Laser-operated chiral molecular switch: quantum simulations for the

controlled transformation between achiral and chiral atropisomers

Dominik Kroner* and Bastian Klaumunzer

Received 20th April 2007, Accepted 9th July 2007

First published as an Advance Article on the web 25th July 2007

DOI: 10.1039/b705974d

We report quantum dynamical simulations for the laser controlled isomerization of 1-(2-cis-

fluoroethenyl)-2-fluorobenzene based on one-dimensional electronic ground and excited state

potentials obtained from (TD)DFT calculations. 1-(2-cis-fluoroethenyl)-2-fluorobenzene supports

two chiral and one achiral atropisomers, the latter being the most stable isomer at room

temperature. Using a linearly polarized IR laser pulse the molecule is excited to an internal

rotation around its chiral axis, i.e. around the C–C single bond between phenyl ring and ethenyl

group, changing the molecular chirality. A second linearly polarized laser pulse stops the torsion

to prepare the desired enantiomeric form of the molecule. This laser control allows the selective

switching between the achiral and either the left- or right-handed form of the molecule. Once the

chirality is ‘‘switched on’’ linearly polarized UV laser pulses allow the selective change of the

chirality using the electronic excited state as intermediate state.

1. Introduction

The effect of molecular chirality on chemical or biochemical

processes is an important topic of research nowadays. To

reach perfect control of the stereoselectivity in chemical reac-

tions is, for instance, one of the major challenges in chemistry.

The influence of electro-magnetic fields on the enantiomeric

excess in chemical synthesis was particularly investigated by

experimentalists. The difference in the absorption coefficients

of two enantiomers for circularly polarized light may be used,

e.g. to induce enantioselectivity in a photochemical reaction.1,2

Yet, traditional chemistry offers a variety of effective and well

established ways for stereoselective synthesis, e.g. by employ-

ing chiral catalysts which drive a reaction towards the desired

stereoisomer.3–5 Here, a change of the chirality of the catalyst,

e.g. by external laser fields, could control which stereoisomer is

produced in the reaction. Indeed, chemical compounds, so-

called chiroptical switches, exist that undergo, often cis–trans,

isomerization upon irradiation at the appropriate wavelength

resulting in a change of the chirality of the system. Feringa and

coworkers presented a chiroptical molecular switch with per-

fect stereo-control6 based on a modified version of his light-

driven unidirectional molecular rotor.7 Various applications

of chiroptical switches are possible in the field of nanoscale

devices ranging from liquid crystal displays to data storage

and information processing.8 In general, research on photo-

switchable compounds has mainly focused on cis–trans iso-

merization and photocyclization reactions.9,10 For example,

Geppert et al. proposed a laser control scheme for the rever-

sible ring-opening of cyclohexadiene, a model system for a

molecular switch.11 Characteristic for these isomerization

processes is that a bond is broken and/or (re)formed in

the intermediate state. Yet, also conformational changes

without affecting the bond grade can be the basis for a

photo-switchable chiral system. Umeda et al. performed

quantum simulations for the optical isomerization of helical

difluorobenzo[c]phenanthrene.12 Recently, Hoki et al. pre-

sented quantum simulations for the change of axial chiral

1,10-binaphthyl from its P- to M-form by laser induced torsion

around a single bond.13

Various theoretical investigations have been carried out

describing molecular chirality by means of quantum me-

chanics with the aim to control chirality with light14–17 or to

determine the parity violating energy difference between en-

antiomers.18–20 For instance, in quantum simulations for axial

chiral molecules it was shown that linearly polarized laser

pulses can be used to purify a racemate.21–32 Gerbasi et al.

applied coherent control21 to enhance the fraction of one

enantiomer in a racemic mixture of randomly oriented mole-

cules in a so-called laser distillation mechanism.22,23 Kral and

et al. proposed a cyclic population transfer that results in the

selective excitation of one enantiomer relative to its mirror

image based on laser induced interferences in a 3-level sys-

tem24 and extended this approach to purify a racemate.25 At

the same time, the laser controlled excitation of an enantiomer

as well as its selective transformation into its counterpart

starting from a racemic mixture was also accomplished by

others and us for various axial chiral molecular model sys-

tems.26–32 The developed laser control mechanisms range from

sequences of state selective linearly26 or circularly polarized

pump/dump pulses27 and stimulated Raman adiabatic passage

(STIRAP)28,29 to enantioselective laser pulses.30–32 Interest-

ingly, the molecular model systems 1,3-dimethylallene22 and

(4-methyl-cyclohexylidene)-fluoromethane32 show many simi-

larities to experimental chiroptical switches8 due to their

ability to change their chirality upon laser-induced isomeriza-

tion of a double bond. In all these studies the initial state of the

system describes a racemate, i.e. a 1 : 1 mixture of the two

enantiomeric isomers of the molecule. The laser controlInstitut fur Chemie, Universitat Potsdam, Karl-Liebknecht-Str. 24-25,D-14476 Potsdam, Germany. E-mail: kroener@uni-potsdam.de

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induces a transformation of one enantiomer into its counter-

part, thereby increasing the amount of the target enantiomer.

