Page 1

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.

1. Introduction

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

one.

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@

univie.ac.at.

†E-mail: hans.lischka@univie.ac.at.

5168

J. Phys. Chem. A 2005, 109, 5168-5175

10.1021/jp050834+ CCC: $30.25 © 2005 American Chemical Society

Published on Web 05/20/2005

Page 2

We also present ab initio results for the vertical spectrum of

fluoroethylene, including in total six valence and Rydberg

singlet-excited states.

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

Page 3

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

question further.

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

Table 3.

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

B3LYP/cc-pVTZ level.

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

L1b

1.338

1.357

1.085

1.085

1.085

121.6

126.3

118.8

121.5

L2c

1.325

1.338

1.073

1.071

1.073

121.5

126.2

119.3

121.2

CC2d

1.327

1.358

1.090

1.088

1.089

122.0

126.4

118.9

121.9

exptle

1.329

1.346

1.077

1.081

1.081

121.5

125.4

118.6

120.9

C1C2

C1F

C1H

C2HC

C2HT

C2C1F

C2C1H

C1C2HC

C1C2HT

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-

pVTZ.dRI-CC2/aug′-cc-pVTZ.eReference 24.

5170 J. Phys. Chem. A, Vol. 109, No. 23, 2005

Barbatti et al.

Page 4

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

energy (eV)

MR-CISD+Qa

0.00f

7.42

8.06

8.26

7.86

8.37

13.05

state

N

π-3s

π-3pyz

π-3pyz

V

π-3px

Z

MCSCF

0.00d

5.89

6.49

6.72

8.33

6.82

14.09

MR-CISD

0.00e

7.15

7.78

7.98

7.86

8.17

13.51

CC2b

0.00g

7.12

7.74

7.99

7.72

8.51

exptlc

oscillator strengtha

11A′

11A′′

21A′

31A′

21A′′

31A′′

n1A′

6.98 0.06

0.00

0.00

0.29

0.10

0.00

7.44h

8.09

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

function.

TABLE 3: Ground- and Excited-State Energies of the

Stationary Structures Optimized for the State Sk(k ) 0, 1)a

energy (eV)

L1Q

0.00c

7.94

2.98

4.36

3.41

4.03

2.25

5.18

3.18

5.32

structure

planar

k

0

state

S0

S1

S0

S1

S0

S1

S0

S1

S0

S1

L1

0.00b

8.24

3.11

4.68

3.51

4.27

2.26

5.19

3.14

5.27

L2

0.00d

8.29

3.24

4.72

3.63

4.31

2.31

5.23

3.25

5.35

L2Q

0.00e

7.99

3.13

4.43

3.55

4.10

2.32

5.23

3.30

5.40

twisted0

twisted1

CH3CF0

CH2FCH0

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)/

aug′-cc-pVTZ.

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

energy (eV)

L1Q

3.92

3.96

4.28

4.92

5.50

5.88

6.11

structureb

cis pyramidal

trans pyramidal

twisted ci

CH2FCH MXS

CH3CF MXS

CH3CF C3Vc

H-migration

L1

4.10

4.12

4.39

4.83

5.47

5.82

6.38

L2

4.15

4.19

4.42

4.91

5.48

5.82

6.48

L2Q

3.91

3.94

4.21

5.00

5.50

5.86

6.24

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

Page 5

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

parameters:

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.

σx)s01‚x ˆ

dgh

(1a)

σy)s01‚y ˆ

dgh

(1b)

∆gh)(g2- h2)

dgh

2

(1c)

dgh) (g2+ h2)1/2

(1d)

x ˆ ) g01/g,

g ) ||g01||

h ) ||h01||

(2)

y ˆ ) h01/h, (3)

5172 J. Phys. Chem. A, Vol. 109, No. 23, 2005

Barbatti et al.

Page 6

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

ethylidene one.10,11

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

environment-restricted systems.70

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

Intersectionsa

parameters

structureb

cis pyramidal

trans pyramidal

twisted CI

CH2FCH MXS

CH3CF MXS

H-migration

σx

σy

∆gh

-0.01

0.18

0.08

0.22

0.30

-0.50

dgh(eV/Å)

5.46

6.04

6.76

0.82

2.16

7.15

-0.377

-0.700

-0.925

-4.610

3.148

0.327

-0.408

0.000

0.006

1.232

-0.051

-0.006

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

2(x2- y2))

1/2]

(4)

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

Page 7

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

energy.77

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.

4. Conclusions

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.

