Regioselectivity of third-row maingroup dicarbides, C2X (X = K-Br) for CO interaction: Fukui function and topological analyses

Accepted Manuscript Regioselectivity of third-row maingroup dicarbides, C2X (X=K-Br) for CO interaction: Fukui function and topological analyses Saroj K. Parida, Sridhar Sahu, Sagar Sharma PII: DOI: Reference:

S0009-2614(16)30448-1 http://dx.doi.org/10.1016/j.cplett.2016.06.053 CPLETT 33962

To appear in:

Chemical Physics Letters

Received Date: Accepted Date:

11 April 2016 21 June 2016

Please cite this article as: S.K. Parida, S. Sahu, S. Sharma, Regioselectivity of third-row maingroup dicarbides, C2X (X=K-Br) for CO interaction: Fukui function and topological analyses, Chemical Physics Letters (2016), doi: http://dx.doi.org/10.1016/j.cplett.2016.06.053

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Regioselectivity of third-row maingroup dicarbides, C2 X (X=K-Br) for CO interaction: Fukui function and topological analyses. 1

Saroj K. Parida1 , Sridhar Sahu1 ,* and Sagar Sharma2,a Department of Applied Physics, Indian School of Mines, Dhanbad, Jharkhand-826004, India and 2 Department of Organic Chemistry, Weizmann Institute of Science, Rehovot-76100, Israel∗

Abstract In this work, we present our calculations, based on density functional theory (DFT) to explore chemical reactivity of C2 X (X=KBr) towards CO molecule. Computed condensed Fukui function (f − ) reveals the carbon atom of C2 X (X=K-Br) to be the most ¯ ) for active site for the CO interaction. This fact is also confirmed by the comparatively lesser average local ionization energy (I(r) the active carbon atom. Bader’s topological parameters such as electron density ρ > 0.30 a.u. with negative ∇2 ρ and HBCP (total energy density) at the bond BCP of the carbon atoms of both C2 X (X=K-Br) and CO infers the CO interaction in all the cases to be of shared-kind. Keywords: Main-row group dicarbides, Regioselectivity, Density functional theory, Fukui function, QTAIM.

I.

INTRODUCTION

Clusters containing a small number of atoms are of particular interest in catalysis because small changes in their size and composition can have a significant influence on the activity and selectivity of a reaction [1]. Hence investigation of the reactivity of the small clusters not only provides important informations about their catalytic behavior but also reveal their chemical stability and formation of novel composite materials. One of the important aspects while studying the interaction phenomenon in clusters is to predict their most active adsorption sites, because in theoretical calculations, a priori knowledge of reactivity tendency can save substantial computational effort. Of different theoretical models proposed to explore the most active adsorption site of a cluster while interacting with a guest molecule, condensed Fukui function (CFF) analysis has been proved to be one of the most powerful tools for such purposes [2–5]. However, the standard practice such as considering HOMO (highest occupied molecular orbital) or LUMO (lowest unoccupied molecular orbital) density for evaluating condensed Fukui function for a cluster, might, in some cases, provide incorrect results [6–8]. These shortcomings was also pointed out by Fukui himself, who, in such nonHOMO driven reaction cases, suggested to consider neighboring FMO (frontier molecular orbital) [9]. In this regard, a technical definition of FMO along with a criterion called frontier effective-for-reaction molecular orbital (FERMO) for choosing suitable FMO was proposed by Silva et al [10]. Sablon et al., however, reported to have solved this discrepancy by introducing so called orbital-averaged Fukui function (OAFF) technique [11]. Notwithstanding, it can be shown that, OAFF method, in principle, is same as the concept of average local ionization energy (ALIO) proposed by Sjoberg et al. [12]. Since the detection of small molecules such as C2 S, C2 Si and C4 Si in the circumstellar envelop of carbon star CW Leonis, a lot of theoretical and experimental works on small neutral and ionic hetero-atom doped carbon clusters were published by various authors [13–18]. Most of the works reported so far dealt with the study of the structural and electronic properties of these interstellar carbides [19, 20]. Though a lot of works on the reactivity of other carbonbased clusters were reported by various authors, however,