However, the respective molecules possess no stable achiral

molecular isomer.

In this paper we address the concept of a molecular system

that supports an achiral form and a pair of chiral forms. Our

aim is not the purification of racemic mixtures, but to intro-

duce a new type of laser-operated chiroptical molecular

switch. The quantum simulations are based on 1-(2-cis-fluoro-

ethenyl)-2-fluorobenzene, a F-substituted styrene derivative,

which can be transformed from its achiral isomer to a chiral

isomer and from one enantiomer to the other by internal

rotation. A new laser control mechanism is presented which

induces the selective change of the molecular conformation

and thereby controls the chirality of the system. Note that the

most stable form of the molecule proposed in this work is

achiral, whereas the chiroptical switches discussed above have

only chiral stereoisomers. Our molecular switch has, therefore,

a true ‘‘off’’ state, i.e. no chirality is observed, which is not

caused by racemization but is due to the symmetric molecular

structure of one of its isomers.

The rest of the paper is organized as follows: The model

system and the applied theoretical methods are explained in

section 2, the results of the quantum chemical as well as the

quantum dynamical calculations including the stereoselective

laser control are presented and discussed in section 3, and

section 4 summarizes the results.

2. Model and theory

2.1 Quantum chemistry

1-(2-cis-fluoroethenyl)-2-fluorobenzene possesses two chiral,

(aS) and (aR), and one achiral atropisomers, the latter being

the most stable conformation at room temperature, see Fig. 1.

The three stereoisomers of 1-(2-cis-fluoroethenyl)-2-fluoroben-

zene are interconnected by torsion around the C–C single

bond between phenyl ring and ethylene group.

The molecule is assumed to be pre-oriented with its C1–C10

bond along the space-fixed z-axis, as depicted in Fig. 2(a). The

degree of internal rotation (torsion) is measured by the

dihedral y between C2, C1, C10 and C2

0, cf. Fig. 2(a). The 4

atoms lying along the z-axis (H–C4, C1, C10) form the chiral

axis of the molecule. A torsion around the C1–C10 bond

changes, therefore, the chirality of the molecule.

The geometry of the molecule was optimized using MP2/6-

311G(d) level of theory, as implemented in GAUSSIAN03

package.33 The minimum energy geometry (y = 1801) was

used as reference geometry to calculate the potential energy

surface (PES) for the ground and the electronic singlet excited

states along y while keeping the rest of the geometrical

parameters frozen. In particular, density functional theory

(DFT) and time-dependent DFT (TDDFT) were employed

using the hybrid functional B3LYP34,35 with a 6-311G(d) basis

set. Permanent and transition dipole moments along y have

been obtained at the same level of theory as the PESs.

2.2 Model Hamiltonian

To obtain the torsional eigenenergies esv and eigenfunctions fsv

of the electronic ground (s= g) and the first electronic excited

state (s = e) the time-independent Schrodinger equation

HsmolðyÞfs

v ðyÞ ¼ esvfsv ðyÞ ð1Þ

is numerically solved. The molecular Hamiltonian is given by

HsmolðyÞ ¼ �

�h2

2Iz

@2

@y2þ VsðyÞ ð2Þ

with Vs(y) being either the ground (s = g) or excited state (s= e) potential obtained from (TD)DFT calculations (Fig. 3).

Iz is the moment of inertia for the rotation of the ethenyl group

around the space-fixed z-axis: Iz = Simir2i = 769 466.45mea

20.

Eqn (1) was numerically solved by the Fourier grid Hamilto-

nian method36 using 1024 grid points.

The overall rotation of the molecule is neglected in this

approach. We assume that the phenyl ring is fixed to a solid

surface by linking substituents in the C3 and C5 position, as

sketched in Fig. 1. For a description of internal rotation

Fig. 1 Atropisomers of 1-(2-cis-fluoroethenyl)-2-fluorobenzene che-

misorbed on a solid surface by appropriate linking groups (schematic).

The achiral isomer corresponds to the minimum energy geometry.

Fig. 2 Optimized geometries of 1-(2-cis-fluoroethenyl)-2-fluoroben-

zene obtained fromMP2/6-311G(d): (a) Minimum energy geometry of

the achiral stereoisomer with a torsion angle of y= 1801, the molecule

is oriented in the space-fixed coordinate system as shown. (b) Geo-

metry of the (aR)-atropisomer with y = 310.71; for the corresponding

(aS)-enantiomer y = �310.71 = 49.31 (not shown).

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coupled to the overall rotation of an axial chiral molecule the

reader is referred to ref. 27.

