Excited states and photodissociation mechanism of HMgNC and HMgCN

Context. The complexes HMgNC, MgNC, and MgCN were previously detected in the outer shells of the star IRC+10216 and were thought to be formed through radiative association of Mg + and cyanopolyynes followed by dissociative recombination. The presence of these species in the outer shells of IRC+10216 consequently provoked a question regarding whether HMgNC could be an astronomical reservoir of MgNC and MgCN. Aims. The aim of this study is to investigate the evolution of the lowest singlet and triplet excited states for HMgNC and HMgCN along the MgH, MgC, and MgN stretching coordinates. Additionally, the vertical excitation energies, photoabsorption cross section, and oscillator strengths of the lowest electronic singlet states are calculated. Methods. Coupled cluster quantum chemistry methods were used to calculate the equilibrium electronic structure. Multi-reference methods were then used to characterize the photochemical pathways of the excited electronic states and simulate the electronic absorption spectrum. Results. HMgNC and HMgCN are thermodynamically stable relative to the first dissociation limit and photostable in the near-ultraviolet–visible region ( λ > 220 nm). Both isomers strongly absorb in the 170 nm < λ < 200 nm range and may produce MgNC and MgCN in their first excited state (A 2 Π ). This process competes with the photoproduction of MgH and CN. The photodissociation to produce MgNC and MgCN in their ground states is not a plausible mechanism.


Introduction
The chemistry of metal-bearing molecules is of great importance in the interstellar medium (ISM), due to its role in the connection between the solid-state constituents of the ISM and gas phase matter.For instance, the presence of a giant planet is strongly dependent on the stellar metallicity (Mortier et al. 2013;Johnson et al. 2010).In previous astronomical models (Dunbar & Petrie 2002;Petrie 1996a), metal-bearing molecules such as sodium, aluminium, or magnesium were suggested to be formed through radiative association processes Eq. ( 1) where M represents a metal such as Na, Al, or Mg and n = 0,...,4.This process is followed by dissociative recombination of MNC 2n+1 H + with an electron.Joint theoretical and experimental investigations on the electronic structure of many possible candidates were crowned by the detection of HMgNC (Cabezas et al. 2013), KCN (Pulliam et al. 2010), MgC 3 N (Cernicharo et al. 2019), AlNC (Ziurys et al. 2001), FeCN (Zack et al. 2011), and the tentative detection of CaNC (Cernicharo et al. 2019) via rotational spectroscopy.According to the previous models, other species are still missing and are expected to exist, such as the hydrides of the detected species or their corresponding cyanides or isocyanides such as HAlNC and HAlCN (Redondo et al. 2022), HFeCN and HFeNC (Redondo et al. 2016), and HCaCN and HCaNC (Redondo et al. 2020).The detection of triatomic MgNC (Kawaguchi et al. 1993) and its metastable isomer MgCN (Ziurys et al. 1995) preceded these models.All the magnesium species (i.e., MgCN, MgNC, HMgNC, and MgC 3 N) were detected in the same region, IRC +10216.The line profile of HMgNC (Cabezas et al. 2013) arises from the outer shells of IRC+10216 as the related radical MgNC (Guélin et al. 1993).The temperature and matter densities of this region are relatively low and similar to those of the molecular cloud.These conditions make photochemical processes a plausible mechanism to explain the destruction and formation of [H,M,N,C] species.The photodissociation mechanism is an important source of small molecules (two or three atoms) and atomic ions in the ISM, where ultraviolet (UV) photons play a critical role (Heays et al. 2017;Trabelsi & Francisco 2018;Valiev et al. 2017Valiev et al. , 2020)).
Given the Mg-bearing molecule detection and the uncertainty of the formation mechanism of the triatomic species, we think that the photochemistry processes of the detected HMgNC molecule must be studied.These processes may compete with the previous model to explain the formation of the triatomic MCN and MNC molecules, and may predict the possible products for the isoelectronic system, such as HCaNC and HCaCN, or more usually HMNC and HMCN (M = Al, Na, Ca, and K).These systems are expected, and their nondetection may be due to the dominance of the photodissociation processes that favor H + MNC.
