Skip to main content
NCBI home page
Frontiers in Chemistry logoLink to Frontiers in Chemistry
. 2026 Aug 14;14:1874752. doi: 10.3389/fchem.2026.1874752

Computational perspective on structure, energetics, and bonding of FeC2O isomers with astrochemical significance

Abhirami R J 1, Senthur Pandi Rajasabai 1,*
PMCID: PMC13522136  PMID: 42666363

Abstract

Iron in its elemental form has rarely been detected in the interstellar medium despite being the most abundant refractory element. The presence of iron oxides in the interstellar medium and the recent discovery of FeC in the circumstellar envelope of IRC+10,216 suggest iron-carbon-oxygen molecules as potential interstellar species. In light of this possibility, the potential energy surface of FeC2O has been investigated computationally using different levels of density functional theory calculations, yielding fourteen, seven, and twenty isomers across the quintet, triplet, and singlet electronic states, respectively. Within the examined DFT frameworks, the lowest energy isomer of FeC2O is in the quintet electronic state with a linear structure. Single-point (U)CCSD(T) calculations with T1 diagnostics reveal considerable multireference character in certain geometries. CASSCF optimizations are performed on quintet state geometries to account for the multireference character. Various computational tools, such as adaptive natural density partitioning (AdNDP) analysis, molecular orbital (MO) analysis, and Wiberg Bond Indices (WBI), are employed to elucidate the bonding characteristics of the global minimum geometry. The spectroscopic parameters in both infrared and microwave domains have been successfully computed. The total and the partial density of states are plotted to evaluate how different atoms contribute to the electronic structure. The structural, energetic, and spectroscopic parameters presented in this work have significant implications for future astronomical research.

Keywords: bonding analysis; density functional theory; density of states; interstellar medium; Iron–bearing molecules; missing iron; spectroscopic parameters, astrochemistry

1. Introduction

The interstellar medium (ISM) is of great importance to astrophysicists and astrochemists, as it encompasses a wide range of matter, from ions and atoms to molecules and dust grains. The composition includes interstellar clouds, star-forming regions, and planetary systems (Watson, 1977). Dense molecular clouds do not undergo ionization due to the absence of stellar radiation, leading to the predominance of molecular species. Conversely, diffuse interstellar clouds consist primarily of atoms because stellar radiation dissociates molecules. The grains in dense clouds consist of a silicate or graphite core enclosed in a mantle of various ices, mainly water ice (Herbst, 1995).

There have been numerous investigations into the composition of the ISM. Nearly 340 molecules have been identified in the ISM or circumstellar envelopes. Molecular hydrogen is the most abundant species, followed by carbon monoxide (Endres et al., 2016; Herbst, 2001). Iron, the sixth-most-abundant element, notably affects stellar nucleosynthesis and the life cycles of stars. Iron is obtained from Type Ia supernovae, core–collapse supernovae, and outflows emitted by Asymptotic Giant Branch (AGB) stars (Temple et al., 2020; Matteucci and Greggio, 1986). Iron lines are one of the significant components in the spectra of quasars (Temple et al., 2020; Matteucci, F. and Greggio, 1986; Yadav et al., 2023; Satyapal et al., 2021; Negus et al., 2021; Rose et al., 2015) and active galactic nuclei (AGNs) (Dong et al., 2008; Rodríguez-Ardila et al., 2004; Rubin et al., 1997). They are also found in the photoionized H II regions (Rodríguez, 2002). The atomic processes related to iron have always fascinated researchers, as they are used in astrophysical and laboratory plasmas (Schippers et al., 2017; Schippers et al., 2021; Beerwerth et al., 2019; Schippers and Müller, 2020; Olthof and Pottasch, 1975). Though Type Ia supernovae produce large amounts of Fe atoms, Fe grain formation has not yet been observed due to the ineffective homogeneous nucleation of iron grains in the interstellar environment (Kimura et al., 2017). Iron is strongly depleted from the gas phase into solids, with over 90% in dust, mostly in silicates (Dwek, 2016; Zhukovska et al., 2018). Iron missing from the ISM can precipitate onto pre-existing carbon or composite grains, potentially being sequestered as an impurity or incorporated into other particles, such as hydrogenated iron nanoparticles (Bilalbegović et al., 2017; Kimura et al., 2017). The missing iron can also be attributed to the formation of Fe–H nanoparticles by the interaction of iron atoms with hydrogen (Bilalbegović et al., 2017).

Most of the dust in the ISM is composed of five elements: C, O, Mg, Si, and Fe (Tielens and Allamandola, 1987). Only three chemical species containing iron have been identified in the ISM so far: FeCN (Zack et al., 2011), FeC (Koelemay and Ziurys, 2023), and FeO (Furuya et al., 2003; Merer et al., 1982; Walmsley et al., 2002), though it is the main refractory element prevalent there. Hence, the quest for further iron species in the ISM is imperative. The facts that oxygen and carbon are the third and fourth most prevalent components in the ISM, and iron is an abundant dust species only at the carbon–to–oxygen abundance ratio close to unity (Jones, 1990) indicate the possibility that iron can kinetically nucleate with carbon and oxygen, forming iron–carbon–oxygen systems in the ISM. Carbon is widely distributed in the ISM as atomic carbon (Sofia et al., 1997). It can exist in different forms, ranging from simple molecules such as carbon monoxide (CO) (Wilson et al., 1970; Solomon et al., 1971; Smith and Stecher, 1971) to complex organic compounds (Duley and Williams, 1981; Herbst and Van Dishoeck, 2009). The presence of CO, which forms the basis of interstellar ice, also increases the likelihood of detecting iron, carbon, and oxygen systems in the ISM. Moreover, ISM contains significant amounts of oxygen in solid–state components, such as dust and ice, and in gas–phase species, such as atoms and molecules, to support an oxygen–rich chemistry (Jensen, et al., 2008).

The presence of FeC radical was observed in the envelope of IRC+10216 (Koelemay and Ziurys, 2023). As FeC has the potential to function as a precursor species for FeCN, it may also facilitate the formation of Fe–C–O systems, which have yet to be explored. Also, iron oxide is likely to be a substantial part of interstellar grains. Investigations carried out by Jones (Jones, 1990) about iron and iron oxides within the ISM suggests that the expulsion of iron–enriched particulates into the interstellar environment, characterized by a relatively high concentration of atomic oxygen, will lead to their rapid conversion into iron (II) oxide and, subsequently, into magnetite. Another study to provide evidence suggests that iron oxides like maghemite (γ–Fe2O3) or magnetite (Fe3O4) cause the 21 μm infrared (IR) emission band (Cox, 1990). These possibilities also indicate the existence of Fe–C–O systems in ISM. Halfen et al. noted that FeCO+ is likely to be present in molecular clouds, where CO is highly concentrated, and that gas–phase iron is expected to be in the form of Fe+ (Halfen and Ziurys, 2007).

Although pure iron, its oxides and sulfides, and hydrogenated iron nanoparticles are discussed as components of interstellar dust grains (Bilalbegović et al., 2017; Merer et al., 1982; Jones, 1990; Cox, 1990; Köhler et al., 2014), iron–carbon–oxygen systems have not been studied extensively in the astrophysical literature. Hence, the present work aims to explore the potential energy surface (PES) of iron–carbon–oxygen systems in the ISM, focusing on systems containing one iron, two carbon, and one oxygen atom, using the density functional theory (DFT). A computational study of the equilibrium geometries, binding energies, and electronic structures of neutral FeCn clusters (n < 3) concluded that DFT provides a reliable method for explaining experimental outcomes and can be used to accurately examine larger FeCn systems, especially when other quantum chemical methods are computationally challenging (Nash et al., 1996). Also, DFT simulations were used to investigate the structural, electronic, vibrational, and rotational properties of small cyclic molecules containing iron, carbon, and hydrogen (Chandra, 2013). The dicationic and neutral species of FeC4H2 have also been examined, with implications for astrophysical contexts; extensive investigations and analyses have been conducted on iron, carbon, and hydrogen systems that closely resemble the earlier findings (Shajan et al., 2024; Shajan and Thirumoorthy, 2024).

By comparing radio astronomical data with laboratory rotational spectra, it is possible to accurately identify most molecules in the ISM. However, identifying, characterizing, and synthesizing such transitory species in the laboratory is complicated. Consequently, theoretical studies of the chemical composition and electronic properties of these critical molecules in astrophysics could aid in detecting them in the ISM and the laboratory for radioastronomers and molecular spectroscopists. In this context, the current study provides structural and spectroscopic data of FeC2O isomers in the neutral state using DFT. The obtained data could support subsequent molecular spectroscopic observations and radio astronomical searches (Roy et al., 2021; Satpati et al., 2023a; Satpati et al., 2023b; Thirumoorthy et al., 2018). Investigating the structure, energetics, bonding, and spectroscopic properties of these molecules will be advantageous for future astronomical observations. The formation of FeC2O in ISM is expected to be difficult from an astrochemical perspective. Although a detailed kinetic analysis is beyond the scope of the present study, a few feasible gas-phase formation pathways are qualitatively discussed based on known ISM conditions. Identifying FeC2O in the ISM will deepen our understanding of metal–carbon chemistry, illuminate catalytic processes in molecular clouds, and help account for the missing iron in the ISM.

