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Interaction of second-row dicarbides with molecular oxygen: A theoretical study
Computational and Theoretical Chemistry 999 (2012) 184–189
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Computational and Theoretical Chemistry journal homepage: www.elsevier.com/locate/comptc
Interaction of second-row dicarbides with molecular oxygen: A theoretical study Sridhar Sahu Max-Planck-Institut für Physik Komplexer Systeme, Nuthnitzer Strasse-38, Dresden, Germany
a r t i c l e
i n f o
Article history: Received 20 June 2012 Received in revised form 10 August 2012 Accepted 23 August 2012 Available online 5 September 2012 Keywords: Density functional theory Second-row dicarbides Molecular adsorption ELF
a b s t r a c t In this work, we report our calculations, based on density functional theory (DFT) to investigate the molecular adsorption of O2 on the second-row dicarbides, C2X, with X = Na, Mg, Al, Si, S, P, and Cl. It is found that all the second-row dicarbides, except C2Si, almost retain their structures while reacting with O2 molecule, whereas the ground-state structure of C2Si which is reported to be cyclic, however, becomes linear in presence of O2. Similarly, the ground-state structure of C2S cluster which is reported to be triplet becomes singlet while interacting with O2 molecule, with the triplet state 1.08 eV higher in energy. The O–O stretching frequencies in the complex C2XO2 are red-shifted as compared to that in O2 molecule, whereas the C–C stretching frequencies are observed to increase. Negative adsorption and Gibb’s free energies indicate that the adsorptions are thermodynamically favorable. Moreover, the existence of disynpatic basins V (C, O) and their corresponding higher covariance values based on ELF topological analysis infers that the electrons are delocalized in these areas giving rise to shared-electron interactions. Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction Over the past few decades, pure carbon clusters, especially linear and cyclic carbon chains have received increasing attention largely because of their potential application in various fields [1]. For example, carbon chains have been proposed to play important roles in the formation of nanostructures in carbon plasma, polycyclic hydrocarbons, cyanopolyyenes, carbon solids such as carbyne and carriers of dense interstellar cloud. In addition, heteroatomdoped carbon clusters have also been the subject of extensive investigation from both experimental and theoretical point of view for last many years. The remarkable discoveries of C2Si and C4Si clusters in the circumstellar envelop of carbon-rich IRC + 10216 have stimulated the research of small neutral and ionic carbon clusters doped with second-row elements [2–4]. Specific examples include the experimental and theoretical studies of dicarbides and other small heteroatom-doped carbon clusters such as C2Na, C2Mg, C2Al, C2Si, C3Si, C2P, C2S, C3S and C2Cl [5–20]. More elaborate theoretical explorations of heteroatom-doped medium-sized carbon chains have been performed by Tang et al. and Largo and co-workers [21–25]. Similar studies of CnP and CnSi clusters have also been carried out by Pascoli and Lavendy [26] and Fey and Jarold [27]. Moreover, a considerable amount of works on carbon chains doped with third-row elements have also been reported by many authors [28–33]. However, most of the work on heteroatom-doped carbon chains cited above have basically dealt with the study of their structural and electronic properties. As far as the reactivities of these carbon E-mail address: [email protected] 2210-271X/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.comptc.2012.08.037
chains and other carbon based materials are concerned, only a handful of work have been published so far. Liu et al. in a recent theoretical study investigated H2 adsorption on hydrogen and alkali metal (Li, Na) terminated carbon chains [34]. Their results reveal that for metal capped carbon chain, H2 molecules are absorbed not only on the metals but also on the carbon atoms, whereas H2 molecules are physisorbed on H-terminated chain. Experimental study by Guo et al. on the reactivity of di- and tri-carbon clusters towards unsaturated hydrocarbons highlighted the formation of hydrogendeficient carbonaceous molecules in the circumstellar envelop of carbon stars [35]. Similarly, Dibben and coworkers, performing both theoretical and experimental studies revealed the interaction of H2O with linear carbon clusters indicating the photoproducion of CnO compounds [36]. Furthermore, Eichelberger et al. experimentally studied the reactivity of ionic carbon chains with H, N, and O and found that the ionic chains are more reactive towards O than H and N [37]. Reaction of hydrogen sulfide with dicarbon has been explored both theoretically and experimentally by Kaiser et al. [38]. Similarly, Moras and co-workers showed theoretically that the chemisorption of O2 molecules on carbon chains results in cleavage and shortening of the carbynoid structures [39]. However, to the best of our knowledge, reactivities of dicarbides or higher carbon chains doped with second-row elements have not been investigated thoroughly. Realizing that the reactivities of the carbon chains doped with second-row elements might disclose some new prospects, in this paper we theoretically investigate the interaction of molecular oxygen with second-row dicarbides. The rest of the paper has been organized as follows: In Section 2 we discuss the detailed computational work, in Section 3 we analyze the results and in Section 4 we present the conclusion.
