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 Álvaro Vega-Vega, Antonio Largo, Pilar Redondo, and Carmen Barrientos ACS Earth Space Chem., Just Accepted Manuscript • DOI: 10.1021/ acsearthspacechem.7b00019 • Publication Date (Web): 10 Apr 2017 Downloaded from http://pubs.acs.org on April 13, 2017

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ACS Earth and Space Chemistry

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Structure and Spectroscopic Properties of [Mg,C,N,O] Isomers: Plausible Astronomical Molecules

Álvaro 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 *

Author to whom correspondence should be addressed. Electronic address: [email protected].

ACS Paragon Plus Environment


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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 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 magnesium fulminate radical MgCNO, 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. In order 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 the 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 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 Debye, respectively, at the CCSD/aug-cc-pVTZ level). These two factors will likely make observation of both systems easier either with 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.


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Key words: astrochemistry – ISM: general – ISM: molecules – ISM: structure – molecular data – MgNCO isomers.



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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 low-mass star-forming region L1527. Despite it was 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 submillimeter 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 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


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In this context it was emphasized the astrochemical interest of isomeric systems since 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 assigned to transitions of MgNC. The detection in the circumstellar envelope IRC+10216 of millimeter lines of two isotopomers was reported in 199513 and a few years later magnesium isocyanide was also observed in proto-planetary nebulae.14 The magnesium cyanide isomer, MgCN, was detected toward the star IRC+10216 in 1995.15 More recently, in 2013 it was reported the identification of hydromagnesium isocyanide, HMgNC, 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 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



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an analysis of the bonding in the context of the Bader’s theory.17 To date, there 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 second order Møller–Plesset theory (MP2),22 and for the more stable isomers we performed subsequent coupled-cluster calculations with singles and doubles excitations (CCSD) and with a perturbative inclusion of triple excitations (CCSD(T)).23In the former the T1 diagnostic24 was used in order 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 than 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 IR spectroscopy anharmonic vibrational frequencies calculations were performed for the most stable isomers. Anharmonic


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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 semidiagonal quartic force constants. From the CFF calculations vibration-rotation interaction constants can also be evaluated, allowing to correct 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 functions 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. In order 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 fullelectron calculation and a frozen-core one by using the CCSD level with the aug-ccpCVTZ basis set.34,35 Thus, the core-valence corrections for structural parameters (∆r), equilibrium rotational constants (∆Be) and electronic energies (∆E) were obtained as: ∆r/∆Be/∆E(CV)=r/Be/E(CCSD-full/aug-cc-pCVTZ)–r/Be/E(CCSD/aug-cc-pVTZ) 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 parameters were computed at CCSD/aug-cc-pVTZ level using the Keith‘s AIMAll40 package including standard thresholds. The accuracy of the integration over



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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 B3LYP/aug-cc-pVTZ level of theory.

3.

RESULTS AND DISCUSSION

We have searched for various potentially stable [Mg,C,N,O] isomers including openchain (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, so 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, since 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 can be seen in Figure 1b. The same pattern was found in the HNCO/HOCN system, since 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


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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/aug-cc-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 potential energy surface 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 0.00001 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 cyanide-κC-

oxidemagnesium, OMgCN (Figures 1c and 1d, respectively). These isomers, which show a linear arrangement with 2Σ+ ground state, are located 46.8 kcal/mol and 48.2 kcal/mol, respectively, higher in energy than magnesium isocyanate radical at the B3LYP/aug-cc-pVTZ level. Magnesium fulminate radical, MgCNO (2Σ+), and magnesium isofulminate radical, MgONC (2A’), shown in Figures 1f and 1e, 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, (67. and 87.1 kcal/mol, respectively42) were found with respect to isocyanic acid. We have also found a Y-shape MgCON (2A’) isomer, namely cyanate-κCmagnesium (Figure 1g), located 115.2 kcal/mol (at the B3LYP/aug-cc-pVTZ level) above magnesium isocyanate radical. In principle, it could be seen as derived from



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either formylnitrene or oxazirine. This issue will be discussed below in subsequent sections. Higher in energy, see Figures 1h and 1i, are other possible isomers such as those arising from the interaction of 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 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 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 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


