State-Selective Control for Dissipative Vibrational Dynamics of HOD

J. Phys. Chem. 1996, 100, 13927-13940

13927

State-Selective Control for Dissipative Vibrational Dynamics of HOD by Shaped Ultrashort Infrared Laser Pulses M. V. Korolkov,† J. Manz, and G. K. Paramonov*,† Institut fu¨ r Physikalische und Theoretische Chemie, Freie UniVersita¨ t Berlin, WE 3, Takustrasse 3, D-14195 Berlin, Germany ReceiVed: March 27, 1996X

Ultrafast state-selective manipulation of populations under the control of shaped picosecond infrared laser pulses is investigated by means of computer simulations within the reduced density matrix formalism beyond the Markov approximation for the HOD molecule coupled to an unobserved quasi-resonant environment. The laser-driven dissipative quantum dynamics in a classical electric field is simulated for discrete vibrational levels within a two-dimensional model of the HOD stretches in the electronic ground state. Efficient population transfer with the probability up to 80-90% is demonstrated on a picosecond time scale in the presence of the environmental degrees of freedom which reduce the lifetimes of vibrational bound states into a picosecond time domain.

1. Introduction The laser control over molecular dynamics and the related problem of manipulating the outcome of chemical reactions continue to attract considerable and ever-increasing attention.1-12 Recent experimental achievements, realized on a femtosecond time scale, include selective population control in the wavepacket motion of isolated molecules,13 laser control of unimolecular reactions,13,14 and two-laser control of atom-molecule reactions.9,10 The theoretical approaches to the problem may be classified, in general, as (1) weak-field control with continuous wave (CW) laser fields8,15-21 and (2) control by tailored laser pulses,22-41 which often requires strong-field control schemes with ultrashort laser pulses and explicitly determined laser-molecule time-dependent interactions.42-45 Several approaches, for example the coherent control scheme,19-21 adiabatic passage control scheme,32-35 and wave-packet focusing on electronic surfaces,38-41 have been already investigated theoretically and realized experimentally.32,33,41,46-49 An important line in the field of the laser control of molecular dynamics is selective manipulation of populations, in particular, localization of population at a prescribed energy level of a molecule, or the population transfer. This may serve, for example, as a very important intermediate step in lasercontrolled isomerization reactions.50-55 In mode-selective laser chemistry, it is most desirable to achieve the state-selective vibrational excitation, i.e., to localize population at a prescribed vibrational level. Until now, the vast majority of the theoretical studies in this line have been carried out for isolated molecules within the Schro¨dinger wave function formalism, neglecting any environmental degrees of freedom. Examples include the OH radical,36,37,42,44,56 HOD, H2O, HF, SiH2, and NH2 molecules.43,57-60 In a recent work61 the state-selective excitation of vibrational overtones has been simulated with the Liouville equation for the density matrix, but the environmental effects have not been considered. On the other hand, the environmental and solvent effects have been taken into account in the theoretical formulations of optimal control of molecular dynamics with weak laser fields,38,39 but state-selective laser control has not been specified as a target therein. † Permanent address: B. I. Stepanov Institute of Physics, Belarus Academy of Sciences, Skaryna ave. 70, 220602 Minsk, Republic of Belarus. X Abstract published in AdVance ACS Abstracts, August 1, 1996.

S0022-3654(96)00930-6 CCC: $12.00

In a realistic situation, the state-selective preparation of a molecule may be achieved if the laser field steering the molecule to a specified target can compete against such processes as intramolecular vibrational redistribution (IVR) and dissipation. This calls, in general, for a statistical description of the stronglylaser-driven multilevel quantum systems in terms of the reduced density matrix. A few results have been reported62 on the stateselective ultrafast excitation of one-dimensional model diatomic systems coupled to an environment, which have been simulated within the reduced density matrix formalism in Markov approximation. However, the applicability of the Markovian analysis to the ultrafast processes stimulated by strong laser fields is questionable. In the previous work63 of two of us (see also ref 64) it has been shown, for example, that the Markov approximation, when compared to non-Markov approaches, results in a 20-30% lower level of the ultrafast state-selective population transfer in a one-dimensional model system tailored to the local OH bond of the HOD and H2O molecules. In the present work we address ourselves to non-Markov analysis of the stateselective dissipative vibrational dynamics of a two-dimensional model of the HOD molecule in the electronic ground state, which generalizes our previous wave-function-based analysis of the state-selective preparation of the isolated HOD molecule.43 With the aim to study the limits of ultrafast stateselective laser control, an extremely unfavorable situation is considered: the quasi-resonant environment, with the maximal strengths of the molecule-environment coupling corresponding to all molecular frequencies. Therefore, the 80-90% stateselective population transfer, demonstrated below, should be considered as a reference. It may be substantially higher for any other specific environment, such as a surface or matrix, if the environment is off the exact resonance with the molecular frequencies. The outline of the paper is as follows. The two-dimensional model, the vibrational-level structure of HOD, and its interaction with the laser field are described in section 2. The quasiresonant environment and the equation of motion for the reduced density matrix beyond a Markov-type approximation are defined in section 3. The laser control schemes together with the optimization procedure used, and the state-selective preparation of HOD coupled to the environment, are presented in section 4. The results obtained are summarized and discussed in section 5. © 1996 American Chemical Society

