A Multireference Configuration Interaction Investigation of the Excited-State Energy
Surfaces of Fluoroethylene (C2H3F)
Mario Barbatti,* Ade ´lia J. A. Aquino, and Hans Lischka†
Institute for Theoretical Chemistry, UniVersity of Vienna, Wa ¨hringerstrasse 17, A-1090 Vienna, Austria
ReceiVed: February 17, 2005; In Final Form: April 22, 2005
Multireference configuration interaction with singles and doubles (MR-CISD) calculations has been performed
for the optimization of conical intersections and stationary points on the fluoroethylene excited-state energy
surfaces. For the planar ground state geometry, the vertical spectrum including 3s and 3p Rydberg states was
calculated. From this geometry, a rigid torsion around the CC bond strongly reduces the energy gap between
S0 and S1 states. Furthermore, a search for the minimum of the crossing seam shows that there exists a
conical intersection close to the twisted structure and two additional ones for cis and trans pyramidalized
structures. These three intersections are connected by the same seam. We have shown that the Hula-Twist
process is an alternative way to the direct CC twisting in order to reach this part of the seam. Other conical
intersections were also located in the CH3CF and CH2FCH, H-migration, and C3Vstructures. The photodynamics
of the system is discussed based on topological features of these intersections.
It is well-known that conical intersections act as funnels
allowing fast, radiationless transfer to another electronic state.
Actually, these intersections span a (N-2)-dimensional space,
the intersection seam.1,2The properties of the conical intersec-
tions make the crossing seam the very heart of the ultrafast
photodynamical processes and a great effort has been devoted
to its characterization, mainly of its minima. Despite the
significant progress achieved in the last years in the development
of methods2-5and in the study of the conical intersections for
even relatively large molecules,6-9several questions still arise,
such as those concerning the extension of the seam and the role
that each part is playing during the dynamics. Attempts to
answer this kind of question have been recently performed by
using ethylene as a prototype molecule.10,11The break of
symmetry introduced by substituted ethylenes, such as H2Cd
XH2or C2HnX4-n, can furnish valuable information about the
electronic structures involved in the crossing seam. Recently,
silaethylene (CSiH4)12and the methyleneimmonium cation
(CNH4+)13have been studied in our group. The haloethylenes
C2HnX4-n(X ) F, Cl, Br), and in particular fluorethylene (X
) F, n ) 3)sthe subject of the present workscomprise
examples of a different kind since the polarity of the π bond is
achieved by a link to the CdC bond and not by substitution of
a carbon atom.
An important topic in the research of haloethylenes is the
determination of the elementary processes resulting in the
molecular fragmentation, such as the hydrogen halide and
molecular hydrogen eliminations.14-17These eliminations can
involve the H and the halide atoms attached to the same C atom
(three-center RR-elimination) or atoms on different C atoms
(four-center R?-elimination). Since the work of Berry and
Pimentel,14which presented the first experimental results for
the HF elimination after a photoexcitation, numerous theoretical
and experimental investigations have been dedicated to this
subject,14,23especially in treating the ground-state structures and
processes. Kato and Morokuma15showed that in the case of
fluoroethylene the simple determination of the reaction path was
not sufficient to decide between the three- and four-center HF
elimination. On the basis of the HF translational energy release
after 157 nm (ππ*) photoexcitation, Sato and co-workers23
concluded that the four-center R?-elimination should be the
dominant process. However, the HX (X ) F, Cl, Br) rovibra-
tional distribution obtained from the photolysis of CH3X at 193
nm16,17has shown that the three-center process is the dominant
Besides HF elimination, Kato and Morokuma15investigated
several reaction channels on the ground and first triplet energy
surfaces of fluoroethylene including H-migration and cis-trans
isomerization. Smith, Coffey, and Radom24systematically
studied the ground-state equilibrium geometry at several ab initio
levels. Martı ´nez-Nu ´n ˜ez and Va ´squez25investigated the frag-
mentation reactions in the ground state. Recently, they have
furnished theoretical results about the rovibrational distribution
of the HF fragments in the photodissociation process.22Also
recently, Ljubic ´ and Sabljic ´26and Lie and co-workers27have
investigated the reaction mechanisms of fluoroethylene and
ozone. Kunsa ´gi-Ma ´te ´ et al.21have employed AM1 semiempirical
molecular dynamics to investigate the influence of the environ-
ment on the HF elimination. To the best of our knowledge,
Bacskay28was the only one to perform ab initio calculations
on the first singlet-excited state of fluoroethylene investigating
the isomerization and fragmentation processes.
