Structure and Spectroscopic Properties of [Mg,C,N,O] Isomers

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Structure and Spectroscopic Properties of [Mg,C,N,O] Isomers: Plausible Astronomical Molecules Á lvaro Vega-Vega, Antonio Largo, Pilar Redondo, and Carmen Barrientos* Departamento de Química Física y Química Inorgánica, Facultad de Ciencias, Universidad de Valladolid, 47011 Valladolid, Spain ABSTRACT: Theoretical methodologies have been employed to study [Mg,C,N,O] isomers, which are possible species of interstellar interest. It has been found that, at all levels of theory used, the most stable isomer is the magnesium isocyanate radical. The corresponding cyanate counterpart lies 15.8 kcal/mol, at the CCSD(T) level of theory, above MgNCO. Other isomers, such as the magnesium fulminate radical, MgCNO, the magnesium isofulminate radical, MgONC, and the two compounds that arise from the insertion of the magnesium atom between either O−N or O−C bonds, namely, OMgNC and OMgCN, are located clearly higher in energy than MgNCO. The barrier for the MgOCN → MgNCO process has been calculated to be 4.6 kcal/mol, suggesting a slow rate for the isomerization reaction. To examine the bonding interactions in the different [Mg,C,N,O] isomers, a natural bond orbital analysis, together with a topological analysis of the electron density in the framework of Bader’s quantum theory of atoms in molecules, has been carried out. For the two lowest lying isomers, predictions for the thermodynamic stabilities and spectroscopic parameters, which could aid in the detection of these species, have been made. The infrared (IR) spectra of both MgNCO and MgOCN are dominated by intense bands associated with the σ-NCO asymmetric stretching mode, especially in the case of MgNCO. Both MgNCO and MgOCN have large dipole moments (4.84 and 7.59 D, respectively, at the CCSD/augcc-pVTZ level). These two factors will likely make observation of both systems easier with either space-based IR or ground-based sum-mm telescopes. The global analysis of the relative stabilities and spectroscopic parameters suggests two linear isomers, namely, MgNCO (2Σ+) and MgOCN (2Σ+), as possible candidates for laboratory and space detection. KEYWORDS: astrochemistry, interstellar medium general, interstellar medium molecules, interstellar medium structure, molecular data, MgNCO isomers reported8 in 2009, and in addition, four consecutive transitions of HOCN were tentatively identified in the Galactic center source Sgr B2(OH). One year later, the Sgr B2(OH) region was widely studied and the interstellar detection of cyanic acid in the galactic center clouds was definitively confirmed.9 In this context, the astrochemical interest of isomeric systems was emphasized because they can help constrain the chemical processes leading to their formation and depletion, whether they occur in the gas phase or on the surfaces of dust particles.9,10 In 1986, three doublets were detected in the envelope of the carbon star IRC+10216, which were tentatively assigned to a new free radical.11 The most likely candidates for such a radical were HSiCC, HCCSi, and HSCC. Some years later, the first radioastronomical identification of a magnesium-bearing molecule in space, magnesium isocyanide, MgNC, was reported.12 It was detected by laboratory microwave spectroscopy, and then the six unidentified lines in IRC+10216 were

1. INTRODUCTION Isocyanic acid, HNCO, was one of the earliest molecules to be observed in space.1 It was detected in emission through the 40,4−30,3 ground-state rotational transition at 3.4 mm in the Galactic center source Sgr B2(OH) in 1972. This identification was confirmed by the detection of a second transition at 1.4 cm.2 Isocyanic acid was also found in dark clouds,3 such as TMC-1, in 1981, and more recently, in 1999, it has been detected in three translucent clouds (CB 17, CB 24, and CB 228) and two dark clouds (TMC-1 and L183).4 The first detection in space of one of the isomers of HNCO, fulminic acid, HCNO, was reported in 2009.5 It was discovered in three starless cores, B1, L1544, and L183, and in the lowmass star-forming region L1527. Despite it being searched for, it was not detected toward the cyanopolyyne peak of TMC-1 or the Orion Hot Core region, where isocyanic acid was found. A third isomer of isocyanic acid, cyanic acid, HOCN, was a primary candidate, together with protonated carbon dioxide, HOCO+, for a harmonic series of rotational lines in Sgr B2.6 However, subsequent laboratory observation by sub-millimeter wave spectroscopy of these lines7 gave a definitive confirmation of the assignation of the astrophysical data to protonated carbon dioxide. The laboratory detection of HOCN was © 2017 American Chemical Society

Received: Revised: Accepted: Published: 158

March 6, 2017 March 31, 2017 April 10, 2017 April 10, 2017 DOI: 10.1021/acsearthspacechem.7b00019 ACS Earth Space Chem. 2017, 1, 158−167

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ACS Earth and Space Chemistry

Figure 1. Relative energies, including zero-point corrections, in kcal/mol of the [Mg,C,N,O] isomers at different levels of theory using the aug-ccpVTZ basis set. In the CCSD(T) results, core−valence corrections are included.

