Strong chemisorption of CO₂ on B₁₀–B₁₃ planar-type clusters

All calculations were carried out using first-principles plane-wave pseudopotential density functional theory (DFT) method, as implemented in the Quantum ESPRESSO package [41]. The spin-polarized Perdew–Burke–Ernzerhof (PBE) [42] exchange-correlation functional within the generalized gradient approximation (GGA) was employed. We used scalar-relativistic Vanderbilt ultrasoft pseudopotentials [43] generated from the following atomic configurations: $2s^{2}2p^{1}$ for B, $2s^{2}2p^{2}$ for C and $2s^{2}2p^{4}$ for O. A non-linear core correction was included in the B pseudopotential. We employed a cubic supercell with sides of 21 $\mathring{\rm A}$ for all calculations to avoid cluster interactions. A $1 \times1\times 1$ Monkhorst–Pack k-point mesh was used with a Gaussian level smearing of 0.001 Ry. Threshold for electronic convergence was set to 10⁻⁷ Ry, and structures were optimized until the forces on each atom were below 10⁻⁴ Ry/a.u.

The CO₂ adsorption energy ($E_{\rm ads}$) on the B clusters was computed as [6]:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle \label{eq:E_ads} E_{\rm ads}=E_{{\rm B}_{n}-{\rm CO_{2}}}-{E}_{{\rm B}_{n}}-{E}_{\rm CO_{2}}, \nonumber \end{align} \tag{ 1 }$$

where $E_{{\rm B}_n-{\rm CO}_2}$ is the total energy of the atomically relaxed system consisting of the B_n cluster and adsorbed CO₂ molecule, $E_{{\rm B}_n}$ is the total energy of the isolated (relaxed) B_n cluster, and $E_{{\rm CO}_{2}}$ is the total energy of the CO₂ molecule in the gas phase. Convergence tests for the plane-wave expansion of the electronic orbitals indicated that changing the kinetic energy cut-off from 64 Ry to 96 Ry resulted in $E_{\rm ads}$ changes within 1 meV. We used the former wave-function cut-off, together with a 384 Ry cut-off for the augmentation charge density, in all calculations reported here.

The initial boron-cluster structural configurations were constructed based on previous work [17] that catalogued the stable structures of B_n clusters (for ${n \leqslant 13}$). We performed structural optimization resulting in the lowest-energy cluster geometries and bond lengths, shown in figure 1 that are consistent with the results in [17]. It can be seen that B₁₀ and B₁₂ clusters exhibit quasiplanar structures, while B₁₁ and B₁₃ clusters have planar structural geometries. Moreover, B₁₂ and B₁₃ clusters are characterized by three inner atoms that are compactly bound forming an inner triangle. The longest B–B bonds of $\geqslant$1.8 $\mathring{\rm A}$ existing in these clusters belong to B₁₁ and B₁₃ clusters, and form a square configuration within the cluster (see figure 1). Among the B_n clusters studies, B₁₂ is the energetically most stable with a binding energy of 5.37 eV/atom (calculated binding energies are given in the supplementary material, Part I: table S1 (stacks.iop.org/JPhysCM/31/145504/mmedia)).

Zoom In Zoom Out Reset image size

We considered different initial configurations of CO₂ relative to the B_n clusters including various adsorption sites and orientations of the molecule. We found strong chemisorption of the CO₂ molecule along the contour edges of the B_n clusters. In addition, physisorption states of the CO₂ molecule were observed at larger distances from the cluster or when placed on top of the B-cluster plane. The strong binding of CO₂, with adsorption energies between  −1.6 and  −1 eV, is a common feature for all four B_n-clusters.

