Why Are MgC3H Isomers Missing in the Interstellar Medium?

Considering the recent findings of linear doublet (2Σ+) MgCnH isomers (n = 2, 4, and 6) in the evolved carbon star IRC+10216, various structural isomers of MgC3H and MgC3H+ are theoretically investigated here. For MgC3H, 11 doublet and 8 quartet stationary points ranging from 0.0 to 71.8 and 0.0 to 110.1 kcal mol-1, respectively, have been identified initially at the UωB97XD/6-311++G(2d,2p) level. To get accurate relative energies, further energy evaluations are carried out for all isomers with coupled cluster methods and thermochemical modules such as G3//B3LYP, G4MP2, and CBS-QB3 methods. Unlike the even series, where the global minima are linear molecules with a Mg atom at one end, in the case of MgC3H, the global minimum geometry turns out to be a cyclic isomer, 2-magnesabicyclo[1.1.0]but-1,3,4-triyl (1, C2v, 2A1). In addition, five low-lying isomers, magnesium-substituted cyclopropenylidene (2, Cs, 2A'), 1-magnesabut-2,3-dien-1-yl-4-ylidene (3, Cs, 2A″), 1-magnesabut-2-yn-1-yl-4-ylidene (4, Cs, 2A″), 2λ3-magnesabicyclo[1.1.0]but-1,3-diyl-4-ylidene (5, C2v;, 2A1), and 1-magnesabut-2,3-dien-2-yl-4-ylidene (6, C∞v, 2Σ+), were also identified. The doublet linear isomer of MgC3H, 1-magnesabutatrienyl (10, C∞v, 2Σ+) turns out to be a minimum but lies 54.1 kcal mol-1 above 1 at the ROCCSD(T)/cc-pVTZ level. The quartet (4Σ+) electronic state of 10 was also found to be a minimum, but it lies 8.0 kcal mol-1 above 1 at the same level. Among quartets, isomer 10 is the most stable molecule. The next quartet electronic state (of isomer 11) is 34.4 kcal mol-1 above 10, and all other quartet electronic states of other isomers are not energetically close to low-lying doublet isomers 2 to 6. Overall, the chemical space of MgC3H contains more cyclic isomers (1, 2, and 3) on the low-energy side unlike their even-numbered MgCnH counterparts (n = 2, 4, and 6). Though the quartet electronic state of 10 is linear, it is not the global minimum geometry on the MgC3H potential energy surface. Isomerization pathways among the low-lying isomers (doublets of 1-4 and a quartet of 10) reveal that these molecules are kinetically stable. For the cation, MgC3H+, the cyclic isomers (1+, 2+, and 3+) are on the low-energy side. The singlet linear isomer, 10+, is a fourth-order saddle point. The low-lying cations are quite polar, with dipole moment values of >7.00 D. The current theoretical data would be helpful to both laboratory astrophysicists and radioastronomers for further studies on the MgC3H0/+ isomers.

Introduction

Finding molecules many light years away is not only an open challenge to the scientific community but also an essential study that needs to be undertaken for a thorough understanding of star-forming regions, the formation of planets, and astrobiology.[1−9] To confirm the molecules in an unambiguous manner in the interstellar medium (ISM) and circumstellar shells, laboratory rest frequencies are an essential prerequisite in most cases.[10−23] Therefore, logically analyzing astrochemical issues requires a coordinated effort from experts across the scientific community, which includes radioastronomers, astrophysicists, molecular spectroscopists, organic chemists, electrical engineers, and quantum information scientists.[24−33] As an example, let us take the case of a linear MgC2H radical. The pure rotational spectrum of 1-magnesaprop-2-yn-1-yl (MgC2H, 2Σ+) was recorded by Ziuyrs and co-workers in 1995.[34,35] It was speculated at that time that MgC2H would be present in the ISM because it is isoelectronic with MgNC[36] and MgCN.[37] Through ab initio calculations, Woon suggested the formation pathways of MgC2H, MgC2H+, and cyclic-MgC2 in the ISM.[38,39] Nearly two decades later, MgC2H was tentatively assigned in the evolved carbon star, IRC+10216, in 2014.[40] Five years later, in 2019, the presence of MgC2H was finally confirmed along with the findings of MgC4H and MgC3N.[41] It is noted here that the confirmation of MgNC (2Σ+) in IRC+10216 triggered interest in this molecule as well as in other organomagnesium compounds.[42−48] MgNC has also been identified in two protoplanetary nebulae, CRL 2688 and CRL 618.[49,50] The metastable isomer of the MgNC radical, MgCN, was also confirmed in IRC+10216 in 1995.[37] In 2021, the presence of MgC6H (1-magnesahept-2,4,6-triyn-1-yl) was also confirmed.[51] Naturally, these observations consequently provoke a question regarding the presence of odd series of MgCH isomers (where, n = 3, 5, 7, etc.,) in IRC+10216 and/or in other interstellar sources. Thus, in this work, we have theoretically characterized the potential energy surfaces of MgC3H and MgC3H+ using density functional theory and coupled-cluster methods.

