ChemInform Abstract: Aromaticity in Polyacenes and Their Structural Analogues

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As featured in:

See Lee et al., Phys. Chem. Chem.

Phys., 2012, 14, 4333.

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Theoretical Chemistry Research Laboratory of

Professor Pratim Kumar Chattaraj at the Indian

Institute of Technology Kharagpur

Title: Some novel molecular frameworks involving

representative elements

Professor Pratim Kumar Chattaraj and his research group have been

actively engaged in research work comprising density functional

theory, ab initio calculations, chemical reactivity, nonlinear

dynamics, aromaticity in metal clusters, hydrogen storage, etc. for

the last quarter of a century. The stability of diff erent types of novel

helical molecular assemblies as well as a series of fi ve membered

and six membered star-like clusters has been explored.

As featured in:

See Chattaraj et al., Phys. Chem. Chem.

Phys., 2012, 14, 14784.

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View Article Online / Journal Homepage / Table of Contents for this issue

http://dx.doi.org/10.1039/C2CP41424D

http://pubs.rsc.org/en/journals/journal/CP

http://pubs.rsc.org/en/journals/journal/CP?issueid=CP014043

14784 Phys. Chem. Chem. Phys., 2012, 14, 14784–14802 This journal is c the Owner Societies 2012

Cite this: Phys. Chem. Chem. Phys., 2012, 14, 14784–14802

Some novel molecular frameworks involving representative elementsw

Arindam Chakraborty,aSateesh Bandaru,

aRanjita Das,

aSoma Duley,

a

Santanab Giri,bKoushik Goswami,

aSukanta Mondal,

aSudip Pan,

a

Soumya Senaand Pratim K. Chattaraj*

a

Received 3rd May 2012, Accepted 6th June 2012

DOI: 10.1039/c2cp41424d

Several new molecular frameworks with interesting structures, based on clusters of main group

elements have been studied at different levels of theory with various basis sets. Conceptual density

functional theory based reactivity descriptors and nucleus independent chemical shift provide

important insights into their bonding, reactivity, stability and aromaticity.

1. Introduction

The first hint of the application of quantum chemistry1 in

molecular modeling dates back to the earlier half of the last

century when Heitler and London2 discussed the bonding

pattern of the simple H2 molecule. The development of quantum

chemistry from the self-consistent field method to more sophisti-

cated techniques like the complete active space-SCF (CASSCF)

and CASPT2 is well known3–17 and has been broadly applied.

High-level computations surely yield more accurate results, but,

at the same time are more expensive than the SCF methods.

Density functional theory (DFT) developed by Hohenberg

and Kohn18,19 is another unique approach to elucidate the

bonding and reactivity in molecules. The foundation of conceptual

density functional theory (CDFT)20–24 by Robert G. Parr20

proved to be a very powerful algorithm towards modeling

molecular structures and predicting their subsequent chemical

reactivity trends.

The idea of modeling new molecular motifs, over the past

few decades has become a wide arena of fundamental research

for both the experimentalists and theoreticians. While an

experimentalist exploits the best instrumental techniques and

plausible reactions to discover new molecules, a theoretician

applies sophisticated mathematical algorithms and computer

software to design and predict the stability of novel molecular

assemblies. The theoretical design of a new molecular frag-

ment along with an idea about its stability and reactivity does

serve as a useful pathfinder for the experimental chemists

to synthesize and hence utilize them to serve nature. Compu-

tational chemistry in this regard has progressed a lot and a

plethora of molecular motifs has been designed, which can

potentially serve as medicinal drugs,25,26 building blocks for

multi-decker bulk cluster assemblies27–31 useful for various

applications and hydrogen storage templates32–40 required for

the trapping of H2 gas and its further use as an alternative

energy and fuel source. Conceptual DFT as a useful mathe-

matical tool has been successfully implemented in this regard

to model various types of novel molecular clusters suitable for

practical usage. The various CDFT based global reactivity

descriptors like electronegativity41,42 (w), hardness43,44 (Z) andelectrophilicity45–48 (o) as well as local indices like atomic

charges49 (Qk), Fukui functions50 (f(r)) and their condensed-to-

atom variant51 (fk), which, in turn, are a set of mathematical

response functions, provide invaluable insights into predicting

the bonding, stability and reactivity patterns of the molecules.

Additional inputs explaining the intricate bonding patterns and

stability criteria of the molecular clusters can be gained, which

in turn may be utilized for the further refinement of associated

experimental data. A rigorous benchmarking of the choices of

the level of theory and the type of basis set for a particular row

of elements also provides more accurate results that are closely

on a par with experimental findings. The stability of these

cluster molecules can also be assessed by virtue of the existence

of an ‘‘aromaticity criterion’’ which, in turn, can be computed

and compared through the various aromaticity indices.52–58

In this article, we have made an attempt to design different

types of novel molecular assemblies under a conceptual DFT

paradigm. These include boron–carbon linked compounds,

representing a family of cage-like carboranes. Boron–carbon–

hydrogen based 1,7-C2B5H7, 1,6-C2B4H6 and 1,5-C2B3H5

closo-carborane units have been further chosen as the building

blocks towards modeling straight chain-like, planar sheet-like,

helical and twisted carborane structures. Half-cage templates

comprising a continuous C–N based saturated and/or unsatu-

rated network have also been designed for possible practical

applications. Some innovative ‘‘star-shaped’’ molecules con-

sisting of the different second and third row elements in the

basal plane with a Li-atom occupying the vertices of the

geometric star have been designed for their utility as possible

aDepartment of Chemistry and Center for Theoretical Studies,Indian Institute of Technology, Kharagpur – 721 302, India.E-mail: [email protected]

bCIMAT, Universidad de Chile & QTC,Pontificia Universidad Catolica de Chile, Santiago, Chile

w Electronic supplementary information (ESI) available. See DOI:10.1039/c2cp41424d

PCCP Dynamic Article Links

www.rsc.org/pccp PAPER

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http://dx.doi.org/10.1039/c2cp41424d

http://dx.doi.org/10.1039/c2cp41424d


This journal is c the Owner Societies 2012 Phys. Chem. Chem. Phys., 2012, 14, 14784–14802 14785

hydrogen storage materials. The Li-center has been supposed

to serve as the active site towards binding with a hydrogen

atom/molecule. The stability of these molecular ‘‘stars’’ in

terms of an aromaticity criterion has been assessed from the

nucleus independent chemical shift (NICS)52,53 values com-

puted at the ring-center (NICS(0)) on the basal plane or n A

(NICS(n)) vertically away from the ring. A series of clusters

with planar pentacoordinated boron centers have also been

proposed in silico. The stability and reactivity of some metal-ion

doped cationic complexes, comprising an alkali or an alkaline

earth metal ion bound to neutral molecules (like HF, NH3 and

H2O) have been reported. The ability of these cationic complexes

as possible hydrogen binding templates has also been proposed.

The bonding and stability of a range of isomeric [Be8]2� clusters

and a variety of double-decker sandwich complexes have further

been analyzed. A natural population analysis (NPA) of the

different atomic centers of the various molecular motifs modeled

in this study further invokes the proneness of the given sites

towards plausible chemical attack.

2. Theoretical background

The stability of a molecular system is often dictated by a subtle

interplay of molecular properties that, in accordance with

theoretical chemistry practice, are conventionally referred to

using global reactivity descriptors like hardness (Z)43,44 and

electrophilicity (o).45–48 Deeper insights into the stability of a

molecular species and subsequent reactivity upon chemical

response can be obtained from a careful scrutiny of the valida-

tion of various electronic structure principles like the Principle of

Maximum Hardness59–61 (PMH), Minimum Polarizability

Principle62,63 (MPP) and Minimum Electrophilicity Principle64,65

(MEP). For an N-electron system, the electronegativity41,42 (w)and hardness43,44 (Z) can be defined as follow:

w ¼ �m ¼ � @E

@N

� �vð~rÞ

ð1Þ

Z ¼ @2E

@N2

� �vð~rÞ: ð2Þ

Here E is the total energy of the N-electron system and m and

v(-r) are its chemical potential and external potential respec-

tively. The electrophilicity45–48 (o) is defined as:

o ¼ m2

2Z¼ w2

2Z: ð3Þ

A finite difference approximation to eqn (1) and (2) can be

expressed as:

w ¼ I þ A

2ð4Þ

and

Z = I – A (5)

where I and A represent the ionization potential and electron

affinity of the system respectively.

The local reactivity descriptor, Fukui function50 (FF) measures

the change in electron density at a given point when an

electron is added to or removed from a system at constant v(-r).

It may be written as:

f ð r*Þ ¼ @rð r*Þ@N

!vð r*Þ

¼ dm

dvðr*Þ

!N

ð6Þ

Condensation of this Fukui function, f(-r) to an individual

atomic site k in a molecule gives rise to the following expres-

sions in terms of electron population51 qk

f+k = qk(N+1) � qk(N) for nucleophilic attack (7a)

f �k = qk(N) � qk(N � 1) for electrophilic attack (7b)

f 0k = [qk(N+1) � qk(N � 1)]/2 for radical attack (7c)

3. Computational details

The molecular geometries of the different types of cluster motifs

have been optimized at various levels of theory which include

the standard DFT-based B3LYP procedure as well as other

methods, viz. MP2 and M052X. The computations have been

performed with several basis sets by using the GAUSSIAN 03

program package.66 Their existence at a minimum on the

potential energy surface (PES) has been confirmed by computing

the harmonic vibrational frequency at the same level and by

ensuring that no imaginary frequency is present. Single point

calculations have been further performed to evaluate the

energies of theN� 1 electron systems by adopting the geometries

of the corresponding N-electron systems optimized at the given

level of theory. The I and A values have been calculated using the

DSCF technique. The CDFT based global reactivity descriptors

have been computed by utilizing eqn (3)–(5).

