Chemical Physics 364 (2009) 105–110

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Chemical Physics

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New molecular species of potential interest to interstellar chemistry:A theoretical study of MgSiN, MgNSi and related species

Bhaskar Mondal, Deepanwita Ghosh, Abhijit K. Das *

Department of Spectroscopy, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India

a r t i c l e i n f o a b s t r a c t

Article history:Received 11 May 2009Accepted 8 September 2009Available online 13 September 2009

Keywords:MgSiNMgNSiHeats of formationIonisation energiesProton affinitiesBond dissociation energiesReaction enthalpiesAb initio study

0301-0104/$ - see front matter � 2009 Published bydoi:10.1016/j.chemphys.2009.09.012

* Corresponding author. Tel.: +91 33 24734971; faxE-mail address: spakd@iacs.res.in (A.K. Das).

An ab initio study has been performed to characterize the probable magnesium containing interstellarspecies MgSiN, MgNSi and their ionized, hydrogenated and protonated forms. We are able to locate fourprotonated and four hydrogenated magnesium species with planar geometry at MP2(Full)/cc-pVTZ levelof theory. MgNSi is found to be more stable than MgSiN and their connecting transition state is alsolocated. The ionization potential for both MgSiN and MgNSi are small, 7.91 eV and 7.01 eV, respectively.All possible protonation sites are considered for these two species but the preferred protonation sites arefound to be silicon for MgNSi and nitrogen for MgSiN. Enthalpies of formation at 0 K (DfH�) and bond dis-sociation energies (Do(X–Y)) are computed for all the species at G3 and G3MP2 level of theory. Finally, thereaction enthalpies for ion–molecule processes are calculated and most of the processes are found to beexothermic and hence thermodynamically favorable in interstellar region.

� 2009 Published by Elsevier B.V.

1. Introduction

Magnesium containing molecular radical MgNC has alreadydrawn an enormous attention of theoretical and experimentalchemists. MgNC was the first Mg-containing molecule detectedin circumstellar envelope IRC + 10216 [1,2]. The metastable isomerMgCN was also detected subsequently within IRC + 10216 [3,4].Many theoretical works related to the electronic structure andproperties of MgNC and MgCN can be found in literature [5–7].According to Kawaguchi et al. [2], the source of MgNC may bethe ion–molecule association and dissociative recombination reac-tions in the outer region of the circumstellar envelope IRC + 10216.An ion–molecule association can occur between two existing inter-stellar species Mg+ and HCN/HNC and the dissociative recombina-tion of the product formed MgNCH+/MgCNH+ may produce MgCN/MgNC. The parallel mechanism for the formation of MgCN was pro-posed by Ziurys et al. [4]. According to Ziurys et al. the neutral-rad-ical association reactions between Mg and CN may also be thesource of MgNC and MgCN. On the basis of existing and predictedinterstellar species we have modeled the formation of two Mg-containing species MgNSi and MgSiN which can be a potentialinterest in atmospheric chemistry like MgNC and MgCN. The for-mation of MgNSi can be modeled by a combination of the ion–

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molecule association (1) and dissociative recombination (2)reactions:

Mgþ þHSiN!MgNSiHþ þ hm ð1ÞMgNSiHþ þ e!MgNSiþH ð2Þ

A similar mechanism involving association with HNSi can formMgSiN

Mgþ þHNSi!MgSiNHþ þ hm ð3ÞMgSiNHþ þ e!MgSiNþH ð4Þ

A neutral-radical association reaction may be an alternative path-way for the formation of MgNSi/MgSiN as proposed by Ziurys etal. for MgNC/MgCN

Mgþ SiN!MgNSiþ hm ð5aÞMgþ SiN!MgSiNþ hm ð5bÞ

In this context it is important to note that SiN is a reported interstel-lar species [8] whereas HSiN and HNSi are predicted to be potentialcandidates for interstellar detection [9,10].