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2. Model, Vibrational-Level Structure, and Interaction with Laser Field In our computer simulations of the state-selective dissipative dynamics we use a two-dimensional model of stretching vibrations in a nonbending and nonrotating HOD molecule in the electronic ground state, which includes kinetic coupling between the OH and OD bonds. The model is similar to those used previously,43,65 and below we summarize some basic properties and nomenclature used in the subsequent analysis. The coordinates presenting the OH and OD bonds are denoted rH and rD, with the associated conjugate momenta being, respectively, pH and pD. The atomic masses are MH ) 1.008 amu, MO ) 16.00 amu, MD ) 2.014 amu. Atomic units are used if the others are not explicitly indicated. The coupled vibrational stretches of the unperturbed HOD molecule are defined by the molecular Hamiltonian

Hmol ) HH + HD + HH,D + D0

(1)

where HH and HD stand for the individual OH and OD bonds, HH,D represents the kinetic coupling, and D0 ) 0.1994Eh is the well depth. The OH bond, for example, is specified by the Hamiltonian

HH ) pH2/2mH + VH(rH)

(2)

V ) 1, 2, ..., Vmax ) (KH + 1)(LD + 1)

It is also suitable to label the vibrational eigenstates |ψV〉 with the ordered pairs (m, n) of quantum numbers m and n, indicating approximately m vibrational quanta in the OH bond (the first quantum number) and n vibrational quanta in the OD bond (the second quantum number) as follows:

V f (m, n), |ψV〉 f |m, n〉, EV f E(m,n)

V(t) ) -µ(rH, rD)‚e0(t) (3)

is a Morse potential with equilibrium distance r0 ) 1.821 a0 and Morse parameter β ) 1.189 a0-1. The zero-order vibrational states |kH〉 of the individual OH bond, satisfying the Schro¨dinger equation

HH|kH〉 ) EkH|kH〉

(4)

for kH ) 0, 1, ..., KH ) 21, are determined by the well-known Morse oscillator wave functions.66,67 Similar expressions hold for the individual OD bond, with the respective zero-order states denoted by |lD〉, where lD ) 0, 1, ..., LD ) 29. The kinetic coupling between the OH and OD bonds is presented in the molecular Hamiltonian Hmol (eq 1) by the term

HH,D ) (cos θ/MO)pHpD

(5)

where the bending angle θ ) 104.5° is assumed to be fixed. The eigenstates |ψV〉 of the unperturbed total molecular Hamiltonian Hmol (eq 1) are approximated within the finite expansion approach65 as follows:

|ψV〉 )

∑ Ck ,l ,V|kH〉|lD〉

kH,lD

H D

(6)

The energies EV and coefficients CkHlD,V are calculated, as usual, by inserting expansion 6 into the time-independent Schro¨dinger equation

Hmol|ψV〉 ) EV|ψV〉

(7)

operating with the zero-order states 〈l′D|〈k′H|, and solving the eigenvalue problem. The vibrational eigenstates |ψV〉 are ordered according to increasing eigenenergies EV and labeled by the eigenenergylevel quantum number

(9)

This labeling is defined by the dominant coefficients CkH)m,lD)n,V in the finite expansions 6. The 50 lowest vibrational levels of the two-dimensional model of HOD and their energies are displayed in Figure 1. Similar to the previous work,43 we shall also refer to (m > 0, n ) 0) states as local OH states, to (m ) 0, n > 0) states as local OD states, and to (m, m) states, which have equal numbers of vibrational quanta in each local band, as “symmetric” states. Sometimes, the manifolds of local OH and OD states will be referred to as local OH and OD modes, respectively, and a combined labeling V(m, n) will be used too. The excitation of vibrational stretches in the HOD molecule by a shaped laser field is described semiclassically within the electric dipole approximation by the time-dependent interaction Hamiltonian

where mH ) MHMO/(MH + MO) is the reduced mass, and

VH(rH) ) D0{exp[-β(rH - r0)] - 1}2 - D0

(8)