2. Computational methodology

The isomers of FeC2O are explored in singlet, triplet, and quintet electronic states in the neutral charge state. Chemical intuition is used to generate preliminary geometries of the FeC2O system. Density functional theory has been used with and without an effective core potential for optimizations. The methods used are TPSSh (Becke, 1988; Cirera et al., 2018) and ωB97XD (Chai and Head-Gordon, 2008; Grimme et al., 2010), employing the basis sets 6–311++G (2d,2p) (Chan, 2023; Krishnan et al., 1980; Clark et al., 1983; Pham and Nguyen, 2015; Tam et al., 2015; Louis et al., 2023) and SDD (Kreutzer et al., 2016; Bergner et al., 1993; Szilagyi and Winslow, 2006). The quintet and triplet states are treated using the unrestricted formalism. TPSSh is a hybrid functional derived from the TPSS functional (Tao–Perdew–Staroverov–Scuseria) (Tao et al., 2003) and contains a 10% exact-exchange contribution (Marzouk et al., 2011), whereas the ωB97XD functional includes long–range and empirical dispersion corrections (Grimme et al., 2010; Panda et al., 2022). The 6–311++G (2d,2p) and the combination of SDD and 6–311++G (2d,2p) basis sets have been used with both methods for optimization and frequency calculations. The iron atom has been treated with SDD (Zayed et al., 2019; Moustafa et al., 2020), while the 6–311++G (2d,2p) basis set has been utilized for C and O atoms (Clark et al., 1983). The Stuttgart/Dresden (SDD) method accounts for the relativistic effects in the Fe atom (Fuentealba et al., 1982; Szilagyi and Winslow, 2006).

Geometry optimizations and frequency calculations have been performed using the Gaussian 16 program (Frisch et al., 2016). Harmonic vibrational frequencies are calculated for each optimized geometry in order to determine whether the stationary point on the PES is a minimum, transition state, or higher–order saddle point. Wavefunction stability analyses are performed for the optimized triplet and quintet minima, confirming convergence to stable electronic solutions.

To assess the sensitivity of the DFT energy ordering to a correlated wavefunction approach, single-point (U)CCSD(T) (Purvis and Bartlett, 1982; Raghavachari et al., 2013) calculations were carried out on ωB97XD/6–311++G (2d,2p) optimized geometries. T1 diagnostic values are also calculated for all quintet, triplet, and singlet isomers at the (U)CCSD(T)/6–311++G (2d,2p)//UωB97XD/6–311++G-(2d,2p) level of theory in order to evaluate the multireference character (Lee and Taylor, 1989), following the approach adopted in recent computational studies of metal systems from an astrochemical perspective (Roy et al., 2024). Moreover, the quintet isomers are further optimized at the UCCSD/6–311++G (2d,2p) level to verify the robustness of the quintet energetic ordering beyond single-point comparisons. To account for the multireference character of the quintet isomers, complete active space self-consistent field (CASSCF) (Bjorn and Ross, 1980; Roos, 1980) optimizations have been performed with an active space of (10,10) and def2-tzvp basis set using ORCA software (Neese et al., 2020).

The spectroscopic study, including IR spectra and calculations of rotational and centrifugal distortion constants, has been performed using Gaussian 16 at the UωB97XD/6–311++G (2d,2p) level of theory. The rotational and centrifugal distortion constants have been derived from the harmonic force field through vibration–rotation analysis.

Further, the chemical bonding characteristics of the FeC2O global minimum have been studied at the UωB97XD/6–311++G (2d,2p) level of theory, which was chosen for the detailed bonding analysis due to its balanced description of Fe-C and Fe-O interactions and its appropriateness for charge-transfer effects (Jacquemin et al., 2011; Berryman et al., 2014; Shajan et al., 2024; Shajan and Thirumoorthy, 2024). The chemical bonding characteristics of the global minimum geometry of FeC2O in the quintet electronic state are comprehensively characterized by using quantum chemical tools such as adaptive natural density partitioning (AdNDP) analysis (Osorio, 2023; Zubarev and Boldyrev, 2008), molecular orbital (MO) analysis (Prabhaharan et al., 2014), and Wiberg bond indices (WBIs) (Wiberg, 1968). Additionally, the natural atomic charges (NAC) (Glendening et al., 1998; Reed et al., 1985) derived from Natural Bond Orbital (NBO) analysis (Reed et al., 1985), Electron Localization Function (ELF) (Becke and Edgecombe, 1990; Burdett and McCormick, 1998; Savin et al., 1997), Atoms in Molecules (AIM) (Matta et al., 2007; Bader, 1991), and the Laplacian of the electron density (Mierzwa et al., 2015) are provided in the Supplementary Material. Estimation of WBIs, NACs, and MO analysis has been performed using Gaussian 16, while analysis of the Laplacian of the electron density, bond critical points, and the density of states (DOS) plot has been carried out using the Multiwfn program (Lu and Chen, 2012).

3. Results and discussion

The PES of FeC2O in the quintet electronic state has been scrutinized using different theoretical frameworks, as noted earlier. The results obtained by using the different theoretical frameworks: UTPSSh/6–311++G (2d,2p), UTPSSh/SDD&6–311++G (2d,2p), UωB97XD/6–311++G (2d,2p) and UωB97XD/SDD&6–311++G (2d,2p) for the quintet electronic state are compared and analyzed. The geometric optimization culminated in the identification of fourteen distinct isomers of FeC2O in its quintet state. Although a preliminary extensive investigation of the PES revealed multiple stationary points, vibrational analysis suggests that only a few correspond to true minima. At the UωB97XD/6–311++G (2d,2p) level of theory, six isomers (q1, q2, q3, q6, q7, and q8) correspond to minima, and four (q4, q5, q9, and q10) pertain to transition states and higher-order saddle points. The discussion is hence confined to these experimentally significant structures shown in Figure 1. The isomers with non-zero imaginary frequencies are shown in Supplementary Figure S1 in the Supplementary Material. Beneath the geometry, the point group symmetries, total energy, permanent dipole moments, and the number of imaginary frequencies (Nimag) for each stationary point are displayed. The isomers are designated by their spin multiplicity (q = quintet, t = triplet, s = singlet) and are sequentially numbered according to their respective energies within each spin state. Comparisons among various spin states are primarily based on structural similarity rather than numerical designations. The optimized geometries of FeC2O isomers in the quintet state, which are unattainable with the UωB97XD/6–311++G (2d,2p) level, but achievable with the UTPSSh/6–311++g (2d,2p), UTPSSh/SDD&6–311++G (2d,2p), or UωB97XD/SDD&6–311++G (2d,2p) theoretical levels are presented in Supplementary Figures S2–S4 in the Supplementary Material. The geometry optimization of FeC2O in its triplet electronic state performed at the UωB97XD/6–311++G (2d,2p) theoretical level yielded seven isomers, which are shown in Supplementary Figure S5 of the Supplementary Material. Supplementary Figure S6 in the Supplementary Material shows the sixteen isomers of FeC2O in the singlet electronic state, optimized at the ωB97XD/6–311++G (2d,2p) level, and Supplementary Figures S7–S9 show FeC2O isomers in the singlet state, which are unattainable with the ωB97XD/6–311++G (2d,2p) level, but attainable with other levels of theory. The point group, total energy (in a. u), zero point correction (in a. u), zero point vibrational energy (ZPVE) corrected total energy (E + ZPVE; in a. u), relative energy with ZPVE corrections (ΔE + ZPVE; in a. u), relative energies with ZPVE corrections (ΔE + ZPVE) in kcal mol–1, absolute dipole moment (in Debye) and the number of imaginary frequencies (Nimag) for FeC2O in its quintet state optimized at the different levels of theories can be found in Supplementary Tables S1–S4 in the Supplementary Material. Supplementary Table S5 presents the details for FeC2O isomers in the triplet electronic state at the UωB97XD/6–311++G (2d,2p) level of theory, while Supplementary Tables S6–S9 provide the specifics for FeC2O singlets optimized at the different levels of theory. Also, Supplementary Table S10 compares the ZPVE corrected relative energies of FeC2O isomers (in kcal mol–1) in their corresponding singlet electronic states obtained at different levels.

FIGURE 1.

Six isomers of FeC2O isomers (iron (brown), carbon (gray), and oxygen (red) spheres ) in quintet electronic state having zero imaginary frequency with labels indicating the name, relative energies, point groups, dipole moments and NImag.

Open in a new tab

Isomers of FeC2O representing minima (without imaginary frequencies) in their corresponding quintet electronic states, with their point group, ZPVE corrected relative energies (in kcal mol–1), dipole moment (in Debye), and number of imaginary frequencies (Nimag) obtained at the UωB97XD/6–311++G (2d,2p) theoretical level. The corresponding singlet states are included in parentheses.

3.1. Structure and energetics

The number of FeC2O isomers identified in the quintet electronic state depends on the level of theory employed. The maximum number of isomers of FeC2O in the quintet electronic state, totalling thirteen, is obtained at UTPSSh/SDD and 6–311++G (2d,2p) theoretical level, followed by twelve isomers found at the UTPSSh/6–311++G (2d,2p) theoretical level. Using the UωB97XD method, ten isomers are obtained without SDD, and nine with SDD. Isomer q1 shown in Figure 1 is the global minimum for FeC2O in the quintet electronic state found at the UωB97XD/6–311++G (2d,2p) level of theory. The same linear structure is obtained as the minimum-energy structure at the UωB97XD/SDD and 6–311++G (2d,2p) level of theory also. In contrast, the UTPSSh method yields isomer q11 as the lowest-energy structure, with or without SDD. The energy difference between q11 and q1 in these methods is very minimal. All levels of theory employed in this study consistently provide isomers q1, q2, q4, q5, q6, q7, and q10, implying that these structures represent robust portions of the PES. The UTPSSh/SDD and 6–311++G (2d,2p) level introduces an additional highest-energy isomer q14, which is not obtained at the other levels of theory. It resembles q5, with slightly elongated peripheral bonds and an absence of a C-C bond. At the UωB97XD/6–311++G (2d,2p) level of theory, both the lowest- and highest-energy quintet isomers are linear structures. The lowest energy is achieved when Fe is terminally bonded to C2, whereas the maximum energy is achieved when Fe comes between C2 and C3. Also, linear structures with terminal Fe atoms are minima, while those with Fe in the middle have two imaginary frequencies. Isomer q11 is obtained at all the theoretical levels except the UωB97XD/6–311++G (2d,2p) level of theory. Isomers q12 and q13 are obtained only with the UTPSSh method. Table 1 compares the ZPVE–corrected relative energies of FeC2O isomers in the quintet electronic state, calculated using different computational methods. The optimized geometrical parameters, bond lengths in angstroms (Å), and bond angles in degrees for FeC2O isomers in their quintet and singlet electronic states, computed at different levels of theory, are respectively tabulated in Supplementary Tables S11, S12 in the Supplementary Material.

