J . Phys. Chem. 1987, 91, 5 166-5 169
5166
ARTICLES
Low-Lying Electronic States of Se,
K. Balasubramanian*
Department of Chemistry, Arizona State University, Tempe, Arizona 85287 (Received: September 19, 1986)
Complete active space MCSCF (CASSCF) followed by first-order CI (FOCI) calculations are carried out on 20 low-lying
electronic states of Se2. The spin-orbit interactions for some of these electronic states are introduced through a relativistic
configuration interaction scheme. Among the calculated states without spin-orbit coupling 15 electronic states are found
to be bound for which spectroscopic properties are calculated. These calculations enable the assignment of the experimentally
observed X, b, a, A, and B states. A number of new electronic transitions among the calculated electronic states are predicted
which are yet to be observed.
1. introduction
There is considerable interest in the electronic structure and
' ground
spectroscopy of group VI (group 16) d i m e r ~ . I - ' ~ . ~The
state and a number of low-lying excited states of the lighter
analogues namely 0, and S2are well characterized now. In 0,
the first allowed strong electronic transition, B3Z,--X3Z; gives
rise to the well-known Schumann-Runge bands, which occur in
the UV region. The ground state (X) of the lighter analogues
is the 3Z; state. For heavier dimers such as Se, and Tez, the
spin-orbit interaction may become more important (especially
for Te,) and the separation of the excited states from the ground
state shrinks. Thus, electron correlation and configuration interaction become more important for the heavier dimers.
The Se, dimer has been studied by a number of investigator^.^"
The earlier works on the spectroscopy of Se2 are summarized in
ref 3. The 0, analogues of the Schumann-Runge bands which
are attributed to the B-X system are observed in the region of
26000 cm-'. These bands are found to be perturbed by an A
state.]' The B-X and A-X as well as a-x systems have also been
observed in the matrix by Bondybey and E n g l i ~ h .Prosser
~
et aLI0
have observed a BO,+-b IZg+system by populating the B and A
electronic states with a 4131-A krypton ion laser. In addition,
a c-X system is also observed in the region of 53 000 cm-'. At
present, below 26000 cm-', five A-s states and some of their
spin-orbit components of Se, have been observed. These states
are designated B, A , a, b, and X states. Among these B, A, b.
and X states have been tentatively assigned.
The nature of the state perturbing the B3Z,- state is not
well-known. This has been the subject of many
Further, unlike O,, the nature of electronic states below the B
state is not clearly understood. Theoretical investigation of the
low-lying electronic states of Se, can thus be extremely useful in
not only assigning the observed electronic bands but also in
predicting several new electronic transitions which are yet to be
observed. The main objective of the present investigation is to
shed light on the low-lying electronic states of Se,. W e assign
the experimental spectra by a comparison of calculated and observed values. More detailed theoretical analysis would be needed
to understand other features of the potential energy curves such
as curve crossings and predissociation. Saxon and Liu30 have
shown that such theoretical calculations yield reasonable spectroscopic constants for O2even if errors in D,may be appreciable.
Theoretical investigation of molecules and clusters of heavy
atoms is a topic of considerable activity in recent
Relativistic effects such as mass velocity, Darwin, and spin-orbit
corrections make significant contributions to the electronic and
*Alfred P. Sloan Fellow: Camille and Henry Drelfus Teacher-Scholar.
0022-3654/87/2091-5166$01.50/0
TABLE I: A Few Low-Lying Electronic Configurations of Se2 and
A-s and w-w States Arising from Them"
electronic confign
A-s
states
w-w
states
0;+
3,, 2,. 1,
3Z"3Z"+
'A"
0,-,I,
9"'
2,
O"+
'4
""
O"+, 1,
I,. 2,, 3"
I"
o"-,
4
O"+
"The lu,*luU2shell arising from the valence s is now shown
TABLE 11: Dissociation Relationships for a Few Low-Lying States of
Sez
atomic energy of
molecular states
states the atoms4
"Energies in cm-l
spectroscopic properties of such molecules. A systematic study
of the low-lying electronic states of dimers of heavy atoms would
( 1 ) Bondybey, V. E.; English, J. H. J. Chem. Phys. 1978, 72, 1865.
(2) Bondybey, V. E.; English, J. H. J. Chem. Phys. 1980, 72, 3 1 1 3 .