(10)

where e0 is the polarization unit vector of the electric field (t), and µ(rH, rD) is the electric dipole moment function represented for the HOD molecule in the electronic ground state by a bond dipole model,68

µ(rH, rD) ) rHµ0 exp(-rH/r*) + rDµ0 exp(-rD/r*) (11) with µ0 ) 7.85 D/Å and r* ) 0.6 Å. At a linear polarization of the laser electric field, which is assumed to be aligned along the D-H direction in the HOD plane, the interaction Hamiltonian (eq 10) takes the form

V(t) ) -(t) cos φ µ(rH, rD)

(12)

where φ ) (π - θ)/2, and

µ(rH, rD) ) µ0[rH exp(-rH/r*) - rD exp(-rD/r*)] (13) The laser fields to be used for control of the state-selective dissipative dynamics of the HOD molecule may be composed, in general, of several sequential or overlapping laser pulses. The corresponding electric field strength is

(t) ) ∑isin2[π(t - t0i)/tpi] cos(ωit + φi)

(14)

i

where pulse i starts at t ) t0i, its duration is tpi, with the current time interval being

t0i e t e t0i + tpi

(15)

i is the electric field amplitude, ωi is the laser carrier frequency, and φi is the phase. The phases of the laser pulses, φi, are of no importance if the pulses are not overlapping, and they are of minor importance if the carrier frequencies ωi of the overlapping pulses are not very close to each other.44 The latter is just the case for the optimal laser control schemes developed in this study, and the results below will be presented for φi ) 0. The sin2-type shape of the driving laser pulses, used in this study as in several previous works,22,23,43,50-55 is a suitable but

Dissipative Vibrational Dynamics of HOD

J. Phys. Chem., Vol. 100, No. 33, 1996 13929 The environment coupling operator F({zu}) is assumed to be linear and factorized with respect to the environmental degrees of freedom as follows:

F({zu}) ) ∑ Kuzu, u ) 1, 2, ...

(21)

u

The molecule-environment coupling operator (eq 17) is nonlinear, but it becomes linear in the harmonic limit for the HOD stretches, as detailed above. The environment Hamiltonian He({zu}) is treated as an infinite ensemble of harmonic oscillators:

He({zu}) ) ∑Hu(zu)

(22)

Hu(zu) ) pu2/2mu + (mu/2)Ωu2zu2

(23)

u

Figure 1. Energy-level structure for a two-dimensional model of HOD stretching vibrations in the electronic ground state. The target states are indicated by asterisks. The notation V/(m, n) indicates the Vth level with approximately m and n vibrational quanta in the OH and OD bonds, respectively.

with

rather arbitrary choice, which is not of primary importance; similar results can be obtained with other “bell”-type shapes of the pulses, for example, Gaussian,36 or soliton-type, hyperbolic secant shape.61,69

where mu is the effective mass, Ωu is the frequency, and u ) 1, 2, .... The eigenstates of the environment are determined by the well-known harmonic oscillator wave functions with eigenenergies

3. Quasi-Resonant Environment and Equation of Motion

Enu ) pΩu(nu + 0.5), nu ) 0, 1, ...

The total Hamiltonian for the HOD molecule coupled to the environment can be written in the form

H(rH, rD, {zu}, t) ) Hmol(rH, rD) + V(rH, rD, t) + W(rH, rD, {zu}) + He({zu}) (16) where the unperturbed molecular Hamiltonian Hmol(rH, rD) is defined by eq 1, and V(rH, rD, t) describes the interaction of the molecule with a shaped laser field as specified in eqs 10-13. The laser field is assumed to excite only molecular vibrations, and it doesn’t influence the environmental degrees of freedom. The Hamiltonian W(rH, rD, {zu}) presents the interaction between the molecule and the environment, and He({zu}) is the Hamiltonian for the environment, with {zu} standing for the environmental degrees of freedom. The Hamiltonian W(rH, rD, {zu}) for the coupling between the molecule and environment is assumed to be presented in the form

W(rH, rD, {zu}) ) ΛQ(rH, rD) F({zu})

