Carbonyl Vibrational Wave Packet Circulation in Mn2(CO)10 Driven byUltrashort Polarized Laser Pulses

Mahmoud K. Abdel-Latif1, 2 and Oliver Kuhn1, a)

1)Institut fur Physik, Universitat Rostock, D-18051 Rostock, Germany2)Chemistry Department, Faculty of Science, Beni-Suef University, Beni-Suef,Egypt

(Dated: 30 October 2018)

The excitation of the degenerate E1 carbonyl stretching vibrations in dimanganese decacarbonyl is shown totrigger wave packet circulation in the subspace of these two modes. On the time scale of about 5 picosecondsintramolecular anharmonic couplings do not cause appreciable disturbance, even under conditions where thetwo E1 modes are excited by up to about two vibrational quanta each. The compactness of the circulatingwave packet is shown to depend strongly on the excitation conditions such as pulse duration and field strength.Numerical results for the solution of the seven-dimensional vibrational Schrodinger equation are obtained fora density functional theory based potential energy surface and using the multi-configuration time-dependentHartree method.

I. INTRODUCTION

Recently, considerable attention has been paid to theexcitation of degenerate electronic and vibrational statesusing circularly polarized laser light. Manz and cowork-ers have been the first to focus on the possibility of theexcitation of electronic ring currents by laser-triggeredformation of time-dependent hybrid states, e.g. in a Mg-porphyrin model1,2 as well as in the diatomic AlCl.3 Aparticularly interesting aspect has been the accompany-ing generation of giant magnetic fields.4 Subsequently,this work was extended to the vibrational domain in theelectronic ground state. Here, degenerate bending vibra-tions of linear triatomic species such as 114CdH2

5 andFHF− 6 have been excited to yield unidirectional pseu-dorotations. In contrast to previous work on the pseu-dorotation of Na3 in the electronic B state excited bylinearly polarized light,7 unidirectionality is achieved bycircular polarization.

The present contribution is motivated by the ques-tion whether the dynamics of degenerate vibrationscan be driven in more complex molecules, where onehas to compete with intramolecular vibrational energyredistribution.8 Promising candidates are metal-carbonylcompounds due to the strong and spectrally distinct in-frared (IR) absorption of the carbonyl stretching vibra-tions. Previous studies of metal-carbonyl compoundshave been focused especially on laser-driven CO vibra-tional ladder climbing.9–11 A particularly interesting ex-ample has been the experimental demonstration of lad-der climbing up to the vCO = 6 state in carboxyhe-moglobin by Joffre and coworkers.11 For this example,Meier and Heitz have developed a non-reactive gas phasemodel to simulate the excitation dynamics by using localcontrol theory.12 It should be noted, however, that themain goal of the experiment had been to achieve con-

a)Electronic mail: oliver.kuehn@uni-rostock.de

trolled metal-carbonyl bond breaking assisted by anhar-monic couplings between the initially excited CO modeand the metal-CO bond. A quantum dynamics studyemploying a reactive model provided support for the ex-perimental finding that this anharmonic coupling is tooweak to cause bond breaking on the time scale of a fewpicoseconds.13,14 The lack of sufficient anharmonic metal-CO coupling has also been found in the related modelstudy of MnBr(CO)5 using a three-dimensional reactiveHamiltonian.15 Further experimental progress in vibra-tional ladder climbing has been reported in Ref. 16 wherean evolutionary algorithm was used for pulse shapingsuch as to highly excite a CO mode in W(CO)6.

In the following we will consider dimanganese de-cacarbonyl Mn2(CO)10 (cf. Fig. 1) as a model sys-tem. In the past it was in particular the photochem-istry of Mn2(CO)10 that attracted most attention (see,e.g., Ref. 17 and references cited therein). More re-cently, the prospect of having ten coupled carbonyl vi-brations attracted the interest of two-dimensional IRspectroscopists.18–21 This included in particular a de-tailed investigation of the coupled CO fundamental andlow-order overtone and combination tone vibrations us-ing anharmonic vibrational perturbation theory for thesubset of CO modes, which were treated by anharmoniccouplings up to the fourth order.19 The anharmonic levelshifts for all CO vibrations were found to be below 10cm−1 .