2.3 Quantum dynamics

The laser-driven quantum dynamics are performed by numeri-

cally solving the time-dependent Schrodinger equation

i�h@

@tCðy; tÞ ¼ Hðy; tÞCðy; tÞ ð3Þ

for

Cðy; tÞ ¼ Ceðy; tÞCgðy; tÞ

� �ð4Þ

with Cg(t) and Ce(t) being the wavefunction of the electronic

ground (g) and excited state (e). The Hamilton operator H(y,t)is given by

Hðy; tÞ ¼ He

molðyÞ � m!eeðyÞ � E

!ðtÞ �m!

egðyÞ � E!ðtÞ

�m!geðyÞ � E

!ðtÞ H

g

molðyÞ � m!ggðyÞ � E

!ðtÞ

!;

ð5Þ

where ~mss(y) are the permanent dipole moments of the ground

(gg) and electronic excited state (ee), and ~mst(f) are the

electronic transition dipole moments. For the dynamical cal-

culations we used ~mee(y) = ~mgg(y) and ~meg(y) = ~mge(y).The electric field ~E(t) of the laser pulses used for control is

given by the following analytical expression

E!ðtÞ ¼ e

!a E

0 cosðoðt� tcÞ þ ZÞ sin2 pðt� tcÞ2fwhm

þ p2

� �; ð6Þ

for |t � tc|r fwhm. Z is the time-independent phase, fwhm the

full width at half maximum (2fwhm equals the pulse duration)

and tc the pulse center, i.e. the time when the sin2-shape

function reaches its maximum. The polarization vector ~ea =

~excos a + ~eysin a is perpendicular to the z-axis and oriented

along the polarization angle a, where ~ex/y are the unit vectors

along the x/y-axis. E0 is the electric field amplitude. The laser

frequency o can be linearly chirped by _o ¼ dodt:

oðtÞ ¼ o0 þ _oðt� tcÞ; ð7Þ

where o0 is the central frequency at t = tc. All quantum

dynamical propagations were carried out by the wavepacket

program package37 using second-order operator splitting38 in

grid representation (1024 points) with a time step of 0.1 fs.

3. Results and discussion

3.1 Potential energy surfaces and dipole functions

In the minimum energy geometry, obtained from MP2/6-

311G(d),39 y = 1801, i.e. the F-substituents point in opposite

x-directions, see Fig. 2(a). The molecule is planar and has CS-

symmetry, thus, it is achiral. Two further stable atropisomers

are found for y = 49.3 and 310.71, see Fig. 2(b). They are

mirror images of each other, but cannot be superimposed,

therefore, they are enantiomers.

The geometries were also optimized using 6-311G(d,p) and

6-311+G(d). For the minimum energy geometry y = 1801

irrespective of the employed basis set. For the chiral geome-

tries y varies from 49.3/310.71 (6-311G(d,p)) to 49.1/310.91

(6-311+G(d)), i.e. the differences to the 6-311G(d) basis are so

small that they are negligible for our needs. Qualitatively all

three basis sets give the same results. The quantitative differ-

ences for the remaining geometrical parameters are also very

small. A normal mode analysis using MP2/6-31G(d) shows

that the main vibrational excitations start above B700 cm�1

which is about one order of magnitude higher in energy than

the torsion considered here. Still, a weak coupling to an out-

of-plane phenyl ring–ethenyl twisting, which actually mimics

the torsion around the C1–C10 bond, at B19 cm�1 with a very

low IR intensity cannot completely be ruled out.

The unrelaxed PESs along y for the electronic ground S0and two lowest singlet excited states S1 and S2, calculated at

B3LYP/6-311G(d) level of theory, are shown in Fig. 3. The

potential curves are fitted from 92 single point calculations

using cubic spline interpolation.

Due to the CS-symmetry of the reference geometry (Fig.

2(a)) the PESs are symmetric with respect to y = 1801. Each

minimum of the ground state potential Vg(y) is related to one

of the three stereoisomers: the lowest minimum at y = 1801

corresponds to the achiral isomer, while the two equivalent

minima at y E 47.51 and y E 312.51 correspond to the (aS)-

and (aR)-enantiomers, see Fig. 3. The torsional angles at the

potential minima differ slightly from the angles of the opti-

mized geometries, because all geometrical parameters, except

the torsional angle, were kept frozen for the calculation of the

PESs.

Low barriers are found between achiral and chiral stereo-

isomers (yE 85/2751), see Fig. 3. They are not caused by steric

interactions of the substituents, but are due to the loss of

conjugation between the aromatic systems and the ethenyl

group. With approx. 2100 cm�1 (25 kJ mol�1) these maxima

are about two times higher than the torsion barrier of ethane

(B12.6 kJ mol�1). The outer, higher potential barrier at y =

01, where the two fluorine substituents are closest to each

other, is with about 11 300 cm�1 (135 kJ mol�1) more than five

Fig. 3 Potential energy surface of 1-(2-cis-fluoroethenyl)-2-fluoro-

benzene along the torsion angle y for the electronic ground state S0(Vg), the first singlet excited state S1 (Ve) and the second singlet excited

state S2 (dashed line) resulting from B3LYP/6-311G(d) calculations.

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times higher than the low barriers. At room temperature the

achiral isomer is almost exclusively found.

