Indi an Jo urn al of Chemistry
Vo l. 41 A, March 2002 , pp. 462-471
A quantum chemical study of the physical process of planar (D 3h ) to pyramidal
(C3v ) structural reorganization of boron trifluoride molecule
Dulal C Ghosh*, libanananda lana & Arindam Chakraborty
Department of Chemistry, Uni versity of Kalyani , Kalyani 741 235, Indi a
Received 17 No vember 2000; revised 26 November 2001
The dynamic process o f planar (D lI ,) to pyramidal (C3 1') reorgani za ti o n prior to th e event of chemical reac tio n o f boron
trifluo ride. BF, . mo lec ul e has been studi ed by locali zed mo lec ul ar orbital and energy partitioning methods. T he energy of
reorganizatio n, the st retching of B-F bond and alterati on of charge density distribution are computed for a w ide range of
mo lec ul ar conformations ge nerated by defo rming th e equilibrium geo metry of the molecule. The large activation barrier of
the molecu le is correlated to its hi gh energy of reo rgani zati o n prior to the event of chemical reacti o n due to ihe e liminati o n
of partia l double bond character and the weakening of the B-F bo nd on stretch in g. The B-F bond stretches through
0.023A. The bo ndin g in th e equilibrium geometry is computed in term s of locali zed mo lec ul ar orbitals, LMO's. The
quan tum mechanical hyb ridi zati o n of orbitals on Band F atoms forming th e a-(B-F) bond is compu ted for all th e
confo rmati ons of th e mol ec ul e th rough the generated LMO's. The total energy of the mo lec ul e at all its con fo rmati ons is
decomposed into o ne- and two ce nter co mpo nents. The weakening of th e B-F bo nd and variati o n of the percentage of the
s-characters of the hybrids o n Band F atoms formin g the bond in a series of conform ati ons are co rre lated and has been
fo und to be in accordance w ith Coul son's obse rvati o n in simil ar situatio n.
The mo lecule boron trifluo ride, BF3, is class ified as a
Lewis I acid. The molecule exists in a planar (D 3" )
fo rm at th e eq uilibrium state with partial double bond
characte r between Band F atoms. The characteristic
electron defici ent nature and the equilibrium structure
of BF, are usually correlated by assigning a Sp 2
hyb ridi zat io n of boro n orbitals in terms of Paulin g's2
hyb ridi zat ion model. Thi s mode of hybridization
leaves one empty 2p: orbital on boron ato m, which
endows the property of Lew is acidity and other
chem ical characteristics to the molecule. In terms of
Pearso n's3 HSAB classification, BF3 is a hard acid.
The mo lecul e is chemically very important and forms
a large number of stabl e adducts (super molecules)
with electron-pair do nors (sub-systems) known as
Lewis bases I. The adducts , known as donor-acceptor
comp lexes, have a w ide range of stability starting
from stron g covalent type at one e nd to the weak van
der Waals compl exes at the other throu gh a series of
co mpl exes of intermediate stability . An observed
ge neral stru ctural characteri stic of the BF3 mol ecule is
that th e BF3 fragment always assumes a pyramidal,
C.!" shape in the adduct supe r mo lecule: Thus while
form in g th e donor-acceptor complexes, the BF3 subsystem undergoes a physical process of reorganization
of th e molecular geo me try from D 3" to C3" point group
during the event of its chemical interaction with th e
donor molecules. Ghosh and Janat. have recently
studied the physical process of D 3" to C ,
reorganization of the shape of BF3 mo lecule in term s
of frontier orbital theory and density functional theory
and have found that the chemical reactivity of BF1
molecule becomes significantly modifi ed and
enhanced as a function of deformation of th e
equilibrium structure. We may , therefore, suggest an
intuitive structure and dynamics of the phys ical
process of evolution of mo lecul ar shape of BF.1 from
D 3" to C3v sy mmetry type in respo nse to chemical
attack as follow s:
Wh en a li gand, L, begins to
approach the BF3 moiety along the Z (C3 ,·) ax is, the
BF3 molecule, in respon se to the chemical attack.
begins to deform quickly and reorganizes from its
equilibrium planar form to pyramidal shape. After the
event o f chemical reaction through a process of
charge tran sfer and the form at ion of boron-li gand
bond, the BFJ frag ment remains collapsed in C3,· for m
opposite to the direction of attack by the li gand . The
structure a nd dynamics of th e above physical and
chemical process is schematically depicted in Fig. I.
The suggested reorganization o f the molecular
shape of BF3 in responsive to chemical attack not onl y
occurs for th e sake of inc reas in g chem ica l reactivity"
of the mol ecule but also for th e necessary require ment
of symmetry (Fig. I) . From symmetry considerati on it
can be shown that such D 3" to C3 1' reorganization or
GHOS H
X~X
.. .. . . L
el
al .: QUA NTU M CHEMI CA L STUDY OF STRUCTUR A L REO RG ANI ZATI ON OF BF,
-x~"'
x
.. . . .. ... L _
/
L
X?
X
X
(T .S)
Sub-Syste ms
x"' n _
(C,.)