In order to understand this proposed mechanisms for siliconcontaining molecules we have carried out a detailed theoreticalstudy of MgNSi, MgSiN and their ionized, hydrogenated and pro-tonated forms. This provides information about the molecularstructure and properties of possible precursor of MgNSi and MgSiN,about the energetic of some ion–molecule reactions involved inmagnesium chemistry and ionization potential and proton affinity

106 B. Mondal et al. / Chemical Physics 364 (2009) 105–110

of MgNSi and MgSiN. It is true that one of the most importantproperties of a molecule in gas-phase is its proton affinity, a mea-sure of its basicity, particularly in proton-rich interstellar mediumwhere proton-transfer reactions play an important role. The under-standing of the proton-transfer reaction is very important in thecontext of interstellar chemistry. Several theoretical works werecarried out on MgNC, MgCN and their related compounds but fortheir important silicon analogues MgNSi and MgSiN, no studyhas been made so far. The probable reason for this is that theMg-containing silicon compounds are not yet detected in the inter-stellar medium. To facilitate the detection of such species, we havemade a systematic study of [Mg, Si, N]-containing species designedto furnish reliable theoretical data for the bond energies, ionizationenergies and formation enthalpies. In the present article, we haveemployed G3 and G3MP2 method to study MgNSi, MgSiN, andtheir protonated, hydrogenated and ionized forms.

2. Computational details

Ab initio molecular orbital calculations are carried out to charac-terize the species under investigation using Gaussian 03 suite ofquantum chemical programs [11]. All the equilibrium geometriesand transition states are obtained using second order M�øller–Ples-set perturbation theory (MP2) with a correlation-consistent polar-ized valence triple zeta cc-pVTZ basis set [12,13]. The valance aswell as core electrons are considered with ‘Full’ option for theMP2 method. For the doublet species studied here the spin con-taminant is not severe; i.e., the hS2i values of doublet Mg-speciesare less than 0.76, very close to the expected value of the pure dou-blet states 0.75. To locate the transition states we have used syn-chronous transit-guided quasi-Newton (STQN) methods at theMP2(Full)/cc-pVTZ level of theory. Frequency calculation at thesame level of theory confirms the equilibrium structures (no imag-inary frequency) and a first order saddle point (one imaginary fre-quency). For the accurate evaluation of the thermochemicalparameters G3 and G3MP2 methods are used. The G3 andG3MP2 methods are composite techniques in which a sequenceof well-defined ab initio molecular orbital calculations is performedto arrive at a total energy of a given molecular species. The totalenergy obtained by G3 method can be written in the followingway:

E0ðG3Þ ¼ E½MP4=6-31GðdÞ� þ DEðþÞ þ DEð2df ;pÞ þ DEðQCIÞþ DEðG3largeÞ þ DEðSOÞ þ EðHLCÞ þ EðZPEÞ

where the terms on the right hand side are essentially the singlepoint energies. DE(+) is the correction for diffuse function,DE(+) = E[MP4/6-31 + G(d)] � E[MP4/6-31G(d)], DE(2df, p) is thecorrection for higher polarization functions, DE(2df, p) = E[MP4/6-31G(2df, p)] � E[MP4/6-31G(d)], DE(QCI) is the correction for corre-lation effects beyond fourth order perturbation theory using thequadratic configuration interaction method, DE(QCI) = E[QCISD(T)/6-31G(d)] � [MP4/6-31G(d)] and DE(G3large) is the correction forlarger basis set effects and for the nonadditivity caused by theassumptions of separate basis set extensions for diffuse functionsand higher polarization functions, DE(G3large) = E[MP2(full)/G3lar-ge]� E[MP2/6-31G(2df, p)]� E[MP2/6-31 + G(d)] + E[MP2/6-31G(d)].The DE(SO) and E(HLC) are spin–orbit corrections and high-levelcorrections respectively. The HLC is –Anb–B(na � nb) for moleculesand –Cnb–D(na � nb) for atoms (including atomic ions). The nb andna are the number of b and a electrons, respectively, with na P nb.The number of valence electron pairs corresponds to nb. Thus, A isthe correction for pairs of valence electrons in molecules, B is thecorrection for unpaired electrons in molecules, C is the correctionfor pairs of valence electrons in atoms, and D is the correction forunpaired electrons in atoms. The entire calculation is done with

the MP2(full)/6-31G(d) equilibrium geometry and the HF/6-31G(d) harmonic vibrational frequency scaled by a factor of0.8929 [14].

