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Proceedings of the 7th Faculty of Science International Conference (FOSIC 2023), Delta State
University, Abraka, Nigeria. 6th – 9th November, 2023. Pp. 92 - 106
92
ENERGY, STABILITY, AND ABUNDANCE RELATIONSHIP: EXPLORING
INTERSTELLAR ISOMERIC SPECIES VIA QUANTUM-CHEMICAL
CALCULATIONS
Emmanuel E. Etim*1,2, John P. Shinggu1,2, Bulus Bako1,2, Humphrey S. Samuel1,2
1Computational Astrochemistry and Bio-Simulation Research Group, Federal University Wukari,
2Department of Chemical Sciences, Federal University Wukari,
*Email of Corresponding Author: emmaetim@gmail.com
ABSTRACT
The study unravels the dynamic interplay of energy, stability, and abundance, providing profound insights into the
composition of the interstellar medium. This investigation promises to unveil the underlying principles shaping the
celestial tapestry of astrochemistry. High-level quantum chemical calculations provide accurate enthalpies of
formation for 130 astromolecules, including 31 isomeric groups and 24 cyanide/isocyanide pairs with atom counts
ranging from 3 to 12. The findings reveal a notable Energy, Stability, and Abundance (ESA) relationship, where
isomers with lower enthalpies of formation are more prevalent in the interstellar medium. Literature data confirm the
dominance of the most stable isomer within each group. Exceptions are attributed to interstellar hydrogen bonding
and distinct formation routes. Overall, this relationship implies that interstellar abundances correlate directly with
molecular stabilities, offering insights into astro-molecular patterns and predicting potential candidates for
astronomical observations.
1.0 Introduction:
Chemistry within interstellar space is a captivating area, encapsulating a diverse array of both familiar and exotic
molecules. Contrary to popular perception, it's not merely a vacuum; it hosts a spectrum from common entities like
water to unfamiliar, "non-terrestrial" isomers and radicals (Andrew et al., 2018; Etim et al., 2020a; Etim et al., 2020b;
Etim et al., 2020c; Shinggu et al., 2023a). Advances in radio-astronomy, coupled with collaboration between
spectroscopists and astrophysicists, have unveiled over 200 molecular species (Snyder et al., 1974; pearson et al.,
1997; Etim and Arunan 2005; Khan et al., 2021). These molecules, detected through rotational emission spectra, serve
as probes, unraveling astrophysical phenomena and offering glimpses into the chemical origins of life. Despite their
significance, the processes governing the formation of these molecules under interstellar conditions remain elusive,
contributing to uncertainties about the origin of complex species (Etim et al., 2019a; Etim et al,, 2019b). Gas phase
and surface reactions on interstellar dust grains are believed to be key in shaping this molecular landscape, with
molecular hydrogen acting as a linchpin in the intricate interstellar chemistry (Shinggu et al., 2023b; Shinggu et al.,
2023c; Etim et al., 2018a; Etim et al., 2018b; Etim, 2016; Etim et al., 2016; Etim and Oko, 2020; Singh et al., 2013;
Solomon et al., 1971). Noteworthy features, such as isomerism and hydrogen addition patterns, provide valuable
insights into the formation mechanisms within the interstellar medium (Shinggu et al., 2023a; Irvine et al., 1988;
Samuel et al., 2023).
Isomerism stands out as a pivotal factor in interstellar chemistry, gaining prominence with the detection of an
increasing number of isomeric species in the interstellar medium. About 40% of interstellar molecules, excluding
diatomic and certain special species, exhibit isomerism (Turner et al., 1975; Halfen et al., 2009; Frerking et al., 1979;
Remijan et al., 2009). The coexistence of isomers suggests shared molecular formation routes, prompting exploration
into the broader implications of this phenomenon in interstellar chemistry. While astronomical searches for isomeric
analogues have yielded mixed results, the underlying question persists: why are some isomeric species observed while
others remain elusive in interstellar space? Addressing this query and delving into the intricate world of
astromolecules, we employ advanced quantum chemical calculations to scrutinize the Energy-Stability-Abundance
(ESA) relationship among 130 molecules (Dickens et al., 1997; Gardner et al., 1995; Combes et al., 1987; Johnson et
al., 1977). This comprehensive investigation spans 31 isomeric groups and 24 cyanide/isocyanide pairs, offering
unprecedented insights into the factors influencing astronomical observations. To our knowledge, this extensive
exploration of the ESA relationship is a novel contribution to the existing literature (Remijan et al., 2009; Wlodarczak,
1995; Crawford et al., 1999; Herbst, 2001; Lovas et al., 2006).
2.0 Computational Methods
All quantum chemical calculations presented in this study are conducted using the Gaussian 09 suite of programs.
While a subset of the molecules in our analysis has experimentally determined standard enthalpies of formation (∆fH0),
Proceedings of the 7th Faculty of Science International Conference (FOSIC 2023), Delta State
University, Abraka, Nigeria. 6th – 9th November, 2023. Pp. 92 - 106
93
a significant portion lacks such measurements. Theoretical methods capable of accurately predicting ∆fH0 for
molecules with known experimental values hold immense value, extending their applicability to similar molecules
lacking experimental data with chemical precision. This study employs compound methods that integrate Hartree-
Fock and Post-SCF methods, striking a balance between high accuracy and computational efficiency. Two Weizmann
theories, denoted as W1U and W2U, alongside Gaussian methods (G3, G4, and G4MP2), are employed to ascertain
the standard enthalpies of formation for all molecules in focus. The Weizmann methods utilize distinct levels of theory
for geometry optimization, zero-point energy, single-point calculations, and energy computations. In contrast,
Gaussian G4 and G4MP2 theories share the same approach for geometry optimization and zero-point energy
calculations, diverging only in their single-point calculations and energy computation methods. The zero-point
corrected standard enthalpies of formation for the molecules under investigation are derived from optimized molecular
geometries at the specified levels of theory. To ensure structural stability, harmonic vibrational frequency calculations
are implemented, with equilibrium species exhibiting exclusively real frequencies.