iron. Furthermore, magnesium isocyanide is one of the most abundant metal−(CN) compounds in space, and isocyanic acid and its isomers are important astrochemical molecules. In this context, it should be interesting to study [Mg,C,N,O] compounds as possible new interstellar magnesium-bearing molecules. In this paper, we present a theoretical study of tetratomic [Mg,C,N,O] isomers providing predictions of their stabilities, molecular structures, as well as spectroscopic parameters, which could help in their laboratory or astronomical detection. In addition, we present an analysis of the bonding in the context of Bader’s theory.17 To date, there

assigned to transitions of MgNC. The detection in the circumstellar envelope IRC+10216 of millimeter lines of two isotopomers was reported in 1995,13 and a few years later, magnesium isocyanide was also observed in protoplanetary nebulae.14 The magnesium cyanide isomer, MgCN, was detected toward the star IRC+10216 in 1995.15 More recently, in 2013, the identification of hydromagnesium isocyanide, HMgNC, was reported in the carbon-rich evolved star IRC +10216 after laboratory characterization.16 Magnesium is one of the most abundant metals in space, with a cosmic abundance comparable to those of silicon and 159

DOI: 10.1021/acsearthspacechem.7b00019 ACS Earth Space Chem. 2017, 1, 158−167

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parameters were computed at the CCSD/aug-cc-pVTZ level using Keith’s AIMAll40 package, including standard thresholds. The accuracy of the integration over the atomic basin (Ω) was assessed by the magnitude of the corresponding Lagrangian function, L(Ω) (−1/4 times the atomic integral of the Laplacian of the electron density), which, in all cases, was lower than 10−4 au. A complementary analysis of the intermolecular interactions from a natural bond orbital (NBO) analysis41 was also carried out at the B3LYP/aug-cc-pVTZ level of theory.

have been no previous theoretical or experimental studies on these [Mg,C,N,O] compounds.

2. COMPUTATIONAL METHODS The stationary points on the potential energy surface (PES) were characterized by optimizing molecular geometries initially at the density functional theory (DFT) level. In this context, the B3LYP hybrid exchange correlation functional,18,19 which includes the Lee−Yang−Parr20 correlation functional and a hybrid exchange functional proposed by Becke,21 was chosen. In addition, ab initio methodologies were employed in geometry optimizations. In particular, we employed secondorder Møller−Plesset theory (MP2),22 and for the more stable isomers, we performed subsequent coupled-cluster calculations with single and double excitations (CCSD) and with a perturbative inclusion of triple excitations [CCSD(T)].23 In the former, the T1 diagnostic24 was used to check the possible multireference character. In all cases, it was found below the 0.02 value25 that indicates that a multiconfigurational procedure is not necessary. Energetic calculations were carried out using the same levels of theory as those employed in geometry optimizations. The connection between the transition-state structures and minima has been checked through the intrinsic reaction coordinate (IRC) formalism.26 Harmonic vibrational frequencies and zero-point vibrational energies were computed on the optimized geometries at B3LYP, MP2, and CCSD levels using analytic second derivatives of the energy. The nature of the stationary points on the PES was tested by checking the number of negative eigenvalues of the analytical Hessian. To help in a possible experimental detection by infrared (IR) spectroscopy, anharmonic vibrational frequency calculations were performed for the most stable isomers. Anharmonic corrections were computed at the CCSD level of theory using the second-order perturbation treatment (VPT2).27 It is based on a full cubic force field (CFF) and semi-diagonal quartic force constants. From the CFF calculations, vibration−rotation interaction constants can also be evaluated, allowing for correction of rotational constants, including vibrational effects. The accuracy of the VPT2 method when used in conjunction with high-level methodologies has been widely pointed out.28 In all calculations, Dunning’s correlated consistent polarized valence triple ζ augmented with diffuse function basis sets,29,30 namely, aug-cc-pVTZ, were used. In correlated computations, the valence electrons of the carbon, nitrogen, and oxygen atoms and the 2s, 2p, and 3s electrons of magnesium were included. To refine the geometrical parameters, equilibrium rotational constants, and electronic energies computed at the CCSD(T)/ aug-cc-pVTZ level, we applied a composite procedure31−33 based on an additivity scheme for the electron correlation. In this scheme, core−valence effects were computed through the difference between a full-electron calculation and a frozen-core calculation using the CCSD level with the aug-cc-pCVTZ basis set.34,35 Thus, the core−valence corrections for structural parameters (Δr), equilibrium rotational constants (ΔBe), and electronic energies (ΔE) were obtained as Δr/ΔBe/ΔE(CV) = r/Be/E(CCSD-full/aug-cc-pCVTZ) − r/Be/E(CCSD/aug-ccpVTZ). Both GAUSSIAN 0936 and CFOUR37 packages of programs were used for quantum calculations. The nature of chemical bonds and interactions was analyzed in terms of the quantum theory of atoms in molecules (QTAIM) of Bader.17,38,39 In the present work, QTAIM