The small closo-carboranes 1,5-C2B3H5 and 1,6-C2B4H6

units have been modeled according to the structures reported

by Astheimer et al.67 and Shapir et al.68 The structure of

1,7-C2B5H7 has been obtained by placing a boron atom at the

B4 square plane of square bi-pyramid 1,6-C2B4H6 resulting in

a pentagonal bi-pyramidal structure. Dimers of 1,5-C2B3H5,

1,6-C2B4H6 and 1,7-C2B5H7 have been obtained by joining

axial –CH groups with removal of a H2 molecule. Single-stranded

chain structures of 1,5-C2B3H5, 1,6-C2B4H6 and 1,7-C2B5H7 units

have been generated similarly by joining six dimers of each

through C–C linkages. These optimized (at the same level of

theory) single stranded structures have been joined through

the B atom of a –BH unit with the simultaneous replacement

of twelve hydrogen molecules, which thereby results in a

double stranded structure in each case. The optimization and

subsequent frequency calculation of all the above-mentioned

structures have been carried out at the M052X/6-31G(d) level.

For the sake of simplicity, all the structures throughout the text

C2B3, C2B4, and C2B5 have been written in place of 1,5-C2B3H5,

1,6-C2B4H6 and 1,7-C2B5H7 respectively.

The boron–carbon based carborane cages and the C–N

based saturated and/or unsaturated half-cage templates have

also been optimized at the M052X level of theory using

6-311+G(d,p) and 6-31G(d,p) as basis sets respectively.

The geometry optimizations followed by subsequent frequency

calculations for all the star-like motifs have been performed at

three different levels of theory, viz., B3LYP/6-311++G(d,p),

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MP2/6-311++G(d,p) and M052X/6-311++G(d,p). The NICS(0)

values at the ring plane of the star moieties and the subsequent

NICS(n) (n 4 0) values have been computed through the

Schleyer’s52,53 method at B3LYP/6-311++G(d,p) level. The

conceptual density functional theory (CDFT) based descrip-

tors for all star-like clusters have been computed at the

B3LYP/6-311++G(d,p) level. In case of planar pentacoordinated

boron clusters, the related studies have been made at the

B3LYP/6-311+G(d) level.

For the metal-ion doped cationic complexes (with neutral

molecules like HF, NH3 and H2O), single point calculations at

the MP2 and M052X levels have been performed at even higher

basis sets by adopting the molecular geometry optimized at the

respective levels of theory. The CCSD(T) single point energies

have however been computed by adopting the corresponding

geometries optimized at the B3LYP level of theory.

All the isomeric analogues of the [Be8]2� system have been

optimized at the B3LYP level of theory using 6-311+G(d) as

basis set whereas the stabilities of double-decker sandwich

complexes have been scrutinized at HF/6-311+G(d), B3LYP/

6-311+G(d) and M052X/6-311+G(d) levels of theory.

The atomic charges (Qk) on the possible active sites of the

different molecular clusters have been computed by applying

the natural population analysis (NPA) scheme. The frontier

molecular orbitals (FMOs) have been generated through the

Gaussview 03 program package.66

4. Results and discussion

A. Polymeric single stranded and double stranded

closo-carboranes

From the pyrolysis reaction of closo-carboranes C2B3, C2B4 and

their mixture, Astheimer et al.67 synthesized and characterised

the dimer as well as trimer of C2B3 and mixed dimer of C2B3

and C2B4. They have shown that their obtained dimers and

trimers are attached through B–B linkage or B–C linkage. Here

modeling, optimization, and frequency calculation of all the

above reported compounds have been done and the obtained

geometries, bond lengths and bond angles are quite identical

with the reported values. In addition, dimers of C2B3 and C2B4,

modeled through C–C linkage represent true minima on the

potential energy surface (PES) at the M052X/6-31G(d) level of

theory (Fig. 1 and 2). At the same level of theory the minimum

energy structures of C2B5 as well as a dimer of C2B5 (modeled

through a C–C linkage) have also been obtained (Fig. 3). The

molecular point groups (PGs) and important geometrical para-

meters like the bond lengths and the associated bond angles of

C2B3, C2B4 and C2B5 units have been presented in Table S1.wThe polymers of C2B3, C2B4, and C2B5, which have been

modeled by joining six dimers of each through a C–C linkage

also turn out to be at minima on the PES. Measured point

groups of C2B3 and C2B4 single stranded polymers remain

(D3h and D4h respectively) the same as their corresponding

monomer units but the point group of the C2B5 polymer

changes from D5h (PG of monomer) to C2h. Point groups

(PGs), bond lengths and the associated bond angles of

polymers of C2B3, C2B4 and C2B5 units have been presented

in Table S2.wTwo strands of C2B3 polymer have been taken parallel to each

other and fused through –BH units resulting in a ladder-like

Fig. 1 The optimized molecular geometries of a single C2B3H5 sub-

unit and its corresponding linear single stranded and helical double

stranded forms at the M052X/6-31G(d) level.


unit and its corresponding linear single stranded and double stranded

forms at the M052X/6-31G(d) level.


unit and its corresponding linear single stranded and helical double

stranded forms at the M052X/6-31G(d) level.

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double strand structure. Similar ladder-like structures of C2B4

and C2B5 have also been modeled. In case of polymeric double

stranded C2B3 and C2B5 structures, two B-DNA (a long, thin

form of deoxyribonucleic acid in which the helix is right-

handed) like helical geometries with D2 point groups have

been obtained at minima on the PES whereas in case of

polymeric double stranded C2B4, a perfect ladder-like struc-

ture has been identified. Table S3w elaborates the geometrical

parameters for the single and double stranded (ladder-like and

helical) analogues of the monomeric C2B3, C2B4 and C2B5

units. Fig. 1 depicts the molecular geometry of a single C2B3

sub-unit, its dimer and corresponding single stranded and

helical double stranded forms. An analogous portrayal of

the molecular structure of the monomeric C2B4 and C2B5

units and its associated single and double stranded conforma-

tions have also been provided in Fig. 2 and 3 respectively.

Geometrical constraints of the double stranded ladder-like

and helical structures have been measured by considering the

middle units. The total energy (E, au), electronegativity

(w, eV), hardness (Z, eV) and electrophilicity (o, eV) of the

monomeric C2B3, C2B4 and C2B5 systems and their associated,

polymeric single stranded and double stranded (linear and

helical) structures have been given in Table S4.wFig. 4 illustrates a ball and stick depiction of a DNA model

containing 10 A–T base pairs adopted from elsewhere69 as well

as the helical double stranded C2B3 and C2B5 systems. While

the C2B3 system consists of eight pairs of C2B3 sub-units in a

single loop, the C2B5 system comprises seven pairs of C2B5

sub-units in the same. Both the helical forms of the polymeric,

three and five-membered C2B3 and C2B5 systems, respectively,

resemble with DNA double helix structure in many respects.

A detailed scrutiny of the Tables S1–S3w and Fig. 1–3 reveal

some interesting facts on the structural patterns of the B–C–H

based stranded molecules. The bond lengths and the allied

bond angles of the monomeric C2B3, C2B4 and C2B5 units

show slight alterations upon conversion to the polymeric

single and double stranded structures. However the molecular

point groups of the given moieties do change upon trans-

formation from the single to double stranded forms. Fig. 1–3

clearly show that the double stranded structures containing

the C2B3, and C2B5 units attain a helical alignment while the

double stranded C2B4 unit is parallel. The double stranded

moiety containing the C2B4 unit attains a non-helical, parallel

configuration due to a symmetric, orthogonal alignment of the

hydrogen atoms around the B4 rings of the two adjoining

strands. Such an arrangement renders two H-atoms from the

two strands to be spaced in a ‘‘face-to-face’’ manner which

hinders the possibility of any twisting amongst the two

strands. Thus the C2B4 units assume a ‘‘ladder-like’’ geometry.

In spite of a symmetrical alignment, the hydrogen atoms

around the Bn (n = 3, 5) rings of the double stranded C2B3,

and C2B5 systems are not held eclipsed with the repeated units

and thus, unlike the C2B4 polymer, do avoid a ‘‘head-to-head’’

disposition in between two adjoining strands, which might

have attributed to the helical nature of the same. In practice,

however, it has also been observed that for the double

stranded DNA helix, both the base-pairs connecting the

adjoining strands contain a five-membered (odd) ring moiety.

Such an outcome seems to be quite relevant to this present study

as the helical nature of the newly designed C2B3, and C2B5 closo-

carborane based polymeric structures closely mimic a double-

stranded DNA molecule. Deeper insights into the structure of

a DNA molecule from Fig. 4 shows a 61 tilt in the double helix

(B-DNA).70 A similar depiction of the double stranded C2B3

and C2B5 systems in Fig. 4, however, shows an upright helix

with no tilting. A tilted helix in the double stranded DNA

molecule may be due to the fact that the chemical environment

around the adjacently connected five-membered rings is not

similar. The rings are heterocyclic in nature and contain

different types of atoms. On the other hand, for the double

stranded C2B3 and C2B5 helices, the adjoining all-boron three

and five-membered rings offer a homogeneous chemical

environment around the helical structure. This seems to minimize

the possibility of any tilting. All the other parameters corre-

sponding to the DNA helix and the same computed for the

two helical forms of the C2B5H7 system are quite comparable,

excluding the helix radius, as given in Table 1.