Though several experimental studies have been carried out to record the electronic transitions of MgC2H (n = 1–3) in the visible region (in the gas phase),[52−55] the number of experimental studies for the odd series MgC2H (n ≥ 2) appears to be limited. In the past, Largo and co-workers carried out theoretical studies for MgC3 and MgC3H+ isomers at the MP2(full)/6-311G(d) and B3LYP/6-311G(d) levels.[56,57] Dong et al. have observed a great number of magnesium carbon hydride clusters (MgCH) by the ablation of Mg foil into a mixture of 10% CH4/He expansion gas in their mass spectra.[58] Notably, in their experiments, clusters with odd mass numbers (that is, systems containing an odd number of electrons) are detected, and no signal related to MgC3H isomers was observed.[58] Graham and co-workers have recorded the vibrational spectrum of the linear MgC3– anion using Fourier transform infrared (FTIR) spectroscopy.[59]

Theoretical studies including structures, energetics, and spectroscopic properties of MgC3H isomers have been missing until now in the literature. Thus, isomers of MgC3H in their doublet and quartet electronic states (Figures and 2) are characterized for the first time in this work. Six low-lying doublet isomers, 2-magnesabicyclo[1.1.0]but-1,3,4-triyl (1), magnesium-substituted cyclopropenylidene (2), 1-magnesabut-2,3-dien-1-yl-4-ylidene (3), 1-magnesabut-2-yn-1-yl-4-ylidene (4), 2λ3-magnesabicyclo[1.1.0]but-1,3-diyl-4-ylidene (5), and 1-magnesabut-2,3-dien-2-yl-4-ylidene (6), and one low-lying quartet isomer, 1-magnesabutatrienyl (10), could be considered to be suitable target molecules for experimental observations. Unlike the MgCH (where, n = 2, 4, 6, etc.) even series, where the global minima are linear molecules with the magnesium atom at one end, here for MgC3H, a cyclic isomer (1) was identified to be the global minimum geometry. Considering the presence of Mg+ and C3H (both prop-1-yn-3-ylidyne and cycloprop-1-yn-3-yl) radicals in the ISM,[60−65] it is anticipated that isomers of MgC3H could also be present. However, the prerequisite for detecting these molecules many light years away is the availability of laboratory rest frequencies,[66−74] but there appear to be no laboratory astrophysical studies for this system at the moment. Thus, computational studies are undertaken, which may aid not only the laboratory studies but also the radioastronomical observations.

Figure 1

Isomers 1–11 of MgC3H in their doublet ground electronic states. Relative energies (ZPVE inclusive, in kcal mol–1) and dipole moments (in Debye) are calculated at the ROCCSD(T)/cc-pVTZ level. Values shown in parentheses are calculated at the CBS-QB3 level. The number of imaginary frequencies (NImag) obtained for each geometry is also given. Here, NA stands for not applicable, which means that the geometry either did not converge or led to some other geometry at that particular level.

Figure 2

Isomers 1–11 of MgC3H in their quartet ground electronic states. Relative energies (ZPVE inclusive, in kcal mol–1) and dipole moments (in Debye) are calculated at the ROCCSD(T)/cc-pVTZ level. Values shown in parentheses are calculated at the CBS-QB3 level. The number of imaginary frequencies (NImag) obtained for each geometry is also given.

Computational Details

For the doublet and quartet electronic states of MgC3H and also for the triplet electronic states of MgC3H+, the geometry optimization calculations are initially carried out at the UωB97XD[75]/6-311++G(2d,2p)[76,77] level. For the singlet electronic states of MgC3H+, calculations are made at the same level using restricted Hartree–Fock (RHF) wave functions. Vibrational frequencies (harmonic) are calculated for each stationary point to confirm whether it is a minimum, transition state, or nth-order saddle point. The number of imaginary frequencies (NImag) obtained for each stationary point is indicated underneath the geometry. To obtain better relative energies, single-point energy calculations are carried out using the coupled-cluster (CC) method at either the UCCSD(T)[78,79]/6-311++G(2d,2p) or RCCSD(T)/6-311++G(2d,2p)/ωB97XD[75]/6-311++G(2d,2p) level on top of the optimized geometries obtained from density functional theory (DFT). The ωB97XD functional has been purposefully chosen because it incorporates empirical dispersion corrections[80] as well as long-range corrections. Full geometry optimization and frequency calculations for all MgC3H isomers (doublets and quartets) are also carried out at the ROCCSD(T)/cc-pVTZ level. To further evaluate the relative energies, calculations are made using the composite methods, G3//B3LYP,[81] G4(MP2),[82,83] and CBS-QB3.[84,85] These relative energies are documented in Tables and 2 for MgC3H and MgC3H+ isomers, respectively.