3. RESULTS AND DISCUSSION We have searched for various potentially stable [Mg,C,N,O] isomers, including open-chain (linear and bent) structures, with either the magnesium atom located at one end of the chain or in a middle position, and ring structures. In all cases, the quartet state of a given isomer lies considerably higher in energy than the corresponding doublet; therefore, we have only considered the doublet states in our study. 3.1. Energetics. The relative energies, with respect to the most stable isomer, of all species corresponding to true minima on the [Mg,C,N,O] PES are collected in Figure 1. In this figure, relative energies are tabulated at different levels of theory. According to our preliminary B3LYP calculations, magnesium isocyanate, MgNCO, in its 2Σ+ ground state (Figure 1a) is the most stable [Mg,C,N,O] isomer. This result is in concordance with experimental evidence, because isocyanates are often the final products in attempts to generate other isomers.42 The corresponding cyanate counterpart, MgOCN (2A′) lies around 18 kcal/mol (at the B3LYP level of theory) above MgNCO, as seen in Figure 1b. The same pattern was found in the HNCO/HOCN system, because at a similar level of theory [B3LYP/6-311G(d,p)] cyanic acid is 28.7 kcal/mol higher in energy than isocyanic acid.43 Both MgNCO and MgOCN can be seen as the result of substitution of the hydrogen atom in either isocyanic or cyanic acid by a magnesium atom. It should be noted that, at the B3LYP/augcc-pVTZ level, linear MgOCN with a 2Σ+ ground state has an imaginary frequency of 15i cm−1 toward bending out of the linear structure. However, the PES along the Mg−O−C bending mode is extremely flat. Additional B3LYP calculations were carried out for MgOCN bent geometries from Mg−O−C fixed bond angle values ranging from 170° to 180° and optimizing the remaining structural parameters. The energies obtained from the scan were all of them within differences smaller than 0.000 01 au, reflecting the extremely flat PES in the vicinity of the minimum for MgOCN. Following in energy, we found two isomers that arise from the insertion of the magnesium atom between either O−N or O−C bonds, of the corresponding ONC and OCN units, namely, cyanide-κN-oxidemagnesium, OMgNC, and cyanideκC-oxidemagnesium, OMgCN (panels c and d of Figure 1, respectively). These isomers, which show a linear arrangement with the 2Σ+ ground state, are located 46.8 and 48.2 kcal/mol, respectively, higher in energy than the magnesium isocyanate radical at the B3LYP/aug-cc-pVTZ level. The magnesium fulminate radical, MgCNO (2Σ+), and the magnesium isofulminate radical, MgONC (2A′), shown in panels f and e of Figure 1, lie 77.1 and 82.8 kcal/mol, respectively, higher in energy than the most stable isomer, MgNCO, at the B3LYP/aug-cc-pVTZ level. At similar relative energies, fulminic acid, HCNO, and isofulminic acid, HONC 160


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ACS Earth and Space Chemistry (67. and 87.1 kcal/mol, respectively42), were found with respect to isocyanic acid. We have also found a Y-shaped MgCON (2A′) isomer, namely, cyanate-κC-magnesium (Figure 1g), located 115.2 kcal/mol (at the B3LYP/aug-cc-pVTZ level) above the magnesium isocyanate radical. In principle, it could be seen as derived from either formylnitrene or oxazirine. This issue will be discussed below in subsequent sections. Higher in energy (see panels h and i of Figure 1) are other possible isomers, such as those arising from the interaction of the magnesium atom with the NOC moiety at either nitrogen [MgNOC (2A′)] or carbon [MgCON (2Σ+)] ends. These two isomers are located around 154 and 175 kcal/mol, respectively, higher in energy than MgNCO. Regardless of the level of calculation employed, the most stable isomer of the [Mg,C,N,O] system is the magnesium isocyanate radical, with the magnesium cyanate radical located 15.8 kcal/mol higher in energy at the best level of theory employed in the present work [CCSD(T)/aug-cc-pVTZ including core−valence corrections]. Thus, MgNCO and MgOCN are the primary targets for experimental studies. When going from B3LYP to the MP2 methodology, the stability order of some isomers is slightly modified mainly concerning OMgNC/OMgCN and MgNOC/MgCON pairs. In both cases, it seems that the MP2 theory favors isomers with magnesium−carbon bonds. On the other hand, the only discrepancy observed, regarding the energetic order, when passing from B3LYP to coupled cluster methodologies refers to the fulminate/isofulminate pair. The CCSD level predicts both isomers to be almost isoenergetic, with MgONC being slightly preferred. Let us now analyze the interconversion process between the two most stable isomers. The transition state for the MgOCN → MgNCO isomerization process is depicted in Figure 2. At

To obtain additional information on the thermodynamic stability, we considered various dissociation pathways of the most stable [Mg,C,N,O] isomers. In Table 1, we show the Table 1. Dissociation Energies, in kcal/mol, Calculated at the CCSD/aug-cc-pVTZ Level, Including Zero-Point Vibrational Corrections process MgNCO MgOCN MgNCO MgOCN OMgCN OMgNC

