Computational and Theoretical Chemistry 1032 (2014) 1–6

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Computational and Theoretical Chemistry

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Interaction of third-row main group dicarbides, C2X (X = K–Br)with molecular oxygen: A density functional study

2210-271X/$ - see front matter � 2014 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.comptc.2014.01.021

⇑ Corresponding author.E-mail address: sridharsahu@gmail.com (S. Sahu).

Saroj K. Parida a, Sridhar Sahu a,⇑, Sagar Sharma b

a Department of Applied Physics, Indian School of Mines, Dhanbad, Jharkhand 826004, Indiab Department of Organic Chemistry, Weizmann Institute of Science, Rehovot 76100, Israel

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

Article history:Received 21 November 2013Received in revised form 20 January 2014Accepted 20 January 2014Available online 30 January 2014

Keywords:Density functional theoryThird-row main group dicarbidesOxygen adsorptionELFAIM

In this work, we present our calculations, based on density functional theory (DFT) to investigate themolecular adsorption of O2 on the third-row main group dicarbides, C2X, with X = K, Ca, Ga, Ge, As, Se,Br. The structures of the host C2X clusters, except C2Ga and C2Ge, are found to be weakly modified in pres-ence of O2 adsorbate. C2Ga and C2Ge clusters which show cyclic ground-state structures become linearwhile interacting with O2 molecule. It is observed that the O–O stretching frequencies in C2XO2 arered-shifted in comparison to that in O2 molecule, whereas the C–C stretching frequencies are found tobe increased. The calculated adsorption (Eads) and Gibbs’ free energies (dG) for the clusters with evennumber of electrons are found to follow the order of C2CaO2 > C2GeO2 > C2SeO2, whereas the increasein O–O bond lengths follows the reverse order, i.e. (O–O)C2SeO2

> (O–O)C2GeO2 > (O–O)C2CaO2. On the otherhand, for the clusters with odd number of electrons, Eads and O–O bond lengths follows almost the sameorder. Existence of disynaptic basins V (C,O) and their corresponding lower relative fluctuation andhigher covariance values based on ELF topological analysis infers that the electrons are delocalized inthese areas giving rise to shared-electron interactions. In addition, large electron density at the bond crit-ical point (BCP) between C (of host cluster) and O (of adsorbate) also infers the C–O bonding to be shared-type. This fact is also found to be supported by large delocalization index for C and O as compared to thatfor X and O.

� 2014 Elsevier B.V. All rights reserved.

1. Introduction

Over last few decades pure and heteroatom-doped interstellarcarbon clusters have received considerable attention due to theirnovelty and wide potential applications in various research areas[1–3]. Since the discovery of small molecules such as C2S, C2Siand C4Si clusters in the circumestellar envelop of carbon-richIRC + 10216, small neutral and ionic carbon clusters doped withs-, p-, and d-block elements have been the subject of extensiveinvestigation from both experimental and theoretical point of view[4–6]. Specific examples include the experimental and theoreticalstudies of heteroatom-doped ionic and neutral dicarbides such asC2Li, C2O, C2Na, C2Mg, C2P, C2S, C2Cl and so on [7–15]. Extensivetheoretical investigations of these heteroatom-doped carbonchains have been further carried out by Tang et al. and Largo andco-workers [16–20]. In addition, elaborate theoretical work onstructural and bonding nature of the dicarbides doped withthird-row main group elements such as K, Ca, Ga, Ge, As, Se, andBr has been performed by Largo et al. using correlation-consistentwave function based methodologies [21,22]. Moreover, dicarbides

and other medium-sized carbon chains doped with transition met-als such as Ti, V, Fe, Co, Ni, and Zn have been investigated by manyauthors [23–29]. Similarly, both experimental and theoreticalworks of carbon clusters doped with other elements have also beencarried out by few researchers. For example, Jarrold and co-work-ers explored the structures of LaCþn and NbCþn clusters using in-jected ion drift tube techniques [30,31].

