# Unique Bonding Nature of Carbon-Substituted Be2 Dimer inside the Carbon (sp2) Network

Rafal Roszak, Szczepan Roszak, D. Majumdar, Lucyna Firlej, Bogdan Kuchta, Jerzy Leszczynski

► To cite this version:

Rafal Roszak, Szczepan Roszak, D. Majumdar, Lucyna Firlej, Bogdan Kuchta, et al. Unique Bonding Nature of Carbon-Substituted Be2 Dimer inside the Carbon (sp2) Network. Journal of Physical Chemistry A, 2014, 118 (30), pp.5727-5733. 10.1021/jp504618h. hal-01937956

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# Unique Bonding Nature of Carbon-Substituted Be₂ Dimer inside the Carbon (sp²) Network

Rafal Roszak,†,‡ Szczepan Roszak,*,†,‡ D. Majumdar,*,† Lucyna Firlej,§ Bogdan Kuchta,∥ and Jerzy Leszczynski*,†

**ABSTRACT:** Controlled doping of active carbon materials (viz., graphenes, carbon nanotubes etc.) may lead to the enhancement of their desired properties. The least studied case of C/Be substitution offers an attractive possibility in this respect. The interactions of Be₂ with Be or C atoms are dominated by the large repulsive Pauli exchange contributions, which in turn offsets the attractive interactions leading to relatively small binding energies. The Be₂ dimer, e.g., after being doped inside a planar carbon network, undergoes orbital adjustments due to charge transfer and unusual intermolecular interactions and is oriented perpendicular to the plane of the carbon network with the Be–Be bond center located inside the plane. The present theoretical investigation on the nature of bonding in C/Be₂ exchange complexes, using state of the

art quantum chemical techniques, reveals a sp² carbon-like bonding scheme in Be₂ arising due to the molecular hybridization of σ and two π orbitals. The perturbations imposed by doped Be₂ dimers exhibit a local character of the structural and electronic properties of the complexes, and the separation by two carbon atoms between beryllium active centers is sufficient to consider these centers as independent sites.

<figure><img src="image_2.png" /></figure>

## INTRODUCTION

The beryllium compounds are probably the least studied substances containing the second row elements.¹ Despite their unique chemical properties, not much work has been done so far to use such properties for practical applications. Part of the problem is due to the toxicity of the metal. There is also sufficient evidence for the carcinogenic properties of beryllium compounds causing lung cancer.² Beryllium, as one of the lightest atoms, on the other hand, offers an interesting possibility to functionalize carbon materials through carbon substitution. The carbon substitution by lithium, boron, nitrogen, and oxygen or their addition inside the carbon networks was extensively studied with the aim to replace heavy metals as catalysts.³ The beryllium atom as well as beryllium dimer are interesting alternatives in search of new nanomaterials due to their unusual chemistry. For example, some of these Be-containing materials are promising alternatives for hydrogen storage media. Several microporous coordination polymers (MCPs) with Be-based secondary building units and metal organic framework (MOF) were synthesized with favorable adsorbent properties.⁴⁻⁶ The direct Be substitution was also suggested as an efficient way to improve hydrogen adsorption.⁷ There are two important bonds in such Be-substituted carbon networks that modulate their adsorption properties, viz. Be–C and Be–Be bonds. The Be–C bonding properties are not well

studied so far, although a range of organoberyllium compounds are synthesized.⁸⁻¹⁰ On the contrary, the Be–Be bond has drawn constant interest due to its unusual bonding properties.¹¹ The unusual character of beryllium compounds may be demonstrated from the properties of the Be₂ dimer. The dissociation energy of Be₂ (2.66 kcal/mol)¹¹ is an order smaller than the corresponding energy of covalently bonded dimer Li₂ (24.3 kcal/mol),¹² suggesting weak van der Waals type interactions in Be₂. The unusual nature of Be₂ dimer is further demonstrated in the bond distance of Be₂ dimer. The Be–Be bond distance (2.54 Å)¹¹ is shorter than that of Li₂ (2.67 Å) and also much shorter than weakly bonded Ne₂ (3.10 Å)¹³ (characterized by typical nonbonding interactions of 0.08 kcal/mol). The bond distance of Be₂ shows that the dimer may be classified as one possessing significant covalent contribution, although energetically it is far from chemical bond characteristics of second row dimers viz. B₂ (Rₑ = 1.59 Å, D_o = 69.3 kcal/mol).¹⁴

