Planar to 3D Transition in the B6Hy Anions - The Journal of Physical

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Planar to 3D Transition in the BH Anions Jared K Olson, and Alexander I. Boldyrev J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/jp310162v • Publication Date (Web): 18 Jan 2013 Downloaded from http://pubs.acs.org on January 20, 2013

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The Journal of Physical Chemistry

Planar to 3D Transition in the B6Hy Anions J.K. Olson and A.I. Boldyrev* Utah State University, 0300 Old Main Hill, Logan, UT 84322-0300, USA

ABSTRACT: Potential energy surfaces of anionic B6Hy clusters were sampled using the Coalescence Kick method. We found that the planar to three-dimensional transition occurs in this system when y = 4. This is an important discovery because this transition suggests a major structural change as a function of de-hydrogenation for the stoichiometric BnHn- polyhedral boranes. We also found that the B6H3- global minimum structure has an optical isomer. The chemical bonding patterns revealed by the Adaptive Natural Density Partitioning (AdNDP) analysis explain the geometric structure of all clusters presented here. From our chemical bonding analysis we concluded that the 2D-3D transition occurs at B6H4-, because the addition of one extra hydrogen atom further destroys the network of the peripheral 2c-2e B-B σ-bonding making planar structures less stable and because the distorted octahedral structure provides some occupation of all s- and p-AOs of boron avoiding the presence of any empty atomic orbitals. Theoretical vertical electron detachment energies (VDEs) were calculated for comparison with future experimental work.

KEYWORDS: cage structure borohydrides, vertical electron detachment energy, AdNDP, octahedral borohydride.

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INTRODUCTION It is known that BnHn2- (n = 6 – 12) boranes form 3D deltahedral structures.1 It was expected that the singly charged BnHn- species should also possess 3D structures similar to doubly charged anions,2 which however, should undergo distortion due to the Jahn-Teller effect. However, the joint experimental and computational investigations over the past decade have shown that boron clusters exhibit planar or quasi-planar structures in their ground states at least to B21− in the anions,3-15 B20 in the neutrals,5 and B16+ in the cations.16 Since cage structures, in particular, like the icosahedral B12 cage, dominate the boron allotropies17 and boranes,1 it was hypothesized that 3D cage structures might occur for small boron clusters in early experimental studies.18 Subsequent computational studies suggested that icosahedral cage structures for B12 and B13 were unstable, however.18 Further computational studies proposed that neutral and cationic boron clusters up to 14 atoms were more stable in the planar or quasi-planar (2D) geometries.18 Previous calculations by Ricca and Bauschlicher on BxH+ indicate that the H atom bonds to the peripheral of the planar Bx+ clusters.21 Alexandrova et. al.22 computationally showed that B7H2 and B7H2- are planar. Li et. al.23 reported systematic study of BnH2 neutrals (n = 4, 6, 8, 10, 12) and BnH2 monoanions (n = 3, 5, 7, 9, 11). They found that planar D2h B4H2, C2h B8H2, and C2h B12H2 are the lowest-lying isomers of the systems at density functional theory (DFT) which turn out to be the borene analogues of ethylene C2H4, 1,3-butadiene C4H6, and 1,3,5-hexatriene C6H8. Li et al.24 in a joint experimental and theoretical study of the BnH2− clusters for n = 8−12 have shown that they have planar ladder structures. They stated that the boron dihydrides clusters are similar to conjugated alkenes: in particular they found that π orbitals of H2B7−, H2B8, H2B9−, are similar to those in butadiene and π orbitals of H2B102−, H2B11−, H2B12, are similar to those in 1,3,5hexatriene. Planar boron-rich boron hydride were also predicted for B4Hn0/- (n = 1–4)25 and B16Hn


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(n = 1–6)26 clusters. Bai and Li27 reported a systematic investigation on the effect of hydrogenation of B120/- clusters and found that there exists a 2D–3D transition between n = 3–4 in B12Hn0/- (n = 1–6). Boyukata et al.28 also reported DFT studies of the BmHn (m= 5–10 and n≤m) clusters. In this article we report the systematic study of the B6Hy- clusters with the goal to find the 2D3D transition upon the hydrogenation and to rationalize this transition in terms of changes in chemical bonding. The B6- cluster is known to be planar,3b while B6H6- is distorted octahedron.2 Thus, one should expect that the 2D to 3D transition should occur at some degree of hydrogenation along the B6Hy- series. In this article we present the systematic study of the B6Hyseries and we established that the 2D to 3D transition occurred at y=4. COMPUTATIONAL DETAILS To search for the 2D – 3D transition in B6Hy- clusters, potential energy surfaces of anionic B6Hy (y = 2 – 4) clusters were sampled for every stoichiometry using the Coalescence Kick (CK) program written in our group by Averkiev.29 The Coalescence Kick method subjects large populations of randomly generated structures to a coalescence procedure with all atoms gradually pushed to the molecular center of mass to avoid generation of fragmented structures and then optimizes them to the nearest local minima. In the CK method, a randomly generated structure is checked for connectivity as follows: if all atoms in the structure belong to a single fragment, the structure is considered to be connected, and the geometry optimization procedure is applied to that structure.