Table 1

ZPVE-Corrected Relative Energies of MgC3H Isomers in their Doublet and Quartet Ground Electronic States Calculated at Different Levels

	doublets
	1	2	3	4	5	6	7	8	9	10	11
level	2A1	2A′	2A′	2A″	2A1	2Σ+	2A1	2A1	2A′	2Σ+	2Σ+
ROωB97XD/6-311++G(2d,2p)	0.0	6.9	28.0d	30.2	30.3	34.5	51.0	b	b	32.1	72.6
UωB97XD/6-311++G(2d,2p)	0.0	6.8	25.6d	28.1	29.1	32.3	49.6	52.5	52.8	54.1	71.8
UCCSD(T)/6-311++G(2d,2p)a	0.0	8.1	27.0d	14.3	31.9	33.1	55.3	49.4	49.4	54.2	65.2
G3//B3LYP	0.0	7.9	c	17.7	29.2	30.1	50.8	50.8	52.5	8.7e	66.2
G4MP2	0.0	7.8	c	18.5	29.2	33.2	51.1	51.4	52.1	59.8	68.1
ROCCSD(T)/cc-pVTZ	0.0	8.6	17.7	21.7	28.8	31.7	50.9	b	b	54.1	68.5
CBS-QB3	0.0	7.9	c	13.5	29.0	31.1	50.5	45.7	46.5	4.8f	68.2

Calculated at the UCCSD(T)/6-311++G(2d,2p)//UωB97XD/6-311++G(2d,2p) level.

Geometry optimization at this level for isomer 8 or 9 leads to isomer 1.

Geometry optimization at this level for isomer 3 or 4 leads to isomer 10.

The electronic state is 2A″.

The wave function is highly spin-contaminated (⟨S2⟩ = 1.799861) at this level, and thus the relative energies are not in order.

The wave function is highly spin-contaminated (⟨S2⟩ = 1.796338) at this level, and thus the relative energies are not in order.

Geometry optimization at this level for isomer 9 leads to isomer 8.

Table 2

ZPVE-Corrected Relative Energies of MgC3H+ Isomers in their Singlet and Triplet Ground Electronic States Calculated at Different Levels

	singlets
level	1	2	3	4	5	6	7	8	9	10	11
ωB97XD/6-311++G(2d,2p)	0.0	16.0	22.4	29.6	78.4	62.6	89.3	b	b	35.2	123.1
CCSD(T)/6-311++G(2d,2p)a	0.0	15.4	19.0	21.6	71.9	52.8	81.2	b	b	35.2	108.1
G3//B3LYP	0.0	14.7	19.3	19.0	70.7	51.6	80.6	b	b	33.7	110.6
G4MP2	0.0	14.2	19.7	18.3	69.1	52.4	80.5	b	b	35.2	111.0
CCSD(T)/cc-pVTZ	0.0	15.6	19.6	21.4	70.0	52.3	80.6	b	b	33.4	110.4
CBS-QB3	0.0	15.7	20.7	21.2	72.8	54.8	83.6	b	b	35.1	112.6

Calculated at the (U)CCSD(T)/6-311++G(2d,2p)//U)ωB97XD/6-311++G(2d,2p) level.

Geometry optimization at this level for isomer 8 or 9 leads to isomer 1.

Geometry optimization at this level for isomer 3 or 4 leads to isomer 10.

For the low-lying doublet isomers, appropriate transition states have been identified at the UωB97XD/6-311++G(2d,2p) level, and isomerization pathways were confirmed through intrinsic reaction coordinate (IRC)[86,87] calculations at the same level. To accurately determine the activation energy barriers, single-point energy calculations were made at the UCCSD(T)/6-311++G(2d,2p)//UωB97XD/6-311++G(2d,2p) level. To assess the multireference character, T1 diagnostic values[88] have been calculated at the UCCSD/6-311++G(2d,2p)//UωB97XD/6-311++G(2d,2p) level of theory. To check the kinetic stability of isomers 1 (2A1) and 10 (4Σ+), ab initio molecular dynamics (AIMD) simulations using the atom-centered density matrix propagation (ADMP)[89] method are carried out at the UωB97XD/6-311++G(2d,2p) level of theory. All DFT calculations, calculations that involve composite methods, and AIMD simulations are carried out with the Gaussian suite of programs.[90] All coupled-cluster calculations have been carried out with the CFOUR (2.00 beta version) program package.[91]

Results and Discussion

Optimized structures of isomers 1–11 of MgC3H0/+ in doublet, quartet, and singlet electronic states are shown in Figures , 2, and 3, respectively. For brevity, triplet electronic states of MgC3H+ are not shown here because all of them energetically lie above singlets. Zero-point vibrational energy (ZPVE)-corrected relative energies obtained at various levels for MgC3H and MgC3H+ isomers are shown in Tables and 2, respectively. Various spectroscopic parameters of isomers 1, 10, and 2 are collected in Tables , 4, and 5, respectively.

