CHAPTER VIII
ELECTRON CONFIGURATIONS AND CONCLUSIONS
The object of this chapter is to discuss what
electronic states are expected for the SbF molecule on
a theoretical basis and to compare this theoretical ,
prediction with observations.
Our knowledge of the different electronic states
from observed molecular spectra is complete only for a
few diatomic molecules *
In most of the molecules the
number of electronic states identified from the observed
spectra are not more than three or four.
It is obvious
that an understanding of the electronic states of molecules
must be built upon a prior knowledge of the electronic
states of their constituent atoms.
Wigner and Witmer
(1928), on the basis of quantum mechanics have derived
rules for determining what types of molecular states
result from given states of the separated atoms.
These
rules have been discussed in detail by Mullilten (1930,1932)
and Herzberg (1950),
The manifold of the electronic states can be
.
obtained by bringing together the component atoms of a
molecule (building up principle) or by splitting up the
hypothetical united atom.
We are still lacking an exact
criterion to determine the stability of these molecular
states.
However, mathematical methods have been developed
to express the energy of a given system of two atoms
separated by a large distance (Heitler and London, 1927)
•and it is found possible to infer the nature of the
variation of potential energy U(r) as atoms approach each
other making
r
smaller*
This enables us to determine
whether a state will be repulsive or stable.
On the other hand a procedure analogous to that
for atoms is employed in which the individual electrons
are added one after another to the nuclei and these
electrons occupy themselves certain orbitals.
The
different arrangement of electrons then give the
possible molecular states.
The two atoms that form the SbF molecule belong
to different periods of the periodic table and thus
have very different nuclear charges.
In such a case
the closed shells of the separated atoms need not be
taken into account while assigning electronic configu­
rations to the molecule.
It is sufficient for practical
purpose to consider the electrons outside the filled
shells.
The lowest electronic configuration for the
two atoms in the present case is as follows:
Sb :
F :
K L M N
. 5s2 5p3
spd
r
K 2s3 2p5
where Ki M... represents the closed shells.
In the
Sb atom only the spd sub-groups are filled in the N
shell.
Following Mullilten's (1932) notations, the lowest
electronic configuration for the SbF molecule may be
written as
(k k l m NSpd)(zo“)2(ycr)2(xcr)2(wTr)4(vi?)2
(1)
where (zar) and (yer) represent respectively the bonding
and antibonding orbitals of the type (5sfir*sl;+2s<rp,S') and
(5sS^b-2s<S^,i S’) , (x<5) represent the bonding orbital of
the type (5p(j^b+2p<5|,, €) and (wfl) and (vtr) represent
respectively the bonding and antibonding orbitals of
the type
(5P?CSJ;)+2P%> TO
and ( 5p^b-2pKF,7l) .
This
Q __
configuration gives the electronic terms
of which
3
»
A
X »
A.and
X
—
jL
Hund* s rule.
is expected to lie lowest according to
3
This low-lying X state must be the ground
-
state of the molecule.
The probable low-lying electronic levels of the
molecule SbF can also be derived from the low-lying
electronic levels of the separated atoms Sb and F, The
ground state of the molecule is expected to dissociate
4
2
into Sb( Sg^>) and F( P0y9) atoms which represent respecti­
vely, the ground state of the Sb and F atoms.
The electronic
terms that can be derived from Sb( 4 s) + F( 2 P) atoms are
V» 3_n> 5x
and \f.
A consideration of the problem
from the approach of the united atom will help us to find
out which of these four states are low lying states. The
electronic terms of SbF molecule are expected to be quite
similar to those of the NF molecule, as Sb belongs to the
same group of the periodic table as N.
Nitrogen has seven
electrons with the configuration Is 2 2s 2 2p 3 and Fluorine
has nine electrons with the configuration is
2
2s
2
5
2p «
169
The molecule NF can be supposed to have been formed by
splitting the united atom Sulfur which has sixteen
electrons.
The electronic terms of the molecule that
result by splitting the sulfur atom in its low-lying
3
P0 . n
states are
3
—
XI and
3
TT«
These two states
are expected to lie lowest of all the electronic states
of the NF molecule and therefore also of the SbF molecule.
Of the four different states ^X > ^7T>
and ®TT
that are derived from the separated atoms Sb( 4 S)+F( 2 P) ,
:
only
3
-
X,
and
3
_
n can be expected to be stable as these
only can be correlated to the corresponding lowest states
derived from the united atom approach.