Q(rH, rD) ) QH(rH) + QD(rD)

(18)

where the couplings QH(rH) and QD(rD) for the individual OH and OD bonds are assumed to be nonlinear,70

QH(rH) ) (1/β){1 - exp[-β(rH - r0)]}

The density matrix for the total system “molecule plus environment” is denoted in the Schro¨dinger picture by σ(t). Time evolution of the density matrix in the interaction picture is governed by the Liouville equation71

∂σI(t) ) (i/p)(t)[µI(rH, rD, t), σI(t)] ∂t i(Λ/p)[QI(rH, rD, t) FI({z}, t), σI(t)] (25) where the density matrix in the interaction picture is related to the Schro¨dinger picture as follows:

σI(t) ) exp[i(Hmol + He)t/p]σ(t) exp[-i(Hmol + He)t/p] (26) with corresponding relations for the operators µ, Q, and F. The statistical description of the HOD molecule coupled to an unobserved environment is provided by its reduced density matrix F(t), which is defined in the interaction picture as

(17)

where Λ is a constant measuring the strength of the moleculeenvironment coupling, while Q(rH, rD) and F({zu}) are the molecular and the environment coupling operators, correspondingly. The molecular coupling operator is taken in the form

(19)

FI(t) ) Tre[σI(t)]

(20)

which yield linear couplings, QH(rH) f (rH - r0) and QD(rD) f (rD - r0), in the harmonic limit for the individual OH and OD bonds: D0 f ∞, β f 0, and D0 β2 f const.

(27)

where Tre is the trace over all environmental degrees of freedom. The equation of motion for FI(t) can be obtained as usual71 by making use of the formal solutions of the Liouville equation (25):

σI(t) ) σI(0) + (i/p) ∫0 dt′{[(t′) µI(rH, rD, t′), σI(t′)] t

Λ[QI(rH, rD, t′) FI({zu}, t′), σI(t′)]} (28)

Substituting eq 28 back into eq 25 and evaluating the trace (27) under the assumption of the basic condition of irreversibility,

and

QD(rD) ) (1/β){1 - exp[-β(rD - r0)]}

(24)

σI(t) ) FI(t) Fe(0)

(29)

Fe(0) ) exp(-He/kBT)/Tre[exp(-He/kBT)]

(30)

where

(see, for example, ref 71 for details), we obtain finally the

13930 J. Phys. Chem., Vol. 100, No. 33, 1996

Korolkov et al.

equation of motion for the reduced density matrix in the interaction picture,

∂FI(t) ) (i/p)(t)[µI(rH, rD, t), FI(t)] ∂t (Λ/p)2RI(rH, rD, t) (31)

assumptions we can change in eq 35 from the infinite sum over u to the finite sums over V > V′ containing the integrals

〈F(t′′) F(0)〉 )

t

{[QI(rH, rD, t), QI(rH, rD, t - t′′) FI(t - t′′)]〈F(t′′) F(0)〉 [QI(rH, rD, t), FI(t - t′′) QI(rH, rD, t - t′′)]〈F(0) F(t′′)〉} (32)

The time correlation functions 〈F(t′′) F(0)〉 and 〈F(0) F(t′′)〉 in eq 32 are defined, as usual,71 by

〈F(t′′) F(0)〉 ) Tre[FI({zu}, t′′) FI({zu}, 0) Fe(0)] (33) 〈F(0) F(t′′)〉 ) Tre[FI({zu}, 0) FI({zu}, t′′) Fe(0)] (34) For the environment treated as an ensemble of harmonic oscillators (see eqs 22-24), the traces in eqs 33 and 34 can be evaluated analytically, and we get

〈F(t′′) F(0)〉 ) 1/2(p/muΩu) ∑ Ku2Φ(Ωu, t′′, T)