The structure and the spectroscopy of the electronic ground state of the [H,Mg,N,C] molecular system were theoretically investigated, and the most stable isomer was predicted to be linear HMgNC (Gronowski & Kołos 2013).The HMgCN isomer is also linear and very close in energy to HMgNC, predicted to be 8.7 kJ mol −1 above it (Gronowski & Kołos 2013).This small energy gap makes HMgCN a potential candidate for radio astronomical detection.Stiles et al. (2003) reported the infrared spectra for the weakly bound complexes Mg-HCN and Mg-NCH.Although several experimental (Cabezas et al. 2013;Steimle & Bousquet 2001) and theoretical (Bludskỳ et al. 2004;Hirano et al. 2002;Ishii et al. 1993;Woon 2022;Petrie 1996b) studies have been carried out to investigate the electronic ground state of [Mg,N,C] and [H,Mg,N,C] molecular systems, the number of experimental (Wright & Miller 1999;Fukushima & Ishiwata 2002) and theoretical studies on the electronic spectroscopy and photochemistry of these systems is limited.The electronic transition and photostability of these systems in the near-UV-Vis region are also unknown.Knowing the low ionization potential (IP) of the Mg atom (IP = 7.64 eV; Kaufman & Martin 1991) and the high adiabatic electronic affinity of CN (AE = 3.86), these systems present an ionic state (i.e., Mg + CN − or (HMg) + (CN) − ), which reaches the near-UV-Vis region, and the production of MgH + , Mg + and CN − may be plausible.
The reactivities of MgNC with H demonstrate the limitations of gas phase chemistry in very cold low-density astrophysical environments.The addition of H to MgNC to yield HMgNC is exoergic by 68.2 kcal mol −1 , but radiative association is expected to be very inefficient for a system with just four atoms (Woon 2022).The presence of MgNC, MgCN, and HMgNC in the outer shells of IRC+10216 consequently provoked a question regarding whether HMgNC could be an astronomical reservoir of MgNC and MgCN.To the best of our knowledge, the photochemistry of HMgNC and HMgCN to produce H + MgNC/MgCN, MgH + CN or other related molecules has not yet been investigated, either theoretically or experimentally, and detailed analysis of the following reactions has yet to be carried out: The evolutions of the lowest singlet and triplet electronic states along the stretching coordinates and the electronic spectra are also unknown.Considering the lack of theoretical studies on the electronic excited states of HMgNC, we investigate the electronic spectra of this molecule and the possible products upon photon absorption in the visible and UV regions.Computational chemistry is a powerful tool for predicting the plausible mechanism and the UV-Vis spectra (Trabelsi et al. 2019a;Trabelsi & Francisco 2022) and the analysis of reactions (2)-(4) may improve the astrochemical models.

Methodology
Geometry optimization and bond dissociation energy calculations were performed using coupled clusters with single and double excitations and the perturbative inclusion of triple excitations including all electrons, CCSD(T)-AE (Raghavachari et al. 1989).For the atomic basis set, we used Dunning's augmented correlation-consistent quintuple zeta with weighted core-valence aug-cc-pWCVQZ (Dunning Jr et al. 2001) basis sets.For comparison, aug-cc-pV(X+d)Z (X = Q and 5) basis sets were also used for full valence active space CCSD(T) calculations (Feller 1996;Pritchard et al. 2019).The evolutions of the lowest singlet and triplet electronic states along the MgH, MgC, and MgN stretching coordinates were examined using the complete active space self-consistent field CASSCF (Kreplin et al. 2019;Werner & Knowles 1985) followed by multireference configuration interaction MRCI+Q (Werner & Knowles 1988;Knowles & Werner 1992, 1988) including the Davidson correction.In this calculation, the atoms were described by the aug-cc-pV(T+d)Z basis sets with an extra tight d-function for the Mg atom (Prascher et al. 2011).For the MRCI+Q calculations, the CASSCF reference wavefunction was state-averaged over the lowest three singlet states with the same spin-multiplicity and spatial symmetry.For the triplet state, only the state correlated to the first dissociation limit was calculated.In the CASSCF computations, a larger active space of ten electrons in 14 orbitals (CAS (10,14)) was used; in other words, we included one additional molecular orbital (MO) in the standard full valence active space.All configurations in the CI expansion of the CASSCF wavefunctions with a weight larger than 0.001 were considered.To simulate the electronic absorption spectra of HMgNC and HMgCN, the ground-state geometry was optimized, and normal mode analysis was performed at the CCSD(T) level of theory with the aug-cc-pV(5+d)Z basis set.Following this, a set of initial geometries was obtained using a Wigner distribution based on the ground-state equilibrium geometry and harmonic vibrational frequencies.For each Wigner geometry, vertical excitation energies and transition dipole moments were calculated using the equation of motion (EOM)-CCSD method with aug-cc-pV(T+d)Z.