The stability of a double-helical, polymeric C2B5 system

along with its close correspondence to the DNA molecule

offers new ideas and even better possibilities for the experi-

mentalists to design such purely inorganic helical structures

for further practical applications.

Fig. 4 Ball and stick depiction of a DNA model containing 10 A–T

base pairs adopted from J. Phys. Chem. B, 2006, 110, 15742–15748 as

well as the helical double stranded C2B3H5 and C2B5H7 systems

optimized at M052X/6-31G(d) level.

Table 1 Calculated structural features of double stranded helicalpolymers of C2B5 and C2B3 closo-carboranes and their comparisonwith B-DNA (ref. 69)

Structural properties C2B5 C2B3 B-DNA

No. of stacked pairs in a loop 8 7 10Stacking height 3.446 A 3.643 A 3.380 ATwist angle 25.6531 25.0631 361Helix radius 3.46 A 2.625 A 10 ATilt/roll angle 01 01 61

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B. Hydrogen-bridged carboranes

Two innovative cage-like hydrogen-bridged carborane struc-

tures (Fig. 5) have been proposed here which may serve as

plausible reaction templates particularly for the binding and

storage of hydrogen. A closer look at the nature of chemical

bonding in the B–C–H based carborane cages in Fig. 5 clearly

shows the existence of an electron-deficient three-centered–

two-electron (3c–2e) ‘banana’ bonding among the B–H–B

centers. While the (C12B6H6)2H6 molecule contains single

3c–2e type linkages in between the B–H–B centers, the given

cage upon further hydrogenation yields (C12B6H6)2H12, which

shows the existence of two such electron-deficient bonds

amongst B–H–B centers, thereby, mimicking the bonding

pattern of the stable diborane molecule. Table S5w presents

the molecular point groups and the important geometrical

parameters (bond lengths and bond angles) of the hydrogen-

bonded carborane cages. The bridged B–H bond lengths in

(C12B6H6)2H6 carborane (1.34 A) and (C12B6H6)2H12 carborane

(1.35 A) are very much comparable with those of other

molecules containing 3c–2e bonds e.g., diborane (B–H bond

length = 1.31 A).71 The higher stability of (C12B6H6)2H12 than

its former analogue is also reflected through the increasing

hardness and decreasing electrophilicity values from Table S6.wBoth the hydrogen-loaded carborane cages are shown to be

considerably stable and therefore deserve to be synthesized

experimentally.

C. C–N based half-cages

In this part, an attempt has been made to design some novel

C–N based half cages. In this regard, three new half-cage

frameworks namely C12N6, C12N6H12 and C12N6H18 have

been proposed (Fig. 6). Table S7w outlines the molecular point

groups and the important geometrical parameters (bond

lengths and bond angles) of the bare C–N based unsaturated

framework as well as its associated hydrogen-bonded clusters.

The total energy (E, au) and the various conceptual DFT

based global reactivity descriptors for the C–N based clusters

have been given in Table S8.w A careful scrutiny of Fig. 6

shows that gradual hydrogen loading on to the unsaturated,

hemispherical C12N6 molecule induces saturation. The resulting

C12N6H12 cluster contains only one unsaturated benzenoid

ring which upon further hydrogenation becomes unsaturated

and non-planar to yield C12N6H18. Associated hardness and

electrophilicity values of the C12N6 cluster and its hydrogen-

bound complexes in Table S8w presupposes an increase in

molecular stability with gradually increasing Z values followed

by a hand-in-hand decrease in the respective magnitudes of o.Thus, all the studied hydrogenated C–N based hemispherical

clusters obey the principles of maximum hardness59–61 and

minimum electrophilicity64,65 which often serve as useful

pathfinders towards molecular stability, reaction spontaneity

and the theoretical modeling of molecular motifs. Hydrogena-

tion of the C–N based half-cage structures, therefore, seems to

be favorable and endows an increasing molecular stability. So

these cluster frameworks can act as useful reaction vessels for

hydrogen binding and storage, important for further industrial

applications.

D. Star-shaped molecules

The design of molecular clusters resembling popular geome-

trical configurations has always catapulted both the physicists

and chemists to introduce new ideas and methods. In this

regard, an arrangement of atoms in a molecule producing a

‘‘star-like’’ geometry is quite innovative and attractive at the

same time. Modeling of three-dimensional (3D) ‘‘molecular

stars’’ has been detailed in a few relevant articles.72,73 The

designing of 2D-molecular stars and their plausible usage as

effective hydrogen trapping materials have also been recently

reported.74 In this study we have chosen a variety of well-

known five-membered and six-membered aromatic organic

molecules and substitute the H-centers with an Li-atom to

create a ‘‘star-like’’ moiety. Computations at three different

levels namely B3LYP/6-311++G(d,p), MP2/6-311++G(d,p)

andM052X/6-311++G(d,p) have been performed to assess their

stability. The electronic states, molecular point groups (PGs),

total energy (E, au) of the optimized geometrical structures

Fig. 5 The optimized molecular geometries of the carboranes at the

M052X/6-311+G(d,p) level.

Fig. 6 The optimized molecular geometries of C–N based half-cage molecular networks at the M052X/6-31G(d,p) level.

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containing the five-membered and six-membered rings

(computed at different levels of theory) and their allied con-

ceptual DFT based global reactivity descriptors have been

presented in Tables S9 and S10 respectively.w The NICS values

of the five and six-membered planar rings constituting a

molecular star have been computed at the basal plane

(NICS(0)) and up to 3 A vertically away from the ring-center

at regular intervals of 0.5 A, the corresponding values being

outlined in Tables S11 and S12 respectively.w Fig. 7(a–h) and

Fig. 8(a–c) depict the optimized geometries and the important

occupied molecular orbitals of the given ‘‘molecular stars’’

containing the five and six-membered rings respectively.

A comparative variation of the NICS(n) (n = 0, 1, 2) values

for the five-membered and six-membered ‘‘molecular stars’’ can

be envisaged from Fig. 9 and Fig. 10 respectively. We segregate

this discussion into a few sub-sections depending on the nature

of the ring involved in creating the ‘‘star-like’’ moiety.

Stars containing five-membered rings

Pentalithio furan star. Furan (C4H4O) is a very well-known

aromatic heterocyclic organic compound and has been first

prepared by Heinrich Limpricht75 in 1870, initially named as

tetraphenol. Here an attempt has been made to explore the

viability of beautiful star-like models based on furan as the

mother motif. For that purpose, five Li atoms have been

introduced by replacing four H atoms and it has been found

that the Li centers prefer bridging positions as a result of ionic

character in bonding.72,73,76,77 Now starting with a C4OLi5molecular formula, the obvious choice of a structural arrange-

ment corresponds to a C2V point group and 2A1 electronic

state (Fig. 7(a)) which has been found to have NIMAG = 0

structure (at the minimum on the potential energy surface) at

both B3LYP and M052X levels whereas at MP2 level it turns

out to be a saddle point having nmin = 115.6i. An effort to

bring it to the minimum on the PES at MP2 level, a structure

having a C1 point group with a 2A electronic state is obtained

which is 33.4 kcal mol�1 more stable than the corresponding

C2V analogue (Table S9w) although the structure with a C1

point group differs marginally from that of C2V. To assess

whether the structure with a C1 point group is energetically

more stable than that of the C2V structure at the B3LYP and

M052X levels, a free optimization taking the C1 symmetrized

structure at the above mentioned two levels has been per-

formed which, however, brings it back almost to the same

structure as that of the C2V point group (almost the same

energy values and same values of global reactivity descriptors).

The aromaticity of the pentalithio furan star (C4OLi5) has

been assessed in terms of the nucleus independent chemical shift

(NICS) criterion which has turned out to be quite negative,

affirming the existence of a favorable aromaticity phenomenon –

a useful benchmark towards assessing molecular stability. The

values further reveal a steady decreasing trend up to 1 A

(NICS(1)) from the ring-center, which goes on increasing

further with distance (Table S11w). This observation becomes

pictorially quite relevant from Fig. 9 where the NICS(1) value

corresponding to C4OLi5 is lower than the corresponding

NICS(0) value. These facts trigger the existence of a favorable

aromatic p-ring current of the pentalithio furan star which

remains quite dominant up to a certain distance from the base

and eventually ceases with increasing vertical height. A molecular

orbital analysis tells the origin of aromaticity in pentalithio furan

star and it is due to the presence of three delocalized p-MOs

namely HOMO-1, HOMO-5 and HOMO-7 (Fig. 7(a)).