Despite extensive theoretical and experimental studies of struc-tural, electronic, magnetic, and thermodynamic properties of het-ero-atom doped carbon clusters, however, only a handful of workhave been published reporting the adsorption phenomena in thesecarbon chains and other carbon based materials. Though roles ofencapsulated metal carbides in fullerene cages have been widelydiscussed by many authors, however, interactions of carbide clus-ters with important molecules such as O2, and CO2 are yet to be ex-plored explicitly [32,33]. In a recent theoretical study, Liu et al.investigated H2 adsorption on hydrogen and alkali metal (Li,Na)terminated carbon chains and found that for metal capped carbonchain, H2 molecules are absorbed both on the terminated metalsand the carbon atoms [34]. Reactivity of di- and tri-carbon clusterstoward unsaturated hydrocarbons were experimentally exploredby Kaiser et al. who thereby shed light on the formation of hydro-gen-deficient carbonaceous molecules in certain interstellar clouds

2 S.K. Parida et al. / Computational and Theoretical Chemistry 1032 (2014) 1–6

[35]. The same group also reported crossed beam and ab initiostudy of the reaction of hydrogen sulfide with dicarbon [36]. Sim-ilarly, the experimental investigation was carried out by Eichelber-ger et al. who revealed that the ionic chains are more reactivetowards O than H and N atoms [37]. Dibben and co-workers, per-forming both experimental and theoretical studies, explained theinteraction of H2O molecules with linear carbon clusters and con-sequently revealed the photoproducion of CnO and C2H2 com-pounds from Cn�H2O complexes [38]. Moras et al. performedtheoretical calculation and showed that the chemisorption of O2

molecules on carbon chains results in cleavage and shortening ofthe carbynoid structures [39]. Similarly, crossed-beam reaction ofdicarbon with benzene molecule to synthesize phenylethynyl rad-ical was carried out by Gu and co-workers. [40]. In a previous work,the author studied the interaction of O2 molecule withC2X; ðX ¼ Na—ClÞ chains [41]. In this paper, we study the interac-tion of molecular oxygen with dicarbides doped with third-rowmain group elements such as K, Ca, Ga, Ge, As, Se, and Br.

The rest of the paper has been organized as follows: In Section 2we discuss the detailed computational work, in Section 3 we ana-lyze the results and in Section 4 we present the conclusion.

2. Computation

For the present study, all structures were optimized usingBecke’s three-parameter hybrid exchange functional and the Lee–Yang–Parr correlation functional (B3LYP) and 6-311++G (d,p) basissets in the framework of density-functional theory (DFT) [42–45].We also optimized the clusters at B3LYP/LANL2DZ level of theoryto check the effect of basis sets on the geometries of the clusters.All the clusters were optimized with O2 molecule placed at differ-ent possible sites of C2X with X = K, Ca, Ga, Ge, As, Se, Br, and theoptimization was accomplished without any imaginary harmonicfrequencies. In this article we have only focused on the molecularadsorptive mechanism of O2 even though the reactivity profile in-cludes both adsorption and dissociation of O2 molecule. All the cal-culations were performed using the computational chemistryprogram Gaussian 09 and the graphical user interface Gaussviewand Chemcraft softwares [46,47]. Furthermore, to explore the reac-tivity of the clusters towards O2 molecule, we also employed elec-tron localization function (ELF) analysis and Bader’s theory ofatoms in molecules using Top-Mod and AIMALL computationalpackages respectively [48,49].

Adsorption energies (Eads) and change in Gibb’s free energies(dG) of C2XO2 clusters were calculated using the followingequations:

Eads ¼ ½EðC2XO2Þ � ½EðC2XÞ þ EðO2Þ�

dG ¼ E0 þ Gð ÞC2XO2� E0 þ Gð ÞC2X þ E0 þ Gð ÞO2

n o

where EðC2XÞ; EðO2Þ; EðC2XO2Þ, denote the calculated total ener-gies of C2X, O2, and C2XO2 clusters respectively. ðE0 þ GÞ is thesum of the total electronic energy (including zero-point vibrationalenergy (ZPVE)) and correction in Gibbs free energy (at 298 K) for thecorresponding subscripted compounds.