The electronic excited state potentials show two minima at

y = 0 and 1801 for both S1 and S2, as well as two maxima at

y E 92/2681 or at y E 95/2651 for S1 or for S2, respectively

(Fig. 3). The vertical electronic excitation energies at y = 1801

are 4.74 eV for S0 - S1 and 5.11 eV for S0 - S2. For

comparison, experimental UV spectra of unsubstituted styrene

show two absorption bands, the positions of the 0–0 transi-

tions to the first two excited singlet states have been deter-

mined at 4.31 eV40 and 4.88 eV;41 ab initio calculations result

in 4.81 and 4.97 eV (TDDFT-B3LYP)42 or 4.34 and 4.97 eV

(CASPT2)43 for S0 - S1 and S0 - S2, respectively.

In Table 1 the dominant electronic transitions for the

configurations describing the S1 and S2 state are listed for

y = 0, �49.3 and 1801. The electronic excitation from S0 to

either singlet excited states S1 or S2 is mainly characterized by

transitions from orbitals 35 and 36 (HOMO�1 and HOMO)

to orbitals 37 and 38 (LUMO and LUMO+1). The relevant

orbitals involved in the electronic transitions (35–38) are

shown in Fig. 4 exemplarily for y = 1801. They are qualita-

tively in good agreement with calculated MOs of unsubstituted

styrene.44 In general, substitution of a benzene ring lowers the

symmetry lifting the degeneracy of the p- and p*-orbitals of

the aromatic system. Therefore, two occupied p-type orbitals,HOMO�1 (35) and HOMO (36), and two p*-type orbitals,

LUMO (36) and LUMO+1 (37), are found for our styrene

derivative, see Fig. 4. The S0 - S1 and S0 - S2 transitions can

be assigned to p - p* transitions, cf. Table 1. Note that the

length of all p-bonds will slightly increase upon electronic

excitation due to the p* character of the excited states. Here we

restrict ourselves to the torsion around y and neglect the effect

of other modes on the efficiency of the laser induced electronic

transitions. In the following we will consider electronic transi-

tions only between S0 and S1,45 the respective potential curves

along y are labeled Vg and Ve, see Fig. 3.

The calculated x-, y- and z-components of the permanent

dipole moment ~mgg as well as of the transition dipole moment

~meg are depicted in Fig. 5(a) and (b). The x- and z-components

are symmetric with respect to y = 1801, whereas the y-

components are anti-symmetric. Two dipole components with

opposite symmetry, here mggx and mggy , are required for stereo-

selective laser pulses,31 cf. section 3.3. The respective IR laser

pulses are polarized in the x,y-plane, i.e. they propagate along

the z-axis. For electronic transitions the laser fields were

chosen to be z-polarized, because megz undergoes the largest

change along y.For comparison relevant points of the PESs and the (transi-

tion) dipole moments along y were also calculated employing

6-311G(d,p) and 6-311+G(d) basis sets. The results obtained

from all basis sets agree qualitatively well. PESs and (transi-

tion) dipole moments for 6-311G(d) and 6-311G(d,p) are

Table 1 Main configurations describing the S1 and S2 states withrespective coefficients at y = 0, �49.7 and 1801 of 1-(2-cis-fluoroethe-nyl)-2-fluorobenzene calculated at the B3LYP/6-311G(d) level oftheory

Statey = 01 y = �49.31 y = 1801Transition/coeff. Transition/coeff. Transition/coeff.

S1 35 - 37/0.38 35 - 37/0.37 35 - 37/0.4136 - 37/0.47 36 - 37/0.46 36 - 37/0.4136 - 38/0.31 36 - 38/0.32 36 - 38/0.35

S2 35 - 37/0.32 35 - 37/0.40 35 - 37/0.3936 - 37/0.41 36 - 37/0.43 36 - 37/0.4636 - 38/0.41 36 - 38/0.28 36 - 38/0.22

Fig. 4 Orbitals 35–38 of 1-(2-cis-fluoroethenyl)-2-fluorobenzene for

y = 1801 as obtained from TDDFT calculations.

Fig. 5 x-, y- and z-component along y for (a) the permanent dipole

moment ~mgg and (b) the transition dipole moment ~meg (B3LYP/6-

311G(d)).

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quantitatively in good agreement, too. For 6-311+G(d) some

differences are found due to the diffuse functions: The small

barriers of Vg are lowered byB10% and the PESs of S1 and S2are lowered in energy compared to 6-311G(d) and 6-311G(d,p)

by B150 cm�1 (19 meV) and B550 cm�1 (68 meV) depending

on y. Small difference in the order of about 5–10% are also

found for (transition) dipole moments. However, since our

simulations focus on the laser pulse control of molecular

dynamics the small variations between the basis sets are not

further considered in this work.

3.2 Torsional eigenstates and localized wavefunctions

A selection of torsional eigenenergies of the ground state egv islisted in Table 2. The corresponding eigenfunctions fg

v are

either symmetric (denoted +) or anti-symmetric (denoted �)with respect to y = 1801. Up to v = 57� torsional eigenfunc-

tion are exclusively localized in the central well (y = 1801),

they characterize the achiral isomer.