Super molccuIe
Fig. I- T he intui tive struct ure and c1 y n ~lI11 ic s o f th e physica l
process or reorga ni zat ion of SF, Illolec ul e in response to cheill ica l
attack and th e rorillati on o f super Illolec ul es.
the molecul ar shape of BF, sys tem is a prerequi site
co ndition of th e event of chemi ca l reac ti on to occur
s
between BF, and Lewi s bases (L ). Fukui suggested a
molecul ar orb ital method of elucidation o f electro nic
structure especiall y suited for th e donor- acceptor
super molecules. Th e ori gin of transfer of charge and
the mechani sm of th e form ati on o f bond between the
interactin g molecul es are straight fo rward in thi s
meth od. Ghosh() has cas t the meth od in a simpl er
mathemati ca l form and appli ed to a number of
i nterac ting sys tems. The ca lcul ati on and analys is of
the results o f a number of sys tems demonstrate th at a
phys ica l process of si multaneous donati on and bac kdonat ion of charge in vo lving th e two fronti er orbitals,
HOMO and L UMO, of both the in terac ting subsystems tell s th e whole story of charge transfer and
bond form ati on of donor-acceptor interac ti on leading
to the formation of super-molecu les. It has been
es tab li shed th at th e orbital-pairs invo l ved in charge
transfer or back- tran sfers mu st belong to th e simil ar
irreducible represe ntati ons of th e point groups of th e
sub-sys tems. But i f th e orbital-pairs in vo lved i n
charge transfer process is of di fferent sy mmetry type
or hav ing no matching sy mmetry th en th e overl ap
integral between such orb itals vanishes identi ca ll y
and no charge tran sfer process can be initi ated. It has
been co nvi nc i ng ly establi shed th at i f th e B F] subsystem remains in the ( 0 1/,) form it is chemi ca ll y
n
almos t inert . I t ca n be shown that i f th e BFl
molecule remain s in th e (D I/J fo rlll . th e f ron ti er
molecu lar orbi tals of BF, and th e donor sub-sys tems
do not match in sy mmetry types. Hence, th e ov erl ap
integral betwee n th e molecular orbitals in vcl/ ved in
the ph ys ica l process or charge transfer va ni shes
iden ti ca ll y anc! the eve nt of chemical reac ti on ca nnot
occ ur between planar BF; and the donur mo lecul es
whose str uc tural reorgani zati on is eit her nil or
ins igni fican t. Hence, i n order to initiate and occur a
chemica l react ion between BFl and th e elec tron pair
donors through a process of charge tran si"er, th e
change or point group of BF} sub- sys tem by a
struc tu ra l deformati on acco rding to Fig. 1 tS a
prerequi site cond iti on.
463
One very important aspect of th e chemical kineti cs
of the BF, sys tem is th at it has a hi gh reac ti on barri er
or energy of acti vati on'). A n examinati on of' th e
chemica l and ph ys ica l characteri sti cs reveals that th e
BF} molecule exhibits poor L ewi s acidity and th e
B- F bond length is much shorter than expected i n
the equilibrium form t(). Thi s shorter bond length and
poor acidit y of th e molecul e has been correlated by
th e form ati on of a pn-pn bond between F and B atoms
by th e donati on of lone pair of electron s fro m flu orine
into th e empty 2p~ orbital of boron in addition to th e
CJ- CB- F) bond . Thi s engagement of th e empty orbital
of boron makes BF) a co mparati ve ly poor L ewi s ac id
in the D 311 form and develops a parti al double bond
character in th e B-F bond . However, w hen BF,
molecul e is deformed fro m its pl anar D .lh fo rm, the
pn-pn bond w ill be eliminated because of th e change
of hybridi zati on of boron orbital s from sp" type, th e
B- F bond is certain to stretch because of its sin toale
bond character now. Thu s th e ph ys ica l process of D ill
to C3 1' reorgan izati on of BF, molecule shall req uire a
large am ount of energy for breakin g the n bond and
for th e stretching of CJ bond between B and F atoms. It
is w idely kn own th at, on adduct form ati on, the B- F
bond is stretched signi f icantl y and the length of the
B- F bond is a sensiti ve probe o f th e magnitude of
. II - I '] . T he rall.onal e of large
(Ionor-acceptor .
Interactton
9
reac ti on barri er of B F, molecul e is straight fo rward
because both th e loss o f parti al double bond charac ter
and lengthening of B-F bond assoc iated w ith th e
ph ys ical process of changing of th e molec ul ar shape
in vo l ve energy.
As the mo lecul e evo l ves graduall y fro m its
eq uilibriu m shape in a chem ica l response, the
assumes
an
in fini te
num ber
of
molecul e
co nfo rmati ons, one separated from th e other by
energy , th e L FBF an gle, and th e B- F bond length.
T hus, in order to understand th e ph ysical and
chem ica l charac teri sti cs of the BF1 sub-system. it is
necess ary to know th e dynam ics, the energetics, an d
th e physica l process of reorga ni zation of th e stru ctu re
anc! the electron density reorgani za ti on during the
process of its confo rm at ional change from planar to
pyra midal f'Jrm. Such co nfor mat ions can never be
iso lated anl i studied by ex perimen tal techniques and it
is no t poss ible to foll ow such a fa st evo lu tion
of molecular geome try by ex peri me nt. Howeve r,
mol ec ul ar qu antu m mechanics ca n ex trac t informati on
rega rding electronic struct ure, reac tivi ty and other
mo lecul ar prope rt ies of the sys tems hav ing elusive
464
INDIAN J CHEM., SEC. A, MARCH 2002
geometries, electronically excited molecules and the
transition states having fleeting existence l 4-16. Thus it
is appropriate to invoke a suitable paradigm of
molecular quantum mechanics to follow and study the
stretching of the B-F bond length and the change in
charge density distribution associated with the
phenomenon of the physical process of reorganization
of molecular structure of BF) from its equilibrium
form to pyramidal shape. Molecular quantum
mechanics can compute the B-F bond length and
energy for any conformation for which the spectral
determination may not be feasible. It is already
mentioned that one important aspect associated with
the change of shape of the BF) molecule is the
physical stretching of the B-F bond. The orbitals of
Band F atoms forming the a-(B-F) bond will
undergo a continuous change in hybridization due to
its continued stretching.