References and Notes

(1) v. Neumann, J.; Wigner, E. Phys. Z. 1929, 30, 467.

(2) Yarkony, D. R. In Conical Intersections; Advanced Series in

Physical Chemistry 15; Domcke, W., Yarkony, D. R., Ko ¨ppel, H., Eds.;

World Scientific: Singapore, 2004; p 129.

(3) Atchity, G. J.; Xantheas, S. S.; Ruedenberg, K. J. Chem. Phys.

1991, 95, 1862.

(4) Bearpark, M. J.; Robb, M. A.; Schlegel, H. B. Chem. Phys. Lett.

1994, 223, 269.

(5) Lischka, H.; Dallos, M.; Szalay, P. G.; Yarkony, D. R.; Shepard,

R. J. Chem. Phys. 2004, 120, 7322.

(6) Molnar, F.; Ben-Nun, M.; Martı ´nez, T. J.; Schulten, K. J. Mol.

Struct. (THEOCHEM) 2000, 506, 169.

(7) Ruiz, D. S.; Cembran, A.; Garavelli, M.; Olivucci, M.; Fuss, W.

Photochem. Photobiol. 2002, 76, 622.

(8) Migani, A.; Olivucci, M. In Conical Intersections; Advanced Series

in Physical Chemistry 15; Domcke, W., Yarkony, D. R., Ko ¨ppel, H., Eds.;

World Scientific: Singapore, 2004; p 271.

(9) Robb, M. A.; Garavelli, M.; Olivucci, M.; Bernardi, F. In ReViews

in Computational Chemistry; Lipkowitz, K. B., Boyd, D. B., Eds.; Wiley-

VCH Publishers: New York, 2000; Vol. 15, p 87.

(10) Ben-Nun, M.; Martı ´nez, T. J. J. Chem. Phys. 2000, 259, 237.

(11) Barbatti, M.; Ruckenbauer, M.; Lischka, H. J. Chem. Phys. 2005,

122, 174307.

(12) Pitonak, M.; Lischka, H. Mol. Phys. 2005, 103, 855.

(13) Lischka, H.; Aquino, A. J. A.; Barbatti, M.; Solimannejad, M. In

Lecture Notes in Computer Science; Gervasi, O., et al., Eds.; Springer-

Verlag: Berlin, 2005; Vol. 3480, p 1004.

(14) Berry, M. J.; Pimentel, G. C. J. Chem. Phys. 1969, 51, 2274.

(15) Kato, S.; Morokuma, K. J. Chem. Phys. 1981, 74, 6285.

(16) Lin, S.-R.; Lin, S.-C.; Lee, Y.-C.; Chou, Y.-C.; Chen, I.-C.; Lee,

Y.-P. J. Chem. Phys. 2001, 114, 160.

(17) Lin, S.-R.; Lin, S.-C.; Lee, Y.-C.; Chou, Y.-C.; Chen, I.-C.; Lee,

Y.-P. J. Chem. Phys. 2001, 114, 7396.

(18) Gu ¨the, F.; Locht, R.; Leyh, B.; Baumga ¨rtel, H.; Weitzel, K.-M. J.

Phys. Chem. A 1999, 103, 8404.

(19) Gu ¨the, F.; Locht, R.; Baumga ¨rtel, H.; Weitzel, K.-M. J. Phys. Chem.

A 2001, 105, 7508.

(20) Yoon, S. H.; Choe, J. C.; Kim, M. S. Int. J. Mass Spectrom. 2003,

227, 21.

(21) Kunsa ´gi-Ma ´te ´, S.; Ve ´gh, E.; Nagy, G.; Kolla ´r, L. Chem. Phys. Lett.

2004, 388, 84.

(22) Martı ´nez-Nu ´n ˜ez, E.; Va ´squez, S. A. J. Chem. Phys. 2004, 121, 5179.

(23) Sato, K.; Tsunashima, S.; Takayanagi, T.; Fijisawa, G.; Yokoyama,

A. Chem. Phys. Lett. 1995, 242, 401.

(24) Smith, B. J.; Coffey, D., Jr.; Radom, L. J. Chem. Phys. 1992, 97,

6113.

(25) Martı ´nez-Nu ´n ˜ez, E.; Va ´squez, S. A. Struct. Chem. 2001, 12, 95.

(26) Ljubic ´, I.; Sabljic ´, A. J. Phys. Chem. A 2002, 106, 4745.

(27) Li, L.-C.; Deng, P.; Xu, M.-H.; Wong, N.-B. Int. J. Quantum Chem.