The following eigenfunctions with 57�o vo 105�, i.e. foreigenenergies up to the top of the low barriers (y E 85/2751),

show oscillations either in both outer wells (y E 50/3101) or in

the region of the central minimum. Those eigenfunctions fgv

that can exclusively be assigned to both side minima describe

the torsion of the two chiral isomers. The respective eigen-

energies form near degenerate doublets due to the symmetry of

the potential, see Table 2.

The eigenfunctions of the near degenerate doublets are used

to construct wavefunctions localized in only one of the two

outer wells. These localized wavefunctions CuS/R are defined

by either positive or negative superpositions of the + and

� eigenfunctions, fgv+ and fg

v0�, of a doublet u:46

CuS ¼1ffiffiffi2p fg

vþ þ fgv0�

� �ð8Þ

CuR ¼1ffiffiffi2p fg

vþ � fgv0�

� �: ð9Þ

The wavefunction CuS is localized in the left potential mini-

mum (yE 501), whereas,CuR is localized in the right well (yE3101). Thus, CuS and CuR correspond to the (aS)- and the

(aR)-enantiomer, respectively. Eqn (8) and (9) apply only to

those states in the range of 58+r vr 104+ which form near

degenerated doublets of eigenstates, see Table 2. Altogether

eleven doublets, denoted u = 0, 1, � � �, 10, can be assigned to

the chiral isomers. For two highest doublets u= 9 and u = 10

the respective eigenfunctions fg99�/f

g100+ and fg

103�/fg104+

already show some density in the region of the central well.

Strictly speaking, they cannot be assigned exclusively to one

type of isomer. However, they mainly characterize the chiral

isomers and are, therefore, used to construct localized wave-

functions CuS/R. The same problem applies to the eigenfunc-

tions fg98+, fg

101� and fg102+ which are mainly localized in the

inner well, but also show increasing amplitudes in the outer

wells with increasing energy. Still, for convenience they are

considered to belong to the achiral conformer.

The localized wavefunctions CuS and CuR are not eigen-

functions of the molecular Hamiltonian (2). Thus, they are not

stationary, but tunnel through the potential barriers. The

‘‘lifetime’’ tu of an enantiomer, i.e. the time of the correspond-

ing localized wavefunction to tunnel through the potential

barriers until it overlaps with its counterpart, is given by:

Deutu ¼h

2; Deu ¼ jev0� � evþj: ð10Þ

Deu is the energy splitting of doublet u of near degenerate

states v+/v0�. The energy splittings of the doublets of eigen-

states with u = 0–8 listed in Table 2 are not zero, because the

potential barriers are finite. Yet, the calculated energy differ-

ences Deu for u = 0–6 are smaller than the numerical error,

which is in the order of 1� 10�13 cm�1, resulting in ‘‘lifetimes’’

tu in the order of at least minutes. For u = 7, 8, 9 and 10,

Deu = 3.2 � 10�10, 2.1 � 10�6, 2.3 � 10�3 and 4.3 � 10�1

cm�1; the respective ‘‘lifetimes’’ are tu = 5.2 ms, 7.9 ms, 7.3 ns

and 39 ps. Except for the highest doublet u = 10 the resulting

‘‘lifetimes’’ are very long compared to the simulation time (fs

to ps) and should allow for an experimental monitoring of the

result of the laser control. However, in the dynamical simula-

tions extra attention was paid to the two highest doublets u =

9 and 10 since they may reduce the success of the employed

control strategies.

For v Z 105�, i.e. energies above the low barriers, fgv

shows oscillations in the region of all wells, i.e. achiral and

Table 2 The four lowest torsional eigenenergies of the electronicground state egv for the achiral isomer and the eleven energy doublets u,corresponding to the two enantiomers, with their assigned localizedwavefunctions CuS/R

State v egv/cm�1 CuS/R

0+ 13.2893 – (achiral)1� 40.1446 – (achiral)2+ 67.5522 – (achiral)3� 95.4485 – (achiral)

58+ 1587.71�

0S/0R59� 1587.71

63� 1651.19�

1S/1R64+ 1651.19

67� 1712.03�

2S/2R68+ 1712.03

72+ 1770.43�

3S/3R73� 1770.43

76+ 1826.43�

4S/4R77� 1826.43

81� 1879.91�

5S/5R82+ 1879.91

85� 1930.59�

6S/6R86+ 1930.59

90+ 1978.05�

7S/7R91� 1978.05

94+ 2021.85�

8S/8R95� 2021.85

99� 2061.37�

9S/9R100+ 2061.38

103� 2094.88�

10S/10R104+ 2095.31

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chiral isomers cannot be distinguished anymore in terms of

torsional quantum states.

3.3 Selective laser pulse control

For the quantum dynamical simulations the system is initially

assumed to be in the torsional ground state, i.e. C(t = 0) =

fg0. The goal of laser control is, first, to induce internal

rotation of the ethenyl group around the C1–C01 axis and,

second, to stop the rotation when the desired enantiomer is

reached.

