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Chemical Physics 303 (2004) 157–164
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Ab initio study of the singlet–triplet relative stability of2,6-dibromo-20,60-bistrifluoromethyl-diphenylmethylene
Elena Rodr�ıguez, Rosa Caballol, Mar Reguero *
Departament de Qu�ımica F�ısica i Inorg�anica, Universitat Rovira i Virgili, Pl. Imperial Tarraco 1, 43005 Tarragona, Spain
Received 16 March 2004; accepted 19 May 2004
Available online 15 June 2004
Abstract
Diphenylmethylene is the main parent system in the search of stable carbenes, singlet as well as triplet ones. The substituents of
the phenyl rings are the keys to favour one state in front of the other, but the mechanism of this influence is little known. A model of
one of the first stable triplet carbenes that has been synthesized, the 2,6-dibromo-20,60-bistrifluoromethyl-diphenylmethylene, has
been the subject of this theoretical study. Singlet–triplet energy differences have been calculated using high level ab initio methods
(CASSCF for optimum geometries and DDCI for vertical energy differences and CASPT2 and B3LYP-Broken Symmetry for
comparison purposes). For the model carbene the results showed that the triplet state, with a large carbenic angle, was more stable
than the singlet one. Two additional series of calculations have been carried out to analyze the electronic and steric influence of the
phenyls and the phenyl substituents on the singlet–triplet relative stability.
� 2004 Elsevier B.V. All rights reserved.
Keywords: Diphenylcarbene; Singlet–triplet relative stability; Correlated ab initio calculation
1. Introduction
The study of reactive intermediates at chemical and
structural levels is of prime importance for under-
standing physical organic chemistry. In this field, stable
carbenes can provide an insight into transient organicchemistry and are of considerable importance in syn-
thetic chemistry. As early as 1910 Staudinger’s studies
on the decomposition of diazo compounds led to
carbenes being recognised as reactive species [1]. Their
role as transient intermediates has become of great im-
portance in the last five decades. The ground state spin
multiplicity is determinant on the carbene reactivity, so
it is a crucial factor that must be controlled. Althoughin the 70’s a lot of experimental as well as theoretical
work was devoted to carbenes [2] the search for stable
singlet carbenes in normal conditions was only suc-
* Corresponding author. Tel.: +34-977-559718; fax: +34-977-559563.
E-mail address: reguero@quimica.urv.es (M. Reguero).
0301-0104/$ - see front matter � 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.chemphys.2004.05.013
cessful in the late 1980s, when macroscopic amounts of
these compounds were isolated at room temperature [3].
Nowadays, there is still a considerable amount of re-
search activity in this area, attempting to find singlet
species with a sufficiently long life but with the char-
acteristic reactivity of these compounds [4]. Althoughtriplet carbenes have also been known experimentally
for some decades [5] and Zimmerman did some work on
them in 1964 [6], it was only in the 1990s that stable
triplet species (diphenylmethylenes derivatives) were
first synthesized [7]. Development was fast, going from a
half life of a few seconds in special conditions at room
temperature for the 2,20,4,40,6,60-hexabromo-diphe-
nylmethylene [8] to 200 s in normal conditions for the2,20,6,60-tetrabromo-4,40-di-tert-butyldiphenylmethylene
[9] and 1 h in solution at room temperature and infinite
stability at )40 �C for the 2,6-dibromo-4-tert-butyl-
20,60-bistrifluoromethyl-40-isopropyldiphenylmethylene
1, ‘‘a triplet carbene that can almost be bottled’’ [10].
The newest triplet carbenes synthesized are stable for
hours at room temperature [11].
158 E. Rodr�ıguez et al. / Chemical Physics 303 (2004) 157–164
BrCF3
BrCF3
r1 r2
θ
12
3
5
64
1'2'
3'
4'
5'
6'
φ1 = < C2C1C1'C2'
78
7'8'
0
1
To control the ground state spin multiplicity, it is
necessary to know the factors that favor the stabilization
of one species or the other. In general, electronic effects
(enlargement of the electronegativity of the substituents
and inductive or mesomeric effects) stabilize the singlet
via thermodynamic stabilization, while steric effects due
to bulky substituents stabilize both singlet and triplet
species by protecting the reactive carbene center (kineticstabilization). Stabilization of the triplet relative to the
singlet state seems only to be possible by substituents
that enlarge the carbenic angle, a. Thus, if electronic
effects are negligible, steric effects determine the ground
state multiplicity [12,13].