TABLE 1.

ZPVE-corrected relative energies of FeC2O isomers (in kcal mol–1) in their corresponding quintet electronic states obtained at different levels. The isomers are arranged in the order of energy computed at the UωB97XD/6–311++G (2d,2p) level of theory.

Isomers ZPVE corrected relative energy in kcal mol–1
UωB97XD/6–311++G (2d,2p) UTPSSh/6–311++G (2d,2p) UTPSSh/SDD and
6–311++G (2d,2p)		 UωB97XD/SDD and
6–311++G (2d,2p)
q1 0 0.34 1.84 0
q2 66.7 60.38 81.65 79.17
q3 67.87 55.31 63.3 NA
q4 69.66 68.15 75.36 71.53
q5 74.29 74.04 82.99 92.13
q6 74.58 75.51 70.43 73.52
q7 75.98 65.04 56.52 75.17
q8 77.33 NA NA 81.12
q9 78.71 74.99 76.56 NA
q10 85.48 55.62 61.1 69.91
q11 NA 0 0 4.93
q12 NA 48.88 54.69 NA
q13 NA 104.26 108.46 NA
q14 NA NA 113.66 NA
Open in a new tab
*

NA (not applicable) indicates that the geometry did not converge at that level.

The minimum energy geometry of FeC2O in the quintet and triplet electronic states is a similar linear structure, whereas it is different in the singlet electronic state. Wavefunction stability studies are conducted for the optimized quintet global minimum. Following orbital optimization, the final wavefunction was validated as stable against internal perturbations. The stability study verifies that the wavefunction represents a true minimum.

The ⟨S2⟩ value of q1 (6.001) approximates the ideal quintet value (6.00), signifying negligible spin contamination. A similar study carried out with the triplet minimum yielded an ⟨S2⟩ value post-spin annihilation of 2.27, indicating moderate spin contamination. Isomers t2, t3, and t6 show only minor deviations from the ideal triplet value (2.00). Nevertheless, a few triplet structures, such as t4, t5, and t7, exhibit noticeable spin contamination. Such contamination results from mixing higher-spin electronic configurations into the unrestricted wavefunction and may affect the quantitative relative energies of closely spaced triplet isomers. This is consistent with the UCCSD(T) results, where the low-spin-contaminated t2 structure is the triplet minimum rather than the t1 structure predicted by DFT. These observations, along with the T1 diagnostic and CASSCF investigations, imply that electron correlation and multiconfigurational effects are significant for the energy ordering of the triplet state. However, the very small spin contamination in q1, together with the correlated wavefunction calculations, suggests that the assignment of the quintet global minimum is unaffected.

A comparison of the minimum-energy geometries across the three electronic states reveals that the global minimum for FeC2O, q1, occurs in the quintet state and adopts a linear configuration akin to t1 and s3. The triplet counterpart of q1 possesses an energy elevation of merely 3.74 kcal/mol. The stability order of the minimum energy geometry in the singlet, triplet, and quintet electronic states, along with their point group, ZPVE corrected relative energies with respect to q1 (in kcal mol–1), the dipole moment (in Debye), and the number of imaginary frequencies (Nimag) obtained at the UωB97XD/6–311++G (2d,2p) level of theory for FeC2O are depicted in Figure 2.

FIGURE 2.

Energy order of the minimum energy geometries of FeC2O in the singlet, triplet and quintet electronic states with respect to q1 with labels indicating the name, relative energies, point groups, dipole moments and NImag.

Open in a new tab

Energy order of the minimum energy geometry in the singlet, triplet, and quintet electronic states, including their point group, ZPVE corrected relative energies (in kcal mol–1) with respect to q1, dipole moment (in Debye), and number of imaginary frequencies (Nimag), obtained at the UωB97XD/6–311++G (2d,2p) level of theory for FeC2O. The corresponding positions of singlet states are included in parentheses.

To facilitate direct comparison of spin-state energetics among the identified isomers, the relative energies of all observed minima are compiled in Table 2. Energies are referenced to the global minimum (q1) across all spin configurations. For open-shell states, the ⟨S2⟩ values post-annihilation were validated. The calculated relative energy demonstrates a distinct dependence on spin states. Most of the isomers preferentially stabilize in the quintet state, with q1, q2, q3, q6, q8, and q5 exhibiting quintet ground states. In contrast, the isomers that did not converge in the quintet state (t2, t3, t6) prefer the triplet multiplicity. An exception is isomer q7. Isomers s2, s5, and s6 converged exclusively in the singlet state. The ⟨S2⟩ values for triplet (≈2.04–2.64) and quintet (≈6.00–6.02) states indicate generally acceptable spin purity, with minor spin contamination observed in selected cases. Overall, the results demonstrate that the preferred multiplicity strongly depends on the structure.

TABLE 2.

ZPVE corrected relative energies of FeC2O isomers (in kcal mol–1) of the optimized structures of FeC2O across singlet, triplet, and quintet electronic states computed at the UωB97XD/6 311++G (2d,2p) level of theory.

Isomer Multiplicity ZPVE corrected relative energy (kcal/mol) ⟨S2⟩ Lowest energy multiplicity
q1 singlet † 60.58 - Quintet
Triplet 3.74 2.27
Quintet 0 6.00
q2 singlet † 105.47 - Quintet
Quintet 66.70 6.02
q3 Singlet 102.04 ​ Quintet
Quintet 67.87 6.00
q6 Singlet 115.70 - Quintet
Quintet 74.58 6.00
q7 singlet ‡ 133.35 - Triplet
triplet ‡ 52.46 2.64
Quintet 75.98 6.00
q8 Singlet 78.83 - Quintet
Quintet 77.33 6.00
t2 Singlet 38.77 - Triplet
Triplet 36.00 2.07
t3 Singlet 62.32 - Triplet
Triplet 38.69 2.04
t6 Singlet 112.15 - Triplet
Triplet 78.79 2.04
s2 Singlet 57.53 - Singlet
s5 Singlet 65.63 - Singlet
s6 Singlet 77.36 - Singlet
q5 Singlet 144.17 - Quintet
triplet † 75.43 2.37
quintet † 74.29 6.00
Open in a new tab

Entries marked “—” indicate that a corresponding minimum was not located for that multiplicity. The superscript.

†

indicates transition states, and.

‡

indicates a higher-order saddle point.

To elucidate the energetic hierarchy of FeC2O isomers across various spin states, the relative energies of all singlet, triplet, and quintet configurations are benchmarked against the global minimum quintet isomer (q1). The resultant energy landscape of the isomers with energy below 70 kcal/mol is depicted in Figure 3. The triplet minimum is situated at merely 3 kcal mol-1 above q1, suggesting that other spin states may be energetically attainable. Conversely, the singlet structures exist at considerably elevated energy, indicating that they are inaccessible in frigid interstellar environments, although they may still be relevant for understanding the broader PES.

FIGURE 3.

Energy level diagram showing seven horizontal lines labeled q1, q2, t1, t2, t3, t4, and s1 with respective energy values in kcal/mol. q1 at zero is the global minimum, q2 at sixty-six point seven, t1 at three point seven five, t2 at thirty-six, t3 at thirty-eight point seven, t4 at fifty-two point four seven, and s1 at thirty-eight point seven seven. Colors distinguish line types: magenta for q1 and q2, green for t1-t4, and orange for s1. The y-axis is labeled Energy (kcal/mol).

Open in a new tab

Relative energies of the low-lying FeC2O isomers in singlet (orange), triplet (green), and quintet (pink) spin states referenced to the global minimum (q1). Relative energies are given in parentheses in kcal mol-1; obtained at the (U)ωB97XD/6–311++G (2d,2p) level of theory.

3.2. Correlated wavefunction assessment of the FeC2O PES

To analyze the sensitivity of DFT to a correlated wavefunction approach, single-point (U)CCSD(T)/6–311++G (2d,2p) calculations were implemented on the singlet, triplet, and quintet structures optimized at the UωB97XD/6–311++G (2d,2p) level of theory. Despite several energetic reorderings occurring at the single point (U)CCSD(T) level of calculations, the preference for the linear quintet structure q1 as the global minimum of FeC2O remains consistent, indicating that the ground-state assignment is unaffected by the treatment of electron correlation. However, the relative ordering of certain high-energy isomers is modified at the UCCSD(T) level. especially for low-lying open-shell states with significant multiconfigurational character, as further indicated by the T1 diagnostic values.

At the UTPSSh level, the linear quintet structure q1 exhibits a second-order saddle point, whereas q11 represents the minimum energy geometry. The relative energy difference between these structures at the UTPSSh/6–311++G (2d,2p) level of theory is only 0.34 kcal mol-1. Due to this disparity, additional single-point UCCSD(T)/6–311++G (2d,2p) calculations were performed on the UTPSSh-optimized geometries of q1 and q11. The CCSD(T) results indicate that q1 is lower in energy than q11 by 6.71 kcal mol-1, indicating the qualitative energetic preference for q1 over q11 at the correlated wavefunction level. These results further substantiate q1 as the global minimum geometry, despite the UTPSSh prediction of q11 as the minimum.

The most significant change occurs in the triplet state, where the bent structure t2 (like s1) becomes the triplet minimum, rather than the linear structure t1 predicted at the UωB97XD/6–311++G (2d,2p) level of theory. Isomer s1, with a bent structure, attains lower energy than its triplet structural counterpart t2. Also, certain high-energy quintet isomers, particularly q10, q4, and q7, exhibit significant stabilization, and further energetic shifts are observed for certain singlet isomers. These variations suggest that the FeC2O PES is sensitive to the treatment of electron correlation. Nevertheless, it has been observed that the lowest singlet (s1) and triplet (t2) structures, respectively, remain 16.22 and 18.02 kcal mol-1 above q1, indicating that the quintet ground state is well separated from the low-spin states. Consequently, while the energetic ordering of the low-lying excited states is method-dependent, q1 is consistently preserved as the global minimum structure.

