Quantum model simulations of symmetry breaking and control of bondselective dissociation of FHF− using IR+UV laser pulsesNadia Elghobashi, Leticia González, and Jörn Manz Citation: J. Chem. Phys. 120, 8002 (2004); doi: 10.1063/1.1691022 View online: http://dx.doi.org/10.1063/1.1691022 View Table of Contents: http://jcp.aip.org/resource/1/JCPSA6/v120/i17 Published by the AIP Publishing LLC. Additional information on J. Chem. Phys.Journal Homepage: http://jcp.aip.org/ Journal Information: http://jcp.aip.org/about/about_the_journal Top downloads: http://jcp.aip.org/features/most_downloaded Information for Authors: http://jcp.aip.org/authors

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Quantum model simulations of symmetry breaking and control of bondselective dissociation of FHF À using IR ¿UV laser pulses

Nadia Elghobashi, Leticia Gonzalez,a) and Jorn ManzInstitut fur Chemie-Physikalische und Theoretische Chemie, Freie Universita¨t Berlin, Takustrasse 3,D-14195 Berlin, Germany

~Received 10 April 2003; accepted 9 February 2004!

Symmetry breaking and control of bond selective dissociation can be achieved by means ofultrashort few-cycle-infrared~IR! and ultraviolet~UV! laser pulses. The mechanism is demonstratedfor the oriented model system, FHF2, by nuclear wave packets which are propagated ontwo-dimensional potential energy surfaces calculated at the QCISD/d-aug-cc-pVTZ level of theory.The IR laser pulse is optimized to drive the wave packet coherently along alternate bonds. Next, awell-timed ultrashort UV laser pulse excites the wave packet, via photodetachment of the negativebihalide anion, to the bond selective domain of the neutral surface close to the transition state. Theexcited wave packet is then biased to evolve along the pre-excited bond toward the target productchannel, rather than bifurcating in equal amounts. Comparison of the vibrational frequenciesobtained within our model with harmonic and experimental frequencies indicates substantialanharmonicities and mode couplings which impose restrictions on the mechanism in the domain ofultrashort laser fields. Extended applications of the method to randomly oriented or to asymmetricsystems XHY2 are also discussed, implying the control of product directionality and competingbond-breaking. ©2004 American Institute of Physics.@DOI: 10.1063/1.1691022#

I. INTRODUCTION

This paper presents a mechanism for symmetry breakingfollowed by selective bond breaking using an ultrashort IRlaser pulse consisting of few cycles and an ultrashort visible~vis! or UV laser pulse, respectively. Both types of pulseshave been previously studied, however, the combination pre-sented in this paper should provide an efficient tool for quan-tum control of symmetry breaking and selective bond break-ing. The proposed scheme is demonstrated using laser drivenmolecular wave packets which are propagated onab initiopotential energy surfaces~PESs! in reduced dimensionality,for which the oriented bihalide anion FHF2 serves as abenchmark model system. Although the resulting products,either F1HF8 or FH1F8, are chemically indistinguishable,the present approach allows for the selection of one or theother, such that either the atomic or the molecular fragmentsare driven in a preselected direction, whereas the other frag-ments are driven in the opposite direction, i.e., we aim forspatial separation of the products, see Scheme 1.

Ultrashort IR laser pulses containing few cycles occur onthe time scale of a few vibrational periods of the targetedmode.1,2 In the impulsive limit, such pulses have been intro-duced by Nelson and co-workers and applied to create co-herent excitations of phonons of low frequency~approxi-mately 100 cm21! in ionic crystals.3 While these phononmodes vibrate at a much lower frequency than the stretchingvibrations of bihalide anions such as FHF2

(;600– 1500 cm21), impulsive laser pulses in the vis/UVfrequency domain have also been applied to unravel4 andcontrol5 the ground state dynamics of molecules or ions,

such as I32 , in real time creating effects such as ‘‘hole burn-

ing’’ in vibrational ground state nuclear wave packets. Thepresent application considers optimized ultrashort few-cycleIR laser pulses that assist photochemistry by creating near-coherent excitations of selective vibrations and consequentlycause dynamical symmetry breaking. Related effects havebeen predicted by Quack and co-workers using IR laser

a!Electronic mail: leti@chemie.fu-berlin.de

Scheme 1.

Gedanken experiment to detect selective bond breaking in an ensemble oforiented FHF2 molecules.~a! Traditional cw UV or IR1UV lasers wouldbreak both bonds, producing equal amounts of F and HF products in oppo-site directions.~b! Few-cycle IR1UV laser pulses, as proposed in this work,can break the symmetry of the system and induce selective fragmentation,thereby leading to spatial separation of the products.

JOURNAL OF CHEMICAL PHYSICS VOLUME 120, NUMBER 17 1 MAY 2004

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pulses which yield dynamical chirality in nonchiralmolecules;6 by Zhao and Ku¨hn with IR laser pulses, eitherwith analytical shapes or fields designed by local optimalcontrol and position tracking techniques7,8 for molecularphotodissociation competing against intramolecular vibra-tional redistribution; and by Henriksen and co-workers forselective bond breaking in HOD~Ref. 9! and in isotopicallylabeled O3, i.e., an asymmetric ozone.10

Likewise, quantum control by means of ultrashort vis orUV laser fields have been proposed by Tannor and Rice11

~see also Ref. 12! to induce near vertical Franck–Condon~FC!-type transitions between different electronic states suchthat the evolution of a molecular wave packet is excited fromone PES to the other, and ultimately guided to a desiredproduct. For comparison with the present approach, it ishelpful to consider the original Tannor–Rice mechanism as asequence of four steps:~i! FC-transfer of the initial wavepacket from the electronic ground state to a suitable excitedstate by a vis/UV pump laser pulse, followed by~ii ! evolu-tion of the wave packet on the excited PES until it arrives,after a specific time delay, at another FC-domain suitable for~iii ! back-transfer of the wave packet to the electronic groundstate by a vis/UV dump laser pulse, and finally,~iv! evolutionof the wave packet towards the target product. Steps~i! and~iii ! and steps~ii ! and ~iv! may be considered as active andpassive effects of the pump and dump laser pulses, respec-tively. Extensions of the pump–dump scheme include thepump-control mechanism, in which step~iii ! of the dumplaser pulse is replaced by a transition to another suitableelectronic state induced by a well-timed control laser pulse~see the first experimental demonstration in Ref. 13!, or ap-plications in which transform-limited UV laser pulses aresubstituted by chirped ones.14,15As a consequence of its widerange of applications, ultrashort UV laser pulses are ubiqui-tous in many types of quantum control.