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rate. Thus, despite the extremely long cosmological timescales, it is likely that both MgNCO and MgOCN could be present simultaneously in the interstellar medium if efficient synthesis processes exist. To get 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 CCSD/aug-cc-pVTZ dissociation energies corresponding to pathways leading to two different processes: a) processes forming a magnesium atom plus a NCO unit; b) processes giving two diatomic moieties. In the latter case the dissociation energy for MgNCO is the energy associated to the production of MgN and CO fragments, whereas for MgOCN, OMgCN and OMgNC the dissociation energy corresponds to formation of MgO and CN units. As can be seen from Table 1, for both MgNCO and MgOCN isomers the dissociation energies corresponding to formation of Mg and NCO are rather high (142.4 and 127.3 kcal/mol respectively), whereas the corresponding ones associated to 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 into 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(NC)=1.2140 Å and r(C-O)=1.1664 Å) determined from pure rotational spectra.44 On the



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other hand, when comparing the common structural parameters of MgNCO and those of MgNC reported from rotational spectroscopy of several MgNC isotopomers45 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 24

MgNC/25MgNC); r0(Mg-N)=1.924 Å (determined from

24

MgNC/26MgNC). On the

other hand, our computed N-C bond length (1.2029 Å) is somewhat larger than the measured ones r0(N-C)=1.169 Å (determined from Å (determined from

24

MgNC/25MgNC); r0(N-C)=1.172

24

MgNC/26MgNC). It can be noted that some small differences

between experimental and theoretical bond lengths should be expected due to 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 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 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:


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As it was pointed out in the energetics section, at the B3LYP level of theory 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, 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 be now triple in nature. The C-O bond distance in MgOCN (1.2643 Å) is clearly longer than in MgNCO (1.1830 Å). However the C-O bond length is somewhat shorter than typical C-O single bond. Thus, based on 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 magnesium cyanate radical can be mainly described through these two resonant structures:

The two isomers that have magnesium in an intermediate position of the chain, OMgNC and OMgCN, show C-N bond distances 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 magnesium fulminate radical (1.1704 Å at the CCSD/augcc-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.



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In the same way, for 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. Regarding geometrical parameters for the Y-shape-MgCON isomer, we observe that the C-N and C-O distances are 1.2549 Å and 1.3911 Å, respectively, at the MP2/aug-cc-pVTZ 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 it does 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 ones in magnesium isocyanate radical and magnesium cyanate radical. Likewise, the Mg-N and Mg-O bond lengths in the transition state are larger than 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, it should be expected a threemember cyclic structure for MgOCN-TS. As can be 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.


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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 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 typical C-O single bond distance. However, the stabilizing interaction is lower in MgOCN than in MgNCO and, consequently, it should be expected a shorter C-O bond distance in MgNCO than in MgOCN as it was found in our geometry results. Regarding 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).



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Based on the overall NBO analysis the valence-bond structures for MgNCO and MgOCN can be schematized by:

Opposite to 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 based only on electronegativity values one should expect that the Mg-O bond were stronger than the Mg-N one, and thus the cyanate arrangement should be favored over the isocyanate one. 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 one. 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 in


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spite of showing |V(r)|/G(r) ratios closed to one, these bonds can be classified as closedshell 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 carbonnitrogen 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 one and two. 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-shape-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 Y-shape-MgCON isomer is the lack of a bond critical point between oxygen and



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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. The topological properties corresponding to the transition state MgCON-TS are also included in Table 3. As can be 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 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 radical and magnesium cyanate radical, are provided in Table 4. The Be rotational constants were computed at the CCSD(T)/aug-cc-pVTZ level taking into account corevalence 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 including also core-valence corrections. The differences between B0 and Be rotational constants for MgNCO and MgOCN are on the order of 11.3 MHz and 18.9 MHz respectively.