(3) Huber, K . P.; Henzberg, G. Consranrs of Diatomic Molecules; Van
Nostrand: Princeton, NJ, 1979.
(4) Ricks, J. M.; Barrow, R. F. Can. J . Phys. 1969, 47, 2423.
(5) Bondybey, V. E.; English, J. H. J . Chem. Phys. 1982, 76, 2165.
(6) Barrow, R. F.; Chandler, G. C.; Meyer, C. B. Philos Trans. R. Sot.
A . 1966, 260, 395.
( 7 ) Gouedard, G.; Lehmann, J. C. J . Phys. B. 1976, 9 , 21 13.
(8) Ibbs, K. G.; McCaffery, A. J. J . Chem. Soc., Faraday, Trans 2 1981,
77, 631, 637.
(9) Bondybey, V. E.; English, J . H. J. Chem. Phys. 1980, 72, 6479.
( I O ) Prosser, S. J.; Barrow, R. F.; Verges, J.; Effantin, C.; d'Incan, J. J .
Ph.vs. B 1980. 13, LS47.
0 1987 American Chemical Society
Low-Lying Electronic States of Se2
The Journal of Physical Chemistry, Vol. 91, No. 20, 1987 5167
TABLE 111: Valence Gaussian Basis Set Employed for the S e Atom'
type
exponent
type
exponent
type
exponent
s
1.340
0.3717
0.1322
p
p
p
2.1420
0.3854
0.1195
d
0.25
s
s
4 T h i s basis set was optimized for the 3P ground state of S e atom as
reported in ref 27.
TABLE I V Number of Configurations Included in the CASSCF and
FOCI Calculations of Se2
.
state
CASSCF
FOCI
'A,
3A2
'BI
'B,
104
96
96
80
7304
10752
10680
7136
" T h e configuration counts a r e in C, symmetry.
certainly provide significant insight into the electronic properties
and bonding of these clusters. The present investigation on Se,
is undertaken for the above reasons. Section 2 outlines the method
of our investigation. Section 3 contains the Results and Discussion.
0 13(
0 11(
0 09c
0 07(
0O
X
0 03(
0 01(
0
-0 01c
-0 03(
2. Methodology of Calculations
Table I shows a few low-lying electronic configurations of Se,
and the A s and o-o states arising from them. As seen from Table
-0050
I, the most probable candidate for the ground state of Se, is the
32; (0,)'
state arising from the l u ~ l ~ , ~ 2 u ~ ~configul r , ~ l r ~
ration. Promotion of a ru
bonding electron to the r, antibonding
-0070
orbital leads to a number of u states among which the 3 X ; state
is the most important one from experimental standpoint since the
32;-38, transition is an allowed electric-dipole transition. Table
-0 090
I1 shows the dissociation relationship of some of the low-lying
electronic states. This table gives an idea on how many low-lying
-0 110
molecular electronic states exist for Se2 which dissociate into the
ground state or low-lying excited states of atoms. As one can see
from Table I1 there are a large number of low-lying electronic
R (A)
states many of which could be bound.
Figure
1.
Potential
energy
curves
of
some low-lying states of Sez.
We first carry out M C S C F calculations to generate orbitals
for configuration interaction calculations. These calculations were
space of orbitals. For Se,, we included all the orbitals which
made with relativistic effective core potentials treating the outer
correlate a t infinite separation into 4s and 4p atomic orbitals of
s2p4shell of the S e atom as the valence shell. Gaussian fits of
the selenium atom. In Dmhsymmetry, these are 1ug, 1uur2u,, 2uu,
relativistic numerical potentials of Se atom have been reported
lx,, and lx, orbitals. CASSCF and C I calculations were carried
by Hurley et aL2' These authors have also obtained a 3s3p valence
out in the C, symmetry group. The molecule was oriented along
Gaussian basis set optimized for the 3Pground state of the Se atom
the z axis which was also chosen as the C, axis. In this orientation,
which is shown in Table 111. To the (3s3p) set we added a d
the active space consisted of 4al, 2b2, and 2bl orbitals.
polarization function with the exponent shown in that table. The
Configuration interaction (CI) calculations were carried out
d exponent was optimized for the ground state of Se2 a t its
following the CASSCF. The C I calculations carried out were
equilibrium geometry. The M C S C F calculations were carried
first-order C I (FOCI) calculations. The FOCI calculations inout using the complete active space M C S C F (CASSCF) method.
cluded all configurations in the CASSCF (12 electrons distributed
In this method, valence electrons are distributed in all possible
in all possible ways in the internal space) and the configurations
ways among a chosen set of orbitals referred to as the internal
generated by distributing 11 electrons in the internal space and
one electron in the orthogonal external space in all possible ways.