Coul son l7 suggested a
correlation between variation of the strength of a bond
with the change of the percentage of s-charac.ter of the
hybrid forming the bond .
The popular method of computing charge density
reorganization on change of geometry is the
hybridization scheme of Pauling2. But the method is a
qualitative one and is effective for certain fixed
geometries only, and there is no whisper of
computation of hybridization for dynamic structural
isomers in Pauling's scheme. Pauling's method
suggests the Sp2 hybridization to the plane triangle
geometry and Sp3 hybridization for all the pyramidal
forms- an infinite number of conformations. Ghosh
el a/. 18 have recently shown that unambiguous
quantum mechanical hybridization of bond pairs and
lone pairs for any conformation or shape of molecules
can be computed by converting the canonical
molecular orbitals, (CMO's) of the conformation into
a set of localized molecular orbitals, (LMO's) by an
unitary transformation. It is also demonstrated 18 that
Coulson's suggested correlation of variation of s-p
ratio of the hybrid forming a bone: and the strength of
such bond is quite valid and satisfied during the
physical process of the evolution of geometry from
equilibrium conformation to transition state through a
series of unstable, non-isolable conformers. The
obvious formalism of the molecular quantum
mechanics rests upon the Hartree-Fock-Roothaan's 19
method. But the concept of lone pair and bond pair
vanishes in thi s formalism and the generated
molecular functions are called canonical molecular
orbitals (CMO's) or spectroscopic molecular orbitals
(SMO'S)20. However, the freedom of unitary
transformation in Hartree-Fock space has been
conveniently exploited to generate orbitals which are
localized and the conceptual aspect of chemistry--the
lone pair and bond pair, is quantum mechanically
restored 21,22. Sinanoglu 22 suggested a method of
localization where the n-bonq and a-bond separation
is maintained along with the identification of lone pair
and bond pair. Sinanoglu also pointed out that the
unambiguous quantum mechanical hybridization
could be calculated through the generated LMO's .
Ghosh et a/. 18,2) have calculated the quantum
mechanical hybridization of a number of simple
diatomic systems and the dynamic conformations
assumed by the ammonia molecule during the
physical process of its umbrella inversion in terms of
localized molecular orbitals invoking Sinanoglu's
method. The localized molecular orbitals have been of
considerable interest in quantum chemistry recently in
· structure theory 24 .
e Iectromc
It is already mentioned that during the physical
process of D 3/t to C3v evolution of molecular geometry
of BF) molecule the strength of B-F bond will
gradually decrease with its stretching. The only
available formalism of computing the bond energy is
the energy partitioning analysis of Kollmar and
Fischer25 under an all-valence electron ZOO method
25
of Pople and co-workers 26 . Kollmar and Fischer
decomposed the total energy into one and two-center
terms and furnished a meaningful rationale of the
physical components of the total energy .
We have, therefore, taken up the present study of
following the physical process of evolution of the
geometry of BF) molecule associated with the
dynamic transformation of the equilibrium planar
shape (D 31t) to pyramidal (C3v ) conformations
invoking the localized molecular orbital and energy
partitioning methods.
Procedure of Calculation
Since the localization technique of Sinanoglu 22
and the energy partitioning analysis of Kollmar and
Fischer25 are within the framework of formalism of
Pople 26 and co-workers, we have invoked the
CNOO/2 method in the present study. The geometry of
the molecule is optimized by energy optimization
technique at each of its conformations starting
from equilibrium shape. The molecular distortion is
GHOSH
el
al .: QUANTUM CHEMICAL STUDY OF STRUCTURAL REORGANIZATION OF SF,
465
where EA U , E/ and EA K are total monatomic orbital
initiated by decreasing the LFBF angle in steps of 1°
energy, electron-electron repulsion energy and nonand the bond length of the generated conformation is
classical exchange energy respectively .
optimized. The molecule has two geometric
parameters-(i) the B-F bond length and (ii) the
R
V
JEKE N
... (3)
EAB = EAI] + EA/J + E'\IJ + AIJ + "IJ
LFBF angle, but since the bond angle is made an
where EAI/ is the contribution of the resonance
independent variable parameter, only a single
integrals to the energy of A-B bond and is the
parameter- the B-F bond length, is required to be
principal feature of covalent bond, EA/ signifies the
optimized. The energy and wave function of each of
total potential attraction of all electrons of A in the
the conformers including the equilibrium form at
field of the nucleus of B plus those of B in the field of
optimized bond length is calculated. Then the
the nucleus of A, EA/ estimates the total electrongenerated canonical molecular orbitals (CMO's) are
electron repulsion energy between two centers- A and
localized through the procedure developed by
B, while E,,/ stands for nuclear repulsion and EAI/
Sinanoglu 22 • The computed total energy of each of the
defines the total exchange energy arising out of
conformations is partitioned into one and two-center _ quantum mechanical exchange effect between
components through the formulae laid down by
electrons of A and B and is an important quantity in a
25
Kollmar and Fischer . A bonding analysis of the
chemical bond .
molecule at all its co nformations is attempted in terms
Standard parameters 24 and STO basis set are used.
of the LMO's.