G3MP2 theory is based on MP2(full)/6-31G(d) geometries usingall electrons [15]. The total energy obtained by G3MP2 method canbe written as

E0ðG3MP2Þ ¼ E½QCISDðTÞ=6-31GðdÞ� þ DEMP2 þ DEðSOÞ þ EðHLCÞþ EðZPEÞ

The correction at the second order Moller–Plesset level (MP2) is gi-ven by

DEMP2 ¼ E½MP2=G3MP2large� � E½MP2=6-31GðdÞ�

As MP2 geometries are good enough for Mg-containing molecularspecies, we use G3 and G3MP2 methods with MP2 geometry to cal-culate the energies accurately. Some inconsistent results are ob-tained using G3 and G3B3 for HMgNSi molecule. This may be dueto the non-existence of HMgNSi on HF surface because both G3and G3MP2 use the frequency value from HF calculation. UsingG3B3 and CBS-QB3 methods, we observe that the frequency fromthe density functional calculation improves the results for HMgNSi.Our main objective of this article is to explore the thermochemicalproperties which may govern the formation of MgNSi and MgSiNwithin the circumstellar envelopes and interstellar clouds. For thispurpose, the values of the heat of formation (DfH�) at 0 K and bonddissociation (Do(X–Y)) are essential. The atomization approach [16]is used to calculate the heat of formation values and in the calcula-tion of heat of formation and bond dissociation energies for ionicspecies, the dissociation to Mg+ is considered. All the species re-ported here are in their ground state. For the linear and non-linearcharged species, the origin is considered on N atom and Si atom,respectively to evaluate the dipole moment.

3. Results and discussion

The equilibrium geometries and transition states obtained byMP2(Full)/cc-pVTZ method are shown in Fig. 1. The total energiesand ground electronic states for all the species at MP2, G3 andG3MP2 level of theories are displayed systematically in Table 1.Some important molecular constants for MgNSi and MgSiN arepresented in Table 2. Atomization energies and enthalpies of for-mation at 0 K calculated using two different methods are listedin Table 3. Ionization energies, proton affinities and bond dissocia-tion energies are summarized in Tables 4 and 5, respectively.

3.1. [Mg, N, Si]

On the potential energy surface of [Mg, Si, N] species we havelocated two linear isomers I and II at MP2(Full)/cc-pVTZ level oftheory. In the previous studies with MgCN and MgNC moleculesa cyclic isomer was also located along with two linear isomersand the cyclic isomer was found to be the most stable species[6,7]. At the same level of theory we could not find any cyclic iso-mer for [Mg, N, Si]. Among the two linear isomers obtained for [Mg,N, Si] system I is stable over II by 57.40 kcal mol�1 at G3MP2 levelof theory. This order of stability is also reflected in their heat of for-mation values which are 70.71 kcal mol�1 and 128.12 kcal mol�1

for I and II, respectively at 0 K. Our search for an interconnectingtransition state for MgNSi M MgSiN conversion is successful to lo-cate a transition state TS1 having bent structure with\MgSiN ¼ 114:33�. In I the Mg–N and N–Si bond distances are1.922 Å and 1.585 Å, respectively and in II the Mg–Si and Si–Nbond distances are 2.572 Å and 1.637 Å, respectively. The typicalSi–N bond length is 1.71–1.78 Å which is much greater than theSi–N bond length obtained for the MgNSi/MgSiN isomeric pairs