Figure 3

Isomers 1–11 of MgC3H+ in their singlet ground electronic states. ZPVE-corrected relative energies (in kcal mol–1) and dipole moments (in Debye) are calculated at the CCSD(T)/cc-pVTZ level. Values in parentheses are calculated at the CBS-QB3 level. The number of imaginary frequencies (NImag) obtained for each geometry is also given.

Table 3

Inertial Axis Dipole Moment Components, Absolute Dipole Moment (in Debye), Rotational and Centrifugal Distortion Constants (in MHz), Harmonic Vibrational Frequencies (in cm–1), and IR Intensities (Given in Parentheses, in km mol–1) of the 2A1 Electronic State of Isomer 1 Calculated at Different Levelsa

	6-311++G(2d,2p)		cc-pVTZ
parameter	ROωB97XD	UωB97XD	ROCCSD(T)	UCCSD(T)	description
μa	–0.1908	–0.1832	–0.1871	–0.1844
μb
|μa|	0.1908	0.1832	0.1871	0.1844
Ae	37 353.86	37 353.83	35 921.12	35 920.68
Be	5040.82	5040.82	5023.66	5023.01
Ce	4441.45	4441.45	4407.29	4406.78
ΔJ			0.1886 × 10–2	0.1887 × 10–2
ΔK			0.2392	0.2392
ΔJK			0.2579 × 10–1	0.2584 × 10–1
δJ			0.2545 × 10–3	0.2545 × 10–3
δK			0.1947 × 10–1	0.1950 × 10–1
ω1 (a1)	3238.4 (1.6)	3238.7 (1.7)	3238.6 (1.6)	3238.6 (1.6)	C–H stretch
ω2 (a1)	1620.3 (18.7)	1620.3 (18.7)	1577.1 (15.7)	1577.1 (15.7)	C–C–C stretch
ω3 (a1)	876.9 (35.2)	876.8 (35.4)	825.9 (29.1)	825.8 (29.1)	C–C stretch
ω4 (a1)	451.9 (106.1)	451.9 (106.0)	463.9 (94.2)	463.8 (94.2)	Mg–C2 stretch
ω5 (b1)	886.6 (1.2)	887.0 (1.2)	862.5 (1.3)	862.4 (1.3)	C–H wagging (out of plane)
ω6 (b1)	232.4 (8.1)	232.9 (8.0)	225.9 (6.5)	225.9 (6.5)	C–C–C twist (out of plane)
ω7 (b2)	1346.8 (5.6)	1347.0 (5.6)	1329.9 (4.6)	1329.9 (4.6)	CCC bend (in plane)
ω8 (b2)	1007.2 (9.9)	1007.4 (9.9)	1010.7 (10.7)	1010.7 (10.7)	C–H wagging (in plane)
ω9 (b2)	271.5 (60.3)	271.6 (60.2)	287.6 (52.2)	287.4 (52.2)	CCMg bend (in plane)

Centrifugal distortion constants are from the A-reduced Hamiltonian.

Table 4

Inertial Axis Dipole Moment Components, Absolute Dipole Moment (in Debye), Rotational and Centrifugal Distortion Constants (in MHz), Harmonic Vibrational Frequencies (in cm–1), and IR Intensities (in Parentheses, in km mol–1) of the 4Σ+ Electronic State of Isomer 10 Calculated at Different Levels

	6-311++G(2d,2p)		cc-pVTZ
parameter	ROωB97XD	UωB97XD	ROCCSD(T)	UCCSD(T)	description
μa	1.7020	1.6977	1.5565	1.5837
μb
|μa|	1.7020	1.6977	1.5565	1.5837
Be	2396.12	2390.48	2359.18	2359.85
DJ			0.2704 × 10–3	0.2694 × 10–3
DK			0.2704 × 10–3	0.2694 × 10–3
DJK			–0.5408 × 10–3	–0.5387 × 10–3
ω1 (σg+)	3460.9 (78.1)	3451.8 (70.8)	3439.8 (74.5)	3445.4 (76.2)	C–H stretch
ω2 (σg+)	1664.5 (0.5)	1661.8 (4.9)	1618.5 (2.1)	1661.1 (4.7)	C–C stretch
ω3 (σg+)	1270.8 (41.0)	1322.3 (40.6)	1283.5 (36.2)	1288.3 (36.2)	C–C–Mg stretch
ω4 (σg+)	439.4 (99.0)	439.0 (97.3)	438.3 (84.4)	439.2 (83.8)	C–Mg stretch
ω5 (π)	455.6 (5.7)	449.5 (0.3)	556.8 (39.5)	444.7 (0.7)	C–C–H bend
ω6 (π)	439.2 (49.5)	292.9 (52.1)	507.9 (4.9)	183.0 (46.1)	C–C–H bend
ω7 (π)	119.1 (11.5)	118.5 (10.9)	123.3 (20.1)	114.3 (7.6)	C–C–Mg bend