3. Results

In this section, we present the results of our density functionalcalculations regarding the molecular adsorption of O2 on C2X clus-ters with X = K, Ca, Ga, Ge, As, Se, Br (henceforth, X, in general, rep-resents the element from K to Br unless otherwise specified).

Before we investigate the interaction of C2X with O2, weoptimized the bare C2X clusters at B3LYP/6-311++G (d,p) andB3LYP/LANL2DZ levels to cross-check our results with those

reported by other authors. Results obtained for all the bare clustersat B3LYP/6-311++G (d,p) level of theory are similar to those re-ported by other authors. For example, the lowest-energy structuresof C2K and C2Ca are found to be cyclic with the electronic states of2A1 and 1A1 respectively which are exactly same as obtained atQCISD/aug-cc-pVTZ by Largo and co-workers [22]. Similar resultsare found in the cases of C2As, C2Se, and C2Br. However, atB3LYP/LANL2DZ, we find a mismatch in the cases of C2Ga andC2Ge clusters. In contrast to the previous results (at B3LYP/6-311++G (d,p)), the lowest-lying structures of C2Ga and C2Ge atB3LYP/LANL2DZ level are obtained to be linear with the electronicstates of 2Rþ and 1Rþ respectively.

In Fig. 1, we present the optimized structures of C2XO2 alongwith few high-energy configurations. Some other possible high-energy structures of these clusters are provided in the Supplemen-tary material. It is observed that in presence of O2 adsorbate,structures of the host C2X clusters, except C2Ga and C2Ge, areweakly modified resulting in C2XO2 complexes. The two clusters,C2Ga and C2Ge, which have cyclic ground-state structures, how-ever, become linear in presence of O2 molecule.

The bond length and vibrational frequency of small moleculesabsorbing on the clusters are considered to be two important indi-cators of chemical activities of the clusters. In Table 1, we presentthe bond lengths of C2X clusters with and without O2 adsorbate. Itis observed that, in comparison with their respective bond lengthsin bare C2X clusters, the C–C bond lengths in the cases of C2GeO2,C2AsO2, and C2SeO2 are increased by 0.8–1.7% whereas for the restof the clusters these are decreased by 0.15–5.6%. In the same way,the C–X bond lengths are found to be decreased by 1.2–1.6% in thecases of C2GaO2, C2GeO2, and C2AsO2 whereas for the other clus-ters, the C–X bond lengths are increased by 0.3–4.6%. Similarly,as compared to the free O2 molecule with bond length of1.205 Å, the O–O bond lengths, in C2XO2 clusters are found to beincreased by 12.61–30.20% being maximum in C2SeO2 cluster. Acti-vation of O2 molecule accompanied by an increase in O–O bondlength beyond its superoxide state (1.33 Å) is known to be causedby the charge transfer from the highest molecular orbital (HOMO)of host cluster to the degenerate 2p� anti-bonding orbitals of O2