In order to obtain a sufficient internal rotation a compact

wavepacket moving above the low barriers is desired. This is

accomplished by an y-polarized IR laser pulse which formally

excites the molecule from v= 0+ to v= 1�. However, due to

the near-harmonicity of the central potential well a so-called

ladder climbing is induced, i.e. population is further trans-

ferred to higher states. To account for the small changes of the

spacing between the torsional energies the pulse frequency is

linearly chirped,47–49 a small frequency increase with time of

_o = 0.004 cm�1 fs�1 was found beneficial. Note that the

spacing of the states of the achiral isomers is not systematically

changing due to the mixing with the states of the chiral

isomers. For highly excited torsional states with small energy

spacings multiple excitations are also likely to be induced by

the IR pulse towards the end of its pulse duration when its

frequency is highest. Fig. 6(a) shows the optimized electric

field E(t), all laser parameters are listed in Table 3. The

resulting time evolution of the expectation value of the torsion

angle hyi and of the torsional momentum hli are depicted in

Fig. 6(b) and (c). hli(t) maps the shape of the potential, at

t E 2650 ps hli increases again after passing through a small

minimum, i.e. the system has accumulated enough energy to

overcome the low barrier at y E 2751. Afterwards hyi oscil-lates between B3301 and B301.

The following IR pulse is designed to dump the wavepacket

into the right outer minimum (y E 3101). That requires the

electric field ~E to be polarized such that it only interacts with

the desired (aR)-enantiomer while its interaction with the

(aS)-enantiomer is suppressed30,31

e!ahCuRjm!jCu0Ria0 ð11Þ

e!ahCuSjm!jCu0Si ¼ 0 uau0: ð12Þ

From eqn (12) an expression for the polarization angle a can

be derived

tan a ¼ � CuS mx Cu0Sjjh iCuS my Cu0Sj

��� : ð13Þ

For the dump pulse u was set to 0 and u0 to 1 similar to the

stereoselective dump pulse used in a system of two diaster-

eomeric pairs of enantiomers.50 The resulting polarization

angle a = �39.21 allows a transition from 1R to 0R, but

suppresses 1S - 0S. Note that a change of the sign of a will

change the enantioselectivity of the laser, i.e. for a = +39.21

1R - 0R is suppressed. For further details on stereoselective

laser pulses the reader is referred to ref. 32. The frequency of

the pulse is first downchirped and then upchirped; note that in

this case | _ofwhm| 4 o0. The downchirp leads to a additional

decrease in the kinetic energy of the wavepacket (not shown),

whereas the upchirp ensures that transitions between ‘‘chiral’’

states (u+ 1)- u are induced which are higher in energy than

neighboring (v+ 1)- v transitions between states assigned to

the achiral isomer.

In Fig. 6(a) and Table 3 all data for the stereoselective dump

pulse are found. After the dump pulse (tf = 5800 fs) the

wavepacket is localized in the right well (hyiE 3041), see Fig.

6(b), and it is only slowly moving, see small oscillations of hliaround zero in Fig. 6(c). At final time tf the total energy egtot is1701 cm�1 which is lower than the top of the small barriers

Fig. 6 Laser pulse sequence for the transformation of the achiral

isomer into the (aR)-enantiomer employing a stereoselective dump

pulse (for laser parameters see Table 3). Time evolution of (a) the

x- and y-component of the electric field, (b) the expectation value of

the torsion angle, (c) the expectation value of the angular momentum.

The results obtained when changing the phase Z of the pump pulse by

p are plotted with dotted lines (see text).

Table 3 Laser pulse parameters for the three laser pulse sequencesdepicted in Fig. 6–8, each consisting of pump (p) and dump (d) pulse

Fig.6 7 8

Parameter/type IR (p) IR (d) IR (p) UV (p/d)a UV (p) UV (d)

E0/GV m�1 5.5 6.5 5.5 2.24 1.22 1.30

a/1 +90.0 �39.2 �90.0 —b —b —b

(o0/2pc)/cm�1 30.5 19.5 30.5 36 901 38 050 37 650

( _o/2pc)/cm�1 fs�1 +0.004 +0.079 +0.004 +2.0 +0.5 �0.2fwhm/fs 2000 900 2000 500 250 250

tc/fs 2000 4900 2000 4980 250 690

Z/rad 1.35 �0.3 1.35 0.0 0.0 0.0�I/TW cm�2 4.0 5.6 4.0 0.0666 0.198 0.224

a Laser acts as pump and dump pulse. b ~ea = ~ez.

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(B2100 cm�1). A population analysis confirms that after the

pulse sequence (tf) about 95% of the population is found in

states 0R to 10R. Most of the population is found in states 1R

(43%) and 0R (35%); the part of the population in the ‘‘short’’

living states 9R and 10R sums up to only 2.2%. For 0S to 10S

the population is less than 1%. The remaining 5% of the

population are found in ‘‘delocalized’’ states above the small

barriers; this part of the wavepacket causes the very small

overall decrease of hyi after tf in Fig. 6(b).

It should be noted that the mean peak intensities

(�I ¼ 12e0cjE0 j2) of both IR pulses are very high, see Table 3,

making an experimental realization difficult. The high laser

amplitudes could be decreased by using longer pulse dura-

tions. However, longer pulses would increase the chance of

losing efficiency due to energy relaxation.