The interaction with the third body (atom or molecular fragment) drastically changes the properties of Be₂ with several-fold increase of bonding energy. This phenomenon was

<footnote>†Interdisciplinary Center for Nanotoxicity, Jackson State University, Jackson, Mississippi 39217, United States</footnote>

<footnote>‡Institute of Physical and Theoretical Chemistry, Wroclaw University of Technology, Wyrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland</footnote>

<footnote>§Laboratoire Charles Coulombs, Universite Montpellier 2, 34095 Montpellier, France</footnote>

<footnote>∥Laboratoire MADIREL, Universite Aix-Marseille, 13396 Marseille, France</footnote>
<table><caption>Table 1. Molecular Orbitals Involved in the Binding in Be₂, Be₃, and Be₂C</caption><thead><tr><th colspan="2">Be₂</th><th colspan="2">Be₃</th><th colspan="2">Be₂C</th></tr></thead><tbody><tr><td>Symmetry<br>C<sub>6h</sub></td><td>Image: Green octahedron with 6 vertices in a regular octahedron.</td><td>Symmetry<br>D<sub>3h</sub></td><td>Image: Green octahedron with 3 vertices in a regular tetrahedron and 3 vertices in a regular square.</td><td>Symmetry<br>C<sub>2v</sub></td><td>Image: Green octahedron with 2 vertices in a regular square.</td></tr><tr><td>LUMO+1<br>π<sub>u</sub></td><td>Image: Red and blue clouds. Red cloud represents σ<sup>2</sup> configuration, blue cloud represents σ<sup>1</sup> configuration.</td><td>LUMO<br>a<sub>2''</sub></td><td>Image: Red and blue clouds. Red cloud represents σ<sup>2</sup> configuration, blue cloud represents σ<sup>1</sup> configuration.</td><td>HOMO<br>b<sub>1</sub></td><td>Image: Red and blue clouds. Red cloud represents σ<sup>2</sup> configuration, blue cloud represents σ<sup>1</sup> configuration.</td></tr><tr><td>LUMO<br>π<sub>u</sub></td><td>Image: Red and blue clouds. Red cloud represents σ<sup>2</sup> configuration, blue cloud represents σ<sup>1</sup> configuration.</td><td>HOMO<br>e<sup>*</sup></td><td>Image: Red and blue clouds. Red cloud represents σ<sup>2</sup> configuration, blue cloud represents σ<sup>1</sup> configuration.</td><td>HOMO-1<br>a<sub>1</sub></td><td>Image: Red and blue clouds. Red cloud represents σ<sup>2</sup> configuration, blue cloud represents σ<sup>1</sup> configuration.</td></tr><tr><td>HOMO<br>σ<sub>u</sub></td><td>Image: Red and blue clouds. Red cloud represents σ<sup>2</sup> configuration, blue cloud represents σ<sup>1</sup> configuration.</td><td>HOMO-1<br>e<sup>*</sup></td><td>Image: Red and blue clouds. Red cloud represents σ<sup>2</sup> configuration, blue cloud represents σ<sup>1</sup> configuration.</td><td>HOMO-2<br>b<sub>2</sub></td><td>Image: Red and blue clouds. Red cloud represents σ<sup>2</sup> configuration, blue cloud represents σ<sup>1</sup> configuration.</td></tr><tr><td>HOMO-1<br>σ<sub>g</sub></td><td>Image: Red and blue clouds. Red cloud represents σ<sup>2</sup> configuration, blue cloud represents σ<sup>1</sup> configuration.</td><td>HOMO-2<br>-<sub>1</sub><sup>*</sup></td><td>Image: Red and blue clouds. Red cloud represents σ<sup>2</sup> configuration, blue cloud represents σ<sup>1</sup> configuration.</td><td>HOMO-3<br>a<sub>1</sub></td><td>Image: Red and blue clouds. Red cloud represents σ<sup>2</sup> configuration, blue cloud represents σ<sup>1</sup> configuration.</td></tr></tbody></table>