∗ Electronic

address: [email protected]

only a handful of work investigating such properties of hetero-atom doped interstellar carbon chains have been reported so far [21, 22]. For example, spin-polarized DFT calculation by Moras et al. showed that the chemisorption of O2 on carbon chains, resulted in cleavage and shortening of the carbynoid structures [23]. Eichelberger et al . performed experimental investigation on the reactivity of ionic carbon chains with H, N, and O atoms and observed that the ionic chains are more reactive towards O than H and N [24]. Furthermore, Diben et al . investigated both theoretically and experimentally, the interaction of carbon chain with H2 O and found the photoproduction of Cn O compound from Cn -H2 O complexes [25]. Crossed molecular beam investigations to study the reaction of small carbon chain clusters with other molecules have been reported by Kaiser and co-workers [26]. Methane activation by ironcarbide cluster anions was characterized by mass spectrometry by Li et al. who noticed a cleavage of C−H bond due to large dipole moment of iron-carbide anions [27]. In addition, theoretical study of the interaction of O2 molecule with C2 X, (X = Na-Zn) chains was reported by Sahu et al . [28]. However, reactivity properties of main-group carbides are yet to be studied even though these elements capped with fullerenes and nanotubes have been potentially used for hydrogen adsorption [29]. In this paper, we studied the interaction of main-row group dicarbides, C2 X (X=K-Br) with CO using CFF method, ALIO as well as topological analysis using Bader’s theory of atom in molecule (AIM). II. A.

THEORETICAL ANALYSES Condensed Fukui function:

Within the framework of Kohn–Sham theory, the Fukui function (FF) can be defined, as proposed by Senet as, 2 f α (r) =| Φα λ (r) |

where Φ(r) represents frontier molecular orbital (FMO) and chosen depending upon the value of λ as HOMO or LUMO. The superscript, α is for electrophilic or nucleophilic attack [30]. Now expanding Φ(r) in terms of atomic basis functions, we can get an orbital component of Fukui function namely, X fµα =| cµα |2 +cµα cνα Sµν (2) ν6=µ

1

(1)

where cνα is the orbital coefficient and Sµν is the overlap matrix between two basis functions. For an atom, say, A, Eq. for all µǫA, obeys the normalization condition P (2), α f = 1. Now using Eq. (2) the condensed Fukui µǫA µ function (CFF) localized at the atom A, can be written as, fA− =

X

fµ− =

µǫA

fA+ =

X µǫA

X

| cµH ′ |2 +

µǫA

fµ+ =

X

XX

cνH ′ cµH ′ Sµν

(3)

cνL′ cµL′ Sµν

(4)

µǫA ν6=µ

| cµL′ |2 +

µǫA

XX µǫA ν6=µ

where the subscripts H’ and L’ refer to the frontier molecular orbital, and in most cases, are considered as HOMO and LUMO orbitals respectively. Again, for any molecular system, Eq.P (3) Pand Eq. (4) also obey the normalization condition, A µǫA fµα = 1. B.

Average local ionization energy

Another parameter introduced by Sjoberg et al. [12], as mentioned above, to understand the local reactive site of a ¯ cluster is the local average ionization energy (I(r)), and is defined as, ¯ = I(r)

P

i

ρi (r) |εi | ρ(r)

(5)

where ρi (r) and εi are the density and orbital energy of the ith molecular orbital respectively and ρ(r) is the total ¯ is interpreted as the averelectronic density function. I(r) age energy required to remove an electron from the point r in the space of an atom or molecule. The lowest values ¯ reveal the locations of the least tightly bound elecof I(r), trons, most readily available for transfer or sharing with an electrophile. As mentioned above, Sablon et al. introduced the orbitalP averaged Fukui function fe± (r) = i wi fi± (r) wi being the weighting factor, to deal with the failure of HOMO driven reaction [11]. However, following the proof worked out by Toro-Labbé et al. [31], it can be inferred that both fe± (r) ¯ in principle, are the same, wi being proportional and I(r), to the orbital energy εi . III.

COMPUTATION DETAILS

All clusters were optimized at various levels such as B3LYP/6-311++G(d,p), B3LYP/6-311+G(3df), PBE1PBE/6-311++G(2d,p) and B3PW91/LANL2DZ within the framework of density functional theory (DFT) [32–34]. All the host clusters were optimized, with different spin multiplicities, without and with CO molecule placed at different possible sites of C2 X, X=K-Br (henceforth, X, in general, represents the element from K to Br unless otherwise specified) and the optimizations were accomplished without any imaginary harmonic frequencies. Single point calculations at CCSD (T)/6-311++G(d,p) were also performed for comparative analyses. Geometry optimizations of all the clusters and their structural analyses were carried out using Gaussian 09 and the graphical 2

user interface Gaussview and Chemcraft softwares [35, 36]. In Addition, reactivity of the clusters towards CO molecule was also investigated employing Bader’s theory of atoms in molecules using AIMALL computational packages [37]. Because we obtained similar results for CO interaction with C2 XCO clusters at all levels of theory, in this paper, we present our calculation at B3LYP/6-311++G(d,p), and those at the remaining levels are provided in the supplementary material.