Supplementary Figure S10 in the Supplementary Material compares the relative energy of the minimum energy geometry in the singlet, triplet, and quintet electronic states acquired from single-point energy calculations. The comparison of relative energies (ΔE + ZPVE) of isomers optimized at the (U)ωB97XD/6–311++G (2d,2p) level of theory, together with single-point energy calculations at the (U)CCSD(T) level and 6–311++G (2d,2p) basis sets, is presented in Supplementary Tables S13–S15.

The T1 diagnostic values were computed for the singlet, triplet, and quintet FeC2O isomers to examine the multireference nature and are reported in Supplementary Tables S13–S15 of the Supplementary Material. The calculated T1 values imply that the multireference character is significant across a large region of the FeC2O PES. In the quintet state, certain isomers, including q3, q4, q8, q9, and q10, have large T1 values, consistent with their pronounced energy shifts between DFT and UCCSD(T). The q7 isomer is an extreme case, with an exceptionally large T1 value, which implies that its electronic structure is poorly described by a single-reference wavefunction and that its UCCSD(T) relative energy should be interpreted with considerable caution. The triplet state also exhibits large multireference character, including the low-lying t1 and t2 structures, for which the ordering is reversed at the UCCSD(T) level. The singlet state also exhibits high T1 values, even for the lowest-energy singlet structures, providing further evidence that the low-lying FeC2O PES is not purely single-reference in nature. Therefore, the UCCSD(T) single-point energies are employed here primarily as qualitative correlated-wavefunction comparisons to evaluate energetic trends and spin-state ordering, rather than as definite quantitative reference values for the entire FeC2O PES.

To analyze the robustness of the quintet energetic ordering beyond single-point comparisons, the quintet isomers are further optimized at the UCCSD/6–311++G (2d,2p) level. Among the structures that converged successfully at this level (shown in Supplementary Figure S11 in the Supplementary Materials), q1 remained the lowest-energy quintet isomer, while q2, q4, and q5 remained higher in energy. Similarly, the higher energy structures q13 and q14 were identified well above q1. The UCCSD optimizations failed to converge for certain quintet isomers, consistent with the high electronic complexity and multireference sensitivity indicated by the T1 diagnostics and the UCCSD(T) energetic reordering. Although these CCSD optimizations do not provide a complete description of the quintet state, they further substantiate the stability of q1 as the preferred lowest-energy quintet FeC2O structure within the explored theoretical framework.

To further study the multireference character of the quintet isomers, as indicated by the T1 diagnostic values, CASSCF geometry optimizations have been performed. The CASSCF calculations also identify q1 as the lowest energy quintet structure. The relative energies of certain higher-energy quintet isomers are different from the DFT results, especially for q7. These differences are consistent with the considerable multiconfigurational character suggested by the T1 diagnostic values. Moreover, the energy difference between q1 and q11 at the CASSCF/def2-tzvp level of theory is negligible (0.000048 kcal/mol). Overall, the CASSCF calculations support the conclusion that multireference character alter the relative energies of several higher-energy isomers, but the identification of q1 as the preferred low-energy quintet structure remains consistent. Supplementary Tables S16, S17 in the Supplementary Material compare the relative energies of FeC2O quintet isomers obtained at the UωB97XD/6–311++g (2d,2p) with those obtained at the UCCSD/6–311++G (2d,2p) and the CASSCF/def2-tzvp levels of theory, respectively.

3.3. Dissociation pathways and intrinsic stability of q1

The local minima can be qualitatively considered as resulting from interactions between Fe and various C-O fragments (as Fe + C2O or FeC + CO). Open-chain linear structures correspond to end-on coordination of Fe with the C2O fragment, while cyclic or bending geometries result from side-on or perpendicular interactions that involve simultaneous Fe–C and Fe–O contacts. To determine the intrinsic stability of FeC2O, two fragmentation channels, Fe + C2O and FeC + CO, are studied on the quintet PES, associated with q1. At the UωB97XD/6–311++G (2d,2p) level of theory, the calculated bond dissociation energies are 216.3 and 338.9 kcal mol-1, respectively, indicating that FeC2O is strongly bound with respect to these dissociation pathways. Additionally, relaxed potential-energy scans are done along the Fe–C and C–C coordinates. They show a steady increase in energy with bond elongation, and no stationary points are observed. While detailed kinetic modeling and reaction-rate computations are beyond the scope of the present study, the large dissociation energies suggest that FeC2O is strongly bound relative to the investigated fragmentation channels, indicating its intrinsic stability that requires consideration in future astrochemical studies.

3.4. Bonding analysis

To understand the nature of bonding within the isomers, AdNDP analysis has been performed on the alpha orbitals. This technique provides exhaustive information on both localized and delocalized bonding in molecules through wavefunction interpretation and thereby serves as a powerful enhancement of NBO for electron density. In AdNDP analysis, the occupancy number (ON) denotes the total number of electrons associated with a specific bonding element. The highest possible value for ON that describes the electronic structure in terms of n-center two–electron (nc−2e) bonds is two (Zubarev and Boldyrev, 2008). AdNDP analysis is particularly well-suited to systems with a high degree of electron delocalization, providing essential insights into lone pairs, aromaticity, delocalized bonding elements, and chemical bonding patterns. It is helpful for studying systems that are hardly characterized by conventional methods due to their complex bonding patterns. Figure 4 shows the α-spin AdNDP bonding patterns of q1, with ONs. It supports WBI and NAC analysis interpretations. The 2c–2e σ bonds, distinctly observed for Fe–C2, C2–C3, and C3–O, establish the essential structural linkage. The well–defined π bonds in both the C2–C3 and C3–O connections imply that each π interaction is predominantly concentrated between its corresponding atom pair in the high–spin state. This localization indicates minimal involvement of Fe d orbitals in π bonding, consistent with diminished backbonding in a quintet structure. The AdNDP orbitals collectively affirm that the characteristics of the C=C and C=O double bonds are preserved. At the same time, Fe predominantly provides σ-bonding support to the carbon core, consistent with the WBI and charge distributions. The β-spin AdNDP analyses are also conducted to verify the adequacy of the bonding description. Similar to α-spin analysis, β-spin analysis reproduces the fundamental bonding framework, encompassing localized Fe–C, C–C, and C–O bonding interactions, as well as oxygen lone-pair orbitals. Consequently, the qualitative bonding representation is unaffected by the chosen spin state. The β-spin AdNDP orbitals of q1 are shown in Supplementary Figure S12 in the Supplementary Material.

FIGURE 4.

The AdNDP bonding patterns of q1 with occupation numbers. Top row: oxygen lone pair, σ bond, and σ bond visualized with red contours. Bottom row: π bond, σ bond, and π bond shown using red and green contours.

Open in a new tab

The AdNDP bonding patterns of q1 with occupation numbers (ONs) obtained at the UωB97XD/6–311++G (2d,2p) level.

MO analysis is conducted to substantiate the bonding interpretation derived from AdNDP. Figure 5 displays the lowest unoccupied molecular orbital (LUMO) and highest occupied molecular orbital (HOMO) alpha orbitals of q1. Here, HOMO, HOMO–1, HOMO–5, HOMO–6, and HOMO–7 are π delocalized orbitals, while HOMO–2 is a σ delocalized orbital. The d orbitals of Fe predominantly exhibit nonbonding characteristics, aligning with the AdNDP characterization.

FIGURE 5.

The molecular orbitals of q1 showing LUMO, HOMO, and HOMO–1 to HOMO–7 as colored electron density plots. An energy gap of 6.28 electron volts is marked between HOMO and LUMO.

Open in a new tab

The molecular orbitals of q1 obtained at the UωB97XD/6–311++G (2d,2p) level (isovalue = 0.03).

The bonding properties are further analyzed using WBI. Figure 6 displays the WBIs of all the bonds of q1 determined at the UωB97XD/6–311++G (2d,2p) level of theory. The WBI value of 1.03 between Fe and C2 indicates a single covalent bond between them. The quintet state of the molecule, characterized by a high–spin iron center, contributes fewer electrons to π bonding, hence constraining Fe→ligand backbonding and leading to a predominance of σ Fe–C interactions, which supports a WBI of approximately 1.03. This bonding pattern can be favorable in ISM, where the molecules must be stable with negligible electronic support from the metal. The C–C–O section develops a conjugated π system with enhanced localization of light atoms owing to reduced metal participation. The C2–C3 and C3–O bonds have WBI values of 1.90 and 1.79, respectively, indicating double bonds.

FIGURE 6.

The WBI (in blue) of q1.

Open in a new tab

The WBI (in blue) of q1 obtained at the UωB97XD/6–311++G (2d,2p) level.

Additional analyses, including NAC, ELF, AIM, and the Laplacian of the electron density, exhibit consistent trends and are hence not elaborated here; results are available in the Supplementary Figures S13, S14.