S. Sahu / Computational and Theoretical Chemistry 999 (2012) 184–189
185
Fig. 1. Few of the optimized structures of C2XO2 clusters with X = Na to Cl, depicting molecular adsorption of O2 at different sites of C2X. Other possible structures are provided in the supplementary material.
2. Computation For the present study, all the structures were optimized using Becke’s three-parameter hybrid exchange functional and the Perdew and Wang’s 1991 gradient-corrected correlation functional (B3PW91) and 6-311 + G (d,p) basis sets by solving the Kohn–Sham equation in the framework of density-functional theory (DFT) [40– 43]. All the clusters were optimized with O2 molecules placed at different possible positions with respect to C2X, X = Na, Mg, Al, Si, P, S, and Cl. Though the reactivity profile includes both adsorption and dissociation of O2 molecule, however, in this article we have
only focused on the molecular adsorptive mechanism of O2. Moreover, while performing optimization, we considered both singlet and triplet ground states of C2MgO2, C2SiO2, and C2SO2 clusters, and doublet for others. All of these clusters were characterized as energy minima without imaginary harmonic frequencies. Realizing any error which may arise due to the superposition of the basis sets of two reacting systems, we calculated counter-poise corrected calculations and also report binding energy with basis set superposition error (BSSE) correction. All the calculations were performed using the computational chemistry program Gaussian 03 and the graphical user interface Gaussview and Chemcraft softwares
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S. Sahu / Computational and Theoretical Chemistry 999 (2012) 184–189
Table 1 Electronic states (C2X/C2XO2), C–C (C2X/C2XO2) bond lengths, C–X (C2X/C2XO2) bond lengths, O–O bond lengths, O–O stretching frequencies (xOO) in C2XO2 clusters, C–C (C2X/C2XO2) stretching frequencies (xCC), and NBO charges (QNBO) on O2. X
State
NA
2
A1/2A
Mg
1
Al
2
Si
1
P
2
S
3
Cl
2
A1/1A A1/2A 1
A1/ A1 2
P/ A
R/1A P/2A
C–C (Å) 1.263/ 1.265 1.253/ 1.271 1.253/ 1.267 1.307/ 1.265 1.314/ 1.308 1.294/ 1.315 1.201/ 1.272
C–X (Å) 2.371/ 2.480 2.020/ 2.122 1.921/ 2.102 1.840/ 1.670 1.613/ 1.590 1.570/ 1.568 1.621/ 1.633
O–O (Å)
xOO
xCC
(cm1)
(cm1)
1.389
860
1.517
687
1.486
812
1.548
799
1.539
832
1.522
841
1.342
1054
1833/ 1898 1769/ 1958 1795/ 1966 1833/ 1901 1718/ 1888 1724/ 2045 1673/ 2330
QNBO 0.598 0.507 0.839 0.215 0.418 0.408 0.285
Table 2 Adsorption energies (Eads), change in Gibb’s free energies (dG), BSSE-BE, and E (HOMOcluster) E (LUMOO2) gap ðMC2 X—O2 Þ C2XO2 clusters. X
Eads (eV)
dG (kcal/mol)
BSSE-BE (eV)
MC2 X—O2 (kcal/mol)
Na Mg Al Si P S Cl
3.535 3.968 3.679 3.611 4.202 3.647 3.592
69.74 78.76 71.56 70.38 85.22 71.84 73.03
3.547 4.004 3.726 3.644 4.219 4.615 3.751
28.502 19.185 44.851 49.163 35.535 62.261 67.773
[44,45]. To explore the reactivity of the clusters towards O2, we also employed electron localization function (ELF) analysis using Top-Mod computational package [46]. Adsorption energies (Eads) and change in Gibb’s free energies (dG) of C2XO2(X = Na, Mg, Al, Si, P, S, and Cl) clusters were calculated using the following equations:
Eads ¼ EðC2 XO2 ½EðC2 XÞ þ EðO2 Þ dG ¼ ðE þ GÞC2 XO2 fðE þ GÞC2 X þ ðE þ GÞO2 g where E(C2X), E(O2), E(C2XO2), denote the calculated total energies (including zero point vibrational energy (ZPVE) of C2X, O2, and C2XO2 clusters respectively. (E + G) is the sum of the total electronic energy and correction in Gibbs free energy (at 298 K) for the corresponding sub-scripted compounds. 3. Results In this section, we present the results of our theoretical calculations regarding the molecular adsorption of O2 on C2X clusters with X = Na, Mg, Al, Si, P, S, and Cl (henceforth, X, in general, is the second-row element from Na to Cl unless otherwise specified). The optimized structures of C2XO2 clusters are shown in Fig. 1. Total energies and the corresponding zero-point vibrational energies (ZPVEs) have been supplied in the supplementary material. In addition to the optimized lowest-energy structures, we also present few high-energy configurations of C2XO2 clusters, and the other possible stable configurations are supplied in the supplementary material. It is found that all the second-row dicarbides, except C2Si, almost retain their original structures while interacting with O2 molecule. For example, the ground-state cyclic structure of C2Na cluster is found to retain almost this geometry while interacting with O2 to form the complex, C2NaO2. However, the ground-