observed in the case of Be₃ (Be atom as a third body) and Be₂C (C as the third body).¹⁵ The Be₂ dimer, as a closed shell $\sigma_g^2\sigma_u^2$ complex of two interacting Be(¹S) atoms, is stabilized by the correlation energy due to low-energy 2p beryllium orbitals. The electronic ground state for Be₂ of $X^1\Sigma_g^+$ with the $\sigma_g^2\sigma_u^2$ configuration is accompanied by two deep low-lying excited electronic states: $1^3\Sigma_u^+$ with the $\sigma_g^2\sigma_u\sigma_g'$ configuration ($T_e = 0.9$ eV; $T_e$ is the transition energy from the ground to the desired excited state) and $1^3\Pi_g^+$ resulting from $\sigma_g^2\sigma_u\pi_u$ configuration ($T_e = 1.08$ eV).¹¹ These configurations are isoelectronic with carbon possessing ground ³P(2s²2p²), and low-lying excited ¹D and ¹S electronic states. Additionally, $T_e$'s between similar electronic states of C (1.263 eV for the C(³P) to C(¹D) transition) and Be₂ are alike.¹⁶

The aim of this work is to determine the properties of the Be₂ dimer fragment after the substitution of a single carbon atom (by Be₂ dimer) in the sp² carbon network. The interactions of Be₂ with the rest of the system (the third body) modify its properties and impart new chemical properties to this center. Structures as well as the nature of bonding are being investigated using state of the art quantum chemical techniques. The newly evolved bonding characteristics of the Be₂ fragment in Be₃, Be₂C, CH₂Be₂H₂ (ethylene derivative), substituted aromatic compounds (benzene and naphthalene), and modified extended carbon materials (ovalene) was investigated. The computed geometric, orbital properties, charge distribution, and interaction energy decomposition results were not only found to be useful to enhance the present knowledge on Be-Be and Be-C chemical bonds but also could be used to predict the special chemical behavior of the Be center.

## METHODS OF COMPUTATION

The computation of structural parameters of small molecules (Be₂, Be₃, Be₂C, and ethylene derivatives) were carried out using the Møller-Plesset second-order perturbation (MP2) methodology¹⁷ with the aug-cc-pVTZ basis set for atoms.¹⁸ For benzene and naphthalene derivatives the basis set was reduced to aug-cc-pVDZ.¹⁹ The optimizations of Be doped ovalene (C₃₂H₁₄) structures were carried out at the density functional theory (DFT)²⁰ level using the B3LYP functional.²¹⁻²³ The test DFT calculations for smaller systems indicates that the method preserves the features observed at the MP2 studies. No symmetry constraints were imposed during the geometry optimizations. However, to model the planar extended structures, the position of the external ring was frozen in the geometry of C₃₂H₁₄. The computed energy values were further refined using single-point MP2-level energy calculations on the optimized structures with cc-pvdz basis set of atoms.

A hybrid variational-perturbational interaction energy decomposition scheme²⁴ was used to compute contributions of various energy terms in such interactions. The SCF interaction energy ($\Delta E^{HF}$) is partitioned into first-order electrostatic ($\epsilon_{el}^{(10)}$), Heitler-London exchange ($\epsilon_{ex}^{(10)}$), and higher order delocalization ($\Delta E_{del}^{HF}$) energy terms.

$$ \Delta E^{HF} = \epsilon_{el}^{(10)} + \epsilon_{ex}^{HL} + \Delta E_{del}^{HF} \quad (1) $$

The electron correlation effects are taken into account by means of the MP2 theory. The $\epsilon_{MP}^{(2)}$ interaction energy term, which includes the dispersion and correlation contributions to the Hartree-Fock components, is calculated in the super-molecular approach as the difference of MP2 energy corrections of the supermolecule and the monomers (eq 2).

$$ \epsilon_{MP}^{(2)} = E_{AB}^{(2)} - E_{A}^{(2)} - E_{B}^{(2)} \quad (2) $$
The energy terms on the right-hand side of eq 2 represent the difference between the MP2 and Hartree-Fock energies of the supermolecule (AB) and the monomers (A and B).