Pentalithio pyrrole star. Pyrrole is another aromatic five-

membered heterocyclic organic compound, with the molecular

formula C4H4NH and can be prepared industrially by the

exposure of NH3 upon furan in presence of solid acid catalysts.78

Here a replacement of five H atoms by five Li atoms (at bridging

positions) gives a beautiful star-like structure with a C2v point

group and a 1A1 electronic state with a molecular formula

of C4NLi5 (Fig. 7(b)). The C2v symmetrized structure of

the pentalithio pyrrole star (C4NLi5) turns out to be with

NIMAG= 0, thereby confirming its existence at the minimum

on the potential energy surface (PES) at all the studied levels

(Table S9w). The high hardness value (4.607 eV) of C4NLi5and the existence at a minimum on the PES at all the studied

levels imply the stability of this configuration (Table S9w). Thepentalithio pyrrole star, being analogous to the earlier furan

system, also sustains an aromaticity criterion with a high

negative NICS value at the ring center as well as different

distances perpendicular to the ring plane, as evident from

Table S11w and Fig. 9. The presence of aromaticity in a

pentalithio pyrrole star can be properly justified by molecular

orbital analysis in which it has been found that three delocalized

p-MOs, namely HOMO, HOMO-2 and HOMO-6 (Fig. 7(b)),

are present satisfying Huckel’s (4n + 2; n = 1) p electron rule.

Here an assessment of the stability of the C4NLi5 cluster in

terms of atomization energy has also been performed. In this

present case atomization energy (AE) has been defined as

AE = [EC4NLi5� (4EC + EN + 5ELi)]. The atomization energy

for the C4NLi5 cluster has been found to be �1068.3 kcal mol�1,

implying the high stability of the studied cluster in the given

configuration.

Pentalithio oxazole star. Oxazole is a member of azole

family having an oxygen and a nitrogen atom separated by

one carbon atom. This aromatic heterocyclic oxazole

(C3H3NO) molecule is taken as mother template to design

star-like motif. In order to design star-like clusters, five Li

atoms replacing three H atoms have been incorporated into

the system offering Cs symmetry and 1A0 electronic state. In

both B3LYP and M052X levels, the Cs symmetrized geometry

turns out to be minimum on the PES (NIMAG = 0) but at

MP2 level it turns out to be a second order saddle point

(NIMAG = 2) as given in Table S9.w At B3LYP level, the Cs

symmetrized geometry has all the Li centers in a bridging

position, whereas at M052X level the optimized structure (Cs)

differs from that of the B3LYP level with one Li center in an

open position (terminal position), as displayed in Fig. 7(c).

Now the presence of two imaginary frequencies at MP2 level

hints at the probable existence of a lower energy structure. A

structure having C1 point group and 1A has been obtained at

minimum on the PES at MP2 level which is 48.9 kcal mol�1

lower in energy than the corresponding Cs analogue. In the C1

structure, the Li centers bend slightly from the C3NO ring.

Again, to evaluate the stability of this C1 geometry at the

B3LYP and M052X levels, a free optimization taking this

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Fig. 7 (a) The optimized geometries of pentalithio furan star (C4OLi5) and their occupied delocalized pi molecular orbitals at the B3LYP/

6-311++G(d,p) level (other levels are mentioned below the structures). (b) The optimized geometries of pentalithio pyrrole Star (C4NLi5) and their

occupied delocalized pi molecular orbitals at the B3LYP/6-311++G(d,p) level. (c) The optimized geometries of pentalithio oxazole Star (C3NOLi5)

and their occupied delocalized pi molecular orbitals at the B3LYP/6-311++G(d,p) level (other levels are mentioned below the structures). (d) The

optimized geometries of pentalithio pyrazole Star and pentalithio imidazole star (C4NLi5) and their occupied delocalized pi molecular orbitals at

the B3LYP/6-311++G(d,p) level (other levels are mentioned below the structures). (e) The optimized geometries of pentalithio-1,2,3-triazole star

and pentalithio-1,2,4-triazole star (C2N3Li5) and their occupied delocalized pi molecular orbitals at the B3LYP/6-311++G(d,p) level (other levels

are mentioned below the structures). (f) The optimized geometries of pentalithio phosphole star (C4PLi5), phosphole and their occupied delocalized

pi molecular orbitals at the B3LYP/6-311++G(d,p) level (other levels are mentioned below the structures). (g) The optimized geometries of

Pentalithio-1,3-aza phosphole, Pentalithio-1,4-aza phosphole (C3PNLi5 and their occupied delocalized pi molecular orbitals at the B3LYP/

6-311++G(d,p) level. (h) The optimized geometries of Pentalithio thiophene (C4SLi5) and their occupied delocalized pi molecular orbitals at the

B3LYP/6-311++G(d,p) level.

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C1 geometry at both levels has been carried out and found to

be slightly at a higher energy than that of Cs (Table S9w). Thearomaticity of the pentalithio oxazole star has been confirmed

by both negative NICS values as evident from Table S11wand Fig. 9, as well as from the presence of three delocalized

p-MOs, viz. HOMO-1, HOMO-5 and HOMO-7 (Fig. 7(c)).

Fig. 8 (a) The optimized geometries of hexalithio borazine (B3N3Li6), hexalithio boroxine star (B3O3Li6) and their occupied delocalized pi

molecular orbitals at the B3LYP/6-311++G(d,p) level. (b) The optimized geometry of B3C3Li6 and its occupied delocalized pi molecular orbitals at

the B3LYP/6-311++G(d,p) level. (c) The optimized geometries of hexalithio pyridazine, pyrimidine and pyrazine stars and their occupied

delocalized pi molecular orbitals at the B3LYP/6-311++G(d,p) level.

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Pentalithio pyrazole and imidazole stars. Pyrazole and

imidazole (common molecular formula of C3H4N2) are two

other candidates in the azole family, having two nitrogen atoms

adjacent to each other in pyrazole, whereas in imidazole two

nitrogen atoms are separated by a carbon atom. A substitution

of four H atoms by five Li atoms provides a star-like shape to

the given system (Fig. 7(d)). Pentalithio pyrazole star (C3N2Li5)

with a C2v point group and 2A1 electronic state turns out to be

at minimum on the PES at each studied level (Table S9w),thereby, confirming the viability of this configuration. But

in the case of the pentalithio imidazole star (C3N2Li5), the C2v

symmetrized geometry is a minimum on the PES at the B3LYP

and M052X levels but is a first order saddle point at MP2 level

(Table 9). The pentalithio imidazole star having Cs point

group is a minimum on the PES at MP2 level (27.1 kcal more

stable than C2v) but a re-optimization taking Cs geometry at

B3LYP and M052X levels drives back to the C2V configu-

ration (same energy for C2v and Cs at both B3LYP and

M052X levels and same value of global reactivity descriptors)

(Table S9w). The NICS data in Table S11w and Fig. 9 imply the

presence of a favorable aromaticity phenomenon in penta-

lithio pyrazole and imidazole stars. In pentalithio pyrazole

star, the p-aromaticity arises due to the presence of HOMO-2,

HOMO-3 and HOMO-7 delocalized p-MOs whereas in

pentalithio imidazole star, HOMO-1, HOMO-5 and HOMO-7

are responsible for the p-aromaticity as displayed in Fig. 7(d).

Pentalithio triazole stars. Triazole implies either one of a

pair of isomeric chemical compounds namely 1,2,3-triazole and

1,2,4-triazole having general formula C2H3N3. 1,2,3-Triazole,

a basic aromatic heterocycle has a five membered ring having

two carbon atoms and three nitrogen atoms. At first, by

placing five Li atoms in the bridging positions by replacing

three H atoms, a star-like structure (pentalithio-1,2,3-triazole

star) having a C2V point group and a 1A1 electronic state

(Fig. 7(e)) has been generated which has been found to be at a

minimum on the PES at the B3LYP and MP2 levels but at

M052X level, it has a small imaginary frequency (nmin = 33i)

(Table S9w). This imaginary frequency corresponds to an out-

of-plane bending mode of all Li centers. Therefore, an effort

has been made to search for lower energy structures by moving

all the Li centers slightly out of plane at M052X level and has

been obtained as a minimum energy structure having a C1

point group which is 0.483 kcal mol�1 more stable than the

C2V geometry at the studied level (Table S9w). Then, a free

optimization taking the C1 structure as an initial input has

been carried out at both the B3LYP and MP2 levels. At the

B3LYP level, all the Li centers come to the plane of the ring

and give a structure which is very close to that of C2V geometry,

but at the MP2 level a new lower energy (58.7 kcal mol�1

lower than C2V geometry) non-planar structure has been

attained at a minimum on the PES, as displayed in Fig. 7(e).

Now, to design star-like structures based on the 1,2,4-triazole

mother motif, another basic aromatic heterocycle, the placing

of five Li atoms at the bridging position by replacing three

H atoms has been done to generate a structure with a Cs

symmetry (pentalithio-1,2,4-triazole star) (Fig. 7(e)) which has

been found to be a minimum energy structure at both the

B3LYP and MP2 levels but has an imaginary frequency

(nmin = 74.6i) at the M052X level (Table S9w). Following

the mode of imaginary frequency, a new non-planar minimum

energy structure (Fig. 9(e)) has been obtained at the M052X

level which is 6.9 kcal mol�1 more stable than the corre-

sponding Cs geometry (Table S9w). Now unlike pentalithio-

1,2,3-triazole, this C1 geometry turns out to be at a minimum

on the PES at both the B3LYP and MP2 levels which are

1.2 kcal mol�1 and 3.6 kcal mol�1 higher and a lower-energy

structure than the corresponding Cs geometry, respectively

(Table S9w). Therefore different levels of theory show different

pictures regarding the stability of a given configuration.