→ → → → → →

Mg + NCO Mg + NCO MgN + CO MgO + CN MgO + CN MgO + CN

D0 (kcal/mol) 142.4 127.3 247.6 267.8 242.2 243.8

CCSD/aug-cc-pVTZ dissociation energies corresponding to pathways leading to two different processes: (a) processes forming a magnesium atom plus a NCO unit and (b) processes giving two diatomic moieties. In the latter case, the dissociation energy for MgNCO is the energy associated with the production of MgN and CO fragments, whereas for MgOCN, OMgCN, and OMgNC, the dissociation energy corresponds to the formation of MgO and CN units. As seen from Table 1, for both MgNCO and MgOCN isomers, the dissociation energies corresponding to the formation of Mg and NCO are rather high (142.4 and 127.3 kcal/mol, respectively), whereas the corresponding dissociation energies associated with fragmentation into diatomic units are even higher, ranging from 242 to 267 kcal/mol. Consequently, these isomers will be stable against dissociation into either Mg + NCO units or diatomic fragments. 3.2. Structure. The structural properties for the [Mg,C,N,O] isomers obtained at different levels of theory are given in Table 2. In general, a good agreement among the structural parameters obtained at different levels of theory was observed. At the CCSD(T) level, including core−valence corrections, the lowest lying isomer MgNCO has a N−C bond length of 1.2029 Å and a C−O bond distance of 1.1830 Å. Both distances are not too far from the corresponding bond lengths in HNCO [r(N−C) = 1.2140 Å, and r(C−O) = 1.1664 Å] determined from pure rotational spectra.44 On the other hand, when comparing the common structural parameters of MgNCO and those of MgNC reported from rotational spectroscopy of several MgNC isotopomers,45 we note that our computed Mg− N bond distance in magnesium isocyanate (1.8856 Å) is slightly lower than experimental Mg−N bond lengths: r0(Mg−N) = 1.925 Å (determined from 24MgNC/25MgNC), and r0(Mg−N) = 1.924 Å (determined from 24MgNC/26MgNC). On the other hand, our computed N−C bond length (1.2029 Å) is somewhat larger than the measured bond lengths: r0(N−C) = 1.169 Å (determined from 24MgNC/25MgNC), and r0(N−C) = 1.172 Å (determined from 24MgNC/26MgNC). It can be noted that some small differences between experimental and theoretical bond lengths should be expected as a result of the neglect of the zero-point vibration in the theoretical data. The CO bond length in MgNCO (1.1850 Å) is close to the typical C−O double bond value (1.2000 Å). The spin density distribution for this molecule is 0.945e (Mg), 0.035e (N), 0.029e (C), and −0.006e (O). In addition, the magnesium natural atomic charge is 0.906. Consequently, taking into account the bond distance values, the charge densities, and the

Figure 2. PES corresponding to the MgOCN → MgNCO isomerization reaction. CCSD/aug-cc-pVTZ energies are given in kcal/mol and include zero-point vibrational corrections.

the CCSD/aug-cc-pVTZ level, the isomerization barrier for the MgOCN → MgNCO process is 4.6 kcal/mol (2290 K). It should be noted that this activation energy value is relative to the MgOCN energy; thus, the isomerization from MgNCO to MgOCN takes 19.6 kcal/mol. This barrier indicates that the isomerization reaction between the two most stable [Mg,C,N,O] compounds should have a very slow rate. Thus, despite the extremely long cosmological time scales, it is likely that both MgNCO and MgOCN could be present simultaneously in the interstellar medium if efficient synthesis processes exist. 161


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Table 2. Optimized Geometries of [Mg,C,N,O] Isomers Computed at Different Levels of Theory Using the aug-cc-pVTZ Basis Seta level isomer MgNCO (2Σ+)

MgOCN (2A′/2Σ+)

OMgNC (2Σ+)

OMgCN (2Σ+)

MgONC (2A′)

MgCNO (2Σ+)

Y-MgCON

MgOCN-TS

a

r(Mg−N) r(N−C) r(C−O) r(Mg−O) r(C−O) r(N−C) ∠Mg−O−C r(Mg−O) r(Mg−N) r(N−C) r(Mg−O) r(Mg−C) r(N−C) r(Mg−O) r(N−O) r(N−C) ∠Mg−O−N r(Mg−C) r(N−C) r(N−O) r(Mg−C) r(C−O) r(N−C) ∠Mg−C−O ∠O−C−N r(Mg−O) r(Mg−C) r(Mg−N) r(O−C) r(C−N) ∠Mg−O−C

B3LYP

MP2

CCSD

CCSD(T)

1.9031 1.1967 1.1789 1.8324 1.2581 1.1615 172.9 1.8609 1.9071 1.1731 1.8616 2.0358 1.1562 1.8876 1.3045 1.1700 124.8 2.0447 1.1730 1.2066 2.1461 1.3715 1.2490 133.7 80.2 2.0979 2.1640 2.5247 1.2469 1.1802 75.9