To demonstrate the stereoselectivity of the dump pulse the

initial phase Z of the pump pulse, which controls the direction

the wavepacket is initially moving, is changed by p. The laserfield is shown in Fig. 6(a) as a dotted curve. Due to the change

of the phase the wavepacket is now moving in the opposite

direction, as shown in Fig. 6(b) (dotted line). The dump pulse

is still polarized such that it only interacts with the (aR)-

enantiomer. Therefore, the wavepacket is not dumped when it

is above the left well. From the time-evolution of hyi and hli inFig. 6(b) and (c) (dotted lines) it is concluded that the system is

still strongly rotating back and forth after the laser pulse

sequence. However, about 13% of the population at final time

tf is found in states 0S to 10S, but most of it (B12%) in the

three highest states (8S, 9S and 10S) close to the top of the low

barriers. The remaining 87% of the population is spread

among the ‘‘delocalized’’ states above the lower maxima. In

conclusion, while the timing of the dump pulse certainly

determines its efficiency, its enantioselectivity is controlled by

the polarization of the laser field. The presented pulse se-

quence selectively transforms the achiral stereoisomer to the

desired enantiomer; the chirality of the system is ‘‘switched

on’’.

The application of stereoselective laser pulses requires that

the optimal polarization of the electric field is known, which

depends on the orientation of the molecule. There are theore-

tical and experimental ways for orienting or aligning polar

molecules e.g. in strong electric fields,51,52 using elliptically

polarized lasers53 or applying optimal control theory.54 Alter-

natively, alignment of chiral molecules can be achieved by

adsorbing them onto solid surfaces where they form domains

of unique chirality.55,56 Here we suggest connecting the mole-

cule to a surface by linking groups as sketched in Fig. 1.

In any case, the better the molecule is oriented the higher the

achieved stereoselectivity of the laser control.57 Hence, an

alternative approach to ‘‘switch on’’ the chirality of the

molecule, setting stereoselective laser pulses aside, is proposed:

while the pump pulse remains the same, except for a change of

Z (see below), the new second laser pulse uses the first electro-

nic excited state S1 as an intermediate state. Table 3 lists all

parameters of the UV pulse, in Fig. 7(a) E(t) is plotted. In Fig.

7(c) the population dynamics of the electronic ground and

excited state potential Vg and Ve are depicted. The single UV

pulse induces first a transition from Vg to Ve and then back

from Ve to Vg, i.e. it acts as pump and dump pulse. In both

cases more than 95% of population are transferred. Due to the

shape of the excited state potential the time period in whichCe

moves from one Franck–Condon (FC) point (y E 501) to the

other (y E 3101) is short enough for the UV pulse to induce

both transitions. The wavepacket is excited to Ve (around t =

4900 fs) when it passes the minimum of the left well of Vg (hyig(4900 fs) = 471), i.e. when its kinetic energy is high. The

momentum of the wavepacket is conserved during electronic

excitation such that Ce is additionally (yet to a small degree)

accelerated towards the minimum of Ve(0/3601) in addition to

the acceleration caused by the steep slope of Ve at the FC point

(y E 471). Shortly before Ce reaches its turning point on Ve,

i.e. when it is slowed down, it is above the right well of Vg.

That is when the second part of the UV pulse de-excites the

system. Here the linear increase of the laser frequency ( _o =

2 cm�1 fs�1) compensates for the increasing potential energy

of Ce which is still moving up the slope of Ve.

At final time (tf = 5480 fs) the wavepacket is localized in the

region of the right well (yE 3101), as can be observed from hyiin Fig. 7(b). Please note that the wavepacket on Ve figuratively

leaves the potential on the left side and re-enters on the right

side. Due to the definition range of the torsion angle the

expectation value function hyi(t) in Fig. 7(b) is not discontin-

uous but passes 1801 although the wavepacket never reaches

Fig. 7 Laser pulse sequence for the transformation of the achiral

isomer into the (aR)-enantiomer via the electronic excited state

potential employing an UV pump/dump pulse (for laser parameters

see Table 3). Time evolution of (a) the y-component and z-component

of the electric field, (b) the expectation value of the torsion angle, (c)

the population in Vg and Ve. The results obtained when changing the

phase Z of the pump pulse by p are plotted with dotted lines (see text).

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this region. A population analysis at tf confirms that 92% of

the population is distributed among the states 0R to 10R; the

population of states with some coupling to the achiral isomer

(9R and 10R) combine to only 2.4%. Another small part of

the population (1.2%) is located in states 0L to 10L, i.e. the

stereoselectivity is high in the case of the UV pulse, too. The

remaining population is spread among ‘‘delocalized’’ states

above the low barriers.