In the present work, our main goal is to characterize the
lowest excited-state energy surfaces of fluoroethylene with
particular emphasis on the crossing seam between the S0and
S1states, and to discuss the role that it has in the photochemistry
of this system. Although our research is not primarily concerned
with the fragmentation topic, we believe that the characterization
of the first singlet excited state and of the S0/S1crossing seam
can furnish new and valuable information about this process.
* Address correspondence to this author. E-mail: mario.barbatti@
J. Phys. Chem. A 2005, 109, 5168-5175
10.1021/jp050834+ CCC: $30.25 © 2005 American Chemical Society
Published on Web 05/20/2005
We also present ab initio results for the vertical spectrum of
fluoroethylene, including in total six valence and Rydberg
2. Computational Details
State-averaged multiconfiguration self-consistent field (SA-
MCSCF) and multireference configuration interaction with
singles and doubles (MR-CISD) calculations were carried out.
In the SA-MCSCF calculations equal weights were used for all
states. Two different active spaces were chosen in the MCSCF
calculations. For the description of valence states, the wave
function was a CAS(2,2) in the π and π* orbitals. State
averaging was performed over the states N (π2), V (ππ*), and
Z (π*2). The same CAS(2,2) was used as reference space in
the subsequent MR-CISD calculations. The final expansion
space for the MR-CISD calculations in terms of configuration
state functions (CSFs) consisted of the reference configurations
and of all single and double excitations thereof into all internal
and external orbitals. The interacting space restriction29was
applied. The three core orbitals were always kept frozen in the
post-MCSCF calculations. Analogous principles for the con-
struction of the CI wave function were applied for the larger
reference space used in the calculation of the Rydberg states
described below. The MR-CISD/CAS(2,2) calculations were
used for the determination of the minima on the crossing seam
(MXS), for the calculation of stationary points, and for the cuts
of the potential energy surface. In general, all optimizations were
performed without symmetry restrictions. The aug-cc-pVDZ
basis30,31was selected in these calculations. All stationary points
and MXSs were reoptimized with an aug′-cc-VTZ basis set,
which was derived from the original aug-cc-pVTZ set by
omitting the augmented f functions on the carbon atoms and
all d functions on the hydrogen atoms. Size-extensivity correc-
tions were taken into account by means of the extended
Davidson correction32,33and will be denoted by +Q.
For the joint calculation of valence and Rydberg states, the
ππ*-CAS(2,2) was augmented by four auxiliary (AUX) orbitals
representing the 3s and 3p Rydberg orbitals. Only single
excitations were allowed from the CAS to the AUX space. In
addition to the three valence states N, V, and Z, four Rydberg
states (π-3s, π-3px, π-3py, and π-3pz) were considered
leading to a state-averaging over seven states at the MCSCF
level. The same configuration space was used as reference space
in the MR-CISD calculations and is denoted as MR-CISD/SA-
7-CAS(2,2)+AUX(4). A d′-aug-cc-pVDZ basis30,31,34,35was
chosen to take into account the diffuseness of the Rydberg
orbitals. On this basis, d′ stands for the original d-augmented
set of diffuse basis functions but omitting the doubly augmented
d functions on the carbon atoms and the doubly augmented p
function on the hydrogen atoms.
Although the calculations at the MR-CISD/SA-7-CAS-
(2,2)+AUX(4)/d′-aug-cc-pVDZ level produce satisfactory re-
sults in torsional angles larger than 20°, for the planar and
quasiplanar geometries the treatment at this level is not
sufficient. The π-3pxstate is located below the ππ* state, in
contradiction to the experimental results (see Subsection 3a).