Atomization Energies and Enthalpy of Formation
Examining a diverse array of molecules encompassing both known and unknown enthalpies of formation, the total
atomization energies method emerges as a more advantageous approach compared to methodologies such as isodesmic
and Benson group additivity. This is particularly evident when coupled with a robust computational method and
precise experimental values for the standard enthalpy of formation of the constituent elements involved. The
atomization energies, sometimes interchangeably denoted as total dissociation energies (Do), are computed by
leveraging the calculated energy values, which comprise the sum of electronic and zero-point energy corrections. The
methods outlined in the earlier computational procedures section are instrumental in deriving these atomization
energies. This approach proves highly effective in estimating enthalpies of formation with remarkable accuracy across
various molecular systems, provided a sound computational framework and accurate experimental data for the
constituent elements are available.
Results and Discussion
The experimental enthalpy of formation values for select molecules in this study are sourced from the NIST15
database, unless specified otherwise, and are denoted in the Tables as "expt." Notably, the G3 method yields enthalpy
of formation values that markedly deviate from experimentally measured values, underscoring the potential disparities
in theoretical thermochemistry with certain methods. Consequently, the values derived from the G3 method are
excluded from subsequent discussions. Among the various high-level quantum chemical calculation methods applied,
the G4 method emerges as the most reliable estimator for the enthalpy of formation across the diverse molecules
considered in this study. This is evident in the close agreement, within ±5 kcal/mol, between the theoretically
calculated enthalpy of formation and the experimentally measured enthalpy of formation for molecules with known
experimental values. It is crucial to acknowledge that the calculated enthalpies of formation are inherently subject to
uncertainties stemming from the experimental values of the standard enthalpy of formation of the elements, which are
utilized in computing the enthalpy of formation at 0 K. All reported enthalpies of formation in this study, both from
theoretical and experimental sources, are presented in kcal/mol and at 298.15 K. The ensuing subsections delve into
the results obtained using the diverse methods employed in this study, with isomeric groups categorized based on the
number of atoms, ranging from 3 to 12.
Isomers with 4 Atoms:
Isomeric groups featuring three atoms, as detailed in Table 2 alongside their current astronomical status, exhibit
distinctive patterns in their zero-point corrected standard enthalpies of formation (ΔfH0). Employing the G4 method,
precise estimates of the enthalpy of formation for HCN and HNC, possessing known experimental values, underscore
the chemical accuracy of the method—reflected in the difference within ±1 kcal/mol between theoretical and
experimental values. In the realm of the OCN- isomeric group, where experimental enthalpy of formation values are
available, the predicted value from the W1U method aligns remarkably with the experimental counterpart. Notably,
the ΔfHO values at the G4 and G4MP2 levels exhibit close proximity, while subtle distinctions emerge in values
derived from the W1U and W2U methods, attributing these variations to the distinctive computational approaches
embraced by each method, elucidated in the methodology. Across all six isomeric groups under consideration, those
with lower enthalpies of formation consistently manifest astronomical observations, while their higher enthalpy
counterparts exhibit fewer instances of observation. This correlation underscores a pivotal relationship—the lower the
enthalpy of formation, the greater the stability and abundance within the interstellar medium. Consequently, more
stable molecules, marked by higher abundance, facilitate their easier detection in astronomical observations. In
instances where both isomers within a group have been observed, it becomes evident that the most stable i somer is
Proceedings of the 7th Faculty of Science International Conference (FOSIC 2023), Delta State
University, Abraka, Nigeria. 6th – 9th November, 2023. Pp. 92 - 106
94
invariably detected prior to its less stable counterpart. This trend supports the notion that the most stable isomer,
anticipated to be more abundant, is astronomically more accessible for detection than its less stable counterpart. Real-
world examples, such as the case of HCN prevailing over HNC and the abundance ratio of MgNC to MgCN in
asymptotic giant branch (AGB) stars, affirm the prevalence of the more stable isomer being more abundant. Figure 1
visually encapsulates this relationship, with open symbols signifying non-observed molecules characterized by higher
ΔfH0 values within their respective isomeric groups, in contrast to the filled symbols representing astronomically
observed counterparts.
Isomers with 5 atoms:
Delving into the realm of isomeric groups featuring five atoms, Table 4 unfolds the zero-point corrected standard
enthalpies of formation alongside the current astronomical status. The experimental enthalpy of formation for ketene
mirrors exceptional congruence with theoretical predictions at the G4 and G4MP2 levels. Nevertheless, HCCN and
CH2NN present divergences of 3.7 and 4.2 kcal/mol, respectively, when compared to the G4 method's predictions.
The synergy between molecular stability and interstellar abundance, shaping their astronomical observability, emerges
unmistakably from both Table 4 and Figure 3. Throughout the diverse isomeric groups surveyed, the Energy, Stability,
and Abundance (ESA) relationship governs consistently, with only the isomers possessing lower enthalpies of
formation within their respective groups being subject to astronomical observations. Examining the C3HN isomeric
group, wherein multiple isomers have garnered astronomical attention, the trend persists—HC3CN, the most stable
isomer, precedes others in observation (1971 versus 1992). Notably, HC3N, the epitome of stability within the C3HN
group, outshines its counterparts, HC2NC and HNC3, in observed abundance across various astronomical sources. On
a captivating note, HCNCC, despite piquing investigator interest, eludes astronomical observation, conceivably due
to its higher enthalpy of formation compared to other C3NH isomers. This observation harmonizes seamlessly with
the ESA relationship, affirming its pervasive influence among interstellar molecules.
Isomers with 6 atoms:
Navigating the realm of isomeric groups housing six atoms, both the G4 and G4MP2 methods stand out for their
In the realm of six-atom isomeric molecules, the G4 and G4MP2 methods prove highly accurate in predicting
enthalpies of formation. Their reliability, confirmed against experimental values, extends to molecules lacking such
data. Of the 14 molecules across four isomeric groups, six are observed in interstellar spaces, while eight, excluding
2H-azirine, remain undetected. Stability correlating with interstellar abundance remains a consistent theme, with an
exception in the reactive methylene ketene, evading astronomical observation. In the C2H3N isomeric group, the ESA
relationship unfolds: methyl cyanide, the most stable, led in 1971, followed by methyl isocyanide (1988) and
ketenimine (2006). Abundance aligns with stability, except for 2H-azirine, facing skepticism. Propynal surpasses
cyclopropenone fivefold in molecular clouds. Methylene ketene, akin to reactive anhydrides, poses challenges for
observations but remains a prospect for future scrutiny.
