis-glycol. | 0.0580094 | -228.9212260 | -228.6703893 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 0.0581834 | -228.9210520 | -228.6702153
trans-glycol. | 0.0573127 | -228.9164340 | -228.6657254 |  $\cdots$ |  $\cdots$ |  $\cdots$ | 0.0575827 | -228.9161640 | -228.6654554
TS4 | 0.0573502 | -228.9088970 | -228.6584216 | 0.0573392 | -228.9089080 | -228.6584326 | 0.0577352 | -228.9085120 | -228.6580366
TS2 | 0.0600335 | -229.4097680 | -229.1589584 | 0.0601215 | -229.4096800 | -229.1588704 | 0.0602595 | -229.4095420 | -229.1587324
TS3 | 0.0593101 | -229.4062560 | -229.1554853 | 0.0593541 | -229.4062120 | -229.1554413 | 0.0595801 | -229.4059860 | -229.1552153
TS6 | 0.0655148 | -229.4296790 | -229.1763225 | 0.0655518 | -229.4296420 | -229.1762855 | 0.0656418 | -229.4295520 | -229.1761955
TS5 | 0.0653994 | -229.4268160 | -229.1734414 | 0.0654434 | -229.4267720 | -229.1733974 | 0.0655344 | -229.4266810 | -229.1733064
TS13 | 0.0609195 | -229.3601960 | -229.1100554 | 0.0632915 | -229.3578240 | -229.1076834 | 0.0610185 | -229.3600970 | -229.1099564
TS14 | 0.0653815 | -229.3670180 | -229.1169700 | 0.0654045 | -229.3669950 | -229.1169470 | 0.0654905 | -229.3669090 | -229.1168610
TS7 | 0.0634609 | -229.3994910 | -229.1500129 | 0.0635699 | -229.3993820 | -229.1499039 | 0.0637089 | -229.3992430 | -229.1497649
TS8 | 0.0633366 | -229.3961210 | -229.1464462 | 0.0633176 | -229.3961400 | -229.1464652 | 0.0635386 | -229.3959190 | -229.1462442
TS9 | 0.0644655 | -229.4015020 | -229.1511907 | 0.0657745 | -229.4001930 | -229.1498817 | 0.0643685 | -229.4015990 | -229.1512877
TS15 | 0.0600088 | -229.3654950 | -229.1127957 | 0.0600808 | -229.3654230 | -229.1127237 | 0.0600658 | -229.3654380 | -229.1127387
TS11 | 0.0603418 | -229.4056530 | -229.1538475 | 0.0631358 | -229.4028590 | -229.1510535 | 0.0603118 | -229.4056830 | -229.1538775
TS12 | 0.0596056 | -229.3983880 | -229.1466282 | 0.0624006 | -229.3955930 | -229.1438332 | 0.0595566 | -229.3984370 | -229.1466772
ep-CH2OCHOH | 0.0586722 | -228.8896970 | -228.6405600 | 0.0588572 | -228.8895120 | -228.6403750 | 0.0588512 | -228.8895180 | -228.6403810
E-ethen-1,2-diol | 0.0578453 | -228.9017050 | -228.6505168 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$
Z-ethen-1,2-diol | 0.0582662 | -228.9087230 | -228.6576349 | 0.0583272 | -228.9086620 | -228.6575739 | 0.0703752 | -228.8966140 | -228.6455259
H |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |
ethylene oxide |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |
OH |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |
formaldehyde |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |
H2COH | 0.0345569 | -114.9900310 | -114.8642944 | 0.0344919 | -114.9900960 | -114.8643594 |  $\cdots$ |  $\cdots$ |  $\cdots$
Table 5: Involved energies Part 3, in Hartrees. | D5
---|---
| ZPE B2 | ZPE-corr | ZPE-corr
|  | B2PLYPD3 | B2//CCSD(T)
CH2CH2OH | 0.0625548 | -154.2475970 | -154.0738052
O |  $\cdots$ |  $\cdots$ |  $\cdots$
RI1 | 0.0683890 | -229.4431730 | -229.1943732
RI2 |  $\cdots$ |  $\cdots$ |  $\cdots$
TS1 | 0.0673133 | -229.4374480 | -229.1882799
RI3 | 0.0688927 | -229.4611900 | -229.2114113
RI4 | 0.0683401 | -229.4569100 | -229.2069494
TS10 | 0.0675745 | -229.4538300 | -229.2039131
cis-glycol. |  $\cdots$ |  $\cdots$ |  $\cdots$
trans-glycol. |  $\cdots$ |  $\cdots$ |  $\cdots$
TS4 |  $\cdots$ |  $\cdots$ |  $\cdots$
TS2 | 0.0627545 | -229.4070470 | -229.1562374
TS3 | 0.0620581 | -229.4035080 | -229.1527373
TS6 | 0.0656298 | -229.4295640 | -229.1762075
TS5 | 0.0655574 | -229.4266580 | -229.1732834
TS13 | 0.0610165 | -229.3600990 | -229.1099584
TS14 | 0.0655005 | -229.3668990 | -229.1168510
TS7 | 0.0649069 | -229.3980450 | -229.1485669
TS8 | 0.0647136 | -229.3947440 | -229.1450692
TS9 | 0.0643795 | -229.4015880 | -229.1512767
TS15 | 0.0627688 | -229.3627350 | -229.1100357
TS11 | 0.0601708 | -229.4058240 | -229.1540185
TS12 | 0.0594846 | -229.3985090 | -229.1467492
ep-CH2OCHOH |  $\cdots$ |  $\cdots$ |  $\cdots$
E-ethen-1,2-diol |  $\cdots$ |  $\cdots$ |  $\cdots$
Z-ethen-1,2-diol |  $\cdots$ |  $\cdots$ |  $\cdots$
H |  $\cdots$ |  $\cdots$ |  $\cdots$
ethylene oxide |  $\cdots$ |  $\cdots$ |  $\cdots$
OH |  $\cdots$ |  $\cdots$ |  $\cdots$
formaldehyde |  $\cdots$ |  $\cdots$ |  $\cdots$
H2COH |  $\cdots$ |  $\cdots$ |  $\cdots$