1.9002 1.2081 1.1868 1.8305 1.2635 1.1799 180 1.8578 1.9083 1.1865 1.8595 2.0284 1.1780 1.8459 1.2852 1.1876 148.3 2.0349 1.1570 1.2039 2.1206 1.3911 1.2549 135.0 77.9 2.0149 2.2166 2.7403 1.2620 1.1938 81.6

1.8934 1.1975 1.1782 1.8201 1.2624 1.1634 180 1.8536 1.8974 1.1775 1.8545 2.0285 1.1622 1.8314 1.2936 1.1713 147.6 2.0362 1.2936 1.2099

1.8856 1.2029 1.1830 1.8133 1.2643 1.1700 180

2.0818 2.1401 2.4699 1.2488 1.1816 75.4

Bond distances are given in angstroms, and angles are given in degrees. In the CCSD(T) results, core−valence corrections are included.

cyanate radical can be mainly described through these two resonant structures:

spin density distribution, the most important valence structure for magnesium isocyanate radical could be a cumulene type. However, the C−N bond length (1.2029 Å) is closer to a typical C−N triple bond (1.15 Å) than to a normal C−N double bond (1.27 Å), and the following resonant form should also be considered:

The two isomers that have magnesium in an intermediate position of the chain, OMgNC and OMgCN, show C−N bond distance values compatible with double and triple C−N bond pictures, respectively. On the other hand, the spin density distribution places the unpaired electron at the oxygen atom in both isomers. The C−N bond length in the magnesium fulminate radical (1.1704 Å at the CCSD/aug-cc-pVTZ level) is compatible with a normal triple bond, whereas the N−O bond distance (1.2099 Å at the CCSD/aug-cc-pVTZ level) is clearly shorter than typical N−O single bonds. In the same way, for the magnesium isofulminate radical, the C−N (1.1713 Å at the CCSD/aug-cc-pVTZ level) and N−O (1.2936 Å at the CCSD/aug-cc-pVTZ level) bond lengths are compatible with typical pictures of triple and single bonds, respectively. With regard to geometrical parameters for the Y-shaped MgCON isomer, we observe that the C−N and C−O distances

As pointed out in the Energetics section, at the B3LYP level of theory, the magnesium cyanate radical shows a slightly bent equilibrium structure with a ∠Mg−O−C angle of 172.9° and a linear OCN group. However, when ab initio methodologies are used, MgOCN becomes a linear structure. At the CCSD(T) level of theory, the magnesium cyanate radical has a shorter C− N bond distance (1.1700 Å) than its isocyanate counterpart (1.2029 Å), suggesting that the C−N bond could now be triple in nature. The C−O bond distance in MgOCN (1.2643 Å) is clearly longer than that in MgNCO (1.1830 Å). However, the C−O bond length is somewhat shorter than a typical C−O single bond. Thus, on basis of the bond length values, on the spin density distribution [0.968e (Mg), 0.013e (O), 0.034e (C), and 0.011e (N)] and on the magnesium natural atomic charge (0.937), the valence structures for the magnesium 162


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Table 3. Local Topological Properties (in au) of the Electronic Charge Density Distribution Calculated at the Position of the Bond Critical Points for the Different [Mg,C,N,O] Speciesa species MgNCO ( Σ ) 2 +

MgOCN (2Σ+)

OMgNC (2Σ+)

OMgCN (2Σ+)

MgONC (2A′)

MgCNO (2Σ+)

Y-MgCON (2A′)

MgOCN-TS (2A′)

bond

ρ(r)

∇2ρ(r)

|V(r)|/G(r)

H(r)

Mg−N N−C C−O Mg−O O−C C−N O−Mg Mg−N N−C O−Mg Mg−C C−N Mg−O O−N N−C Mg−C C−N N−O Mg−C C−O C−N Mg−O O−C C−N

0.067 0.443 0.444 0.067 0.356 0.469 0.056 0.069 0.465 0.075 0.059 0.486 0.067 0.408 0.406 0.055 0.409 0.510 0.051 0.288 0.416 0.041 0.381 0.457

0.477 −0.775 −0.036 0.604 −0.242 −0.149 0.487 0.474 −0.466 0.569 0.308 −0.188 0.577 −0.744 0.692 0.300 1.000 −1.162 0.217 −0.503 −0.970 0.300 −0.508 −0.484

1.001 2.317 2.011 0.950 2.113 2.044 0.959 1.018 2.152 1.010 1.059 2.053 0.957 2.662 1.803 1.036 1.738 2.679 1.069 2.465 2.519 0.912 2.242 2.167

−0.0001 −0.804 −0.810 0.007 −0.595 −0.886 0.005 −0.002 −0.882 −0.001 −0.005 −0.937 0.006 −0.467 −0.707 −0.003 −0.705 −0.718 −0.004 −0.396 −0.710 0.006 −0.652 −0.847