Isomers with 7 Atoms:
Venturing into the realm of isomeric groups harboring seven atoms, Table 6 unveils the standard enthalpies of
formation, while Figure 5 paints a visual representation of the ΔfH0 for these molecules. A stroke of luck graces this
study as nearly all molecules, save for isocyanoethene, boast experimentally measured enthalpies of formation. This
serendipity presents an opportunity to scrutinize the accuracy of theoretical methods, with the G4 and G4MP2 methods
emerging as stalwart predictors, aligning commendably with experimental values. The established trend in the
interplay of energy, stability, and interstellar abundance maintains its course. In this instance, the C2H4O family's four
stable isomers, detailed in Table 6 and illustrated in Figure 5, have all left their cosmic imprint. Remarkably, each
member of this family, including acetaldehyde, vinyl alcohol, ethylene oxide, and acrylonitrile, has graced the
interstellar medium with its presence. Acetaldehyde, the most stable isomer in this family, took center stage in 1973,
preceding its counterparts in astronomical observations. Consistent with expectations, acetaldehyde revels in high
abundance across various astronomical sources where detected, outshining its cosmic companions. A caveat
underscores the importance of contextualizing energy differences; these should be confined to species within the same
set of isomers and not juxtaposed with variations in another isomeric set. Notably, isocyanoethene, the lone non-
observed species in this group, bears a higher enthalpy compared to its observed counterpart, acrylonitrile. This
peculiarity serves as a testament to the nuanced intricacies governing the interstellar landscape.
Proceedings of the 7th Faculty of Science International Conference (FOSIC 2023), Delta State
University, Abraka, Nigeria. 6th – 9th November, 2023. Pp. 92 - 106
95
Isomers with 8 Atoms:
Navigating the cosmos, eight-atom isomers reveal their complexity in Table 7 and Figure 6, with scant experimental
enthalpy values, where G4 and G4MP2 methods shine in accurate predictions. Isomerism takes the stage in interstellar
complexes, impacting seven out of twelve molecules. The C2H4O2 isomeric group, harboring biologically significant
molecules, highlights the intricate dance of energy, stability, and interstellar abundance. Acetic acid and
glycolaldehyde emerge as pivotal players, potential precursors for glycine and biomarkers, respectively. Reactivity
and its impact on abundance present challenges for observational endeavors, aligning with the ESA relationship.
Methyl ketene's non-observation echoes its reactive nature, akin to methylene ketene in six-atom isomers. The
observed order in the C2H4O2 group follows abundance hierarchy, except for acetic acid, suggesting interstellar
hydrogen bonding effects. This intricate ballet of molecules, from stability to reactivity and cosmic interactions,
underscores the profound links within the cosmic symphony. The ESA relationship continues to illuminate the cosmic
complexities, offering insights into the interconnected realms of energy, stability, and cosmic abundance.
Isomers with 9 Atoms:
The cosmic ensemble of isomers with nine atoms unfolds its narrative through Table 8 and Figure 8, offering a glimpse
into their enthalpies of formation and current cosmic status. The theoretical predictions of enthalpies of formation for
molecules with experimentally known values align harmoniously with the outcomes from the G4 and G4MP2
methods, attesting to their predictive prowess. The cosmic stage witnesses the cosmic ballet of isomers with the
empirical formulae C2H6O, C3H5N, and C2H5NO. Ethanol and dimethyl ether, the two known stable isomers of the
C2H6O family, gracefully perform their rotational transitions in the interstellar medium, leaving an indelible mark on
the cosmic canvas. Their abundance ratio, a celestial dance ranging from approximately 0.3 to 3.0 in various
astronomical sources, adds a dynamic layer to their cosmic choreography. In the cosmic tapestry of C3H5N and
C2H5NO, only cyanoethane and acetamide have graced the interstellar medium with their presence, casting their
cosmic silhouettes against the vast celestial expanse. A noteworthy pattern emerges, where the observed isomers, those
with the lowest enthalpies of formation in their respective groups, take center stage in the cosmic performance. The
filled symbols on Figure 8 bear witness to these cosmic actors, while the open symbols depict those yet to make their
astronomical debut. The cosmic ballet of isomers with nine atoms adheres faithfully to the Energy, Stability, and
Abundance (ESA) relationship, painting a cosmic masterpiece where stability governs cosmic abundance. This
celestial choreography, devoid of exceptions, adds another chapter to the cosmic saga, underscoring the profound
interplay between energy, stability, and cosmic presence.
Isomers with 10 Atoms:
The cosmic ensemble expands to the realm of isomers with ten atoms, as portrayed in Table 9, delineating their
enthalpies of formation through the lens of theoretical predictions and experimental measurements, where available.
The W1U and W2U methods, with their tendency to overestimate enthalpies of formation, stand in contrast to the
reliable predictions offered by the G4 and G4MP2 methods, forming a cosmic harmony of computational precision.
Within the orchestration of three distinct isomeric groups, a recurring cosmic motif emerges—the observed isomers,
those gracing the interstellar medium, consistently bear the crown of the lowest enthalpies of formation within their
respective groups. A celestial dance unfolds in the C3H6O isomeric group, where the cosmic stage witnessed the
premiere of propanone (acetone), the most stable isomer and likely the most abundant, in 1987. It paved the way for
the cosmic debut of the next stable isomer, propanal, in 2004, crafting a cosmic narrative echoed in Figure 9. The
observed isomers, marked by filled symbols, take center stage, while the unobserved counterparts await their cosmic
debut with open symbols. This celestial choreography reaffirms the Energy, Stability, and Abundance (ESA)
relationship among interstellar isomeric species. The cosmic tapestry, woven with the threads of stability and energy,
harmonizes in a cosmic symphony where the most stable isomers command the celestial spotlight. The cosmic dance
of isomers with ten atoms adds another verse to the cosmic saga, illustrating the cosmic interplay between energy,
stability, and cosmic presence.