In Section II A we will present results on the quan-tum chemical characterization of the global minimumstructure of the Mn2(CO)10 model system. Based onthis structure we will develop a seven-dimensional (7D)model Hamiltonian in Section II B, which is designedsuch as to describe the dynamics of the two degenerateE1 CO vibrational normal modes and their anharmoniccoupling to the remaining degrees of freedom, which willbe called a bath. Further, we will comment on the nu-merical solution of the time-dependent Schrodinger equa-tion, which is done using the multiconfiguration time-dependent Hartree (MCTDH) approach to wave packet

arX

iv:1

105.

5727

v1 [

quan

t-ph

] 2

8 M

ay 2

011

2

FIG. 1. Optimized D4d structure of Mn2(CO)10 usingDFT/BP86 with a TZVP basis set.

dynamics.22,23 Numerical results on the laser-driven dy-namics will be discussed in Section III and conclusionsare present in Section IV.

II. THEORY

A. Characterization of the Equilibrium Geometry

The structure of Mn2(CO)10 (cf. Fig. 1) has been op-timized under D4d symmetry constraint employing Den-sity Functional Theory (DFT) with the BP86 functionaland a triple zeta (TZVP) basis set as implemented in theGaussian 03 program package.24 Available crystal struc-ture data are well reproduced as seen from the compari-son given in Tab. I.

The stationary points were further characterized by anormal mode frequency analysis. The results for the IRactive CO stretching vibrations are summarized in Tab.II. Overall, the agreement with experiment is quite rea-

calc. Ref. 25 Ref. 26 Ref. 27

Mn-Mn 2.97 2.92 2.98 2.90

Mn-COax 1.81 1.73 1.80 1.82

Mn-COeq 1.85 1.83 1.87 1.86

C-Oax 1.16 1.16 1.15 1.15

C-Oeq 1.15 1.16 1.15 1.14

Mn-Mn-COeq 86.8 86.2 86.6 86.1

TABLE I. Comparison between calculated geometrical pa-rameters of the D4d stationary point of Mn2(CO)10 and crys-tal structure data (bond lengths in A, bond angles in degrees).

sonable even at the level of the harmonic approximation.Moreover, comparison with Ref. 19 indicates, that thereis only a small dependence on the basis set (double vs.triple zeta).

B. Model Hamiltonian and Equations of Motion

The potential energy surface has been expressed interms of normal mode coordinates, i.e. V = V (Q,q).Thereby, the two normal mode displacement coordinatesdescribing the degenerate E1 modes Q = (Q1, Q2), whichare treated beyond harmonic approximation, have beenseparated from the remaining 3N − 8 harmonic bathmodes q. The coupling, Vc(Q,q), between both sets ofcoordinates is modeled in linear order with respect to q.Neglecting any contributions from global rotations themolecular Hamiltonian becomes

Hmol = HQ +Hq + Vc(Q,q), (1)

with the part describing the anharmonic coordinates

HQ =1

2(P 2

1 + P 22 ) + V (Q,q = 0), (2)

the harmonic bath part

Hq =1

2

∑i

(p2i + ω2

i q2i

), (3)

and the interaction

Vc(Q,q) =∂V (Q,q = 0)

∂qq = −F(Q)q . (4)

For Mn2(CO)10 there are 58 bath modes, but not all ofthem will couple appreciably to the Q modes. Using theforces F(Q) the reorganization energy has been calcu-lated according to the assumption that the frequencies

do not change, i.e. E(reorg)i = [Fi(Q)/ωi]