##  Appendix B GEOMETRIES

CH2CH2OH

C 1.232920 -0.271107 -0.008952

H 2.125654 0.101853 -0.485779

H 1.288279 -1.185206 0.562369

C -0.005441 0.539806 0.032131

H -0.024020 1.254202 -0.796671

H -0.062224 1.126275 0.954803

O -1.192797 -0.256587 0.041870

H -1.150186 -0.856623 -0.708756

RI1

C -0.665516 0.600616 -0.243231

H -0.680218 0.705686 -1.332409

H -1.141144 1.479384 0.188953

O -1.413347 -0.525848 0.171215

H -0.917795 -1.308601 -0.094782

C 0.780402 0.508725 0.231273

H 1.370941 1.396615 -0.029110

H 0.790069 0.440096 1.334495

O 1.399450 -0.645306 -0.170639

RI2

C 0.000000 0.740070 0.000000

H -0.485785 1.154026 0.886696

H -0.485785 1.154026 -0.886696

O 1.399587 1.005160 0.000000

H 1.540173 1.954868 0.000000

C -0.153530 -0.771585 0.000000

H 0.361246 -1.216022 -0.866941

H 0.361246 -1.216022 0.866941

O -1.445826 -1.210383 0.000000

TS1

C -0.571160 0.559832 0.050761

H -0.372345 1.120069 -0.864881

H -0.822570 1.270282 0.834520

O -1.715787 -0.276449 -0.081277

H -1.639962 -0.778788 -0.897329

C 0.698158 -0.232201 0.409719

H 1.040491 -0.005070 1.434793

H 0.476099 -1.310619 0.443693

O 1.785324 -0.006259 -0.382932

RI3

C -0.673146 0.632927 0.213735

H -0.725842 0.737681 1.302874

H -1.187125 1.486600 -0.231125

C 0.726539 0.567617 -0.269325

H 1.314403 1.450850 -0.461503

O -1.362924 -0.601524 -0.045648

H -1.404824 -0.716082 -1.001428

O 1.467182 -0.515066 0.098140

H 0.848973 -1.229596 0.304778

RI4

C -0.583004 0.495629 0.154325

H -0.721823 0.973031 1.128737

H -0.409785 1.290883 -0.576895

C 0.580983 -0.424801 0.141213

H 0.607477 -1.298354 0.780213

O -1.807157 -0.194283 -0.090639

H -1.692297 -0.711086 -0.894439

O 1.774329 0.166861 -0.179454

H 2.491176 -0.460065 -0.050096

TS10

C -0.587440 -0.493297 0.194036

H -0.369097 -1.299872 -0.506876

H -0.827591 -0.958706 1.155437

C 0.608516 0.390352 0.287982

H 0.500681 1.465559 0.244071

O -1.738098 0.191798 -0.309655

H -2.150157 0.670954 0.413262

O 1.768097 -0.159708 -0.198370

H 2.479718 0.483011 -0.133811

cis-glycol.