MgSiN

Mg N Si1.922 1.585

0.335 -0.488 0.152Mg Si N2.572

1.637

0.422 0.023 -0.446Mg Si

N

2.4681.563

114.3

0.335 0.058

-0.394

I II TS1

MgSiN+

Mg N Si1.840 1.595

1.052 -0.470 0.418Mg Si N2.516 1.678

1.001 0.294 -0.295Mg Si

N

2.3531.534

121.8

0.871 0.359

-0.231

I + II + TS1+

HMgSiN

H Mg Si N1.678 2.512 1.635

-0.210 0.577 0.059 -0.426

H Mg N Si1.6841.914

176.8

1.589-0.237 0.554 -0.488 0.171

Mg Si NH2.516

1.5670.997

174.5

159.00.142 0.210

-0.582 0.230

III IV V

MgN

Si

H

1.911 1.606

1.523141.8

128.3

0.315 -0.44

0.196

-0.070

VI

HMgSiN+

H Mg

Si

N1.648

2.859 1.503178.3

161.6

-0.084 0.825

0.325

-0.066 H Mg N Si1.6641.962

1.500

-0.113 0.752 -0.424 0.785

Mg Si N H3.015 1.511 0.998

178.80.805 0.361 -0.440

0.274

III+ IV+ V+

Mg N

Si

H

159.7

120.21.822

1.5001.602

1.043 -0.459 0.386

0.030

VI+

Fig. 1. MP2/cc-pVTZ geometries of the species involved (Mulliken charges on individual atoms are shown in italics).

B. Mondal et al. / Chemical Physics 364 (2009) 105–110 107

[17]. The TS1 is much like II and the Mg–Si and Si–N bonds areshortened by 0.104 Å and 0.074 Å, respectively as we move fromII to TS1. The structure labeled as TS1 has one imaginary vibra-tional frequency corresponding to the bending mode with value180.3i. The G3MP2 bond dissociation energies Do(Mg–NSi) = 75.45 kcal mol�1 for I and Do(Mg–SiN) = 18.04 kcal mol�1

for II are very much consistent with the calculated G3 bond disso-ciation energies for I and II. During G3 and G3MP2 calculations, ageometry optimization is performed at MP2(Full)/6-31G(d) level

and the bond distances obtained by G3 and G3MP2 level are in fullagreement with MP2(Full)/cc-pVTZ result. A wave function basedmethod QCISD with a relatively large basis set like 6-311++G(d,p)is also applied to verify the geometries of [Mg, N, Si] species. TheQCISD method yields Mg–Si and Si–N bond lengths 2.644 Å and1.587 Å, respectively for species I and Mg–N and N–Si bond lengths1.939 Å and 1.581 Å, respectively for species II. All the Mg-contain-ing species discussed here are electrostatically bonded as observedfrom the Milliken charges on the individual atoms shown in Fig. 1.

Table 1Total energies (au) for magnesium compounds and related species.

Species MP2(Full)/cc-pVTZ ZPVE G3 G3MP2

MgSiN (X2R+) �543.351540 0.003745 �543.895170 �543.315935MgNSi (X2R+) �543.434843 0.004759 �543.984548 �543.407422MgSiN+ (X1R+) �543.077631 0.00369 �543.602836 �543.024944MgNSi+ (X1R+) �543.180132 0.004592 �543.724946 �543.149461HMgSiN (X1A0) �543.957001 0.008638 �544.501279 �543.921741HMgNSi (X1A0) �544.044635 0.009887 �544.596443 �543.9947773MgSiNH (X3A0) �543.950411 0.014161 �544.499196 �543.923548MgNSiH (X1A0) �543.961038 0.010649 �544.523806 �543.947469HMgSiN+ (X2A0) �543.575943 0.008909 �544.162285 �543.584869HMgNSi+ (X2R+) �543.680735 0.011625 �544.232685 �543.658043MgSiNH+ (X2A0) �543.752570 0.017225 �544.295161 �543.718385MgNSiH+ (X2A) �543.717346 0.011432 �544.262231 �543.687680MgH (X2R+) �200.205233 0.003652 �200.454148 �200.199396MgH+ (X1R+) �199.953199 0.004115 �200.197566 �199.943698HSiN (X1R+) �344.254991 0.009744 �344.551231 �344.231121HNSi (X1R+) �344.350112 0.013921 �344.655606 �344.3358413HNSi (3A0) �344.196636 0.011036 �344.525025 �344.204167SiN (X2R+) �343.366935 0.003454 �343.958129 �343.636334