ρ(r), electronic charge density; ∇2ρ(r), Laplacian, |V(r)|/G(r), relationship between the potential energy density V(r) and the Lagrangian form of kinetic energy density G(r); and H(r), total energy density.

a

MgNCO and MgOCN also indicates the presence of five lone pairs: one of them is placed on nitrogen; three are at oxygen; and the remaining one is actually an unpaired electron sited in magnesium with mainly s character. The second-order perturbation theory analysis of the Fock matrix in NBO basis for MgNCO shows that the interaction between each one of the oxygen p-character lone pairs and the πCN antibonding NBO gives rise to a strong stabilization of 58 kcal/mol. This stabilizing interaction could explain the short C−O bond distance found in MgNCO. In a similar way, a moderate stabilization of 24 kcal/mol between each one of the p-character lone pairs on oxygen and the πCN antibonding NBO was found for MgOCN. This effect leads to a decrease of the C−O bond distance from a typical C−O single-bond distance. However, the stabilizing interaction is lower in MgOCN than in MgNCO, and consequently, a shorter C−O bond distance should be expected in MgNCO than in MgOCN, as found in our geometry results. With regard to the bond orders for MgNCO and MgOCN, we also found significant differences between the Wiberg bond orders of both N−C and C−O bonds in MgNCO and MgOCN. Whereas MgNCO has a larger C−O bond order than MgOCN (1.78 and 1.20, respectively), the opposite is true in the case of the N−C bond order (2.08 and 2.71, respectively). On the basis of the overall NBO analysis, the valence-bond structures for MgNCO and MgOCN can be schematized by

are 1.2549 and 1.3911 Å, respectively, at the MP2/aug-ccpVTZ level, suggesting single C−O and double C−N bonds as in oxazirine. However, the N−O distance is perhaps too long (1.6660 Å) to expect a bonding interaction, as in oxazirine. The structural parameters for the transition state corresponding to the MgOCN→MgNCO process are also included in Table 2. As expected, the N−C and C−O bond distances in MgOCN-TS are midway between the corresponding bond distances in magnesium isocyanate and magnesium cyanate radicals. Likewise, the Mg−N and Mg−O bond lengths in the transition state are larger than those in MgNCO and MgOCN, respectively. It should be noted that, for MgOCN-TS, the Mg− C distance (2.1401 Å at the CCSD/aug-cc-pVTZ level) seems short enough to give a bonding interaction between magnesium and carbon atoms. Consequently, in principle, a three-member cyclic structure should be expected for MgOCN-TS. As observed from Table 2, the C−N bond lengths in isomers with a terminal nitrogen, such as MgOCN and OMgCN, are shorter than the corresponding bond distances in isomers containing nitrogen in a middle position, such as MgNCO, OMgNC, MgCNO, or MgONC. Thus, it seems that bonding through both sides of nitrogen slightly weakens the C−N bond, whereas when the bonding takes place through the carbon atom, the C−N bond is slightly reinforced. 3.3. Bonding Analysis. The NBO analysis on MgNCO and MgOCN leads to similar results. The N−C bond is triple in nature. One of the NBOs is a σ bond between the C and N atoms, whereas the other two 2-center bonds connecting carbon and nitrogen are equivalent π-type bonds resulting from the overlap of either px or py orbitals on C with either px or py orbitals on N. On the other hand, the C−O interaction is considered a σ single bond. The NBO analysis for both 163


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The topological properties corresponding to the transition state MgCON-TS are also included in Table 3. As observed from the data collected in this table, no bond critical point was found for the Mg−C connectivity in the transition state. Consequently, even though the Mg−C distance is short enough to expect a bonding interaction and, therefore, a cyclic transition state, the QTAIM results support a bent structure for MgOCN-TS. It should be noted that the bond critical point data for carbon−nitrogen bonds reflect the general trend pointed out in the preceding comments on the structure of these isomers. The electronic densities for C−N bond critical points are always slightly larger for isomers with nitrogen in a terminal position than for those containing nitrogen in a middle position in the chain. These observations reflect the strengthening/weakening of the C−N bond upon the formation of these compounds. 3.4. Spectroscopic Parameters. The relevant spectroscopic parameters to rotational spectroscopy, together with computed dipole moments, for the most stable isomers, namely, magnesium isocyanate and magnesium cyanate radicals, are provided in Table 4. The Be rotational constants