With this in mind, it is easy to understand how it is
possible to stabilize the singlet state and isolate singlet
carbenes but it is not such an easy task to stabilize thetriplet state to get triplet stable carbenes. Although some
experiments with dialkylmethylenes have been successful
recently [13], most of the research has concentrated on
diphenylmethylenes. The sterically hindered polyhalo-
genated and polymethylated diphenylmethylenes are
potentially good parent compounds for stable triplet
carbenes [1,9,10,14] but further stabilization via new
substituents in the phenyl ring is required if a compoundis to be stable in normal conditions at room tempera-
ture. Some recent studies focus on this point [14], but
light still needs to be shed on the different possible ways
of influence of the phenyl substituents.
Likewise, little is known about the structure of triplet
diphenylmethylenes. Because the compounds of this
family synthesized so far have a short life, the X-ray
crystallographic structure is known for only one com-pound, bis(2,4,6-trichlorophenyl)methylene, trapped in
a crystal [15].
Fortunately, these gaps in knowledge are gradually
being filled by theoretical studies, which have proved to
be an essential complement to experimental studies. In
this respect, carbenes have also created considerable
early interest. The first ab initio calculations had to fo-
cus on small carbenes [16] and these systems, althoughapparently simple, have not become stale [17]. They are
still considered a challenge and used as benchmarks to
check the accuracy of new theoretical methods
[17a,17b,17i]. Larger systems with bulky substituents
have not been the subject of theoretical studies until
short ago, when several studies on phenyl- and diphe-
nylmethylenes and derivatives were carried out using
density functional theory (DFT) methods. Structures,
energies and the effects of changes on substituents and
geometry were analysed [15,18] and reactivity studied[19]. Nevertheless, because DFT methods have difficul-
ties in accurately describing some open shell structures
or systems that cannot be described at a single reference
level, it seems advisable to study some of these larger
systems with high-level multireference methods, which
provide eigenfunctions of bS2, so as to have other reliable
theoretical data for purposes of comparison. In this
paper we present a computational study of the 2,6-dib-romo-20,60-bistrifluoromethyl-diphenylmethylene, spe-
cies 2, as a model of the triplet stable carbene 1. The
differences between species 1 and 2 are expected to have
a negligible effect on the singlet–triplet energy difference.
This hypothesis will be justified later on.
BrCF3
BrCF3
r1 r2
θ
12
3
5
6 4
1'2'
3'
4'
5'6'
φ1 = < C2C1C1'C2'
0
2
The difference dedicated configuration interaction
(DDCI)method [20] is used to compute the singlet–triplet
energy gap.Thismethodhas already been tested in several
types of systems and has given very accurate energy dif-
ferences [17i,21]. In particular, when it was used to cal-
culate singlet–triplet gaps for small carbenes, thecomparison with full configuration interaction (FCI) re-
sults was highly satisfactory. Agreement with experi-
mental data was also excellent for halogenated carbenes
[17i]. We have ran complete active space self-consistent
field (CASSCF) calculations to optimize the structures
and have carried out some CASPT2 and DFT calcula-
tions for comparison purposes.Wehave also analyzed the
main factors that determine themultiplicity of the groundstate of the derivatives of the diphenylmethylene.
2. Computational details
The singlet–triplet vertical energy differences have
been evaluated with the DDCI method [20]. DDCI is a
multireference selected single and double CI methodthat uses a minimal CAS as reference space. The selec-
tion of the configurations is based on the fact that up to
second order perturbation theory all the configurations
that arise from double excitations from the doubly oc-
E. Rodr�ıguez et al. / Chemical Physics 303 (2004) 157–164 159
cupied to the virtual orbitals on top of the CAS do not
contribute to the energy difference of the electronic
states of interest and hence, can be eliminated. This
considerably reduces the computational effort in the
diagonalization of the CI space. However, the procedurestill gives rise to huge CI expansions at the DDCI level.