(35)

u

where

Φ(Ωu, t′′, T) ) {[nj(Ωu) + 1] exp(-iΩut′′) + nj(Ωu) exp(iΩut′′)} (36) with

nj(Ωu) ) [exp(pΩu/kBT) - 1]-1

(37)

and 〈F(0) F(t′′)〉 ) 〈F(t′′) F(0)〉*. The specific values of the parameters Ku, mu, and Ωu in eqs 35-37 should be derived from the characteristics of a particular environment and the molecule-environment coupling. For a model quasi-resonant environment under consideration some parameters can be chosen arbitrarily and have to be checked afterwards by simulating, for example, the “free” relaxation, with the laser field being switched off. The relaxation rate and the lifetime of vibrational states of HOD will be characterized by the parameter Λ, measuring the strength of the moleculeenvironment interaction; see eq 17. It is also suitable to assume in eq 35 that p/muΩu ) a02, which yields the environment coupling F({zu}) of the same order of magnitude as the molecular coupling Q(rH, rD). The quasi-resonant nature of the molecule-environment coupling is taken into account under the assumption that the environmental frequencies Ωu are closely spaced near the molecular frequencies ωVV′ ) (EV - EV′)/p. The density of the environmental frequencies near each molecular frequency ωVV′ is chosen as a Lorentzian-type distribution

1 gVV′(Ω) ) (γVV′/Ω0)p π γ

γVV′ VV′

2

+ (ωVV′ - Ω)2

(38)

where (γVV′/Ω0)p is a normalization factor, Ω0 is a scaling parameter, and γVV′ > 0 determines the width of the distribution gVV′(Ω), which has a maximum at Ω ) ωVV′. Under these

2

a02 Vmax

where RI(rH, rD, t), which will be referred to as the timedependent relaxation matrix, is given in the interaction picture by

RI(rH, rD, t) ) ∫0 dt′′ ×

a02

2

∑u Ku2Φ(Ωu, t′′, T) w

V-1

KVV′2 ∫A ∑ ∑ V)2 V′)1

BVV′ VV′

dΩ Φ(Ω, t′′, T) gVV′(Ω) (39)

where AVV′ < ωVV′ < BVV′. The Bose-Einstein distribution function nj(Ω) is approximated in each frequency interval AVV′ e Ω e BVV′ by the respective “central” values nj(ωVV′). With the assumption that the reasonable choice of γVV′ provides small overlap of the neighboring distributions gVV′(Ω), we can set AVV′ ) -∞ and BVV′ ) ∞, which yields tabulated integrals72 in eq 39. The final expression obtained for the time correlation function 39 reads

〈F(t′′) F(0)〉 )

a02 Vmax 2

V-1

KVV′2(γVV′/Ω0)p exp(-γVV′|t′′|) × ∑ ∑ V)2 V′)1

{[nj(ωVV′) + 1] exp(-iωVV′t′′) + nj(ωVV′) exp(iωVV′t′′)} (40) The choice for the values of four parameters, KVV′, γVV′, Ω0, and p, in the correlation function (eq 40) is rather arbitrary and flexible, which makes it possible to specify furthermore the particular molecule-environment interactions, for example, such as described below. The well-known treatment of the time-dependent relaxation matrix (eq 32) in eq 31 in Markov approximation71 includes the substitution FI(t - t′′) f FI(t) and the extension of the upper limit of integration over t′′ to infinity. On the contrary, in the present work we represent an equation of motion (eq 31) in the form suitable for numerical integration beyond the Markov approximation in the Schro¨dinger picture by making use of the transformation

FI(t) ) exp(iHmolt/p) F(t) exp(-iHmolt/p)

(41)

for the reduced density operator FI(t) and for the operators µI(rH, rD) and QI(rH, rD). Taking matrix elements between molecular eigenstates |V〉 yields

〈V|FI(t)|V′〉 ) exp(iωVV′t) F(t)VV′

(42)

〈V|µI(rH, rD, t)|V′〉 ) exp(iωVV′t)µVV′

(43)

〈V|QI(rH, rD, t)|V′〉 ) exp(iωVV′t)QVV′

(44)

The matrix elements µVV′ and QVV′ are represented, by making use of the expansion 6, with the respective superpositions of matrix elements

〈lD|〈kH|µ(rH, rD)|k′H〉|l′D〉

(45)

〈lD|〈kH|Q(rH, rD)|k′H〉|l′D〉

(46)

and

between the zero-order states of the individual OH and OD bonds, which are evaluated following methods developed in refs 67 and 70, respectively. Substitution of eqs 42-44 into eqs 31 and 32 results in the equation of motion for the reduced


J. Phys. Chem., Vol. 100, No. 33, 1996 13931

Figure 2. “Free” relaxation from the initially populated local OH state 23(5, 0), local OD state 24(0, 7), and symmetric state 26(3, 3) of the HOD molecule coupled to the quasi-resonant environment. Vibrational states are indicated near the curves. The laser field is switched off.