Figure 2 shows the obtained optimized configurations of the B_n–CO₂ systems characterized by the strongest adsorption energy ($E_{\rm ads}$, shown in table 1), together with their corresponding initial configurations, shown as insets. The strongest adsorption overall was found for the B₁₂–CO₂ system with a chemisorption energy of  −1.6 eV, followed by close values of about  −1.4 eV for B₁₁ and B₁₃, and somewhat weaker, but still robust chemisorption on B₁₀. Besides similar strong values of the CO₂ adsorption, all four B_n–CO₂ systems share common features regarding the adsorption geometry. Thus, chemisorption occurs when the CO₂ molecule is initially placed near the edge sites and in-plane with respect to the B_n cluster (see the insets in figure 2) for all clusters. Furthermore, final configurations indicate that chemisorbed B_n–CO₂ systems tend to keep a planar geometry. The CO₂ molecule bends by a similar angle of  ∼122° for all B clusters considered as it chemisorbs on the B cluster. It should be noted that this angle corresponds to the equilibrium geometry predicted theoretically for the negatively charged CO₂ molecule [44]. Following the formation of a C–B and O–B bond (with lengths of  ∼1.6 and  ∼1.4 $\mathring{\rm A}$, respectively), the O–C bond lengths of the molecule (initially 1.18 $\mathring{\rm A}$) also elongate asymmetrically to  ∼1.2 $\mathring{\rm A}$ (the O–C bond further away from the cluster) and to  ∼1.5 $\mathring{\rm A}$ (for the O–C bond that is linked to the B cluster). Distances between B atoms at which O and C atoms are bound (denoted B⁽¹⁾ and B⁽²⁾ respectively, in figure 2, with the binding O denoted O⁽¹⁾) increase by 0.3–0.7 $\mathring{\rm A}$ with respect to their bond lengths in isolated clusters. Other edge chemisorption sites were also found for all the four clusters (with $E_{\rm ads} < -1.10$ eV).

Zoom In Zoom Out Reset image size

Table 1. Strongest adsorption energies (in eV) obtained for the relaxed configurations with adsorbed CO₂ molecule on the B_n, ${n}$  =  10–13, clusters and with dissociated molecule (CO  +  O) in the cases of B₁₁ and B₁₃ (second line). The adsorption energies correspond to the final configurations shown in figures 2 and 3. The adsorption energy of the dissociated CO₂, $E_{\rm ads}^{\rm dissociated}$, was obtained using equation (1).

	B10	B11	B12	B13
$E_{\rm ads}$ (eV)	−1.11	−1.42	−1.60	−1.43
$E_{\rm ads}^{\rm dissociated}$ (eV)	—	−2.19	—	−1.66

Dissociation of CO₂ was also observed in B₁₁ and B₁₃ clusters at some specific B sites, wherein some of B bonds broke in order for the dissociated O and C–O fragments to bind to the (deformed) cluster, as shown in figure 3. For B₁₁ and B₁₃ clusters with dissociated CO₂, the chemisorption energies ($E_{\rm ads}^{\rm dissociated}$) are  −2.19 eV and  −1.66 eV, respectively.

Zoom In Zoom Out Reset image size

We also found physisorbed CO₂ configurations with physisorption energies ranging from  −11 to  −30 meV for distances between 3.5 and 4 $\mathring{\rm A}$ from the B_n cluster (measured as the smallest interatomic separation). The physisorption configurations include the CO₂ molecule placed above the cluster or placing the C of the molecule further away in the cluster plane, with the O atoms in or out of the cluster plane (as shown in figure 4 for the case of B₁₂). An example describing the in-plane physisorption and chemisorption states of CO₂ on B₁₂ cluster is given in Part II of supplementary material.

Zoom In Zoom Out Reset image size

The binding energies we have found here for the chemisorbed CO₂ molecule on the neutral, metal-free planar-type clusters (in the range 1.1–1.6 eV for B$_{10{{\rm \mbox{--}}}13}$) are significantly larger than previously obtained for 3D-type cluster structures (∼0.4 eV for B₄₀ and  ∼0.8 eV for B₈₀ [6, 37, 38]). To the best of our knowledge, this is the first study that provides evidence of the strong chemical binding of the CO₂ molecule to planar-type B clusters, although good adsorption was theoretically found for a few diatomic molecules on selected B clusters [45–47]. The CO₂ binding energies to B$_{11{{\rm \mbox{--}}}13}$ we obtained are also larger than those reported for the chemically engineered TM-B$_{8{{\rm \mbox{--}}}9}^-$ clusters and for the metallated/charged fullerenes (1.1–1.2 eV) [37–39]. We note that previous studies have indicated that charging the boron fullerenes or engineered TM-B$_{8{{\rm \mbox{--}}}9}$ negatively tends to enhance the adsorption of CO₂ [38, 39], which suggests that even stronger adsorption could be obtained for B$_{n}^-$ planar clusters.