Many times, however, the randomly generated structure is

fragmented (i.e. the structure contains fragments which are not bonded to each other, including instances where a single atom is not bonded to other fragments). In this case, a coalescence


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process is applied whereby all fragments in the structure are pushed toward the center of mass simultaneously. A 0.2 Å shift was used in the current version of the CK program. The magnitude of the shift was selected so that the shift at each coalescence step is small enough to prevent the atoms from approaching too closely, but large enough to allow the coalescence procedure to converge in a reasonable amount of time. Two fragments “coalesce” when they approach closely enough to form a new fragment, and then this new fragment is pushed to the center of mass as a whole in the subsequent coalescence steps. To avoid the problem of having two atoms placed too closely together in the initial random structure, the initial structures are generated in a large box where the x, y, and z dimensions are each 4 times the sum of the atomic radii of the atoms in the structure. We allow the CK algorithm to run until the total number of structures generated and submitted for geometry optimization is greater than 10 times the number of atoms in the system being studied in the global minimum search. For the global minimum search, we used a hybrid method known as B3LYP30-32 with small split-valence basis sets (3-21G) for energy and gradient calculations. Geometries were then re-optimized and frequencies were calculated for all structures within 30 kcal/mol of the global minimum using B3LYP with polarized split-valence basis sets (6-311++G**).33-36

If a saddle point was

encountered, we followed the normal mode of the first imaginary frequency until a local minimum was found. Following this re-optimization, for the few lowest structures found at the B3LYP/6-311++G** level of theory, we re-optimized geometries and calculated harmonic frequencies at the coupled-cluster with single, double, and non-iterative triple excitations method [U(R)CCSD(T)]37-39 using the 6-311++G** basis set for both calculations. Relative energies reported in this work were corrected for zero-point energies (ZPE) at the corresponding level of theory. Energies of these lowest energy isomers were also recalculated by extrapolating to the


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infinite basis set from correlation–consistent polarized valence double and triple zeta (aug-ccpvDZ and aug-cc-pvTZ) basis sets40-44 at the U(R)CCSD(T) level of theory as proposed by Truhlar.45 Truhlar’s method uses double- and triple-zeta basis sets to conduct the extrapolation using the Hartree-Fock and correlation energies from both the DZ and TZ calculations in order to obtain accurate energies comparable to 6Z basis set calculations at a fraction of the computational expense.

Theoretical vertical electron detachment energies (VDEs) were

calculated using three levels of theory: U(R)CCSD(T)/aug-cc-PVTZ method, the outer valence Green Function method [U(R)OVGF/aug-cc-PVTZ]46-49 at the U(R)CCSD(T)/6-311++G** geometries, and the time-dependent DFT method [TD-B3LYP/aug-cc-PVTZ]50,51 at the optimized B3LYP/6-311++G** geometries. In the last approach, the first VDE was calculated at the B3LYP level of theory as the lowest transition from the anion into the neutral cluster. The vertical excitation energies of the neutral species (at the TD-B3LYP level) were then added to the first VDE to obtain the second and higher VDEs. Core electrons were frozen in treating the electron correlation at the RCCSD(T) and ROVGF levels of theory. We performed chemical bonding analysis using the Adaptive Natural Density Partitioning (AdNDP) method developed by Zubarev and Boldyrev.52-54 The AdNDP analysis is based on the concept of electron pairs as the main elements of chemical bonding. It represents the electronic structure in terms of ncenter–two-electron (nc-2e) bonds with n ranging from one to the total number of atoms in the whole cluster. AdNDP recovers both Lewis bonding elements (1c-2e or 2c-2e objects, i.e., lone pairs or two-center two-electron bonds) and delocalized bonding elements, which are associated with the concepts of aromaticity. Pictures of bonds recovered by the AdNDP analysis were made using the MOLEKEL program.55 The B3LYP, CCSD(T), OVGF, and TD-DFT calculations were


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performed using Gaussian 0356 and Gaussian 09.57 Molecular structure visualization was done using the MOLDEN 3.4 program.58 RESULTS AND DISCUSSION Results of our final relative energies for a few lowest structures (either the first or first and second local minima) are summarized in Figure 1.


