next to carbon - based chemistry , boron chemistry is surely one of the most active areas of research .
boron exhibits a variety of polymorphisms which involve three - center two - electron ( 3c2e ) bonds , planar aromatic structures , nano - tubes , nano - ribbons , and fullerene - like cages . from the point of view of nano - technology ,
aromatic boron materials are of particular interest , because delocalized electron clouds in these materials will lead to large linear and non - linear optical susceptibilities , just like corresponding carbon - based structures . in order to achieve aromaticity
indeed , aromaticity in boron - based clusters has been the subject of many recent investigations .
zhai et al .   in a recent joint theoretical and experiment study probed the issue of planarity and aromaticity of boron clusters .
in another theory -- experiment study , zhai et al .   reported the discovery of planar boron clusters b8 and b9 clusters with  molecular wheel-like structures and exhibiting both  and  aromaticity .
aihara and coworkers   presented a theoretical investigation of aromaticity into several planar and quasi - planar boron clusters using the concept of  topological resonance energy  .
johansson   demonstrated theoretically the existence of strong magnetically induced ring currents in b20 and other toroidal clusters of boron , as an evidence of underlying aromaticity .
rincon et al .   theoretically demonstrated the  aromaticity in several planar boron clusters performing an analysis of the electron - localization function ( elf ) .
similarly , wu et al .   using an ab initio approach investigated the aromaticity of planar boron -- carbon complex c6b12 .
another possible approach to achieve planarity , and , therefore , aromaticity in boron clusters is by hydrogenation of boron clusters .
for example alexandrova et al .   have demonstrated by means of theoretical calculations , that quasi - planar b7 cluster , upon hydrogenation , acquires a planar structure for b7h2 . in a recent theoretical work ,
szwacki et al .   proposed a novel planar aromatic cluster which can be obtained by hydrogenation of quasi - planar b12 cluster .
they argued that the cluster is aromatic by performing a detailed analysis of its molecular orbitals and by examining magnetic properties such as nucleus - independent chemical shift ( nics ) , and anisotropy of magnetic susceptibility ( ams ) .
having thus demonstrated the similarities between the aromaticities of this cluster and benzene ( including the number of -electrons ) , they called it the boron analogue of benzene and named it borozene . encouraged by the work of szwacki et al . , forte et al .   performed ab initio calculations to predict larger aromatic compounds which can be constructed using borozene as formula unit .
it is a well - known fact that the carbon - based aromatic materials including molecules such as benzene , napthalene , anthracene , and longer -conjugated polymers exhibit intense linear and non - linear optical response .
therefore , it is of considerable interest to explore similar properties of aromatic materials consisting of elements other than carbon . with this aim in mind , here we present a systematic theoretical study , based upon a large - scale configuration - interaction ( ci ) methodology , of linear optical response of borozene .
we believe our results will be useful in optical characterization experiments on this material , as also in exploring its possible application in nano - optics .
furthermore , we also perform calculations of static polarizability of this cluster , with the aim of exploring the signatures of aromaticity in its dielectric response .
therefore , the consequences of this delocalization of electrons will be manifest in various properties of materials , including their magnetic as well as dielectric response . with the electrons delocalized along the plane of the molecule for conjugated systems as benzene , one would expect its  in - plane  dielectric response to be significantly more than its  perpendicular  response .
thus , this anisotropy in the static polarizability tensor ij can also be viewed as a signature of the aromaticity , in such systems .
indeed , this anisotropy in  has been verified theoretically by other authors in the past calculations on conjugated molecules [ 17 - 19 ] and has been used to formulate an  aromaticity scale  for such systems .
introduction  section , we briefly describe the theoretical methodology employed for the present calculations and also discuss the geometry of the molecule . this
is followed by the presentation and discussion of our results in  results and discussion  . finally , in 
the basic structure of borozene is presented in fig . 1 , and it corresponds to point symmetry group d3h . before proceeding with our calculations , for the purpose of verification , we decided to perform the geometry optimization on our own using the b3lyp - based hybrid dft approach employing the 6 - 311++g(d ) basis set as implemented in gaussian03 program .
the optimized structure thus obtained belonged to the d3h point group symmetry with uniform value of b 
h bond length 1.18  , and four distinct values of b  b bond lengths 1.63 , 1.66 , 1.81 , and 1.86  .
we , however , are interested in exploring an even more symmetric structure of borozene , so as to make the comparison with benzene more transparent .