The
X
and
TT
states are expected to be higher and are probably repulsive,
as these cannot be derived from the low-lying
states of the united atom*
3
The conclusion that
states lie lower than 5—5
X and TT
1
1
P, S or D
3
—
JZ
and
3
Tf
states is in agreement
with what one expects from the generalization of the Heitler
London theory for complex cases.
Thus considering the correlation of the separated
and united atom approaches it is clear that the 3 X. and 3 TT
-
are the low-lying states of the SbF molecule and that they
dissociate into Sb( AO
s) and F( p) atoms.
Of these,
2
X— is
170
3 —
jr state which arises from
to bo correlated with the
the lowest electronic configuration (zo) 2 (yC) 2 (xcr) 2 (w7T) 4 (vJt) 2
and which is the ground state of the molecule,.
The other two terms
1 4
£
-
1
and
&
that are derivable
from the same configuration cannot dissociate into
Sb( 4 S) + F( 2 P) atoms and go to higher dissociation limits,
The first excited state of Fluorine above the ground
3/2
l/2 at 404 cm
i
„
This
2
P.jy2 s^ate
1_+
jjT
Fluorine would not provide the two molecular states
and
1,
£
when combined with
4
state of Sb atom and the
next excited states of Fluorine have too high energies to
be considered*
and
2
The next excited states of Sb are
at 8511.9 cm
—1
and 9853,5
The combination of Sb in the
ground
—1
cm
respectively.
D state and Fluorine in its
2„
F state would give rise to singlets and triplets
oisha), 2.‘,ir(3),AC2),<t>
viz.
2
D^y^
1 +
1
jr and &
states.
The two singlet term
which can be derived from the ground
state configuration of the molecule can be correlated with
the states derivable from the combination of Sb in its
first excited state
2
D and F in its ground
Thus out of the three states viz.
2
P state.
and
*
which can be derived from the ground state configuration
of the SbF molecule, the
£
state which is the ground
172
state of the molecule will dissociate into the normal
n + F( 2 p)
Sb( 4 3)
atoms and the remaining two viz. 1 A and
1 +
2
jr will dissociate into Sb in its first excited D
x
2
state and F in its ground P state.
The first excited state configuration of the SbF
molecule may be written as
( K K L M Nspd)(z(j)2(y(r)2(x{r)2(w7T)3(v7l)3
(2)
This configuration gives rise to the following terms:
1 —» +
X
i
3_+
X
)
1 _r
X )
3_r
X j
1*
«>
The upper states of all the visible systems of the SbF
molecule for which the vibrational constants are very
near can be attributed to the electronic levels arising
from the above configuration.
The reduction in the
vibrational frequency of each of the upper state,, of the
visible systemsrelative to the ground state is in harmony
with the fact that in this configuration an electron goes
from a bonding (w/r) orbital to the corresponding antibonding (vjt) orbital.
The electronic states arising from the above
configuration can be correlated with the atomic states
172
of the component atoms if the Sb atom is considered to
2 state and Fluorine in its
be in its second excited "'P
ground state.
is at 2P1^2 = 16394
Combination of this
ground
2
2
The second excited
2P3//2
cm-1 and
2
P state of Sb atom
= 18463 cm-1,
P state of the Sb atom with the
P state of the Fluorine atom gives rise to the
following electronic terms:
2P(Sb) + 2P(F) — 1Z+(2)
,1f‘,17r(2)
,1A,3Z+(2)>32",37r(2),3^.
All the electronic states arising from the first excited
state configuration of the SbF molecule (eonfiguration-2)
can be correlated with the above electronic levels and
hence the upper state of all the visible systems can be
expected to be dissociating into Sb in its second excited
2
P state and F in its ground state.
The second excited state configuration of the SbF
molecule can be written as
p
o
(K K L M N d)(z<r) (yff) (xff)
spd
o
a
(wit)
i»sr) - 1ir,3irr
± %
(vTl) ..
o
x(nps) - V
(3)
in which an electron goes from an antibonding (vjf) orbital
to a non-bonding
ns$”
or npy
orbital of the Rydberg type.
The molecular states arising from the above configuration
173
are expected to show an increase in the vibrational
frequency relative to the ground state.
of all the ultraviolet systems (B,
The upper states
, C2 and Cg) which
show an increase in frequency relative to the ground state
can be attributed to the molecular levels arising from
the above configuration.
The vibrational and rotational constants derived
for the different electronic levels of the SbP molecule
from the present study are collected in Table XXIX and
Table XXX respectively.
From the rotational analysis of the 0^ system, the
lower state X2 with a frequency 615.95 cm
confirmed to be the
state configuration«
1
-1
has been
A state arising from the ground
Out of the three states arising
from the ground state configuration
the ground state of the molecule.