state structure of C2Si cluster which is reported to be cyclic becomes linear in presence of O2. The clusters with even number of electrons, such as C2MgO2, C2SiO2, and C2SO2, are all found to have singlet ground-states, even though the ground-state of C2S cluster is reported to be triplet with a linear structure. In all these cases the triplet states are found to be 0.68–1.08 eV higher in energy than their respective singlet ground-states. In Table 1 we present the bond lengths of C2X clusters with and without O2 adsorbate. The C–C bond lengths of the second-row dicarbides are in excellent agreement with those reported earlier [21– 25]. In the presence of O2, however, the C–C bond lengths increase slightly except in the cases of C2SiO2 and C2PO2 clusters, in which the C–C bond lengths decrease a little. Similar variations are also observed in the cases of C–X bond lengths. One of the indicators of the activation of O2 is that the O–O bond lengths in C2XO2 clusters are found to be more than even that of the superoxide state (1.33 Å) suggesting that some of the charges are transferred from the C2X clusters to the degenerate 2p⁄ anti-bonding orbitals of O2 molecule. Because of these charge transfer, the systems get distorted from their original conformations. We also present in Table 1, the O–O and C–C stretching frequencies in the complex as well as the C–C stretching frequencies in the bare C2X clusters. It is observed that the C–C stretching frequencies in C2XO2 clusters are increased as compared to those in the respective C2X clusters. On the contrary, the O–O stretching frequencies in C2XO2 clusters are red-shifted as compared to that in O2 molecule. This indicates that maximum electron population is transferred from the carbon atoms of C2X clusters to O2molecule. However, though the charge transfer to O2 shows somewhat odd–even characteristics for C2XO2 clusters except for X = S and X = Cl, no specific correlation between the charge transfer and the O–O bond lengths (or, the stretching frequencies) is found. One of the reasons is the uneven distribution of NBO charges over X and C atoms of the C2X clusters. For example, it is observed that NBO charges on Na, Mg, Al, and Si of C2Na, C2Mg, C2Al, C2Si clusters are approximately same (1e), whereas those on P, S, and Cl of C2P, C2S, and C2Cl clusters are comparatively lower. This also explains why some of the second-row dicarbides are more ionic than others. In Table 2 we present adsorption energies (Eads) and Gibb’s free energies (dG) of C2XO2 clusters. Negative adsorption and free energies for all the clusters indicate that the adsorptions are thermodynamically favorable. Even though it is observed that the stronger adsorption energies are accompanied by the activation of O–O bond lengths to about 0.3 Å or more, however, no specific correlation is found between the measure of Eads (or, dG) and O–O bond lengths of C2XO2. For example, for the clusters with odd number of electrons such as C2NaO2, C2AlO2, C2PO2, and C2ClO2, Eads and dG of C2ClO2 are found to be less than those of C2NaO2 even though the former has larger O–O bond length than the later. Similarly, for the clusters with even number of electrons such as C2MgO2, C2SiO2, and C2SO2, Eads and dG of C2SiO2 are found to be less than those of C2MgO2 and C2SO2 despite having the largest O–O bond length. So, in general, the degree of activation of O2 molecule does not seem to be the sole criterion to explain the measure of Eads and dG of C2XO2 clusters. The inconsistencies noted above can be apprehended by considering the nature of the interactions in C2X clusters together with the distortions (for example, changes in C–C and C–X bond lengths) resulted in C2X due to the adsorption of O2 molecule. It has been reported that the interactions in C2Na, C2Mg, and C2Al are ionic in nature whereas that in C2Cl is purely covalent [47]. Largo et al. have pointed out that for T-shape isomer of C2Si, the interaction is quite likely ionic [47]. On the other hand, C2P and C2S show intermediate interactions [47]. As far as the distortions in C2X in presence of O2 are concerned, we have already mentioned above that in C2SiO2 and C2PO2, the variations in C–C and C–X bond lengths are different than the rest of the clusters.