The present approach shares some aspects of the previ-ous pump–dump or pump-control mechanisms, yet it is dif-ferent in that the method is targeted at preparing a desiredproduct in fewer steps. Specifically, the few-cycle IR pulseaims at achieving the effect of the active plus passive steps,~i! and~ii !, by a single active one. If the system is symmetric,as is FHF2, this ultrashort IR pulse will also break the mol-ecule’s symmetry. Consequently, the initial wave packet isshifted directly to the bond-selective FC-domain of the sub-sequent ultrashort UV pulse which then plays a similar roleas the dump or control laser pulse of the Tannor–Ricemechanism, step~iii ! followed by ~iv!. This scheme is differ-ent from the Tannor–Rice approach, in which the initial shiftoccurs in the electronic excited state, followed by a UV tran-sition either back to the ground state or to another excitedstate. As an aside, we note that direct shifts of wave packetsto target domains in the excited state have been achievedpreviously by means of chirped UV laser pulses.16 Moreover,the present approach of ultrashort IR1UV laser pulse controlis also different to vibrationally mediated chemistry whichemploys continuous wave~cw! or nanosecond17–19 orpicosecond20 IR lasers to prepare vibrationally excited eigen-states as an intermediate step, followed by UV laser excita-tion and photodissociation; note that in this case, only the

front lobes of the pre-excited eigenstate are transferred bythe UV pulse. Our approach, on the contrary, might be con-sidered as an extension of the work of Henriksen andco-workers9,10 for control of selective bond breaking ofasymmetric systems such as HOD or isotopically markedozone, by means of few cycle IR1UV laser pulses.

Some connections can also be found with the approachof Brumer and Shapiro, who use coherent control with 112photon interferences to induce symmetry breaking.21 Basi-cally, the corresponding selection rules allow the preparationof a superposition of two~near! degenerate states with dif-ferent parities. The relative phase of these states depends onthe relative phase of the one- and two-photon lasers, anddetermines the directionality~or more generally the differen-tial cross-sections! of the products. This type of coherentcontrol has been applied e.g. to symmetry breaking of H2

1

(5p1e2p1),22–24 and the present FHF2 may be also con-sidered as an analogous heavy–light–heavy particle system;beyond this similarity, we are not aware of any implementa-tion of the Brumer–Shapiro-type of coherent control to sym-metric molecular or ionic system allowing competing bondbreaking, e.g., FHF2→F1HF1e2 versus→FH1F1e2.The physics underlying some analogy of the Brumer–Shapiro approach and the present one will be described inmore detail in Sec. III.

The technology for preparing IR pulses with a durationof only a few vibrational periods in molecules or ions hasbeen developed only rather recently,25–27 ~see also Ref. 28!,whereas ultrashort UV pulses in the time domain of a fewfemtoseconds, corresponding to a few cycles of electronicmotion, have been available since the mid-1980s~see Ref.29; for extensions into the attosecond time domain, see Ref.30!. The availability of both ultrashort IR and UV laserpulses has thus motivated the combination of the two pulsetypes for quantum control, as suggested in this investigation.

Our approach can be developed for broad applications inmany systems.9,10 An especially interesting class of mol-ecules, the bihalide ions XHX2 or more generally XHY2,plays an important role in hydrogen bond chemistry due tothe strong hydrogen bonds those molecules contain. Addi-tionally, XHX2 or XHY2 systems have been used previ-ously for applications in the field of transition statespectroscopy,31 a method that relies on rather long~nanosec-onds! cw lasers. In that approach, assuming that the geom-etry of the stable XHY2 anion is similar to that of the neutraltransition state XHY‡, negative ion photodetachment pro-vides a direct spectroscopic probe of the transition state re-gion of the potential energy surface for the neutral hydrogentransfer reaction.32 For theoretical simulations and experi-mental photoelectron spectra of bihalide ions see, e.g., Refs.33–37. Note that in these papers, the aim is the characteriza-tion of the vibrations of XHY‡ and therefore, the UV fre-quency of the laser has to exceed the resonant frequencycorresponding to the energy gap between the neutral systemand the anion precursor, implying nonzero kinetic energies~non-ZEKE! of the detached electrons. Here, it is more con-venient to employ resonant UV frequencies, correspondingto ZEKE-type photodetachment processes. In particular,FHF2 possesses the strongest hydrogen bonds of this type

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and therefore, considerable effort has been devoted to char-acterizing its potential energy surfaces and to reproducing itsvibrational frequencies.38–45 The present model systemFHF2 has therefore been chosen based on its interestingproperties and on our ongoing interest in laser pulse controlof hydrogen transfer~see e.g. Refs. 46, 47!.

The present work may thus be considered as an exten-sion of transition state spectroscopy—from cw or nanosec-ond lasers to IR1UV femtosecond laser pulses, and fromspectroscopic analysis to control. An alternate method forcontrolling neutral reactions by exploiting the vibrationalresonances observed in transition state spectroscopy has beensuggested in Ref. 48.

The rest of the paper is organized as follows: SectionII A describes the quantum chemical calculations used toprovide the potential energy surfaces and Sec. II B summa-rizes the methods employed in the quantum dynamical cal-culations. Results are presented in Sec. III and Sec. IV sum-marizes and concludes.

II. METHOD OF CALCULATION

A. Quantum chemistry

The geometry of FHF2 has been optimized using thequadratic configurational interaction method including singleand double excitations~QCISD! ~Ref. 49! with Dunning’spolarized valence correlation consistent triple-split basis set,doubly-augmented with diffuse functions on H and F,d-aug-cc-pVTZ.50 The one-dimensional~1D! potential en-ergy curves for the linear FHF2 and FHF systems were gen-erated underC2v symmetry, assuming that the molecule isoriented along thez-axis, such that the hydrogen is able tomove collinearly between the two fluorine atoms. The two-dimensional~2D! potential energy surfaces~PESs! were con-structed in the (Fa– H)wR1 and (Fb– H)wR2 coordinates,that is, including the symmetric and asymmetric stretchingvibrations; the bending vibration and rotations were not con-sidered. Varying the R1 and R2 distances from 0.6 to 3.0 Å,we calculated a total of N•~N11!/25136 ab initio single-points for the PES of the anion and neutral species; takingadvantage of symmetry, we constructed a square grid ofN2

5256 data points.Dipole moment surfaces were obtained at the same level

of theory as the PES. In calculating the permanent dipolemoment of the anion, the center of mass was chosen as thecoordinate origin in order to guarantee adequate asymptoticdynamics of the dissociating products, with the mean forceacting between the separating atom and the center of mass ofthe target diatomic fragment, analogous to Ref. 51.