2.8 This quan-tity has been averaged on the Q grid and the result isused to select the most relevant bath modes. The cut-offfor the selection has been chosen such that modes whoseaveraged reorganization energy is substantially smallerthan their harmonic frequencies are neglected. This gavea total of five relevant bath modes, which are combined

mode polariz. calc. exp.28 exp.29 calc.19

B2 z 1988 (788) 1983 1992 1981

E1 (x,y) 2014 (2224) 2014 2025 2005

B2 z 2045 (1348) 2045 2053 2036

TABLE II. Comparison between calculated (harmonic, notscaled) and measured (Ref. 29 in gas phase, Ref. 28 in n-hexane) frequencies of IR active carbonyl stretching vibra-tions (in cm−1 ). Calculated IR intensities are given in paren-thesis (in km/mol).

3

TABLE III. Most important bath modes according the aver-aged reorganization energy 〈E(reorg)〉 (average over the full Qgrid and - in parentheses - over a reduced grid from -1 to 1a0(a.m.u.)1/2). The parameters of the MCTDH implementa-tion (NDVR: number of DVR points, NSPF: number of singleparticle functions) are given as well. Notice that modes q2and q5 as well as q3 and q4 have been combined.

mode ωi 〈E(reorg)〉 grid NDVR NSPF

(cm−1) (cm−1) (a0(a.m.u.)1/2)

q1 (A1) 425 468 (72) -7.5:7.5 45 10

q2 (A1) 1999 822 (122) -1.7:1.7 25 10

q3 (E2) 2016 1426 (204) -1.7:1.7 25 10

q4 (E2) 2016 1649 (239) -1.7:1.7 25 10

q5 (A1) 2106 4646 (692) -1.7:1.7 25 10

with the anharmonic coordinates to a seven-dimensionalmodel. The bath mode parameters are compiled in Tab.III. Notice that the average reorganization energy de-pends, of course, on the grid size. In the table we reportthe average over the full grid as well as over a reducedgrid onto which the wave packet will be mostly localized.The major effect on the dynamics of the Q modes willcome from the coupling to the other CO vibrations, notonly because the forces are the largest, but also becauseof the near resonance. Among the lower-frequency modesonly q1 couples appreciably; it is a breathing mode of allequatorial CO groups with respect to the two Mn centers.

The molecular Hamiltonian is supplemented by themolecule-field interaction that is described in dipole ap-proximation

Hfield(t) = −d(Q)E(t), (5)

where the dipole moment surfaces for the different po-larization directions have been obtained along with thepotential energy surface for the selected anharmonic de-grees of freedom. Notice that within the approximationgiven by Eq. (4) there is no coupling to the other twoIR active carbonyl modes (cf. Tab. II). Moreover, thelatter are polarized in z-direction and will not be directlyexcited by the circularly polarized laser pulse. For the dy-namics simulations it will be assumed that the moleculehas been pre-oriented with the coordinate system as in-dicated in Fig. 1. The laser field will be taken to be ofthe form

E(t) =

Ex(t)

Ey(t)

0

= E0Θ(t)Θ(tp − t) sin2(tπ/tp)

cos(ωt)

sin(ωt)

0

. (6)

Here tp is the total pulse duration, ω the carrier fre-quency, and E0 the field strength. These parameters

will be chosen such as to achieve the excitation of a vi-brational superposition state with respect to the two E1

modes, which corresponds to a wave packet performinga clockwise circulation on the potential energy surfaceV (Q,q = 0). The respective normal mode displacementsare shown in Fig. 2. Close inspection of this figure showsthat during this circulation, the antisymmetric combina-tion of stretching motions of equatorial CO groups whichare opposite to each other ”moves” around the symmetry(z) axis. Of course, this classical picture applies only aslong as the wave packet stays compact and an importantquestion to be addressed will be the regime of validity ofthis classical analogue.