S. Sahu / Computational and Theoretical Chemistry 999 (2012) 184–189
Fig. 2. ELF of C2X and C2XO2 clusters at isovalues >7.0.
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Another descriptor of reactivity of different clusters toward O2 is the relative energy difference between the HOMO of the bareclusters and the LUMO of O2[48]. Due to the high electronegativity of oxygen, O2 is supposed to withdraw electron density from C2X clusters. For all the clusters investigated here, energies of the bare-cluster HOMOs are lower than that of the O2-LUMO. So for a given cluster, most of the electron density transferred to O2 comes from that bare-cluster HOMO, and higher is the HOMO energy, more charge transfer likely to happens. In other word, the smaller be the E (HOMOcluster) E (LUMOO2) gap ðMC2 X—O2 Þ, the more charge gets transferred to O2, which leads to stronger interaction of O2 with the clusters. In Table 2, we present MC2 X—O2 of all the clusters. However, no definite correlation between MC2 X—O2 and the charge transferred to O2is noted. This is again, as explained earlier, due to the uneven charge distribution over X and C atoms of the second-row dicarbides. We also describe electron localization function (ELF) to explore the nature of bonding in the complexes. As proposed by Silvi and Savin, the existence of an isosurface in the bonding region between two atoms at low value of ELF (less than 0.5) signifies the delocalization of the electrons in that region [49,50]. In Fig. 2 we present ELF of C2X as well as C2XO2. Topological analysis clearly infers that, because of the existence of disynpatic basins V (C, O) in the clusters, the bondings between O2 molecule and the respective carbon atom of C2X are shared-electron interactions. Moreover, the high value of covariance for V (C, O) in C2XO2 clusters also indicate a delocalization between the two basins [51]. Though the existence of disynpatic basins V (X, O), and their corresponding higher covariance values point out the possibility of shared-interaction between X and O, however structures constructed due to such interactions are found to slightly higher in energies. In the supplementary material we present detailed analysis of basin populations with covariance values. 4. Conclusion In conclusion, an investigation based on density functional theory (DFT) of the interaction of second-row dicarbides with molecular oxygen have been performed at B3PW91/6-311 + G (d,p) level of theory. It is observed that all the second-row dicarbides, except C2Si, almost retain their ground-state structures while interacting with O2 molecule. The ground-state structure of C2Si which is reported to be cyclic, however, becomes linear in presence of O2. The clusters with even number of electrons, such as C2MgO2, C2SiO2, and C2SO2, are all found to have singlet ground-states, even though the ground-state of C2S cluster is reported to be triplet with a liner structure. The C–C stretching frequencies in C2XO2 clusters are found to be increased as compared to those in the respective C2X clusters, whereas, the O–O stretching frequencies in C2XO2 clusters are red-shifted in comparison to that in O2 molecule. Although these changes have been explained in terms of the charge transferred to O2 molecule from the bare clusters, C2X, however, no specific correlation is found. The calculated adsorption, and Gibbs’ free energies are found to be all negative concluding that the adsorptions are thermodynamically favorable. In addition, the existence of disynpatic basins V (C, O) and their corresponding higher covariance values based on ELF topological analysis infers that the electrons are delocalized in these areas giving rise to shared-electron interactions. Acknowledgment Author gratefully acknowledges a visit to Professor P. Fulde’s group in Max-Planck-Institut für Physik Komplexer Systeme, Dresden where the major part of this work was done.