All calculations have been performed using the softwareprogramGAUSSIAN 98.52

B. Quantum dynamics

The simulation of the photodissociation dynamics atnear-ZEKE conditions~neglecting the electronic continuumof the photodetached electrons! relies on molecular wavepackets calculated as solutions of the time-dependent Schro¨-dinger equation

i\]

]t S ca

cnD5S Ha Han

Hna HnD S ca

cnD , ~1!

whereca(q,t) andcn(q,t) are the 1D or 2D~depending onthe coordinateq! wave functions of the anion or the neutralmolecule, respectively, oriented along thez-axis. Under theseconditions, the UV laser pulses induce near-resonant transi-tions between the initial anion and the neutral molecule. Theinteraction with the time-dependentz-polarized electric field,

E~ t !5S 00

E~ t !D ~2!

is treated in the semiclassical dipole approximation. Then,the entire Hamiltonian represents two coupled ionic and neu-tral systems,

S Ha Han

Hna HnD

5S T1Va2ma~q!•E~ t ! 2man~q!•E~ t !

2mna~q!•E~ t ! T1Vn2mn~q!•E~ t !D ~3!

with the permanent and transition dipole moments

ma~q!5S 00

ma~q!D , mn~q!5S 0

0mn~q!

D ,

and man~q!5mna~q!5S 00

man~q!D . ~4!

Va and Vn , and T are the potential and kinetic energies,respectively. The dipole momentsma(q) and mn(q) for theanion are calculated byab initio methods along with thePESs whereas, for simplicity, we made the Condon approxi-mation for the transition dipole between the anionic and neu-tral surface, settingman(q)5man51 ea0 . The subsequent re-sults do not depend on the value ofman since smaller orlarger values ofman may be compensated by larger andsmaller UV field amplitudes, respectively. The specific UVfield amplitudes were chosen such that the population trans-fer from theVa to Vn is below ;0.10, implying negligibleeffects of strong fields such as intrapulse pump–dump pro-cesses. The present IR and UV field strengths correspond tomaximum intensities

I max5e0c maxbE~ t !2c ~5!

well below the Keldish limit of;1013W/cm2, thus avoidingcompeting processes such as double ionization.

In the 1D model, the coordinateq represents the asym-metric mode and it is defined as the distance betweenH andthe center-of-mass of the fluorine atoms,

q5qas5RH,F25 1

2~R12R2!. ~6!

The anionic Hamiltonian is then given by

Ha52\2

2mas

]2

]q21Va~q!2ma~q!•E~ t !, ~7!

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whereVa(q) is the adiabatic Born–Oppenheimer PES andmas is the reduced mass corresponding to the asymmetricstretching vibration,

mas5~mF1mF!* mH

~mF1mF!1mH, ~8!

with valuesmH51.008 amu andmF519.00 amu. Similarly,the two-dimensional molecular Hamiltonian for the collinearanionic (k5a) molecule or neutral (k5n) species is givenby

Hk52\2

2m1

]2

]R12

\2

2m2

]2

]R21

\2

mH

]

]R1

]

]R2

1Vk~R1 ,R2!2mk~R1 ,R2!•E~ t !, ~9!

where the massesm1 andm2 are given by

m15m25mF* mH

mF1mH. ~10!

We assume that the molecular system is initially in thelowest vibrational eigenstatefv50 in the electronic groundstate of the FHF2 system,

S ca~ t50!

cn~ t50! D5S fv50

0 D . ~11!

The FHF2 vibrational eigenstatesfv are obtained solvingthe time independent Schro¨dinger equation by means of theFourier grid Hamiltonian method,53 which relies on the fastFourier transform technique,54 using linear or square grids of128 or 6436454096 splined data points for the 1D or 2Dmodel systems, respectively. The eigenstates are labeled withquantum numbers v1D5vas or v2D5vsvas, for vs

5$0,1,2,...% andvas5$0,1,2,...% for the 1D and 2D systems,respectively. For convenience, the notationv50 is used forboth the 1D and 2D vibrational ground states.

The propagation of the time-dependent wavefunctionson the PES was carried out using the split-operatormethod55,56 with a time stepDt50.01 fs and spatial discreti-zation of 128~1D! or 6436454096 ~2D! grid points. Thelocalizations of the asymmetric 2D wave packet for the an-ionic system,Pa(R1>R2) and Pa(R2>R1), were calculatedby summing the densityuca(q,t)u2 in the domains for whichR15R2 and R25R1 , respectively. Likewise, branching ra-tios for the 2D neutral dissociative system,Pn(R1.R2) ver-susPn(R2.R1), were obtained by summing the normalizedpopulation densityucn(q,t)u2 over the two grid halves,R1

>R2 andR2>R1 , respectively.

III. RESULTS AND DISCUSSION

A. Potentials and vibrational frequencies

The geometry of FHF2 optimized at theQCISD/d-aug-cc-pVTZ level of theory yields an equilib-rium F–F distance of 2.274 Å, in excellent agreement withthe experimental value of 2.278 Å.57 Equilibrium geometriesobtained at lower levels of theory44 differ from our results byas much as 0.05 Å. The one-dimensional energy profiles forthe anionic and neutral species, FHF2 and FHF, are shown inFig. 1~a!, together with the dipole moment for the FHF2

anion @Fig. 1~b!#. Contour plots for the two-dimensionalPESs for the neutral and anionic species along the Fa– H~R1)and Fb– H~R2) bond lengths are shown in Figs. 2~a! and 2~b!,respectively. As expected, the anionic surface is bound whilethe neutral one is dissociative. The lowest calculated vibra-tional eigenfunctions for FHF2 are shown in Fig. 3 with thecorresponding eigenvalues. From the two-dimensional vibra-tional eigenstates, the anharmonic symmetricn1 and asym-metric n3 stretching frequencies can be obtained and theseare listed in Table I. For our subsequent analysis of the laserdriven wave packet dynamics, it is illuminating to comparethese 2D results with the harmonic and anharmonic frequen-cies of the 1D model, as well as with the experimental re-sults, to be considered as exact 3D frequencies. As a refer-ence, all relevant frequencies are listed in Table I. Note thatthe harmonic 1D frequencies are the same as the~decoupled!normal mode frequencies of the 2D model, and that these arein very good agreement with those reported in Refs. 44 and45, based on a similar level of calculation.