The 7D time-dependent Schrodinger equation

i~∂

∂tΨ(Q,q; t) = [Hmol +Hfield(t)]Ψ(Q,q; t) (7)

has been solved using the MCTDH approach22,23 as im-plemented in the Heidelberg program package.30 Theseven-dimensional wave function Ψ(Q,q; t) is representedon a grid in terms of a harmonic oscillator discrete vari-able representation (DVR). A total of 25 DVR points onthe grid [−1.7 : 1.7]a0(a.m.u.)1/2 together with 12 sin-gle particle functions (SPFs) are used for each of the Qmodes which are treated as a combined MCTDH parti-cle. The parameters for the bath modes are compiledin Tab. III. Potential energy and dipole moment sur-faces have been fitted on this grid using the POTFITalgorithm.23 Using this set of SPFs the natural orbitalpopulations have been below 10−5. The actual propaga-tion is performed using the variable mean field schemewith a 6th order Adams-Bashforth-Moulton integrator.The vibrational ground state, |Ψ0〉, has been calculatedusing the improved relaxation scheme31; some uncoupled(one-dimensional zero-order) states in the Q-subspacewill be used for the discussion of the dynamics.

III. RESULTS AND DISCUSSION

In the following we will present results for the time-dependent wave packet dynamics which have been ob-tained for a carrier frequency ω, fixed to the funda-mental transition of the E1 modes, which is at 2014cm−1 . The total propagation time has been set to5 ps. First, we will discuss the effect of changingthe field strength E0, before the variation of the pulselength is addressed. A global analysis of the dy-namics will be given in terms of the following quan-tities: (i) the energy absorbed by the molecule atthe end of the pulse: ∆Emol = 〈Ψ(tp)|Hmol|Ψ(tp)〉-〈Ψ0|Hmol|Ψ0〉, (ii) the maximum energy change of thebath modes reached during the considered time inter-

val of 5 ps: ∆E(max)bath =max(〈Ψ(t)|Hq|Ψ(t)〉-〈Ψ0|Hq|Ψ0〉),

(iii) the maximum expectation value of the E1 modes’coordinate operators during the 5 ps time interval:Q(max)=max(〈Ψ(t)|Q|Ψ(t)〉), and (iv) the population

4

FIG. 2. Classical picture of vibrational wave packet circulation triggered by excitation of the two degenerate E1 modes bymeans of a circularly polarized laser field. Shown are the displacement vectors for the superposition of the modes along a unitcircle in steps of 45◦. In the central panel the two-dimensional potential V (Q,q = 0) is shown (contour lines in steps of 2000cm−1 starting at 2000 cm−1 ).

of the ground state at the end of the pulse: P0 =|〈Ψ(tp)|Ψ0〉|2.

A. Dependence on the Field Strength

A global analysis of the dynamics in dependence onthe field strength and for a pulse duration of tp = 500 fsis given in Tab. IV. Overall, we observe a monotonousdecrease of the ground state population P0 with increas-

ing field amplitude. For the highest amplitude used, theground state is completely depopulated. At the sametime the absorbed energy ∆Emol increases, indicating vi-brational ladder climbing. In fact for E0 = 1.5 mEh/ea0

the absorbed energy is compatible with an appreciable si-multaneous population of the third vibrationally excitedstate in each of the two Q modes. Analysis of the popula-tion shows that in fact many overtone and combinationtransitions are excited with the (ν1 = 2, ν2 = 2) statehaving the largest population. For the more moderate

5

TABLE IV. Analysis of the laser-driven wave packet dynam-ics for a 500 fs pulse which is resonant to the fundamentaltransition of the E1 modes (cf. Eq. (6)).

E0 ∆Emol ∆E(max)bath Q(max) P0

(mEh/ea0) (cm−1 ) (cm−1 ) (a0√

a.m.u)

0.1 71 6 0.05 0.97

0.2 277 18 0.09 0.87

0.3 621 62 0.13 0.73

0.4 1099 164 0.18 0.57

0.5 1708 341 0.22 0.42

1.5 12733 4553 0.50 0.00

excitation with E0 = 0.5 mEh/ea0 the populations ofthe Q modes’ states is about 20% for (0, 1) and (0, 1),8% for (1, 1) and 4 % for (2, 0) and (0, 2).