In order to obtain the (aR)-enantiomer at final time, the

phase of the IR pulse was changed by p in contrast to the

original IR pump pulse, compare dashed lines in Fig. 7(a) with

Fig. 6(a). This corresponds to a change of the sign of a (see eqn(6)), because the electric field is y-polarized, see Table 3. If the

phase of the IR pump pulse is changed by p again, the

opposite isomer, the (aS)-enantiomer, is prepared, see dotted

lines in Fig. 7(a) and (b). Therefore, the stereoselectivity of this

mechanism is controlled by the phase of the IR pump pulse,

i.e. by the direction of the internal rotation. But the molecule is

still changed from achiral to chiral independent of the initial

direction of the torsion, whereas in the previous mechanism,

using an explicitly stereoselective dump pulse, the change of

the initial phase prevented the chirality from being ‘‘switched

on’’ for the most part. Another difference of the UV pulse is its

small, experimentally more feasible intensity compared to the

stereoselective IR pump pulse, see Table 3.

However, if the IR-UV mechanism has resulted in the

undesired handedness of the molecular switch, a UV

pump–dump pulse sequence can be used to change the chir-

ality from (aR) to (aS) or vice versa. Fig. 8(a)–(c) show the

electric field of the chirality switching laser pulse sequence as

well as the resulting time evolution of hyi and of the popula-

tion in Vg and Ve for the case (aR) - (aS) starting from C0R.

The pump pulse transfers almost 100% of the population to

the electronic excited state, see Fig. 8(c). On Ve the wavepacket

moves towards the minimum of the potential at y = 0/3601.

Finally, the dump pulse transfers the population back to the

ground state when Ce has reached its turning point on Ve

which is roughly above the left minimum of Vg, see Fig. 8(b).

At final time (tf = 940 fs) the electronic ground state is

populated by 99.5%. About 93% of the ground state popula-

tion is localized in states 0L to 10L, however, some part of it

(7.7%) is found in states 9L and 10L. The total energy egtot at tfis with 1889 cm�1 indeed closer to the top of the small maxima

(B2100 cm�1) compared to egtot(tf) in the IR–IR mechanism.

Even if the population of the states 9L and 10L are considered

to belong to the achiral isomer, 85.3% is still localized in the

correct potential well. In addition, less than 1% population is

found in the uR states. Thus, we can conclude that the

handedness of the molecule was effectively switched.

4. Conclusions

We presented quantum simulations for a laser-operated chiral

molecular switch. The proposed molecule 1-(2-cis-fluoroethe-

nyl)-2-fluorobenzene possesses three stable stereoisomers, one

achiral and two enantiomeric atropisomers. The developed

laser control allows for the selective transformation of the

achiral isomer into either the left- or right-handed form of the

molecule, i.e. to ‘‘switch on’’ the chirality. Linearly polarized

laser pulses are used to control the chirality of the system. The

handedness of the molecule can also be ‘‘switched’’ using the

electronic excited state as intermediate state.

Initially, the molecule is excited to an internal rotation using

a IR laser pulse. Here, the phase of the laser field determines

the direction of the torsion. Afterwards, a second laser pulse

stops the torsion to prepare the target enantiomer. This is

accomplished by applying either a linearly polarized stereo-

selective IR pulse or a UV pulse using the electronic excited

state as an intermediate state. The former strategy allows for a

high stereoselectivity even if the direction of the torsion is

changed, because the polarization of the laser field is tuned to

allow interactions with only one enantiomer. The latter ap-

proach ensures that the chirality is ‘‘switched on’’ independent

of the direction of internal rotation which determines the

resulting handedness of the molecule. In addition, the UV

pulse is experimentally more accessible than the IR pulse.

Once a pure enantiomer is prepared the handedness of the

system can be changed by a UV pump–dump laser sequence.

Most certainly the achieved handedness of the molecular

switch will be lost with time due to energy relaxation, e.g.

via intramolecular vibrational redistribution (IVR). But the

system will merely return to its ‘‘off’’ position from where it

can be ‘‘switched on’’ again.

So far have we assumed that molecule is fixed to a

solid surface via linking groups resulting in orientation of

the molecule to a certain degree. Yet, different molecular

Fig. 8 Laser pulse sequence for the transformation of the (aR)-

enantiomer into the (aS)-enantiomer using the excited potential as

intermediate state (for laser parameters see Table 3). Time evolution of

(a) the z-polarized electric field, (b) the expectation value of the torsion

angle, (c) the population in Vg and Ve.

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orientations are possible upon chemisorption depending on

the symmetry of the surface. The effect of different orienta-

tions on the efficiency and selectivity of the laser control

cannot be predicted easily and is, therefore, currently under

investigation. Note that the coupling of the vibrational and

electronic degrees of freedom of the molecule to the surface

degrees of freedom (phonons, electron–hole pairs) may inten-

sify energy dissipation depending on the nature of the solid

and the linking groups.

Interestingly, the laser control schemes presented here con-

tain the excitation of an directional internal rotation which is a

precondition for a laser-driven molecular rotor.58,59 Yet, to

achieve a full rotation and maintain an uni-directional

torsional motion is a challenging task.

Acknowledgements

We thank Prof. P. Saalfrank for stimulating discussions and

S. Eich for her assistance. Financial support by the German

Research Foundation, project KR 2942/1-1, is gratefully

acknowledged.

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