All the interaction energy terms are calculated consistently in the dimer-centered basis set and are therefore free from the basis set superposition error due to the full counterpoise correction.²⁵ The dispersion energy was also calculated directly by applying the expression for the second-order energy $\epsilon_{disp}^{(20)}$. The atomic charges were computed using natural bond orbital (NBO).²⁶

The geometry optimization calculations at MP2 and DFT/B3LYP were carried out using the Gaussian-09 code.²⁷ The interaction energy decomposition scheme implemented in the GAMESS code²⁸ was used for energy partitioning.²⁹ The molecular graphics have been generated using Jmol software.³⁰

## RESULTS AND DISCUSSION

**a. Be₃ Bonding Properties.** The Be₂ dimer is a weak complex due to interactions of closed 2s valence-shells of Be atoms. The third body, in the form of an additional beryllium atom, changes the orbital space organization and interactions lead to the D₃h triangle geometry of Be₃ with the significant dissociation energy. The Be-Be distance is reduced from 2.54 to 2.22 Å¹¹ due to such interactions. The inspection of molecular orbitals (MOs) indicates that the MO picture interpreted as a complex of Be₂ dimer and Be atom does not dramatically change the topological features. The $\sigma_g\sigma_u\pi_u$ orbitals of dimer could be easily projected onto three occupied orbitals (a₁', e', e') of the trimer (Table 1). The low-lying virtual $\pi_u$ orbital, being transformed into a₂'' within the D₃h symmetry representation, does not directly take part in the bonding at the HF level. However, this effect significantly stabilizes the beryllium trimer when the correlation energy is included.

$$ \begin{aligned} \Psi_4(a_1') &= 2s(\text{Be}_1) + 2s(\text{Be}_2) + 2s(\text{Be}_3) \\ \Psi_5(e') &= 2p_x(\text{Be}_1) + 2s(\text{Be}_2) - 2s(\text{Be}_3) \\ \Psi_6(e') &= 2s(\text{Be}_1) + [2p_y - 2s](\text{Be}_2) + [2p_y - 2s](\text{Be}_3) \end{aligned} \quad (3) $$

The simplified molecular orbital composition of valence atomic components (eq 3), in contrast to the beryllium dimer, indicates the increasing role of atomic p orbitals. They are responsible for significant covalent bond contribution in the bonding.

The interaction energy decomposition for the Be₂ + Be system indicates the high values of interaction energy components compared to the total interaction energy. The attractive interaction energy terms offset the extremely high exchange repulsion contribution $\epsilon_{ex}^{HL}$ (Table 2), resulting in small bonding energy. The delocalization energy $\Delta E_{del}^{HF}$ (responsible for induction interactions) constitutes the largest attraction term. It is totally quenched by the exchange interaction energy. The electrostatic $\epsilon_{el}^{(10)}$ and dispersion energies $\epsilon_{disp}^{(20)}$, although smaller in value, are very important in the final balance of bonding energy. The results of the interaction energy partitioning thus indicate the importance of covalent forces to the overall bonding mechanism. The large values of energy components canceling the small total interaction energy constitutes a major characteristic feature of molecular bonding of Be clusters. The large and dominating