The overlap and coulomb integrals are computed not
The explicit formulae of energy decompos ition are
through empirical methods but through the explicit
27
laid down below.
analytical formulae laid down by Roothaan . The
The total CNDO energy of a system can be writte n
geometry is optimized at each of the conformations
as sum of one center and two-center terms as follows:
and the cycle of computation is re peated at each
conformation. The optimized B-F bond length and
reorganization e nergy, the difference of energy
. . . (I)
between the equilibrium shape and anyone of th e
conformers generated through the deformation of the
where EA are monatomic terms and E,\IJ are diatomic
terms . The monatomic terms EA and the diatomic
molecule are plotted as function of LFBF angles as
terms EAB can be further broken down into physically
reaction coordinates in Fig . 2. The variation of the
meaningful components as follows:
gross atomic charges on boron and fluorine atoms is
EA = E,\ U + E/ + E/
... (2)
plotted as a function of the reaction coordinates in
1.47~
.,---------------------------------:-:----,
Numbers indicate angles in degrees
0.15
1.47
0. 13
0.11
o<l:
£
1.46
0."
c
~
1J
114
C
116
0
118
,
l1.
1I~
117
1.43
IU
en
II~
112
10
1.4~~
.0
.
>-
B-F bond length
(J\
:l
0
~
0.17
0.15
0
~N
C
0
(J\
0
0.13
J.H
'c"
'"
c
Reorganizat io n energy
1 . 44~
E'
'"
0::
0.01
· 1.01
I . U~
Reaction coordinates (Q), deg
Fig. 2- Plut o f 8 -F bond length and reorgani za ti on energy as a fu nction o f planar
trinuoride molec ule
10
pyramida l angular reorgani za ti on
of
boron
~
0'1
0'1
Tablt:
I-Th~
LMO's of BF3 at equilibri um geometly.
I.p(l) r 2
o B-FI
I.p.(2) F2
oB-F.1
I.p,P ' p2
I.p.(I) F3
I. p.(2) F3
cr D-F2
I.p.(1l FI
I.p.(3) F.1
I.pY) F1
I.p,o) F J
B2s
0.0 188
-0.3559
-0.0001
0.3559
0.0000
-0.0188
-0.0000
0.3558
0.0000
00000.
0.0000
-0.0187
.....
B2px
0.0 142
-0.0000
0.0649
0.3675
0.0000
0.01 43
-0.0650
-0.3676
0.0000
0.0000
0.1300
0.0000
B2py
0.0082
-0.4244
-0. 1125
-0.2123
0.0000
-0.0082
-0.11 25
-0.2122
0.0000
0.0000
-0.0000
0.0164
;;
0.2350
0.0000
0.0000
0.0000
-0.2350
0.2350
0.0000
0.0000
0.0 191
-0.0085
0.0000
0.0000
0.0000
0.8361
LMO's
AO's
B2pz
0.0000
0.0000
0.0000
0.0000
F2.1
I
F2p >
I
F2py
I
F2p<
2
F2s
F2p/
-0.0037
-0.4556
0.0190
-0.0086
0.0000
0.0039
-0.0010
-0.0000
-0.0047
-0.0199
0.0000
-0.0011
0 .0046
0.0198
0.0000
0.0000
0.9903
-0.0000
-0.0271
0.0207
0.0000
0.0000
0.0000
0.5478
F2p/
F2pz2
3
F2s
F2p/
F21'/
F2p/
z
0
z
'-<
n
::r::
tTl
3:
[.I)
0.0062
0.6954
-0.0269
0.0207
0.0000
-0.0062
0.0000
0.0000
0.0000
0.0000
-0.0288
0.0000
0 .0000
0.0000
-0.97 11
-0.0288
0.0000
0.0000
-0.8361
0.0084
0.000 1
-0.0085
0.0000
0.0038
-0.0189
0.4556
0.0000
0.0000
0.0190
0.0040
0.4744
0 .0080
0.4951
-0.0277
0.0000
0.0048
-0.0258
0.6023
0.0000
0.0000
0.0210
0.0058
0.2737
0.0277
-0.8577
0.0067
0.0000
0.0039
-0.0093
0.3477
0.0000
0.0000
Om77
0.0022
0.0000
0.0000
0.0000
0.0000
0.9711
0.0000
0.0000
0.0000
0.Q208
-0.0288
0.0000
0.0000
-0.0039
0.0084
-0.0190
0.4556
0.0000
0.8361
-0.0000
-0.0084
0.0000
0.0000
0.0188
0.0039
0.0048
-0.0081
0.0259
-0.6023
0.0000
0.4744
-0.4950
0.0280
0.0000
0.0000
0.0210
-0.0059
-0.0040
0.0275
-0.0094
0.3476
0.0000
-0.2738
-0.8577
0.0067
0.0000
0.0000
-0.0176
0.0022
0.0000
0.0000
0.0000
0.0000
-0.0289
0.0000
0.0000
0.0000
0.O21111
0.9711
0.0000
0.0000
tTl
0
?>
3:
>;>0
n
::r::
IV
8IV
GHOS H
I!I
al.: QUANTUM CHEMI CA L STUDY OF STRUCTURAL REORGANIZATIO
f ig.3.
We have not reported all the LMO's
generated in th e course of study but that of
equilibrium geometry is shown in Tabl e I. Th e
unambiguous quantum mechanical hyb ridi zation of
Band F orbital s forming th e cr- (B-F) bond is
co mputed and shown in Table 2. The monatomi c
and diatomic energy com ponents as a function of
ang le of di storti on are shown in Tabl es 3-5
respec ti ve ly. The percentage of .I·-character of th e
hyb rids on Band F atoms formin g th e cr-( B-F)
bond and th e energy of th e B- F bond are plotted as
a function of th e reac ti on coo rdinate in Fig. 4.