(11) Jenouvrier, A. Can J . Phys. 1983, 61, 1531.
The dimensions of the CASSCF and FOCI spaces are shown in
(12) Ahmed, F.; Nixon, E. R . J . Mol. Spectrosc. 1980, 83, 64.
Table IV. It has been demonstrated that CASSCF/FOCI ap( 1 3) Krishnamachari, S.L.N.G.; Venkatachalam, T. V. Chem. Phys. Lett.
proach yields reasonable results (75-95% of the true values) for
1979, 67, 69.
(14) Winter, R.; Barnes, I.; Fink, E. H.; Wildt, J.; Zabel F Chem. Phys.
the main-group dimers.21~24~25
The CASSCF/CI calculations were
Lett. 1980, 73, 297.
carried out by the present author's28 modification of ALCHEMY
(15) Heaven, M.; Miller, T. A,; English J. H.; Bondybey, V. E. Chem.
II package29of codes to include relativistic effective core potentials.
Phys. Lett. 1982, 91, 251.
Spin-orbit interaction is introduced to some of the electronic
(16) Yee, K. K.; Barrow, R. F. J . Chem. Soc., Faraday Trans. 2 1972.68,
1181.
states of Se, (32;, 'Zgf, 311,(0,+),311,,(1,,)) with the objective of
(17) Drowart, J.; Smones, S. J . Chem. Soc., Faraday Trans 2 1977, 73,
estimating the effect of spin-orbit interaction. This is introduced
-
1755.
(18) Pitzer, K . S.Ace. Chem. Res.
1979, 12, 271.
(19) Pitzer, K. S. Int. J . Quantum Chem. 1984, 25, 131.
(20) Krauss, M.; Stevens, W. J. Annu. Reu. Phys. Chem. 1984, 35, 357.
(21) Basch, H.; Stevens, W. J.; Krauss, M . Chem. Phys. Lett. 1984, 109,
212.
(22) Hay, P. J. J . A m . Chem. Sor. 1981, 103, 1390.
(23) Cohen, J. S.; Wadt, W. J.; Hay, P. J. J . Chem. Phys. 1979, 71, 2955.
(24) Balasubramanian, K. J . Mol. Spectrosc., 1987, 123, 228.
(25) Balasubramanian, K. J . Chem. Phys. 1986, 85, 3401.
(26) Balasubramanian, K. J . Chem. Phys. 1986, 85, 1443.
(27) Hurley, M. M.; Pacios, L. F.; Christiansen, P. A,; Ross, R. B.; Ermler,
W. C. J . Chem. Phys. 1986, 84, 6940.
(28) Balasubramanian, K Chem Phys. Lett. 1986, 127, 5 8 5 .
(29) The major authors of the ALCHEMY I I codes are Liu, B.; Yoshimine,
M.; Lengsfield, B.
(30) Saxon, R. P.; Liu, B. J . Chem. Phys. 1977, 67, 5432.
(31) In this paper the periodic group notation in parentheses is in accord
with recent actions by IUPAC and ACS nomenclature committees. A and
B notation is eliminated because of wide confusion. Groups I A and IIA
become groups 1 and 2. The d-transition elements comprise groups 3 through
12, and the p-block elements comprise groups 13 through 18. (Note that the
former Roman number designation is preserved in the last digit of the new
numbering: e.g., 111 3 and 13.)
-
5168 The Journal of Physical Chemistry, Vol. 91, No. 20, 1987
through a relativistic configuration interaction scheme. In this
method low-lying w-w states of the same symmetry are mixed in
a relativistic C I scheme. Since our relativistic CI code is set up
for Slater-type orbitals, we optimized a double-zeta STO basis
set for the 3P ground state of the Se atom. The w-w states arising
states were obtained by using the orbitals
from 32;, ]A,, and
generated from S C F calculations of the 3Z,- state. The w-w states
arising from 311uand In, states were calculated by using the 311u
S C F orbitals since 3Z; SCF does not produce a good 2u, orbital
as this is unoccupied in the ' 2 ; state.