IV.

RESULTS AND DISCUSSION

Before we explore the interaction of C2 X with CO, we optimized the bare C2 X clusters at all levels of theory to cross-check our results with those reported by other authors. Results obtained for all the bare clusters at all levels are found to be similar to those reported by others. For example, in the case of C2 As, C-As and C-C bond lengths are 1.735 Å and 1.298 Å respectively at B3LYP/6311++G(d,p) and 1.732 Å and 1.293 Å respectively at B3LYP/6-311++G(3df), which match well with the experimental results by Wei et al. and Sun et al [38, 39]. However, values at B3PW91/LANL2DZ and CCSD (T) are slightly overestimated (Data are provided in the Supplementary Material).The optimized structures of C2 XCO clusters and few of their high-energy configurations are presented in Fig. 1 and the remaining configurations are provided in the supplementary material. We found that, the adsorbate molecule is more likely to interact with carbon site of C2 X rather than the third-row main group elements, and in some cases (such as C2 K, C2 Ca, C2 Ga, and C2 Ge) the interaction leads to noticeable distortion (from cyclic to linear) in the parent geometries whereas in others (such as C2 As, C2 Se and C2 Br) , the structures are found to be least susceptible to the adsorption. For example, < XCC in C2 K is 76.6o , whereas < XCC angle in C2 KCO is 175.7o. On the other hand < XCC in C2 As is 180.0o , whereas < XCC in C2 AsCO is 180.0o. In Table I, we present C-O bond lengths along with corresponding CO harmonic frequencies (ωCO ). The C-O bond length of the clusters is found to be increased at all levels of theory being maximum for C2 KCO. In Table I we also present change in Gibb’s free energies (dG) and the adsorption energy (Eads ) of the clusters (corrected with basis set superposition error (BSSE)) calculated as Eads = E(C2 X) + E(CO) − [E(C2 XCO)], where E(C2 X), E(CO), E(C2 XCO), denote the calculated total energies of C2 X, COand C2 XCO clusters respectively. It is found, for example, that the adsorption energies of C2 KCO to C2 GeCO (with cyclic bare clusters) clusters are comparatively less than those of C2 AsCO to C2 BrCO (with linear bare clusters) indicating that the later clusters interact comparatively more strongly with CO. It is also observed that for the clusters are having odd number of electrons,|dG| and|Eads | follow the order of C2 AsCO > C2 BrCO > C2 GaCO > C2 KCO at all the computational levels, whereas, for the clusters with even number of electrons, the order follows C2 SeCO > C2 GeCO > C2 CaCO, and the order is found to be almost reversed to C-O bond lengths in both the cases as shown in Fig. 2. We also provide in Table I, the change in effective Mulliken charge (∆qCO ) in CO molecule that occurs due redistribution of the net charge transferred from the host C2 X clusters to CO causing an increase in bond length in the

(a) C2 KCO (0.0)

(e) C2 GaCO (0.0)

(i) C2 AsCO (0.0)

(b) C2 KCO (0.04 eV)

(f) C2 GaCO (3.07 eV)

(j) C2 AsCO (1.63 eV)

(m) C2 BrCO (0.0)

(c) C2 CaCO (0.0)

(g) C2 GeCO (0.0)

(k) C2 SeCO (0.0)

(d) C2 CaCO (0.65 eV)

(h) C2 GeCO (3.12 eV)

(l) C2 SeCO (4.11 eV)

(n) C2 BrCO (2.64 eV)

Figure 1: Few of the optimized structures of C2 XCO clusters with X=K to Br, depicting molecular adsorption of CO at different sites of C2 X. Other possible structures are provided in the supplementary material.