3 X is expected to be
The structure of the
C2 system consisting of two close components rules out
the possibility of attributing the lower state X^ to the
ground
X.
state as was done by Rao and Rao (1962),
The most probable electronic transitions for the
various band systems of the SbF molecule can be best
illustrated with the energy level diagram given in Fig.15
(not to the scale) .
,
X?
Tx
X,
_ %
B
H
X
.
-
New system
—
IT
3
A"
—
-
+ T
3s T
V
V
X
+ I
3
New system
3
+ 8
A'
A°
3130-3340
3300-5000
3620-5070
4200-^5000
4050-5450
4730-5770
XX
22588,64
20004,73
Faint system 31099.25
with bands
degraded to
shorter wave
length side,
ban ds
Red degraded 27910,44
Most intense 23993.53
system with
red degraded
bands
bands
Red degraded 21885.21
bands
red degraded
Intense
Faint bands
degraded to
red.
cm
700,96
412,15
420.37
415,36
418.93
417,79
cm
T-
“ >'e
2.89
11,88
1,76
2.44
2.64
2,42
cm
I-
c
r
Nature of
the bands
CD
i
Region
X
i
a a
Electronic
transition
contd
612,62
612.50
612,47
615.60
2.36
2.55
2.57
2.59
2,61
2,54
608.70
608.83
cm
cm
09
System
designation
T-
0
I
I
SPECTROSCOPIC DATA OF THE SbF MOLECULE FROM THE PRESENT STUDY (VIBRATIONAL)
T-
_
uXi9.09
0
-n
J
C3
-
xa
X3.
TTC
or
1
—
T
T
II
il
%
% —
Ci
A
Electronic
transition
1
UJ.
TL
T
+
%
+
System
designation
2200-2430
2200-2430
2200-2430
"
side
Degraded
to shorter
wave length
si de .
Intense
bands
degraded
to shorter
wave length
2530-2770
A0
Nature of
the bands
n
Region
44747.78
43517.73
43514.11
37937.57
cm
c
r
701.67
701.44
700.90
697.81
cm
e
oil
TABLE XXIX (contd.)
3.00
2.93
2.80
1.37
cm
e e
C0’X»
608.95
612.59
612.59
615.63
cm
Cd
2.63
2.61
2.61
2.54
cm
(jQ"X»
e e
175
i
i
|
i*h
11
i a
1 o
1 -—
1
1 o*
1
1
1
KO -H
1I t
cn i o a
1 , -H O
1 w
1 >
CO 1 C|
Cd 1
■H&
Tfl
1
o
rH
H
CO
00
ft
o
a
*
o
o
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oe
o
+1
30
to
OD
03
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a
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cq
>
•
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mo
03
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o9
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+1
00
03
t~
CM
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II
CQo
v*i
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T-l
•
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t•H
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■H
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ri<
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ft
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<$'
tH
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30
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+1
t-
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4:’
to
03
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CM
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CPt3
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ft
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to
00
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CM
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CO
le­
ft
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ft
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+i
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to
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ft
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cq
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30
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ft
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o
o o
II
11
o pf1
•H
1_
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l
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tol
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00
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•
ft
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1 1
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■H'O
>
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»
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o
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03
03
■H
*
o
t■H
•
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’tjt
O
o
o
ft
o
+1
. to
00
03
30
CO
o
o
o
•
o
41
tto
O
o
o
ft
o
+
1
CM
T"!
03
CM
o•
1
30
T-l
*
o
lO
•
o
O
o
o
ft
o
4l
30
to
-H
CO
o•
it
cq<5
o
o
o
ft
o
+!
30
toO
C
o•
IIo
•H
vH
Cd
pH
pCO
Q
rH
1«
a
o
at
le v e l
E le c tr o n ic
MOLECULE FROM THE PRESENT STUDY (ROTATIONAL)
SbF
SPECTROSCOPIC DATA FOE FEW ELECTRONIC LEVELS OF THE
176
o
o
o
■ft
o
+1
00
00
03
•
o
II
o
cq
‘w
CO
"'tc
V
o
+1
to
"Stf
o
o
o
6
O
+1
co
CM
t03
♦
O O
II
II
m° v-i
«
0M
£
CM
M
03
03
CM
ft
o* o
II
11
o
m pf4
+H
tH
H
CO
1
CM
•
o
lio
m
'p
tH
■H
O
O
pq
*H
co
CM
O
o T^
!=■£
CO
o
cm
TT
701-44
o
700-90
M
Cj 701-67
1TT
Ct 697-61
%
B
700-96
•As 411-15
A?