<table><caption>**Table 2. Interaction Energy Decomposition Terms for Be₂, Be₃, and Be₂C Interacting Complexes (Energies in kcal/mol)**</caption><thead><tr><th rowspan="2">interacting fragments</th><th>Be₂</th><th>Be₃</th><th>Be₂C</th></tr><tr><th>Be + Be</th><th>Be₂ + Be</th><th>Be₂ + C(<sup>1</sup>S)</th></tr></thead><tbody><tr><td>ε<sub>el</sub><sup>(10)</sup></td><td>-10.0</td><td>-43.7</td><td>-205.1</td></tr><tr><td>ε<sub>ex</sub><sup>HF</sup></td><td>24.8</td><td>104.0</td><td>486.9</td></tr><tr><td>ΔE<sub>del</sub><sup>HF</sup></td><td>-10.6</td><td>-72.2</td><td>-363.7</td></tr><tr><td>ΔE<sup>HF</sup></td><td>4.2</td><td>-11.8</td><td>-81.8</td></tr><tr><td>ε<sub>di</sub><sup>(20)</sup></td><td>-7.7</td><td>-28.3</td><td>-59.1</td></tr><tr><td>ε<sub>MP</sub><sup>(2)</sup></td><td>-5.1</td><td>-30.3</td><td>-28.3</td></tr><tr><td>ΔE<sup>MP2</sup></td><td>-0.9</td><td>-21.8</td><td>-110.1</td></tr><tr><td>ΔE<sup>CCSD(T)</sup></td><td>-0.9</td><td>-21.7</td><td>-145.7</td></tr></tbody></table>

Pauli exchange repulsion term canceling attractive contributions is also a typical characteristics for the Be-Be bonding.

**b. Nature of the Chemical Bond in the Be₂C Complex.** The Be₂C complex is formed with an atomization energy of 129.1 kcal/mol. The lowest energy structure of the ¹A₁ (C₂v symmetry) electronic state possesses the T-shaped geometry and is characterized by Be-Be: 2.117 Å and Be-C: 1.584 Å bond distances. These results are in good agreement with extended CCSD(T) (2.068 and 1.598 Å) and CASSCF (2.087 Å and 1.607 Å) calculations.¹¹ It is to be noted that the inclusion of electronic correlation is essential for the proper determination of the electronic ground state structure. The lower level of theory leads to the wrong prediction of geometry of the ground electronic state.¹¹⁻¹³ The Be-Be bond in Be₂C is much shorter than the one in the Be₂ dimer; however, the composition and topology of the orbitals are preserved (compared to the Be₂ dimer) and are well visible as molecular orbital components of Be₂C. The $\sigma_g$, $\sigma_u$, $\pi_u$ and $\pi_u'$ orbitals of the Be₂ fragment form MOs with 2s, 2pₓ, 2pᵧ, and 2p_z of carbon, respectively (Table 1). The HOMO of $\pi$ character stabilizes the structure by forming three center-two electron (3c2e) delocalized bond. The other bonds are also delocalized and cover the whole molecule. The NBO atomic charges (C: -1.611; Be 0.805 electron) indicate atomic charge separation in the molecule. The Be-Be distance in Be₂C correlates with Be₂⁺ (2.211 Å) rather than Be₂ (2.54 Å).¹¹ This confirms that the computed charge distribution pattern leads to significant ionic contribution to the C-Be bond. Similar to the Be₃ case, the intermolecular interactions are dominated by the exchange repulsion term $\epsilon_{ex}^{HL}$ (Table 2). The largest attractive contribution is of induction origin ($\Delta E_{del}^{HF}$, delocalization term); however, the electrostatic contribution is also significant. The absolute values of interaction energy contributions are large with respect to the total Hartree-Fock (HF) interaction energy. It is an indication that chemical manipulation on the bonding properties will greatly influence the final energy. The already attractive HF energy is further enhanced by the correlation contribution.