The photoabsorption cross section P(E) was determined via Eq.( 5), where g is a Lorentzian line shape function given by Eq. ( 6), f N i j is the oscillator strength at each point N; m e and e are the mass and charge of an electron, respectively; and c is the speed of light.The internal sum in Eq. ( 1) is over the total number of Wigner geometries (N tot = 100), while the external sum includes transitions from the initial state (i.e., (X 1 A)) to the final states j (2 1 A, 3 1 A, 4 1 A and 5 1 A) in the C1 symmetry group.The parameter δ is a broadening factor that is arbitrarily set to 0.1 eV.The Wigner points were generated using Sharc-md (Richter et al. 2011) software, and all calculations were performed using MOLPRO (Werner et al. 2012) software.The fundamental modes and rotational constants were calculated using vibrational second-order perturbation theory (VPT2; Ramakrishnan & Rauhut 2015).

Ground-state spectroscopy and bond dissociation energy
We first calculate the equilibrium geometry, rotational constants, and anharmonic vibrational frequencies of the ground state X 1 Σ + A79, page 2 of 8 of HMgNC and HMgCN, as listed in Table A.1.The available experimental and theoretical data are also listed in Table A.1.For the nondetected HMgCN isomer, we estimate the rotational constant of B 0 = 4666.74MHz and quartic centrifugal distortion constant of D 0 = 1.766 kHz.From a comparative point of view, this value differs by 42.5 MHz relative to that derived from the composite scheme (Gronowski & Kołos 2013).The rotational constants for the equilibrium geometry Be are also calculated at the high CCSD(T) level in conjunction with the aug-cc-pV(5+d)Z and aug-cc-pWCVQZ basis sets.The predicted rotational constants for all vibrationally excited states of HMgCN (X 1 Σ + ) are calculated and listed in Table A.2 to help with laboratory and astronomical detection.
In agreement with previous theoretical studies (Gronowski & Kołos 2013; Petrie 1996b), we confirm that the linear HMgNC isomer is the global minimum on the ground-state potential energy surface (PES).The energy difference between HMgNC and HMgCN is calculated to be 0.05 eV (403 cm −1 ) at the CCSD(T)-AE/aug-cc-pWCVQZ level and 0.09 eV (725 cm −1 ) at the CCSD(T)/aug-cc-pVTZ level (Gronowski & Kołos 2013).At the G2 level Petrie (1996b), the energy difference is calculated to be 0.01 eV (80.6 cm −1 ).The core valence correction to the total energy and the quadrupole zeta basis sets improve the HMgNC-HMgCN energy gap.This small difference makes the coexistence of the two isomers plausible, and we recommend a ∆E of 0.05 eV for future investigations.We expect that the vibrational spectroscopy of these species is relatively complicated due to the similarity of some modes.For instance, in the two isomers the MgH stretch differs by only 2.8 cm −1 and the HMgN bending mode (ν 4 = 308 cm −1 ) differs by 9.3 cm −1 relative to the HMgC mode (ν 4 = 317.3cm −1 ).Furthermore, the two isomers present Fermi resonance (type 2), such that ν 1 ≈ ν 2 + ν 3 .
H-MgNC and HMg-NC dissociation limits.The first dissociation limit is predicted to be 2.95 eV above the global minimum for H-MgNC.This value is 0.03 eV greater than that predicted by Petrie (1996b).Both the CCSD(T)-AE and G2 values are greater than the experimental BDE of free MgH, which is measured to be 1.28 eV (Shayesteh et al. 2007), meaning that the hydrogen atom is strongly bonded to the magnesium atom.