C 0.826101 0.488051 -0.000000

H 1.420428 1.416543 0.000002

O 1.354025 -0.601632 -0.000004

C -0.667402 0.649429 0.000002

H -0.940852 1.244818 0.879492

H -0.940851 1.244816 -0.879490

O -1.334428 -0.581691 0.000003

H -0.647690 -1.264467 0.000002

trans-glycol.

C 0.261298 -0.762205 0.000000

H -0.647846 -1.389527 0.000000

O 1.370923 -1.236843 0.000000

C 0.000000 0.726038 0.000000

H 0.477464 1.154604 0.885555

H 0.477464 1.154604 -0.885555

O -1.405564 0.916839 0.000000

H -1.597739 1.857353 0.000000

TS4

C -0.812122 0.368151 -0.259305

H -1.150065 1.051941 -1.062078

O -1.544305 -0.495696 0.156713

C 0.609541 0.573067 0.256378

H 1.019851 1.505268 -0.140520

H 0.573258 0.635997 1.342221

O 1.444623 -0.536066 -0.047054

H 1.569892 -0.586418 -0.999332

TS2

C -0.688803 0.636953 -0.136554

H -0.873974 1.005642 -1.156596

H -1.032802 1.409301 0.551869

O -1.373116 -0.559861 0.109977

H -0.723000 -1.270556 0.009685

C 0.811459 0.453501 -0.037354

H 1.426434 1.359535 -0.171765

H 0.963126 0.747216 1.675734

O 1.311151 -0.664372 -0.093161

TS3

C 0.530279 -0.547980 0.048479

H 0.545950 -1.303446 -0.744375

H 0.449612 -1.057604 1.009549

O 1.657176 0.310567 -0.025786

H 2.459270 -0.214772 0.022016

C -0.710651 0.291448 -0.182338

H -0.409780 1.410898 1.153774

H -0.538245 1.206897 -0.779232

O -1.835248 -0.123414 0.043464

TS5

C -0.774386 0.584499 0.017971

H -0.579570 1.100826 -0.912598

H -0.617988 1.125411 0.937882

O -1.851822 -0.237719 0.074655

H -2.067464 -0.565388 -0.804312

C 1.001170 -0.550592 0.059957

H 0.732556 -0.963553 1.044888

H 0.659603 -1.157528 -0.796742

O 1.915841 0.269817 -0.066741

TS6

C -0.916588 0.613010 -0.260055

H -0.713418 0.673133 -1.322515

H -1.312617 1.488241 0.235862

O -1.430244 -0.535764 0.217880

H -0.926507 -1.275033 -0.153088

C 1.095015 0.473522 0.265749

H 1.396154 1.401634 -0.245349

H 0.850638 0.588877 1.333191

O 1.384642 -0.638741 -0.203163

TS13

C 0.290507 0.236734 0.426816

H 0.328353 0.131863 1.501216

H 0.622409 1.781508 0.648934

O 1.406011 -0.055979 -0.308370

H 1.739609 -0.916701 -0.035033

C -0.980476 0.493968 -0.287966

H -1.732150 1.100599 0.212893

H -0.855129 0.714721 -1.345648

O -0.901421 -0.843547 0.081437

TS14

C -0.045627 -0.609930 0.008475

H -0.182908 -1.118319 0.943641

H -0.170151 -1.160955 -0.903213

O -1.838019 0.037287 -0.088497

H -1.934111 0.521944 0.744518

C 0.614408 0.739741 -0.038661

H 0.512259 1.265008 -0.983789

H 0.498487 1.368354 0.841693

O 1.570985 -0.244149 0.030780

TS7

C 0.728784 0.629676 0.134856

H 0.850615 0.919019 1.189552

H 1.213079 1.391987 -0.473265

O 1.369610 -0.601870 -0.123812

H 0.789235 -1.295584 0.212010

C -0.737342 0.582537 -0.163385

H -1.312513 1.505308 -0.123083

H -1.183254 -0.282076 -0.982745

O -1.407837 -0.587122 0.167400

TS8

C 0.564374 0.516431 -0.049784

H 0.451828 1.203331 0.791760

H 0.592263 1.118908 -0.961026

O 1.796000 -0.189328 -0.010475

H 1.853187 -0.661848 0.824899

C -0.616696 -0.405575 -0.122698

H -0.530144 -1.283838 -0.761200

H -1.370792 -0.587540 0.876578

O -1.881301 0.132559 0.043461

TS9

C 0.455914 -0.077084 0.466631

H -0.328392 -1.099419 0.203930

H 0.625977 -0.111446 1.541411

O 1.580239 0.014524 -0.324934

H 2.225897 -0.641948 -0.045717

C -0.737703 0.680711 -0.014300

H -1.214195 1.331601 0.716317

H -0.559428 1.206588 -0.951607

O -1.462630 -0.552916 -0.197356