The relativistic CI calculations of the 0
,
' state included single
and double excitations from Cartesian reference configurations
arising from l u 2 1 u , 2 2 u g 2 1 r u 4 1 r g 2 ( 3 2 , - , 'Z,'),
and
1 ~ ~ 1 0 , ~ 2 ~ , 1 r B, ~(311,).
1 r , The 1, state included five reference
configurations arising from ' 2 ; (I,), 311,( l & and In, (1,). The
2, state included eight reference configurations arising from 'A,
and 'II,. W e also carried out relativistic C I of the ,',O I,, and
2, components of the lIIUstate. The 0
,
' state included limited
single and double excitations from 24 reference configurations
arising from a number of 311ureferences and 3L;[ references. The
1, state calculations included 3rIu,In,, and 3Zu+references, while
the 2, calculations included only 'nu references.
3. Results and Discussion
Table V shows calculated spectroscopic properties (Re,Te, and
we) of low-lying electronic states of Se,. The potential energy
curves of some of these states are shown in Figure 1. As one can
see from that table the ground state (X) is the 3Z; state arising
from the 1ug21u,22ug217r,41~g2
configuration. The discrepancies
in calculated Re and we values of the ground state are within
3%-6% of the experimental values. The w,'s of the various states
in Table V were calculated by using a cubic polynomial fit of
energies at near-equilibrium geometries. The small discrepancy
between calculated and observed values arises partly from the
errors in fits (usually within *15 cm-I) and partly from higher
order correlation corrections and basis set effects which influence
the o, values.
The strongest electronic transition originating from the ground
state is the B3Z;-X3Z;
system. The calculated properties of the
32; state are in very good agreement with the spectroscopic values
confirming the earlier assignment of this system.
There have been a few experimental investigations which have
revealed the existence of other electronic states below the B state.
Specifically, the A state in the A-X system has been identified
by Heaven et al." The Te value of A state reported by these
authors is about 24 11 1 cm-l. Our calcdations reveal the existence
of a 311u(
0
,
'
) state with a calculated Te of 21 277 cm-' in this
region. Thus the A state is most consistent with 311,(0,'). The
311u
state is split into 0
,
'
. ,;O l,, and 2, substates by the spin-orbit
interaction. The 3n,(0,') could mix with 3ZU-(Ouf).However,
our relativistic CI calculations show that this contamination is
negligible for 311u(Ou+) a t its equilibrium geometry. Similarly the
'nu(l,), 3Z;(l,), and lII,(lu) states could mix in the presence
of spin-orbit interaction. However, the splitting of electronic states
due to spin-orbit interaction, is relatively small for the selenium
dimer. This is discussed further later. Our calculated Re value
for the A state does not agree well with the value calculated from
the experimental spectroscopic data. The 'II, state is weakly
bound and its surface is shallow. The basis set which we use in
conjunction with effective core potentials do not appear to be
sufficient to calculate especially the Re and we values of weakly
bound excited states with reliable accuracy. Also, diffuse basis
functions and polarization functions may be important for the 311u
and '11, excited states.
Bondybey and English' have observed bands with a Te value
of 16 321 cm-' which they attributed to a weak electronic transition. (These authors call this a-x system, although this designation could also bc used to the 4000-cm-' system.) Our calculations reveal a '-1, state in the neighborhood of the observed
electronic bands. The calculated and observed w, values are also
in very good agreement. Further, the 'A,
3Z,- transition is
dipole-forbidden supporting the experimental observation that
-
Balasubramanian
the electronic bands are weak in this system. The above reasonings
lead to the assignment of this system to the 3A,-3Z,- forbidden
transition.
An electronic state (b) with a Tevalue of 7958 cm-' has been
characterized by Prosser et a1.I0 as well as Winter et al.14 Prosser
b fluorescence
et aLI0 have observed the b state in the BO,'
by populating the excited B state with a krypton ion laser. Winter
et
have observed the near-infrared b X32; emission system.