**c. Ethylene vs CH₂Be₂H₂ Derivative.** The structure of the CH₂Be₂H₂ complex matches closely with CH₂CH₂. The Be-Be axis is perpendicular to the ideal plane defined by carbon and hydrogen atoms and the midpoint X of the Be-Be bond (Figure 1S, Supporting Information). The molecular orbital pictures of substituted ethylene and its parent molecule are very similar (Table 3) with the HOMO having $\pi$ character. The perturbations in the ethylene skeleton, imposed by the C/Be₂ substitution, do not change the basic topological features of the MOs and the correspondence between the orbitals is obvious and easily tractable within the D₂h to C₂v transformation (Table
<table><caption>Table 3. Valence Molecular Orbitals for CH₂Be₂H₂ Complex and Complementary Ethylene Molecules</caption><thead><tr><th colspan="2">CH<sub>2</sub>Be<sub>2</sub>H<sub>2</sub></th><th colspan="2">CH<sub>2</sub>CH<sub>2</sub></th></tr></thead><tbody><tr><td>Symmetry<br>C<sub>2v</sub></td><td></td><td>Symmetry<br>D<sub>2h</sub></td><td></td></tr><tr><td>HOMO<br>b<sub>1</sub></td><td></td><td>HOMO<br>b<sub>3u</sub></td><td></td></tr><tr><td>b<sub>2</sub></td><td></td><td>b<sub>3g</sub></td><td></td></tr><tr><td>a<sub>1</sub></td><td></td><td>a<sub>g</sub></td><td></td></tr><tr><td>b<sub>2</sub></td><td></td><td>b<sub>2u</sub></td><td></td></tr><tr><td>a<sub>1</sub></td><td></td><td>b<sub>1u</sub></td><td></td></tr><tr><td>a<sub>1</sub></td><td></td><td>a<sub>g</sub></td><td></td></tr></tbody></table>

3). The XH₂ angle (114.9°) is very close to one in the complementary -CH₂ fragment (111.2°) and in ethylene (117.4°). The orbitals in the valence space of the Be₂ dimer in the complex ($\sigma_u, \sigma_w, \pi_u, \pi_w$) transform from $\sigma_u, \pi_u, \pi_w$ into the $\sigma\pi^2$ configuration (Figure 1). This transformation is analogous to the hybridization of 2s, 2pₓ, 2pᵧ atomic orbitals in carbon. The $\sigma_u$ orbital, not involved in the hybridization, corresponds to the orthogonal p_z orbital in the sp²-hybridized carbon. The center of molecular hybrids ($\sigma\pi^2$) is located at the midpoint X of the Be-Be bond. The additional $\sigma_g$ (LUMO) is not included

<figure><img src="image_3.png" /><figcaption>**Figure 1.** Ethylene and C₂Be₂H₂ combined HOMO $\sigma$ orbitals corresponding to the sp² hybridization ($\sigma\pi^2$ in case of beryllium derivative): (a) ethylene b₃g, a₁, b₁u; (b) C₂Be₂H₂ b₂, a₁, a₁.</figcaption></figure>

in the bonding scheme and constitutes the reactive orbital on the Be-Be axis with no analogue available in pure ethylene. Due to the substitution, the character of double C=C bond is preserved and in the X=C case is represented by $\pi(b_{3u} \rightarrow b_1)$ and $\sigma(a_g \rightarrow a_1)$ orbitals.

The electronic population analysis, due to the delocalized character of molecular orbitals, is very sensitive to the method of computation. The NBO population analysis indicates the local character of perturbation associated with the C/Be₂ substitution. The charges on hydrogens in the CH₂ group are similar to that in the ethylene case (Figure 1S, Supporting Information). The value of -Be₂H₂ to -CH₂ charge transfer (-0.924 electron) should be treated with a caution considering the rather low dipole moment of the molecule of 2.323 D. The much shorter Be-Be distance of 1.718 Å with respect to the Be₂ dimer (2.54 Å) and Be₂⁺ cation (2.11 Å) indicates large involvement of beryllium atoms in the bonding mechanism. The very short Be-Be distance compares well with deeply bound excited states of Be₂⁺ and suggests the importance of contribution from low-lying electronic states to the bonding in studied systems.³¹,³²

**d. Substituted Aromatic Systems.** The C/Be₂ and (C/Be₂)₂ substitutions were studied in benzene and naphthalene. In all the cases, substitution leads to the same structural
modification preserving the planar ring, and the Be₂ axis being
perpendicular to the plane of the complex (Figure 2). The