molecule due to the large electronegativity of oxygen. Similar toour previous study on second-row dicarbides, the C–C stretchingfrequencies in these cases are also found to be increased as com-pared to those in their respective C2X clusters. On the contrary,the O–O stretching frequencies in C2XO2 clusters are red-shiftedas compared to that (1633 cm�1) in O2 molecule. This indicatesthat maximum electron population is transferred from the carbonatoms of C2X clusters to O2 molecule. In Table 1, we also providetotal atomic charge (Mulliken) on O2 molecule in C2XO2 clusters.Though total charges (Q) on O2 shows somewhat odd–even charac-teristics for C2XO2 clusters except for X = Ge, no specific correlationbetween the charge transfer and the O–O bond lengths (or, C–Cbond lengths) is found. However, the fact that why C2K and C2Caare donating more electrons to O2 as compared to others can beunderstood by analyzing their electron affinities. Electron affinities(�ELUMO) of C2K and C2Ca are found to be 2.93 eV and 2.77 eVrespectively, which are almost 20–91% less than those of the oth-ers. So in a way, C2K and C2Ca clusters behave as electron donorsdonating maximum population to O2 molecule. This fact is alsomarked by the total atomic charge transfered to O2 molecule,which, in the cases of C2KO2 and C2CaO2, are comparatively more.Another reason is also the nature of bondings in C2X clusters. It hasbeen reported that C2K and C2Ca are more ionic whereas C2Se andC2Br are more covalent in nature [22]. The nature of bondings inother clusters have been described to be intermediate kind. Thisfact is also reflected in the value of dipole moment (l) of therespective clusters in our calculations, and it is found that l is veryhigh in the cases of C2K and C2Ca while very less for C2Br.

Fig. 1. Few of the optimized structures of C2XO2 clusters with X = K to Br, depicting molecular adsorption of O2 at different sites of C2X. Other possible structures are providedin the Supplementary material.

Table 1Electronic states (C2X/C2XO2), C–C (C2X/C2XO2) bond lengths, C–X (C2X/C2XO2) bond lengths, O–O bond lengths, C–C (C2X/C2XO2) stretching frequencies (xC—C), O–O stretchingfrequencies in C2XO2 clusters, Mulliken charges (Q) on O2, and dipole moments (l) of C2XO2 clusters. Results provided here are computed at B3LYP/6-311++G (d,p) level andcorrespond to the most stable C2XO2 isomers.

X State C–C (Å) C–X (Å) O–O (Å) xC—C (cm�1) xO—O (cm�1) Q l (D)

K 2A1/2A00 1.263/1.261 2.718/2.843 1.408 1825/1901 816 �0.391 8.36Ca 1A1/1A 1.264/1.251 2.214/2.272 1.530 1823/1964 745 �0.529 9.57Ga 2A0/2A 1.263/1.224 2.083/2.053 1.358 1795/2126 997 �0.167 3.25Ge 1A0/1A0 1.283/1.305 1.787/1.759 1.565 1805/1851 713 �0.148 2.33As 2A00/2A00 1.298/1.309 1.735/1.714 1.555 1739/1851 766 �0.170 1.85Se 3A00/3A00 1.303/1.323 1.720/1.752 1.569 1725/1772 740 �0.110 1.00Br 2A0/2A 1.275/1.203 1.786/1.792 1.357 1694/2283 1008 �0.194 2.71

S.K. Parida et al. / Computational and Theoretical Chemistry 1032 (2014) 1–6 3

In this context, we also present in Table 2, a computationalparameter DC2X—O2 which is an important indicator of reactivityand represents the relative energy difference between the HOMOof the bare-clusters and the LUMO of O2[50]. Because for a givencluster, most of the electron density transferred to O2 comes fromthat bare-cluster HOMO, and higher is the HOMO energy or, lowerwill be DC2X—O2 , more charge gets transferred to O2, which leads tostronger interaction of O2 with the clusters. Even though lower

DC2X—O2 values in the cases of C2KO2 and C2CaO2 explains largeamount of charge transferred to O2, however, no definite correla-tion between DC2X—O2 and the charge transferred to O2 is noted.One of the reasons is the uneven charge distribution over X andC atoms of the C2X clusters leading to nonuniform ionicities.

In Table 2, we also present adsorption energies (Eads) correctedwith basis set superposition error (BSSE) and Gibb’s free energies(dG) of C2XO2 clusters. Values of BSSE have been provided in the

Table 2E (HOMOcluster)–E (LUMOO2

) gap (DC2 X—O2 in eV), adsorption energies (Eads in eV) corrected with the basis set superposition error (BSSE), change in Gibb’s free energies (dG, in kcal/mol), and chemical hardness (g in eV) of most stable C2XO2 isomers at 6-311++g (d,p) and LANL2DZ levels.