This effect occurs due to a strong mixing between the π and
3pxmolecular orbitals, which also appears in other systems such
as ethylene36and butadiene.37
To obtain a more adequate description of the vertical
excitations, the aforementioned CAS(2,2)+AUX(4) reference
space was augmented by a restricted direct product (RDP)
space38constructed for all σ orbitals. The RDP space is
composed of 14 orbitals grouped in seven subspaces, one for
each σ bond and the lone pair, i.e., three [σ-σ*]CH, one
[σ-σ*]CC, one [σ-σ*]CF, and two [σ-σ*]n(F)pairs. Each σ-σ*
subspace is restricted to singlet pairing. The MCSCF calculation
based on the RDP wave function resulted in localized orbitals
very similar to those obtained in generalized valence bond
(GVB) calculations.39The molecular orbitals obtained in this
RDP(σ)+CAS(2,2)+AUX(4) space were used for the subse-
quent MR-CISD calculation. The reference space was composed
of all previously used CAS(2,2)+AUX(4) configurations plus
all single excitations from the σCCand σCForbitals to the CAS,
AUX, σCC*, and σCF* orbitals. The remaining σ orbitals were
transferred to the reference doubly occupied space and the
corresponding σ* orbitals to the virtual space. We denote this
level as MR-CISD/SA-7-[RDP+CAS(2,2)+AUX(4)].
Although the π* and 3pxorbitals resulting from the MCSCF
calculation in this improved RDP space are still strongly mixed,
the introduction of the σ-π correlation at the reference level
and of concomitant higher excitations at the MR-CISD have a
significant effect on the final result by stabilizing the V state
and reducing the mixing with the π-3pxstate.
The ground-state geometry and the vertical spectrum were
calculated also by means of the resolution of the identity
approximate coupled cluster singles and doubles (RI-CC2)
method.40-43For the geometry optimization of the ground state
the aug′-cc-pVTZ basis set was used. The vertical excitation
spectrum was obtained with the d′-aug-cc-pVDZ basis set.
For the geometry optimizations, analytic MR-CISD energy
gradients were computed by using the procedures described in
refs 44-47. Determinations of the minima on the crossing seam
(MXS) were performed by using the analytic MR-CI nonadia-
batic coupling vectors4and the direct inversion in the interactive
subspace (GDIIS) procedure developed in ref 48. Standard
GDIIS optimization49was used for the determination of station-
ary points. Natural internal coordinates were constructed ac-
cording to the directions given in ref 50.
Optimized geometries, energies, and conical intersections
were obtained with the COLUMBUS program system.51-54The
atomic orbital (AO) integrals and AO gradient integrals have
been computed with program modules taken from DALTON.55
The RI-CC2 calculations were performed with the TURBO-
MOLE program package.56
3. Results and Discussions
3.a. Vertical Excitations, CC Torsion, and Rydberg States.
The ground-state equilibrium geometry of the C2H3F system is
planar and belongs to the Cs point group (Figure 1). The
computed geometries are in good agreement with the experi-
mental ones24(see Table 1). The effect of improving the basis
set from the double to the triple-? level is to get an overall
reduction of the CC and CH bond distances by about 0.01 Å
(0.02 Å in the case of the CF bond distance). The same pattern
of bond-distance shortening is also observed in the optimization
of all other stationary structures and conical intersections that
will be discussed in Subsections 3.c and 3.d.
The absorption spectra of several haloethylenes were mea-
sured by Be ´langer and Sadorfy.57The spectrum of the C2H3F
species shows a broad peak for the V-state (ππ*) centered at
7.44 eV, superimposed by several sharp peaks assigned to
Rydberg transitions. Different from ethylene, the fluoroethylene
absorption spectrum does not present a long low-energy
progression. The π-3s transition was assigned to the 6.89 eV
peak. The 8.09 eV peak was assigned as the π-3pxtransition.