The b state has been tentatively assigned to the '2,' electronic
state. As seen from Table V our calculations support this assignment. The fqct that the calculated T, and the observed Te
values of this state are in excellent agreement and that there is
no other electronic state with this Te value enables unambiguous
assignment of the b state to the IZg+ state arising from the
I ag21uu22ug217r,41ag2
configuration.
Yee and Barrow16 have studied the absorption and fluorescence
spectra of gaseous Sez. The fluorescence series in the 5 145-4880-ii
a
region observed by these authors were assigned to a n
transition where the upper state is believed by these authorsI6 to
be a relatively weakly bound 1, state which perturbs the B3Z;(0,+)
state. The a state is predicted to be approximately 4000 cm-'
above the X3Z;(0,')
ground state and was tentatively assigned
to ]Ag based on lower vibrational frequency of this state in comparison to the ground-state we. Our calculated spectroscopic
properties for the 'Ag(2,J state reported in Table V certainly
support this assignment. However, the experimental w e value of
320 cm-l does not follow the theoretical trend in Table V which
implies that the w e value of the ' A (*g) state should be about 20
cm-' less than the w e value of the 'Z;(O,+,l
) states. While the
spinvorbit coupling lowers the Tevalue of the f 1,state by 95 cm-l,
it does not change Re and w e values a t all. This is primarily a
consequence of the fact that the 'A, state is not contaminated with
other A-s states which give rise to 2, w-w state such as 311g.While
it is possible that small errors could be introduced by the procedure
we use to calculate wes by fitting energies by a cubic polynomial
in the near-vicinity of the equilibrium geometry, we rule this out
based on the fact that identical distances were used for all the
four states namely, ,'O I,, 2,, and O,'(II). Thus, the experimental
we value of the a('$) state (320 cm-') is somewhat low and should
be about 368 cm-' which we arrive at by decreasing the experistate by 19 cm-' as implied by
mental w e value of the 'Z;(l,)
the theoretical calculations.
The we of the XIOg' state is slightly smaller than that of the
X21, state. The Re and w e values of the 1, state in fact are the
same as those of ' 2 ; state obtained in the absence of spin-orbit
,
' state is
interaction implying a parallel shift. However, the 0
a mixture of 3Zg-(81%) and '2,' (8%) A-s states in the vicinity
of equilibrium geometry. The Re value of the 'Eg' is larger than
the corresponding value for 32; state while the we value is smaller
than that of the 32; state. The Re and o,values of the 32; and
IZ,' states when weighted with appropriate spin-orbit contaminations (81%, 8%) are in accord with the theoretical Re and or
values for the X,O,' state in Table V.
Jenouvrier" has studied the perturbations of the bands in the
B(3Z,-(0,+))-X system. It is unfortunate that one of the states
which perturbs the B state is designated A, while the same symbol
is used to designate A3II,(OUf). The A state which perturbs the
B state was assigned to A311,(1), by Jenouvrier." W e will refer
to these two states with their quantum number in parentheses.
The A3n,(l,) state is about 1000 cm-' below the BO,+ state.
There is also another state designated A' assigned to A'('II,( 1,))
by Jenouvrier" which is also attributed to be responsible for
perturbing the B state. The A' state was found to be only 1 1 I O
cm-' below the B state." From Table V it can be seen that the
calculated 1, state which is predominantly 'nuis 685 cm-' above
the 3rI,(Ou+) state. The corresponding experimental splitting
reported by Jenouvrier" is 829 cm-' and is thus in reasonable
agreement with the predicted spin-orbit splitting for this state.