Table 5

Inertial Axis Dipole Moment Components, Absolute Dipole Moment (in Debye), Rotational and Centrifugal Distortion Constants (in MHz), Harmonic Vibrational Frequencies (in cm–1), and IR Intensities (in Parentheses, in km mol–1) of 2A′ Electronic State of Isomer 2 Calculated at Different Levelsa

	6-311++G(2d,2p)		cc-pVTZ
parameter	ROωB97XD	UωB97XD	ROCCSD(T)	UCCSD(T)	description
μa	–3.9832	3.9723	3.1792	3.1531
μb	–1.9716	–1.9572	2.6699	2.6659
|μa|	4.4444	4.4284	4.1516	4.1291
Ae	36 269.11	36 269.12	35 529.29	35 543.24
Be	3730.78	3730.78	3718.44	3722.60
Ce	3382.81	3382.81	3366.15	3369.68
DJ			0.5380 × 10–2	0.7064 × 10–2
DK			–0.5034	–0.9187
DJK			0.6839	1.1186
D1			–0.5432 × 10–3	–0.7347 × 10–3
D2			–0.4687 × 10–3	–0.7684 × 10–3
ω1 (a′)	3231.7 (4.07)	3231.7 (4.0)	3227.0 (4.5)	3227.4 (4.5)	C–H stretch
ω2 (a′)	1640.7 (9.8)	1639.9 (8.2)	1606.5 (13.6)	1607.3 (13.5)	C=C stretch
ω3 (a′)	1302.3 (22.2)	1301.6 (23.7)	1281.1 (15.0)	1281.2 (15.0)	C–C–H bend
ω4 (a′)	976.7 (10.0)	975.5 (10.5)	947.6 (9.8)	947.8 (9.7)	CCC bend
ω5 (a′)	940.8 (19.1)	941.1 (18.7)	925.4 (17.6)	925.7 (17.8)	C–H wag (in plane)
ω6 (a′)	411.3 (50.5)	410.4 (48.6)	426.8 (46.5)	427.4 (46.5)	C–Mg bend
ω7 (a′)	87.9 (15.8)	88.4 (15.5)	45.6 (15.2)	38.9 (15.3)	C3H kink
ω8 (a″)	891.7 (6.0)	892.0 (6.1)	868.0 (6.2)	867.8 (6.2)	C–H wag (out of plane)
ω9 (a″)	216.2 (0.1)	216.1 (0.0)	208.7 (0.1)	207.7 (0.2)	CCMg bend (out of plane)

Centrifugal distortion constants are from the S-reduced Hamiltonian.

Energetics

MgC3H

After analyzing the doublet and quartet electronic states of various isomers of MgC3H, one could arrive at a conclusion that the doublet electronic state (2A1) of 2-magnesabicyclo[1.1.0]but-1,3,4-triyl (1) is the most stable isomer at various levels (see Table ). From the energetic perspective, the first six isomers of the doublet (1–6) and the quartet of isomer 10 lie within 1.5 eV (∼34.6 kcal mol–1). Therefore, the possibility of finding these molecules in the laboratory is quite high. Among the doublets, isomers 1 (μ = 0.19 D) and 5 (μ = 0.42 D) are less polar whereas 2, 3, 4, and 6 are quite polar, with dipole moment values of 4.15, 2.77, 4.32, and 4.25 D, respectively. Isomer 10 of the quartet is also moderately polar (μ = 1.56 D). Though the doublet of 10 is highly polar (μ = 7.90 D), it lies 54.1 kcal mol–1 above 1 at the ROCCSD(T)/cc-pVTZ level. It is noted here that the relative energies obtained with respect to G3//B3LYP and CBS-QB3 methods for the doublet electronic state of isomer 10 are not in good agreement compared with other methods (see Table ). The reason for this discrepancy is due to a large amount of spin contamination in both the G3//B3LYP and CBS-QB3 methods. Both methods use the UB3LYP functional for the geometry optimization. Ideally, for a doublet electronic state, the ⟨S2⟩ value should be 0.75. However, the values we obtained for isomer 10 were 1.799861 and 1.796338, respectively. The initial wave function is certainly very badly spin-contaminated; consequently, the energies are not in the correct order compared to other levels. We did do a stability analysis of the optimized geometries of 10 obtained through the G3//B3LYP and CBS-QB3 methods.[92] It is noted here that the wave functions are symmetry-broken and show UHF instabilities.[93] For these reasons, the energies reported with respect to the G3//B3LYP and CBS-QB3 methods for isomer 10 are unreliable. Thus, we rely on coupled-cluster data and other levels of theory for the relative energy of this isomer.