For the Mg-N bond, the BDE is predicted to be 4.93 eV, which is on the same order of magnitude as that of similar species, such as Al-NCO (5.40 eV; Trabelsi et al. 2019b), and smaller than that of Mg-NCO (6.17 eV; Vega-Vega et al. 2017).For future investigations, we recommend the calculated BDE at the CCSD(T)-AE/aug-cc-pWCVQZ level of theory.2. The corresponding photoabsorption cross sections are shown in Fig. 3 for HMgNC (left panel) and HMgCN (right panel), respectively.The neutral and ionic dissociation limits are calculated using the experimental values of the adiabatic electron affinity and the excitation energy of CN (Bradforth et al. 1993;Herzberg & Phillips 1948).For better accuracy, the adiabatic IP of diatomic MgH is calculated at CCSD(T)-AE/aug-cc-pWCVQZ and is predicted to be 6.91 eV.

HMgNC
In Fig. 1 (left panel) the ground state correlates adiabatically to the first dissociation limit H( 2 S) + MgNC(X 2 Σ + ).The first excited triplet state is repulsive and correlates to the same dissociation limit.The adiabatic dissociation of HMgNC to give H + MgNC is accessible in the visible region, requiring 398 nm photons.In the deep and vacuum UV region (λ < 200 nm), the density of the electronic states increases and favors mixing of their wavefunctions, for instance via spin-orbit interactions between singlet and triplet states, vibronic coupling between states with the same spin multiplicity and spatial symmetry, or the Renner-Teller effect if the excited states exhibit a linear configuration.Along the H-Mg stretching coordinate, no excited states are stable relative to the first dissociation limit H( 2 S) + MgNC(X 2 Σ + ).The 2 1 Σ + and 2 1 Π states show a deep potential well with a minimum located above the first dissociation limit.
The 1 1 Π state is flat, correlates to H(2 S ) + MgNC(A 2 Π), and is crossed by the 2 1 Σ + state.At the MRCI+Q level, the 1 1 Π ← X 1 Σ + transition is predicted to occur at 190.7 nm.This state exhibits a multireference character and mainly arises from the promotion of an electron from the highest occupied molecular orbital (HOMO) (9σ) to the (3π x ) MO.This transition is in good agreement with the EOM-CCSD result, which is calculated to be 188.36nm.The oscillator strength of this transition is large and calculated to be 0.1653, meaning that this transition is likely bright and occurs easily.Upon the 1 1 Π ← X 1 Σ + transition, the wavepacket explores the 1 1 Π PES, and the molecule undergoes a large amplitude of motion along the H-Mg coordinate.The flat PES may lead to the H( 2 S) + MgNC(A 2 Π) product.
The 2 1 Σ + ← X 1 Σ + transition is predicted to occur at 184.22 nm at the MRCI+Q level.This value is in better agreement with that calculated with EOM-CCSD (177.70 nm).This transition is the strongest, with a calculated oscillator strength of 0.2565 and an MRCI+Q transition dipole moment of 1.5 Debye for the equilibrium geometry.The 2 1 Σ + state shows a minimum at a large H-Mg distance, and small vibrational frequencies are expected.Upon UV absorption (λ ≈ 185 nm), this state will be populated and may produce the H( 2 S) + MgNC(A 2 Π) product through the 1 1 Π state and via spin-orbit interactions at the crossing point.The 2 1 Π state requires energetic photons (λ ≈ 175 nm) to be populated, and we expect that this state will be crossed by a repulsive triplet state, which may contribute to the production of H and excited MgNC.
In Fig. 1 (right panel), the adiabatic dissociation of HMgNC to give MgH + NC in their ground electronic states is not accessible in the visible region, requiring 242 nm photons.All electronic states are unstable relative to the first dissociation limit since all their minima are located above it.The ground state, X 1 Σ + , correlates to the first dissociation limit MgH(X 2 Σ + ) + CN(X 2 Σ + ) and forms an avoided crossing with the first excited state 2 1 Σ + at R MgN ≈ 5 Å.The 2 1 Σ + state exhibits an ionic character (HMg + NC − ) and correlates to the MgH + (X 1 Σ + ) + CN − (X 1 Σ + ) dissociation limit.This state exhibits a multireference character and mainly arises from promotion of an electron from the HOMO (9σ) to the lowest unoccupied molecular orbital (LUMO) (10σ), with the weight predicted to be 0.33.The second contribution is the promotion of an electron from the (8σ) to (10σ) MO with a weight of 0.53.For the optimized equilibrium geometry, the CASSCF/aug-cc-pV(T+d)Z Mulliken population analysis (PA) for this state shows a positive charge on N (+0.23e) and a negative charge on C (−0.16e), Mg (−0.02e), and H (−0.04e).This distribution changes as the MgN distance λ(nm) f HMgNC 190.74 188.36 0.1653 (0.47) 199.01 197.42 0.1104 (0.63) 177.12 174.13 0.0000 173.64 170.07 0.0000 Notes.In parentheses, the weight of the configuration on the corresponding wavefunction and core represent the lowest 7σ, π x , and π y doubly occupied molecular orbitals.increases.For MgN = 8 Å, the PA shows a positive charge on Mg (+0.97e) and H (+0.02e) and a negative charge on N (−0.58e) and C (−0.41e).We note that there is no noticeable change in the ground state for the equilibrium geometry and at a long range.