X 6-311++G (d,p) LANL2DZ

DC2X—O2 Eads dG g DC2X—O2 Eads dG g

K �2.440 �1.861 �34.972 1.38 �1.680 �1.824 �38.170 1.36Ca �1.734 �2.489 �48.884 1.58 �1.127 �2.221 �47.670 0.78Ga �3.922 �1.745 �32.479 1.46 �3.344 �1.810 �37.643 1.32Ge �3.827 �1.529 �27.560 1.70 �3.278 �0.990 �20.363 2.02As �3.002 �2.023 �40.896 1.18 �2.526 �1.690 �35.802 1.10Se �4.134 �1.226 �22.841 0.91 �3.682 �0.933 �19.829 0.84Br �4.430 �1.845 �34.786 1.55 �4.070 �1.307 �26.277 1.68

Fig. 2. ELF of C2XO2, (X = K–Br) clusters at isovalues > 7.0.

4 S.K. Parida et al. / Computational and Theoretical Chemistry 1032 (2014) 1–6

suplementary material. Negative adsorption and free energies forall the clusters indicate that the adsorptions are thermodynami-cally favorable. Even though activation of the O–O bond length(about 0.3 Åor more) is somehow related to the adsorption energyof C2XO2, however, it is observed that the correlation is differentfor the clusters with even and odd number of electrons. For exam-ple, for the clusters with even number of electrons, jEadsj (or, jdGj)follows the order of C2CaO2 > C2GeO2 > C2SeO2, whereas the in-crease in O–O bond lengths follows the reverse order, i.e.(O–O)C2SeO2 > (O–O)C2GeO2 > (O–O)C2CaO2. However, in the cases ofthe clusters with odd number of electrons, both jEadsj and activa-tion of O–O bond lengths follow almost the same order, i.e.C2AsO2 > C2KO2 > C2BrO2 > C2GaO2. It is noted that, except forC2KO2 and C2CaO2, jEadsj (or, jdGj) are slightly more at B3LYP/LANL2DZ as compared to those at B3LYP/6-311++G (d,p) level.

Another parameter which describes the reactivity of a moleculeis its global hardness (g) which is calculated as g ¼ IP—EA=2,where IP and EA are vertical ionization potential and electron affin-ity of the molecule respectively. According to the paradigm set byPearson, a molecule having larger chemical hardness hardly allowsany change in its electron distribution promoting the system to-wards a more stable configuration [51]. So, in short, molecule hav-ing larger chemical hardness are less reactive. In Table 2, wepresent g computed both using LANL2DZ and 6-311++G (d,p) basissets. We find that the correlation between g and O–O bond lengthsfollow the similar trend as explained above for jEadsj (or, jdGj).However, it can be noted that hardness of the third-row main-group dicarbides are comparatevely less than those of the sec-ond-row dicarbides, which infers that the formers are slightlymore reactive toward O2 molecule. This fact is also supported bythe activation of O–O bond lengths which, in the cases of main-group dicarbides, are comparatevely larger [41].

We also use the topological analysis of electron localizationfunction (ELF) to explore the nature of bonding in the complexes.Topological analysis indicates that, because of the existence ofdisynaptic basins V (X,O) and V (C,O) in the clusters, the bondingbetween O2 molecule and carbon atoms (and/or, with third-rowmain group elements) are shared-electron interactions. This factis also supported by low value of relative fluctuation and high va-lue of covariance for V (C,O) in each of the C2XO2 clusters [52]. InSupplementary material we present detailed analysis of basin pop-ulations with relative fluctuations. In Fig. 2, we present ELF ofC2XO2 clusters. Similar to our previous work in the cases of sec-ond-row dicarbides interacting with O2, the existence of an iso-surface in the bonding region between C and O atoms of each ofthe C2XO2 clusters at low value of ELF (less than 0.5) indicates thatthe electrons are delocalized in between C and O resulting in thebondings somewhat of covalent nature [53,54]. Though the exis-tence of disynaptic basins V (X,O), and their corresponding highercovariance values point out the possibility of shared-interactionbetween X and O, however structures constructed due to suchinteractions are found to be slightly higher in energies.