To overcome this difficulty, we used the dedicated mo-
lecular orbitals (DMO) strategy [22] to truncate the MO
set. As has been pointed out, the orbital energies are not
a good criterion for cutting the orbital space and suc-
cessive truncations give a poor convergence with the size
of the MO space. Instead, a sound hierarchic order of
the MOs can be obtained by diagonalizing the differenceof the two density matrices associated to the two states
involved in the energy difference. The resulting orbitals
are known as dedicated orbitals and the corresponding
eigenvalues, the so called participation numbers, give an
indication of how important each dedicated orbital is in
the magnetic coupling. In this way, the MO space can be
reduced with almost no loss of accuracy. A final re-
finement to the method prevents the results from de-pending on the starting MOs by improving them
iteratively (IDDCI) [23] to better describe the transition
studied.
When DFT calculations have been carried out, we
have used the broken symmetry (BS) approach [24].
DES–T has to be calculated as
DES–T ¼ 2 EBS � ETð Þ2� S2h i ; ð1Þ
where hS2i is the expectation value of cS2 .
CASSCF and geometry optimization calculations
have been carried out with the MOLCAS package (5.4version) [25] and DFT, B3LYP and UB3LYP (Broken
Symmetry) calculations with the GAUSSIANAUSSIAN 98 package
[26]. The DDCI calculations have been performed with
the casdi code [27] and dedicated and IDDCI orbitals
were obtained with the natural program [28]. For
CASSCF and DDCI calculations of all compounds a
minimal basis set was used for all C, H and F atoms
except for the carbenic carbon, for which an extendedbasis set, (10s6p4d)/[5s3p2d] was used. Goddard et al.
[29] have shown that to minimize the correlation error
due to basis set limitation, it is much more effective to
extend the basis on the central C than on the substitu-
ents. For Br atoms the effective core potential of Ba-
randiaran and Seijo (Cowan–Griffin relativistic ab initio
core Potential type) [30] was used with a (9s8p4d)/
[1s1p2d] basis set for the external electrons. For theUB3LYP (Broken Symmetry) calculations, the aim of
which was to make comparisons with other published
DFT results, we used the same basis set as in these
previous calculations, that is, the Pople triple-f split
valence set, 6-311G(d,p) [31]. The geometry of species 2
was optimized without any restriction. The use of ef-
fective core potentials for Br atoms precludes the pos-
sibility of carrying out frequency calculations (in the
Molcas 4.1 package), so ZPE corrections could not be
taken into account for this compound.
In all the DDCI calculations the core orbitals were
frozen. For compound 2, the largest system studied here,21 orbitals were frozen, which yielded around 2� 106
determinants for the DDCI wave functions. For com-
pounds 3a, 3b, 4 and 5, the 1s orbitals of the C, Br and F
atoms were frozen. When the Dedicated-MO DDCI
approximation was used with a threshold of 10�3 for the
participation number, approximately 20% of the mo-
lecular orbitals were discarded and the number of de-
terminants of the wave function reduced to 106
approximately.
3. Results and discussion
The hypothesis of the negligible influence of the
substituents in 4 and 40 positions in species 1 is based on
some recent experimental work that systematicallystudied the effect of para substituents on diphenylm-
ethylenes [14]. This work showed that para substituents
do not modify the geometry of the carbene but, when
the unpaired electron on the p orbital of the triplet
carbene is delocalized, the triplet is stabilized thermo-
dynamically. But as the authors pointed out, this is not
the case for the para-t-butyl group, which stabilizes the
singlet and triplet carbenes equally, only at the kineticlevel, because it hinders any possible dimerization in the
para position. The same effect is expected of the para-
isopropyl substituent. For this reason it is expected that
para substituents will not affect the singlet–triplet energy
difference. In fact, as our results will show later, the
ground state of compound 2 is also the triplet, like in
compound 1.