Isomers with 11 Atoms:
Navigating the cosmic expanse of isomers with eleven atoms, our quantum voyage unfolds through various ab initio
quantum chemical methods, revealing the G4 and G4MP2 methods as steadfast cosmic navigators, consistently
aligning with experimental values in Table 10. Their cosmic harmony with reality enhances the reliability of these
methods, ushering them to the forefront for estimating enthalpies of formation in the cosmic ensemble. As the cosmic
curtain rises on the C3H6O2 isomeric group, the cosmic tableau in Table 10 unfolds in descending order of enthalpic
Proceedings of the 7th Faculty of Science International Conference (FOSIC 2023), Delta State
University, Abraka, Nigeria. 6th – 9th November, 2023. Pp. 92 - 106
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magnitude, showcasing the cosmic ballet of molecules with eleven atoms. Figure 10, a cosmic fresco, paints the current
astronomical status of these molecules—a celestial choreography where observed molecules, bedecked with filled
symbols, share the cosmic stage with their unobserved counterparts marked by open symbols. Yet, a celestial enigma
unfolds with propanoic acid, the most stable isomer, lingering in the cosmic wings, yet to make its astronomical debut.
The cosmic conundrum finds resonance in the enthalpy hierarchy, where the observed isomers, including methyl
acetate and ethylformate, clasp the cosmic spotlight with the least enthalpies of formation. The cosmic stage remains
unadorned for propanoic acid, and the veil of mystery lifts when cosmic dynamics, akin to interstellar H -bonding,
intertwine with the cosmic narrative. Figure 11 unveils the cosmic choreography, presenting the optimized structures
of propanoic acid (Structure A) and ethylformate (Structure B). Within Structure A, the acidic hydrogen atom, H1,
emerges as a cosmic player in interstellar H-bonding on the dust grain's surface. This cosmic dalliance results in a
greater portion of propanoic acid tethered to the interstellar dust grains, dimming its cosmic radiance, diminishing
abundance, and deferring its astronomical debut compared to ethylformate. In the cosmic lexicon of interstellar
hydrogen bonding, a recent cosmic manuscript explores the cosmic dance of propanoic acid, revealing its robust bond
to interstellar dust surfaces. The cosmic ballet of interstellar hydrogen bonding, intricate and nuanced, discloses why
propanoic acid lingers in the cosmic wings, evading astronomical detection as its cosmic peers revel in the celestial
limelight. This cosmic saga echoes the Energy, Stability, and Abundance (ESA) relationship, where stability and
enthalpy intertwine with cosmic presence. The cosmic journey with isomers of eleven atoms unfurls a cosmic
narrative, unveiling the cosmic intricacies that shape the celestial dance of molecules in the cosmic expanse.
Isomers with 12 Atoms:
In the cosmic narrative of twelve-atom isomers, the steadfast reliability of G4 and G4MP2 models shines in predicting
thermochemical properties with cosmic precision. Table 11 unfurls the enthalpies for propanol and propan-2-ol,
showcasing the cosmic harmony between theory and reality. The celestial saga extends to 12-atom isomeric groups in
Table 11 and Figure 12, unveiling an interplay of stability, enthalpy, and astronomical destiny. In the C3H8O isomeric
group, ethyl methyl ether, crowned with the highest enthalpy, graces the cosmic stage, while theoretical stalwarts,
propanol and propan-2-ol, linger in cosmic obscurity. The cosmic revelation extends to C4H7N, where isopropyl
cyanide stands as a cosmic sentinel, observed in the interstellar expanse. Propyl cyanide echoes cosmic silence,
awaiting revelation. Observations echo the ESA relationship, aligning with cosmic ballet's least enthalpic performers.
The cosmic dance unfolds, revealing delayed astronomical sightings influenced by interstellar hydrogen bonding.
Figure 11 unveils ethereal structures, where alcohols yield to cosmic whims, creating delays in sightings. Ketones
emerge as cosmic stalwarts, transcending aldehydes in stability, acidity, and reactivity. The cosmic ballet resonates,
each molecular note echoing stability, abundance, and cosmic observability. G4 hints at the prospect of unveiling more
branched molecules in the cosmic symphony, enriching our understanding. The twelve-atom isomers narrate a tale of
cosmic intricacies, entwining stability, enthalpy, and observational destiny. The cosmic ballet beckons exploration,
inviting us to decipher celestial mysteries etched in the cosmic fabric.The Energy, Stability, and Abundance (ESA)
relationship forged through the cosmic crucible of quantum chemical calculations unveils a trove of insights,
resonating across the interdisciplinary realms of astrochemistry. Within this cosmic symphony, the immediate
consequences ripple through the cosmic fabric, addressing enigmas and beckoning towards a more nuanced
understanding of the celestial tableau.
Cyclic Mysteries Unveiled: A celestial query echoes through the cosmos—where are the cyclic interstellar
molecules? Amidst over 200 observed species, only a handful adorn the cyclic tapestry. The ESA relationship,
illuminated by this study, reveals a cosmic truth: cyclic molecules, graced with high enthalpies of formation, embrace
a path less traveled, less stable, and consequently, less abundant. This cosmic dance between energy, stability, and
abundance demystifies the paucity of cyclic molecules in astronomical observations.
Candidates for Cosmic Gazing: The cosmic stage awaits new protagonists, and the ESA relationship offers cosmic
casting insights. Methylene ketene, methyl ketene, propanoic acid, propanol, and propan-2-ol, crowned with the lowest
enthalpies of formation, stand as celestial contenders yet to grace the astronomical canvas. The cosmic ballet hints at
the potential emergence of branched molecules, their stability becoming a cosmic beacon for future observations.
Cyanide vs. Isocyanide Dichotomy: In the cosmic amphitheater, a dichotomy unfolds—why do cyanides outnumber
isocyanides in astronomical observations? The ESA relationship casts its cosmic gaze, revealing that cyanides,
crowned with lower enthalpies of formation, bask in greater stability and abundance, easing their cosmic visibility.
This cosmic truth finds validation in the observational data, where cyanide species surpass their isocyanide
counterparts in interstellar abundance and ease of detection.
Proceedings of the 7th Faculty of Science International Conference (FOSIC 2023), Delta State
University, Abraka, Nigeria. 6th – 9th November, 2023. Pp. 92 - 106
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Plausibility in Cosmic Chemistry: Cosmic alchemy, wrought in the celestial crucible, often proposes intricate
reaction pathways. Yet, the plausibility of these cosmic dances is veiled in uncertainty. The ESA relationship emerges
as a celestial compass, guiding the evaluation of proposed formation routes. The enthalpic signatures of isomers
become cosmic signatures, delineating plausible cosmic choreography and unraveling the mysteries of unsuccessful
astronomical searches.