density matrix elements in the Schro¨dinger picture,

∂ F(t) ) -iωVV′F(t)VV′ + (i/p)(t)[µ, F(t)]VV′ ∂t VV′ (Λ/p)2[Q, G(t)]VV′ (47) where the time-dependent relaxation matrix elements G(t)kl have the form

G(t)kl ) ∫0 dt′′ exp(-iωklt′′) × t

{〈F(t′′) F(0)〉 [QF(t - t′′)]kl - 〈F(0) F(t′′)〉[F(t - t′′) Q]kl} (48)

The time correlation functions in eq 48 are defined by eq 40, where under the assumption of the resonant moleculeenvironment coupling we set KVV′2 ) δVk δV′l for particular matrix elements G(t)kl. The parameter γVV′ in eq 40 is chosen as γVV′

) (∆Ha /2), where ∆Ha is the anharmonicity constant of the OH bond, which yields the correlation time of the environment τc ≈ 0.7 ps. In our computer simulations we also set p ) 1 and choose a scaling parameter Ω0 ) ω21. The strength of the molecule-environment coupling is defined by a dimensionless parameter

λ ) (Λa02/pω21)

(49)

The integro-differential equation (47) is the basic equation of motion in our present study. It can be solved by using straightforward modifications of standard numerical methods73 (details will be reported elsewhere). The solution provides, in particular, the time-dependent populations of the vibrational states of the HOD molecule,

F(t)VV ) PV(t) f P(m,n)(t)

(50)

13932 J. Phys. Chem., Vol. 100, No. 33, 1996

Korolkov et al.

where the V f (m, n) correspondence is specified in Figure 1. We conclude this section with a demonstration of the properties of the model quasi-resonant environment constructed above. Figure 2 shows the time-dependent populations of the vibrational levels of HOD obtained from the numerical solution of the equation of motion (47) at λ ) 0.15 and at T ) 300 K, with the laser field (t) being switched off, corresponding to “free” relaxation from three vibrational states: the local OH state 23(5, 0), the local OD state 24(0, 7), and the symmetric state 26(3, 3), which are treated as prepared selectively at t ) 0. It is seen from Figure 2A,B that the “free” relaxation from the initially prepared local OH state proceeds predominantly via lower local OH states, and it is somewhat faster than relaxation from the initially prepared local OD state, which is mode-selective too and proceeds via lower local OD states. “Free” relaxation from the initially prepared symmetric state, Figure 2C, proceeds via both OH and OD branches, and therefore it is faster than relaxation from local states. The lifetimes of all three states are about 1 ps at the λ ) 0.15 chosen. The states 23(5, 0), 24(0, 7), and 26(3, 3) are also chosen as targets for state-selective laser-controlled preparation at thermal equilibrium of HOD and the environment at T ) 300 K, which is considered in the next section. The state-selective preparation of these states in HOD in the absence of an environment has been investigated previously43 within the wave-function-based treatment. 4. State-Selective Laser Control for Dissipative Vibrational Dynamics of HOD The HOD molecule is supposed to be initially in thermal equilibrium with the environment at T ) 300 K. This corresponds to the initial conditions

[

/∑

F(0)V′V ) exp(-EV/kBT)

V′′

]

exp(-EV′′/kBT) δV′V (51)

in the equation of motion (47). Because of the large vibrational quanta of HOD, only the vibrational ground state |V ) 1〉 is predominantly populated initially at T ) 300 K, while the population of the first two excited states are PV)2(0) ) 1.54 × 10-6 and PV)3(0) ) 1.31 × 10-8, for example. For this reason, under the assumption of the quasi-resonant molecule-environment coupling, the density matrix elements F(t > 0)V′V are equal with very good accuracy to their initial values F(0)V′V ≈ δV′ 1 δV 1 until the laser field is switched on. Therefore we shall assume in the following that the laser field is switched on at t ) 0. As the target states for the ultrafast selective preparation, we choose, as in the previous work,43 the local OH state 23(5, 0), the local OD state 24(0, 7), and the symmetric state 26(3, 3), which have almost the same vibrational energies, see Figure 1. Selective preparation of local states is known to be important for mode- or bond-selective laser chemistry, while symmetric states are interesting from the viewpoint of developing strategies for selective preparation of high vibrational states with lifetimes different from those of the local states of similar energy.27,65,74 A. Optimization Procedure. The laser field to be optimized for the state-selective preparation of HOD is composed of several pulses, as specified by eqs 14 and 15. The pulse durations are chosen equal, with tp ) 1 ps, exemplarily. The design of the optimal control scheme is based, in general, on a sequence of individual state-selective transitions, which should lead in the absence of relaxation (i.e., at λ ) 0) from an initial state to a target state via one or more intermediate states. Each individual transition should be accomplished by a single pulse, which is optimized separately in order to yield maximal, close