The anharmonic coupling to the bath modes will in-crease along with the absorbed energy, i.e. if the wavepacket explores configurations away from equilibrium.For moderate excitation conditions the extent of anhar-monic coupling is rather small, e.g. if the amount ofabsorbed energy corresponds to about one quantum ofexcitation in a CO mode (E0 = 0.5 mEh/ea0) we find

∆Emol/∆E(max)bath ≈ 5. The effect of the bath becomes

appreciable only under high excitation conditions, e.g.,

for E0 = 1.5 mEh/ea0 we find ∆Emol/∆E(max)bath ≈ 2.8. In

Fig. 3 we show the expectation values of the Hamiltonianoperators for the system modes, HQ, and the uncoupledbath modes, Hq, for two field strengths. As expectedthe energy of the Q modes rises during laser pulse ex-citation (tp = 500 fs) as seen in panel (a). For thelower field strength the expectation value subsequentlyoscillates around the attained value signaling reversibleenergy exchange with the bath modes. Indeed the corre-sponding oscillations in the bath mode energies are seenin panel (b). Increasing the field strength, the energy ex-change with the bath is more pronounced and instead ofregular oscillations the onset of equilibration among thebath modes is observed in panel (c). Still there is no ap-preciable coupling to lower frequency modes that couldlead to an energy flow out of the selected Q modes. Wenotice from panels (b) and (c) that the low-frequencymode q1, which was selected because it had the largestreorganization energy in the lower-frequency part of thespectrum is not appreciably excited. Finally, we com-ment on the initial partitioning of energy among the bathmodes. Inspecting Tab. III one might have anticipatedthat mode q5 will dominate the bath dynamics. However,the fundamental frequency of the laser-excited Q modesis 2014 cm−1 , which is resonant to q2 − q4, but ratheroff-resonant with respect to q5. Hence, energy exchangebetween the Q and the q5 modes is not very efficient.

The focus of the present investigation is on the wavepacket circulation with respect to the E1 modes. Inspect-ing Tab. IV we notice that the maximum bond elonga-tion increases with the amount of absorbed energy. The

0

2000

4000

6000

8000

10000

12000

0

200

400

600

800

1000

1200

1400

1600

1800

0 1000 2000 3000 4000 5000

t [fs]

q1q2q3q4q5

0

20

40

60

80

100

120

140

E[c

m-1

]E

[cm

-1]

E[c

m-1

]

(a)

(b)

(c)

FIG. 3. (a) Expectation values of HQ for a 500 fs excitationwith field strength E0 = 0.5 mEh/ea0 (lower curve) and 1.5mEh/ea0 (upper curve). The respective expectation values ofHq for the five bath modes are shown in panels (b) (E0 =0.5 mEh/ea0) and (c) (E0 = 1.5 mEh/ea0). With increasingenergy at about 1000 fs the curves correspond to q1, q5, q3,q2, and q4 in panel (c), whereas in panel (b) q2 and q4 areinterchanged (see also key in panel (c)).

value that is reached can be compared, e.g., with the vari-ance of the ground state coordinate distribution which is0.17 a0

√a.m.u for the Q modes. Thus for the largest field

strength we observe that the bond elongation is aboutthree times this ground state variance. A more detailedpicture is provided by inspecting the coordinate oper-ator expectation values, Qi(t) = 〈Ψ(t)|Qi|Ψ(t)〉, whichare shown in Fig. 4. In the parametric plot the expecta-tion values trace a clockwise circulating trajectory on thepotential V (Q,q = 0). For small field strengths the am-plitude of this circulation increases during the excitation

6

TABLE V. Analysis of the laser-driven wave packet dynamicsfor pulses of different duration and amplitude. The integratedfield envelope is identical in all cases.