Furthermore, we expect the strong bonding character obtained here for CO₂ to B$_{10{{\rm \mbox{--}}}13}$ to persist for the larger planar-type B clusters. In fact, we have examined the binding properties of CO₂ to a semi-infinite boron $\alpha$-sheet [48, 49]⁶ and also found chemisorption with ${E_{\rm ads}\approx-0.14}$ eV and a similar type of CO₂ adsorption geometry (including the  ∼122° O⁽¹⁾–C–O bond angle) at the edge of the boron sheet [49]. The latter may be viewed as the edge of a planar B_N cluster in the limit of large N.

Finally, we stress that the large chemisorption energy we find is a robust feature of the system that persists even in the presence of Hubbard on-site interactions that are implemented via GGA+U calculations⁷. The interactions provided by U increase the CO₂ HOMO-LUMO gap (next section), and are actually found to enhance the adsorption strength (binding energy) of the CO₂ molecule to the B clusters.

In order to better understand the strong chemisorption of CO₂ on all considered B planar-type clusters, we have examined the atomic-orbital-resolved density of states of the isolated clusters and bent molecule, focusing on the atoms participating in the formation of the chemisorption bonds. As we have seen in the previous section, the CO₂ bond angle changes from 180° (free molecule) to approximately 122° in the chemisorbed geometry, which is indicative of a negative charging of the molecule. Moreover, the bending itself of the CO₂ molecule significantly modifies its electronic spectrum, and in particular considerably reduces its HOMO-LUMO gap [40]. In fact, an important point to note is that, when the molecule bends, the previously degenerate (from linear CO₂) highest-occupied and lowest-unoccupied $\pi$ states of the molecule both split into in-plane and out-of-plane orbitals, leaving exclusively O and C 2p -related in-plane molecular orbitals as the frontier orbitals of the 122°—bent molecule (see supplementary material, figure S2).

The splitting, after the molecule bends, of the lowest-unoccupied $\pi$ (p _z, p _y) level, in particular, is very large (3.7 eV) compared to the HOMO level splitting (0.4 eV, figure S2) and the overall HOMO-LUMO gap also drastically decreases (by 6.6 eV in our calculations, figure S2(b)) with respect to the linear molecule (figure S2(a)). Figure 5(a) shows, for the resulting bent CO₂, the in-plane components of the 2p -related O⁽¹⁾ and C projected density of states (PDOS) along the B–C bond direction (p _y component) and perpendicular to it (p _x component). The corresponding molecular orbitals for the levels closest to the gap are also displayed in the figure. As can be seen, the bent CO₂ molecule has fully planar-type HOMO and LUMO states (denoted as H_A1 and L_A1 in figure 5), in strong contrast with the linear CO₂ molecule (figure S2(a)). The PDOS in figure 5(a) also shows that, while the HOMO of the bent molecule retains very strong O⁽¹⁾ and C 2p _y-orbital character, the LUMO exhibits both a strong 2p _y component and a substantial 2p _x component (both antibonding) from the O⁽¹⁾ and C atoms.

Zoom In Zoom Out Reset image size

In figure 5(b), we display, for the isolated B₁₂ cluster, the same type of p _x and p _y in-plane components of the density of states projected on the 2p -orbitals of B⁽¹⁾ and B⁽²⁾ atoms (the 2p _z component is shown in the supplementary material, figure S3). Such in-plane states are the ones which may interact/hybridize with the frontier orbitals of the bent CO₂. In figure 5(b), we also display for the levels closest to the HOMO-LUMO gap and having the highest in-plane PDOS, the corresponding molecular orbitals. These states are characterized by lobes protruding over the cluster's edge within the cluster plane.

It can be observed from figure 5(b) (and comparison with the full p -state PDOS in figure S3(b)) that there is an especially large density of in-plane orbitals of the peripheral B atoms (B⁽¹⁾ and B⁽²⁾) in the upper (2–3 eV) region of the cluster occupied-state spectrum. We note that previous calculations indicated that the B clusters which we are considering have in total in the occupied spectrum only 3–4 p _z-type (out-of-plane) molecular orbitals [50], delocalized over all cluster atoms, which is also what we find. The high density of in-plane p _x and p _y orbitals from peripheral (B⁽¹⁾ and B⁽²⁾) atoms in the top (2–3 eV) part of the cluster occupied-state spectrum is a feature common to all four clusters considered in this work.