Table 2Harmonic vibrational frequencies (cm�1), rotational constant (GHz) and dipolemoment (Debye) were obtained at the MP2(Full)/cc-pVTZ level of theory.

MgNSi MgSiN MgNSi+ MgSiN+

m1-Bend 88.4 192.8 93.6 283.7m2-Mg–N/Si stretch 521.3 303.6 542.5 280.0m3-Si–N stretch 1146.7 954.6 1268.1 772.1A 3.18 2.91 3.31 2.96l 0.83 9.22 10.10 17.12

Table 3Atomization energies and heat of formation (kcal mol�1) at 0 K ðDH0

f Þ for MgSiN andrelated species.

Species RDo (G3) RDo (G3MP2) DH0f ðG3Þ DH0

f ðG3MP2Þ

MgSiN 126.20 125.80 127.70 128.12MgNSi 182.30 183.20 71.62 70.71MgSiN+ 122.30 121.98 307.93 308.25MgNSi+ 198.92 200.12 231.31 230.11HMgSiN 192.16 191.03 113.37 114.50HMgNSi 251.87 236.86 53.65 68.67MgSiNH 190.85 192.16 114.68 113.37MgNSiH 206.30 207.17 99.23 98.36HMgSiN+ 158.97 158.43 322.88 323.42HMgNSi+ 203.15 204.35 278.70 277.50MgSiNH+ 242.35 242.21 239.50 239.64MgNSiH+ 221.70 222.95 260.16 258.91

Table 4Ionization energies (eV) and proton affinities (kcal mol�1) for [Mg, Si, N]-containingspecies.

Parameter G3 G3MP2

Ei/eVMgSiN 7.954 7.918MgNSi 7.063 7.019HMgSiN 9.224 9.166HMgNSi 9.898 9.162MgSiNH 5.551 5.582MgNSiH 7.117 7.069

Epa/kcal mol�1

MgSiN 250.71 252.26MgSiN 171.07 168.62MgNSi 173.84 175.46MgNSi 155.63 157.19

Table 5Bond dissociation energies (kcal mol�1) for [Mg, Si, N]-containing species.

Species D0(X–Y)

G3 G3MP2

Mg–SiN 18.58 18.04Mg–NSi 74.66 75.45Mg+–SiN 14.67 14.23Mg+–NSi 91.30 92.37H–MgSiN 65.95 65.23H–MgNSi 69.58 53.66HMg–SiN 55.84 53.97HMg–NSi 115.56 99.80MgNSi–H 24.00 23.97MgSiN–H 64.64 66.37Mg–NSiH 40.88 41.10Mg–SiNH 44.84 43.93HMg+–SiN 4.13 3.03HMg+–NSi 48.30 48.94H–MgSiN+ 36.67 36.44H–MgNSi+ 4.22 4.23Mg+–SiNH 11.44 10.43Mg+–NSiH 56.27 56.87MgSiN+–H 120.05 120.22MgNSi+–H 22.76 22.82