tp E0 ∆Emol ∆E(max)bath Q(max) P0

(fs) (mEh/ea0) (cm−1 ) (cm−1 ) (a0√

a.m.u)

100 2.5 1812 374 0.23 0.40

500 0.5 1708 341 0.22 0.42

1000 0.25 1441 273 0.20 0.47

1500 0.17 1146 205 0.18 0.54

period of 500 fs (upper and middle panel of Fig. 4). Forthe strongest field used (lower panel of Fig. 4) the ampli-tude of the circulation starts to decrease already duringthe interaction with the pulse. Furthermore, after theexcitation pulse is over the behavior shows a strong de-pendence on the field amplitude (right column of Fig. 4).Judging from the amount of energy redistribution givenin Tab. IV the decrease of Qi(t) can only in part be aneffect of the anharmonic coupling to the bath. Instead itis the wave packet dispersion that is mostly responsiblefor this decrease of Qi(t). This is shown in Fig. 5 wheresnapshots of the reduced density are plotted for the caseof E0 = 0.5 mEh/ea0. One notices that the wave packetstays compact in the excitation period only, but thenstarts to disperse. Eventually, the wave packet is ratherdelocalized even though it is still circulating. However,due to the delocalization negative and positive coordinatevalues contribute to the expectation values along the Qaxes and therefore the expectation values become smallerand cannot reflect the wave packet circulation anymore.With increasing excitation more eigenstates contribute tothe wave packet such that the dispersion effect becomesmore pronounced and sets in already during the pulse.

B. Dependence on the Pulse Duration

In the following we investigate the dependence of thelaser-driven wave packet dynamics on the duration of theexcitation pulse. As a reference case we have used tp =500 fs and E0 = 0.5 mEh/ea0. For a given duration tpthe field amplitudes have been chosen such as to keepthe integrated field envelope at the same value as in thereference case. Note that we are not dealing with a twolevel system and that the pulses are no π-pulses. Thepulse parameters are summarized in Tab. V.

Table V also contains the various expectation values,which give a global characterization of the dynamics.First, we notice that the different pulse durations givecomparable depopulations of the vibrational ground statebetween 40 and 54%. The amount of energy absorbed bythe molecule decreases with the pulse duration and islargest for the shortest pulse (tp = 100 fs), although thedifference to the reference pulse is only 6%. At the sametime the excitation of bath modes decreases from a con-

-0.050

0.05Q2

-0.05

0

0.05Q1

0

200

400

600

t HfsL

-0.050

0.05

Q2

-0.0500.05Q1

1.0

1.5

2.0

2.5

3.0

tHpsL

-0.2

0

0.2Q2

-0.2

0

0.2Q1

0

200

400

600

t HfsL

-0.1 0 0.1

Q2

-0.10

0.1Q1

1.0

1.5

2.0

2.5

3.0

t HpsL

-0.5

0

0.5

Q2

-0.5

0

0.5Q1

0

200

400

600

t HfsL

-0.10

0.1

Q2

-0.1

00.1Q1

1.0

1.5

2.0

2.5

3.0

t HpsL

FIG. 4. Parametric plots of (Q1, Q2) (in a0√

a.m.u) for a 500fs laser pulse excitation and a field strength E0 (in mEh/ea0)of 0.2 (upper row), 0.5 (middle row) and 1.5 (bottom row).(Notice the different axes scales).

tribution to the total energy of 21% for tp = 100 fs downto 18% for tp = 1500. Moreover, the maximum radiusof circulation of the expectation value of the Q coordi-nates is reduced slightly. Inspecting the time dependenceof the Qi(t) in Fig. 6 we notice that again we have aninitial period, where the wave packet stays rather com-pact such that the coordinate expectation values give areasonable picture of the moving wave packet. This is fol-lowed by a period where the wave packet disperses suchthat the dynamics cannot be understood from the expec-tation values. As far as the pulse duration dependenceis concerned the most striking observation from Fig. 6 isthat the time span of compact wave packet propagationcan be prolongated by increasing the parameter tp. Inpassing we note that this does also imply that the timespan of circulation at about the full radius is longer, butof course not identical to tp. For tp = 500 fs and 1500