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For MgNCO and MgOCN the dipole moments were calculated to be 4.84 and 7.59 Debye, respectively, at the CCSD/aug-cc-pVTZ level. These values are high enough to allow 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 radical and magnesium cyanate radical, are collected. The IR spectrum of MgNCO is dominated by an intense band associated to 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 can be seen from Table 5, the σ-MgN stretching mode also presents a relatively high intensity. In a similar way the σ-NCO asymmetric stretching mode is again the most intense one in the IR spectrum of 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 to the σ-NCO symmetric stretching mode for MgNCO and MgOCN are clearly different being the IR band for MgOCN much stronger than that for MgNCO isomer. These discrepancies arise from the different nature 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 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



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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 has been recently highlighted.47

4.

CONCLUSION

In this work we have studied the relevant [Mg,C,N,O] isomers in the doublet Potential Energy Surface. All levels of theory employed in this study predict 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 found 37.1 kcal/mol and 38.9 kcal/mol, respectively, higher in energy than magnesium isocyanate radical at the CCSD/aug-cc-pVTZ level. Following in energy are two nearly isoenergetic isomers, magnesium isofulminate radical and magnesium fulminate radical, which lie 81.0 kcal/mol 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 though the extremely long cosmological timescales. On the other hand, both magnesium isocyanate radical and magnesium


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cyanate radical 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 Debyes 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 to the σ-NCO asymmetric stretching mode. However, the IR intensities of the bands associated to 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 either with space-based IR or groundbased sum-mm telescopes.



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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.

Acknowledgements 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. A. V. V. acknowledges funding from the “Junta de Castilla y León” under predoctoral research grant E-47-2015-0175859. The authors thank Jesús Nieto for providing us the picture for the TOC.


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Figure captions Figure 1. Relative energies, including zero point corrections, in kcal/mol of the [Mg,C,N,O] isomers at different levels of theory using aug-cc-pVTZ basis set. In the CCSD(T) results core-valence corrections are included. Figure 2. Potential Energy Surface corresponding to the MgOCN→MgNCO isomerization reaction. CCSD/aug-cc-pVTZ relative energies are given in kcal/mol and include ZPVEs.


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Table 1. Dissociation energies, in kcal/mol, calculated at the CCSD/aug-cc-pVTZ level including zero-point vibrational corrections. Process

D0/(kcal/mol)

MgNCO → Mg + NCO

142.4

MgOCN → Mg + NCO

127.3

MgNCO → MgN + CO

247.6

MgOCN → MgO + CN

267.8

OMgCN → MgO + CN

242.2

OMgNC → MgO + CN

243.8



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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 set.

Isomer MP2 1.9002 1.2081 1.1868

Level CCSD 1.8934 1.1975 1.1782

MgNCO ( Σ )

r(Mg-N) r(N-C) r(C-O)

B3LYP 1.9031 1.1967 1.1789

MgOCN(2A’/2Σ+)

r(Mg-O) r(C-O) r(N-C) ∠Mg-O-C

1.8324 1.2581 1.1615 172.9

1.8305 1.2635 1.1799 180

1.8201 1.2624 1.1634 180

OMgNC (2Σ+)

r(Mg-O) r(Mg-N) r(N-C)

1.8609 1.9071 1.1731

1.8578 1.9083 1.1865

1.8536 1.8974 1.1775

OMgCN (2Σ+)

r(Mg-O) r(Mg-C) r(N-C)

1.8616 2.0358 1.1562

1.8595 2.0284 1.1780

1.8545 2.0285 1.1622

MgONC (2A’)

r(Mg-O) r(N-O) r(N-C) ∠Mg-O-N

1.8876 1.3045 1.1700 124.8

1.8459 1.2852 1.1876 148.3

1.8314 1.2936 1.1713 147.6

MgCNO (2Σ+)

r(Mg-C) r(N-C) r(N-O)

2.0447 1.1730 1.2066

2.0349 1.1570 1.2039

2.0362 1.2936 1.2099

Y-MgCON

r(Mg-C) r(C-O) r(N-C) ∠Mg-C-O ∠O-C-N

2.1461 1.3715 1.2490 133.7 80.2

2.1206 1.3911 1.2549 135.0 77.9

MgOCN-TS

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

2.0979 2.1640 2.5247 1.2469 1.1802 75.9

2.0149 2.2166 2.7403 1.2620 1.1938 81.6

2 +

CCSD(T) 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

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


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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] species. Species 2 +