Except for the π-3pxand π-π* transitions, the RI-CC2 and
MR-CISD methods present quite similar transition energies (see
Excited-State Energy Surfaces of Fluoroethylene
J. Phys. Chem. A, Vol. 109, No. 23, 2005 5169
Table 2) with good agreement for the experimental π-3s
transition. The addition of the Davidson corrections (+Q) to
the MR-CISD results produces a systematic increase of the
Rydberg excitation energies by about 0.3 eV. Our best MR-
CISD+Q result for the vertical π-π* transition is still 0.4 eV
above the experimental result. This shows that similar difficulties
with the description of this state occur as in ethylene (see ref
36 and references therein). Also the RI-CC2 calculations give
only a slightly better value. To resolve this discrepancy
significantly more extended calculations would have to be
performed and possible effects of the vibrational structure and
nonadiabatic couplings similar to ethylene58need to be con-
sidered. Moreover, we note that the experimentally observed
band is very broad and the determination of the band maximum
seems to be somewhat arbitrary. Since our aim is the investiga-
tion of energy surfaces and conical intersections far away from
the region of the vertical excitation, we did not pursue this
The values for the oscillator strength show that, as expected,
the optical absorption is dominated by the V state, but with
some contributions from the π-3pxand π-3s states. The high-
energy π*2state (Z) is shown in Table 2 just because it can be
obtained also within the ππ*-CAS(2,2) space. However, we
should bear in mind that between the V and the Z states a
multitude of other states will be located, including those
involving the σ*(C-F) orbital.
As is shown in Figure 2, the Rydberg states are destabilized
by the torsional coordinate, while the V and Z states decrease
in energy and ultimately become the lowest excited states. A
similar behavior was found in the case of ethylene.58,59This
means that the cis-trans isomerization can occur without barrier
in the V or Z states. The V state crosses all Rydberg states for
torsional angles between 0° and 30°, and after that it becomes
the S1state. Due to its high energy in the planar geometry, the
Z state crosses the Rydberg states in the region from 60° to
75°. Finally, it becomes the S2state.
For ethylene, the Z state crosses the V state at a torsional
angle of 86°10,60and these two states are almost degenerate at
90°. In the present case, the stabilization of the Z state is not
strong enough to allow this crossing and this state lies close to
the Rydberg 3s state for the 90° twisted geometry, about 3.4
eV above the V state. For a rigid torsion one finds only a
relatively small gap of 0.86 eV between the S0and S1states at
90°. If we optimize the twisted structure of the V state, this
gap is reduced to 0.62 eV (see Table 3). As we will show below,
these rather small gaps are a good indication that there is a
crossing between the ground and V states near the twisted
structure in contrast to the situation found for ethylene.
The qualitative difference in the torsional potential energy
curves for ethylene and fluoroethylene can be rationalized by
the 3 × 3 CI analytical model for biradicaloids developed by
Bonac ˇic ´-Koutecky ´ et al.61,62This model predicts that for the
type of nonsymmetric biradicaloids as is the case for fluoro-
ethylene the S1 state can become degenerate with S0 by
increasing the electronegativity difference of the CC bond. The
just-described results for ethylene and fluoroethylene fit very
well into this model.
3.b. Description of Isomers. Besides the planar global
minimum CH2CHF, we have characterized two other isomers
of fluoroethylene on the S0surface, one with the structure CH3-
CF and another with the structure CH2FCH. The structure and
selected geometrical parameters of these isomers are shown in
Figure 1. The energy of each structure is given in Table 3. The
theoretical characterization of these two isomers at the SCF/4-
31G level was carried out many years ago by Kato and
Morokuma15and recently by Bacskay28for CH3CF at the DFT
and MR-CISD levels.
The isomer with the nonsubstituted CH3group is more stable
than that with the CH2F group, lying 2.32 eV (Table 3, L2Q
level) above the ground-state global minimum. The isomer with
the CH2F group, on its turn, has its ground state 3.30 eV above
the global minimum. Although we observe these strong differ-
ences in the ground state energies, the first-excited-state energies
of the two isomers are practically the same, as we can see from
Our result for the vertical S0-S1excitation energy of the CH3-
CF isomer is 2.91 eV (Table 3, L2Q level), which is in good
agreement with the 2.99 eV obtained by Bacskay at the MR-
CISD+Q/cc-pVTZ level, but with geometry optimization at the
3.c. Minima on the Crossing Seam. As we discussed above,
the small S0/S1gap for the 90° twisted structure is an indication
that there should be a crossing near it. Indeed, we succeeded in
locating an intersection in a twisted structure with a slight
character of hydrogen migration. Its geometrical parameters and
energy are shown in Figure 3 and Table 4, respectively. Figure
4a shows the gradient difference vector g01and the nonadiabatic
Figure 1. Structures and selected parameters of the stationary structures
optimized at the L1 (L2) level defined in Table 3. Distances in Å and
angles in deg.
