1198
C. Th. Pedersen et al.
Table 2. Calculated S-T gapA (kJ mol21) of C2Se2 using various multiconfiguration methods together with aug-cc-pVDZ basis set
CASB
Active orbitals
CASSCFC
CASPT2C
CASPT3C
MRCIC
(2,2)
5p2u
46.5
20.9
39.9
14.9
12.9
13.7
16.0
15.0
ꢂ1.6
14.5
ꢂ1.8
0.3
ꢂ1.0
4.4
ꢂ0.4
5.8
(6,4)
4p4g 5p2u
(6,6)
4p4g 5p2u 5p0g
4p4u 4p4g 5p2u 5p0g
ꢂ0.3
0.5
ꢂ0.3
0.5
(10,8)
(12,10)
(12,10)D
(14,12)
(20,16)E
11sg2 4pu4 4p4g 5pu2 5pg0 11su0
0.5
0.8
0.4
11sg2 4pu4 4p4g 5pu2 5pg0 11su0
0.6
0.7
0.6
10su2 11s2g 4pu4 4p4g 5pu2 5p0g 11su0 12sg0
9s2g 9s2u 10sg2 10s2u 11sg2 4p4u 4p4g 5p2u 5p0g 11s0u 12s0g 12su0
0.6
0.6
0.7
1.7
ARelative energy between the singlet 1Dg state and triplet 3Sgꢂ state.
BNumber of electrons and number of orbitals in the active space.
CBased on CASSCF optimised geometries.
DLarger aug-cc-pVTZ basis set.
ECAS(20,16) corresponds to the full-valence CAS of C2Se2.
(at CCSD(T)/aug-cc-pVTZ level) is 11.2 kJ molꢂ1. The pre-
dicted C¼C and C¼Se bond lengths of the triplet ground state
Se
C
C
Se
S
C
C
S
˚
are 1.269 and 1.720 A, respectively (at CCSD/aug-cc-pVTZ
level). The central C¼C double bond is shorter than that in C2S2
˚
(1.278 A) while the C¼Se bonds are weaker than the corre-
˚
C2Se2
C2S2
sponding C¼S (1.572 A). This is not surprising, as the C¼Se p
bond overlap is weaker than that in C¼S.
Fig. 5. Highest occupied molecular orbitals (HOMOs) of C2Se2 and C2S2.
Next, the singlet-triplet (S-T) gap of C2Se2 was investigated
using multiconfiguration methods, which are expected to pro-
vide a proper description of the degeneracy problem involved.
We have carried out a series of complete active space self-
consistent field (CASSCF). CASSCF calculations with active
space systematically expanded from the two-electron, two-
orbital CAS (CASSCF(2,2)) to the 20-electron, 16-orbital
CAS (CASSCF(20,16)), which represents the full-valence
CASSCF, using the aug-cc-pVDZ basis set. The active orbitals
involved in these CAS calculations are given in Table 2. The
dominant configurations arise mainly from the excitation of the
valence p electrons. Hence, one would expect an active space
including all p orbitals (i.e. 4pu, 4pg, 5pu, and 5pg), for
example CASSCF(10,8), to yield reliable result. In fact, further
expansion of the active space to include the valence s orbitals
leads to small changes in the relative energies (Table 2). For our
analogue, C2S2, is 23.0 kJ molꢂ1 [8]
The large reduction in the
.
S-T gap may be attributed to the fact the highest occupied
molecular orbital (HOMO) of C2Se2 (namely 5pu) has a
relatively larger contribution of the p orbitals of the terminal
Se atoms (Fig. 5). In addition, the electron density of the HOMO
is more spread out in C2Se2 because selenium has a larger atomic
radius than sulfur. As a consequence, the electron-electron
1
repulsion in the open-shell singlet Dg state is less severe in
C2Se2. It is important to note that the HOMOs of both singlet and
triplet states of C2S2 and C2Se2 are similar.
The free energies of reaction and activation at 9008C for the
various possible fragmentation pathways of tetraselenafulva-
lene 1 were evaluated at the B3LYP/6–311þþG(3df,2p) level
(Scheme 2). The fragmentation of 1 to CSe2 þ C2H2 is the most
favourable pathway both kinetically and thermodynamically.
This dissociation process involves the loss of C2H2 to form a
diselone-thioketene intermediate 3 in the first step, via transition
state TS1. The observation of m/z 368 ions in EIMS (Fig. 1b) is
consistent with the proposed mechanism. A cleavage of the
central C¼C bond in 1 to form two singlet 1,3-diselenolylidenes
(4, ‘diselenole carbenes’), stabilised by the neighbouring
selenium lone pairs, requires a high activation barrier of
275 kJ molꢂ1 (via transition state 2). A minor peak at 784 cmꢂ1
in the IR spectrum (Fig. 3) may possibly be due to 4 (predicted
frequency of 785 cmꢂ1). Dissociation of 1 to C2Se2 þ selenirene
is the least favourable pathway both kinetically and thermody-
namically. This dissociation process involves initially the for-
mation of a cyclic thioketene intermediate 5 (Scheme 2), which
may correspond to the m/z 288 ions in EIMS (Fig. 1b). This step
also requires a high activation barrier of 281 kJ molꢂ1. The
two possible fragmentations of C2Se2 require high energies
(Scheme 2). Not surprisingly, therefore, there is little or no
evidence for the formation of CSe and C2Se in the experimental
spectra. The corresponding standard free energies of reaction
and activation at room temperature (298 K) and the optimised
1
largest CASSCF calculation, CASSCF(20,16), the singlet Dg
state lies 15.0 kJ molꢂ1 above the triplet 3Sꢂg ground state.
However, inclusion of dynamic electron correlation at MP2
(CASPT2), MP3 (CASPT3), and CI (MRCI) levels significantly
lower the S-T energy gap (Table 2). This clearly indicates that
the CASSCF methods are not sufficient to describe properly the
singlet-triplet gap. For the smaller active space which includes
only the p orbitals, both CASPT3 and MRCI levels yield almost
identical energy for the 3Sgꢂ and 1Dg states. Further expansion of
the p active space leads to a very small preference for the triplet
state (by ,1 kJ molꢂ1). At our best level of theory, CASPT2
(20,16), the triplet 3Sgꢂ state is 1.7 kJ molꢂ1 more stable than the
singlet 1Dg state. To examine the effect of basis set on the S-T
gap, we have also performed CAS(12,10) calculations using the
larger aug-cc-pVTZ basis set. The changes in relative energies
on going from the aug-cc-pVDZ to aug-cc-pVTZ are very small,
particularly at the correlated levels (Table 2). Hence, we have
confidence in the predicted S-T gap of 1.7 kJ molꢂ1. In summa-
ry, all the single- and multi-determinant methods predict a triplet
ground for C2Se2, and there is no evidence for Hund’s rule being
violated. It is clear, however, that the singlet-triplet splitting is
very small. For comparison, the calculated S-T gap for the sulfur