7

-1

0

1

Q2 Ha0Ha.m.uL1�2L

-1 0 1Q1 Ha0Ha.m.uL1�2L

t=0fs

-1

0

1

Q2 Ha0Ha.m.uL1�2L

-1 0 1Q1 Ha0Ha.m.uL1�2L

-1

0

1

Q2 Ha0Ha.m.uL1�2L

-1 0 1Q1 Ha0Ha.m.uL1�2L

t=500fs

t=3ps

FIG. 5. Snapshots of the time evolution of the reduced densitywith respect to the Q modes for laser-driving with a pulsehaving the parameters tp = 500 fs, E0 = 0.5 mEh/ea0, andω/2πc = 2014 cm−1 .

fs the expectation values Qi(t) are within 90% of theirmaximum value during the interval [450 : 800] fs and[950 : 1650] fs, respectively. Since the anharmonic cou-pling is still small in the considered range of the potentialenergy surface corresponding to about one to two quantaof excitation of the E1 modes, intramolecular energy re-distribution doesn’t destroy wave packet circulation evenfor the longest pulse duration of 1.5 ps and subsequent3.5 ps free evolution.

IV. SUMMARY

We have demonstrated laser-driven wave packetcirculation with respect to the two degenerate E1

carbonyl stretching vibrations in a pre-orientedMn2(CO)10 model. The wave packet circulationcorresponds to a vibrational excitation moving around

-0.2

0

0.2Q2

-0.2

0

0.2Q1

0

50

100

150

200

t HfsL

-0.20

0.2

Q2

-0.2

0

0.2Q1

0

1

2

3

t HpsL

-0.2

0

0.2

Q2

-0.2

0

0.2Q1

0.0

0.5

1.0

t HpsL

-0.10

0.1

Q2

-0.10

0.1Q1

2

3

4

t HpsL

-0.10

0.1Q2

-0.1

0

0.1Q1

1.5

2.0

t HpsL

-0.10

0.1

Q2

-0.10

0.1Q1

2.0

2.5

3.0

3.5

4.0

t HpsL

FIG. 6. Parametric plots of (Q1, Q2) (in a0√

a.m.u) for dif-ferent pulse durations. Upper row: tp = 100 fs, E0 = 2.5mEh/ea0, middle row: tp = 1000 fs, E0 = 0.25 mEh/ea0,bottom row: tp = 1500 fs, E0 = 0.17 mEh/ea0. (Notice thedifferent axes scales).

the symmetry axis of the system. It has been shownthat a classical picture holds approximately during theinteraction with the excitation laser pulse. Later on,appreciable wave packet dispersion sets in such thatthe classical picture becomes meaningless, although thewave packet still circulates around the minimum of thepotential energy surface.

The possibility of wave packet circulation upon exci-tation of degenerate vibrational modes with circularlypolarized laser light could have been anticipated fromthe work of J. Manz et al. on triatomic molecules.5,6

Therefore, the most important result of the present studyconcerns the robustness of wave packet circulation withrespect to intramolecular vibrational energy redistribu-tion in a polyatomic molecule. To proof this we haveconsidered the coupling of the two E1 mode to other in-

8

tramolecular degrees of freedom, which have been de-scribed in harmonic approximation. This resulted in aseven-dimensional model for which the time-dependentSchrodinger equation has been solved using the MCTDHapproach. For moderate excitation conditions of one ortwo quanta in the E1 modes, at most about 20 % of theabsorbed energy is disposed into the bath modes withina time span of 5 picoseconds. This finding appears to beencouraging and should stimulate experimental verifica-tion.

ACKNOWLEDGMENT

We gratefully acknowledge financial support from theDeutsche Forschungsgemeinschaft (project Ku952/6-1).

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