From the thermodynamic stability point of view, the quartet of isomer 10 is the second-most-stable isomer because it lies 8.0 kcal mol–1 above the doublet of 1. The doublet of isomer 2 is the third-most-stable isomer because it lies at 8.6 kcal mol–1 above 1. Therefore, further emphasis is mostly given to these three molecules (doublets of 1 and 2 and a quartet of 10) instead of all low-lying isomers. It is noted here that, among the doublets, geometry 8 is a transition state and all others are minima at the ROCCSD(T)/cc-pVTZ level. In the case of quartets, geometry optimization of isomers 3 and 4 leads to isomer 10, whereas isomer 9 geometry optimization leads to isomer 8. Therefore, in total, merely eight stationary points were found within the quartet electronic states.

On the basis of the multireference characteristics of C3H isomers discussed elsewhere,[65] we suspected that some of the isomers of MgC3H may have multireference characteristics. To clarify this, we have computed the T1 diagnostic values[88] for all isomers at the UCCSD/6-311++G(2d,2p)//UωB97XD/6-311++G(2d,2p) level. Calculated T1 diagnostic values for isomers 1, 2, 5, and 11 were 0.013, 0.014, 0.019, and 0.017, respectively. Because these values are less than 0.020, one can state that these isomers are not multireference in character. For isomer 7, the value obtained was 0.022, which is slightly above the threshold. For isomers 3, 4, 6, 8, 9, and 10, the calculated T1 values were 0.118, 0.162, 0.052, 0.139, 0.141, and 0.058, respectively. The quartet of isomer 10 also shows moderate multireference character with a T1 value of 0.039. Although we have not carried out multireference coupled-cluster (MRCC) or complete active space self-consistent field calculations on any of these isomers, we note that such a study is deferred to future work.

MgC3H+

The relative stabilities of both singlet and triplet electronic states of MgC3H+ isomers (1–11) have been calculated at different levels, and they are collected in Table . Like the doublet neutral radicals, on the cation PES, the singlet electronic state of 2-magnesabicyclo[1.1.0]but-1,3,4-triyl (1) is the most stable isomer. The singlets of isomers 2, 3, and 4 are 15.6, 19.6, and 21.4 kcal mol–1 above the singlet of 1, respectively, at the CCSD(T)/cc-pVTZ level. The singlet linear isomer, 10, is a fourth-order saddle point, and isomer 5 turned out to be a transition state at the latter level. Geometry optimization of 8 and 9 at all levels led to 1. All of the stationary points on the cation PES had higher polarity due to the positive charge. The dipole moment values of the first four isomers (1–4) are 7.84, 12.32, 7.32, and 7.93 D, respectively. Therefore, apart from neutrals, the cations are also suitable candidates for microwave spectroscopic and radioastronomical studies. It is noted here that the triplet electronic states of all cations are above the singlet electronic state of 1.

2-Magnesabicyclo[1.1.0]but-1,3,4-triyl (1)

The point-group symmetry of 1 is C2, and the ground electronic state is 2A1. The quartet electronic state (4B1) of 1 is a second-order saddle point and is 83.1 kcal mol–1 above the doublet of 1. Though the former is energetically the most stable molecule for MgC3H at all levels studied here, it remains elusive in the laboratory to date. The binding energy (BE) for 1 (BE = EMgC – (Ec–C + EMg)) is −47.2 kcal mol–1 at the (U)ωB97XD/6311++G(2d,2p) level of theory. Therefore, the molecule is sufficiently bound and the Mg–C bonds are not extremely weak. The transannular C–C bond length obtained at all levels (1.53 to 1.54 Å) reveals that it exhibits single-bond characteristics. Therefore, resonance structure 1a is more dominant than 1b (see Figure ). Though isomer 1 is less polar (μ = 0.19 D), in principle, it can be identified through rotational spectroscopy. We note that there are weakly polar van der Waals complexes such as the Ne–Ar dimer whose dipole moment is just 0.0022 D, yet pure rotational transitions have been measured.[94] Equilibrium rotational constants Ae, Be, and Ce obtained from the optimized geometries at different levels (see Table ) reveal that this molecule is an asymmetric top. In addition, one can also detect isomer 1 through IR spectroscopy. Although two of the low-frequency modes ν9 (287.6 cm–1, CCMg bending) and ν4 (463.9 cm–1, Mg–C2 stretching) are very intense, one cannot confirm these modes easily. On the other hand, ν8 (1010.7 cm–1, C–H wagging) and ν2 (1577.0 cm–1, CCC stretching) modes could readily be seen (see Table ).

Figure 4

Valence structures of isomers 1 and 10 of MgC3H.