3.5. Infrared (IR) and microwave spectroscopic parameters

To identify molecules in the laboratory and, by extension, in the ISM, the most significant evidence lies in spectroscopic parameters. Figure 7 illustrates the IR vibrational spectrum of q1 obtained at the UωB97XD/6–311++G (2d,2p) level of theory. The harmonic vibrational frequency analysis of the optimized quintet global minimum of FeC2O showed no imaginary frequencies, assuring that the structure represents a true minimum on the PES. The spectrum shows two sets of doubly degenerate π-type bending modes at 63.05 and 566.78 cm-1, arising from vibrations perpendicular to the molecular axis in two orthogonal planes, in accordance with the linear geometry of the molecule. The moderate-frequency mode at 508.50 cm-1 corresponds to Fe–C stretching. The medium intensity peak at 1448.89 cm-1 corresponds to symmetric stretching of the C–C–O fragment, which involves motion of the carbon atom bound to Fe and the terminal oxygen. The highest-frequency mode at 2169.66 cm-1 primarily corresponds to the asymmetric stretching of the C–C–O fragment. It results in the most prominent band in the IR spectrum, with remarkably high IR intensity (1832.60 km mol-1), establishing it as a distinct spectroscopic signature that may aid experimental detection. The elevated frequency of this mode, relative to standard carbonyl compounds, signifies diminished Fe→CO π back–donation in the high–spin quintet state. The harmonic vibrational frequencies expressed in terms of wavenumber (cm-1) and their corresponding IR intensities (km mol-1) of q1 computed at the UωB97XD/6–311++G (2d,2p) level are listed in Table 3. All vibrational frequencies reported in this study are harmonic. The IR spectrum suggests a bonding pattern with a strong C2O fragment and a weaker Fe–C bond, consistent with analyses of their electronic structures. Moreover, the identification of similar structures in the actual laboratory can be aided by the computationally predicted IR spectra.

FIGURE 7.

The IR vibrational spectrum of q1 with wavenumber in centimeters inverse on the x-axis and molar absorptivity on the y-axis, showing multiple labeled peaks corresponding to Fe-C-C bend, Fe-C stretch, C-C-O bend, C-C-O symmetric stretch, and C-C-O asymmetric stretch.

Open in a new tab

The IR vibrational spectrum of q1 obtained at the UωB97XD/6–311++G (2d,2p) level.

TABLE 3.

Harmonic vibrational frequencies in terms of wavenumber (cm-1) and corresponding IR intensities (km mol-1) of q1 computed at the UωB97XD/6–311++G (2d,2p) level.

Mode Wavenumber (cm-1) IR intensity (km mol-1) Assignment
ν1 63.05 31.5897 Bending of Fe-C-C framework (degenerate)
ν2 63.05 31.5897 Bending of Fe-C-C framework (degenerate)
ν3 508.50 47.1025 Fe–C stretching
ν4 566.78 12.4840 Bending of C-C-O framework (degenerate)
ν5 566.78 12.4840 Bending of C-C-O framework (degenerate)
ν6 1448.89 16.4866 Symmetric stretch of C–C–O fragment
ν7 2169.66 1832.5953 Asymmetric stretch of C–C–O fragment
Open in a new tab

Rotational constants are handy astronomical tools because they help discover and study specific molecules in celestial bodies or analyze planetary atmosphere spectra. It is necessary to understand the components of the dipole moment to identify molecules in astronomy, study interstellar chemistry, and analyze planetary atmospheres. Centrifugal distortion constants are also essential for astronomical identification, as they enable accurate spectral predictions, distinguish among isotopic variants, and yield insights into molecular structure and dynamics. Knowing all the parameters discussed above can help enhance our understanding of the chemical composition and evolution of celestial objects. From an experimental point of view, only true minima on the PES are expected to be detectable. Consequently, rotational constants are reported only for the structures that display no imaginary frequencies. Rotational constants for saddle points have been excluded because they lack direct experimental significance. The rotational constants reported in this study are equilibrium (Be) values obtained from optimized geometries and do not include vibrational averaging corrections. Table 4 provides the rotational constants and quartic centrifugal distortion constants (τ) for q1 and q7, and Table 5 provides the rotational constants and quartic centrifugal distortion constants (D) for q2, q3, q6, and q8 determined at the UωB97XD/6–311++G (2d,2p) level of theory. The differences in the reported forms are ascribed to the alterations in the mathematical representation of the quartic distortion constants, rather than to any actual deviations in rotational behavior. It is observed that precise spectroscopic predictions for transition-metal systems may necessitate explicit consideration of core–valence correlation at the wavefunction level (Drosou et al., 2022; Xu et al., 2015). Such considerations exceed the parameters of the current exploratory study.

TABLE 4.

Inertial axis dipole moment components, absolute dipole moments (in Debye), centrifugal distortion constants τ (in MHz), and equilibrium rotational constants (in MHz) of the optimized structures FeC2O in their corresponding quintet electronic states derived from harmonic frequency calculations computed at the UωB97XD/6–311++G (2d,2p) level of theory.

Isomer μa μb μc |μ| τa τb τc De Ae Be Ce
q1 8.52 0 0 8.52 0 0 −4.39x10−4 1.09x10−4 0 1881.62 1881.63
q7 13.44 0 0 13.44 0 0 −6.61x10−4 1.65x10−4 0 2151.18 2151.18
Open in a new tab

TABLE 5.

Inertial axis dipole moment components, absolute dipole moments (in Debye), centrifugal distortion constants D (in MHz), and equilibrium rotational constants (in MHz) of the optimized structures FeC2O in their corresponding quintet electronic states derived from harmonic frequency calculations computed at the UωB97XD/6–311++G (2d,2p) level of theory.

Isomer μa μb μc |μ| DJ DK DJK d1 d2 Ae Be Ce
q2 1.03 0 0 1.03 1.03x10−3 3.72x10−2 1.58x10−1 −6.71x10−5 −8.16x10−2 53,008.19 3594.06 3365.85
q3 −0.46 −3.60 0 3.63 4.48x10−3 3.23x10–−1 −2.94x10−2 8.79x10−4 3.79x10−2 20,293.17 5133.55 4869.89
q6 8.26 −1.11 0 8.34 6.53x10−4 7.95x10−1 6.62x10−2 −3.09x10−5 −2.80x10−2 34,399.31 2756.84 2552.29
q8 2.70 −0.69 0 2.79 3.84x10−3 3.98x100 2.43x10−1 −1.86x10−4 −9.99x10−2 52,354.87 3562.43 3335.47
Open in a new tab

3.6. Density of states (DOS)

A DOS plot graphically displays the number of energy states accessible for electrons in a system at various energy levels. The total density of states (TDOS) represents the overall distribution of energy states within the system. The partial density of states (PDOS) signifies the contributions from distinct parts of the molecule or system to the overall DOS. Figure 8 shows the DOS plot for q1. The dashed line indicates the position of the HOMO. Peaks in the DOS correspond to high concentrations of energy levels at that energy, whereas troughs represent regions with a reduced number of available energy states. In Figure 8, the black curve represents TDOS. In addition, the red, blue, green, and pink curves represent the contributions of Fe, C2, C3, and O atoms, respectively. The TDOS shows an evident energy gap near the Fermi level, establishing the molecule’s electronic stability. An orbital composition analysis was conducted with NAO-based orbital decomposition to quantitatively analyze the frontier electronic structure of q1. The spin-resolved atomic composition (%) of the frontier molecular orbitals of q1, obtained at the UωB97XD/6–311++G (2d,2p) level of theory, is shown in Supplementary Table S18 in the Supplementary Material. It indicates that the α-HOMO and β-HOMO are dominated by contributions from the C2O fragment, whereas α-LUMO and β-LUMO are mainly localized on the Fe atom, contributing 86.3% and 94.1%, respectively. This further validates the electronic structure obtained from orbital and charge analysis.

FIGURE 8.

The density of states plot of q1 with five lines representing total density of states (black), partial density of states for iron (red), carbon C2 (blue), carbon C3 (green), and oxygen (magenta).

Open in a new tab

The density of states plot of q1 obtained at the UωB97XD/6–311++G (2d,2p) level.

3.7. Astrochemical implications

While the present study focuses on the intrinsic electronic structure and spectroscopic properties of FeC2O, the possibility of its formation under ISM conditions warrants further investigation. A potential pathway entails the sequential synthesis commencing with Fe and CO to produce FeCO, followed by a reaction with atomic carbon to generate FeC2O. Alternatively, considering that FeC radical has been identified in space (Koelemay and Ziurys, 2023), insertion reactions such as FeC + CO → FeC2O constitute a chemically plausible pathway. A third hypothesis pertains to the interaction of atomic Fe with transitory C2O (ketenylidene) fragments generated by the active processing of ice grain mantles that are rich in CO (Ohishi, et al., 1991; Urso et al., 2019). Although these paths are hypothetical, the synthesis of FeC2O in ISM is expected to happen through gas-phase reactions involving small iron-containing entities, rather than by the direct modification of pure iron grains, as pure iron grains are considered rare there (Kimura et al., 2017). The low gas-phase abundance of iron and the strong reactivity of C2O imply that FeC2O is probably a transient or low-abundance species rather than a significant molecular reservoir. It indicates that although the efficient synthesis of FeC2O is not established, there is potential for its formation under specific conditions, such as intermittent iron release from dust grains in shocked areas or in circumstellar envelopes, making it chemically plausible and spectroscopically identifiable. A quantitative evaluation of reaction energetics and kinetics is beyond the scope of the present study and will be carried out in the future.

The intrinsic electronic stability of FeC2O in isolation is indicated by the studies reported in the present work; however, these studies do not assess its ability to survive in the ISM, where it is exposed to hazards such as cosmic rays and UV radiation. These factors have the potential to induce electronic excitation or photodissociation (Heays et al., 2017; Schippers and Müller, 2020) which implies that FeC2O is unlikely to be abundant or long-lived in space. Under interstellar conditions, FeC2O is anticipated to be a transient or low-abundance species, with detection limited to shielded areas or environments with recent energetic activity.

The non-detection of FeC2O in ISM does not preclude its transient production. In contrast to FeC and FeCN, which possess efficient formation pathways involving carbon- and nitrogen-containing radicals, the production of FeC2O may be impeded by the low quantity and high reactivity of the C2O fragment. The absence of laboratory rotational spectra for neutral FeC2O has certainly impeded astronomical searches. Molecules without laboratory rotational spectra are infrequently investigated in astronomical surveys, potentially leading to non-detection despite their transient presence.