However. the Re value is off. We believe that the basis set should
be extended further with more diffuse functions and polarization
functions since they appear to play a significant role especially
for the weakly bound excited states. It is clear from the calculated
-
-
-
The Journal of Physical Chemistry, Vol. 91, No. 20, 1987 5169
Low-Lying Electronic States of Se,
TABLE V Spectroscopic Properties of Se2
Re, A
Te,cm-'
state
calcd exutl calcd
exutl
X3Z[0,+XI
X3Z;l,X,
1A*(2g)
biZg+Og+(II)
3Au
3Z"+
A311,(0,+)
A311u(lu)
3wL)
B32;
3
I I)
3n,(11)
z;(
'~,(II)
3~u(11)
I A"
In,(II)
IAlI(W
In,(111)
2.244
2.240
2.27
2.30
2.51
2.52
(2.71)
(2.72)
(2.73)
2.54
3.12
3.01
3.32
3.40
2.53
2.58
2.92
2.90
2.166
2.51
2.54
2.44
0.0
0.0
664
512
4652
-4000
8557
7958
15241
16321
15651
21 277
24111
21961
24940
22 837
24822
25980
30 567
31 582
33 325
33712
36814
39 173
41 270
4 2 556
we, cm-I
calcd exutl"
357
360
341
323
246
244
197
194
189
232
133
122
385
387
320
355
268
195
187
246
233
325
141
159
Experimental values for the X I , X,, and B states quoted here are
from Huber and Herzberg's book.3 Experimental values for the IA,,
IZ,+(OB+), %(O,+),
and 'II,(l,) states are from ref 16, 10, 1 1 , and 8
respectively.
bond length in Table V for the B3Z,- state that the calculated
Re values of the excited states are in error primarily due to the
limitations of the basis set. Since spin-orbit contamination of 1,
states is sensitive to bond distances, we do not think our present
level of calculations is adequate enough to calculate the properties
of the state perturbing the B state exactly. The worst case is the
'nustate which actually comes out to be repulsive while the
experimental A' state which is tentatively assigned to In, (1,)l'
is bound but somewhat less than the A states. More extensive
calculations which include diffuse basis functions and polarization
functions are needed to calculate the properties of the states
perturbing the B states.
We report in Table V a number of electronic states of Se2 which
are yet to be observed. Specifically, the 3Z;(II) state which has
the same symmetry as the ground state can be observed in the
(32,,- 3Z -(II)) emission system if one could populate the C
state. The Bn,(II) state has a minimum at a long distance. The
X3Z:,31Tu(II)transition is dipole allowed. This transition
should be observable in the region of 33 000 cm-I. Electronic
spectra in this region have not been studied up to now. The
X3Zi-3Au(II) transition, although dipole-forbidden is observable
since the 3Z;-3Au system appears to have been observed.
Table VI shows the contributions of the leading configuration(s)
to the FOCI wave function of the various electronic states of Se2.
The contributions are reported a t the respective equilibrium geometries. As one can see from that table the 3 Z i , ]Ag,and ]Eg+
states are dominated by the 2u:17r,417r2 configuration. The 3Au
state observed in the 3Au-X3Z; system arises from the
2ug2l7ru3lag3
configuration. The A state is a 311ustate and is a
mixture of 2ug22uu17r,41?rgand 2 a 22uul?r,217rg3configurations.
The B3Z; state is a mixture of 2agBl7rU3l7r2,2 a g 2 a u l a ~ 1 7 and
r~,
2 ~ ~ 2 a , l 7 r , ~ 1configurations.
7r~
This seems to suggest that the
C state observed in the C3Z; system should be dominated by
2ug2uU1a,41:a configuration although since this state is observed
in the region of 53 000 cm-I, contributions from Rydberg configurations will become significant.
The calculated dissociation energy of the ground state of Se2
is 2.91 eV. A number of experimental De values have been obtained from the predissociation of BO,' bands (3.41, 3.16, and
3.10 eV).3 Photoionization and thermochemical studies seem to
favor the higher va1ue.I' Yee and Barrow16 have obtained an upper
bound for De as 27096 + 2X", where 2X" is the Og+-l, splitting.