1-Magnesabutatrienyl (10)

The ground electronic state of 10 is 4Σ+. It lies 8.0 kcal mol–1 above 1 of the doublet at the ROCCSD(T)/cc-pVTZ level. This C-symmetric linear molecule is the second-most-stable isomer for MgC3H, and it is ∼8 times polar than 1 with a dipole moment value of 1.56 D. However, this molecule also remains elusive in the laboratory to date. The binding energy (BE) for 10 (BE = EMgC – (El–C + EMg)) is −45.4 kcal mol–1 at the (U)ωB97XD/6-311++G(2d,2p) level of theory. This implies that the Mg atom is sufficiently bound to the carbon atom. The BE values we have calculated for isomers 1 and 10 indirectly support the relative energy ordering we have obtained for these two isomers because the most stable isomer has the highest binding energy. Six different valence structures are shown in Figure for isomer 10. Three structures (10a, 10c, and 10e) represent the quartet electronic state and the other three (10b, 10d, and 10f) represent the doublet electronic state. On the basis of the bond lengths obtained, it is evident that valence structure 10a is dominant because the C–C bond length of 1.26 Å (connected to the H atom) exhibits triple-bond characteristics whereas the other C–C bond length is intermediate between a double and a triple bond. The rotational and centrifugal distortion constants obtained at various levels are shown in Table . The C–H stretching (ν1) and C–C–Mg stretching (ν3) modes whose frequencies are 3439.8 and 1283.5 cm–1, respectively, at the ROCCSD(T)/cc-pVTZ level could readily be seen in the IR spectra.

Magnesium-Substituted Cyclopropenylidene (2)

The point-group symmetry of 2 is C, and the ground electronic state is 2A′. This molecule is 8.6 kcal mol–1 above the doublet of 1 and is the third-most-stable isomer on the MgC3H potential energy surface. The quartet electronic state (4A″) of 2 is also a minimum, but it lies 53.0 kcal mol–1 above 1. Among the three low-lying minima, isomer 2 is the highest polar molecule with a dipole moment value of 4.15 D at the ROCCSD(T)/cc-pVTZ level. Therefore, the chances of identifying this molecule both in the laboratory and in the ISM are high. Moreover, the inertial axis dipole moment components are in two directions for this molecule (see Table ), and thus both a- and b-type rotational transitions are possible. Moreover, from equilibrium rotational constants Ae, Be, and Ce, one could infer that this molecule is closely approaching the prolate limit because the difference between the Be and Ce rotational constants is not very high. The C=C stretching (ν2) and CCH bending (ν3) modes whose frequencies are 1606.5 and 1281.1 cm–1, respectively, at the ROCCSD(T)/cc-pVTZ level could readily be seen in the IR spectra.

Other Low-Lying Isomers of MgC3H0/+

Apart from the doublet electronic states of isomers 1 and 2 and the quartet electronic state of isomer 10, the doublet electronic states of isomers 3, 4, and 5 of MgC3H could be considered to be low-lying isomers based on the relative energies (below 30 kcal mol–1). Except 5, which is less polar, the other three isomers are quite polar. Likewise, for the cation, apart from singlet 1, the three other singlet isomers (2–4) could be considered to be low-lying isomers. Therefore, the chances of identifying these molecules both in the laboratory and in the ISM are moderate.

Isomerization Pathways

To assess the kinetic stability of the low-lying doublet (1–4) and quartet (10 and 11) isomers, transition states have been identified initially at the UωB97XD/6-311++G(2d,2p) level, and the minimum-energy pathways are confirmed through IRC calculations at the same level. To accurately determine the activation energy barriers, single-point energy calculations are carried out at the UCCSD(T)/6-311++G(2d,2p)//UωB97XD/6-311++G(2d,2p) level. In Figures –7, a schematic outline of the isomerization pathways of isomers 1 to 2, 2 to 3 (as well as 4 and 9), and 10 to 11, respectively, is shown. Altogether, five different transition states (TS1–TS5) have been identified. The dissociation of the C–Mg bond (either one) of 1 leads to TS1 with an activation energy of 8.2 kcal mol–1. The reaction energy calculated for the isomerization of 1 to 2 is just 8.1 kcal mol–1. This indirectly implies that the reverse process (2 to 1) is nearly barrierless. Therefore, isomer 1 is certainly a kinetically stable molecule.

Figure 5

Isomerization pathway of isomer 1 to 2 (doublets). Relative energies are calculated at the UCCSD(T)/6-311++G(2d,2p)//UωB97XD/6-311++G(2d,2p) level.

Figure 7

Isomerization pathway of isomer 10 to 11 (quartets). Relative energies are calculated at the UCCSD(T)/6-311++G(2d,2p)//UωB97XD/6-311++G(2d,2p) level.