Our analysis of the 1D, 2D, and 3D harmonic and an-harmonic frequencies will start with the symmetric stretch.Subsequently, we shall discuss different trends in the asym-metric stretch, pointing to competing effects of anharmonic-ity and mode mixing, with important consequences for thelaser driven dynamics in the present 1D and 2D model sys-tems.

Specifically, the symmetric stretching frequency de-creases systematically from the highest value for the 1D har-monic reference, 649 cm21, to 609 cm21 for the 1D anhar-

FIG. 1. ~a! One-dimensional potential energy curvesVa and Vn for theanion FHF2 and neutral FHF species, respectively, and~b! correspondingdipole moment curve ma for FHF2, calculated at the QCISD/d-aug-cc-pVTZ level of theory.

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monic frequency, then to 593 cm21 for the 2D anharmonicfrequency, and finally to 583 cm21 for the anharmonic 3D~experimental! result. These first, second, and third decreasesare due to the effects of anharmonicity in the 1D model,followed by mode mixing in the 2D and 3D systems, respec-tively. Apparently, for the symmetric stretch, the effects ofanharmonicity are dominant, in comparison with mode mix-ing, but both give rise to the same trends, i.e., decreasingvibrational frequencies.

In contrast, the asymmetric stretching frequency first in-creases from the harmonic reference, 1250 cm21, to 1815cm21 for the anharmonic 1D model, and then it decreases to1448 cm21 and 1331 cm21 for the 2D and 3D systems, re-spectively@cf. the 3D calculations performed by Yamashitaet al., 1371 cm21 ~Ref. 43!#. The first, rather large increase isdue to strong inverse anharmonicity of the 1D asymmetricstretching potential@shown in Fig. 1~a!#, similar to the be-havior of a ‘‘particle-in-a-box.’’ The subsequent decreasesare due to mode mixing in the 2D and 3D models, leading tothe ‘‘boomerang’’-type curvature of the contours of the po-tential shown in Fig. 2; this curvature allows for more effi-cient relaxation of the vibrational wave packet to lower en-ergies than would occur in a hypothetical normal modepotential containing ellipsoidal-type contours. The final, 3Dresult for the asymmetric stretch, 1331 cm21, thus turns outto be rather close to the 1D reference, 1250 cm21, but ouranalysis shows that this near coincidence is due to the com-pensation of the two competing effects, namely anharmonic-ity and mode mixing, which cause strong increases and de-creases of the vibrational frequencies, respectively. As aconsequence, the vibrational eigenenergies for excitations of

the asymmetric stretch in the 2D model,E0051019 cm21,E0152467 cm21, E0254165 cm21 ~see Fig. 3!, are moreequally spaced than for the 1D model,E05782 cm21, E1

52597 cm21, and E254825 cm21 ~not shown!. Surpris-ingly, the effective anharmonicity~a combination of anhar-monicity in the pure asymmetric stretch plus mode mixing!is, therefore, smaller in the 2D than in the 1D model. Onemay anticipate that these results give rise to larger effectiveanharmonicities in the laser driven dynamics for the 1Dmodel than for the 2D system.

FIG. 2. Contour plots of the two-dimensional potential energy surfaces for~a! FHF and for~b! FHF2 calculated at the QCISD/d-aug-cc-pVTZ level oftheory for linear geometries. The equidistant contours (DV50.8 eV) of theenergies are relative to the global FHF2 minimum energy.

FIG. 3. Square of the 2D vibrational eigenfunctionsfv with correspondingeigenenergies~in units of hc cm21!. The two quantum numbersy2D5ysyas

indicateys quanta of energy in the symmetric stretch andyas quanta in theasymmetric stretch.

TABLE I. Harmonic, anharmonic, and experimental fundamental frequen-cies of FHF2 in cm21.

Harmonic Anharmonicd

ExperimentcQCISDa CCSD~T!b QCISDa CCSD~T!b

n1 649 640 593~609!e 595 583n2 1380 1387 ¯ ¯ 1286n3 1250 1244 1448~1815!e 1476 1331

aThis work.bReference 45.cReference 57.dThe effective anharmonicity includes effects of anharmonicities in singlemodes, plus mode mixing.

eValues in parentheses correspond to the frequencies obtained using the 1Dmodel.

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B. Design of a few-cycle IR laser pulse for symmetrybreaking by selective bond stretching

The symmetry breaking and bond-selective photodisso-ciation of FHF2 will now be presented. The results of theseinvestigations can be divided into two parts: the coherentexcitation of the vibrational ground state wave functionca(q,0)5fv50 on the anionic potentialVa(q) by means ofa few cycle IR laser pulse, discussed in this section, followedby the ultrashort UV laser excitation ofca(q,0) from Va(q)to the dissociative neutral surface,Vn(q), presented in Sec.III C.

The objective of the few-cycle IR pulse is a coherentdisplacement of the initial wave functionca(q,0)5fv50

from the equilibrium position to another favorable FC-domain of the anionic potentialVa(q), leading to dynamicalsymmetry breaking in the anion. The displacement ofca(q,0) from its origin is measured using three indicators:~i! the autocorrelation function~acf!,

S5^fv50uca~ t.0!&, ~12!

or its absolute square, i.e., the change in population of theground statev50 of the anion,

Pa~v50!5uSu2, ~13!

~ii ! the mean position of the H atom, and~iii ! the localiza-tion, Pa(R1.R2) or Pa(R2.R1) of the anionic wave packet@or Pn(R1.R2) or Pn(R2.R1) for the neutral wave packet#in the domains for which R1.R2 or R2.R1, respectively.For a given laser pulse, the displacement was consideredoptimal when the modulus of the acf was minimized, and thedisplacement of the starting wave packet and correspondingsymmetry-breaking localizations approach extrema.