therefore , we separately optimized a highly symmetric structure of borozene ( s - borozene , henceforth ) with identical b  b bond lengths , in addition to the b  h ones . for this purpose , as well as for the linear absorption spectrum calculations
, we adopted an indo model hamiltonian   based approach implemented recently in a computer program developed by us .
indo model is an effective valence - electron approach , employing a slater - type minimal basis set , and some semi - empirical parameters .
the geometry optimization using our computer program , performed at the hartree - fock ( hf ) level ( indo - hf , henceforth ) , yielded bond lengths 1.65  for the b  b bond and 1.18  for the b 
h bond length reported both by szwacki et al .   and forte et al . , and the average value of b  b bond length 1.649  reported by forte et al . .
the total energy of the geometry - optimized s - borozene was higher than that of the borozene with distinct b 
( color online ) structure of s - borozene considered in this work , assumed to lying in the xy - plane .
yellow dots indicate boron atoms and violet ones hydrogen atoms next , large - scale correlation calculations were performed on the ground and the excited states of s - borozene , using the multi - reference singles - doubles configuration - interaction ( mrsdci ) approach as implemented in the meld package   but employing the one- and two - electron matrix elements of the indo hamiltonian supplied by our program .
thus , these correlated calculations were entirely within the indo model and will be called indo - mrsdci calculations , henceforth . during these calculations ,
point symmetry group c2v was utilized , as against the d3h symmetry group , because the meld   package is restricted to d2h and its sub - groups .
therefore , we classify the many - electron states of the system in terms of the irreducible representations ( irreps ) of c2v group .
the optical absorption spectra were calculated under the electric - dipole approximation employing the lorenzian line shape .
for both the ground and the excited states , these calculations were performed in an iterative manner , until the optical absorption spectra computed from them converged .
we have extensively used this approach in our earlier calculations on conjugated polymers [ 24 - 27 ] as well as on b12 icosahedral and quasi - planar clusters reported recently .
symmetry group c2v consists of four irreps labeled a1,a2,b1 , and b2 . assuming that the cartesian xy - plane lies in the plane of the molecule ( cf .
1 ) , the symmetry adapted electronic structure of the hf ground state obtained from our code is 1a12a11b13a12b14a11b23b15a14b16a17a18a15b12b21a29a16b17b110a18b1 , leading to a1 many - particle configuration .
some of the lowest unoccupied orbitals in the ascending order of energy are 3b2 , 2a2 , 4b2 , 11a1 , 9b1 etc .
of all the orbitals , the ones belonging to a2 and b2 irreps are  orbitals and a1 and b1 are of  type .
thus , we note that the highest occupied molecular orbital ( homo ) is a  orbital , while the lowest unoccupied molecular orbital ( lumo ) is a  orbital . for the sake of visualization , some of the orbitals
( color online ) molecular orbitals ( iso plots ) of s - borozene from homo1 to lumo+1 , obtained from the indo - hf calculations while our lumo orbital matches perfectly with that reported by szwacki et al .
, however , we have a disagreement on the nature of the homo orbital which was reported to be of -type by them , but we obtain it to be of -type within the indo model . in order to rule out the possibility that this disagreement could due to the use of the indo model , or due to the s - borozene geometry , we studied the nature of the homo obtained using the 6 - 311++g(d ) basis set both at rhf and dft - b3lyp levels of ab initio theory   at various geometries . in all such dft calculations ,
it turned out to be a -type orbital , but for the rhf calculations , the nature of homo was highly geometry sensitive with some geometries yielding it to be -type , while others of -type .
this , in our opinion , is a significant difference between the electronic structures of benzene ( whose homo and lumo both are  type ) and borozene .
thus , borozene , in our opinion is an example of both  and  conjugation because , close to the fermi level , occupied orbitals are mainly of  type , while the unoccupied ones ( lumolumo + 1 , lumo + 2 ) are of  type . before presenting the results of our calculations of linear optical absorption spectrum of s - borozene
, we would like to discuss the influence of geometry on the optical properties of borozene , considering the fact that our calculations were performed on a highly symmetric conformer s - borozene .
for the purpose , we performed the optical absorption calculations at the singles - ci ( sci ) calculations both on the lowest energy structure of borozene with unequal b  b bond lengths and s - borozene .
we found that qualitatively , at the sci level , spectra were very similar for both the geometries , except that for s - borozene it was slightly red - shifted compared to borozene .