TABLE 1: Selected Geometric Parametersafor the Planar
Ground State Minimum
aDistances in Å and angles in degrees.bL1 ) MR-CISD/SA-3-
CAS(2,2)/aug-cc-pVDZ.cL2 ) MR-CISD/SA-3-CAS(2,2)/aug′-cc-
5170 J. Phys. Chem. A, Vol. 109, No. 23, 2005
Barbatti et al.
coupling vector h01. The g-h space is composed mainly of CC
stretching, H-migration, and CC torsion. This situation is similar
to that for the CSiH412and CNH4+13molecules, for which the
simple torsion also ends in an intersection.
For the twisted-orthogonal structure of ethylene there is a
large S0/S1gap of 2.35 eV.59To reach the conical intersection
requires strong pyramidalization and partial hydrogen migration.
For fluoroethylene the twisted structure is already an intersection
and, furthermore, the seam continues along the pyramidalization
of the CH2group and reaches one of the two MXS at angles of
122.4° (cis pyramidalized) and 122.9° (trans pyramidalized).
The two MXS are characterized in Figure 3 and Table 4. In
Figure 5 the path connecting the twisted intersection with the
cis- and trans-pyramidalized MXS is shown in terms of the
pyramidalization angle ?. The geometries used to calculate this
path were obtained by a simple geometrical linear interpolation
between the twisted conical intersection and each of the
pyramidalized MXSs. Very flat curves are obtained. Figure 5
shows that already this procedure leads to a path very close to
the seam. Therefore, we did not consider it necessary to optimize
this path completely. An analogous path on the seam exists in
TABLE 2: C2H3F Vertical Excitations from the Planar Ground State Structure
aMR-CISD+Q/SA-7-[RDP+CAS(2,2)+AUX(4)]/d′-aug-cc-pVDZ.bRI-CC2/d′-aug-cc-pVDZ.cReference 57.dE ) -176.988334 au.eE )
-177.365055 au.fE ) -177.422771 au.gE ) -177.550517 au.hMaximum of the absorption band.
Figure 2. Potential energy curves for the rigid torsion. The curves
are plotted in a diabatic way following the character of the wave
TABLE 3: Ground- and Excited-State Energies of the
Stationary Structures Optimized for the State Sk(k ) 0, 1)a
aThe reference energy level is the planar ground state.bE )
-177.362514 au. L1 ) MR-CISD/SA-3-CAS(2,2)/aug-cc-pVDZ.cE
) -177.413880 au. L1Q ) MR-CISD+Q/SA-3-CAS(2,2)/aug-cc-
pVDZ.dE ) -177.490127 au. L2 ) MR-CISD/SA-3-CAS(2,2)/aug′-
cc-pVTZ.eE ) -177.549453 au. L2Q ) MR-CISD+Q/SA-3-CAS(2,2)/
Figure 3. Geometrical structures and selected parameters for the
conical intersections optimized at the L1 (L2) level defined in Table
3. The pyramidalization angles of the cis and trans pyramidalized MXSs
are 119.2° (122.4°) and 120.4° (122.9°), respectively. Distances in Å
and angles in deg.
TABLE 4: Energies of the S0/S1Conical Intersectionsa
aThe zero energy level is the planar ground state (see Table 3). The
computational levels (L) are defined in Table 3.bci ) conical
intersection. MXS ) minima on the crossing seam.cGeometry
optimized at the S1state restricted to the C3Vpoint group.