The 1 1 Π state correlates to the second dissociation limit MgH(X 1 Σ + ) + CN(A 2 Π) and presents a small barrier of italic R MgN ≈ 2.9 Å, which may be due to an avoided crossing with the upper 2 1 Π state.Unlike the MgH stretch, the 2 1 Π state presents a flat potential and correlates to the third dissociation limit MgH(A 2 Π) + C) N(X 2 Σ + ).The 2 1 Σ + state is crossed by the repulsive 1 3 Σ + state, which correlates to the first dissociation limit.Upon UV absorption to the 2 1 Σ + state, photodissociation to produce MgH and CN in their ground electronic states is a probable mechanism.This process may occur through the avoided crossing with the ground state at R MgN ≈ 5 Å or through the repulsive 1 3 Σ + state.Population of the 1 1 Π and 2 1 Π states may A79, page 5 of 8 A&A 672, A79 (2023) also produce diatomic MgH and CN since they are crossed by the repulsive part of 2 1 Σ + and 1 3 Σ + .The photoabsorption cross section of the HMgNC isomer shows two important peaks at 191 and 175 nm, with predicted intensities of 4.91 × 10 −17 and 8.21 × 10 −17 cm 2 molecule −1 , respectively.These peaks correspond mainly to the 2 1 Σ + ← X 1 Σ + and 1 1 Π ← 1X 1 Σ + transitions.The 1 1 Σ − and 2 1 Σ − states are bound and do not strongly absorb since the oscillator strength is predicted to be zero.

HMgCN
In Fig. 2 (right panel), the high density of electronic states in the UV region is similar to that of HMgNC.The 1 3 Σ + state correlates to the first dissociation limit H( 2 S ) + MgCN(X 2 Σ + ) and forms a shallow potential, which may be due to an avoided crossing with another triplet state.The 1 1 Π state is flat and correlates to the second dissociation limit H( 2 S) + MgCN(A 2 Π).This state strongly absorbs around 200 nm, with a predicted oscillator strength of 0.1104.Upon UV absorption, the wavepacket will explore the 1 1 Π state and may produce H and excited MgCN.The 2 1 Σ + state crosses the 1 1 Π state at R MgC ∼ 2.95 and 3.90 Å and correlates to a higher dissociation limit.
This state is characterized by the greatest oscillator strength, predicted to be 0.4457, which makes the transition likely to occur.Population of the 2 1 Σ + state may favor MgCN in its excited state through the spin-orbit interaction with the 1 1 Π state.The 1 1 Σ − and 2 1 Σ − states are bound and do not absorb in the UV region, meaning that they cannot contribute to HMgCN destruction.The important peak of the photoabsorption cross section of the HMgCN isomer located at 167.5 nm mainly corresponds to 2 1 Σ + ← X 1 Σ + .
In Fig. 2 (right panel), the ground and 1 3 Σ + states adiabatically correlate to the first dissociation limit.The 1 3 Σ + state does not interact with other states and forms a shallow minimum, which may be regarded as a repulsive state.All electronic states are unstable relative to the first dissociation limit.The 1 1 Π state is bound with a deep minimum and forms an avoided crossing with the 2 1 Π state.The 2 1 Σ + state also forms a shallow minimum, which may be due to an avoided crossing with 3 1 Σ + (not shown in Fig. 2, right panel).This state crosses the 1 1 Π and 2 1 Π states many times, and this crossing favors their spin-orbit interaction and vibronic coupling.Similarly to HMgNC, 2 1 Σ + exhibits an ionic character and correlates to the ionic dissociation limit MgH + (X 1 Σ + ) + CN − (X 1 Σ + ).The 2 1 Σ + ← X 1 Σ + transition occurs at 173.89 nm at the MRCI+Q level with a large oscillator strength, making its population easy.Upon 173 nm absorption, many scenarios may occur to produce MgH and CN.The predissociation process may be slow, due to the interaction of the Π and Σ − electronic states.The oscillator strength of A2 1 Π is predicted to be 0.0978, which is important and makes population of this state plausible.Absorption of a photon to this state may produce MgH and CN in their ground and excited states through the spin-orbit interaction with 2 1 Σ + and the avoided crossing with 2 1 Π.