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Figure 1. Lowest isomers for B6Hy- (y = 2 – 4) with their symmetry, spectroscopic state and relative energies at the CCSD(T) infinite basis set extrapolation in curly brackets, at the CCSD(T)/6-311++G** in parentheses, otherwise at B3LYP/6-311++G**.

Our global minimum C2h planar structure for the B6H2- is the same as was predicted by Li et al.23 for the neutral B6H2 cluster, similar to the structure previously found by Alexandrova et al.22 for the B7H2 and B7H2- cluster and consistent with experimentally observed for BxH2- (x=7-12) clusters by Li et al.24 For the B6H2 cluster, Boyukata et al.28 reported a different structure, which has an octahedral boron cage with one hydrogen atom linked to one boron atom. There are two almost degenerate isomers III(IV) and V for the B6H3- stoichiometry. Our most stable B6H3structure has C1 symmetry and therefore it has chirality, e. g. it exists as a pair of optical isomers III and IV. The optical isomers for BxHy- clusters were reported before for B4H5 and B4H5clusters.59 The global minimum structure and the next lowest isomer for B6H3- has a nearly planar B6 kernel similar to what we found for the B6H2- structure. Again, our global minimum structure is very different from reported by Boyukata et al.28 Their structure has an octahedral B6 kernel with three hydrogen atoms connected to tree boron atoms. According to our results, the 2D-3D transition in B6Hy- occurs when y = 4, where three-dimensional structure VIII is slightly more stable than the quasi-planar structure IX. This structure again differs with what was previously reported by Boyukata et al, who reported a structure with D2H point group symmetry.28 The global minimum geometry reported here, found through the unbiased search described above, has D4h point group symmetry.


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The best way to test our theoretical predictions is to make those clusters in molecular beam and record their photoelectron spectra. Those experimental spectra then can be compared with the theoretical ones and good agreement would be a proof for our predictions. Such work was done by Li et. al.24 for the BnH2− clusters for n = 8−12, where planar ladder structures predicted theoretically were confirmed through good agreement between theoretical and experimental vertical electron detachment energies. In order to facilitate such experiments we calculated theoretical VDEs for the global minimum structures of B6Hy- (y=2-4), which we report in Table 1. Table 1. Theoretical Photoelectron Spectrum for the global minimum and low lying structures of B6Hy- (y = 2 – 4). Cluster, Isomer

Final State and Electronic Configuration 1

B6H2I, C2h B6H3III, IV, C1 B6H3V, CS

B6H4VIII, D4h

B6H4IX, C2

2

2

2

2

2

2

2

2

2

2

0

Ag, 1ag 1bu 2ag 2bu 3bu 3ag 1au 4ag 4bu 5ag 1bg Bg, 1ag21bu22ag22bu23bu23ag21au24ag24bu25ag11bg1 3 Ag, 1ag21bu22ag22bu23bu23ag21au24ag24bu25ag11bg1 1 Au, 1ag21bu22ag22bu23bu23ag21au24ag24bu15ag21bg1 2 A, 1a22a23a24a25a26a27a28a29a210a211a1 2 A, 1a22a23a24a25a26a27a28a29a210a111a2 2 A, 1a22a23a24a25a26a27a28a29a110a211a2 2 A, 1a22a23a24a25a26a27a28a19a210a211a2 2 A’, 4a’(2)5a’(2)1a’’(2)6a’(2) 7a’(2) 8a’(2)2a’’(2)9a’(1) 2 A”, 4a’(2)5a’(2)1a’’(2)6a’(2) 7a’(2) 8a’(2)2a’’(1)9a’(2) 2 A’, 4a’(2)5a’(2)1a’’(2)6a’(2) 7a’(2) 8a’(1)2a’’(2)9a’(2) 2 A’, 4a’(2)5a’(2)1a’’(2)6a’(2) 7a’(1) 8a’(2)2a’’(2)9a’(2) 1 A1g, 1a1g21eu41a2u22a1g21b1g22eu41eg41b2g23a1g0 1 B2g, 1a1g21eu41a2u22a1g21b1g22eu41eg41b2g13a1g1 3 B2g, 1a1g21eu41a2u22a1g21b1g22eu41eg41b2g13a1g1 3 Eg, 1a1g21eu41a2u22a1g21b1g22eu41eg31b2g23a1g1 1 Eg, 1a1g21eu41a2u22a1g21b1g22eu41eg31b2g23a1g2 1 B, 1a21b22a22b23a23b24a24b25a26a25b26b0 1 A, 1a21b22a22b23a23b24a24b25a26a25b16b1 3 A, 1a21b22a22b23a23b24a24b25a26a25b16b1 1 B, 1a21b22a22b23a23b24a24b25a26a15b26b1 3 B, 1a21b22a22b23a23b24a24b25a26a15b26b1 3 B, 1a21b22a22b23a23b24a24b25a26a15b16b2 1 B, 1a21b22a22b23a23b24a24b25a16a25b26b1 3 B, 1a21b22a22b23a23b24a24b25a16a25b26b1 1