<figure><img src="image_4.png" /><figcaption>**Figure 2.** Top and side views of single (a) and double ((b) ortho, (c) meta, (d) para) Be₂ derivatives of benzene.</figcaption></figure>

midpoint (X) of the Be–Be bond lies inside the plane of the
ring and constitutes the center of the orbitals related to Be₂
bonding. The hydrogen atom closest to Be₂ complements the
skeleton of the parent benzene molecule. The Be–Be distance
in all the studied structures is close to 1.7 Å, indicating a
similarity of ethylene involvement in Be₂ in bonding. The
molecular orbital picture corresponds to the proposed
molecular model of σπ² hybridization (Figure 3). The

<figure><img src="image_5.png" /><figcaption>**Figure 3.** Combined (a) three HOMO π orbitals (side view) and (b) three HOMO σ orbitals covering the beryllium bond in the plane of the molecular ring (top view) in C₅Be₂H₆ benzene derivative.</figcaption></figure>

combined picture of three molecular orbitals located in the
plane of carbon skeleton (Figure 3) covers two C–X σ bonds
and one X–H bond (X represents the center of the Be–Be
bond). The combined molecular orbital picture of the three
HOMO π orbitals indicates the involvement of the Be₂ orbital
in the overall π bond system. The NBO atomic charge on each
beryllium atom amounts to 0.941 electron. When C is

substituted in two different locations of the benzene ring,
they also have NBO charges close to this value (ortho, 0.512;
meta, 0.970; para, 0.849 electron). The total dipole moment of
C/Be₂ substituted benzene (calculated with aug-cc-pVTZ basis
set) amounts to 0.712 D. The insertion of the second Be dimer
does not change the overall picture of the bonding scheme and
only little perturbation in comparison to the singly substituted
benzene is observed. The substituted naphthalene molecule
follows the same structural trend regardless of the position of
substitution (Figure 2S, Supporting Information). Molecular
orbitals and atomic charges are almost the same as those
observed in the benzene case. The differences between isomers
were also insignificant.

**e. Extended Carbon Systems.** The functionalization of carbon materials may improve their desired properties. The hydrogen storage on pure carbon materials is restricted due to very weak interactions with molecular hydrogen. The substitution of carbon atom or decoration of material with foreign chemical groups provides the direct way to enhance the adsorption properties. The investigated structures in the present section are based on the ovalene model (an extended graphene-like carbon material) (Figure 4). The carbon

<figure><img src="image_6.png" /><figcaption>**Figure 4.** Structures for single and double C/Be₂ substitutions in the C₃₂H₁₄ ovalene base: (a) single C/Be₂ substitution; double (C/Be₂)(C/Be₂) substitutions with (b) Be₂–C–Be₂, (c) Be₂–C₂–Be₂, (d) Be₂–C₃–Be₂ carbon separation.</figcaption></figure>

substitution by Be₂ leads to a similar geometrical picture like
the previously discussed ethylene and aromatic compounds.
The Be₂ axis is perpendicular to the plane of the carbon
skeleton with the midpoint of Be–Be bond lying inside the
plane. Further carbon/beryllium substitution is possible and all
probable isomers of Be₂–Cₙ–Be₂ (n = 1–4) are considered
here. Regardless of the carbon separation with respect to the
beryllium centers, the structural features of these isomers
correspond to the general characteristic of the fragment
 vertic al Be₂ moiety). Only the isomer with a single carbon
separation is slightly perturbed from the perfect perpendicular
geometry of Be₂. All Be–Be distances in such dimers with
doubly substituted centers are within 0.015 Å with respect to the singly substituted moiety. The C–Be bonds are also very similar in these dimers (despite different metal center positions), indicating little influence of the border effects due to the frozen external carbon ring. The picture of molecular orbitals observed for the extended C<sub>31</sub>H<sub>14</sub>Be<sub>2</sub> complex (Figure 5) is similar to the aromatic compounds. The HOMO π orbital