TS15

C -0.751784 0.738214 -0.143326

H -1.403173 1.373093 0.451583

H -0.654444 1.081041 -1.172631

C 0.412592 0.148272 0.480287

H 0.510380 0.083706 1.550092

O -0.986187 -0.667875 0.002001

H -2.309370 -1.079459 -0.401618

O 1.544763 -0.171240 -0.168288

H 1.423153 -0.064367 -1.118893

TS11

C 0.625410 0.589386 -0.133367

H 1.190020 1.473197 -0.384238

H 0.970127 1.044966 1.808993

C -0.715361 0.590378 -0.108089

H -1.291331 1.494529 -0.212596

O 1.272148 -0.634655 -0.132610

H 2.027377 -0.592390 0.462430

O -1.460171 -0.519135 0.084712

H -0.852301 -1.268569 0.157323

TS12

C -0.517063 0.326741 -0.166063

H -0.582308 1.419913 1.561885

H -0.439956 1.292068 -0.653798

C 0.567843 -0.404213 0.122955

H 0.487488 -1.396628 0.537784

O -1.766511 -0.255189 -0.111547

H -2.357360 0.325392 0.378451

O 1.854984 -0.003236 -0.035098

H 1.879675 0.891481 -0.392520

ep-CH2OCHOH

C -0.210676 0.043521 0.466750

H -0.312304 0.297001 1.513076

O -1.460306 -0.118526 -0.091183

H -1.361579 -0.247236 -1.041018

C 0.991370 -0.616439 -0.032043

H 1.822431 -0.834787 0.626178

H 0.919052 -1.230789 -0.921369

O 0.741336 0.800191 -0.256955

E-ethen-1,2-diol

C 0.531710 -0.400037 0.000001

H 0.451489 -1.477582 0.000012

C -0.531710 0.400037 0.000002

H -0.451489 1.477582 -0.000008

O 1.844519 0.007939 -0.000018

H 1.883216 0.969720 -0.000001

O -1.844519 -0.007939 0.000020

H -1.883216 -0.969720 -0.000029

Z-ethen-1,2-diol

C -0.634594 0.634205 -0.000292

H -1.197735 1.553175 -0.018610

C 0.695478 0.609595 0.004670

H 1.284099 1.510850 -0.006688

O -1.324020 -0.565840 -0.051979

H -2.200907 -0.453474 0.320977

O 1.438966 -0.533081 0.008958

H 0.829659 -1.281988 0.022227

ethylene oxide

C -0.730917 -0.375206 -0.000000

H -1.263500 -0.589074 -0.917612

H -1.263500 -0.589075 0.917611

C 0.730917 -0.375206 0.000000

H 1.263500 -0.589074 0.917612

H 1.263500 -0.589074 -0.917611

O 0.000000 0.857347 0.000000

OH

O 0.000000 0.000000 0.108015

H 0.000000 0.000000 -0.864116

Formaldehyde

C -0.000000 0.000000 -0.530112

H 0.000000 0.936285 -1.111690

H -0.000000 -0.936285 -1.111690

O 0.000000 -0.000000 0.675506

H2COH

C -0.684998 0.027451 -0.061564

H -1.232946 -0.883715 0.101050

H -1.114471 0.992303 0.159997

O 0.670106 -0.125695 0.020201

H 1.096556 0.732271 -0.053276

##  Appendix C Deuteration loops of reactions (1)-(5)

Figure 7: Loop of deuteration regarding reaction (1).

It is noticeable that RI1/RI2-D1 leads to RI3/RI4-D1 through TS7/TS8-D1, but
to RI4-D5 through TS9-D1. When we look at the backwards step, we have to
consider that the RI4-D1 leads to RI1/RI2-D3 through TS9-D3 and that
RI3/RI4-D5 lead to RI1/RI2-D4 though TS7/TS8-D5. The last step of the loop is
the passage from both RI1/RI2-D4 and RI1/RI2-D3 to RI3/RI4-D3, through TS9-D5
and TS7/TS8-D3 respectively. For this reaction, it is therefore required to
consider the intermediates RI1/RI2-D1/D3/D4 and RI3/RI4-D1/D3/D5 for the
remaining rearrangements and dissociations. All of this, keeping in mind that
all RI1 and RI2 are connected by their corresponding TS1, and that all RI3 and
RI4 are connected by their corresponding TS10.

Figure 8: Loop of deuteration regarding reaction (2). Figure 9: Loop of
deuteration regarding reaction (3). Figure 10: Loop of deuteration regarding
reaction (4). Figure 11: Loop of deuteration regarding reaction (5).