to 100%, population transfer for the respective transition at λ ) 0. Derivation of the optimal amplitude i and the carrier frequency ωi at a fixed pulse duration tpi consists of two main steps: (1) at the initially reasonable choice of the laser carrier frequency (corresponding, for example, to the exact multiphoton or overtone resonance) the laser pulse amplitude is derived, which yields the maximal population transfer and provides the first approximation to the optimum; (2) at the laser pulse amplitude being fixed to the value obtained in the first step, the laser carrier frequency is derived to yield the maximal increase of the population transfer. Then, both steps are repeated several times until convergence, or the gradient-based procedure is used. The accuracy required for the frequency optimization is usually rather highsδωi/ωi < 10-3 is necessaryswhile the amplitude optimization is less demanding for accuracy: δi/i < 10-1 is sufficient. The sequence of individually optimized, nonoverlapping laser pulses accomplishes the overall population transfer from the initial to the target state in the absence of relaxation, i.e., at λ ) 0. This scheme is insensitive to the phases φi of the sequential pulses, because each individual transition is optimized to almost 100% state selectivity, if the relaxation is “switched off”. In the presence of relaxation, i.e., at λ > 0, the overall population transfer decreases, but the individual laser pulses, optimized as described above, prove to be still optimal for the respective individual transitions. On the contrary, the sequence of nonoverlapping laser pulses is no longer optimal, if the relaxation is “switched on”. It will be shown below that optimally chosen overlaps of the pulses provide substantial increase of the overall population transfer in the presence of relaxation. The phases of overlapping laser pulses, φi, proved still to be of minor importance for the present laser control schemes, because of the difference between the carrier frequencies ωi of overlapping laser pulses involved. B. Selective Preparation of the Local OH States. The optimal approach for selective preparation of the local OH state 23(5, 0) is to divide the overall transition

(0, 0) f (5, 0)

(52)

into two sequential steps to be controlled by two nonoverlapping or overlapping laser pulses.43 Figure 3A shows the population dynamics in the absence of relaxation for the excitation pathway

(0, 0) f (3 photons) f (3, 0) f (2 photons) f (5, 0) (53) which is accomplished via the intermediate local OH state 11(3, 0) by two nonoverlapping 1 ps laser pulses, shown in Figure 3C. The first pulse, optimized for the three-photon transition

(0, 0) f (3 photons) f (3, 0)

(54)

provides the maximal population of the intermediate state max ) 0.9999. The second pulse, optimized for the twoP(3,0) photon transition

(3, 0) f (2 photons) f (5, 0)

(55)

max ) 0.9853, yields the final population of the target state P(5,0) starting from the intermediate state 11(3, 0). The marginal rest of the population is localized for the most part in the local OH state 16(4, 0). In the presence of a sufficiently strong coupling to the environment, relaxation takes place and decreases the maximal population of the intermediate (3, 0) and the target (5, 0) states at the expense of increasing the populations of the lower states


J. Phys. Chem., Vol. 100, No. 33, 1996 13933

Figure 3. Selective preparation of the local OH state 23(5, 0) in the absence of relaxation (A, D) and in the presence of relaxation (B, E) by two nonoverlapping 1 ps laser pulses (C) and by two overlapping 1 ps pulses (F) with the optimal overlap of 0.7 ps. The excitation pathway is defined opt by eq 53. Vibrational states of HOD are indicated near the curves. The optimal parameters of the laser pulses are opt 1 ) 188.2 MV/cm, ω1 ) opt -1 3606.9 cm-1, opt ) 54.7 MV/cm, and ω ) 3161.1 cm . 2 2

(1, 0), (2, 0), and (4, 0), as demonstrated in Figure 3B for the population dynamics controlled by the same nonoverlapping laser pulses at λ ) 0.15. The maximal populations of the max ) 0.9489 and intermediate and the target states are P(3,0) max P(5,0) ) 0.6134, correspondingly. A dissipative population dynamics, displayed in Figure 3B, presents the competition between the laser-controlled state-selective steering of a molecule to a specified target and relaxation, which proceeds as follows. During the laser pulse, especially in the middle part of each pulse, when the laser field is strong, the molecular

coupling to the laser field dominates over the molecular coupling to the environment, and the population dynamics is similar to that in the absence of relaxation. On the contrary, in between the two nonoverlapping pulses and at the end of the second pulse, when the laser field strength becomes weak, relaxation becomes dominant and decreases populations of the intermediate and the target states, correspondingly. After the end of the second laser pulse, the “free” relaxation takes place from the target state 23(5, 0), similar to that presented in Figure 2A. To improve the laser control over the population dynamics, the stage