The geometry optimization of the singlet and tripletstates of 2 was first performed at the CASSCF(2,2) level
with no restrictions. The main geometrical parameters
are shown in Table 1. In both states the two aromatic
rings are almost perpendicular to each other, one nearly
in the plane of the carbene (/1ðsingletÞ ¼ 20�,/1ðtripletÞ ¼ 13�), and the other nearly perpendicular to
it (/2ðsingletÞ ¼ 77�, /2ðtripletÞ ¼ 80�). In a series of
calculations carried out later on, a simplified Cs geom-etry was used. Table 1 also shows the reoptimized pa-
rameters of this geometry with a symmetry plane
ð/1 ¼ 0�, /2 ¼ 90�Þ.In the CASSCF optimized geometry of 2, the triplet
state has a central bond angle of 146�, larger than the
singlet state angle of 127�. In the singlet geometry the
bond distance from the central carbon to the bromine-
substituted ring is slightly shorter than the distance tothe trifluormethyl-substituted one due to the orientation
of the first aromatic ring that allows the electron
donation from the ring to the empty p orbital of the
Table 1
Main geometrical parameters calculated for 2 (C1 and Cs geometries) and 1 (C1 geometry) and measured experimentally for bis(2,4,6-trichloro-
phenyl)methylene
State h dC0–C1dC0–C10 /
2-C1 CASSCF(2,2)a T 145.9 1.395 1.406 82.5
S 127.5 1.396 1.404 80.1
2-Cs CASSCF(2,2)a T 143.0 1.400 1.409 90.0
S 129.3 1.388 1.397 90.0
1-C1 B3LYPb T 176.3 1.368 1.368 90.7
S 134.2 1.393 1.403 79.1
Experimentalc T 142.0 1.437 1.423 76.0
Angles in (�), bond distances in (�A).a This study.bRef. [18a].c Ref. [15].
160 E. Rodr�ıguez et al. / Chemical Physics 303 (2004) 157–164
carbenic center and consequently the bond order is in-
creased. In the triplet state the two atomic orbitals of the
carbene center are singly occupied, so the interactionwith both aromatic rings is similar and the bond dis-
tances dC0–C1and dC0–C10 are also similar.
The accuracy of the geometries obtained cannot be
directly judged, as there are no experimental data for
this system. The structural parameters obtained can only
be compared with the DFT geometry calculated for 1
[18a] at the B3LYP/6-311G(d,p) level (see Table 1 for
the main geometrical parameters) and with the X-raycrystallographic data of the triplet state of the bis(2,4,6-
trichlorophenyl)methylene trapped in a crystal [15] (see
Table 1). The geometrical parameters obtained in this
study are nearer the experimental values than those of
the DFT calculations. In particular the DFT triplet state
gives an almost linear structure for the central carbene.
This unexpected result can be imputed to the flatness of
the triplet surface obtained in [18a].Absolute energies and energy gaps are collected in
Table 2. Vertical energy differences were calculated with
CASSCF(2,2), CASPT2(2,2) and DDCI methods at the
Table 2
Vertical singlet–triplet energy differences (in kcalmol�1) at the optimized ge
Method State Absolute energies
Triplet minimum S
CASSCF(2,2)a S )1193.3343 )T )1193.3731 )
CASPT(2,2)a S )1194.5962 )T )1194.6447 )
B3LYP(BS)b S )6322.6575 )T )6322.6677 )
DDCIa S )1193.4788 )T )1193.5081 )
DDCI-DMOsa S )1193.4767 )T )1193.5063 )
IDDCI-DMOsa S )1193.4992 )T )1193.5231 )
aWith core potentials.bAll electron.
singlet and triplet minima. The triplet state is more
stable than the singlet one and, consequently, the energy
differences are smaller at the singlet minimum. Only atthe IDDCI and DFT B3LYP(BS) level do the energy
curves cross and the singlet state is slightly more stable
than the triplet one (by around 1.5 kcalmol�1) at the
singlet minimum.