Fig. 9 The plot of NICS (0), NICS (1) and NICS (2), in ppm units, of

various five membered star-like clusters at the B3LYP/6-311++G(d,p)

level of theory. [where 1 = C4OLi5 (C2V), 2 = C4OLi5 (C1), 3 =

C4NLi5 (C2V), 4 = C3NOLi5 (Cs), 5 = C3NOLi5 (C1), 6 = C3N2Li5(1,2) (C2V), 7 = C3N2Li5 (1,3) (C2V), 8 = C2N3Li5 (1,2,3) (C2V), 9 =

C2N3Li5 (1,2,3) (C1), 10 = C2N3Li5 (1,2,4) (Cs), 11 = C2N3Li5 (1,2,4)

(C1), 12 = C4PLi5(C2V), 13 = C3PNLi5 (1,2) (Cs), 14 = C3PNLi5 (1,3)

(Cs), 15 = C4SLi5 (C2V), 16 = C4SLi5 (C1)].

Fig. 10 The plot of NICS (0), NICS (1) and NICS (2), in ppm

units, of various six membered star-like clusters at the B3LYP/

6-311++G(d,p) level of theory. [1 = B3C3Li6 (Cs), 2 = B3N3Li6(D3h), 3 = B3O3Li6 (C1), 4 = C4N2Li6 (1,2) (C2V), 5 = C4N2Li6(1,3) (C2V), 6 = C4N2Li6 (1,4) (C2V)].

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The aromatic nature of both the pentalithio-1,2,3-triazole star

and pentalithio-1,2,4-triazole star has been justified by highly

negative NICS values (Table S11w and Fig. 9). The delocalized

HOMO-1, HOMO-4 and HOMO-7 p-MOs in pentalithio-

1,2,3-triazole and delocalized HOMO-2, HOMO-4 and

HOMO-7 p-MOs in pentalithio-1,2,4-triazole are responsible

for their p-aromaticity (Fig. 7(e)).

Pentalithio phosphole star. Phosphole is an organic com-

pound with the chemical formula C4H4PH, formed by a fully

unsaturated five-membered ring containing a phosphorus

atom. The most debated issue regarding the phosphole has

been for a long time its aromaticity.79–81 Now it is well

established that phosphole is basically non-aromatic, since

the stabilization of the planar configuration due to electronic

delocalization is not sufficient to compensate the barrier of

inversion around phosphorus. Hence, it prefers a pyramidal

configuration, reducing the overlap between the phosphorus

lone pair and the cis-1,3-butadiene p-orbitals significantly.

It has been proved that a planar configuration of phosphole

has a greatly enhanced aromaticity with respect to its non-

planar analogue.82,83 Here to design a star-like structure based

on phosphole, two significant outcomes have been attained.

Firstly, a replacement of H atoms by Li atoms (bridging

position) tends to give a nice planar star-like structure (penta-

lithio phosphole star) (Fig. 7(f)). Then the stability of a planar

C2V symmetrized pentalithio phosphole star has been studied,

which is found to be a minimum energy structure at both the

B3LYP and M052X levels, but at the MP2 level a small

imaginary frequency (31.9i) appears (Table S9w). This imaginary

frequency corresponds to an out of plane bending mode of two

Li centers connected to the P atom. Following this mode, a

slightly lower energy structure (0.006 kcal mol�1 more stable

than the C2V analogue) having a Cs point group has been

attained in which two Li centers connected to the P atom are

bent slightly away from the ring plane. But a re-optimization at

both the B3LYP and M052X levels taking this Cs symmetrized

structure gives back the planar C2V structure. Therefore,

phosphole which has a non-planar minimum energy structure,

(Fig. 7(f)) can be planarized by substituting H atoms with Li

atoms. Secondly, another beauty of this planar pentalithio

phosphole star is its high aromaticity as indicated by quite

high negative NICS values given in Table S11w and Fig. 9. So a

nonaromatic phosphole molecule is converted to a highly

aromatic one by substituting H with Li. A molecular orbital

analysis reveals that p-aromaticity arises due to the presence of

three p-MOs namely HOMO, HOMO-3 and HOMO-6. The

HOMO corresponds to the strong overlap between the phos-

phorus lone pair and the cis-1,3-butadiene p-orbitals, whichwas absent in the case of phosphole (Fig. 7(f)).

Pentalithio-1,2- azaphosphole and pentalithio-1,3-azaphosphole.

Now an investigation has been made regarding the potential of

aza phosphole template to be used in designing star-like motifs.

Both 1,2-azaphosphole and 1,3-azaphosphole have been tested in

this regard, but an aromatic Cs-imposed configuration of penta-

lithio-1,2-azaphosphole and pentalithio-1,3-azaphosphole having

the same molecular formula (C3NPLi5) (Fig. 7(g)) turn out as

minimum energy structures only at the B3LYP level, whereas at

the MP2 and M052X levels these structures correspond to a

saddle point with the mode of imaginary frequency towards

out of plane bending of the Li centers, suggesting the presence

of a lower energy structure in a non-planar configuration at

the studied levels (Table S9w). In a planar configuration of both

pentalithio-1,2-azaphosphole and pentalithio-1,3-azaphosphole,

the aromaticity, as indicated by Table S11w and Fig. 9, arises due

to the presence of three delocalized p-MOs namely HOMO-1,

HOMO-4 and HOMO-7(Fig. 7(g)).

Pentalithio thiophene star. Thiophene, commonly known as

thiofuran, is an aromatic heterocyclic compound with molecular

formula of C4H4S, which is now chosen to give a star-like shape.

For this purpose, five Li atoms have been incorporated by

replacing four H atoms resulting in pentalithio thiophene

(C4SLi5). At first, the stability of a planar C2v imposed star-like

geometry (Fig. 7(h)) has been scrutinized and found to be a

saddle point (first order at B3LYP level and higher order atMP2

and M052X levels) at the studied levels of theory (Table S9w).Carefully following the mode with imaginary frequency, a non-

planar geometry of C4SLi5 with a C1 point group has been

obtained at the minimum on the PES at each studied level of

theory, in which one Li atom resides vertically above the five-

membered C4S plane (Fig. 7(h)). The resulting conformation

cannot, therefore, be considered as a star. The non-planar C1

analogue of C4SLi5 is energetically more stable, as well as harder

than its C2v configuration, suggesting its greater stability over

the C2V structure. From the NICS values (Table S11w and

Fig. 9), it has been found that C4SLi5 in its non-planar C1

configuration has almost the same degree of aromaticity as that of

its planar C2V geometry, although a molecular orbital analysis

shows less delocalization of the p-electron cloud in itsC1 structure

compared to that of C2V analogue, as displayed in Fig. 7(h).

Stars containing six-membered rings

Hexalithio borazine and boroxine stars. Borazine (B3N3H6) is

supposed to be the brainchild of inorganic chemists who have

been searching for an inorganic substitute of the typical prototype

of the planar aromatic organic benzene molecule. The molecule

bears some resemblance to benzene and therefore is called

‘‘inorganic benzene’’. But, unlike benzene, the six-membered

B3N3 ring in borazine does not allow a complete p-electron drift

across the heteronuclear plane. Several views on the aromaticity

of borazine have already been reported. Islas et al.84 have

attempted to separate the s and p contributions to the resultant

ring current in borazine. Calculations reveal that the s-electronsare much more localized than the p-electrons, thereby rendering

the borazine molecule as a p-aromatic species but not globally

aromatic like benzene, where electron delocalization is even more

profuse. Some earlier studies85–89 also establish the ‘‘lower’’

aromaticity of borazine with regard to benzene. Assessments of

the aromatic measure based on various aromaticity indices have

also proposed that borazine and boroxine molecules are

‘‘non-aromatic’’ in nature.90,91 A recent study92 further shows

that the aromaticity of the heteronuclear ring of boroxine may

be increased upon substitution with electron-withdrawing

groups. Electron donating groups subsequently reduce the

aromaticity of boroxine. Here the viability of six-membered

star-like clusters based on borazine and boroxine mother motifs

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has been investigated. In case of borazine, substituting six H

atoms with six Li atoms, a beautiful planar star-like structure

(hexalithio borazine star) having a D3h point group and a 1A10

electronic state (Fig. 8(a)) has been obtained at a minimum on

the PES at each studied level of theory, thereby indicating the

stability of this configuration (Table S10w). In case of boroxine,

a star-like geometry of the hexalithio boroxine star, which is

slightly distorted from the D3h configuration, (Fig. 8(a)) has

turned out as the minimum energy structure at both the B3LYP

and MP2 levels, but it does not meet the convergence criterion

at the M052X level. The NICS values provided in Table S12wand Fig. 10 reveal that the hexalithio borazine and boroxine

star are almost nonaromatic, like borazine and boroxine,

although they possess six p electrons as given in Fig. 8(a).

B3C3Li6. An analogous carbon counterpart of borazine,

B3C3Li6 has also been modelled, where the six-membered B3C3

ring is deformed, unlike the benzene-like geometry (Fig. 8(b)). The

structure having a Cs point group and a 2A0 electronic state is of

minimum energy at both the B3LYP and M052X levels of theory,

but at the MP2 level, the calculation does not converge. Another

interesting aspect regarding B3C3Li6 is its high aromaticity, unlike

B3N3Li6 and B3O3Li6, as given in Table S12w and Fig. 10 origi-

nating mainly from the presence of three delocalized p-molecular

orbitals, viz., HOMO-2, HOMO-3 and HOMO-6 (Fig. 8(b)).