Opposite of isocyanic and cyanic acids, magnesium isocyanate and magnesium cyanate show linear arrangements, in which the delocalization of the lone pairs of nitrogen and oxygen into the empty, mainly p in character, antibonding lone pair on magnesium is maximized. In this regard, we found a stabilization of 15 kcal/mol arising from the N−Mg(p) interaction for MgNCO and a stabilization of a similar magnitude resulting from the O−Mg(p) interaction for MgOCN. It should be noted that, on the basis of only electronegativity values, one should expect that the Mg−O bond was stronger than the Mg−N bond, and thus, the cyanate arrangement should be favored over the isocyanate arrangement. However, this effect is not big enough to reverse the relative energy between the isocyanate and cyanate structures, although the relative difference is reduced from 24.23 kcal/mol [at the CCSD(T) level] for the HNCO/HOCN pair to 15.79 kcal/mol [at the CCSD(T) level] for the MgNCO/MgOCN pair. The local topological properties of the electronic charge distribution for the most significant [Mg,C,N,O] isomers are provided in Table 3. For the two low-lying isomers, MgNCO and MgOCN, the QTAIM parameters for both C−N and C−O bond critical points are indicative of typical shared interactions, showing large values of electron density, negative values of its Laplacian, |V(r)|/G(r) ratios greater than 2, and negative values of the total energy density H(r). On the other hand, magnesium-including bonds, Mg−N and Mg−O, have low values of ρ(r) and positive values of the Laplacian, and despite showing |V(r)|/G(r) ratios close to 1, these bonds can be classified as closed-shell interactions. Even though the general characteristics of the topological properties for MgNCO and MgOCN concerning C−N and C− O bond critical points are similar, some aspects should be pointed out. The electronic charge density for the C−N BCP is slightly lower in MgNCO than in MgOCN (0.443 and 0.469, respectively), whereas the opposite is true regarding C−O BCP (0.444 and 0.356, respectively). These results reflect the differences pointed out in preceding comments on the molecular structure of MgNCO and MgOCN. The two isomers containing magnesium in an intermediate position of the molecule, OMgNC and OMgCN, show similar topological properties: for the carbon−nitrogen bond, the QTAIM results are typical of shared interactions, whereas the BCPs involving the magnesium atom, O−Mg, N−Mg, and Mg−C, have topological characteristics of closed-shell interactions. For magnesium fulminate and magnesium isofulminate radicals, the QTAIM analysis, for the carbon−nitrogen bond, gives large values of the electron density and negative values of the total energy density H(r); however, the Laplacian of the electron density has a positive value, and the values of the | V(r)|/G(r) ratio are between 1 and 2. Thus, these links can be classified as shared interactions with some degree of ionicity. The analysis of the local topological properties of the electronic charge distribution for the Y-shaped MgCON isomer shows that both C−O and C−N bonds present typical characteristics of covalent interactions, whereas the Mg−C BCP has topological properties of closed-shell interactions. However, the most significant result concerning the Y-shaped MgCON isomer is the lack of a bond critical point between oxygen and nitrogen atoms, suggesting that this isomer does not present a cyclic structure and could be seen as a derivative of formylnitrene instead of an oxazirine derivative.

Table 4. CCSD/aug-cc-pVTZ Dipole Moments, μ (Debyes), CCSD(T)/aug-cc-pVTZ Including Core−Valence Correction Rotational Constants, Be and B0 (MHz), and CCSD/aug-cc-pVTZ Centrifugal Distortion Constants, D (MHz), of MgNCO (2Σ+) and MgOCN (2Σ+) μ (D) Be (MHz) B0 (MHz) D (MHz)

MgNCO (2Σ+)

MgOCN (2Σ+)

4.84 2620.4 2631.7 0.0032

7.59 2799.4 2818.3 0.0036

were computed at the CCSD(T)/aug-cc-pVTZ level taking into account core−valence corrections. The corresponding rotational constants for the ground vibrational state, B0, were determined from vibration−rotation coupling constants and degeneracy factors for the vibrational modes, also including core−valence corrections. The differences between B0 and Be rotational constants for MgNCO and MgOCN are on the order of 11.3 and 18.9 MHz, respectively. For MgNCO and MgOCN, the dipole moments were calculated to be 4.84 and 7.59 D, respectively, at the CCSD/ aug-cc-pVTZ level. These values are high enough to allow for the observation of the corresponding rotational spectra for both MgNCO and MgOCN using standard microwave spectroscopy instruments. In Table 5, harmonic and anharmonic vibrational frequencies and the corresponding IR intensities, computed at the CCSD/ aug-cc-pVTZ level, for magnesium isocyanate and magnesium cyanate radicals, are collected. The IR spectrum of MgNCO is dominated by an intense band associated with the σ-NCO asymmetric stretching mode. This wavenumber value and the high intensity could mainly be due to resonance effects, which weaken the triple C−N bond. As seen from Table 5, the σMgN stretching mode also presents a relatively high intensity. In a similar way, the σ-NCO asymmetric stretching mode is again the most intense band in the IR spectrum of the magnesium cyanate radical. However, in this case, the corresponding symmetric mode also gives rise to an IR absorption band of similar intensity. On the other hand, we observe that the IR intensities of the frequencies associated 164


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Table 5. CCSD/aug-cc-pVTZ Harmonic, ω, and Anharmonic, ν, Vibrational Frequencies (cm−1) and IR Intensities, IHarm and IAnh (km/mol), of MgNCO (2Σ+) and MgOCN (2Σ+) MgNCO (2Σ+) mode σ σ π σ π

NCO asym stretch NCO sym stretch NCO bend MgN stretch MgNC bend

MgOCN (2Σ+)