The in-plane molecular states of the cluster in the energy region [−5 eV, −1 eV], in figure 5(b), strongly contribute to the electronic charge density of the cluster along its contour edge. In figure 6, we display the electronic charge density of the isolated B₁₂ cluster with the distorted geometry as in the adsorbed B₁₂–CO₂ system. The electronic charge distribution is similar to that of the free/undistorted B₁₂ cluster (figure S1 in supplementary material); it is largely concentrated at the contour edges of the cluster. This inhomogeneous electronic distribution makes the contour edges negatively charged and leaves the inner B atoms with a reduced electron density. These properties are observed in all four clusters investigated here (figure S1 in the supplementary material).

Zoom In Zoom Out Reset image size

To identify the dominant CO₂ molecular orbital involved in the chemisorption, we examined the differential charge density, i.e. the difference between the charge density of the chemisorbed B_n–CO₂ system and that of the isolated B_n and CO₂ fragments. In figure 7, we present differential charge-density isosurfaces illustrating the electronic charge difference associated with the chemisorption of CO₂ on B₁₂. The shape of the energy-gain isosurface in the region of the CO₂ molecule has strong similarities with the probability density isosurface of the LUMO of the bent CO₂ molecule (refer to L_A1 of figure 5). The LUMO CO₂ orbital will interact with some planar high-energy occupied molecular orbital(s) of the cluster (in figure 5(b)) and, based on the probability densities of the molecular orbitals of the interacting B₁₂–CO₂ system (the highest occupied states are shown in figure S4 in the supplementary material), we find that the L_A1 molecular orbital of CO₂ interacts (hybridizes) predominantly with the H_B3 molecular orbital of the cluster (see figure 5(b)). These molecular orbitals have lobes protruding from the edges of the cluster/molecule with substantial orbital overlap suggesting that strong interaction between cluster and molecule can take place in this region.

Zoom In Zoom Out Reset image size

From figure 7 it can be inferred that the CO₂ molecule gained excess negative charge from the B cluster. We performed a Lowdin charge analysis, which (although it cannot provide exact values of the atomic charges in a hybridized system and is basis dependent) is useful to give charging trends. Thus, the C atom (binding with B⁽²⁾) gained $0.27~e$, and the O atom (binding with B⁽¹⁾) gained $0.04~e$, while only a very small charge transfer for the other O atom is seen (∼0.001 e). Similar total amount of Lowdin charge was lost by the B cluster. Strong charge transfer between the B structures and the chemisorbed CO₂ molecule has been reported earlier and related to the Lewis acid-base interactions [5, 6, 39]. The electronic charge transfer from the edges of the cluster (with excess negative charge) to the molecule can be also rationalized considering that the bent CO₂, in difference to the linear molecule, has a net dipole moment which is substantial: 0.724 ea₀ [51]. The positive end of the dipole is closer to the B cluster and the negative side further away from the cluster, facilitating the interaction with the edge sites of B cluster that exhibit higher electronic density.

In addition to the strong chemisorption of the full CO₂ molecule on B clusters, we also found cases where the molecule dissociated into C–O and O fragments (figure 3), each of which is bound separately to the B cluster, having typical bond lengths of 1.2 and 1.5 $\mathring{\rm A}$ (for both B₁₁ and B₁₃), respectively. The dissociation is attributed to the presence of longer bond lengths and lower charge density of the clusters, together with the specific choice of adsorption sites closest to the long B–B bonds. The dissociation of the molecule takes place at B–B edges where the charge density of the cluster is relatively low (figure S1 in the supplementary material) and the B atoms have less bonding with other B atoms. Both B₁₁ and B₁₃ clusters have considerably smaller HOMO-LUMO gap values than the other two clusters which do not display dissociative adsorption (table S1 in supplementary material). The smaller gap indicates higher chances of interaction between the cluster and molecular states, allowing also more varied types of adsorption configurations, as we observe in our calculations.