the first peak for borozene in this sci calculation was obtained at 2.6 ev in perfect agreement with excitation energy of the first excited reported by szwacki et al .
next , we present and discuss the results of our indo - mrsdci - based optical absorption calculations on s - borozene .
comparisons are also made with the absorption spectra of quasi - planar b12 bare cluster , and also with that of benzene . as the ground state of the system is a1 , as per electric - dipole selection rules
, it can make linear optical transitions to excited states belonging to symmetry manifolds a1 , b1 , and b2 through photons polarized along the y - axis , x - axis , and z - axis , respectively .
thus , transitions to a1 and b1 are through photons polarized in the plane of the molecule ( xy - plane in the present case ) , while those to b2 will be through perpendicularly polarized photons .
the indo - mrsdci calculations presented here involved construction and diagonalization of very large ci matrices running into millions of configurations , because simultaneously several states were targeted . for example , for the a1 symmetry manifold , the total number of configurations was more than 2.1 millions , while those for b1 and b2 manifolds were in excess of 2.5 , and 3 millions , respectively .
because of the large - scale nature of these calculations , we believe that the results account for electron correlation effects properly . in fig .
3 , we present the combined optical absorption spectrum of s - borozene , obtained from our indo - mrsdci calculations . as is obvious from the figures that the first absorption feature is a small peak located at 2.25 ev , corresponding to a z - polarized transition into a b2 state .
the many - particle wave function of this peak consists mainly of two single excitations hl + 1 and h  1l(hhomo;llumo ) , both of which are of  type . after this feature at 2.25 ev
, the next peak follows after a large gap of 5 ev and is due to two closely placed states at 7.38 ev ( b1-type ) and 7.55 ev ( a1-type ) .
thus , this intense peak can be reached through photons which are polarized in the molecular plane , but not through the z - polarized ones .
the many - particle wave functions of both these states are dominated by singly excited configurations , with the main configurations being |hl + 3 for the b1 state , and |h  1l + 3 for the a1 state .
linear optical absorption spectrum of s - borozene , computed using the indo - mrsdci approach .
a line width of 0.1 ev was used to compute the spectrum peak iii of the spectrum , which is a weaker feature located at 8.44 ev , corresponds to a b2 state and can be reached through a z - polarized photon .
many - particle wave function of this state is a mixture of several singly excited configurations which include |h  4l , |h  3l + 1 , and |hl + 8 , all of which are  type excitations .
finally , feature iv near 9.1 ev draws its oscillator strength from the transition of the ground state to three closely spaced excited states of symmetries a1,b1 , and b2 located at 9.03 9.01 , and 9.19 ev , respectively .
the peak has mixed polarization features , out of which x- and y - polarized transitions are more intense when compared to the z - polarized one .
 1l + 5 and |hl + 4 , while that of b1 state consists mainly of |h  1l + 4 and |hl + 5 , all of which are of  type .
the dominant configurations in the wave function of the b2 state are |hl + 8 and |h  1l + 7 , which are of  type .
the absorption spectrum of s - borozene consists of several very intense features beyond 10 ev as well , but we are not discussing them here , given the fact that the ionization potential of this material is estimated close to 9 ev . as szwacki et al .  
called borozene the boron analogue of benzene , it is interesting to compare the optical absorption spectra of the two materials .
it is a well - known fact that the first dipole allowed transition in benzene is from the a1 g ground state to the e1u excited state with the peak around 6.99 ev , through photons polarized in the plane of the molecule ( xy - plane in our case ) .
3 ) of s - borozene which is also caused by photons polarized in the the xy - plane and is located around 7.5 ev .
the only difference being that for the the e1u state in benzene corresponds to a  transition , while the peak ii of borozene corresponds to  transitions .
the difference between the optics of the two materials is the presence of low energy feature ( peak i ) in s - borozene corresponding to a z - polarized transition , whose counterpart in benzene does not exist .
recently , we studied the linear optical absorption in quasi - planer b12 cluster which has a convex shape with symmetry group c3v and can be seen as a precursor of borozene .
therefore , a comparison of the optical properties of quasi - planar b12 and borozene can help us understand the influence of hydrogen passivation on the optical properties of b12 . in fig .