The nature of the interaction between O2 adsorbate and the hostC2X cluster can also be analyzed using Bader’s quantum theory ofatoms in molecules (QTAIM) [55]. Generally, for shared-interaction,the electron density (q) is positive and large (>0.2 a.u.) whereas forionic and van der Waals bonds, q < 0.10 a.u. Our calculation showsthat almost in all cases, O2 molecule is more likely to have ashared-interaction with one of the carbon atoms with q > 0.3 a.u.at the bond critical point (BCP). On the other hand, at the BCP of(X,O) of the system, q is found to have value smaller than0.05 a.u. Another quantity which is also useful to characterize thenature of bonding is the delocalization index (d) which is definedas dðA;BÞ ¼ 4

Pi

PjSijðAÞSijðBÞ, where SijðAÞ and SijðBÞ are the overlap

of a pair of spatial orbitals over atoms A and B respectively [56].Larger delocalization index infers higher possibility of shared-

S.K. Parida et al. / Computational and Theoretical Chemistry 1032 (2014) 1–6 5

interaction. For our C2XO2 system, we find the value of dðC;OÞ to bemore than dðX;OÞ indicating that the electron population is moredelocalized in the region between C and O than between X and Oatoms of the system. For example, in case of C2KO2, dðC;OÞ is foundto be 1.16 with percentage of the electron contribution of C and Oin the shared bond are 9.7% and 6.7 % respectively. On the otherhand, value of dðK;OÞ is only 0.14 having very less electron contri-bution from each of the interacting atom. The corresponding dataof Bader’s topological analysis have been provided in the Supple-mentary material.

4. Conclusion

In conclusion, a theoretical investigation of the interaction ofthird-row main group dicarbides with molecular oxygen have beenperformed using density functional theory (DFT). It is observedthat the optimized structures of all the C2XO2 clusters at B3LYP/6-311++G (d,p) level of theory match well with those reported byothers. However, the structures of C2Ga and C2Ge at B3LYP/LANl2DZ are found to be linear against their reported T-shapedgeometries. The structures of the host C2X clusters, except C2Gaand C2Ge, are found to be weakly modified resulting in presenceof O2 adsorbate. The two clusters, C2Ga and C2Ge, which have cyclicground-state structures become linear in presence of O2 molecule.The C–C stretching frequencies in C2XO2 clusters are found to beincreased as compared to those in the respective C2X clusters,whereas, the O–O stretching frequencies in C2XO2 clusters arered-shifted in comparison to that in O2 molecule. Although thesechanges have been explained in terms of the charge transferredto O2 molecule from the bare clusters, C2X, however, no specificcorrelation is found. The calculated adsorption (jEadsj) and Gibbs’free energies (jdGj) for the clusters with even number of electronsare found to follow the order of C2CaO2 > C2GeO2 > C2SeO2 and theincrease in O–O bond lengths follows the reverse order, i.e. (O–O)C2-

SeO2 > (O–O)C2GeO2 > (O–O)C2CaO2, whereas for the clusters with oddnumber of electrons, jEadsj and O–O bond lengths follows almostthe same order. Similar trend is also noted in the evaluation ofchemical hardness of the clusters. In addition, the existence ofdisynaptic basins V (C,O) and their corresponding lower relativefluctuation and higher covariance values based on ELF topologicalanalysis infers that the electrons are delocalized in these areas giv-ing rise to shared-electron interactions. Furthermore, calculationfrom QTAIM shows large electron density at the bond critical pointof C and O which also infers that the interaction between C2X andO2 is shared-type. This fact is also supported by large value of delo-calization index dðC;OÞ for (C,O) pairing.

Appendix A. Supplementary material

Supplementary data associated with this article can be found, inthe online version, at http://dx.doi.org/10.1016/j.comptc.2014.01.021.

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