■A^
.*«
■ A'
*X
ȣ
!r
V
A
±
i
*X‘
JUL
42.0-37
415-36
416-93
417-79
*1
612-55
*2
615-62
X3
606-83
Fig 15
Proposed eTiergy level diagram (not to scale)
JBand systems oj SbF molecule.
177
The nature of the A -doubling and the fall in
intensity of the rotational lines near the origin have
shown that the upper state of the
system can he
attributed to a 13
state or the
component of a 3 JJ
state.
system being the most intense amongst the
ultra\aolet systems, it seems more probable to attribute
an allowed electronic transition 1 TT —
than a forbidden
3
1
1
A to the system
transition,
The assignment of an electronic transition
IT —
51 +
to the C2 system demands that the lower
state of the Cg system must be the ground
the molecule.
3 —
2T state of
This is further supported by the results
obtained from the absorption study on the BiF molecule
(joshi 1961).
The corresponding Cg system of BiF molecule
has been observed in absorption.
An exact decision regarding the nature of the upper
state of the Gg system cannot be taken from the information
obtained from the present study.
The rotational analysis
of the Cg system has shown that the upper state can be
either a 1 TT
state or a component of 3 TT state.
the nature of the observed
/\
How far
-doubling in the upper state
of the Cg system helps the determination of the exact
nature of the state has been discussed earlier in Chapter VII,
i 78
The observed nature of the A -doubling suggests that
an electronic transition of the type
1
Tf—
3 £ Cari 136
ascribed to the system as was done in the case of the
corresponding Cg system of BiP molecule by Chaudhry
et al . (l969).
The intensity distribution of the branch
lines near the origin needs a special mention here. In
the case of
and Cg systems a marked intensity fall
is observed in the positions corresponding to the missinglines in the P branch.
system is a
1
If the upper state of the Cg
Jf state an intensity fall is expected for a
line in the P branch on the longer wave length side of
the band origin.
But no such intensity fall has been
observed for the line in the P branch near the origin.
This can of course happen if all the P branch lines
corresponding to very low J values are very poor in
intensity.
As there is no fall in intensity for any of the
branch lines in the neighbourhood of origin the other
possibility of ascribing the upper state of Cg system
3
to the
7f0
3
component of a
TT
state cannot be ruled out.
In that case the Cg system can be attributed to an
allowed 37T0 — 3 X—
of the
transition.
The observed nature
A-doubling cannot be used to rule out this
179
possibility as the coupling in the upper
3
TT state can
even be expected, to be very near to Bund’s case (b).
If the upper state is a
3
7Tq component, the absence of
the other two expected close components viz.
and
3
1T2 —
3 —
3
7T^ —
3 —
21
cannot be explained.
Attempts to record the rotational structure of
the B system of SbF molecule failed because of its very
poor intensity.
The lower state
of the B system,
common to the Cg, Ag and Ag systems, has been identified
1 +
as the £ state arising from the ground state configu­
ration from the rotational analysis of the C2 system.
An electronic transition of the type
attributed to the B system, the upper
dL
7f—
1
i
21 may
fT state arising
from the same upper state configuration (configuration-3).
All the visible band systems may be attributed
to the allowed electronic transitions as shown in Fig.15,
From Fig.15 it is clear that the separation between the
levels
, X2 and Xg are -still uncertain and hence the
positions of all the excited states except the upper
state of A', A" and Cg systems above the ground state
cannot be fixed
It may be concluded here that the present
investigation has given much information regarding
the nature of the different electronic levels of the
SbF molecule.
The identification of the third lower
state Xg has established the spectroscopic similarity
of the two molecules SbF and BiF.
In addition to
this new lower state Xg, two more new excited states
(the upper states of A* and A" systems) have been
identified from the present study.
The rotational
analyses of the different band systems have shown that
the three lower states X^ , X2 and Xg are to be attri­
buted to the three different electronic levels arising
from the ground state configuration of the molecule
and not to the three different components of a 3 21 state
as suggested by Joshi (l96l) and Rochester (l96l).
Future plan of the work;
The spectroscopi'c similarity of the two molecules
SbF and BiF is excellent as far as the ultraviolet
systems are concerned.
In the visible region of BiF
molecule only one band system (a2 system) has been
established with certainty.
It is planned to undertake
a study of the emission spectra of the BiF molecule in
visible region in search of the remaining corresponding
181
band systems which are observed in the SbP molecule.
Work in this direction has already started in this
laboratory and interesting results have been obtained.
It is also planned to carry out an absorption
study ol the spectra of SbF molecule in order to
establish with certainty the proposed ground state of
the molecule