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Computational and Theoretical Chemistry journal homepage: www.elsevier.com/locate/comptc
Interaction of second-row dicarbides with molecular oxygen: A theoretical study Sridhar Sahu Max-Planck-Institut für Physik Komplexer Systeme, Nuthnitzer Strasse-38, Dresden, Germany
a r t i c l e
i n f o
Article history: Received 20 June 2012 Received in revised form 10 August 2012 Accepted 23 August 2012 Available online 5 September 2012 Keywords: Density functional theory Second-row dicarbides Molecular adsorption ELF
a b s t r a c t In this work, we report our calculations, based on density functional theory (DFT) to investigate the molecular adsorption of O2 on the second-row dicarbides, C2X, with X = Na, Mg, Al, Si, S, P, and Cl. It is found that all the second-row dicarbides, except C2Si, almost retain their structures while reacting with O2 molecule, whereas the ground-state structure of C2Si which is reported to be cyclic, however, becomes linear in presence of O2. Similarly, the ground-state structure of C2S cluster which is reported to be triplet becomes singlet while interacting with O2 molecule, with the triplet state 1.08 eV higher in energy. The O–O stretching frequencies in the complex C2XO2 are red-shifted as compared to that in O2 molecule, whereas the C–C stretching frequencies are observed to increase. Negative adsorption and Gibb’s free energies indicate that the adsorptions are thermodynamically favorable. Moreover, the existence of disynpatic basins V (C, O) and their corresponding higher covariance values based on ELF topological analysis infers that the electrons are delocalized in these areas giving rise to shared-electron interactions. Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction Over the past few decades, pure carbon clusters, especially linear and cyclic carbon chains have received increasing attention largely because of their potential application in various fields [1]. For example, carbon chains have been proposed to play important roles in the formation of nanostructures in carbon plasma, polycyclic hydrocarbons, cyanopolyyenes, carbon solids such as carbyne and carriers of dense interstellar cloud. In addition, heteroatomdoped carbon clusters have also been the subject of extensive investigation from both experimental and theoretical point of view for last many years. The remarkable discoveries of C2Si and C4Si clusters in the circumstellar envelop of carbon-rich IRC + 10216 have stimulated the research of small neutral and ionic carbon clusters doped with second-row elements [2–4]. Specific examples include the experimental and theoretical studies of dicarbides and other small heteroatom-doped carbon clusters such as C2Na, C2Mg, C2Al, C2Si, C3Si, C2P, C2S, C3S and C2Cl [5–20]. More elaborate theoretical explorations of heteroatom-doped medium-sized carbon chains have been performed by Tang et al. and Largo and co-workers [21–25]. Similar studies of CnP and CnSi clusters have also been carried out by Pascoli and Lavendy [26] and Fey and Jarold [27]. Moreover, a considerable amount of works on carbon chains doped with third-row elements have also been reported by many authors [28–33]. However, most of the work on heteroatom-doped carbon chains cited above have basically dealt with the study of their structural and electronic properties. As far as the reactivities of these carbon E-mail address: [email protected] 2210-271X/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.comptc.2012.08.037
chains and other carbon based materials are concerned, only a handful of work have been published so far. Liu et al. in a recent theoretical study investigated H2 adsorption on hydrogen and alkali metal (Li, Na) terminated carbon chains [34]. Their results reveal that for metal capped carbon chain, H2 molecules are absorbed not only on the metals but also on the carbon atoms, whereas H2 molecules are physisorbed on H-terminated chain. Experimental study by Guo et al. on the reactivity of di- and tri-carbon clusters towards unsaturated hydrocarbons highlighted the formation of hydrogendeficient carbonaceous molecules in the circumstellar envelop of carbon stars [35]. Similarly, Dibben and coworkers, performing both theoretical and experimental studies revealed the interaction of H2O with linear carbon clusters indicating the photoproducion of CnO compounds [36]. Furthermore, Eichelberger et al. experimentally studied the reactivity of ionic carbon chains with H, N, and O and found that the ionic chains are more reactive towards O than H and N [37]. Reaction of hydrogen sulfide with dicarbon has been explored both theoretically and experimentally by Kaiser et al. [38]. Similarly, Moras and co-workers showed theoretically that the chemisorption of O2 molecules on carbon chains results in cleavage and shortening of the carbynoid structures [39]. However, to the best of our knowledge, reactivities of dicarbides or higher carbon chains doped with second-row elements have not been investigated thoroughly. Realizing that the reactivities of the carbon chains doped with second-row elements might disclose some new prospects, in this paper we theoretically investigate the interaction of molecular oxygen with second-row dicarbides. The rest of the paper has been organized as follows: In Section 2 we discuss the detailed computational work, in Section 3 we analyze the results and in Section 4 we present the conclusion.