2004, 98, 309.

(28) Bacskay, G. B. Mol. Phys. 2003, 101, 1955.

(29) Bunge, A. J. Chem. Phys. 1970, 53, 20.

(30) Dunning, T. H., Jr. J. Chem. Phys. 1989, 90, 1007.

(31) Kendall, R. A.; Dunning, T. H., Jr.; Harrison, R. J. J. Chem. Phys.

1992, 96, 6769.

(32) Langhoff, S. R.; Davidson, E. R. Int. J. Quantum Chem. 1974, 8,

61.

(33) Bruna, P. J.; Peyerimhoff, S. D.; Buenker; R. J. Chem. Phys. Lett.

1981, 72, 278.

(34) Woon, D. E.; Dunning, T. H., Jr. J. Chem. Phys. 1994, 100, 2975.

(35) van Mourik, T.; Wilson, A. K.; Dunning, T. H., Jr. Mol. Phys. 1999,

96, 529.

(36) Mu ¨ller, T.; Dallos, M.; Lischka, H. J. Chem. Phys. 1999, 110, 7176.

(37) Dallos, M.; Lischka, H. Theor. Chem. Acc. 2004, 112, 16.

(38) Shepard, R. AdV. Chem. Phys. 1987, 69, 63.

5174 J. Phys. Chem. A, Vol. 109, No. 23, 2005

Barbatti et al.

Page 8

(39) Bobrowicz, F. W.; Goddard, W. A., III In Methods of Electronic

Structure Theory; Schaefer, H. F., III, Ed.; Plenum: New York, 1977; p

79.

(40) Christiansen, O.; Koch, H.; Jørgensen, P. Chem. Phys. Lett. 1995,

243, 409.

(41) Ha ¨ttig, C.; Ko ¨hn, A. J. Chem. Phys. 2002, 117, 6939.

(42) Ha ¨ttig, C. J. Chem. Phys. 2003, 118, 7751.

(43) Ko ¨hn, A.; Ha ¨ttig, C. J. Chem. Phys. 2003, 119, 5021.

(44) Shepard, R. Int. J. Quantum Chem. 1987, 31, 33.

(45) Shepard, R.; Lischka, H.; Szalay, P. G.; Kovar, T.; Ernzerhof, M.

J. Chem. Phys. 1992, 96, 2085.

(46) Shepard, R. In Modern Electronic Structure Theory Part I; Yarkony,

D. R., Ed.; World Scientific: Singapore, 1995; p 345.

(47) Lischka, H.; Dallos, M.; Shepard, R. Mol. Phys. 2002, 100, 1647.

(48) Dallos, M.; Lischka, H.; Shepard, R.; Yarkony, D. R.; Szalay, P.

G. J. Chem. Phys. 2004, 120, 7330.

(49) Csa ´za ´r, P.; Pulay, P. J. Mol. Struct. 1984, 114, 31.

(50) Fogarasi, G.; Zhou, X.; Taylor, P. W.; Pulay, P. J. Am. Chem. Soc.

1992, 114, 8191.

(51) Lischka, H.; Shepard, R.; Brown, F. B.; Shavitt, I. Int. J. Quantum

Chem. 1981, 15, 91.

(52) Shepard, R.; Shavitt, I.; Pitzer, R. M.; Comeau, D. C.; Pepper, M.;

Lischka, H.; Szalay, P. G.; Ahlrichs, R.; Brown, F. B.; Zhao, J. Int. J.

Quantum Chem., Quantum Chem. Symp. 1988, 22, 149.

(53) Lischka, H.; Shepard, R.; Pitzer, R. M.; Shavitt, I.; Dallos, M.;

Mu ¨ller, Th.; Szalay, P. G.; Seth, M.; Kedziora, G. S.; Yabushita, S.; Zhang,

Z. Phys. Chem. Chem. Phys. 2001, 3, 664.

(54) Lischka, H.; Shepard, R.; Shavitt, I.; Pitzer, R. M.; Dallos, M.;

Mu ¨ller, Th.; Szalay, P. G.; Brown, F. B.; Ahlrichs, R.; Bo ¨hm, H. J.; Chang,

A.; Comeau, D. C.; Gdanitz, R.; Dachsel, H.; Ehrhardt, C.; Ernzerhof, M.;

Ho ¨chtl, P.; Irle, S.; Kedziora, G.; Kovar, T.; Parasuk, V.; Pepper, M. J. M.;

Scharf, P.; Schiffer, H.; Schindler, M.; Schu ¨ler, M.; Seth, M.; Stahlberg,

E. A.; Zhao, J.-G.; Yabushita, S.; Zhang, Z. COLUMBUS, an ab initio

electronic structure program, release 5.9, 2004.