Hexalithio pyridazine, pyrimidine and pyrazine stars. Pyridazine,

pyrimidine and pyrazine are three isomeric heterocyclic aromatic

organic compounds with the same molecular formula, C4H4N2

and only differing in the positions of two N atoms in the

hexagonal ring. Now in order to design star-like motifs based

on these three mother heterocycles, incorporation of six Li atoms

by replacing four H atoms has been done. The geometry optimi-

zation followed by subsequent frequency calculation give three

perfect star-like isomeric structures of general molecular formula,

C4N2Li6 having a C2V point group at the minima on the PES at

each studied level of theory (Fig. 8(c) and Table S10w). Sincepyrazine has a D2h structure in its ground state, an investigation

has also been made to assess the fate of D2h symmetrized

hexalithio pyrazine on the PES, but it turns out to be a higher

order saddle point (Table S10w). The NICS values (Table S12wand Fig. 10) indicate that these isomeric C4N2Li6 stars are

aromatic, like their mother motifs. The aromaticity arises due

to the presence of three delocalized p-MOs (six p e�s) satisfying

the (4n + 2)p electrons rule, as displayed in Fig. 8(c).

Although here a proposal has been made regarding the stability

of a series of star-like clusters based on well-known molecules,

they may be only local minima on the PES, like the beautiful star-

like perlithio annulenes CnLin (n = 3–6) proposed by Schleyer93

(except C3Li3+) and Minkin.94 Since only the global minimum

energy structure is experimentally obtainable, therefore it is

necessary to survey in detail the potential energy surface of these

clusters taking into account all probable configurations. Here it is

worth mentioning that many Li decorated clusters are stable

and they have been successfully synthesized and characterized

experimentally.95–97 Hence, the proposed Li-decorated star-like

clusters may also be achievable experimentally.

Schemes. Here an effort has been made to provide probable

schemes (Fig. 11) to synthesize these star-like systems taking

pentalithio pyrrole and hexalithio borazine star as model

systems. Tiznado et al.73 prescribed a scheme to derive Si5Li7+

from Si5H5� in which they considered the first step as the loss

of five protons generating Si56� and then seven Li+ ions

interacting with Si56� forming an Si5Li7

+ cluster. Following

the same path, we have considered the first step as the loss of

five and six protons from pyrrole (C4NH5) and borazine

(B3N3H6) generating C4N5� and B3N3

6� respectively. Both

C4N5� and B3N3

6� have been obtained at a minima on the

PES with C2V and D3h point groups, respectively, at B3LYP/

6-311++G(d,p) level (Fig. 11). We guess that a very strong base

would be able to eliminate protons from the mother moiety. So

the challenge to the experimentalists is to derive C4N5� and

B3N36� species by adopting a suitable experimental method.

Then addition of Li+ as counter-ions will produce the desired

star-like molecule. The very high interaction energies provide

Fig. 11 The schemes for the plausible syntheses of C4NLi5 and B3N3Li6 from pyrrole (C4NH5) and borazine (B3N3H6) studied at B3LYP/

6-311++G(d,p) level.

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sufficient justification regarding the feasibility of the subsequent

steps (Fig. 11).

E. Clusters having planar pentacoordinated boron

The molecules having unusual bonding pattern, such as hyper-

coordination, have received considerable attention from scientists

and so far, many such systems are well-known and saturate the

scientific literature.98–101 However, most of the systems are just

local mimima. The first global minimum structure with planar

pentacoordinated carbon (ppC) reported in the literature is

CAl5+ (D5h) with its 18 valence electrons.102 In 1991, Schleyer

and Boldyrev103 first demonstrated the importance of 18 valence

electrons (magic number) in order to provide stability of such

of planar hypercoordinated systems. Based on CAl5+ (D5h)

structure,102 a series of global minima structures of ppCs104–106

have been reported by replacing Al with Be, maintaining

18 valence electrons which, indeed, further justifies the role

of 18 valence electrons towards assessing the stability of such

type of systems. Very recently, Castro et al.107 have shown that

the systems having the formula CBe5E� (E =Al, Ga) are global

minima in which the C atom is in a ppC environment and one Be

atom is in a capping position of the Be–Be bond in-plane. They

satisfy the 18 valence electrons count by considering CBe5E� to

be like CBe4E3� interacting with Be2+. Now, since BAl5 (D5h)

(iso-electronic with CAl5+)108 is already a known system with

planar pentacoordinated boron (ppB), one should be able to

design a series of systems with ppB by replacing Al with Be in

the same spirit of maintaining 18 valence electrons as is the case

for ppCs. A series of systems with ppBs have been successfully

modeled by replacing the Al of BAl5 (D5h) with Be and adjusting

the charge in such a way that 18 valence electrons remain

engaged in bonding around the ppB moiety. In this regard, a

scheme has been provided depicting all the lower energy

structures in Fig. 12. All the computations have been made at

the B3LYP/6-311+G(d) level. It should be mentioned that here

we have tried to explore the probable existence of structures

having ppBs similar to that of ppCs, considering only some

probable planar isomers of a given system for discussion.

BAl5 system. The optimized geometry of BAl5 having a D5h

point group and a 1A10 electronic state has been given in

Fig. S1.w The NPA charge analysis (Fig. S15w) reveals that anet negative charge of �2.71|e| resides on the central B atom,

whereas the same for Al atoms is +0.54|e| indicating signifi-

cant charge transfer from the peripheral Al to the central B.

Here B acts as a s-acceptor, like C in ppCs. However, it is

relevant to mention that the NPA charge on B atom is some-

what smaller than that of C in CAl5+ (�2.9|e|),102 CAl4Be

(�2.87|e|), and CAl3Be2� (�2.96|e|).105 This is presumably due

to the lesser electronegativity of B than C. The Wiberg bond

indices (WBIs)109 for individual B–Al bonds vary from 0.640

to 0.648 (Table S13w) giving a total WBI of 3.218 to the B atom.

It should be noted that the total WBI of B in BAl5 is consider-

ably larger than that of C in CAl5+ (WBIC(Tot) = 1.99).102 The

valence orbital population at B in BAl5 is (2s1.39 2px

1.20 2py1.55

2pz1.55). The higher 2py and 2pz occupancies in comparison to

those in 2px is an outcome of back-donation from the

perpendicular 2px orbital to the p-orbital (HOMO-3) (Fig. S1w)(in this present case, 2px orbital is perpendicular to the plane),

similar to the electronic stabilization mechanism offered by

Hoffmann et al.110 To understand the nature of electron

delocalization in BAl5, a detailed MO analysis has also been

performed (Fig. S1w) in which the presence of two p-electronsin HOMO-3 suggests it to be a p-aromatic system. However,

a NICS study calculated on a triangular plane of BAl5reveals that it is doubly aromatic (both s- and p-aromatic)

(Table S15w).

BAl4Be� and its Li+/Be2+ doped systems. A substitution of

Al of BAl5 with Be� (since Al is iso-electronic with Be�)

produces BAl4Be� (18 valence electrons) having C2V point

group as given in Fig. S2.w In BAl4Be�, the central B atom

gets an NPA charge of �2.51|e| (Fig. S15w) which is smaller

than that of B in BAl5, and this is because of the greater

electropositivity of Al than Be. Incorporation of Be� into BAl5system, replacing Al, results in the removal of degeneracy of

the MO levels (Fig. S2w), as well as improvement of the total

WBI at the B atom (3.386) and the HOMO–LUMO gap

(Tables S13 and S14w). The vertical electron detachment

energy (VEDE) calculated for the HOMO electron using the

outer-valence Green’s functional (OVGF), in conjunction with

the 6-311+G(d) basis set indicates the bound nature of the

HOMO electron (+2.801eV), therefore, it is a stable anionic

species. Since we know that all systems having ppCs or ppBs

can only be detected and characterized experimentally as

anions, in this spirit BAl4Be� should attract attention from

the experimentalists. The effect of counter ions (Li+/Be2+) on

the electronic structure of BAl4Be� has also been tested. For

Li+ doped BAl4Be�, two different isomers have been identi-

fied in which LiBAl4Be (Cs1A0) is energetically more stable

than its C2V analogue (Fig. S3 and Table S14w) whereas in case

of Be2+ doped BAl4Be�, three different isomers have been

obtained at a minima on the PES (Fig. S4w): among them

BAl4Be2+ (Cs

1A0) [1] is the most stable (Table S14w). As

shown in Fig. S15,w the NPA analysis reveals the obvious

charge redistribution within the molecule when Li+/Be2+ has

been doped. The total WBI value at B (Table S13w) and the

HOMO–LUMO gap (Table S14w) are very similar for

BAl4Be� (WBIB = 3.386, gap = 1.941 eV) and LiBAl4Be

(WBIB = 3.384, gap = 1.939 eV), whereas, it improves to

some extent in BAl4Be2+ (WBIB = 3.511, gap = 2.524 eV).

Therefore, BAl4Be2+ seems to be more stable than BAl4Be

�

and LiBAl4Be by virtue of its larger total WBI and larger

HOMO–LUMO gap. The MO analysis (Fig. S2–S4w) showsthat the incorporation of Li+ and Be2+ into the system only

alters the shape of the MO, and in a few cases the associated

energy order (HOMO-4 is of p-type for BAl4Be2+ but

HOMO-5 is of p-type for BAl4Be� and LiBAl4Be). The

valence orbital populations at B are (2s1.33 2px1.43 2py

1.55

2pz1.18) for BAl4Be

�, (2s1.31 2px1.46 2py

1.54 2pz1.16) for

LiBAl4Be, and (2s1.33 2px1.43 2py

1.55 2pz1.18) for BAl4Be2

+.