S. Sahu / Computational and Theoretical Chemistry 999 (2012) 184–189
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Fig. 1. Few of the optimized structures of C2XO2 clusters with X = Na to Cl, depicting molecular adsorption of O2 at different sites of C2X. Other possible structures are provided in the supplementary material.
2. Computation For the present study, all the structures were optimized using Becke’s three-parameter hybrid exchange functional and the Perdew and Wang’s 1991 gradient-corrected correlation functional (B3PW91) and 6-311 + G (d,p) basis sets by solving the Kohn–Sham equation in the framework of density-functional theory (DFT) [40– 43]. All the clusters were optimized with O2 molecules placed at different possible positions with respect to C2X, X = Na, Mg, Al, Si, P, S, and Cl. Though the reactivity profile includes both adsorption and dissociation of O2 molecule, however, in this article we have
only focused on the molecular adsorptive mechanism of O2. Moreover, while performing optimization, we considered both singlet and triplet ground states of C2MgO2, C2SiO2, and C2SO2 clusters, and doublet for others. All of these clusters were characterized as energy minima without imaginary harmonic frequencies. Realizing any error which may arise due to the superposition of the basis sets of two reacting systems, we calculated counter-poise corrected calculations and also report binding energy with basis set superposition error (BSSE) correction. All the calculations were performed using the computational chemistry program Gaussian 03 and the graphical user interface Gaussview and Chemcraft softwares
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Table 1 Electronic states (C2X/C2XO2), C–C (C2X/C2XO2) bond lengths, C–X (C2X/C2XO2) bond lengths, O–O bond lengths, O–O stretching frequencies (xOO) in C2XO2 clusters, C–C (C2X/C2XO2) stretching frequencies (xCC), and NBO charges (QNBO) on O2. X
State
NA
2
A1/2A
Mg
1
Al
2
Si
1
P
2
S
3
Cl
2
A1/1A A1/2A 1
A1/ A1 2
P/ A
R/1A P/2A
C–C (Å) 1.263/ 1.265 1.253/ 1.271 1.253/ 1.267 1.307/ 1.265 1.314/ 1.308 1.294/ 1.315 1.201/ 1.272
C–X (Å) 2.371/ 2.480 2.020/ 2.122 1.921/ 2.102 1.840/ 1.670 1.613/ 1.590 1.570/ 1.568 1.621/ 1.633
O–O (Å)
xOO
xCC
(cm1)
(cm1)
1.389
860
1.517
687
1.486
812
1.548
799
1.539
832
1.522
841
1.342
1054
1833/ 1898 1769/ 1958 1795/ 1966 1833/ 1901 1718/ 1888 1724/ 2045 1673/ 2330
QNBO 0.598 0.507 0.839 0.215 0.418 0.408 0.285
Table 2 Adsorption energies (Eads), change in Gibb’s free energies (dG), BSSE-BE, and E (HOMOcluster) E (LUMOO2) gap ðMC2 X—O2 Þ C2XO2 clusters. X
Eads (eV)
dG (kcal/mol)
BSSE-BE (eV)
MC2 X—O2 (kcal/mol)
Na Mg Al Si P S Cl
3.535 3.968 3.679 3.611 4.202 3.647 3.592
69.74 78.76 71.56 70.38 85.22 71.84 73.03
3.547 4.004 3.726 3.644 4.219 4.615 3.751
28.502 19.185 44.851 49.163 35.535 62.261 67.773
[44,45]. To explore the reactivity of the clusters towards O2, we also employed electron localization function (ELF) analysis using Top-Mod computational package [46]. Adsorption energies (Eads) and change in Gibb’s free energies (dG) of C2XO2(X = Na, Mg, Al, Si, P, S, and Cl) clusters were calculated using the following equations:
Eads ¼ EðC2 XO2 ½EðC2 XÞ þ EðO2 Þ dG ¼ ðE þ GÞC2 XO2 fðE þ GÞC2 X þ ðE þ GÞO2 g where E(C2X), E(O2), E(C2XO2), denote the calculated total energies (including zero point vibrational energy (ZPVE) of C2X, O2, and C2XO2 clusters respectively. (E + G) is the sum of the total electronic energy and correction in Gibbs free energy (at 298 K) for the corresponding sub-scripted compounds. 3. Results In this section, we present the results of our theoretical calculations regarding the molecular adsorption of O2 on C2X clusters with X = Na, Mg, Al, Si, P, S, and Cl (henceforth, X, in general, is the second-row element from Na to Cl unless otherwise specified). The optimized structures of C2XO2 clusters are shown in Fig. 1. Total energies and the corresponding zero-point vibrational energies (ZPVEs) have been supplied in the supplementary material. In addition to the optimized lowest-energy structures, we also present few high-energy configurations of C2XO2 clusters, and the other possible stable configurations are supplied in the supplementary material. It is found that all the second-row dicarbides, except C2Si, almost retain their original structures while interacting with O2 molecule. For example, the ground-state cyclic structure of C2Na cluster is found to retain almost this geometry while interacting with O2 to form the complex, C2NaO2. However, the ground-