However, they use a smaller value of 367 cm-l for this splitting
which is somewhat different from our calculated splitting and the
experimental splitting reported in Table V. If the Og+-l, splitting
is taken to be 512 cm-I, the upper value for De would be 27 6 0 8
cm-' still eliminating the highest of the three possible De values
-
TABLE VI: Leading Configuration@) Contributing to the Low-Lying
States of Se, at Their Equilibrium Geometries"
state
configuration
'2;
'A,
2ug21a,,"17rg2(89%)
2 ~ , ~ 1 n , 4 1 7 r(89%),
,~
2u,217rU217r,4(6%)
iz,+
2u,217r,41a,2 ( a % ) , 2ugz1a,217r,4 (9%)
3 ~ ,
2ug217ru317rg3
(go%), 2u,217ru317rg3(3%)
32,+
2u,217r,31T 3 (go%), 2u,217r,317rg3(3%)
311u
2ug22u,17r,*lng (66%), 2u~2u,l7rU2lag3
(22%)
32;
2u,21 a,31.R,3 (7374, 2",2", I K:i Kg2 ( I 4%), 2ug2u, II:* 7rg4
(4%)
jz;(II)
2ug2u,1 7ru31 7rg3 (42%), 2ugz1 a , 2 ~
(38%), 2ug21a,41
(8%)
3n,(r1) 2u,*2u,1 7ru31
( m ) , 2u:2u,~ K,2i Tg3 (7.3%)
3nu(r1) 2u,22u,17r,217rg3 ( a % ) , 2ug22u,~7r:i7r8 (2381,
2u,2u,*17r,31 7rgz (20%)
3 ~ ~ 1 1 2ug2u,ia,417r
)
2 (38%), 2u,2u,17r,21a,4 (27%), 2u,21a,31p,3
(24%), 2u,f17r,317r$3 (5%)
la,
2u,21 x,3 17rg3 (73%), 2ug2uuI *,41 xg2 ( I a ) , 2ug2u, 1 17 r
(3%)
'n,(II) 2ug17r,417r,) (84%), 2 ~ , 2 ~ , ~ 1 7 r , , "(2%)
1~,
TI,(III) 2u,22a,i x,3 17rg2 (87%)
~
"The lug21uu2shell is not shown.
considered by these authors (27700, 25 710, or 25 166 cm-I). Thus,
the D. value should be about 3.19 eV. Our calculated value of
2.91 e i seems to favor this than the 3.41-eV value. If we assume
3.19 eV to be correct, there is a discrepancy of about 9% between
the theoretical value and this value. Most of this discrepancy could
be attributed to higher order correlation corrections and basis set
errors which tend to increase the Devalue. A more accurate
CASSCF/second-order CI followed by Davidson's correction for
unlinked cluster correction may yield a De value in closer
agreement with the experimental results. Further, our basis set
is somewhat limited for an accurate calculation of De.
As seen from Table I, spin-orbit interaction splits the A-s states
into w-w states. The Ogf-l, splitting of the ground state (32,-)
has been studied by a number of authors. Recently, Jenouvrier"
reported a value of 5 12 cm-I. This is close to the value reported
in ref 3. This value is in very good agreement with our calculated
value of 664 cm-' (see Table V). The spin-orbit splittings of other
states such as B32,- has also been reported to be about 79 cm-'.
Our calculations indicate that the O,+(II) is 58 1 cm-I, above the
IZg+ state. The 0,' component of the 311ustate which is of
experimental interest is 813 cm-' below the 311ustate. The 1,
component of the 3rIustate is 129 cm-l below the 3rIustate. The
2, state is 747 cm-I above the 3rIustate. The spin-orbit splittings
are thus somewhat small in that they do not lead to any significant
difference in our assignment of electronic states. Alternatively,
one can assign the experimental electronic transitions unambiguously within A-s coupling scheme. Thus, the errors in the
calculated T, values due to the neglect of spin-orbit interactions
should be within 5-10%. The spin-orbit interaction would play
a more important role for Te2.
The Ogf ground state of Sez is 81% 32,-and 8% '2,'. The
O,+(II) state is 74% IZ,+and 8% 32;. The I, component of 311u
is actually 73% 311u (1ug21uu22ug22u,1?r,4i?rg),
2% 'nu
( 1 ag21a u 2 2 a ~ 2 u1, ~ 2r1g ) 1,8% 3rIu( 1 ug21uU22ug22u,
1?ru217rg3),
and 0.2% In,, (lu,21uU22ag22u,l.rr,21~g3).
(The spin-orbit contamination of 3Z,,-(Ou+,lu)is negligible at the equilibrium geometry
of 311u(0,+,l,). The spin-orbit contaminations of the ground state
and Ogf(II) are thus small but nonnegligible.
4. Conclusion
In this investigation we carried out CASSCFIFOCI calculations
on a number of low-lying electronic states of Se2. Our calculations
enable the assignment of all the observed bands below 26000 cm-l.
We have predicted a number of new electronic states which are
yet to be observed.
Acknowledgment. This research was supported in part by the
National Science Foundation Grant C H E 8520556. I thank the
referees for their invaluable comments.
Registry No. Se2, 12 185-17-0.