The lower occupancies at the 2pz orbital, compared to the 2pxand 2py orbitals, are due to the p-back-donation (here the 2pzorbital is perpendicular to plane). The NICS study on a three

membered ring of BAl4Be�, LiBAl4Be and BAl4Be2

+ systems

shows that these systems are both s- and p-aromatic

(Table S15w). p-Aromaticity arises due to the presence of

two p-electrons in these systems as shown in Fig. S2–S4.w

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BAl3Be22� and its Li+/Be2+ doped systems. Upon the

introduction of another Be� replacing one Al of BAl4Be�,

two isomers having C2V point group have been obtained in

which BAl3Be22� (C2v

1A1) [1] is more stable than the corre-

sponding C2V analogue (Fig. S5 and Table S14w). The total

WBI at B in BAl3Be22� (3.477) is larger than that in BAl4Be

�

(3.386) (Table S13w) but VEDE calculation shows that the

HOMO electron is not in a bound state (VEDE=�0.984 eV),therefore, it is not a stable dianionic species. Upon Li+

doping, three different isomers have been attained at a minima

on the PES in which LiBAl3Be2� (C2v

1A1) is energetically

more stable than the two others (Fig. S6 and Table S14w).However, upon Be2+ doping, two different isomers have been

obtained in which BAl3Be3 (C2v1A1) is more stable than its Cs

analogue (Fig. S7 and Table S14w). Here it is relevant to

mention that for the electron count, to effectively engage in

bonding within the ppB moiety, LiBAl3Be2� and BAl3Be3

should be considered like BAl3Be22� interacting with Li+

and Be2+, as prescribed by Castro et al.,107 thereby satisfying

the 18 valence electrons criterion. Introduction of Li+ and Be2+

on to BAl3Be22� alters the charge distribution (Fig. S15w) as

well as the nature of LUMO and the associated MO energy

order (Fig. S5–S7w). Moreover, these counter ions have a

significant role in providing molecular stability. Due to

their presence, the energies of all occupied molecular

orbitals become negative and, correspondingly, the asso-

ciated VEDE becomes positive suggesting the bound nature

of the electrons (Table S14w). Additionally, the presence

of Li+ and Be2+ improves the total WBI at B (Table S13w)but the HOMO–LUMO gap is reduced somewhat in

the presence of Li+ but it enhances with the incorporation

of Be2+ (Table S14w), indicating greater stability of BAl3Be3over the others. The valence orbital populations at the

central B are: (2s1.29 2px1.18 2py


2�;

(2s1.26 2px1.16 2py

1.48 2pz1.39) for LiBAl3Be2

�; and (2s1.29

2px1.18 2py

1.54 2pz1.54) for BAl3Be3. Here also the p-back-

donation from 2px orbital to the p-MO is responsible for the

smaller occupancies at the 2px orbital with respect to 2py and

2pz orbitals (here the 2px orbital is perpendicular to the plane).

Both the MO analysis and NICS study reveal that these

systems are both s- and p-aromatic (Table S15w).

BAl2Be33� and its Be2+ doped systems. Upon further

incorporation of Be�, replacing one Al of BAl3Be22�, two

isomers with a C2V point group have been obtained in which

BAl2Be33� (C2v

1A1) [1] is more stable than the other C2V

analogue (Fig. S8 and Table S14w). Here it should be stated

that this trianionic species will surely be unstable with respect to

spontaneous emission of electrons, but still we have analyzed it

in detail to enhance our understanding regarding the impor-

tance of the 18 valence electrons rule to design such planar

hyper-coordinated species and, of course, one can then under-

stand its electronic stability in the presence of counter-ions.

Now, in the presence of one Be2+ ion, three isomers have been

identified at a minima on the PES: among them BAl2Be4�

(Cs1A0) [1] is energetically more stable than the others (Fig. S9

and Table S14w). Again in presence of two Be2+ ions, a total

of five isomers have been obtained, but only two of them

possess a minima on the PES (Fig. S10 and Table S14w).A comparison of the total energy reveals that BAl2Be5

+ (Cs1A0)

[1] is a lower energy structure with respect to others (Table S14w).All the three systems possess two p-electrons, indicating their

p-aromaticity (Fig. S8–S10w), however, the NICS study

implies that the systems are not only p-aromatic but also

s-aromatic (Table S15w). The positive value of VEDE (+2.879 eV)

for BAl2Be4� suggests its stability towards spontaneous emission

Fig. 12 The scheme depicting the optimized geometries of lower energy structures of the studied clusters having ppBs at B3LYP/6-311+G(d)

level.

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of an electron. The valence orbital populations at the central B

are: (2s1.31 2px1.21 2py


3�; (2s1.21 2px1.34

2py1.45 2pz

1.12) for BAl2Be4�; and (2s1.18 2px

1.38 2py1.43 2pz

1.09)

for BAl2Be5+. In case of BAl2Be3

3�, some p-back-donationoccurs from the 2px orbital to the p-MO (HOMO-5) (here the

2px orbital is perpendicular to the plane) whereas in case of

BAl2Be4� and BAl2Be5

+, 2pz orbitals have been engaged in

back-donation to the p-MOs (HOMO-4 and HOMO-3 respec-

tively) (in these cases, 2pz orbitals are perpendicular to plane).

The study of total WBI at the B atom and the HOMO–LUMO

gap reveals that, upon Be2+ doping, both the total WBI at B

atom and the HOMO–LUMO gap improve (Tables S13

and S14w). However, the BAl2Be4� system attains a maximum

HOMO–LUMO gap indicating its greater stability over the

others.

BAlBe44�

and its Be2+

doped systems. The next product as a

result of Be� introduction replacing one Al atom of BAl2Be33�

is BAlBe44� (C2v

1A1) (Fig. S11w). Now, to provide electronic

stability to this tetraanionic species, two Be2+ ions have been

incorporated into the system, producing three isomers, however,

only BAlBe6 (Cs1A0) [1] turns out to be at a minimum on the PES

(Fig. S12 and Table S14w). The higher stability of BAlBe6 than

BAlBe44� can be properly justified by the HOMO–LUMO gap,

which has been found to increase upon Be2+ doping (Table S14w),however, the total WBI at B remains the same (Table S13w).Similar to the earlier cases, the Be2+ doping alters the natural

charge distribution (Fig. S15w) as well as the nature of the LUMO

and energy levels of the occupied MOs (Fig. S11 and S12w). Thevalence orbital populations at the central B have been found to be

(2s1.32 2px1.25 2py

1.48 2pz1.43) for BAlBe4

4� and (2s1.15 2px1.44 2py

1.31

2pz1.08) for BAlBe6, consistent with earlier cases, and it has been

found that the occupancy of one 2p orbital is lower than the other

due to the p-back donation. Here the 2px orbital for BAlBe44� and

the pz orbital for BAlBe6 are perpendicular to the molecular plane,

therefore, they are engaged in the p-back donation. The NICS

study shows that they are doubly aromatic, similar to systems in

the earlier cases (Table S15w).

BBe55�

and its Be2+

doped systems. The last system derived

by substituting last Al atom of BAlBe44� with Be� is BBe5

5�

(D5h1A1

0) (Fig. S13w). Excepting monoanionic systems, any

multianionic species studied here are unstable due to unbound

nature of the HOMO electron, but the total WBI at the B

center reveals that WBIB(Tot) gradually improves with succes-

sive Be� doping into the BAl5 system, replacing Al and finally

it is maximized for BBe55� (WBIB(Tot) = 4.602) (Table S13w).

Now, upon two Be2+ ions doping in BBe55�, two isomers with a

C2V point group have been obtained, however, BBe7� (C2v

1A1)

[1] is a minimum energy structure whereas the other one is just a

saddle point (Fig. S14 and Table S14w). The introduction of two

Be2+ ions to BBe55� increases the HOMO–LUMO gap, indi-

cating increased stability upon Be2+ doping as well as making

the VEDE positive, suggesting its stability towards spontaneous

emission of an electron (Table S14w). The variation of NPA

charge upon the introduction of Be2+ has been depicted in

Fig. S15.w The valence orbital populations at B are (2s1.36

2px1.48 2py

1.48 2pz1.29) for BBe5

5� and (2s1.12 2px1.06 2py

1.36

2pz1.43) for BBe7

� indicating p-back donation from the 2pz

orbital in case of BBe55� (in this case the 2pz orbital is

perpendicular to the plane) and from the 2px orbital in BBe7�

(in this case the 2px orbital is perpendicular to plane). These

two systems are also both s- and p-aromatic as understood

from the NICS calculations (Table S15w).Thus, we have successfully designed a series of clusters with

ppBs by carefully monitoring the 18 valence electrons rule. All

the systems are doubly aromatic (both s- and p-aromatic). In

all cases, the central B atom acts as a s-acceptor and p-back-donor, similar to C in ppCs.

F. Metal-ion doped complexes

The chemical reactivity of a neutral molecule can be enhanced

upon doping with a charged species, such as a metal ion. The

alkali and alkaline earth metal ions, owing to a higher ionic

potential, have the ability to bind smaller molecules or groups to

produce complex motifs. These metal-doped cationic complexes

can therefore serve as suitable templates for the trapping of

small molecules. Some simple neutral molecules like HF, NH3

and H2O doped with alkali metal ions like Li+, Na+ and

alkaline earths like Be2+, Mg2+ have been chosen for this study.