4 , the linear optical absorption spectra of the two clusters are presented , and it is obvious that the first few peaks of s - borozene occur at lower energies when compared to the quasi - planar b12 . moreover ,
the hl transition is symmetry forbidden in s - borozene , which is not the case for quasi - planar b12 , and indeed contributes to the wave function of the first peak in its spectrum .
thus , the main contribution of hydrogen passivation on the optical properties is that it makes the structure completely planar ( as against quasi - planar ) leading to conjugation and higher symmetry .
lower energy gap of s - borozene is most certainly a consequence of conjugated nature of electrons in the system .
a comparison of the linear optical absorption spectra between s - borozene ( solid line ) quasi - planer b12(broken line ) .
the spectrum of s - borozene is significantly red - shifted when compared to that of b12 . a line width of 0.1 ev
was used to compute the spectrum in order to explore the aromaticity of borozene , szwacki et al .   computed and discussed its nics plots and anisotropy of magnetic susceptibility ( ams ) . with a similar aim , we computed the three diagonal cartesian components of the static polarizability tensor , xx , yy , and zz of borozene both at the indo - hf and indo - sdci levels . for the purpose
, we adopted a finite - field approach and computed the second derivative of the total energy of the system numerically , with respect to the three cartesian components of the external electric field , whose values were taken to be 0.005 atomic units .
the numerical values obtained in our calculations correspond to valence - electron contribution to the polarizability because of the nature of the indo hamiltonian . however , our aim here is not to obtain exact numerical values of the polarizability tensor , rather to compare the values of its various components .
it is obvious from the results of our calculations presented in table 1 that : ( a ) inclusion of correlation effects does not change the values of ii very much , and ( b ) the values of in - plane components ( xx and yy ) are significantly larger than the perpendicular component zz . ab initio calculations performed on conjugated molecules like benzene ,   anthracene , and ethane   exhibit similar anisotropy in the components of the polarizability tensor . and , indeed , based upon the magnitude of this  in - plane  vs.  perpendicular  anisotropy , lazzeretti and tossell   argued for an  aromaticity scale  to characterize -conjugated systems . using the same logic , the same anisotropy found in our calculations
clearly implies the aromaticity in borozene , but as a consequence of both  and  conjugation in the plane of the molecule .
this fact is also obvious from the optical absorption spectrum of the material in which intensities of the z - polarized peaks are much smaller than those of x- and y - polarized ones .
values of the components of static dipole polarizability tensor of borozene computed using the indo - hf and indo - sdci methods ( in atomic units )
in conclusion , a correlated study on electronic structure and optical properties of a recently proposed boron - hydrogen cluster , borozene , was presented using the semi - empirical mrsdci - indo method .
our calculations of the linear optical absorption spectrum can be used to characterize this substance in future optical absorption experiments .
we also calculated the diagonal components of the static polarizability tensor ij of the cluster and found significant larger values for the components along the plane of the molecule , when compared to the one perpendicular to it .
this anisotropy in the components of the polarizability tensor implies that the electrons are quite delocalized along the plane of the molecule leading to a considerably larger response to an electric field directed along the plane , when compared to that perpendicular to the plane .
therefore , we argue that this anisotropy in the static dielectric polarizability of the cluster is an evidence of its aromaticity ,   caused both by  and  conjugation along the plane of the molecule .
we gratefully acknowledge useful private communications with dr . c. j. tymczak in which he clarified the optimized geometry obtained in their calculations on borozene .
this article is distributed under the terms of the creative commons attribution noncommercial license which permits any noncommercial use , distribution , and reproduction in any medium , provided the original author(s ) and source are credited .
this article is distributed under the terms of the creative commons attribution noncommercial license which permits any noncommercial use , distribution , and reproduction in any medium , provided the original author(s ) and source are credited .
 in this work , we report electronic structure calculations aimed at computing the linear optical absorption spectrum and static dipole polarizablity of a newly proposed boron - based planar aromatic compound borozene ( b12h6 ) . for the purpose 
 , we use the semiempirical indo model hamiltonian , accompanied by large - scale correlation calculations using the multi - reference singles - doubles configuration - interaction ( mrsdci ) approach . 
 we present detailed predictions about the energetics , polarization properties , and the nature of many - particle states contributing to various peaks in the linear absorption spectrum . 
 our results can be used to characterize this material in future optical absorption experiments . 
 we also argue that one can deduce the aromaticity of the cluster from the optical absorption and static polarizability results . 
Introduction
Theoretical Methodology
Results and Discussion
Conclusions
Acknowledgments
Open Access