To accomplish this goal, an efficient few-cycle IR laserpulse was designed in several steps, starting from a singlehalf-cycle pulse, then extended to a series of half-cyclepulses, and finally tailored to a more realistic ultrashort IRpulse that resembles the series of half-cycle pulses but thathas a smooth (sin2) envelope. Additionally, the design ofsuch IR pulse in the 2D system proceeds from experiencegained in the 1D system. The purpose of our step-by-steppresentation of the design of this IR laser pulse is to providea clear understanding of the mechanism of symmetry break-ing and wave packet displacement, together with some limi-tations of this approach.

First, an ultrashort half-cycle IR laser pulse with sin-shape was applied to the 1D system.~For complementaryinvestigations of applications using half-cycle pulses, seee.g. Ref. 58.! The electric fieldE(t) describing this pulseshown in Fig. 4~a! is given by

E~ t !5E0 sinS pt

tpD for 0<t<tp ~14!

with field strength E053 GV/m (I max51.2 TW/cm2) andpulse durationtp510 fs, which is about half the vibrationalperiod of the asymmetric stretch of the 1D model, 0.5tas

59 fs. As shown in Fig. 4, this laser pulse causes a rathersmall excitation of the ground state wave packet to excitedvibrational states, as indicated by the small decay ofPa(v50). As a consequence, this excitation causes the H atom to

FIG. 4. Coherent excitation of the vibrational ground state of the 1D modelFHF2 using a half-cycle pulse with sin-shape.~a! Electric field vs time; theparameters areE053 GV/m, tp510 fs. ~b! Modulus of the autocorrelationfunction.~c! Time evolution of the expectation value of the mean position ofthe H atom driven by the laser field shown in~a!. ~d! Product yield ofspecies for which R1.R2 vs time.~e! Wave functions at timet50 fs ~solid!andt59.5 fs~dotted! ~maximum displacement of the H atom!, embedded inthe FHF2 potential.

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oscillate coherently in the potential well between 0.075 and20.071 Å @Fig. 4~c!#, reaching a maximum displacement of0.075 Å at 9.5 fs@shown in Fig. 4~e!# close to the end of thelaser pulse. The time delay between the maxima of the laserpulse and the displacement corresponds to;1/4 of the vibra-tional period,;4 fs. Subsequently, the wave packet retainsits compact form and oscillates in a coherent, near-harmonicmanner@see Fig. 4~b!# with negligible dispersion in the po-tential. As a consequence, the symmetry of the system isalmost periodically broken, such that the localizationPa(R1.R2) oscillates, with a product yield of almost 0.80 att59.5 fs @see Fig. 4~d!#. Systematic investigations show thatincreasing field strengths induce larger displacements, at theexpense of the coherence of the wave packet, due to strongereffects of anharmonicity at larger displacements. Similartrends will also be observed for a sequence of half-cyclepulses.

Next, rather than a single half-cycle pulse, a series ofsin-pulses with alternating field strengths is applied to obtainlarger displacements of the H atom. The effect is similar tothat of a driven oscillator: if a new impulse is applied soonafter passing through each turning point, the amplitude of theoscillation will increase, like a swing which is driven byalternating pushes. Exemplarily, this effect is demonstratedby a combination of three sin-pulses with amplitudeE0

53 GV/m and pulse durationstp1510, tp259, and tp3

59 fs, shown in Fig. 5~a!. This series of laser pulsesachieves a more efficient excitation of the original wavepacket than the single half-cycle pulse does, as is indicatedby the substantial sequential decay of the ground state popu-lation Pa(v50) @see Fig. 5~b!#. Indeed, each of the pulsesleads to a greater amplitude of the hydrogen oscillation untilat t526.5 fs, i.e., 1.5 fs before the end of the pulse, a maxi-mum mean displacement of 0.16 Å is obtained@see Figs.5~c! and 5~e!#. The corresponding breaking of the symmetryof the system is illustrated in Fig. 5~d!. Should this IR exci-tation be followed by an ultrashort UV pulse centered at 26.5fs, the near-vertical FC-type transition would prepare theneutral system in an asymmetric configuration of selectivelystretched and compressed bonds, R1.R2. One can anticipatethat the neutral system should then dissociate along the pre-stretched bond R1. After achieving maximum displacementand localizations att526.5 fs, these properties oscillate withrapid decay due to the anharmonicity of the 1D potential,leading to dispersion of the wave packet. Subsequent frac-tional revivals~see e.g., Ref. 13! are irrelevant for the presentpurpose.

In the third step of our design of an ultrashort few-cycleIR laser pulse for efficient, bond-selective dissociation ofFHF‡, the results of the 1D system were extended, serving asa valid reference for the 2D model. The lower 2D asymmet-ric stretching vibrational frequency compared to that of the1D model~see Sec. III A! implies longer vibrational periodsin the 2D model. The corresponding duration of the series ofthree half-cycle pulses driving the 2D wave packet should,therefore, also be slightly longer than that of the 1D model.Accordingly, efficient laser parameters for the 2D system areE053 GV/m ~same as for the 1D case! and tp1512, tp2

511, and tp3511 fs ~slightly longer than the valuestp1

FIG. 5. Coherent excitation of the vibrational ground state of the 1D modelFHF2 using a sequence of three half-cycle IR pulses with sin-shape andalternating field strengths.~a! Electric field vs time; the parameters areE0

563 GV/m, tp1511 fs, tp2510 fs, tp3510 fs. The notation to panels~b!–~e! is analogous to those of Fig. 4.

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511, tp2510, and tp3510 fs obtained in the 1D calcula-tions!, shown in Fig. 6~a!. The smaller effective anharmonic-ity of the 2D system, compared to that of the 1D model,allows larger excitation of the 2D—as indicated by the stron-ger decay ofPa(v50)—than of the 1D system, shown inFig. 6~b! vs Fig. 5~b!, respectively. Close to the end of theseries of half-cycle pulses, i.e., at 31.5 fs, the displacement ofthe hydrogen in the 2D model approaches a local maximumvalue,qas50.197 Å@Fig. 6~c!#. A surprising—albeit minor—result is that the 2D wave packet then swings back andreaches an even slightly larger mean absolute value,uqasu50.201 Å, at t542 fs, a favorable consequence of wavepacket dispersion. For the remainder of the propagation pe-riod, dispersion leads to the normal behavior of decreasingmean amplitudes ofqas. This result may be considered thecombined effect of the anharmonicity in the asymmetricstretch~as in the 1D system! and intramolecular vibrationalredistribution~IVR! due to mode coupling in the 2D system,in accord with the effects noted in Sec. III A. The smallereffective anharmonicity in the 2D system, compared with the1D system, causes less efficient dispersion of the wavepacket and, therefore, slower decay of the wave packet dis-placement and localization in the 2D system than in the 1Dmodel @compare Figs. 6~c!, 6~d! vs 5~c!, 5~d!, respectively#.The compact nature of the 2D wave packet is apparent inFig. 6~e!, in which the evolution of the wave packet onVa isdepicted at the turning points of the oscillation.