At first sight, the discrepancy of the CASPT2 results
is surprising. To know if it is due to the limited size of
the active space, several calculations at the 2-Cs triplet
geometry were run with enlarging active spaces. Anenergy criterion was used to choose the active orbitals
until the whole p system of both aromatic rings were
included in the active space (Table 3). The stability of
the vertical energy difference rules out the size of the
active space as the source of the poor results of the
CASPT2 methods and confirms the validity of our
DDCI calculations based on a (2,2) active space. Other
authors (Schaefer in [19b], Borden in [19e]) have alreadystated the failure of the CASPT2 methods in this kind of
calculations where the electronic configuration of the
states to be compared have different type of orbital oc-
ometries of the singlet and triplet states for 2
DES–T
inglet minimum Triplet minimum Singlet minimum
1193.3561 24.4 2.96
1193.3608
1194.6162 30.4 10.8
1194.6334
6322.6533 13.4 )1.56322.6516
1193.4869 18.4 0.8
1193.4882
1193.4848 18.5 1.0
1193.4864
1193.5049 15.0 )1.41193.5027
Table 3
CASPT2 vertical singlet–triplet energy differences (in kcalmol�1) at the
triplet 2-Cs geometry for different sizes of active space
Active space DES–T
2,2 25.7
4,4 26.8
12,12 26.1
14,14 26.2
E. Rodr�ıguez et al. / Chemical Physics 303 (2004) 157–164 161
cupancy. In the particular case of diphenylmethylene theerror in the adiabatic S–T energy difference is assumed
to be of almost 10 kcalmol�1 [19e] and it is attributed to
an overestimation of the delocalization energy of the
triplet [19b].
The DMO approximation of the DDCI performs
very satisfactorily. The energy differences between these
results and the standard DDCI ones are less than 0.2
kcalmol�1, while the CI space is reduced to almost halfits size when 13 orbitals for the singlet and 15 orbitals
for the triplet are eliminated. With this truncated MO
set, the iterative IDDCI procedure, which improves the
active orbitals, modifies the energy differences stabilizing
the singlet relative to the triplet by 3.5 kcalmol�1 at the
triplet minimum and by 2.4 kcalmol�1 at the singlet one.
This latter change is enough to make the singlet more
stable than the triplet at this geometry.B3LYP (BS) calculations were run with a 6-
311G(d,p) basis set so that they could be compared with
previous DFT results [18a]. The energy differences were
obtained using Eq. (1) and hS2i values of 1.04 and 0.53
for the BS state at the triplet and BS minima, respec-
tively. The geometries optimized at the CASSCF(2,2)
level were used because the BS minimum does not nec-
essarily coincide with the singlet minimum. ET þ DEBS–T
should be optimized if the DFT methods are to give
accurate adiabatic S–T energy gaps, but this is beyond
the scope of this paper. The B3LYP (BS) results show
the best agreement with the IDDCI gaps in spite of the
fact that the basis set used in the calculations was dif-
ferent. We determined the adiabatic S–T energy differ-
ence so that comparisons could be made with previous
DFT results. To do so we had to add the energy dif-ference between the singlet and triplet geometries at the
triplet state to the vertical energy difference at the singlet
geometry. The result is a gap of 8.7 kcalmol�1. Wood-
cock et al. [18a] report an adiabatic S–T energy differ-
ence of 12.0 kcalmol�1 for system 1 calculated at the
B3LYP/6-311G(d,p) level. There were some differences
between these DFT calculations: the DFT results of [15]
were obtained for compound 1 while ours were forcompound 2 and we used the optimized CASSCF(2,2)
geometries). Even so the agreement should be better.
The discrepancy must be due to the different description
of the states. The BS solution may be expressed as
WBS ¼ cSWS þ cTWT;
where WS is the pure closed shell description. It can be
shown that the hS2i values correspond to cT ¼ 0:51 and
0.72 at the BS and T minimum, respectively, which in-dicates that the open shell character is not negligible at
all and consequently that the closed shell wavefunction
is not a suitable description. Furthermore, the descrip-
tion is not consistent along the energy curve since the
spin contamination varies. This poor description of the
singlet state must be the source of the mentioned dis-
crepancy and may also be the source of the errors found
by Tomioka and co-workers [15] in B3LYP results of S–T energy gaps in carbenes which they attribute to an
overestimation of the triplet stability.