The total energy (E, au) of the optimized structures of the metal-

ion doped complexes computed at various levels of theory has

been given in Table S16.w Single point energy calculations at

higher levels or using higher basis sets at a given level of theory

have also been performed and the values have been shown in

Table S17.w Tables S18–S20w present the values of the important

global reactivity parameters and the atomic charges on the metal

centers computed at different levels of theory. The optimized

molecular geometries of the various metal-ion doped molecular

complexes have been pictorially depicted in Fig. 13. The energy

(E, au) trends of the metal-ion bound complexes in Table S16wreveal that the corresponding values of the Na+ and Mg2+

bound systems are lowest, irrespective of the choices of the

parent moiety or the level of theory. A glance at the atomic

charges on the metal centers in Tables S18–S20w clearly shows

that the Na and the Mg centers (for a given parent moiety or at

any level of theory) bear a slightly high positive charge than the

respective Li or Be counterparts. This observation highlights

that the Na+ and the Mg2+ ions have the tendency to bind

more ‘‘strongly’’ with the neutral moieties through a favorable

ion–dipole type of interaction to yield a stable complex.

G. Be82– isomers

Molecular clusters serve as a useful link between smaller assemblies

and bulky multi-dimensional materials. The modeling of small to

medium all-metal 2D as well as large 3D multidecker clusters has

been a widely cultivated topic in the past few years. Conceptual

DFT20–24 in conjunction with the novel concept of all-metal

aromaticity111 has been successfully executed towards deciphering

the structure, bonding, aromaticity and reactivity of a plethora of

metal clusters.112–115 This study reports the modeling of fifteen

plausible isomers of a dianionic all-beryllium [Be82–] system

(Fig. 14). Table S21w describes the optimized molecular geo-

metries along with the respective total energy (E, au) values

and the various conceptual DFT based global reactivity descrip-

tors of all the generated isomeric forms of the [Be82–] molecule.

The atomic charges on the Be-centers and the associated

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geometrical parameters (bond lengths and bond angles) of all

the [Be82–] isomers have been given in Table S22.w The

important frontier molecular orbitals (FMOs) of some repre-

sentative [Be82–] isomers have been depicted in Fig. S16.w The

hardness values of almost all the generated isomers are compar-

able except for structure 14, a linear conformation where Z turnsout to be the lowest among all. The global electrophilicity value

for the linear [Be82–] isomer also shows the highest magnitude,

thereby rendering the given conformation to be a highly reactive

species. Structure 12 of the [Be82–] system has already been

reported28 and has the lowest o value among all the generated

conformers. This may be ascribed to the presence of a favorable

aromaticity criterion in the two trigonal Be32– rings stabilizing

the Be–Be bond in the [Be82–] cluster.

H. Double-decker sandwich-type molecules

The design of all-metal and non-metal complexes assuming a

double-decker or a multi-decker form is already well known.27–31

The various 2D and 3D clusters show the existence of an

aromaticity/antiaromaticity criterion along the various all-metal

and non-metal rings, which have been further stabilized by

appropriate molecular groups above and below the plane. This

study reports the design of some sandwich structures involving a

trigonal [B3(BO)3] unit to bind with an all-metal or non-metal

moiety through a metallic linkage. The optimized molecular

geometries of the given complexes and their corresponding

frontier molecular orbitals (FMOs) have been portrayed in

Fig. 15. The total energy (E, au), molecular point groups (PG)

and the important global reactivity descriptors of the sandwich-

type clusters studied at the HF/6-311+G(d), B3LYP/6-311+G(d)

and M052X/6-311+G(d) levels have been presented in

Tables S23–S25 respectively.w Table S26 illustrates the NICS(0)

values computed at the ring centers of the different complexes.

The values of the relevant parameters in Tables S23–S25 reveal

that for most of the di-anionic complexes, the electronegativity

(w) values are negative which presupposes the reluctance of the

given molecules towards further acceptance of electrons. The

magnitudes of the chemical hardness (Z) of the given complexes

are quite high as compared to their associated electrophilicity (o)values. The molecules are thus supposed to be less reactive and

hence stable. An assessment of the stability norms of these clusters

in terms of an aromaticity criterion can be rationalized from the

corresponding NICS values of the various rings of the respective

complexes in Table S26.w The NICS(0) values for the central

all-metal/non-metal ring of the complexes are negative in most

cases (Be3, Mg3, Al4, C5H5, N5, P4) excepting the all-nitrogen N4

and N6 systems, which show positive NICS(0) values. The

trigonal B3 ring unit positioned above and below the all-metal/

non-metal plane shows a varied trend in the NICS(0) values.

Thus, the central rings mostly retain their aromatic nature upon

complexation, thereby rendering stability to the given multi-

decker systems. Moreover, as is evident from Fig. 15, the Al4,

N4 and N6 bound complexes are not perfect sandwiches, as the

central all-metal/non-metal ring tends to remain more or less

perpendicular with the trigonal B3 unit placed above and below

the same. The important frontier molecular orbitals of the various

sandwich-type clusters show prominent electron delocalization

above and below the different ring planes, which probably justify

the sustenance of a diatropic/paratropic current to establish an

aromaticity/antiaromaticity phenomenon.

Potential utility of molecular clusters in hydrogen storage

applications. The modeling of molecular materials as useful

templates for the storage of hydrogen in its atomic and

Fig. 13 Structures of Mn+@ (–H2O, –NH3, –HF): (M = Li, Na, Be, Mg: n = 1,2).

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molecular forms has become a topic of top priority in chemical

research. Hydrogen has been conceived in the past decade as a

fuel source, as well as an energy carrier for applications in

industry and the automobile sector. An uncontrolled use of

fossil fuels over the past few decades has ultimately met up

with the dual curses of global environmental pollution and a

dearth in the former. So with an aim to mend these crises, the

use of hydrogen as an alternative fuel has become necessary.

Hydrogen, being a clean fuel alternative (generating water as

a harmless by-product) is quite abundant in the universe and

is also available from rocks, soil, air and of course, water.

For practical purposes, to be used as a fuel, hydrogen needs to

be stored in manageable quantities under proper volumetric

and gravimetric standards. In this regard, other than lique-

faction and storage in high-pressure conditions, hydrogen

can be adsorbed in considerable amounts upon various

molecular motifs which can further lead to its prompt release

during use. A plethora of different classes of molecular

clusters have been designed so far which include graphene-

based sheet like materials,116,117 nanomaterials118,119 and cage-

like clusters,120,121 metal hydrides and metal clusters122,123 and

metal–organic frameworks (MOFs).124,125 A recent review126

Fig. 14 Optimized geometries of all the possible isomers of Be82� molecule at the B3LYP/6-311+G(d) level.

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and a few other relevant articles32–40 delineate the modeling of

various molecular assemblies useful for hydrogen storage

applications.

In this present backdrop, with an aim towards further enrich-

ment of the library of hydrogen storage materials, we propose

the plausible usage of the newly designed molecular frameworks

as effective templates for the same. The potency of ‘‘star-like’’

molecules as useful hydrogen trapping materials are already

known.74 Thus the new five and six-membered molecular stars

should aptly perform for the same purpose. Moreover, based on

the efficacy of a metal site towards hydrogen binding,32–34,36,38–40

metal-ion doped cationic complexes can be utilized as effective

storage materials for molecular hydrogen. The ability of the

carborane cages, C–N based half-cage frameworks, as suitable

templates for hydrogen storage is also studied.

5. Conclusion

The application of sophisticated theoretical methods towards

molecular modeling has now become a well advanced topic of

fundamental research. Scientists as diverse as astrophysicists,

biologists, chemists, materials scientists and zoologists can

reach for a handful of utility software programs to design

molecular frameworks of unanticipated complexity. The new

molecules are supposed to possess unique structural features

and can be used for many potential applications. The present

work makes an attempt to design a variety of different forms of

such molecular assemblies which are supposed to have some

fruitful practical usage. Apart from that, they make a very good

case for promoting the use of theoretical methods in order to

avoid following unproductive lines of inquiry in synthesizing

rather exotic, and sometimes very toxic, chemicals. Theoretical

approaches such as this allow the researcher to ‘‘zoom in’’ to

more productive lines of enquiry. The attractive ‘‘star-shaped’’

molecules, carborane cages, C–N based half-cage frameworks

along with the small metal-ion bound cationic complexes have

the ability to act as effective media for the trapping and storage

of hydrogen. The clusters with ppBs will stimulate the curiosity

of scientists for further work. The all-beryllium clusters and the

double-decker, complexed sandwich materials can be used for

further molecular modeling towards building 3D frameworks,

useful for bulk applications. Further work is in progress.

Acknowledgements

P. K. C. would like to thank Professors Gabriel Merino and

Thomas Heine for kindly inviting him to present an article in

this Special Issue of Physical Chemistry Chemical Physics on

‘‘Predicting New Molecules by Quantum Chemical Methods’’.

He also thanks the Indo-EU HYPOMAP project for financial

assistance and DST, New Delhi for the Sir J. C. Bose National

Fellowship. S. M. and R. D. thank UGC and S. P. thanks

CSIR for their research fellowships.

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Fig. 15 The optimized structures of several double-decker sandwich

complexes studied at the B3LYP/6-311+G(d) level.

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ChemInform Abstract: Aromaticity in Polyacenes and Their Structural Analogues

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