Finally, the sequence of half-cycle pulses that leads tothe breaking of symmetry in the 2D system is replaced by thefield

E5E0 sinS tp

tptot

1h D •s~ t !5E0 sin~vt1h!•s~ t !, ~15!

wheres(t) is a smooth shape function. For convenience, wechoose the sin-squared shape

s~ t !5sin2~ tp/tptot! for 0<t<tptot

, ~16!

wheretptotdenotes the total pulse duration andh is the phase.

The subsequent results are not sensitive to the choice ofshape functions with similar form and with equivalent dura-tions. As one can see, these laser pulses with smooth shapesresemble the previous half-cycle pulses, except that the pre-vious individual pulse amplitudesE0 @corresponding tos(t)51 during 0<t<tptot

] are replaced by smoothly varyingamplitudesE0s(t). Additionally, the individual pulse dura-tions can be replaced with an average IR carrier frequency,

v52p

t5

p

tp, ~17!

wheret is the period of one complete oscillation. The con-stant value ofv could be replaced by a chirped frequencythat yields small decreases in the duration of the individualhalf-cycle pulses, thus creating a pulse sequence even moresimilar to the previous series of half-cycle sin-pulses, cf.Fig. 6.

This type of laser pulse with a smooth shape@Eq. ~15!#completes the present design of ultrashort IR laser pulses,which can be prepared more easily experimentally than the

FIG. 6. Coherent excitation of the vibrational ground state of the 2D modelFHF2 using a sequence of three half-cycle IR pulses with sin-shape andalternating field strengths.~a! Electric field vs time; the parameters areE0

563 GV/m, tp1512 fs, tp2511 fs, tp3511 fs. ~b! Modulus of the autocor-relation function.~c! Time evolution of the expectation value of the meanposition of the H atom@see Eq.~6!# driven by the laser field shown in~a!.~d! Product yield of species for which R1.R2 . ~e! Wave functions at timet50 fs, t522 fs, t531.5 fs, andt542 fs ~maximum displacement of thewave packet!.

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previous series of half-cycle pulses, yet they are designed toyield similar laser driven dynamics. These similarities aredemonstrated by the following application in whichE0

54 GV/m (I max52.1 TW/cm2), v51516 cm21 and totalpulse durationtptot

555 fs. The frequencyv corresponds to

that of the pulse durationtp511 fs @see Eq.~17!# in the pre-vious sequence of half-cycle pulses, and the correspondingenergy is close to the mean energy gaps of the ladder ofasymmetric stretching energies:E012E0051448 cm21 andE022E0151697 cm21. As a consequence, the wave packetprepared by this IR laser pulse is composed mostly of thoseeigenstates with different numbers of excited quanta andparities ~6! in the asymmetric mode:f01(21%)(2),f02(22%)(1), f03(9%)(2), f11(11%)(2), f12(11%)3(1), etc. The similarity of this IR laser pulse, shown inFig. 7~a!, with the previous series of half-cycle pulses,shown in Fig. 6~a!, is apparent: both contain three dominantpeaks with similar field strengths and durations, supple-mented by two initial and final subpulses which yield thesmooth switch-on–switch-off behavior required for experi-mental implementation. The slightly larger field strength ofthe central peak compensates for the lower field strengths ofthe neighboring peaks, causingqas to reach 0.207 Å att541.5 fs, shown in Fig. 7~c!. The modulus of the acf dropsto 0.28 att550 fs @Fig. 7~b!#. Despite the high field strengthand longer pulse duration, the wave function att541.5 fsremains relatively compact, with a product yield of 0.86 att541.5 fs@Fig. 7~d!#; snapshots of the wave packet at maxi-mum displacement are shown in Fig. 7~e!. Again, the subse-quent dispersion of the wave packet results in slower decayof the oscillatory displacements and localizations than for the1D system, due to the smaller effective anharmonicity of the2D system compared to the 1D one, cf. Sec. II A.

In general, the effect of the IR pulse is the creation of acoherent wave packet. In other words, interfering IR resonantmultiphoton excitations of a coherent superposition of eigen-states with even and odd parities breaks the symmetry of thereactant ground state of even parity. The corresponding di-rection in which the initial wave packet travels is not deter-mined by its parity but rather by the phase of the IR pulse,e.g., a phase shift ofp would drive the wave function in theopposite direction.

C. Bond selective photodissociation by combinedultrashort IR and UV laser pulses

In the final step of our investigation, we apply an ul-trashort sin2-shaped UV pulse to our now asymmetric 2Dsystem at a well-chosen time to selectively break the pre-excited F–H bond via photoelectron detachment. The IR la-ser parameters are kept from the previous optimized pulse~see Fig. 7!, and after a delay of 42 fs, i.e., when the IR pulseachieves maximum wave packet displacement and localiza-tion in the anionic system, an optimized resonant UV-pulse,with parameters E055 GV/m (I max53.3 TW/cm2),v543548 cm21 ~[5.5 eV!, and tp55 fs, excites the dis-placed wave function to a bond-selective domain ofVn ,causing the wave packet to evolve predominantly along onedissociation channel. The IR~solid! and UV ~dotted! pulses

are shown in Fig. 8~a!. The time evolutions of the meanqas

and localizations of the anion and neutral systems are shownin Figs. 8~c! and 8~d!, respectively, and the evolution ofwave packets onVn is depicted in Fig. 8~e!.