ω

IHarm

ν

IAnh

2310 1430 664 469 71

1663.0 6.5 18.9 116.0 2.5

2266 1435 662 479 85

1581.5 3.3 18.3 113.3 2.4

mode σ σ π σ π

with the σ-NCO symmetric stretching mode for MgNCO and MgOCN are clearly different, with the IR band for MgOCN being much stronger than that for MgNCO isomer. These discrepancies arise from the different natures of the N−C and C−O bonds in both isomers. It should be noted that, for both MgNCO and MgOCN, the bending frequencies involving the magnesium atom are very low in value (85 and 54 cm−1, respectively). This indicates a weakly oriented bonding between Mg and either the NCO or OCN moieties. Consequently, these compounds can be seen as floppy molecules with respect to the bending motion. This behavior was also observed in magnesium isocyanide.46 The highest difference between harmonic and anharmonic frequencies corresponds to the σ-NCO asymmetric stretching mode (43 cm−1 in both isomers). This illustrates the crucial role of anharmonicity for an accurate prediction of IR spectroscopic signatures, as recently highlighted.47

OCN asym stretch OCN sym stretch OCN bend MgO stretch MgOC bend

ω

IHarm

ν

IAnh

2357 1264 549 486 49

441.6 300.7 10.0 90.0 0.3

2313 1256 550 490 54

392.0 283.2 9.2 85.4 0.3

associated with the NCO symmetric stretching mode for MgNCO and MgOCN are clearly different. In both MgNCO and MgOCN, the very low value of the bending anharmonic frequencies involving magnesium (85 and 54 cm−1, respectively) suggests a weakly oriented bonding between Mg and either the NCO or OCN units, and consequently, these compounds can be considered as floppy molecules with respect to the bending motion. For both isomers, the anharmonic effect on the computed vibrational frequencies is especially relevant for the dominating bands associated with the σ-NCO asymmetric stretching mode. The topological properties for the different isomers allow us to characterize C−N, C−O, and N−O bonds as shared interactions, whereas the BCPs involving the magnesium atom, Mg−N, Mg−O, and Mg−C, have topological characteristics of mainly closed-shell interactions. The intense bands associated with the σ-NCO asymmetric stretching mode in the IR spectrum of MgNCO and MgOCN, together with their large dipole moments, will likely make observation of both systems easier with either space-based IR or ground-based sum-mm telescopes. The overall results suggest that both MgNCO and MgOCN isomers are expected to be the most reasonable targets of the [Mg,C,N,O] composition to be detected in the interstellar medium and characterized in the laboratory.

4. CONCLUSION In this work, we have studied the relevant [Mg,C,N,O] isomers in the doublet PES. All levels of theory employed in this study predict the magnesium isocyanate radical, MgNCO, as the lowest energy [Mg,C,N,O] isomer. The corresponding cyanate counterpart, MgOCN, is located 15.8 kcal/mol above MgNCO at the CCSD(T)/aug-cc-pVTZ level, including core−valence corrections. The two isomers that arise from the insertion of the magnesium atom between either O−N or O−C bonds, of either ONC and OCN units, namely, OMgNC and OMgCN, are situated at 37.1 and 38.9 kcal/mol, respectively, higher in energy than the magnesium isocyanate radical at the CCSD/ aug-cc-pVTZ level. Following in energy are two nearly isoenergetic isomers, magnesium isofulminate and magnesium fulminate radicals, which lie 81.0 and 81.7 kcal/mol, respectively, higher in energy than the most stable isomer at the CCSD/aug-cc-pVTZ level of theory. The interconversion process between the two most stable isomers, MgOCN → MgNCO, has a barrier of 4.55 kcal/mol (2290 K), suggesting a slow rate for the isomerization reaction. Consequently, if efficient synthesis processes leading to MgNCO and MgOCN are viable, it is likely that both isomers could be present simultaneously in the interstellar medium, even with the extremely long cosmological time scales. On the other hand, both magnesium isocyanate and magnesium cyanate radicals are stable toward dissociation into Mg + NCO units or into diatomic moieties. The dipole moments for both MgNCO and MgOCN (4.84 and 7.59 D, respectively, at the CCSD/aug-cc-pVTZ level) are high enough that laboratory or interstellar detection using microwave spectroscopy should be possible. The IR spectra of the two most stable isomers are dominated by intense bands associated with the σ-NCO asymmetric stretching mode. However, the IR intensities of the bands

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Antonio Largo: 0000-0003-4959-4850 Carmen Barrientos: 0000-0003-0078-7379 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work results within the collaboration of the COST Action TD 1308. Financial support from the “Junta de Castilla y León” (Grant VA077U13) is gratefully acknowledged. Á lvaro VegaVega acknowledges funding from the “Junta de Castilla y León” under Predoctoral Research Grant E-47-2015-0175859. The authors thank Jesús Nieto for providing the picture for the table of contents.

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REFERENCES

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Structure and Spectroscopic Properties of [Mg,C,N,O] Isomers

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