Resul ts a nd Discussion
Th e quantum mechani ca ll y co mputed bond pair and
lone pair elec tron ic stru cture of the BF} molecul e at
its equilibrium geometry becomes at once revealed
in terms of the locali zed molec ular orbital s, LMO 's,
from Table I . The molecule has three cr-( B- F)
bonds with partial 7! character due to the
contributi on of lone pair of elec trons from fl uorine
to empty orbita l of boron. Eac h flu orine atom forms
a cr- (B-F) bond and th ere are three lone pairs one
of which is in vo lved in forming a partial 7! bond
with th e empty 2p: orbita l of boron. Thus the
quantum mechani ca l elec tronic stru cture of BF,
molecule is simil ar to its qualitative valence bond
stru cture and th e assumption of partial double bond
467
OF BF>
Tabl e 2- The hybrid izali on of boron and Iluorine orbital s lO
1'01'111
th e B- F bond as a fun clion of an gles o f reorga ni zali on.
L FI3F in
degrees
Hybridi zalion of B-alolll
formin g I3 -F bond
120
11 9
11 8
117
11 6
115
11 4
11 3
11 2
.I'plA 5
II I
.I'p
11 0
109
108
107
106
105
104
103
102
101
100
99
98
97
96
95
Hybridi zali on of Falo lll forlllin g B-F
.I'pl.42
.I'p".1.1
1.·1:1
.1'1 ' , .>.1
.I'p1.4>
.I'p , ..15
1..14
.I'p , ..1(,
.I'p
.I'p
.I'J!
7.17
.I'pI.4(,
.1'/.
.I'p lA 7
.lp ,AO
18
.I'p' .4'
sp 2AI
.I'plA8
SfJ "2 ·~"2
.I'p
1.49
.I'J!'A4
1.49
Sp?··H,
1.)0
.I'p
.1'1'
1.-17
::!.-IlJ
.I'pl.)I
.I'p
.I'pl. )I
.1',/ .'1
.I'p 1..1 1
.I'V'I'
·-
.I'p1 5'
sp"2,))
.I'p 1.5>
.I'1' 25~
.I'p15.1
.I'p
1.5·1
"2.51)
.1'1'
.I'p , .61
.I'p 1.)4
.1'1' " .6.1
.1'171.:':'
.I'p 2,{,1
.I'pI.5(,
.I'J!2.70
.I'pl.) 7
.I'p , .7 1
.1'1'1. 57
.I'p
.I'p157
.1'/.77
.I'p
1.5lJ
.I'p
"2 7 ~
"27 1)
2.28 , . . - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - , '. :!52
2.275
)20
7. 25
2.27
7.248
E
.9
7.246
t1..
Charge densit y on
E l.U5
<:1
0
13
I
en
c
o
2.H
c
7.244
0
?:
C
2.2.55
'Vi
c
'"
"0
'"'"
U
7.24 2
2~ 2~
'"
~
<:1
.c
:£
III
~
<:1
Il O
7.2.
2.245
u
7.2.38
2.24
7.2.36
2.235
1-________________________________________________- 4
2.2.3
Reaction co ordinates,(Q) ,if degres
Fig. .
PIOl of charge densil ies on 13 and F alOIllS as a funcli on of an gles of reorga ni zali on
7. U.
.c
U
INDIAN J CHEM., SEC. A, MARCH 2002
468
character of B-F bond 9- 13 finds justification in
quantitati ve calculation. But the quantum mechanical
hybridi zation of Band F orbitals forming the B-F
bond and the lone pairs are different from those of the
qualitative model of Pauling. The computed
hyb ridization s of boron and fluorine orbitals forming
the cr-(B-F) bond are SpL4 2 and S/3 respectively.
Because the B-F bond stretches as a function of
evolution of the conformations of the molecule, the
hybridization of orb itals on Band F centers forming
the cr-(B-F) bond changes. The computed results are
shown in Table 2. The results show that as the
geomet ry evo lves and the B-F bond stretches out,
the percentage of s-character of hybrids of Band F
atoms forming the cr-(B-F) bond decreases steadily .
Thi s decrease in s-character of hybrids has a direct
bearing on the strength of the bond formed 17.
The most important parameters which are required
to be considered espec ially during the evolution of
molecular shape of the BF) system are the stretching
of B- F bond, the energy of reorganization and the
charge den sity redistribution. The process of gradual
stretching of the B-F bond with the evolution of
mol ecular geometry is well visualized from Fig.2. As
soon as the BF) molecule starts deforming from its
plan ar form, the B-F bond stretches out and as the
molecule is deformed further so that the condition of
elimination of partial double bond character occurs,
the rate of stretching becomes a bit accelerated.
However, after the elimination of partial TC bond
character between Band F, the stretch ing is slow and
insensitive to the deformation of structure through 10.