4. Conclusion

The isomers of FeC2O were investigated using two density functional methods with and without an effective core potential, with emphasis on the lowest-energy quintet electronic state. The linear quintet structure q1 is the lowest energy FeC2O isomer within the DFT framework considered in the study, and is identified to be the global minimum at the UωB97XD/6–311++G (2d,2p) level of theory. The chemical bonding characteristics of the global minimum of FeC2O are further investigated at the UωB97XD level with the 6–311++G (2d,2p) basis set. Various quantum-chemical tools were employed to elucidate the nature of chemical bonding and structural properties, including AdNDP, MO analysis, and WBI. These investigations indicate primarily localized Fe–C and C–O bonds, poor Fe–ligand covalency, and a robustly bonded C2O fragment.

The computed IR spectrum, along with a significant HOMO–LUMO gap, suggests increased electronic stability of q1, while the DOS and molecular orbital analysis indicate substantial Fe 3d contributions to the frontier electronic structure and moderate metal–ligand orbital interactions. Dissociation-energy calculations conducted reveal that the Fe + C2O and FeC + CO fragmentation channels are highly endothermic, while the Fe–C and C–C scans show a continuous increase in energy with bond elongation. These findings further establish that q1 as a strongly bound minimum and further substantiate its energetic stability.

Single-point (U)CCSD(T) computations and T1 diagnostic values further reveal that the FeC2O PES is sensitive to electron correlation, and certain singlet, triplet, and quintet structures exhibit substantial multireference character. Additional UCCSD and CASSCF optimizations of quintet isomers confirm that q1 remains the lowest-energy quintet structure, further supporting the assignment of q1 as the preferred low-energy FeC2O candidate within the computational framework employed.

The unique spectroscopic fingerprints and electronic structure of FeC2O make it a viable target for future astrochemical detection, supported by computational studies of iron–carbon–oxygen molecules. The structural and energy parameters, together with the infrared and microwave spectroscopic parameters, including rotational and centrifugal distortion constants, reported in the present work, can substantially assist the experimentalists in identifying this molecule in the ISM.

Acknowledgements

We express our gratitude to Dr. Krishnan Thirumoorthy, Dr. Vijayanand C., and Dr. Shilpa Shajan, Department of Chemistry, Vellore Institute of Technology, Vellore, for their unwavering support and insightful recommendations regarding the systems that were examined in this work. We express our gratitude to Dr. Uma Mahendra Kumar K., Department of Physics, Vellore Institute of Technology, Vellore, for his insightful comments on this work. The first author expresses profound gratitude to the University Grants Commission, New Delhi, India, for awarding the Savitribai Jyotirao Phule Fellowship for Single Girl Child (SJSGC) to conduct doctoral research.

Funding Statement

The author(s) declared that financial support was received for this work and/or its publication. The first author acknowledges funding from the Savitribai Jyotirao Phule Fellowship (SJSGC) under the University Grants Commission (UGC), File No. 82‐7/2022(SA‐III). The authors also wish to extend their gratitude to the management of the Vellore Institute of Technology, Vellore, for covering the article processing charges for this manuscript.

Footnotes

Edited by: Silvia Alessandrini, University of Bologna, Italy

Reviewed by: Yunguo Li, University of Science and Technology of China, China

Tarun Roy, University of Vermont, United States

Data availability statement

The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author.

Author contributions

AR: Conceptualization, Methodology, Investigation, Writing – original draft, Data curation, Formal Analysis. SR: Conceptualization, Writing – review and editing, Supervision, Project administration.

Conflict of interest

The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Generative AI statement

The author(s) declared that generative AI was not used in the creation of this manuscript.

Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Supplementary material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fchem.2026.1874752/full#supplementary-material

Supplementaryfile1.docx (1.7MB, docx)