For the isomerization of 2, three different transition states (TS2, TS3, and TS4; see Figure ) have been identified. By bringing the C–Mg bond closer to the carbene carbon of 2, one could get a puckered four-membered transition state with a trans-annular C–C bond. The activation energy for TS2 is 37.1 kcal mol–1. IRC calculations from this lead to isomer 3 with a reaction energy of 18.9 kcal mol–1. We also identified two more transition states by breaking the C–C single bonds of the cyclopropenylidene ring of 2. The activation energies for TS3 and TS4 are 62.4 and 78.1 kcal mol–1, respectively. These are high-energy transition states; therefore, the conversions of 2 to 9 and 2 to 4 are unlikely to occur. The isomerization of 2 to 3 is also unlikely because it requires an activation of energy of 37.1 kcal mol–1. However, isomerization of 2 to 1 is barrierless and thus 2 is not a kinetically stable molecule. Next, we turned our attention to the low-lying quartet isomers (10 and 11) because the quartet of isomer 10 is the second-most-stable molecule thermodynamically. It is also worth mentioning here that among the quartets, isomer 10 is the most stable molecule. Bending of the C–Mg bond of 10 leads to TS5 and thus the isomerization of 10 to 11 requires an activation energy of 78.5 kcal mol–1, which is quite high. Therefore, we conclude that the quartet linear isomer of 10 is not only a thermodynamically stable but also a kinetically stable molecule.

Figure 6

Isomerization pathway of isomer 2 to others (3, 4, and 9; doublets). Relative energies are calculated at the UCCSD(T)/6-311++G(2d,2p)//UωB97XD/6-311++G(2d,2p) level.

Ab Initio Molecular Dynamics

Apart from identifying transition-state geometries and confirming the minimum-energy paths through IRC calculations, we have also carried out abinitio molecular dynamics simulations to reaffirm the kinetic stability of two of the lowest lying isomers of MgC3H (a doublet of 1 and a quartet of 10). These calculations were made using the ADMP[89] approach as incorporated in the Gaussian 16 program.[90] These simulations were carried out at 298 K and 1 atm pressure for 10 000 fs. For isomers 1 and 10, the time evolutions of total energies are shown in Figures and 9, respectively. To show the geometric changes that are happening to each isomer over 10 000 fs, snapshots at 2000 fs interval are added. These figures show a balanced oscillation in the energies and also firmness in the geometries over the entire time period. Therefore, one can further conclude that these molecules are indeed kinetically stable.

Figure 8

Energy evolution of isomer 1 (2A1) of MgC3H obtained from the AIMD simulation carried out at 298 K and 1 atm pressure for 10 000 fs at the UωB97XD/6-311++G(2d,2p) level.

Figure 9

Energy evolution of isomer 10 (4Σ+) of MgC3H obtained from the AIMD simulation carried out at 298 K and 1 atm pressure for 10 000 fs at the UωB97XD/6-311++G(2d,2p) level.

Conclusions

Various isomers of MgC3H0/+ are studied in this work, which are systems of potential interstellar interest, by using DFT, coupled-cluster, and thermochemical modules. For both MgC3H0/+, the most stable isomer turns out to be isomer 1 (1), which is a cyclic molecule. This is a stark contrast compared to the even-numbered MgCH isomers (n = 2, 4, etc.), where the most stable isomers are linear molecules. Linear isomer 10 within the quartet electronic state (4Σ+) was found to be the second-most-stable isomer thermodynamically at various levels. Though the doublet of 10 turns out to be a minimum at the ROCCSD(T)/cc-pVTZ level, it lies 54.1 kcal mol–1 above the doublet electronic state of 1. The doublet of 10 is certainly the most polar molecule with a dipole moment of 7.90 D. However, it lies in the high-energy region. Considering the presence of cyclic-C3H, linear-C3H, and Mg+ in the ISM, it is postulated here that the formation of isomers 1 and 10 is plausible. Though isomer 1 is less polar (μ = 0.19 D), the detection of 1 in the laboratory should be possible. On the other hand, the quartet electronic state of isomer 10 is moderately polar (μ = 1.55 D). Therefore, identifying isomer 10 in the laboratory may be more straightforward than identifying isomer 1. Among the three low-lying minima, isomer 2 is highly polar with a dipole moment value of 4.15 D. However, 2 is not kinetically stable at all because the isomerization pathway of 1 to 2 indicates that it will quickly revert back to 1. Therefore, the detection of this molecule in the laboratory will be very challenging. It is also noted here that the doublet electronic states of isomers 3, 4, and 6 are quite polar with dipole moments of 7.45, 3.04, and 4.38 D, respectively. Therefore, the detection of these molecules is also possible though they are on the high-energy side. Isomerization pathways indicate that the three low-lying isomers (doublets of 1 and 4 and a quartet of 10) are kinetically stable molecules. For MgC3H+, the cyclic isomers (1, 2, and 3) are on the low-energy side. The singlet linear isomer, 10, turned out to be a fourth-order saddle point at the CCSD(T)/cc-pVTZ level. Moreover, the low-lying cations are quite polar with dipole moment values of >7.00 D. Therefore, they are also suitable candidates for laboratory detection by rotational spectroscopy. To conclude, the structural, energetic, and rotational spectroscopic parameters computed in this work would aid both molecular spectroscopists and radioastronomers in the future.