Excited-State Energy Surfaces of Fluoroethylene
J. Phys. Chem. A, Vol. 109, No. 23, 2005 5171
ethylene connecting the pyramidalized MXS to the H-migration
conical intersection.59,63In fluoroethylene we are observing the
same feature, only displaced to small H-migration angles. An
important distinction between the pyramidalized MXSs in
ethylene and fluoroethylene is that in the former there is a strong
degree of migration in one of the H atoms of the pyramidalized
group, which results in a highly asymmetric structure. In
fluoroethylene, this asymmetry is not observed in any of the
pyramidalized MXSs and, therefore, the structures belong to
the Cspoint group.
In ethylene, Ben-Nun and Martinez10have shown that an
ethylidene (CH3CH) conical intersection exists. Later on,
Toniolo et al.64located the symmetry-required C3V-ethylidene
conical intersection. Recently, we have generalized these
results59by showing that part of the S0/S1 crossing seam of
ethylene lies also in the ethylidene region and that these two
conical intersections belong to this seam. In other previous
work,10we have shown that in the photochemical process, this
region of the seam is responsible from 10% to 30% of the S1
f S0conversions. In analogy to ethylene, we have located three
points of intersection in the CH3CF and CH2FCH regions of
the configuration space of fluoroethylene. The structures of the
CH3CF and CH2FCH MXSs are shown in Figure 3 and the
energies of both and also of the C3Vconical intersection (linear
CCF axis) are given in Table 4.
The C3V conical intersection was studied previously by
Bacskay.28In this work it was pointed out that this conical
intersection could be responsible for the internal conversion
during the CH3CF f CH2CHF isomerization process. A barrier
of 0.89 eV has been computed between the system initially
prepared in the S1state (vertical excitation) of the CH3CF isomer
and the C3V conical intersection. We note, however, that the
true MXS, as mentioned above, is distorted from the C3V
intersection. Our best result for this barrier is 0.27 eV,
significantly reduced in comparison to the 0.89 eV presented
by Bacskay. Therefore this MXS should be considered a better
candidate for the main S1-S0 funnel in this region of the
configuration space than the C3Vconical intersection.
For ethylene, the same seam connects the H-migration conical
intersection and the intersection in the ethylidene region of the
configuration space.59We expect that the same will occur for
fluoroethylene even though we did not search for this path. One
indication that this connection should exist in the present case
also is the H-migration conical intersection that we have found
for large H-migration angles (Figure 3 and Table 4). Probably,
this conical intersection does not correspond to a minimum but
to a saddle point on the crossing seam in analogy to the ethylene
case.63We did not follow this question in more detail here since
the energy of this intersection is relatively high.
It is well-known (see, e.g., Atchity et al.3and Jasper and
Truhlar65) that the topography of the region around a conical
intersection has an influence on the dynamics of the system.
For instance, depending on the inclination or on the symmetry
of the double cone, there will be a different probability of
returning to the upper state. Following Yarkony,2,66these
topographic features can be described in terms of a set of four
where s01is the gradient sum vector and (x ˆ, y ˆ) are unit vectors
based on Schmidt-orthogonalized vectors g (energy gradient
difference) and h (nonadiabatic coupling vector):
Figure 4. (a) Difference gradient vector g01and nonadiabatic coupling
vector h01for the twisted conical intersection optimized at the MR-
CISD/SA-3-CAS(2,2)/aug′-cc-pVTZ level. (b) Linearized adiabatic
energies for the twisted conical intersection in the g-h (x-y) space.
Energy in eV and x and y in Å.
Figure 5. S1and S2potential energy curves for the pyramidalization
of the CH2group.
dgh) (g2+ h2)1/2
x ˆ ) g01/g,
g ) ||g01||
h ) ||h01||
y ˆ ) h01/h, (3)
5172 J. Phys. Chem. A, Vol. 109, No. 23, 2005
Barbatti et al.
In terms of displacements x and y along x ˆ and y ˆ, respectively,
the linear approximation for the adiabatic energies of S0and S1
is given by:66
E ) dgh[σxx + σyy ((1
From eq 4 we see that σi controls the tilt of the cone away
from the vertical direction, ∆ghdetermines the deviation from
cylindrical symmetry, and dghcontrols the pitch of the cone.