Discussion
A close inspection of Figs.1-3 together with Table 2 shows that the two isomers do not absorb in the mid-ultraviolet-visible (UV-Vis) region.This means that these isomers are photostable in this region and cannot be destroyed by photons with wavelengths greater than 220 nm.According to our PES, the production of triatomic MgCN and MgNC from HMgCN and HMgNC, respectively, is a plausible mechanism.This suggestion competes with the previous formation models of MgCN and MgNC, which are believed to be formed through radiative association of Mg + and cyanopolyynes (Dunbar & Petrie 2002;Petrie 1996a).
According to our PES and vertical excitation energies, HMgNC and HMgCN seem to have the potential to be MgNC and MgCN chemical reservoirs, and their destruction occurs via interstellar UV radiation.This work suggests that the CN and MgH products are also possible and compete with the production of MgNC and MgCN.MgCN and MgNC are produced in their first excited state (A 2 Π).Their de-excitation or relaxation back to the ground state occurs with photon emission in the near-UV-Vis region.Notably, MgCN(A 2 Π) and MgNC(A 2 Π) are very reactive, and their reactions with other species are plausible.Considering the photodissociation processes of HMgNC and HMgCN in chemical models will improve our comprehension of the metal chemistry and formation mechanism of cyanide and isocyanate species.In both isomers, the 2 1 Σ + state plays an important role in the predissociation processes to produce H + MgNC/MgCN and MgH + CN.Along the MgX (X = C and N) stretching coordinates, the ground states and the first excited states form an avoided crossing, which plays an important role in the predissociation of HMgNC/HMgCN.The 2 1 Σ + state is ionic and correlates to the MgH + + CN − dissociation limit, which is located 3.06 eV above the MgH(X 2 Σ + ) + CN(A 2 Π) dissociation limit.
We note that this scenario and the behavior of the excited states considered here could be extended to other isoelectronic species containing metals, such as Na, Ca, Mg, K, and Al.The predissociation process may occur in the visible range when the IP of MH or M is low.For triatomic systems, such as the isoelectronic AlNC molecule, we expect that the predissociation processes may require lower-energy photons than HMgNC.The nondetection of some hydrides, such as HMNC/HMCN (M = Ca, Na, Al, and K), may be due to the dominance of the predissociation processes.Future investigations on the dynamics of the excited-state PESs of HMNC and MNC species are needed to better understand their photostability and photochemistry and to predict the production rate and dominant channels.

Conclusion
In summary, we carried out high-level calculations on the electronic structure of the ground states of HMgNC and HMgCN.The evolutions of the lowest singlet and triplet excited states along the MgC, MgH, and MgN stretching coordinates were mapped and investigated.The evolutions of four singlet states and one triplet state for each isomer were carefully examined.The oscillator strength and vertical excitation energy were calculated at the MRCI+Q and EOM-CCSD levels of theory.Our results should help shed light on the formation processes of MgCN/MgNC species and improve previous models and would be helpful for future experimental investigation of the [H,Mg,N,C] molecular system.Our work represents a first step in the study of the photochemistry of HMgNC and HMgCN.The next step is the determination of the rate coefficients to determine the dominant path and major products, which are MgH + CN or MgNC + H.
Fig. 1.MRCI+Q/aug-cc-pV(T+d)Z one-dimensional cuts of the lowest singlet and triplet electronic states of HMgNC along the R MgH (left panel) and R MgN (right panel) distances.The remaining coordinates were kept fixed in their optimized CCSD(T)-AE/aug-cc-pWCVQZ geometry.
Fig. 2. MRCI+Q/aug-cc-pV(T+d)Z one-dimensional cuts of the lowest singlet and triplet electronic states of HMgCN along the R MgH (left panel) and R MgC (right panel) distances.The remaining coordinates were kept fixed in their optimized CCSD(T)-AE/aug-cc-pWCVQZ geometry.