VDE (theo, eV) TD-B3LYPa) 2.8 3.7 4.1 4.5 3.0 3.6 4.2 5.2 3.6 4.2 4.7 5.0 3.6 3.6 3.6 4.1 4.6 2.7 2.7 3.0 4.1 4.2 4.8 4.8 5.1

CCSD(T)b) 2.4 3.2 2.3 4.3 3.2 d) d) d) 3.8 4.2 d) d) 3.7 3.7 3.7 4.0 d) 2.7 d) 3.0 d) d) 4.2 d) d)

OVGFc) 2.9 (0.89) 3.7 (0.88) 3.7 (0.88) 4.3 (0.86) 3.1 (0.89) 3.8 (0.88) 4.3 (0.86) 5.4 (0.84) 3.8 (0.88) 4.1 (0.89) 4.9 (0.87) 5.1 (0.86) 3.7 (0.90) 3.8 (0.91) 3.8 (0.90) 3.9 (0.89) 4.2 (0.90) 2.7 (0.90) 3.1 (0.88) 2.9 (0.88) 4.7 (0.85) 4.6 (0.89) 4.7 (0.85) 5.3 (0.82) 5.7 (0.87)

a)

VDEs were calculated at TD-B3LYP/aug-cc-pvTZ//CCSD(T)/6-311++G** VDEs were calculated at CCSD(T)/aug-cc-pvTZ//CCSD(T)/6-311++G** c) VDEs were calculated at OVGF/aug-cc-pvTZ//CCSD(T)/6-311++G** b)


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d)

VDEs cannot be calculated at this level of theory

We have good agreement for lowest VDEs between all three methods for all three clusters. One can see that two low-lying structures III, IV, and V can be distinguish from the experimental photoelectron spectra due to appreciable difference in the low-lying VDEs. Next, we performed chemical bonding analysis for the global minimum and low-lying isomers of B6Hy- using the Adaptive Natural Density Partitioning (AdNDP) method.38-40

In order to obtain a simple

chemical bonding picture and avoid complications due to spin-polarization, the AdNDP analysis was performed for doubly charged anions B6H22- and B6H42- (an extra electron was added to the semioccupied HOMO) at the optimized geometry of structures I and VIII. Results of the analysis are presented in Figures 2, 3, and 4.

According to the AdNDP analysis, the global minimum B6H2- isomer (see Figure 2) has two 2c-2e B-H σ-bonds (|e| = 1.99), six 2c-2e B-B σ-bonds (|e| = 1.74 – 1.96), one 4c-2e B-B-B-B σbond (|e| = 1.90), and two 4c-2e B-B-B-B π-bonds (|e| = 1.97). Thus, this cluster is σ-aromatic and π-antiaromatic. As in all-boron cluster,3-15 2c-2e B-B σ-bonds form a peripheral ring in this cluster and that is a significant stabilizing factor for planar structures. Chemical bonding in B6H22- is similar to that found for B8H2 by Li et al.23 and for B7H2- and B8H2 by Li et al.24, thus it is also a boron hydride analogue of the conjugated 1,3-butadiene C2h C4H6.


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Figure 2. Bonds recovered by the AdNDP analysis for B6H2- isomer I. AdNDP analysis was performed for the doubly charged B6H2- anion at the optimal geometry of isomer I of B6H2-.

AdNDP analysis of the low-lying isomer III (see Figure 3A) reveals two 2c-2e B-H σ-bonds (|e| = 1.99), one 3c-2e B-H-B σ-bond (|e| = 1.98), four 2c-2e B-B σ-bonds (|e| = 1.774 – 1.95), two 3c-2e B-B-B σ-bonds (|e| = 1.79 – 1.98), and two 3c-2e B-B-B π-bonds (|e| = 1.73 – 1.86). Thus, this bonding in the boron framework in this cluster is π-antiaromatic, similar to the B7H2bonding picture presented by Li et al.24 Interestingly, we now found that there is no longer a complete ring of 2c-2e B-B σ-bonds found in all planar all-boron clusters,3-15 but that two of those bonds are now 3c-2e B-B σ-bonds.