Our results, in particular the variability of the hS2ivalue of the BS eigenfunction, show that it is not pos-
sible to generalize when describing the electronic struc-
ture of carbenes as a whole. Any method with little
flexibility in the wavefunction must be used with extreme
care or only in those cases in which previous knowledgeof the electronic structure ensures its applicability.
It would be interesting to know what the main factors
are that make the triplet state of carbene 1 so stable. In
an attempt to determine these factors, we planned two
series of calculations. The first one focuses on how the
substituents affect the singlet–triplet energy gap. The
second one analyzes the influence of the geometry on
this energy difference.In the first calculations, the DES–T was obtained (at
the DDCI level) for different fragments of compound 2.
To lower the cost of the calculations and eliminate ef-
fects other than the electronic ones, the geometries of the
fragments were taken from an optimized geometry of
the triplet state of species 2 but constrained to Cs sym-
metry. That is, the phenyl rings were on the plane of the
central carbene or perpendicular to it. The fragments,shown in Fig. 1, were methylene, phenylmethylene in
two conformations (3-a and 3-b in Fig. 1), diphenylm-
ethylene, 2,6-dibromo-phenylmethylene (4), 2,6-bis(tri-
fluormethyl)-phenylmethylene (5) and species 2 in a Cs
geometry (2-Cs). In all these calculations an active space
of two electrons in two orbitals was used.
The results for the energy differences are shown in
Table 4. Given that for these compounds the triplet stateis always more stable than the singlet one, DES–T will be
smaller for the species where the singlet state is relatively
more stable. In our previous study of small halocarbenes
and halosilylenes [17i], we found a kind of additive be-
havior: that is to say, in general, the change in DES–T
from CH2 to CX2 was almost twice the change from
CH2 to CHX. This is not the case here. The substitution
of an H atom by a phenyl ring hardly changes the energydifference, independently of the orientation of the ring
(from methylene to 3a or 3b), but when the two H atoms
are substituted the energy gap decreases around
Fig. 1. Fragments of compound 2: phenylmethylene, planar confor-
mation (3a); phenylmethylene, perpendicular conformation (3b);
2,6-dibromo-phenylmethylene, planar conformation (4); 2,6-bis(triflu-
oromethyl)-phenylmethylene, perpendicular conformation (5).
-0.92
-0.91
-0.90
-0.89
-0.88
-0.87
85 95 105 115 125 135 145angle
En
erg
y +
38 (
a.u
.)
S
T
Fig. 2. Potential energy curves for the singlet and triplet states of
methylene when angle h changes from the FCI optimized geometries.
Energies calculated at the CASSCF(2,2)6-311G(d,p) level.
Table 4
Singlet–triplet vertical energy difference at the DDCI level for different
fragments of compound 2
Structure DES–T
(kcalmol�1)
Methylene 22.2
Planar phenylmethylene (3a) 22.3
Perpendicular phenylmethylene (3b) 23.3
Diphenylmethylene (Cs geometry) 17.5
2,6-Dibromo-phenylmethylene (4) 28.3
2,6-Bis(trifluoromethyl)-phenylmethylene (5) 18.3
2,6-Dibromo-20,60-bistrifluoromethyl-
diphenylmethylene (2-Cs)
14.5
DES–T in kcalmol�1.
162 E. Rodr�ıguez et al. / Chemical Physics 303 (2004) 157–164
4.7 kcalmol�1 (from methylene to diphenylmethylene).
The substituents of both phenyl rings, contrary to what
could be expected, have opposite effects: while the bro-
mine substituents stabilize the triplet relative to the
singlet by 6.0 kcalmol�1 (from 3a to 4), the trifluo-
romethyl substituents destabilize the triplet by 5.0
kcalmol�1 (from 3b to 5). The effect of both on diphe-
nylmethylene (to 2-Cs) is a relative destabilization of thetriplet of 3.0 kcalmol�1.