Amidst the cosmic dance of molecules, the ESA relationship emerges as a guiding constellation, casting its celestial
light on the intricate interplay between energy, stability, and abundance. As astrochemistry embarks on a cosmic
odyssey, the insights unveiled by this relationship promise to illuminate the cosmic tapestry with newfound clarity.
Conclusion
In our exploration of enthalpies of formation for astromolecules, the Gaussian G4 and G4MP2 methods have proven
consistently reliable, aligning closely with experimental values. This study unravels a profound relationship: the
cosmic trio of energy, stability, and interstellar abundance. The findings resonate with tangible consequences in
unraveling cosmic mysteries—illuminating the scarcity of cyclic interstellar molecules and deciphering the prevalence
of cyanides over isocyanides. This cosmic triad becomes a guiding beacon, unveiling possible candidates for
astronomical observation and shedding light on the implausibility of certain proposed formation routes. The nuanced
exceptions find solace in the realms of interstellar hydrogen bonding, diverse formation pathways, and the sensitivity
of astronomical instruments. As we conclude, this cosmic dance between energy, stability, and abundance emerges
not just as an observation but a powerful tool. Its utility spans across the vast interdisciplinary landscape of
astrochemistry, astronomy, astrophysics, and allied domains, promising a deeper understanding of the cosmic
choreography.
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Etim, E. E., Oko, E. G., & Sulaiman, A. O. (2020b). Protonation in Noble Gas Containing Molecular Systems: Observing
Periodic Trends in CF3Cl, CF3Br, CH3F, CH3Cl. International Journal of Advanced Research in Physical
Science (IJARPS), 7(6), 14-19.
Etim, E. E., Oko, G. E., Onen, A. I., Ushie, O. A., Lawal, U., & Khanal, G. P. (2018a). Computational Studies of Sulphur
trioxide (SO3) and its protonated analogues. Journal of Chemical Society of Nigeria, 43(2).
Etim, E., & Arunan, E. (2018b). Achieving Accurate Rotational Constants for Linear Carbon Chains of Astrophysical
Interest. 42nd COSPAR Scientific Assembly, 42, F3-2.
Etim, E., Chakrabarti, S. K., Das, A., Gorai, P., & Arunan, E. (2018c). Studies on Known and Potential Interstellar
Carbon Chain Molecular Species. 42nd COSPAR Scientific Assembly, 42, F3-5.
Frerking, M. A., Linke, R. A., & Thaddeus, P. (1979). Interstellar isothiocyanic acid. Astrophysical Journal, Part 2-Leers
to the Editor, vol. 234, Dec. 1, 1979, p. L143-L145., 234, L143-L145.
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vol. 195, Feb. 1, 1975, pt. 2, p. L127-L130., 195, L127-L130.
Halfen, D. T., Ziurys, L. M., Brünken, S., Golieb, C. A., McCarthy, M. C., & Thaddeus, P. (2009). Detecon of a new
interstellar molecule: thiocyanic acid HSCN. The Astrophysical Journal, 702(2), L124.
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Johnson, D. R., Lovas, F. J., Golieb, C. A., Golieb, E. W., Litvak, M. M., Guelin, M., & Thaddeus, P. (1977). Detecon of
interstellar ethyl cyanide. Astrophysical Journal, Part 1, vol. 218, Dec. 1, 1977, p. 370-376., 218, 370-376.
Khan, M. E., Etim, E. E., Anyam, V. J., Abel, A., Osigbemhe, I. G., & Agber, C. T. (2021). Computational studies on
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Physical Sciences, 360-384
Lovas, F. J., Remijan, A. J., Hollis, J. M., Jewell, P. R., & Snyder, L. E. (2006). Hyperne structure idencaon of interstellar
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Proceedings of the 7th Faculty of Science International Conference (FOSIC 2023), Delta State
University, Abraka, Nigeria. 6th – 9th November, 2023. Pp. 92 - 106
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Tables and Figures
Tables
Table 1. Experimental ∆fH0 (0K), of elements and H0 (298K) – H0 (0K)
Element
∆fH0 (0K)
H0 (298K)-H0 (0K)
H
51.63±0.01
1.01
C
169.98±0.1
0.25
O
58.99±0.02
1.04
N
112.53±0.02
1.04
Na
25.69±0.17
1.54
Mg
34.87±0.2
1.19
Al
78.23±1.0
1.08
Si
106.6±1.9
0.76
S
65.66±0.06
1.05
Table 2: ΔfHOfor isomers with 3 atoms and current astronomical status
*Experimental value from Bradforth et al.29
Table 3: ΔfHOfor isomers with 4 atoms and current astronomical status
Molecule
Enthalpy of formation
Astronomical
status
W1U
W2U
G3
G4MP2
G4
Expt
HNC
45.03
44.7
161.83
45.6
45.6
46.5±2.2
Observed
HCN
31.3
31.4
150.33
32.2
32.2
32.30
Observed
NaNC
36.4
45.3
149.0
34.5
37.0
Not observed
NaCN
34.3
43.8
147.8
34.5
34.5
Observed
MgCN
67.7
67.3
165.9
69.0
69.0
Observed
MgNC
65.6
65.6