From Fig.2 we see that the energy of geo metry
reorganization increases steadily with increase in th e
angle of deformation. It is also eviden t from Fig. 2
that as the molecule is gradually mo re and more
deformed , it requires more and more reorganization
energy for the physical process. It is already
mentioned that the reorganization process involves
two simultaneous and additive energet ic effects-one
is deformation of mo lecular structure and th e other is
stretchin g of the bond length a long with th e
elimination of partial double bond character of the
B-F bond at the equilibrium geometry. The
reorgani zation process requires quite a large amo unt
of energy. So it is quite evident that the
pyramidi zation energy of BF3 molecule is quite high
over the entire range of study . The average va lu e of
the LFBF angles in the super molec ules is about
1 J0 0 . The energy required to reorganize the BF.1
molecule from its equilibrium shape to th e
conformation having the LFBF angle at 110° is
Table 3--The monatomic energy (a. lI.) components on Band F centers as a function of angles of reorg;m ization.
LFBF in
Degrees
120
119
11 8
117
116
115
11 4
11 3
11 2
III
11 0
109
108
107
106
105
104
103
102
101
100
99
98
97
96
95
E/Ju
-3. 18 12
-3. 1793
-3.1773
-3. 1752
-3. 1733
-3.1716
-3 .1696
-3. 1674
-3. 1656
-3. 1637
-3 . 161 8
-3. 1596
-3. 1580
-3.1559
-3. 1539
-3. 151 8
-3 . 1498
-3. 148 1
-3.1461
-3. 1444
-3.1426
-3. 1404
-3 . 1387
-3 .1 369
-3. 1350
-3. 1334
E/
1.2253
1.2241
1.2228
1.22 13
1.220 1
1.21 90
1.2 175
1.2161
1.2 150
1.2 137
1.21 23
1.2109
1.2099
1.2083
1.2070
1.2057
1.2041
1.2030
1.2016
1.2005
1.1993
1.1976
1.1966
1.1952
1.1939
1.1928
E/
Eu
-0. 1644
-0.1643
-0.1642
-0.1640
-0.1639
-0. 1638
-0.1639
-0.1639
-0.1635
-0.1635
-0. 1635
-0.1633
-0. 1633
-0. 1633
-0. 1631
-0. 1631
-0.1631
-0. 1630
-0.1629
-0. 1629
-0.1629
-0.1630
-0.1629
-0.1629
-0.1629
-0. 1629
-2.1203
-2 . 11 95
-2. 11 87
-2. 1179
-2.1171
-2.1164
-2.1160
-2.1152
-2 . 1141
-2.1135
-2 .11 30
-2.1120
-2. 1114
-2. 1109
-2.1100
-2.1092
-2.1088
-2. 108 1
-2. 1074
-2. 1068
-2. 1062
-2 . 1058
-2.1050
-2 . 1045
-2.1040
-2.1035
EFU
-48.8 16 1
-48.8187
-48.82 17
-48.8251
-48.8277
-48.8301
-48.834 1
-48.8371
-48.8393
-48.8428
-48.8459
-tS.8493
-48.8517
-48.8556
-48.8585
-48.8622
-48.8660
-48.8685
-48.8719
-48.8744
-48.8775
-48.8821
-48.8844
-48.8880
-48 .89 16
-48.894i
E/
E/
24.7598
24.7622
24.7650
24.7681
24.7706
24.7729
24.7761
24.7792
24.7814
24 .7844
24.7872
24.7902
24.7924
24.7957
24.7985
24.8016
24.8048
24.8071
24.8102
24.8124
24.8 150
24 .8189
24.8209
24.8238
24.8266
24.8289
-3. 15 23
-3. 1525
-3.1529
-3.1532
-3.1535
-3.1537
-3. 1543
-3. 1546
-3.1 547
-3.1 552
-3. 1556
-3. 1559
-3 .1 563
-3. 1567
-3.1570
-3.1574
-3.15 80
-3. 1583
-3. 1587
-3. 1590
-3. 1594
-3 .1 601
-3.1 603
-3.1609
-3 . 1614
-3 .1 617
EF
-27.2086
-27.2090
-27.2096
-27.2102
-27.2106
-27 .2 109
-27.212 3
-27.2125
-27.2 126
-27 .2136
-27.21 43
-27.2150
-27.2 156
-27.2166
-27.2170
-27.2180
-27.2192
-27.2197
-27.2204
-27 .2210
-27.2220
-27.2236
-27 .2239
-27.2251
-27.2262
-27.2270
GHOSH el 01.: QUANTUM CHEM ICAL STUD Y OF STRUCTU RAL REORGANIZATION OF I3F1
469
terms of the charge density reorgani zati on. The EA u,
an attracti on term, increases on B and th at decreases
on F. The E/ , a repul sion term, dec reases on B but
increases on F. The EAK , an attracti on term , increases
on B but decreases on F. This pattern of differential
variation of th e components of the one-center energy
finds justificati on in th e .nature of variat ion of charge
density on B and F centers with th e evolution of
I8 25
geometry of the mo lecul e . .
Table 4 reveals that the F----F non-bonded
interaction increases stead il y with th e evo luti on of
molecu lar conformation. This pattern of va ri ati on of
the non-bonded interaction fi nds just i fication in th e
fact that as the geometry evol ves in th e process, the F
atoms become closer and closer to each other. The
EAt/ and EAl/ terms increase sharpl y (Tab le 4) w hil e
v
K
the E;\/J component decreases sharp ly and the E;\u
term dec reases ex tremely slow ly. Th e resonance term
EAl/ is al ways repulsive and increases slow ly. The
observed pattern of variati on of the componen ts finds
justifi cation in th e increas ing charge density on F
atom and the decreas ing inter nuclear separati on
between th e non-bonded F atoms w ith evo lution of
geometry during the physical process of structural
reorgani zati on 18 .25
0.0434 a. u. or 11 3.74 kJ/mole which justifi es th e hi gh
reaction barrier of BF] molecul e.