<figure><img src="image_7.png" /><figcaption>**Figure 5.** Π HOMO (a) and combined three σ HOMO molecular orbitals (b) (perspective view) of C<sub>31</sub>H<sub>14</sub>Be<sub>2</sub> localized on the beryllium dimer.</figcaption></figure>

above the Be₂ center constitutes part of the extended delocalized π system. The σ combined orbitals representing the σπ² arrangement are also dipped in the sea of delocalized orbitals. The Be–Be distance in all the cases is close to 1.73 Å. The comparison of all considered complexes indicates that perturbations due the Be₂ insertion in the ring are almost independent when Be₂ centers are separated by at least two carbon atoms. The substitution leads to the local modification of properties of original molecules as may be observed by the atomic charge distribution. The beryllium NBO charge was approximately 1.15 electron in single Be₂ as well as in double substitution. More importantly, the characteristics of substitution centers (geometrical or electronic) is also similar to one observed in the single substitution. The difference in properties disappears for Be₂ centers for distances larger than two carbon atoms. The local character of substitutions indicates the existence of independent active centers.

## CONCLUSIONS

The doping of active carbon or nanocarbon materials is a promising direction for controlling their physical and chemical properties. In this work, the beryllium dimers were studied as potential active centers in the carbon body. Be₂ represents a weakly bonded complex, with low-lying excited electronic states. These states, when activated by interaction with the “third body”, lead to complexes of much higher bonding energy. The bonding in complexes results from the competition between the highly repulsive Pauli exchange energy ($ε_{ex}^{HL}$) and the attractive interaction energy terms ($ε_{el}^{(10)}$, $ΔE_{del}^{HF}$, $ε_{disp}^{(20)}$). The values of separate contributions are comparable to those characterizing chemical bonds. Although in CH₂Be₂H₂, the Be–Be distance is significantly shortened due to the interactions with the environment, the molecular orbital picture of the valence space ($σ_g σ_u π_u σ_g$) is preserved and constitutes the basis for the MO formation in larger systems. The substitution of single carbon by the pair of beryllium atoms does not destroy planarity and the aromaticity of the carbon network. The inclusion of Be₂ in the place of carbon preserves the symmetry characteristics of complex with axis of Be₂ being perpendicular to carbon network with the midpoint X of Be–Be bond located in the original carbon position (i.e., plane of the ring). The position of hydrogen (or hydrogens), originally attached to the

replaced carbon is also preserved. This phenomenon was observed in all studied systems where substituted carbon possessed the sp² character. The midpoint X of Be₂ may be considered as a “pseudo sp² carbon atom” with $σπ²$ orbital organization of valence orbitals—an analogue to the atomic sp² case. The molecular orbital pictures, presented for ethylene, benzene, naphthalene, and ovalene derivatives, confirm the proposed model. The $σ_g$ orbital of Be₂ is included in the sea of π molecular orbitals of conjugated molecules (in analogy to the p_z atomic orbital in carbon systems). The perturbations due to the doping were found to possess the local character and may be considered in larger systems as chemically active centers. The positive atomic charges on beryllium atoms are large and shortening of the bond can be attributed to the Be₂⁺ fragment. The results of population analysis should be treated with caution, however, due to the extensively delocalized character of electronic density.

## ASSOCIATED CONTENT

### Supporting Information

Optimized structures of CH₂Be₂H₂ and CH₂CH₂ and views of Be₂-substituted benzene and naphthalene derivatives.

## AUTHOR INFORMATION

### Corresponding Authors

Email: szczepan.roszak@pwr.edu.pl (S.R).

Email: devashis@icnanotox.org (D.M.).

Email: jerzy@icnanotox.org (J.L.).

### Notes

The authors declare no competing financial interest.

## ACKNOWLEDGMENTS

This work has been supported by the PREM (Award No. DMR-1205194) and ONR (Award No. N00014-13-1-0501) grants. S.R. acknowledges the financial support by a statutory activity subsidy from the Polish Ministry of Science and Technology of Higher Education for the Faculty of Chemistry of Wroclaw University of Technology and NCN grant No. 2012/07/B/ST4/01584. We also thank the Mississippi Center for Supercomputing Research, Wroclaw and Poznan Centers for Networking and Supercomputing, and Interdisciplinary Center for Mathematical Modeling of Warsaw University for providing generous computer time.

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