References

  1. Bader R. F. W. (1991). A quantum theory of molecular structure and its applications. Chem. Rev. 91, 893–928. 10.1021/cr00005a013 [DOI] [Google Scholar]
  2. Becke A. D. (1988). Density-functional exchange-energy approximation with correct asymptotic behavior. Phys. Rev. A Coll. Park 38, 3098–3100. 10.1103/PhysRevA.38.3098 [DOI] [PubMed] [Google Scholar]
  3. Becke A. D., Edgecombe K. E. (1990). A simple measure of electron localization in atomic and molecular systems. J. Chem. Phys. 92, 5397–5403. 10.1063/1.458517 [DOI] [Google Scholar]
  4. Beerwerth R., Buhr T., Perry-Sassmannshausen A., Stock S. O., Bari S., Holste K., et al. (2019). Near L-edge single and multiple photoionization of triply charged iron ions. Astrophys. J. 887, 189. 10.3847/1538-4357/ab5118 [DOI] [Google Scholar]
  5. Bergner A., Dolg M., Küchle W., Stoll H., Preuß H. (1993). Ab initio energy-adjusted pseudopotentials for elements of groups 13 – 17. Mol. Phys. 80, 1431–1441. 10.1080/00268979300103121 [DOI] [Google Scholar]
  6. Berryman V. E. J., Baker M. G., Boyd R. J. (2014). Effect of amino acid ligands on the structure of iron porphyrins and their ability to bind oxygen. J. Phys. Chem. A. 118, 4565–4574. 10.1021/jp502541y [DOI] [PubMed] [Google Scholar]
  7. Bilalbegović G., Maksimović A., Mohaček-Grošev V. (2017). Missing fe: hydrogenated iron nanoparticles. Mon. Not. R. Astron. Soc. Lett. 466, L14–L18. 10.1093/mnrasl/slw226 [DOI] [Google Scholar]
  8. Bjorn. O., Ross P. R. T., Sigbahn P. E. (1980). A complete active space scf method (Casscf) using a density matrix formulated super-CI approach. Chem. Phys. 48, 157–173. 10.1016/0301-0104(80)80045-0 [DOI] [Google Scholar]
  9. Burdett J. K., McCormick T. A. (1998). Electron localization in molecules and solids: the meaning of ELF. J. Phys. Chem. A 102, 6366–6372. 10.1021/jp9820774 [DOI] [Google Scholar]
  10. Chai J-Da, Head-Gordon M. (2008). Long-range corrected hybrid density functionals with damped atom-atom dispersion corrections. Phys. Chem. Chem. Phys. 10, 6615–6620. 10.1039/b810189b [DOI] [PubMed] [Google Scholar]
  11. Chan B. (2023). Optimal small basis set and geometric counterpoise correction for DFT computations. J. Chem. Theory Comput. 19, 3958–3965. 10.1021/acs.jctc.3c00298 [DOI] [PubMed] [Google Scholar]
  12. Chandra C. (2013). Small Fe bearing ring molecules of possible astrophysical interest: molecular properties and rotational spectra. Astrophys. Space Sci. 347, 315–325. 10.1007/s10509-013-1516-0 [DOI] [Google Scholar]
  13. Cirera J., Via-Nadal M., Ruiz E. (2018). Benchmarking density functional methods for calculation of state energies of first row spin-crossover molecules. Inorg. Chem. 57, 14097–14105. 10.1021/acs.inorgchem.8b01821 [DOI] [PubMed] [Google Scholar]
  14. Clark T., Chandrasekhar J., Spitznagel G. W., Schleyer P. V. R. (1983). Efficient diffuse function‐augmented basis sets for anion calculations. III. The 3‐21+G basis set for first‐row elements, Li–F. J. Comput. Chem. 4, 294–301. 10.1002/jcc.540040303 [DOI] [Google Scholar]
  15. Cox P. (1990). The 21 micron emission band in the IRAS/LRS spectra of H II regions: evidence of iron oxide in the interstellar medium. Astron. Astrophys. 236, L29–L32. [Google Scholar]
  16. Dong X., Wang T., Wang J., Yuan W., Zhou H., Dai H., et al. (2008). Broad-line balmer decrements in blue active galactic nuclei. Mon. Not. R. Astron. Soc. 383, 581–592. 10.1111/j.1365-2966.2007.12560.x [DOI] [Google Scholar]
  17. Drosou M., Mitsopoulou C. A., Pantazis D. A. (2022). Reconciling local coupled cluster with multireference approaches for transition metal spin-state energetics. J. Chem. Theory Comput. 18, 3538–3548. 10.1021/acs.jctc.2c00265 [DOI] [PMC free article] [PubMed] [Google Scholar]
  18. Duley W. W., Williams D. A. (1981). The infrared spectrum of interstellar dust: surface functional groups on carbon. Mon. Not. R. Astron. Soc. 196, 269–274. 10.1093/mnras/196.2.269 [DOI] [Google Scholar]
  19. Dwek E. (2016). Iron: a key element for understanding the origin and evolution of interstellar dust. Astrophys. J. 825, 136. 10.3847/0004-637x/825/2/136 [DOI] [PMC free article] [PubMed] [Google Scholar]
  20. Endres C. P., Schlemmer S., Schilke P., Stutzki J., Müller H. S. P. (2016). The cologne database for molecular spectroscopy, CDMS, in the virtual atomic and molecular data centre, VAMDC. J. Mol. Spectrosc. 327, 95–104. 10.1016/j.jms.2016.03.005 [DOI] [Google Scholar]
  21. Frisch M. J., Trucks G. W., Schlegel H. B., Scuseria G. E., Robb M. A., Cheeseman J. R., et al. (2016). Gaussian 16, Revision C.01. [Google Scholar]
  22. Fuentealba P., Preuss H., Stoll H., Von Szentpály L. (1982). A proper account of core-polarization with pseudopotentials: single valence-electron alkali compounds. Chem. Phys. Lett. 89, 418–422. 10.1016/0009-2614(82)80012-2 [DOI] [Google Scholar]
  23. Furuya R. S., Walmsley C. M., Nakanishi K., Schilke P., Bachiller R. (2003). Interferometric observations of FeO towards sagittarius B2. Astron. Astrophys. 409, 21–24. 10.1051/0004-6361:20031304 [DOI] [Google Scholar]
  24. Glendening E. D., Badenhoop J. K., Weinhold F. (1998). Natural resonance theory: III. Chemical applications. J. Comput. Chem. 19, 628–646. 10.1002/(sici)1096-987x(19980430)19:6<628::aid-jcc5>3.3.co;2-t [DOI] [Google Scholar]
  25. Grimme S., Antony J., Ehrlich S., Krieg H. (2010). A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys. 132, 154104. 10.1063/1.3382344 [DOI] [PubMed] [Google Scholar]
  26. Halfen D. T., Ziurys L. M. (2007). Laboratory detection of FeCO+ (X4Σ–) by Millimeter/Submillimeter velocity modulation spectroscopy. Astrophys. J. 657, L61–L64. 10.1086/512853 [DOI] [Google Scholar]
  27. Heays A. N., Bosman A. D., Van Dishoeck E. F. (2017). Photodissociation and photoionisation of atoms and molecules of astrophysical interest. Astron. Astrophys. 602, A105. 10.1051/0004-6361/201628742 [DOI] [Google Scholar]
  28. Herbst E. (1995). Chemistry in the interstellar medium. Annu. Rev. Phys. Chem. 46, 27–54. 10.1146/annurev.pc.46.100195.000331 [DOI] [Google Scholar]
  29. Herbst E. (2001). The chemistry of interstellar space. Chem. Soc. Rev. 30, 168–176. 10.1039/a909040a [DOI] [Google Scholar]
  30. Herbst E., Van Dishoeck E. F. (2009). Complex organic interstellar molecules. Annu. Rev. Astron. Astrophys. 47, 427–480. 10.1146/annurev-astro-082708-101654 [DOI] [Google Scholar]
  31. Jacquemin D., Perpète E. A., Ciofini I., Adamo C. (2011). Assessment of the ωB97 family for excited-state calculations. Theor. Chem. Acc. 128 (1), 127–136. 10.1007/s00214-010-0783-x [DOI] [Google Scholar]
  32. Jensen A. G., Markwick-Kemper F., Snow T. P. (2008). Oxygen in the interstellar medium. Rev. Mineral. Geochem. 68, 55–72. 10.2138/rmg.2008.68.5 [DOI] [Google Scholar]
  33. Jones A. P. (1990). Iron or iron oxide grains in the interstellar medium? 245, 331–334. [Google Scholar]
  34. Kimura Y., Tanaka K. K., Nozawa T., Takeuchi S., Inatomi Y. (2017). Pure iron grains are rare in the universe. Sci. Adv. 3, 4–9. 10.1126/sciadv.1601992 [DOI] [PMC free article] [PubMed] [Google Scholar]
  35. Koelemay L. A., Ziurys L. M. (2023). Elusive iron: detection of the FeC radical (X3 Δi) in the envelope of IRC+10216. Astrophys. J. Lett. 958, L6. 10.3847/2041-8213/ad0899 [DOI] [Google Scholar]
  36. Köhler M., Jones A., Ysard N. (2014). A hidden reservoir of Fe/FeS in interstellar silicates? Astron. Astrophys. 565, L9. 10.1051/0004-6361/201423985 [DOI] [Google Scholar]
  37. Kreutzer J., Blaha P., Schubert U. (2016). Assessment of different basis sets and DFT functionals for the calculation of structural parameters, vibrational modes and ligand binding energies of Zr4O2(carboxylate)12 clusters. Comput. Theor. Chem. 1084, 162–168. 10.1016/j.comptc.2016.03.030 [DOI] [Google Scholar]
  38. Krishnan R., Binkley J. S., Seeger R., Pople J. A. (1980). Self-consistent molecular orbital methods. XX. A basis set for correlated wave functions. J. Chem. Phys. 72, 650–654. 10.1063/1.438955 [DOI] [Google Scholar]
  39. Lee T. J., Taylor P. R. (1989). A diagnostic for determining the quality of single‐reference electron correlation methods. Int. J. Quantum Chem. 36, 199–207. 10.1002/qua.560360824 [DOI] [Google Scholar]
  40. Louis H., Chima C. M., Amodu I. O., Gber T. E., Unimuke T. O., Adeyinka A. S. (2023). Organochlorine detection on transition metals (X= Zn, Ti, Ni, Fe, and Cr) anchored fullerenes (C23X). ChemistrySelect 8, e202203843. 10.1002/slct.202203843 [DOI] [Google Scholar]
  41. Lu T., Chen F. (2012). Multiwfn: a multifunctional wavefunction analyzer. J. Comput. Chem. 33, 580–592. 10.1002/jcc.22885 [DOI] [PubMed] [Google Scholar]
  42. Marzouk A., Danset D., Zhou M. F., Gong Y., Alikhani M. E., Manceron L. (2011). Vibrational spectrum and structure of CoO6: a model compound for molecular oxygen reversible binding on cobalt oxides and salts; A combined IR matrix isolation and theoretical study. J. Phys. Chem. A 115, 9014–9021. 10.1021/jp203943x [DOI] [PubMed] [Google Scholar]
  43. Matta C. F., Boyd R. J., Becke A. (2007). An Introduction to the Quantum Theory of Atoms in Molecules. 10.1590/1806-9126-RBEF-2019-0061 [DOI] [Google Scholar]
  44. Matteucci F., Greggio L. (1986). Relative roles of type I and II supernovae in the chemical enrichment of the interstellar gas. Astronomy Astrophysics, 154, 279–287. [Google Scholar]
  45. Merer A. J., Walmsley C. M., Churchwell E. (1982). A search for interstellar and stellar iron monoxide. Astrophys. J. 256, 151. 10.1086/159892 [DOI] [Google Scholar]
  46. Mierzwa G., Gordon A. J., Latajka Z., Berski S. (2015). On the multiple BO bonding using the topological analysis of Electron Localisation Function (ELF). Comput. Theor. Chem. 1053, 130–141. 10.1016/j.comptc.2014.10.003 [DOI] [Google Scholar]
  47. Moustafa H., Mohamed G. G., Elramly S. (2020). Spectroscopic studies, density functional theory calculations, and non-linear optical properties of binuclear Fe(III), Co(II), Ni(II), Cu(II), and Zn(II) complexes of OONN Schiff base ligand. J. Chin. Chem. Soc. 67, 1783–1793. 10.1002/jccs.202000024 [DOI] [Google Scholar]
  48. Nash B. K., Rao B. K., Jena P. (1996). Equilibrium structure and bonding of small iron-carbon clusters. J. Chem. Phys. 105, 11020–11023. 10.1063/1.472901 [DOI] [Google Scholar]
  49. Neese F., Wennmohs F., Becker U., Riplinger C. (2020). The ORCA quantum chemistry program package. J. Chem. Phys. 152, 224108. 10.1063/5.0004608 [DOI] [PubMed] [Google Scholar]
  50. Negus J., Comerford J. M., Müller Sánchez F., Barrera-Ballesteros J. K., Drory N., Rembold S. B., et al. (2021). The physics of the coronal-line region for galaxies in mapping galaxies at apache point observatory. Astrophys. J. 920, 62. 10.3847/1538-4357/ac1343 [DOI] [Google Scholar]