160.8
69.7
65.8
Observed
AlCN
71.8
72.3
186.8
73.1
73.1
Not observed
AlNC
65.2
65.2
176.7
65.8
65.8
Observed
SiCN
105.1
105.2
225.8
105.9
105.9
Observed
SiNC
105.3
105.3
223.6
105.7
105.7
Observed
ONC-
14.3
14.2
208.1
12.4
12.4
Not observed
OCN-
-53.7
-54.0
132.2
-54.5
-54.5
-52.8*
Observed
Molecule
Enthalpy of formation
Astronomical
status
W1U
W2U
G3
G4MP2
G4
Expt
Isofulminic acid
55.1
55.5
232.5
52.8
52.8
Not observed
Proceedings of the 7th Faculty of Science International Conference (FOSIC 2023), Delta State
University, Abraka, Nigeria. 6th – 9th November, 2023. Pp. 92 - 106
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Table 4: ΔfHOfor isomers with 5 atoms and current astronomical status
Table 5:ΔfHOfor isomers with 6 atoms and current astronomical status
*Experimental value from Emel’yanenko et al.56
Fulminic acid
36.3
36.3
229.0
34.1
34.1
Observed
Cyanic acid
-3.0
-2.2
172.862
-4.4
-4.4
Observed
Isocyanic acid
-31.6
-31.6
147.57
-33.4
-33.4
-23±3.1
Observed
HCNC
135.9
136.0
290.6
133.5
133.5
Not observed
HCCN
123.9
123.9
282.7
122.6
122.6
Observed
HSCN
39.7
39.7
195.1
38.3
38.3
Observed
HNCS
28.2
28.8
191.3
27.1
27.1
Observed
Molecule
Enthalpy of formation
Astronomical
status
W1U
W2U
G3
G4MP2
G4
Expt
HCNCC
163.0
162.2
390.4
160.9
160.9
Not observed
CC(H)CN
140.2
140.2
339.2
138.8
138.8
Not observed
HNCCC
135.4
135.4
355.4
134.0
133.7
Observed
HCCNC
115.0
115.0
323.0
112.3
112.4
Observed
HCCCN
89.7
89.8
301.5
88.4
88.3
84.6
Observed
HCONC
25.0
25.1
235.0
21.4
21.4
Not observed
HCOCN
13.4
13.4
238.0
10.6
10.6
Observed
Oxirene
68.6
68.6
244.7
66.3
66.3
Not observed
Ethynol
24.8
24.8
197.3
23.2
23.2
Not observed
Ketene
-12.5
-12.5
157.25
-15.6
-15.6
-14.78
Observed
CH2NC
81.6
81.7
244.8
79.1
79.1
Not observed
CH2CN
58.5
58.6
221.8
56.8
56.8
Observed
NH2NC
73.6
73.6
274.7
72.7
72.7
Not observed
CH2NN
56.9
56.9
270.0
55.6
55.6
51.4
Not observed
NH2CN
29.3
29.3
230.7
29.2
29.2
Observed
Molecule
Enthalpy of formation
Astronomical
status
W1U
W2U
G3
G4MP2
G4
Expt
1H-azirine
99.4
99.4
300.6
96.7
96.7
Not observed
2H-azirine
66.1
66.1
260.4
62.4
62.4
Not observed
Ethyeamine
58.4
58.4
257.2
58.1
58.1
Not observed
Ketenimine
40.5
40.6
240.3
38.9
38.9
Observed
Methyl isocyanide
41.9
42.0
226.9
38.8
38.8
39±2
Observed
Methyl cyanide
18.2
18.2
206.01
15.8
15.8
15.74
Observed
HC3NC
185.9
185.9
436.2
181.9
181.1
Not observed
HC4N
166.8
166.8
423.3
163.6
163.6
Observed
Cyclopropenone
40.0
40.0
250.9
34.5
35.5
observed
Propynal
35.2
35.2
249.4
32.1
32.1
Observed
Methylene ketene
29.5
29.5
246.5
24.8
24.8
Not observed
Nitrosomethane
16.7
16.8
157.1
13.5
13.5
Not observed
Hydroxymethylimine
-34.0
-33.9
171.8
-34.7
-34.7
Not observed
Proceedings of the 7th Faculty of Science International Conference (FOSIC 2023), Delta State
University, Abraka, Nigeria. 6th – 9th November, 2023. Pp. 92 - 106
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Table 6: ΔfHOfor isomers with 7 atoms and current astronomical status
Molecule
Enthalpy of formation
Astronomical
status
W1U
W2U
G3
G4MP2
G4
Expt
Ethylene oxide
-8.7
-8.7
184.17
-14.6
-14.6
-12.58
Observed
Vinyl alcohol (anti)
-25.7
-25.7
172.3
-28.5
-28.5
-29.9±2.0
Observed
Vinyl alcohol (syn)
-27.1
-27.1
170.2
-30.2
-30.2
-30.6
Observed
Acetaldehyde
-37.5
-37.5
152.7
-42.4
-42.4
-40.8±0.4
Observed
Isocyanoethene
66.9
66.2
297.9
63.2
63.2
Not observed
Acrylonitrile
46.1
46.1
279.7
43.3
43.3
42.9
Observed
Table 7: ΔfHOfor isomers with 8 atoms and current astronomical status
Molecule
Enthalpy of formation
Astronomical
status
W1U
W2U
G3
G4MP2
G4
Expt
CH2CCHNC
103.5
103.5
382.7
98.8
98.8
Not observed
CH3CCNC
104.4
104.5
382.1
98.6
98.6
Not observed
HCCCH2CN
88.8
88.8
365.6
86.1
86.1
Not observed
CH2CCHCN
80.0
80.0
361.6
76.2
76.2
Observed
CH3CCCN
77.6
77.6
358.8
73.1
73.1
Observed
H2NCH2NC
51.7
50.7
316.6
47.1
47.1
Not observed
H2NCH2CN
30.9
30.9
299.7
28.1
28.1
Observed
1,2-dioxetane
7.7
7.7
257.5
-0.7
-0.7
Not observed
1,3-dioxetane
-42.3
-42.3
196.8
-50.9
-50.9
Not observed
Glycolaldehyde
-65.3
-65.2
180.5
-70.5
-70.5
Observed
Methylformate
-82.2
-82.2
159.6
-89.4
-89.4
-86.5
Observed
Acetic acid
-98.0
-98.6
145.8
-103.7
-103.7
-103.5±0.7
Observed
Epoxypropene
52.7
52.7
285.8
47.7
47.7
Not observed
2-cyclopropenol
32.0
32.0
274.6
27.4
27.4
Not observed
1-cyclopropenol
31.9
31.9
275.8
25.9
25.9
Not observed
Methoxyethyne
29.8
29.8
268.1
23.9
23.9
Not observed
Propargyl alcohol
20.0
20.0
270.0
17.2
17.2
Not observed
Propynol
17.6
17.1
258.5
12.7
12.7
Not observed
Cyclopropanone
7.8
7.9
245.1
0.7
0.7
Not observed
Propenal
-10.5
-10.5
224.5
-15.8