state structure of C2Si cluster which is reported to be cyclic becomes linear in presence of O2. The clusters with even number of electrons, such as C2MgO2, C2SiO2, and C2SO2, are all found to have singlet ground-states, even though the ground-state of C2S cluster is reported to be triplet with a linear structure. In all these cases the triplet states are found to be 0.68–1.08 eV higher in energy than their respective singlet ground-states. In Table 1 we present the bond lengths of C2X clusters with and without O2 adsorbate. The C–C bond lengths of the second-row dicarbides are in excellent agreement with those reported earlier [21– 25]. In the presence of O2, however, the C–C bond lengths increase slightly except in the cases of C2SiO2 and C2PO2 clusters, in which the C–C bond lengths decrease a little. Similar variations are also observed in the cases of C–X bond lengths. One of the indicators of the activation of O2 is that the O–O bond lengths in C2XO2 clusters are found to be more than even that of the superoxide state (1.33 Å) suggesting that some of the charges are transferred from the C2X clusters to the degenerate 2p⁄ anti-bonding orbitals of O2 molecule. Because of these charge transfer, the systems get distorted from their original conformations. We also present in Table 1, the O–O and C–C stretching frequencies in the complex as well as the C–C stretching frequencies in the bare C2X clusters. It is observed that the C–C stretching frequencies in C2XO2 clusters are increased as compared to those in the respective C2X clusters. On the contrary, the O–O stretching frequencies in C2XO2 clusters are red-shifted as compared to that in O2 molecule. This indicates that maximum electron population is transferred from the carbon atoms of C2X clusters to O2molecule. However, though the charge transfer to O2 shows somewhat odd–even characteristics for C2XO2 clusters except for X = S and X = Cl, no specific correlation between the charge transfer and the O–O bond lengths (or, the stretching frequencies) is found. One of the reasons is the uneven distribution of NBO charges over X and C atoms of the C2X clusters. For example, it is observed that NBO charges on Na, Mg, Al, and Si of C2Na, C2Mg, C2Al, C2Si clusters are approximately same (1e), whereas those on P, S, and Cl of C2P, C2S, and C2Cl clusters are comparatively lower. This also explains why some of the second-row dicarbides are more ionic than others. In Table 2 we present adsorption energies (Eads) and Gibb’s free energies (dG) of C2XO2 clusters. Negative adsorption and free energies for all the clusters indicate that the adsorptions are thermodynamically favorable. Even though it is observed that the stronger adsorption energies are accompanied by the activation of O–O bond lengths to about 0.3 Å or more, however, no specific correlation is found between the measure of Eads (or, dG) and O–O bond lengths of C2XO2. For example, for the clusters with odd number of electrons such as C2NaO2, C2AlO2, C2PO2, and C2ClO2, Eads and dG of C2ClO2 are found to be less than those of C2NaO2 even though the former has larger O–O bond length than the later. Similarly, for the clusters with even number of electrons such as C2MgO2, C2SiO2, and C2SO2, Eads and dG of C2SiO2 are found to be less than those of C2MgO2 and C2SO2 despite having the largest O–O bond length. So, in general, the degree of activation of O2 molecule does not seem to be the sole criterion to explain the measure of Eads and dG of C2XO2 clusters. The inconsistencies noted above can be apprehended by considering the nature of the interactions in C2X clusters together with the distortions (for example, changes in C–C and C–X bond lengths) resulted in C2X due to the adsorption of O2 molecule. It has been reported that the interactions in C2Na, C2Mg, and C2Al are ionic in nature whereas that in C2Cl is purely covalent [47]. Largo et al. have pointed out that for T-shape isomer of C2Si, the interaction is quite likely ionic [47]. On the other hand, C2P and C2S show intermediate interactions [47]. As far as the distortions in C2X in presence of O2 are concerned, we have already mentioned above that in C2SiO2 and C2PO2, the variations in C–C and C–X bond lengths are different than the rest of the clusters.