Table 5 presents σx, σy, ∆gh, and dgh for the MXSs of
fluoroethylene. All conical intersections contain some degree
of asymmetry and tilt, as one can see, for example, in Figure
4b for the twisted conical intersection. In the present coordinate
system, the tilt is in the direction of x for most of the conical
intersections and only the cis-pyramidalized and CH2FHC MXSs
present some appreciable tilt in the direction of y. The
asymmetry parameter ∆ghhas small positive values for most of
the intersections, which means that the cones are slightly
elongated in the direction y. The cis-pyramidalized structure
has practically cylindrical symmetry and the H-migration conical
intersection is strongly elongated in the x direction. There is a
very clear distinction between the pitches of these conical
intersections: while the twisted, the cis- and trans-pyramidalized
and the H-migration conical intersections have similar dghvalues,
the CH2FCH and the CH3CF MXSs show much smaller ones.
For these two latter MXSs, the small dghand large σxvalues
make them particularly sloped and therefore inefficient for the
S1f S0conversion. This situation is quite similar to that found
in ethylene, for which the S1 f S0 conversion occurs more
efficiently at the peaked pyramidalized MXS than at the sloped
3.d. The Hula-Twist Process. In monoolefins and asym-
metrical (polar) conjugated polyenes, after photoexcitation into
the ππ* state, the system is stabilized by a torsion around the
CC bond in which the double bond is broken. Therefore, this
torsional motion or one-bond-flip process (OBF) should be the
main process driving the cis-trans isomerization of these classes
of systems in the gas phase.7An alternative process that can
also allow for cis-trans isomerization is the Hula-Twist
(HT).67,68Different from the OBF process, in the HT process
the variation of the volume is relatively small,69and for this
reason it is used to explain cis-trans photoisomerization in
Since volume restrictions are not imposed in the present case
of fluoroethylene, the cis-trans isomerization in fluoroethylene
is expected to occur mainly through an OBF mechanism.
Nevertheless, fluoroethylene is one of the smallest systems for
which HT is structurally possible. Because of the general
importance of HT we want to give a short discussion on it here
also. In Figure 6 a possible realization of the HT motion as
presented in ref 67 is given in terms of internal coordinates.
Our definition consists of the torsion of the atoms H and HC
around an axis defined by the nonbonded atoms F and C2,
allowing pyramidalization of the C2HCHTgroup also. Moreover,
C1is always kept in the C2FH plane and C2is always located
in the HCHTF plane. Both criteria are achieved by freezing the
out-of-plane angles71C1C2FH and C2HCHTF at the planar
ground-state values. The Hula-Twist angle η itself is defined
as the dihedral angle HCC2FH. For each value of η, all other
internal coordinates (excepting the two frozen out-of-plane
angles) were optimized for the S1state at the MR-CISD/SA-
3-CAS(2,2)/aug-cc-pVDZ level of theory.
Thus, as for the OBF (Figure 1), HT stabilizes the S1state,
and in this state the cis-trans isomerization can occur without
barrier. However, while in OBF we have observed a very small
gap between S0and S1(see Subsection 3.a), in HT the minimum
gap is 1.3 eV occurring at the HCC2FH dihedral angle of 90°.
The 90° structure shows a slight pyramidalization of the twisted-
orthogonal structure, which means that the HT can easily result
in structures near the S0/S1 crossing seam that connects the
twisted conical intersection to the pyramidalized one. As we
discuss in Subsection 3.d, this is the same branch of seam that
is reached by the torsion (OBF) motion.
For larger systems with large momentum of inertia associated
with the rotating groups in OBF, HT may become crucial not
only as a pathway to the cis-trans pyramidalization, but also
as a way of reaching the pyramidalized S0/S1crossing seam.
This can be the case, for example, for stilbene for which
Quenneville and Martı ´nez72have shown the existence of a MXS
at the pyramidalized CHR group (R is the C6H5ring). For a
more complete discussion about the MXSs in stilbene and the
role of the HT process in this system see refs 73 and 74.