MgNCO ( Σ )

2 +

MgOCN ( Σ )

OMgNC (2Σ+)

2 +

OMgCN ( Σ )

2

MgONC ( A')

MgCNO (2Σ+)

2

Y-MgCON ( A')

2

MgOCN-TS ( A')

Bond Mg-N N-C

0.067 0.443

∇2ρ(r) 0.477 -0.775

C-O Mg-O

0.444 0.067

-0.036 0.604

2.011 0.950

-0.810 0.007

O-C C-N

0.356 0.469

-0.242 -0.149

2.113 2.044

-0.595 -0.886

O-Mg Mg-N

0.056 0.069

0.487 0.474

0.959 1.018

0.005 -0.002

N-C O-Mg Mg-C C-N

0.465 0.075 0.059 0.486

-0.466 0.569 0.308 -0.188

2.152 1.010 1.059 2.053

-0.882 -0.001 -0.005 -0.937

Mg-O O-N N-C Mg-C C-N N-O

0.067 0.408 0.406 0.055 0.409 0.510

0.577 -0.744 0.692 0.300 1.000 -1.162

0.957 2.662 1.803 1.036 1.738 2.679

0.006 -0.467 -0.707 -0.003 -0.705 -0.718

Mg-C C-O C-N Mg-O O-C C-N

0.051 0.288 0.416 0.041 0.381 0.457

0.217 -0.503 -0.970 0.300 -0.508 -0.484

1.069 2.465 2.519 0.912 2.242 2.167

-0.004 -0.396 -0.710 0.006 -0.652 -0.847

ρ(r)

|V(r)|/G(r) 1.001 2.317

H(r) -0.0001 -0.804

Note. The electronic charge density [ρ(r)], the Laplacian [∇ ∇2ρ(r)], the relationship between the potential energy density V(r) and the lagrangian form of kinetic energy density G(r), and the total energy density, [H(r)].



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Table 4. CCSD/aug-cc-pVTZ Dipole Moments, µ (Debyes), CCSD(T)/aug-cc-pVTZ including core-valence corrections Rotational Constants, Be and B0, (MHz), and CCSD/aug-cc-pVTZ Centrifugal Distortion Constants, D (MHz) of MgNCO (2Σ+) and MgOCN (2Σ+). MgNCO (2Σ+)

MgOCN (2Σ+)

4.84

7.59

Be/MHz

2620.4

2799.4

B0/MHz

2631.7

2818.3

D/MHz

0.0032

0.0036

µ/D


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33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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 NCO asym stretch σ NCO sym stretch π NCO bend σ MgN stretch π MgNC bend

ω

IHarm

MgOCN (2Σ+)

ν

IAnh

Mode

σ OCN 1581.5 asym stretch σ OCN 3.3 sym stretch

ω

IHarm

ν

IAnh

2357

441.6

2313

392.0

1264

300.7

1256

283.2

2310

1663.0

2266

1430

6.5

1435

664

18.9

662

18.3

π OCN bend

549

10.0

550

9.2

469

116.0

479

113.3

486

90.0

490

85.4

71

2.5

85

2.4

σ MgO stretch π MgOC bend

49

0.3

54

0.3



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34 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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


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



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Isomer (a)

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B3LYP MP2 CCSD CCSD(T)

MgNCO (2Σ+) 0

(b)

0

0

0

16.5

15.1

15.8

46.8

51.2

37.1

48.2

49.8

38.9

82.8

85.2

81.0

77.1

83.4

81.7

MgOCN (2A'/2Σ+) 18.4

(c)

(d)

(e)

(f)

(g)

OMgNC (2Σ+)

OMgCN (2Σ+)

MgONC (2A')

MgCNO (2Σ+)

Y-MgCON (2Α')

115.2 119.6

(h)

MgCON (2Σ+) 175.1 140.8

(i)

MgNOC (2A')

153.8 168.8


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42


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

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