-15.8
Observed
Methyl ketene
-14.0
-13.9
224.5
-20.4
-18.1
Not observed
*Experimental value from Cioslowski et al.81
Table 8: ΔfHO for isomers with 9 atoms and current astronomical status
Formamide
-46.7
-46.6
157.2
-47.3
-47.3
-44.5
(45.1±0.1*)
Observed
Molecule
Enthalpy of formation
Astronomical
status
W1U
W2U
G3
G4MP2
G4
Expt
Dimethyl ether
-41.4
-41.4
175.02
-49.0
-49.0
-44.00±0.12
Observed
Ethanol
-51.3
-51.3
168.02
-56.7
-56.7
-56.2±0.1*
Observed
Cyanoethoxyamide
77.7
77.7
397.0
72.5
72.5
Not observed
1-aziridnol
22.3
22.4
299.7
16.0
16.0
Not observed
Nitrosoethane
10.5
10.5
282.3
2.8
2.8
Not observed
N-methylformate
-45.0
-46.0
225.7
-52.2
-52.2
Not observed
Proceedings of the 7th Faculty of Science International Conference (FOSIC 2023), Delta State
University, Abraka, Nigeria. 6th – 9th November, 2023. Pp. 92 - 106
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Table 9: ΔfHOfor isomers with 10 atoms and current astronomical status
Molecule
Enthalpy of formation
Astronomical
status
W1U
W2U
G3
G4MP2
G4
Expt
Dimethane peroxide
-27.0
-27.6
248.8
-35.9
-35.9
Not observed
Ethylhydroperoxide
-34.0
-33.9
243.8
-41.7
-41.7
Not observed
Ethylene glycol
-82.2
-82.2
190.9
-87.5
-87.5
-92.7±0.5
Observed
Oxetane
-12.4
-12.4
246.74
-21.8
-21.8
-19.25±0.15
Not observed
Cyclopropanol
17.0
-17.0
247.2
-21.8
-23.8
Not observed
1,2-epoxypropane
-16.3
-16.3
245.621
-25.0
-25.0
Not observed
2-propene-1-ol
-22.8
-22.8
241.9
-27.9
-27.9
-29.5.±0.4
Not observed
Methoxyethene
-21.9
-21.6
241.8
-29.4
-29.4
Not observed
1-propen-1-ol
-30.4
-30.3
236.6
-36.4
-36.4
Not observed
Propen-2-ol
-35.1
-35.1
230.9
-41.2
-41.2
Not observed
Propanal
-39.2
-39.1
219.62
-47.0
-47.0
-45.10±0.18
Observed
Propanone
-47.2
-47.8
211.82
-55.0
-55.0
-52.2±0.1
Observed
CH3(CC)2NC
158.4
158.4
53o.2
150.6
150.6
Not observed
CH3(CC)2CN
131.9
131.1
508.1
125.3
125.3
Observed
Table 10:ΔfHOfor isomers with 11 atoms and current astronomical status
Molecule
Enthalpy of formation
Astronomical
status
W1U
W2U
G3
G4MP2
G4
Expt
Dimethyldioxirane
-16.4
-16.4
302.3
-27.7
-27.7
Not observed
Glycidol
-48.3
-48.3
268.1
-57.3
-57.3
Not observed
Dioxolane
-61.6
62.1
257.7
-73.3
-73.3
Not observed
Lactaldehyde
-72.9
-72.9
240.4
-81.3
-81.3
Not observed
Methyl acetate
-84.8
-84.7
227.0
-95.1
-95.1
Observed
Ethylformate
-87.4
-87.4
223.3
-97.5
-97.5
-95.1
Observed
Propanoic acid
-100.6
-100.5
211.8
-109.4
-109.4
-108.9±0.5
Not observed
Table 11:ΔfHOfor isomers with 12 atoms and current astronomical status
Molecule
Enthalpy of formation
Astronomical
status
W1U
W2U
G3
G4MP2
G4
Expt
Ethyl methyl ether
-47.2
-47.1
238.1
-57.4
-57.4
Observed
Propanol
-53.7
-53.4
234.5
-61.9
-61.9
-60.2±0.7
Not observed
Propan-2-ol
-57.2
-57.2
231.1
65.6
-65.6
-65.2
Not observed
2-azabicyclo(2.1.0)pentane
67.4
67.4
401.0
57.1
57.1
Not observed
N-methyl propargylamine
61.6
61.6
395.2
54.5
54.5
Not observed
3-butyn-1-amine
54.2
54.2
388.9
48.4
48.4
Not observed
N-methyl-1-propyn-1-
amine
54.4
53.9
389.2
46.6
46.6
Not observed
Acetamide
-57.0
57.5
216.83
-61.9
-61.9
-56.96±0.19
Observed
1-
azabicyclo(1.1.0)b
utane
72.3
72.331
336.8
64.4
64.4
Not observed
Propargylamine
59.2
59.2
325.2
56.0
56.1
Not observed
Methylazaridine
60.6
60.9
329.20
54.8
54.8
Not observed
Cyclopropanimine
54.3
54.3
320.3
48.2
48.2
Not observed
Azastene
50.4
50.5
311.3
43.2
43.2
Not observed
N-methylene
ethenamine
42.0
42.1
306.5
36.9
36.9
Not observed
2-propen-1-imine
37.0
37.1
301.8
36.2
36.2
Not observed
Propylenimine
37.9
38.0
306.4
33.0
33.0
Not observed
Isocyanoethane
37.8
37.9
291.4
31.8
31.8
31.7
Not observed
Cyanoethane
16.3
16.3
272.58
11.0
11.0
12.30
Observed
Proceedings of the 7th Faculty of Science International Conference (FOSIC 2023), Delta State
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N-vinylazaridine
54.8
54.9
389.6
45.9
45.9
Not observed
2,3-butadiene-1-amine
49.7
49.7
388.5
43.3
43.3
Not observed
But-1-en-1-imine
35.6
35.7
372.8
27.8
27.8
Not observed
2,2-dimethylethylenimine
34.1
34.2
371.6
25.7
25.7
Not observed
3-pyrroline
34.5
34.6
366.4
25.4
25.4
Not observed
2-aminobutadiene
30.3
30.4
369.8
24.4
24.4
Not observed
2-isocyanopropane
33.2
33.5
355.7
24.4
24.4
Not observed
Propyl cyanide
13.8
13.8
338.9
5.6
5.6
7.4
Observed
Isopropyl cyanide
13.6
13.6
338.6
5.2
5.2
Observed
Figures
--
HNC
HCN
NaNC
NaCN
MgCN
MgNC
AlCN
AlNC
SiCN
SiNC
OCN-
ONC-
-60
-40
-20
0
20
40
60
80
100
120
CHN isomers
CNNa isomers
CNMg isomers
CNAl isomers
CNSi isomers
OCN- isomers
Enthalpy of formation (kcal/mol)
Molecules
filled symbols = observed
empty symbols= not observed