3.e. Photodynamics of Fluoroethylene. As discussed in the
Introduction, one important topic in the research of the halo-
ethylenes is the determination of the elementary processes
resulting in hydrogen halide and H2elimination. Since most of
experiments have been performed with excitation energies close
to the ππ* absorption band (see, e.g., refs 14, 16, 17, and 23)
TABLE 5: Topographic Parameters for the S0/S1Conical
aσx ) σy ) ∆gh ) 0 corresponds to a symmetrical and vertical
(peaked) conical intersection.bci ) conical intersection. MXS )
minima on the crossing seam.
2(x2+ y2) +∆gh
Figure 6. Potential energy curves for the Hula-Twist (HT) process. η
is the HT angle and ? is the pyramidalization angle.
Excited-State Energy Surfaces of Fluoroethylene
J. Phys. Chem. A, Vol. 109, No. 23, 2005 5173
and the relaxation to the ground state seems to be a main process
leading to several dissociation channels,17it is a central task to
describe the just-mentioned relaxation processes and their
relevance for the elimination processes.
For the dynamics through the S0/S1seam we can deduct the
following mechanism for the initial stages of the temporal
evolution of fluoroethylene, and probably also of the other
haloethylenes, in comparison to the photochemistry of ethyl-
ene.75,76After photoexcitation to the V (ππ*) state, the system
can quickly evolve through torsional motions (OBF) that have
the general effect of strongly reducing its potential energy. After
just a few tens of femtoseconds, the system reaches the region
of the twisted crossing seam, in which it can return to the ground
state. With the large excess of internal energy, the fragmentation
processes, including the HF elimination, might be completed
in a time scale of a few hundreds of femtoseconds. On the other
hand, in ethylene, the H2elimination is expected to occur in
times from 800 to 3800 fs, depending on the photoexcitation
After a nonadiabatic transition, the acquired-vibrational
energy is concentrated in a small number of vibrational modes
that define the conical intersection.78For the twisted conical
intersection, we can see from Figure 4a that these modes are
composed mainly of torsion, CC stretching, and H-migration.
The two latter modes can promote the formation of the CH2-
FCH isomer, a fact that has not been considered in the analysis
of the experimental data up to now. Since two of the three HF
exit channels in the CH2FCH isomer correspond to three-center
elimination, the presence of this isomer in the ground-state
population should increase the probability of this type of
elimination over the four-center one.
MR-CISD calculations have been performed for conical
intersections and stationary structures on the fluoroethylene
ground- and excited-state energy surfaces with recently devel-
oped methods for the computation of analytic gradients and
nonadiabatic coupling terms.
For the planar ground-state geometry, the vertical spectrum
(including 3s and 3p Rydberg states) was calculated with the
MR-CISD and RI-CC2 methods. We observe a general good
agreement with the experimental results with some need for
further improvements in the notoriously difficult ππ* excitation.
From the planar ground-state geometry, a rigid torsion around
the CC bond strongly reduces the energy gap between the S0
and S1states. Furthermore, the optimization process shows that
there is a conical intersection very close to the twisted structure
and two others in pyramidalized structures. We have also shown
that all three intersections are connected by the same seam and
that the Hula-Twist process is an alternative way to reach the
crossing seam. Other conical intersections were located close
to the CH3CF and CH2FCH and H-migration structures and to
the CH3CF C3Vstructure.
On the basis of topological features of these MXSs, we have
argued that the S1-S0conversion after photoexcitation at the
planar global minimum should take place mainly at the twisted
conical intersection. This process is markedly different from
that in ethylene, in which a strong pyramidalization is needed
before the conversion takes place. We have pointed out that
the occurrence of the nonadiabatic transition through the twisted
conical intersection may imply that the CH2FCH isomer is
significantly populated and therefore it should be taken into
account in the experimental and theoretical analysis of the three-
and four-center HF elimination.
Acknowledgment. The authors acknowledge support by the
Austrian Science Fund within the framework of the Special
Research Program F16 and Project P14442-CHE. Mario Barbatti
thanks the Brazilian funding agency CNPq for financial support.
The calculations were performed in part on the Schro ¨dinger II
cluster of the University of Vienna.
Supporting Information Available: Cartesian coordinates
of all optimized stationary structures and MXSs studied in the
present work. This material is available free of charge via the
Internet at http://pubs.acs.org.
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