(55) Helgaker, T.; Jensen, H. J. Aa.; Jørgensen, P.; Olsen, J.; Ruud, K.;

A ° gren, H.; Andersen, T.; Bak, K. L.; Bakken, V.; Christiansen, O.; Dahle,

P.; Dalskov, E. K.; Enevoldsen, T.; Heiberg, H.; Hettema, H.; Jonsson, D.;

Kirpekar, S.; Kobayashi, R.; Koch, H.; Mikkelsen, K. V.; Norman, P.;

Packer, M. J.; Saue, T.; Taylor, P. R.; Vahtras, O. DALTON, an ab initio

electronic structure program, Release 1.0, 1997.

(56) Ahlrichs, R.; Ba ¨r, M.; Ha ¨ser, M.; Horn, H.; Ko ¨lmel, C. Chem. Phys.

Lett. 1989, 162, 165.

(57) Be ´langer, G.; Sandorfy, C. J. Phys. Chem. A 1971, 55, 2055.

(58) Petrongolo, C.; Buenker, R. J.; Peyerimhoff, S. D. J. Chem. Phys.

1982, 76, 3655.

(59) Barbatti, M.; Paier, J.; Lischka, H. J. Chem. Phys. 2004, 121, 11614.

(60) Krawczyk, R. P.; Viel, A.; Manthe, U.; Domcke, W. J. Chem. Phys.

2003, 119, 1397.

(61) Bonac ˇic ´-Koutecky ´, V.; Koutecky ´, J.; Michl, J. Angew. Chem., Int.

Ed. 1987, 26, 170.

(62) Michl, J.; Bonac ˇic ´-Koutecky ´, V. Electronic Aspects of Organic

Photochemistry; Wiley: New York, 1990.

(63) Laino, T.; Passerone, D. Chem. Phys. Lett. 2004, 389, 1.

(64) Toniolo, A.; Ben-Nun, M.; Martı ´nez, T. J. J. Phys. Chem. A 2002,

106, 4679.

(65) Jasper, A. W.; Truhlar, D. G. J. Chem. Phys. 2005, 122, 044101.

(66) Yarkony, D. R. J. Chem. Phys. 2001, 114, 2601.

(67) Liu, R. S. H.; Asato, A. E. Proc. Natl. Acad. Sci. U.S.A. 1985, 82,

259.

(68) Muller, A. M.; Lochbrunner, S.; Schmid, W. E.; Fuss, W. Angew.

Chem., Int. Ed. 1998, 37, 505.

(69) Liu, R. S. H.; Hammond, G. S. Chem. Eur. J. 2001, 7, 4536.

(70) Wald, G. Science 1968, 162, 230.

(71) Wilson, E. B.; Decius, J. C.; Cross, P. C. Molecular Vibrations:

the theory of infrared and Raman Vibrational spectra; McGraw-Hill: New

York, 1955; p 58.

(72) Quenneville, J.; Martı ´nez, T. J. J. Phys. Chem. A 2003, 107, 829.

(73) Bearpark, M. J.; Bernardi, F.; Clifford, S.; Olivucci, M.; Robb, M.

A.; Vreven T. J. Phys. Chem. A 1997, 101, 3841.

(74) Fuss, W.; Kosmidis, C.; Schmid, W. E.; Trushin, S. A. Angew.

Chem., Int. Ed. 2004, 43, 4178.

(75) Ben-Nun, M.; Quenneville, J.; Martı ´nez, T. J. J. Phys. Chem. A

2000, 104, 5161.

(76) Barbatti, M.; Granucci, G.; Persico, M.; Lischka, H. Chem. Phys.

Lett. 2005, 401, 276.

(77) Pen ˜a-Gallego, A.; Martı ´nez-Nu ´n ˜ez, E.; Va ´zquez, S. A. Chem. Phys.

Lett. 2002, 353, 418.

(78) Domcke, W. In Conical Intersections; Advanced Series in Physical

Chemistry 15; Domcke, W., Yarkony, D. R., Ko ¨ppel, H., Eds.; World

Scientific: Singapore, 2004; p 395.

Excited-State Energy Surfaces of Fluoroethylene

J. Phys. Chem. A, Vol. 109, No. 23, 2005 5175