Now the effect of th e dynamic evo lution of
molecular geometry on th e charge density di stributi on
and redis tributi on in the molecule ca n be co nsidered.
Fig.3 reveals that the charge density is depleted from
B-atom and placed on F-atom . The nature of the
charge density profiles shows that the rate o f growth
of charge density on F-atom and that of the decay on
B-atom
Increases
w ith
increase
in
angular
deform ation of the molecul e. Thi s pattern of charge
densi ty red istribution has a deep bearing on the
energetics of the phy sical process of structural
reorgani za tion .
T he energeti cs of the physical process can be
discussed using Fig.2 w hich indi cates that the energy
of th e system increases stead il y and sharply w ith the
process of stru ctural reorgani zation. The total energy
has been di vided into one and two-center components
as a fu nct ion of reaction coo rdin ates in Tabl es 3-5. A
glance at Tabl e 3 reveals th at th e B-center becomes
more unstabl e because its energy increases wh il e the
F-ce nter becomes more stable with th e evo luti on of
th e molecul ar structure. Th e associated nature of
variat ion of th e components of th e one-center energy
terms fully justifi es the trend. The trend of changes of
th e compo nents of th e one-ce nter terms is justifi ed in
From data in Table 5 it is ev iclent that the strength
of the B-F bond decreases contin uous ly with the
,-------------------------------------------------------------------------. - . ~ 4
45
Nu m bers in dicate angles of reorganization in degref:s
107
\OS
te3
-0.95
101
• • • • • • • • • • 97• • 95•
100
104
102
100
98
96
- O ~6
:::J
liS
120
c
o
116
liZ
30
119
Vl
11 7
115
113
12
~
25
>-
111
ci
108
110
109
106
107
-0.97 ;,
104
Ol
95
L..
'"
'"
105
98
% of s-charac to r o f F-hybr i d
97
96
C
-O~8 -0
c
.I:.
o
o
20
.Q
L..
- U9 ~
~
' co
u
e
o
IS
~
10
Tw o center bonded energy
.I:.
u
...
o
-I
- 1.0 1
120
o -'-----------------------------------.---------------------------------------"-
- 1.02
React ion coordinates . (Q» degrees
Fig. 4--P lot o f pl!I'Ccntage or s-cha rac ters o f boron and flu orin c hybrid s and Ihe two ce nter bonded energy as a fun ction of planar to
pyramida l rcorgani zation of boron triflu oride
470
INDIAN J C1-IEM ., SEC. A, M ARCH 2002
Tab le 4--The deco mpos itio n of the two-center F----F non-bonded interacti on ene rgy (a.u.) into its ph ys ical co mpone nts as a
fun cti on of angles of reorga ni zati on.
LF BF in
deg rees
120
119
118
11 7
11 6
11 5
11 4
11 3
11 2
II I
110
109
108
107
106
105
104
103
102
10 1
100
99
98
97
96
95
E ,\II
J
EAB
11.0478
11.1 012
11.1 525
11.2054
11 .2672
11.3304
11.372 1
11 .4387
11.5 146
11 .5686
11.6322
11.6975
11.7722
I 1.833 1
11.9 11 8
11.976 1
12.0422
12. 1266
12.2048
12.2934
12.3758
12.4354
12.5387
12.6 193
12.702 1
12.8045
N
E AB
10.3255
10.3744
10.42 12
10.4693
10.5259
10.5840
10.62 16
10.6826
10.7524
10.80 16
10.8597
10.9193
10.988 1
11 .0435
11.11 57
11. 1743
11.2347
11.3 122
11 .3839
11 .4654
11.5410
11.5949
11.6903
11.764 1
11 .8400
11.9342
V
E AB
-21.36 11
-2 1.4633
-2 1.56 13
-2 1.662 1
-2 1.7805
-2 1.90 17
-2 1.9809
-22. 1083
-22.2539
-22.3570
-22.4785
-22 .6034
-22.7468
-22 .8629
-23.0 136
-23. 1365
-23.2628
-23.4246
-23.5743
-23.7442
-23 .9020
-24.0154
-24.2 140
-24.3682
-24.5267
-24.723 1
K
-0.004 1
-0.004 1
-0.004 1
-0.004 1
-0.004 1
-0.0042
-0.0042
-0.0042
-0.0042
-0.0042
-0.0042
-0.0043
-0.0043
-0.0043
-0.0043
-0.0043
-0.0043
-0.0044
-0.0044
-0.0044
-0.0044
-0.0044
-0.0044
-0.0044
-0.0044
-0.0045
E AB
II
0.0045
0.0047
0.0049
0.0052
0.0055
0.0057
0.0059
0.0062
0.0066
0.0069
0.0072
0.0075
0.0079
0.0083
0.0087
0.009 1
0.0094
0.0099
0.0105
0.0 11 0
0.0 11 6
0.0 11 9
0.0 127
0.0 132
0.0 138
0.0 146
E Atj
0.0 126
0.0 129
0.0 132
0.0 137
0.0 140
0.0 142
0.0 145
0.0 150
0.0155
0.0159
0.0 164
0.0 166
0.0171
0.0177
0.01 83
0.01 87
0.0 192
0.0 197
0.0205
0.02 12
0.0220
0.0224
0.0233
0.0240
0.0248
0.0257
Table 5-T he deco mpositi on of B-F bond energy (a. u.) into its co mponents as a functi on of ang le of reo rga ni za ti on.