These data do not show a trend and, what is more,
the smallest stability of the triplet relative to the singlet
occurs at the whole system, species 2-Cs, when no geo-
metrical parameters are changed. We can conclude that
the stability of the triplet of species 2 is not governed by
electronic factors.
To understand the steric effect of the substituents on
the relative stability of the triplet and singlet states the
strategy followed here has been different. One must keep
in mind the shape of the potential energy curves (PEC)
when angle h changes. For this purpose, the curves of
the singlet and triplet states of methylene are illustrated
in Fig. 2. They were obtained by using the optimized
Full CI geometry [32] as the starting point and bychanging only angle h between 90� and 140�. Energieswere calculated at the CASSCF(2,2)/6-311G(d,p) level.
These curves show the effect of angle h on the singlet and
triplet energies. If bulky substituents are added and only
steric effects are taken into account (i.e., it is assumed
that the substituents will not affect the electronic dis-
tribution), a positive energy caused by the steric repul-
sion of the substituents must be added to the curves.This energy will be larger for smaller angles, so the
minimum of the singlet will be more affected than the
minimum of the triplet and both will be displaced to
larger h angles. The whole effect of the bulky substitu-
ents will be to stabilize the triplet minimum relative to
the singlet one.
Kinetic stabilization has not been taken into account
here because of the static nature of the study. In anycase, this factor will modify the half-life time of species
in the ground state and will make them more or less
stable in normal conditions, but will have no influence
on the relative energy of the different states.
4. Conclusions
The DDCI method has been used to calculate the S–T
energy differences of 2 as a suitable model for carbene 1
and analyze the factors that make of this compound a
stable triplet species.
E. Rodr�ıguez et al. / Chemical Physics 303 (2004) 157–164 163
The CASSCF(2,2) calculations carried out to opti-
mize the geometries predict a nearly Cs geometry for the
two low lying singlet and triplet states. For the triplet
state the carbenic angle is 146� and the two bond dis-
tances of the central carbene are almost equal. For thesinglet state the carbenic angle is smaller, 127�. The
carbon–carbon bond distance to the bromine substi-
tuted ring is smaller in this state.
When energy differences are calculated at the DDCI
level the triplet is found to be the ground state, with a
vertical gap to the singlet state of 15.0 kcalmol�1 at the
absolute minimum. The use of DMO’s reduces sub-
stantially the DDCI space and the computational effortpreserving the quality of the results.
The effect of the carbene substituents on the relative
stability of the low-lying states has been analyzed through
the singlet–triplet energy differences of several fragments
of the parent molecule. In the phenylmethylene, the ori-
entation of the aromatic ring hardly has any effect on the
relative stability because the effect on the singlet and
triplet states is similar. The effect of the substituents of thephenyl ring is most important in the case of trifluorom-
ethyl, that leads to a relative stabilization of the singlet
state. The two aromatic rings in diphenylmethylenes
stabilize the singlet relative to the triplet.
To understand the effect of the steric impediments we
must take into account that bulky substituentswill always
destabilize the carbene, in a larger extent when the car-
benic angle is smaller. A schematic strategy is to add thiseffect to the potential energy curves of the singlet and
triplet states of the methylene where no steric impedi-
ments are present, without taking into account the pos-
sible electronic effects of the substituents. It is obvious
that on top of a displacement of both minima to larger
carbenic angles, the singlet minimum, located at a smaller
angle, will be destabilized relative to the triplet one.
It can be concluded that the substituents of the2,6-dibromo-20,60-bistrifluoromethyl-diphenylmethylene
decrease the singlet–triplet energy difference at the
electronic level, but the steric effects of these substituents
act in the opposite way and the global effect is a favored
triplet ground state.
Acknowledgements
This work has been supported by DGSIC of the
Ministerio de Educaci�on y Ciencia, Spain (Project No.
BQU2002-04029-C02-02), and by CIRIT of the Gener-
alitat de Catalunya (Grant 2001SGR-00315).
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