FIG. 7. Coherent excitation of the vibrational ground state of the 2D modeFHF2 using one few-cycle sin2-shaped IR pulse.~a! Electric field vs time;the parameters areE054 GV/m, v51516 cm21 ~[0.188 eV!, and tptot

555 fs. The notation to panels~b!–~e! is analogous to those of Fig. 6.

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Comparison of the results illustrated in Figs. 8~b!–8~d!with those of Figs. 7~b!–7~d! shows that the IR laser-drivenwave packet dynamics of the anion is hardly affected by theUV pulse due to its rather low intensity, yielding only arather small~;10%! populationPn(t) of the neutral system@see Fig. 8~b!#. Accordingly, intrapulse pump–dump or othermultiphoton processes are negligible in the present applica-tion. The resulting evolution of the wave packet on the neu-tral surface, shown in Fig. 8~e!, documents that the ultrashortUV pulse creates the wave packetcn(q,t) in the neutralsystem by a near-vertical FC-type transition in the downhilldomain of the potential energy surfaceVn , such thatcn(q,t)dissociates preferably along the selected bond R1. Soon afterformation ofcn(q,t) on Vn , the wave packet dispersion al-lows a small portion ofcn(q,t) to penetrate into the nondes-ired domain R2.R1, such that the initial specific localiza-tion, Pn(R2.R1)'0.85 at t542 fs, drops toPn(R2.R1)'0.75 at t570 fs. This loss of selectivity is switched off,however, as soon ascn(q,t) arrives in the near-asymptoticdomain ofVn ~for which R1 is larger than approximately 2Å!, where the high potential ridge between the competingproduct potential valleys hinders further dispersion ofcn(q,t) into the domain R2.R1. The marginal oscillations,superimposed on the dissociative increase of R1– R2, are dueto small vibrational excitations of the product F1HF, similarto the vibrational coherence in dissociated products discov-ered in Refs. 59 and 60.

The present IR1UV laser pulses then achieve symmetrybreaking in the electronic ground state of the anion and sub-sequent selective bond breaking of the oriented model sys-tem in the neutral surface. The resulting atomic fragment isdriven along the preselected bond, which has been stretchedby the IR laser, whereas the molecular product is driven tothe opposite direction. As a consequence, our approachachieves spatial separation of the products, see Scheme 1.

The same net effect, i.e., selective bond breaking of asymmetric system may be achieved by 112 photon interfer-ence scenario within the coherent control method suggestedby Shapiro and Brumer.21 For example, a single UV photonwill excite the reactant which has even parity to a dissocia-tive state with odd parity, whereas the combination of twophotons~IR1UV! may excite a degenerate dissociative statewith even parity. The coherent superposition of the two dis-sociative states with even and odd parities implies then sym-metry breaking in the dissociative process, i.e., selectivebond breaking. By analogy, the present approach may beinterpreted as 11213141¯ photon scenario of coherentcontrol; i.e. the IR pulse achieves interfering 0,1,2,3,4,...resonant multiphoton excitations in the electronic groundstate, followed by a single UV photon transition. The disso-ciative state may then be interpreted as a coherent superpo-sition of components which are created as 011, 111, 211,311, etc. IR1UV photons, with corresponding alternateodd, even, odd, even, etc., parities. The widths of the ul-trashort laser pulses allows for the degeneracy of those com-ponents, implying coherent control of selective bond break-ing.

The corresponding control parameters in our approachare the phase of the IR laser pulse together with the time

FIG. 8. Coherent excitation of the vibrational ground state of the 2D modelFHF2 using a few-cycle sin2-shaped IR pulse~solid!, followed by an ul-trashort sin2-shaped UV pulse~dotted!. ~a! Electric field vs time; the IR-parameters are the same as those in Fig. 7, and the UV-parameters aretdelay538 fs, E055 GV/m, v543548 cm21 ~[5.5 eV! and tp55 fs. ~b!Modulus of the autocorrelation function for anion~solid! and neutral~dot-ted!. ~c! Time evolution of the expectation value of the mean position of theH atom@see Eq.~6!# driven by the laser field shown in~a! for anion~solid!and neutral~dotted!. ~d! Product yield of anionic~solid! and neutral~dotted!species for which R1.R2 . ~c! Wave functions evolving onVn at time t542 fs, t546.5 fs, andt558.5 fs, andt570 fs.

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delay of the UV pulse. In addition, the frequency of the IRpulse should be near-resonant to the asymmetric stretchingfrequency of the reactant, and the UV photon energy shouldmatch the potential energy gap at the Franck–Condon win-dow, corresponding to the turning point of the coherentasymmetric stretching vibration.

IV. CONCLUSION AND OUTLOOK

The results presented in this paper demonstrate that ul-trashort IR pulses containing few cycles can achieve coher-ent molecular vibrations leading to selective extensions ofspecific bonds; applications to symmetric molecules allowdynamical symmetry breaking. A well-timed ultrashort UVpulse fired at the moment of extreme bond extension maythen be used to induce a near-vertical FC-type transition to adissociative excited state, possibly including photodetach-ment, thus selectively breaking the pre-excited bond.

By extrapolation from the present application for themodel anion FHF2 to other systems, we infer that the suc-cess of the method relies on several conditions. First, the IRlaser pulse should couple efficiently to the molecular targetmode. This requirement calls for strong variations of the mo-lecular dipole component along the vibrational mode whichis to be excited, preferably in the domain of 1ea0 per a0 .Moreover, the selective coherent vibrational excitation has toovercome competing mechanisms, such as wave packet dis-persion due to anharmonicities and mode mixing. This re-quirement calls for relatively small effective anharmonicitiesof the vibrational mode of interest, i.e., the associated ladderof vibrational energies should have preferably equal levelspacing. The present analysis including the comparison ofthe 1D and 2D model systems, is encouraging since it indi-cates that this condition can be satisfied not only in idealsystems with harmonic normal mode behavior, but also insystems in which inverse anharmonicity and vibrationalmode mixing have a compensatory effect. In favorable cases,this compensation could be achieved more easily in poly-atomic molecules with several coupled degrees of freedomthan in systems with quasidecoupled but strongly anhar-monic degrees of freedom. The carrier frequency of the IRlaser should then be tuned close to the mean level spacing ofthe preferably near-harmonic vibrational energies to be ex-cited. Simultaneously, the total pulse duration should not ex-ceed the time scale of wave packet dispersion and associatedintramolecular vibrational redistribution. In the present sys-tem, this condition requires that the IR laser pulse consist ofonly few dominant cycles. We anticipate that one may findmore suitable systems with better effective harmonicity ofthe relevant vibrational ladders, such that even more selec-tive variations of bond lengths or angles can be achieved bymeans of IR fields with smaller intensities or longer pulsedurations.