Table I: Electronic states (C2 X/C2 XCO), C–O bond lengths, C-O stretching frequencies (ωC−C ), change in effective Mulliken charge on CO molecule (∆qCO ) adsorption energies (Eads ) corrected with the basis set superposition error (BSSE), change in Gibb’s free energies (dG) for most stable C2 XCO isomers at B3LYP/6-311++G(d,p) levels. X K Ca Ga Ge As Se Br

Sate A1 /2 A′ 1 A1 /3 Σ 2 A1 /2 Π 1 ’ 3 A/ Σ 2 Π/2 Π 3 Σ/1 Σ 2 ′ 2 ′ A/ A

2

C-O ωC−O ∆qCO (Å) (cm−1 ) (e) 1.194 1999 -0.31 1.177 2237 -0.87 1.170 2261 -1.41 1.170 2269 -0.52 1.167 2262 -0.87 1.162 2325 -0.96 1.165 2286 -0.96

Eads dG (eV) (Kcal/mol) -1.665 -30.722 -0.544 -4.569 -1.858 -33.978 -1.268 -20.253 -2.344 -45.915 -3.261 -66.628 -2.231 -43.843

later. But no specific correlation is found between ∆qCO and C-O bond length. However, we observe that maximum of the charge gets transferred is from C of C2 X to C of CO indicating a bonding between the two atoms (See Supplementary material). The fact is also supported by the Fukui function and Bader’s topological analyses as discussed in the following sections. In Table II, we present the computed values of fA− functions. Though from the optimization scheme and calculated ∆qCO , it is obvious that the end-carbon atom of C2 X cluster is the most active site for CO interaction, however, fA− for all the cases, does not confirm the fact. For example, in the cases of C2 K, C2 Ca and C2 Ge, fA− contributed from their HOMO orbitals are found to have larger values at C as compared to those at third-row maingroup elements and 3

Figure 2: Variation of Eads , C-O bond lengths in C2 XCO clusters at different levels of theory. hence, correctly explains their local reactivity sites, whereas in others, it fails. So we adopt nearest FMOs, such as HOMO-1 and HOMO-2, as suggested by other authors to straighten out the problem [6–8]. In Table II we provide fA− for all the clusters computed using HOMO, HOMO-1 and HOMO-2 orbitals. It can be seen that fA− value (0.95e) for

¯ for C2 X at B3LYP/6-311++G(d,p). The Table II: Condensed Fukui function fA− and average localization energy (I(r)) bracketed value is for the other carbon atom of C2 X having no direct bonding with CO Clusters Atom C2 K C2 Ca C2 Ga C2 Ge C2 As C2 Se C2 Br

C K C Ca C Ga C Ge C As C Se C Br

HOMO-2 0.510(0.485) 0.004 0.457(0.346) 0.196 0.545(0.405) 0.048 0.376(0.304) 0.318 0.581(0.143) 0.274 0.963(0.001) 0.035 0.856(0.038) 0.104

− fA HOMO-1 0.523(0.430) 0.045 0.546(0.396) 0.057 0.497(0.497) 0.005 0.498(0.363) 0.137 0.950(0.003) 0.046 0.241(0.148) 0.609 0.319(0.252) 0.428

active carbon atom in C2 As having electronic configuration, [core]....6π 2 7π 2 12σ 2 9π 1 , contributed from HOMO-1 (and HOMO-2 (0.58e)) explains the true local reactivity site, whereas in C2 Se and C2 Br with electronic configurations, [core]....6π 2 7π 2 12σ 2 9πx1 9πy1 and [core]....6π 2 7π 2 12σ 2 9π 3 respectively, HOMO-2 serve the purpose. We also provide ¯ in Table II in supaverage local ionization energy (I(r)) port of the results inferred by CFF. It can be observed that ¯ (for example, the end carbon atom of C2 X has lower I(r) 3.36 eV for C of C2 K) as compared to those of main-group elements concluding that less energy is required to remove an electron from the end-carbon atom of C2 X leading to the fact that the site is more reactive towards CO. Table III: Electron density (ρ) in a.u. , ∇2 ρ, total energy density (HBCP ) in a.u., and delocalization index (δ) at BCP in carbon of C2 X/carbon of CO. VBCPC−C X ρCC2X −CCO ∇2 ρC−C HBCPC−C