L FBF
in deg rees
120
119
11 8
11 7
11 6
11 5
114
11 3
11 2
III
110
109
109
107
106
105
104
103
102
10 1
100
99
98
97
96
95
EA/)
5.7475
5.7449
5.7390
5.7328
5.7303
5.728 1
5.7 155
5.7 125
5.7 134
5.7043
5.6984
5.6922
5.6900
5.6806
5.6778
5.6686
5.6597
5.6569
5.65 13
5.6486
5.6430
5. 6273
5.628 1
5.6 192
5.6 103
5.608 1
J
EAB
7.6637
7.6637
7.6585
7.6532
7.6532
7.6532
7.6374
7.6374
7.6427
7.6322
7.6270
7.6217
7.62 17
7.6 11 3
7.6 11 3
7.6009
7.5905
7.5905
7.5853
7.5853
7.580 1
7.5596
7.5647
7.5544
7_544 1
7.544 1
N
I'
E AB
E AB
- 13.1259
- 13. 1235
-13. 11 37
- 13. 1037
-1 3. 10 14
- 13.0994
- 13.0750
- 13.0722
- 13.0772
- 13.0603
- 13.0506
- 13.0407
- 13.0387
-1 3.02 14
-13.0 189
-1 3.0020
- 12.9852
-1 2.9826
- 12.9732
- 12.9707
- 12.96 13
- 12.930 1
- 12.9350
- 12.9 183
- 12_90 16
- 12.8996
-0. 1837
-0. 1836
-0. 1834
-0. 1832
-0. 183 1
-0. 183 1
-0. 1826
-0.1825
-0. 1826
-0. 1822
-0. 182 1
-0. 18 19
-0. 18 18
-0. 18 14
-0. 18 14
-0.18 10
-0. 1806
-0. 1806
-0. 1803
-0. 1803
-0. 1800
-0. 1795
-0. 1795
-0. 179 1
-0. 1788
-0. 1787
K
/I
E AB
E ,\11
- 1.1 098
- 1.1 088
- 1. 106 1
-1. 1035
-1.1 022
- 1.1 009
-1.095 1
- 1.0939
- 1.0940
- 1. 0896
-1. 0867
- 1.0838
-1 .0822
- 1.0777
-1.0762
- 1.07 16
-1.0669
- 1.0653
- 1.0620
-1.0603
- 1.0570
- 1.0493
- 1.0487
- 1.0439
- 1.0390
- 1.0369
- 1.0082
- 1.0073
- 1.0057
- 1.0044
- 1.0032
- 1. 002 1
-0.9998
-0.9987
-0.9977
-0.9956
-0.9940
-0.9925
-0.99 10
-0.9887
-0.9873
-0.985 1
-0.9825
-0.98 11
-0.9789
-0.9774
-0.9752
-0.97 18
-0.9704
-0.9678
-0.9650
-0.9630
GHOSH el 01.: QUANTUM C H EM ICAL STUDY OF STRUCTUR AL REORGAN IZATI ON OF BFl
evoluti on of geometry. The stretching of the B-F
bond and th e suggested type of geometry evoluti on is
the mos t important aspec t of the chemical reactivity
of BF} mol ecule. A closer look at Tabl e 5 reveals th at
N
although the repulsion com ponents, EI\/, E/\IJ
decrease to some extent, the attraction co mponents
increase stead il y with the deformation of molecular
geometry resulting in the overall decrease of strength
of the B- F bond. The observed variati on in th e
strength of bond is due to th e co nj oint effec t of
and
charge
density
reorgani zation
stretching
assoc iated w ith the change of shape of the mol ecule.
l7
Coul son sugges ted th at th e variati on in th e strength
of th e bond and th e perce ntage of s-character of th e
hybrids fo rmin g the bond in molecul ar co nform ati on s
should be co rrelated. The percentages o f s-characters
of the hybrids on Band F centers are co mputed as a
functi on of stru ctural reorgani zati on. Th e percentage
of s-character or th e hybrids and th e energy of th e
bond are pl otted as a func ti on of react ion coordinates
in FigA. A close scrutin y of Fi gA reveal s th at th e
percentage of s-character of hyb rids on both the atoms
form ing th e bond decreases slow ly but th e strength of
the bond decreases sharply with evolution o f
geometri ca l shape. Thu s th e co mputed va riati ons o f
th e strength of B- F bond and th e percen tage o f scharacter o f th e hybrids forming th e bond is in
accordance with the general observati on of Coul son 17
in similar occasions.
Thu s the theoretical study of th e phys ical process
of structural evol uti on of BF, molecule from th e
equilibrium shape prior to th e event of chemical
reacti on can suppl y necessary inform ations regardin g
the energetic , kin eti c and structural aspec ts required
for the co rrelation o f its chemica l reac ti vit y. A
number of di ve rse param eters are co mputed and are
found to be intern::i1ly co nsistent to exp lain th e
stru ctural and energeti c aspects o f th e evo luti on of
molecular shape and to co rrelate th e rcac ti vi ly of the
BF, mo lec ul e.
4
5
6
7
8
9
10
II
12
13
14
15
16
17
18
19
20
Ghosh DC & Jana J, 1111 j qllalllll/ll Chelll. (Communi ca ted).
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chell/ Phy.\', 43( 19(5)S97 : Lbwdin P 0 , Qllallllllll Ihl'on' oj"
(/IOI II S.
2
Lewis G N. Va lcllce 011(1 Ihe slmclll r e oj" ([{O lli S III III
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Pauling L . Till' 1I(/111re oj" chelll i mi bOllil. 3rd Ed n (Corn ell
3
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