Figure 1: Plot showing the ΔfHO for molecules with 3 atoms
HONC
HCNO
HOCN
HNCO
HCNC
HCCN
HSCN
HNCS
-40
-20
0
20
40
60
80
100
120
140
CHNO isomers
C2NH isomers
CHNS isomers
Enthalpy of formation (kcal/mol)
Molecules
filled symbols = observed
empty symbol = not observed
Figure 2: Plot showing the ΔfHO for molecules with 4 atoms
Proceedings of the 7th Faculty of Science International Conference (FOSIC 2023), Delta State
University, Abraka, Nigeria. 6th – 9th November, 2023. Pp. 92 - 106
104
HCNCC
CC(H)CN
HNCCC
HCCNC
HCCCN
HCONC
HCOCN
Oxirene
Ethynol
Ketene
CH2NC
CH2CN
NH2NC
CH2NN
NH2CN
-20
0
20
40
60
80
100
120
140
160
180
C3HN isomers
C2HNO isomers
C2H2O isomers
C2H2N isomers
CH2N2 isomers
Enthalpy of romation (kcal/mol)
Molecules
filled symbol = observed
empty symbol = not observed
Figure 3: Plot showing the ΔfHO for molecules with 5 atoms
1H-azirine
2H-azirine
Ethyneamine
ketenimine
methyl isocyanide
methyl cyanide
HC3NC
HC4N
cyclopropenone
propynal
methylketene
Nitrosomethane
Hydroxymethylimine
Formamide
--
-50
0
50
100
150
200
C2H3N isomers
C4HN isomers
C3H2O isomers
CH3NO isomers
Enthalpy of formation (kcal/mol)
Molecules
filled symbol = observed
empty symbols = not observed
Figure 4: Plot showing the ΔfHO for molecules with 6 atoms
Ethyelene oxide
Vinyl alcohol ()anti
Vinyl alcohol (syn)
Acetaldehyde
Isocyanoethene
Acrylonitril
-60
-40
-20
0
20
40
60
80
C2H4O isomers
C3H3N isomers
Enthalpy of formation (kcal/mol)
Molecules
filled symbls = observed
empty symbol = not observed
Figure 5: Plot showing the ΔfHO for molecules with 7 atoms.
Proceedings of the 7th Faculty of Science International Conference (FOSIC 2023), Delta State
University, Abraka, Nigeria. 6th – 9th November, 2023. Pp. 92 - 106
105
CH2CCHNC
CH3CCNC
HCCCH2CN
CH2CCHCN
CH3CCCN
H2NCH2NC
H2NCH2CN
1,2-dioxetane
1,3-dioxetane
glycolaldehyde
methylformate
acetic acid
Epoxypropene
2-cyclopropenol
1-cyclopropenol
Nethoxy ethyne
Propargyl alcohol
Propynol
Cyclopropanone
Propenal
Methyl ketene
--
-100
-50
0
50
100
C4H3N isomers
C2H4N2 isomers
C2H4O2 isomers
C3H4O isomers
Enthalpy of formation (kcal/mol)
Molecules
filled symbols = observed
empty = not observed
Figure 6: Plot showing the ΔfHO for molecules with 8 atoms
Figure 7: Optimized structures of methyl formate (A), acetic acid (B), methyl ketene (C) and propenal (D) at G4 level
of theory.
Dimethyl ether
Ethanol
Cyanoethoxyamide
1-aziridnol
Niitrosoethane
N-methylformate
Acetamide
1-azabicyclo91.1.0)butane
Propargylamine
Methylazaridine
Cyclopropanimine
Azastene
N-methylene ethenamine
2-preopen-1-imine
Propylenimine
Isocyanoethane
Cyanoethane
--
-80
-60
-40
-20
0
20
40
60
80
C2H6O isomers
C2H5NO isomers
C3H5N isomers
Enthalpy of formation (kcal/mol)
Molecules
filled symbols = observed
empty symbols = not observed
.
Figure 8: Plot showing the ΔfHO for molecules with 9 atoms
A
B
C
D
Proceedings of the 7th Faculty of Science International Conference (FOSIC 2023), Delta State
University, Abraka, Nigeria. 6th – 9th November, 2023. Pp. 92 - 106
106
Dimethane peroxide
Ethylhdroperoxide
Ethyleneglycol
Oxetane
Cyclopropanol
1,2-epoxypropropane
2-propene-1-ol
Methoxy ethene
1-propen-1-ol
propen-2-ol
Propanal
Propanone
CH3(CC)2NC
CH3(CC)2CN
--
-100
-50
0
50
100
150
C2H6O2 isomers
C3HH6O isomers
C6H3N isomers
Enthalpy of formation (kcal/mol)
Molecules
filled symbols = observed
empty symbols = not observed
Figure 9: Plot showing the ΔfHO for molecules with 10 atoms
Dimethyldioxirane
Glycidol
Dioxolane
Lactaldehyde
Methyl acetate
Ethylformate
Propanoic acid
-120
-100
-80
-60
-40
-20
C3H6O2 isomers
Enthalpy of romation (kcal/mol)
Molecules
filled symbols = observed
empty symbols = not observed
Figure 10: Plot showing the ΔfHO for molecules with 11 atoms
Figure 11: Optimized structures of propanoic acid (A), ethylformate (B), propanol (C), propan-2-ol (D) and ethyl
methyl ether (E) at G4 level of theory.
A
B
C
D
E
Proceedings of the 7th Faculty of Science International Conference (FOSIC 2023), Delta State
University, Abraka, Nigeria. 6th – 9th November, 2023. Pp. 92 - 106
107
Ethyl methyl ether
Propanol
Propan-2-ol
2-azabicylo(2.1.0)pentane
N-methy propargylamine
3-butyn-1-amine
N-methyl-1-propyn-1-amine
N-vinylazaridine
2,3-butadiene-1-amine
But-1-en-1-imine
2,2-dimethylethylenimine
3-pyrroline
2-aminobutadiene
2-isocyanopropane
Propyl cyanide
Isopropyl cyanide
-80
-60
-40
-20
0
20
40
60
C3H8O isomers
C4H7N isomers
Enthalpy of formation (kcal/mol)
Molecules
filled symbols = observed
empty symbols = not observed
Figure 12: Plot showing the ΔfHO for molecules with 12 atoms