K Ca Ga Ge As Se Br

0.32 0.35 0.35 0.35 0.36 0.35 0.35

-0.93 -1.05 -1.05 -1.07 -1.06 -1.03 -1.05

-0.37 -0.47 -0.47 -0.49 -0.51 -0.52 -0.50

GBCP

δ C−C

δc−x

1.41 1.64 1.61 1.67 1.70 1.66 1.65

0.00 0.03 0.06 0.15 0.18 0.19 0.08

C−C

4.08 3.35 3.35 3.22 3.21 3.08 3.27

To investigate the nature of interaction between C2 X and CO, we employed Bader’s quantum theory of atoms in molecules (QTAIM) [40, 41]. In Table III we provide parameters such as electron-density distribution (ρ), Lapalacian (∇2 ρ), delocalization index (δ) at the bond critical points (BCP) of the clusters. It is found that, in all the cases ρ > 0.30 a.u. (with negative ∇2 ρ) at the bond BCP of the carbon atoms of both C2 X and CO, inferring a sharedtype interaction between C2 X and CO. This fact is also supported by the calculated total energy density (HBCP ), which, in all the cases, is negative, which suggests that potential energy density (VBCP ) dominates over kinetic energy density (GBCP ) at the BCP, indicating a shared-type 4

¯ (eV) I(r) HOMO 0.579(0.415) 0.005 0.457(0.440) 0.102 0.162(0.121) 0.715 0.690(0.230) 0.079 0.222(0.057) 0.719 0.241(0.148) 0.609 0.336(0.243) 0.419

3.36(3.36) 17.66 3.46(3.46) 18.91 3.32(3.32) 29.22 3.67(3.49) 31.29 3.44(3.05) 33.30 3.39(2.98) 32.89 3.49(3.35) 35.52

interaction between carbon C2 X and CO. Moreover, δ C−C is found to predominate over δ C−X concluding the fact that the shared-bond between the CO with X atom of C2 X is less likely. It can be found that the electron density along the BCP of C-O correlates well with C-O stretching frequencies (ωC−O ) of the C2 XCO cluster. For example, the electron density follows the order of C2 SeCO (0.470 a.u.) > C2 BrCO (0.465 a.u.) > C2 AsCO (0.463 a.u.) > C2 GeCO (0.460 a.u.) > C2 GaCO (0.459 a.u.) > C2 CaCO (0.451 a.u.)> C2 KCO (0.435 a.u.), whereas, ωC−O follows the order of C2 SeCO > C2 BrCO > C2 GeCO > C2 AsCO > C2 GaCO > C2 CaCO > C2 KCO. Topological data at other levels of theory are provided in the Supplementary material.

V.

CONCLUSION

In summary, we studied the CO interaction with C2 X (X=K-Br) using electronic structure, condensed Fukui function (CFF) and Bader’s topological analyses at different computational levels within the framework of density functional theory . |Eads | and |dG| were computed for the optimized structures and it is found that for the clusters having odd number of electrons, |Eads | and |dG| followed the order of C2 AsCO > C2 BrCO > C2 GaCO > C2 KCO at all the computational levels, whereas, for the clusters with even number of electrons, the order followed C2 SeCO > C2 GeCO > C2 CaCO, and the order was found to be almost reversed to C-O bond lengths in both the cases. Though, CFF (fA− ) was usually contributed from HOMOs of the system, in some cases such as C2 Ga, C2 As, C2 Se and C2 Br, however, fA− was computed from HOMO-1 and HOMO-2 as suggested by other authors. The fA− thus computed was found to be comparatively more at the carbon atom of C2 X (X=K-Br) clusters inferring it to be the most active site for the CO interaction. This fact was also confirmed by the av¯ which was found to be erage local ionization energy (I(r)) less for carbon atom of C2 X (X=K-Br). We also analyzed the nature of CO interaction with C2 X (X=K-Br) employing Bader’s topological analysis and found that in all the cases the C2 X-CO interaction was of shared-kind which was

confirmed by electron density ρ > 0.30 a.u. with negative ∇2 ρ and negative total energy density (HBCP ) at the bond

BCP of the carbon atoms of both C2 X and CO.

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5

   

Interaction of C2X (X=K-Br) with CO has been investigated using DFT. Condensed Fukui function (CFF) infers carbon atom is the most active site in CO interaction. Average local ionization energy also concluded carbon atom is the most active site. Bader’s quantum theory of atoms in molecules (QTAIM) revealed shared-kind interactions in the systems.

Variation of adsorption energy (Eads) of C2X (X=K-Br)-CO interaction at different computational levels within density functional theory (DFT)