108 B. Mondal et al. / Chemical Physics 364 (2009) 105–110

3.2. [Mg, N, Si]+

We have located two equilibrium structures I+ and II+ on the po-tential energy surface of [Mg, N, Si]+ systems with their intercon-necting transition state TS1+ at the MP2(Full)/cc-VTZ level. Theorder of relative stability of these three species at the same levelof theory is as follows: I+ (0.0 kcal mol�1) > II+ (63.75kcal mol�1) > TS1+ (84.91 kcal mol�1). As expected, like neutralspecies, no cyclic isomer is found for [Mg, N, Si]+ species which iscontrary to the earlier theoretical work with similar type of species[Mg, N, C] where both neutral and cationic potential energy sur-faces contain a stable cyclic isomer [6,7]. Unlike carbon, inclusionof silicon destabilizes the cyclic system and always optimizes toone of the linear isomeric forms. The Mg–N distance in I+ andMg–Si distance in II+ are 1.840 Å and 2.516 Å, respectively, bothdistances are somewhat smaller than those in the neutral counter-part. This observation is corroborated with the fact that after re-moval of one electron from I and II more positive chargeconcentrates on Mg and hence the electrostatic attraction betweenMg and Si and Mg and N increases. Very high dipole moment of II+

indicates a strong charge separation in the species and can be con-

Table 6Reaction enthalpies (kcal mol�1) for some possible ion–molecule process for theproduction of precursors of MgSiN at the indicated level of theory.

Reaction DrH (G3) DrH (G3MP2)

Mg+ + HSiN ? MgNSi+ + H �33.18 �33.72Mg+ + HSiN ? MgSiN+ + H 43.39 44.36Mg+ + HNSi ? MgNSi+ + H 32.77 32.45Mg+ + HNSi ? MgSiN+ + H 109.36 110.55

MgH+ + HSiN ? MgNSiH+ + H �8.87 �9.04MgH+ + HSiN ? MgSiNH+ + H �29.35 �28.12MgH+ + HNSi ? MgNSiH+ + H 57.08 57.14MgH+ + HNSi ? MgSiNH+ + H 36.60 38.05

MgH+ + HSiN ? MgNSi+ + H2 �89.74 �90.53MgH+ + HSiN ? MgSiN+ + H2 �13.15 �12.43MgH+ + HNSi ? MgNSi+ + H2 �23.77 �24.34MgH+ + HNSi ? MgSiN+ + H2 52.80 53.74

B. Mondal et al. / Chemical Physics 364 (2009) 105–110 109

cluded as Mg2+–SiN-. The calculated G3MP2 ionization energy for Iis 7.019 eV which is little lower than the ionization energy7.918 eV of II. These ionization energies deviate very little for dif-ferent theories. The Si–N distances in I+ and II+ are 1.595 Å and1.678 Å, respectively, both values are increased from their neutralcounterparts. As expected this is the opposite case of Mg–Si or Mg–N bonds. In this system we also located the interconnecting transi-tion state (TS1+) for the conversion I+

M II+ at the MP2(Full)/cc-pVTZ level. Like the neutral species, here the TS1+ is close to II+

with the \MgSiN ¼ 121:8�. The transition state TS1+ is more dif-fuse than TS1 as the angle \MgSiN is increased by 7.45� fromTS1 to TS1+. TS1+ has the negative imaginary frequency of235.40i due to the bending mode of vibration and both the Mg–Si and Si–N bonds get shortened compared II+. We also appliedthe MP2 geometry based methods G3 and G3MP2 for the calcula-tion of thermochemical parameters of the cationic species. The val-ues for heat of formation for I+ and II+ are 230.11 kcal mol�1 and308.25 kcal mol�1, respectively at G3MP2 level of theory. The suf-ficiently high dissociation energy of II+ (Do(Mg+–SiN) = 14.23kcal mol�1) and I+ (Do(Mg+–NSi) = 92.37 kcal mol�1) indicates asmall degree of covalent character in these two species.

The harmonic vibrational frequencies, rotational constants anddipole moments for the species I, II, I+ and II+ are displayed in Table2 at the MP2(Full)/cc-pVTZ level.