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Fig. 2. ELF of C2X and C2XO2 clusters at isovalues >7.0.
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Another descriptor of reactivity of different clusters toward O2 is the relative energy difference between the HOMO of the bareclusters and the LUMO of O2[48]. Due to the high electronegativity of oxygen, O2 is supposed to withdraw electron density from C2X clusters. For all the clusters investigated here, energies of the bare-cluster HOMOs are lower than that of the O2-LUMO. So for a given cluster, most of the electron density transferred to O2 comes from that bare-cluster HOMO, and higher is the HOMO energy, more charge transfer likely to happens. In other word, the smaller be the E (HOMOcluster) E (LUMOO2) gap ðMC2 X—O2 Þ, the more charge gets transferred to O2, which leads to stronger interaction of O2 with the clusters. In Table 2, we present MC2 X—O2 of all the clusters. However, no definite correlation between MC2 X—O2 and the charge transferred to O2is noted. This is again, as explained earlier, due to the uneven charge distribution over X and C atoms of the second-row dicarbides. We also describe electron localization function (ELF) to explore the nature of bonding in the complexes. As proposed by Silvi and Savin, the existence of an isosurface in the bonding region between two atoms at low value of ELF (less than 0.5) signifies the delocalization of the electrons in that region [49,50]. In Fig. 2 we present ELF of C2X as well as C2XO2. Topological analysis clearly infers that, because of the existence of disynpatic basins V (C, O) in the clusters, the bondings between O2 molecule and the respective carbon atom of C2X are shared-electron interactions. Moreover, the high value of covariance for V (C, O) in C2XO2 clusters also indicate a delocalization between the two basins [51]. Though the existence of disynpatic basins V (X, O), and their corresponding higher covariance values point out the possibility of shared-interaction between X and O, however structures constructed due to such interactions are found to slightly higher in energies. In the supplementary material we present detailed analysis of basin populations with covariance values. 4. Conclusion In conclusion, an investigation based on density functional theory (DFT) of the interaction of second-row dicarbides with molecular oxygen have been performed at B3PW91/6-311 + G (d,p) level of theory. It is observed that all the second-row dicarbides, except C2Si, almost retain their ground-state structures while interacting with O2 molecule. The ground-state structure of C2Si which is reported to be cyclic, however, becomes linear in presence of O2. The clusters with even number of electrons, such as C2MgO2, C2SiO2, and C2SO2, are all found to have singlet ground-states, even though the ground-state of C2S cluster is reported to be triplet with a liner structure. The C–C stretching frequencies in C2XO2 clusters are found to be increased as compared to those in the respective C2X clusters, whereas, the O–O stretching frequencies in C2XO2 clusters are red-shifted in comparison to that in O2 molecule. Although these changes have been explained in terms of the charge transferred to O2 molecule from the bare clusters, C2X, however, no specific correlation is found. The calculated adsorption, and Gibbs’ free energies are found to be all negative concluding that the adsorptions are thermodynamically favorable. In addition, the existence of disynpatic basins V (C, O) and their corresponding higher covariance values based on ELF topological analysis infers that the electrons are delocalized in these areas giving rise to shared-electron interactions. Acknowledgment Author gratefully acknowledges a visit to Professor P. Fulde’s group in Max-Planck-Institut für Physik Komplexer Systeme, Dresden where the major part of this work was done.
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