  51. Ohishi M., Suzuki H., Ishikawa S., Chikashi Y., Kanamori H., et al. (1991). Detection of a new carbon-chain molecule, CCO. Astrophys. J. 380, L39–L42. 10.1086/186168 [DOI] [PubMed] [Google Scholar]
  52. Olthof H., Pottasch S. R. (1975). On the iron abundance in interstellar gas. Astron. Astrophys. 43, 291–295. [Google Scholar]
  53. Osorio E. (2023). “Describing chemical bonding in exotic systems through AdNDP analysis,” in Atomic Clusters with Unusual Structure, Bonding and Reactivity (Elsevier; ), 1–17. 10.1016/B978-0-12-822943-9.00016-4 [DOI] [Google Scholar]
  54. Panda S., Sivadasan D., Job N., Sinjari A., Thirumoorthy K., Anoop A., et al. (2022). Why are MgC3H isomers missing in the interstellar medium? J. Phys. Chem. A 126, 4465–4475. 10.1021/acs.jpca.2c02220 [DOI] [PMC free article] [PubMed] [Google Scholar]
  55. Pham H. T., Nguyen M. T. (2015). Effects of bimetallic doping on small cyclic and tubular boron clusters: B7M2 and B14M2 structures with M = Fe, Co. Phys. Chem. Chem. Phys. 17, 17335–17345. 10.1039/c5cp01650a [DOI] [PubMed] [Google Scholar]
  56. Prabhaharan M., Prabakaran A. R., Srinivasan S., Gunasekaran S. (2014). Experimental and theoretical spectroscopic analysis, HOMO-LUMO, and NBO studies of cyanuric chloride. Spectrochim. Acta A Mol. Biomol. Spectrosc. 127, 454–462. 10.1016/j.saa.2014.02.040 [DOI] [PubMed] [Google Scholar]
  57. Purvis G. D., Bartlett R. J. (1982). A full coupled-cluster singles and doubles model: the inclusion of disconnected triples. J. Chem. Phys. 76, 1910–1918. 10.1063/1.443164 [DOI] [Google Scholar]
  58. Raghavachari K., Trucks G. W., Pople J. A., Head-Gordon M. (2013). Reprint of: a fifth-order perturbation comparison of electron correlation theories. Chem. Phys. Lett. 589, 37–40. 10.1016/j.cplett.2013.08.064 [DOI] [Google Scholar]
  59. Reed A. E., Weinstock R. B., Weinhold F. (1985). Natural population analysis. J. Chem. Phys. 83, 735–746. 10.1063/1.449486 [DOI] [Google Scholar]
  60. Rodríguez M. (2002). Iron abundance in H II regions. Astron. Astrophys. 389, 556–567. 10.1051/0004-6361:20011823 [DOI] [Google Scholar]
  61. Rodríguez-Ardila A., Pastoriza M. G., Viegas S., Sigut T. A. A., Pradhan A. K. (2004). Molecular hydrogen and [Fe II] in active galactic nuclei. Astron. Astrophys. 425, 457–474. 10.1051/0004-6361:20034285 [DOI] [Google Scholar]
  62. Roos B. O. (1980). The complete active space SCF method in a fock‐matrix‐based super‐CI formulation. Int. J. Quantum Chem. Quantum Chem. Symp. 14 (18), 175–189. 10.1002/qua.560180822 [DOI] [Google Scholar]
  63. Rose M., Elvis M., Tadhunter C. N. (2015). Coronal-line forest AGN: the best view of the inner edge of the AGN torus? Mon. Not. R. Astron. Soc. 448, 2900–2920. 10.1093/mnras/stv113 [DOI] [Google Scholar]
  64. Roy T., Ghosal S., Thimmakondu V. S. (2021). Six low-lying isomers of C11H8 are unidentified in the laboratory-a theoretical study. J. Phys. Chem. A 125, 4352–4364. 10.1021/acs.jpca.1c02247 [DOI] [PubMed] [Google Scholar]
  65. Roy T., Satpati S., Sinjari A., Anoop A., Thimmakondu V. S., Ghosal S. (2024). Energetic and spectroscopic properties of astrophysically relevant mgc4h radicals using high-level ab initio calculations. J. Phys. Chem. A 128, 1466–1476. 10.1021/acs.jpca.3c06828 [DOI] [PMC free article] [PubMed] [Google Scholar]
  66. Rubin R. H., Dufour R. J., Ferland G. J., Martin P. G., O’Dell C. R., Baldwin J. A., et al. (1997). [Fe IV] in the orion nebula. Astrophys. J. 474, L131–L134. 10.1086/310437 [DOI] [Google Scholar]
  67. Satpati S., Roy T., Anoop A., Thimmakondu V. S., Ghosal S. (2023a). Energetic and spectroscopic properties of the low-lying isomers of C5H: a high-level ab initio study. Atoms 11, 115. 10.3390/atoms11090115 [DOI] [Google Scholar]
  68. Satpati S., Roy T., Giri S., Anoop A., Thimmakondu V. S., Ghosal S. (2023b). Structure and bonding patterns in C5H4 isomers: pyramidane, planar tetracoordinate carbon, and spiro molecules. Atoms 11, 1–18. 10.3390/atoms11060096 [DOI] [Google Scholar]
  69. Satyapal S., Kamal L., Cann J. M., Secrest N. J., Abel N. P. (2021). The diagnostic potential of JWST in characterizing elusive AGNs. Astrophys. J. 906, 35. 10.3847/1538-4357/abbfaf [DOI] [Google Scholar]
  70. Savin A., Nesper R., Wengert S., Fässler T. (1997). The electron localization function ELF. Angew. Chem. Int. Ed. Engl. 36, 1808–1832. 10.1002/anie.199718081 [DOI] [Google Scholar]
  71. Schippers S., Müller A. (2020). Photoionization of astrophysically relevant atomic ions at PIPE. Atoms 8, 1–17. 10.3390/ATOMS8030045 [DOI] [Google Scholar]
  72. Schippers S., Martins M., Beerwerth R., Bari S., Holste K., Schubert K., et al. (2017). Near L-edge single and multiple photoionization of singly charged iron ions. Astrophys. J. 849, 5. 10.3847/1538-4357/aa8fcc [DOI] [Google Scholar]
  73. Schippers S., Beerwerth R., Bari S., Buhr T., Holste K., Kilcoyne A. L. D., et al. (2021). Near L-edge single and multiple photoionization of doubly charged iron ions. Astrophys. J. 908, 52. 10.3847/1538-4357/abcc64 [DOI] [Google Scholar]
  74. Shajan S., Thirumoorthy K. (2024). FeC4H2: a potential astrophysical molecule featuring planar tetracoordinate iron to unveil the mystery of missing iron in interstellar medium. ACS Earth Space Chem. 8, 2078–2089. 10.1021/acsearthspacechem.4c00178 [DOI] [Google Scholar]
  75. Shajan S., Thirunavukkarsu K., Chandrasekaran V., Thimmakondu V. S., Thirumoorthy K. (2024). FeC4H2 2+ encompassing planar tetracoordinate iron: structure and bonding patterns. Atoms 12, 11. 10.3390/atoms12020011 [DOI] [Google Scholar]
  76. Smith A. M., Stecher T. P. (1971). Carbon monoxide in the interstellar spectrum of zeta ophiuchi. Astrophys. J. 164, L43–L47. 10.1086/180689 [DOI] [Google Scholar]
  77. Sofia U. J., Cardelli J. A., Guerin K. P., Meyer D. M. (1997). Carbon in the diffuse interstellar medium. Astrophys. J. 482, L105–L108. 10.1086/310681 [DOI] [Google Scholar]
  78. Solomon P., Jefferts K. B., Penzias A. A., Wilson R. W. (1971). Observation of CO emission at 2.6 millimeters from IRC+ 10216. Astrophysical J. 163, L53–L56. 10.1086/180665 [DOI] [Google Scholar]
  79. Szilagyi R. K., Winslow M. A. (2006). On the accuracy of density functional theory for Iron—Sulfur clusters. J. Comput. Chem. 27, 1385–1397. 10.1002/jcc.20449 [DOI] [PubMed] [Google Scholar]
  80. Tam N. P., Tan H., Duong L. V., Pham-Ho M. P., Nguyen M. T. (2015). Fullerene-like boron clusters stabilized by an endohedrally doped iron atom: BnFe with n = 14, 16, 18 and 20. Phys. Chem. Chem. Phys. 17, 3000–3003. 10.1039/c4cp04279d [DOI] [PubMed] [Google Scholar]
  81. Tao J., Perdew J. P., Staroverov V. N., Scuseria G. E. (2003). Climbing the density functional ladder: nonempirical meta–generalized gradient approximation designed for molecules and solids. Phys. Rev. Lett. 91, 3–6. 10.1103/PhysRevLett.91.146401 [DOI] [PubMed] [Google Scholar]
  82. Temple M. J., Ferland G. J., Rankine A. L., Hewett P. C., Badnell N. R., Ballance C. P., et al. (2020). Fe III emission in quasars: evidence for a dense turbulent medium. Mon. Not. R. Astron. Soc. 496, 2565–2576. 10.1093/mnras/staa1717 [DOI] [Google Scholar]
  83. Thirumoorthy K., Karton A., Thimmakondu V. S. (2018). From high-energy C7H2 isomers with a planar tetracoordinate carbon atom to an experimentally known carbene. J. Phys. Chem. A 122, 9054–9064. 10.1021/acs.jpca.8b08809 [DOI] [PubMed] [Google Scholar]
  84. Tielens AGGM, Allamandola L. J. (1987). “Composition, structure, and chemistry of interstellar dust,” in Interstellar Processes. Editors Hollenbach D. J., Thronson H. A. (Dordrecht: Springer; ), 397–469. 10.1007/978-94-009-3861-8_16 [DOI] [Google Scholar]
  85. Urso R. G., Palumbo M. E., Ceccarelli C., Balucani N., Bottinelli S., Codella C., et al. (2019). C2O and C3O in low-mass star-forming regions. Astron. Astrophys. 628 A72. 10.1051/0004-6361/201834322 [DOI] [Google Scholar]
  86. Walmsley C. M., Bachiller R., Forêts G. P., Schilke P. (2002). Detection of FeO toward sagittarius B2. Astrophys. J. 566, L109–L112. 10.1086/339694 [DOI] [Google Scholar]
  87. Watson W. D. (1977). Interstellar chemistry. Acc. Chem. Res. 10, 221–226. 10.1021/ar50114a005 [DOI] [Google Scholar]
  88. Wiberg K. B. (1968). Application of the pople-santry-segal CNDO method to the cyclopropylcarbinyl and cyclobutyl cation and to bicyclobutane. Tetrahedron 24, 1083–1096. 10.1016/0040-4020(68)88057-3 [DOI] [Google Scholar]
  89. Wilson R. W., Jefferts K. B., Penzias A. A. (1970). Carbon monoxide in the orion nebula. Astrophy. J. 161, L43–L44. 10.1086/180567 [DOI] [Google Scholar]
  90. Xu X., Zhang W., Tang M., Truhlar D. G. (2015). Do practical standard coupled cluster calculations agree better than Kohn-Sham calculations with currently available functionals when compared to the best available experimental data for dissociation energies of bonds to 3d transition metals? J. Chem. Theory Comput. 11, 2036–2052. 10.1021/acs.jctc.5b00081 [DOI] [PubMed] [Google Scholar]
  91. Yadav F., Goyal A., Singh N. (2023). Analysis of line intensity ratio for optical transitions of 3d6 levels and plasma screening effect on atomic structure of Fe III ion. Radiat. Phys. Chem. 206, 110795. 10.1016/j.radphyschem.2023.110795 [DOI] [Google Scholar]
  92. Zack L. N., Halfen D. T., Ziurys L. M. (2011). Detection of FeCN (X4Δi) in IRC+10216: a new interstellar molecule. Astrophys. J. Lett. 733, L36. 10.1088/2041-8205/733/2/L36 [DOI] [Google Scholar]
  93. Zayed E. M., Zayed M. A., Abd El Salam H. A., Noamaan M. A. (2019). Novel triazole thiole ligand and some of its metal chelates: synthesis, structure charactertization, thermal behavior in comparison with computational calculations and biological activities. Comput. Biol. Chem. 78, 260–272. 10.1016/j.compbiolchem.2018.12.008 [DOI] [PubMed] [Google Scholar]
  94. Zhukovska S., Henning T., Dobbs C. (2018). Iron and silicate dust growth in the galactic interstellar medium: clues from element depletions. Astrophys. J. 857, 94. 10.3847/1538-4357/aab438 [DOI] [Google Scholar]
  95. Zubarev D. Y., Boldyrev A. I. (2008). Developing paradigms of chemical bonding: adaptive natural density partitioning. Phys. Chem. Chem. Phys. 10, 5207–5217. 10.1039/b804083d [DOI] [PubMed] [Google Scholar]

Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

Supplementaryfile1.docx (1.7MB, docx)

Data Availability Statement

The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author.

Articles from Frontiers in Chemistry are provided here courtesy of Frontiers Media SA

RESOURCES