3.3. [Mg, N, Si, H]

On the potential energy surface of [Mg, N, Si, H] species four dif-ferent isomers are located at MP2(Full)/cc-pVTZ level and out ofthem only the isomer III is linear which is opposite in nature towhat we observed in the previous study on [Mg, C, N, H] specieswhere most of the isomers were linear [7]. Among the four iso-meric species, III, IV and VI are located on their singlet surfacebut the isomer V is not found on its singlet surface; it is locatedon its triplet surface. The heat of formation, ionization energyand bond dissociation energy for these species calculated usingG3 and G3MP2 methods are summarized in Tables 3–5, respec-tively. It can be seen from the Tables 3 and 5 that the calculatedvalues for IV at two different levels of theories are inconsistent.For example, DfH�(HMgNSi) = 53.65 and DfH�(HMgNSi) = 68.67 atG3 and G3MP2 level, respectively, Do(H–MgNSi) = 69.58 (G3 value)and Do(H–MgNSi) = 53.66 (G3MP2 value) and Do(HMg–NSi) = 115.56 (G3 value) and Do(HMg–NSi) = 99.80 (G3MP2 value).This may be due to the non-existence of the species IV on Hartree–Fock (HF) surface which is the base of G3 and G3MP2 methods. Toovercome this inconsistency we have applied two density func-tional based methods G3B3 and CBS-QB3 to IV. We obtained satis-factory results at the G3B3 and CBS-QB3 level of theory. The resultsare as follows: DfH�(HMgNSi) = 51.66 (G3B3 value), DfH�(HMgNSi)= 51.33 (CBS-QB3 value), Do(H–MgNSi) = 71.37 (G3B3 value),Do(H–MgNSi) = 70.07 (CBS-QB3 value), Do(HMg-NSi) = 115.77(G3B3 value) and Do(HMg–NSi) = 115.92 (CBS-QB3). All values gi-ven in this section are in kcal mol�1. Among the four singlet spe-cies, IV is found to be the most stable one which is confirmed bydifferent level of theories.

3.4. [Mg, N, Si, H]+

On the search of the protonated species of [Mg, N, Si], we haveconsidered the protonation of each terminal atom in each of MgNSiand MgSiN and we obtained four stable protonated species on thedoublet potential energy surface of [Mg, N, Si, H]+. Among thesespecies the isomer IV+ and V+ are optimized to linear minima butIII+ and VI+ are optimized to non-linear minima at the MP2(Full)/cc-pVTZ level. The G3MP2 proton affinities of MgSiN are calculatedto be 252.26 kcal mol�1 and 168.62 kcal mol�1 due to protonation

to terminal nitrogen atom and protonation due to terminal magne-sium atom, respectively. Similarly, the G3MP2 proton affinities ofMgNSi are 175.46 kcal mol�1 and 157.19 kcal mol�1 due to proton-ation to terminal silicon and magnesium atom, respectively. Fromthe protonation enthalpies it is clear that the protonation to theterminal nitrogen or silicon atom is more favorable than the termi-nal magnesium atom. The production of the magnesium-hydroge-nated species V+ and VI+ from MgH+ + HNSi is endothermic innature. The H–Mg bond dissociation energies for III+ and IV+ are36.44 kcal mol�1 and 4.23 kcal mol�1, respectively. The bond be-tween Mg and central heavy atom is weaker by �7.5 kcal mol�1

for the Mg-hydrogenated species III+ and IV+ than for the N or Si-hydrogenated species V+ and VI+. This observation is similar to thatpreviously found by Petrie for [Mg, N, C, H]+ compounds [7].

3.5. Reaction enthalpies

As discussed earlier the formation of [Mg, N, Si] species may in-volve dissociative recombination and neutral-radical association. Adiscussion regarding the reaction enthalpies for some of the possi-ble processes for the production of precursors of [Mg, N, Si] is nec-essary in order to observe these species in the interstellar medium.In Table 6 we have listed some of the processes which could be ini-tiated by Mg+, where MgH+ can be formed by the processMgþHþ3 !MgHþ þ H2. The reaction enthalpies are calculatedusing G3 and G3MP2 methods. We also used MP2 (Full)/cc-pVTZmethod to calculate the reaction enthalpies and also to verify withthose obtained by G3 and G3MP2 methods. We found that the MP2(Full)/cc-pVTZ values are consistent with G3 and G3MP2 results. AsHSiN and HNSi are predicted to be potential candidates in theinterstellar medium, both of their reactions are considered.