The main purpose of such an IR laser pulse is to drivethe molecular wave packet coherently from its original loca-tion in the reactant’s potential well along specific bonds,bond angles, or other coordinates, to new regions of the PES.In favorable cases, one or more of these new configurationsmay serve as FC-windows for near-vertical transitions touseful domains of PESs of electronic excited states. For ex-

ample, if the topology of these PESs is repulsive from thedomain along the vibrationally pre-excited bond toward dis-sociated products, the molecular wave packet which is pre-pared in the excited state is then predisposed to evolve se-lectively. This mechanism has been demonstrated in thepresent example of FHF2: first, the few-cycle IR laser pulsebreaks the symmetry and causes a specific bond stretch at agiven time; next, a very short, well-crafted UV pulse selec-tively photodissociates this bond. By analogy, one may an-ticipate other scenarios in which the PES of the excited stateis not repulsive but attractive, or it has a potential well at theselected FC-window. The UV pulse could then induce selec-tive isomerization or trapping in the quasibound configura-tion of the excited state, instead of leading to photodissocia-tion. Clearly, the desired target processes and products limitthe choice of the FC-windows that have to be prepared bythe IR pulse. After successful preparation of the ground statesystem, additional constraints on the UV pulse exists, namelyits frequency should be near resonant to the energy gap be-tween the ground and excited state PESs at the chosen FC-window. But, a proper choice of the UV frequency is notenough to guarantee selectivity. In addition, the time delay ofthese short UV pulses has to match the corresponding cycleand phase of the previous IR laser pulse;~note that a narrow-band width pulse, similar to those employed in traditionalvibrationally mediated chemistry17–19 cannot satisfy this re-quirement!. For example, if the present UV pulse is delayedby just half the period of the IR pulse then the~undesired!bond R2 would be broken instead of R1 . Also, the transitiondipole intensity and the UV laser field strength~and relatedintensity! should be strong enough to transfer a significantpart of the ground state wave function to the excited state,while simultaneously remaining weak enough to avoid othercompeting multiphoton processes that would lead to, for ex-ample, double ionization. Last but not least, the duration ofthe UV pulse should be short enough to catch the wavepacket in the ground state just as it enters the chosen FC-window. In the present case, in which the residence time inthe FC-window is determined by the short period of theasymmetric stretch of FHF2 ~essentially the motion of thelight hydrogen atom vs the heavy atoms!, this condition im-plies UV pulse durations on the order of a few fs. Othervibrations with lower frequencies, e.g., torsions of heavymolecular fragments, would accordingly allow longer UVpulse durations for the desired FC-transition and, therefore,more efficient population transfer from the electronic groundstate to excited states. In ideal cases, in which the IR laserdriven wave packet is localized coherently close to the targetFC-window, the UV laser could achieve even completepopulation transfer. This possibility points to more efficientapplications of the present approach, in contrast with tradi-tional vibrationally mediated chemistry in which the cw- orns-UV laser may transfer only a small fraction of the inter-mediately excited, delocalized vibrational eigenstate, i.e., itsportion which is close to the FC-window.

The present results stimulate further investigations ofisotope effects, applications to nonsymmetric systems, andeffects of additional degrees of freedom, for example, rota-tions or additional vibrations. For the present system, FHF2,

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in addition to the symmetric and asymmetric stretch, onemight take into account the bending mode. This extensionfrom the 2D system to a 3D model is promising because thecompeting effects of inverse anharmonicity and mode mix-ing ~discovered in Sec. III A! point to reduced effective an-harmonicities and, therefore, to even more efficient selectivebond stretches and, therefore, better selectivity of bondbreaking for the 3D than for the 2D model. Work along theselines is in progress.

Moreover, the present approach of coherent IR-assistedphotochemistry should allow for extensions to more generalsystems, e.g., ensembles of randomly oriented molecules,and/or asymmetric molecules, XHY2, where X and Y repre-sent two different ligands, not necessary halogen atoms. Ex-emplarily, consider a randomly oriented asymmetric systemlike FHBr2 ~see Ref. 48!. Opposite directionalities of selec-tive products can be achieved as a consequence of the asym-metric PESs. Specifically, the IR field may drive the centralH atom towards the F or Br atoms depending on the oppositeorientations of the FHBr2 anion, but the carrier frequency ofthe sequel UV pulse may be chosen resonant to the potentialenergy gap of a single product, excluding the channel towardthe other product because of nonresonance. The dependenceof the initial orientation can be developed in a similar man-ner as the one designed by Henriksenet al.61,62 for diatomicsystems. In the case of symmetric systems, as the one in thispaper, FHF2, the dynamical symmetry and bond breaking oforiented systems then implies opposite directionalities of theatomic and molecular fragments, i.e., spatial separation ofthe products F vs HF, produced by few-cycle IR1UV laserpulses, see Scheme 1. Applications to randomly oriented en-sembles are considered in Ref. 63. See also application toFDF2 in Ref. 64. For a different mechanism of selectivebond breaking of isotopomers, see Ref. 65, in which theselective dissociation of H1OD vs D1OH in HOD is dis-cussed. Most recently, we could also demonstrate that few-cycle IR1UV fields may be used for quantum ignition ofmolecular rotors.66

ACKNOWLEDGMENTS

We thank H. H. Limbach for bringing our attention tothe FHF2 system and for useful discussions. Also, manythanks are given to K. Nelson for providing us with hisstimulating experimental papers and advice on impulsive IRexcitation, to N. E. Henriksen for discussions on his ap-proach to quantum control by means of IR1UV laser pulses,and to D. Neumark for encouraging conversations about theexperimental realization of the present approach. This workis supported by the Deutsche Forschungsgemeinschaft Gra-duiertenkolleg Project 788 ‘‘Hydrogen Bonding and Hydro-gen Transfer.’’ Continuous support from the Fonds der Che-mischen Industrie to J.M. is also gratefully acknowledged.The computations were carried out on our HP 9000 comput-ers and on the SGI Origin 3400 computer of the ZEDAT,Berlin.

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