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Figure 3. A. Bonds recovered by the AdNDP analysis for B6H3- isomer III. B. Bonds recovered by the AdNDP analysis for B6H3- isomer V.

The AdNDP bonding analysis of low-lying isomer V (see Figure 3B) reveals three 2c-2e B-H σbonds (|e| = 1.94 – 1.99), six 2c-2e B-B σ-bonds (|e| = 1.69 – 1.96), one 4c-2e B-B-B-B σ-bond (|e| = 1.92), and one 5c-2e delocalized over five boron atoms π-bond (|e| = 1.99). AdNDP analysis of the three-dimensional global minimum B6H4- isomer VIII (see Figure 4) reveals four 2c-2e B-H σ-bonds (|e| = 1.99) and eight 3c-2e B-B-B σ-bonds (|e| = 1.99). Every face of the distorted octahedron has its own 3c-2e B-B-B σ-bonds. It was previously shown60 that boron atoms are avoiding sp2 hybridization because having empty pz-AOs is highly unfavorable in the planar structures boron compounds. Moving part of σ-electron density into π−density makes planar boron structures more stable but at the expense of the scarifying of the classical 2c-2e σ-


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bonding.

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That is the major reason why we have multicenter bonding in boron and

boronhydrides. We believe from our chemical bonding analysis that the 2D-3D transition occurs at B6H4-, because the addition of one extra hydrogen atom further destroys the network of the peripheral 2c-2e B-B σ-bonding making planar structures less stable and because the distorted octahedral structure provides some occupation of all s- and p-AOs of boron avoiding the presence of any empty atomic orbitals. The similar 2D-3D transition was found for B6-nAln2series at n=4 by Huynh and Alexandrova, and they explained this transition through the s-p hybridization of atomic orbitals affordable for the B versus Al atoms.61 The chemical bonding patterns revealed by the AdNDP analysis are consistent with the geometric structures of all isomers and global minima presented here.


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Figure 4. A. Bonds recovered by the AdNDP analysis for B6H4- isomer VIII. B. Bonds recovered by the AdNDP analysis for B6H4- isomer IX. AdNDP analysis was performed for the doubly charged B6H42- anion at the optimal geometry of isomer VIII of B6H4-.

SUMMARY AND CONCLUSIONS We performed an unbiased search for the global minimum B6Hy- (y=2-4) clusters and found that the 2D-3D transition occurs when y = 4. This is an important issue because this transition would suggest a major structural change as a function of de-hydrogenation for the stoichiometric BnHn-


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polyhedral boranes. Chemical bonding in the global minimum and low-lying isomers was analyzed using the AdNDP method. From our chemical bonding analysis we concluded that the 2D-3D transition occurs at B6H4-, because the addition of one extra hydrogen atom further destroys the network of the peripheral 2c-2e B-B σ-bonding making planar structures less stable and because the distorted octahedral structure provides some occupation of all s- and p-AOs of boron avoiding the presence of any empty atomic orbitals. An understanding of major structural changes that occur on hydrogenation and dehydrogenation is important for potential hydrogen storage materials to help determine if the materials can be recycled after hydrogenation or dehydrogenation.

Chemical bonding patterns revealed by this analysis are consistent with

structures of the studied clusters. An optical isomer exists for the global minimum B6H3- cluster, similar to optical isomerism predicted for other boron-hydride species. The VDEs calculated for the global minimum B6Hy- clusters may help to interpret future experimental photoelectron studies. AUTHOR INFORMATION Corresponding Author [email protected] Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Funding Sources The authors gratefully appreciate support by the National Science Foundation (Grant No. CHE1057746). Computer times from the Centers for High Performance Computing at the University


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of Utah and Utah State University are gratefully acknowledged. The Wasatch cluster at USU was funded by USDA NIFA through the High Performance Computing Utah grant. Dedication We dedicate this publication to our friend and colleague Professor Ivan Černušák (Comenius University), to commemorate his 60th birthday ACKNOWLEDGMENT We gratefully acknowledge funding from the National Science Foundation (Grant No. CHE1057746). Computer times from the Centers for High Performance Computing at the University of Utah and Utah State University are gratefully acknowledged. REFERENCES (1)

(a) Lipscomb, W. N. Boron Hydrides. New York, Benjamin, W. A. 1963. (b) Muetterties, E. L. Boron Hydride Chemistry, New York, Academic Press, 1975.

(2)

McKee, M. L.; Wang, Z. X.; Schleyer, P. v. R. Ab Initio Study of the Hypercloso Boron Hydrides BnHn and BnHn-. Exceptional Stability of Neutral B13H13. J. Am. Chem. Soc. 2000, 122, 4781-4793.

(3)

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