The reaction of Mg+ with HSiN for the production of MgNSi+ isthe only exothermic process among the four processes. A muchhigher stability of MgNSi+ over MgSiN+ is reflected from the reac-tion enthalpy value. In the reaction of Mg+ with HNSi forming bothMgNSi+ and MgSiN+, a significant amount of endothermicities arefound. The last set of channels regarding the production of MgSiN+

and MgNSi+ can be compared with the channel discussed above.Association of MgH+ with HSiN and HNSi can produce MgSiN+

and MgNSi+ via H2 elimination. Here only the fourth channel isendothermic and the endothermicity is lowered by half of that ofthe fourth channel of the first set of reactions involving hydrideelimination. The other three channels are substantially exothermicand for the first channel the exothermicity is almost thrice than thefirst one of the first set of reactions. Analyzing these results we canconclude that the formation of the MgSiN+ and MgNSi+ are morefavorable by the association of MgH+ and HSiN/HNSi rather thanby the association of Mg+ and HSiN/HNSi.

110 B. Mondal et al. / Chemical Physics 364 (2009) 105–110

The productions of MgNSiH+ and MgSiNH+ from the reactionMgH+ + HSiN are calculated to be exothermic. It should be notedthat even if exothermic processes are required for gas-phase inter-stellar chemistry, exothermicity is not enough to ensure that theprocess will occur. No barrier must appear along the reaction pathsas is the case here for the reactions presented on Table 6 and thereactions must be, ultimately and whatever the reaction paths, dis-sociative in order to transform the excess energy (exothermicity)into kinetic energy for the fragments.

4. Conclusions

A detailed theoretical study of the [Mg, N, Si] and its ionized,protonated and hydrogenated forms has been carried out. Geome-try optimizations at a correlated level of theory with a correlation-consistent basis set give a number of stable isomers of the studiedspecies. No stable cyclic isomer is possible for [Mg, N, Si], they canonly exists in linear minima among which MgNSi is stable overMgSiN by 57.40 kcal mol�1 at G3MP2 level. The ionized [Mg, N,Si] species have the same geometrical characteristics as the neutralspecies. Proton affinities of different terminal atoms of [Mg, N, Si]are different, protonation of N and Si are more favorable than theprotonation of Mg of MgSiN and MgNSi respectively. Proton affin-ities for both the isomers are relatively high, 252.26 kcal mol�1

(MgSiN) and 175.46 kcal mol�1 (MgNSi), and therefore these spe-cies should yield protonated derivatives in proton-rich medium.The important properties like ionization energies and bond ener-gies of the probable precursors of [Mg, Si, N] are discussed system-atically. Comparable ionization energies have been found for all thehydrogenated species except MgSiNH, its ionization is the lowestamong all the species. Among the hydrogenated species lowestbond dissociation energy has been found for H–Si bond and amongthe protonated species, lowest bond dissociation energy has beenobtained for H–Mg bond in H–MgNSi+. We have calculated thereaction enthalpies for many ion–molecule processes related to

the formation of [Mg, Si, N] species. The formations of MgNSi+

are exothermic for Mg+ + HSiN association as well as MgH+ + HSiNassociation and MgSiN+ formation is exothermic only forMgH+ + HSiN association. Our detailed theoretical study may behelpful for the probable detection of [Mg, N, Si] and [Mg, N, Si]+

in interstellar medium.

Acknowledgements

B. Mondal is grateful to the Council of Scientific and IndustrialResearch (CSIR), Govt. of India for providing him Junior ResearchFellowship (JRF) to carry out research works. Thanks are due tothe reviewer for his constructive comments and valuable sugges-tions to improve the manuscript.

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