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Figure 4. (A-F) Selective preparation of the local OH state 23(5, 0) in the absence of relaxation (A, D) and in the presence of relaxation (B, E) by two nonoverlapping 1 ps laser pulses (C) and by two overlapping 1 ps pulses (F) with the optimal overlap of 0.7 ps. The excitation pathway opt opt opt -1 is defined by eq 56. The optimal parameters of the laser pulses are opt 1 ) 188.2 MV/cm, ω1 ) 3606.9 cm , 2 ) 140.5 MV/cm, and ω2 ) 6321.1 cm-1. (G-I) Selective preparation of the state (5, 0) in the absence (G) and in the presence (H) of relaxation by a single 1 ps laser pulse opt -1 (I) with the excitation pathway 58. The optimal pulse parameters are opt 1 ) 427.8 MV/cm and ω1 ) 3425.5 cm .

where relaxation dominates should be diminished. This can be fulfilled, for example, by special tailoring of laser pulse shape, making the electric field strong enough up to the end of the pulse, without decreasing the state selectivity of the process. This problem is under investigation now and will be considered elsewhere. Two other approaches to increase the lasercontrolled stage of the process are presented below. An efficient and universal approach to suppress the relaxation in the intermediate stage between the two laser pulses is to

employ the overlapping pulses. The population dynamics controlled by two 1 ps laser pulses, which are overlapped by the time interval of 0.7 ps, but are otherwise identical to those shown in Figure 3C, is presented in Figure 3D in the absence of relaxation and in Figure 3E in the presence of relaxation at λ ) 0.15, as in Figure 3B. The global laser field resulting from the overlap of the pulses is shown in Figure 3F. It is clearly seen from comparison of Figure 3D with Figure 3A that the rather larger overlap of the laser pulses decreases, by about 3%,


J. Phys. Chem., Vol. 100, No. 33, 1996 13935

the maximal population of the target state (5, 0) in the absence max ) 0.9572. At the same time, the overlap of relaxation: P(5,0) of the pulses increases the field strength in the intermediate stage of the process, diminishing the role of relaxation, as shown in Figure 3E, and the maximal population of the target state max ) 0.7603 is by about 15% greater, as compared to the P(5,0) case of nonoverlapping pulses shown Figure 3B. The 0.7 ps overlap of the pulses is optimal with respect to maximizing the population of the target state 23(5, 0). Another efficient, but not universal, approach to suppress the relaxation is the usage of stronger laser pulses. Although strong laser fields can efficiently compete against relaxation, the field strength cannot be chosen arbitrarily large, because it should be optimal with respect to the state selectivity of the target level on the one hand, and it should not induce other competing processes, such as “side transitions”43 in the HOD molecule, on the other hand. This is illustrated below by two examples of the state-selective preparation of the same target level 23(5, 0) with two different excitation pathways, which also differ from excitation pathway 53. The first example, shown in Figure 4 A-F, demonstrates selective preparation of the state (5, 0) by two nonoverlapping (Figure 4A,B,C) and overlapping (Figure 4D,E,F) laser pulses with the excitation pathway

(0, 0) f (3 photons) f (3, 0) f (1 photon) f (5, 0) (56) where in the second step the overtone transition

(3, 0) f (1 photon) f (5, 0)

(57)

(58)

with a single laser pulse, shown in Figure 4I, which requires a substantially stronger optimal laser field than in both previous cases. The state selectivity of the process in the absence of relaxation is not very high, as seen from Figure 4G. The maximal population of the target state, achieved at the end of max ) 0.7692. The rest of the population is the pulse, is P(5,0) localized predominantly at the levels 9(2, 1) and 15(3, 1), which indicates the competition of “side transitions”,

(59)

stimulated by the strong laser field, which deplete the overall state selectivity of the process. On the contrary, the large field strength can efficiently suppress the relaxation, as demonstrated in Figure 4H. The maximal population of the target state achieved at λ ) 0.15 is only by about 5% smaller than in the absence of relaxation. For the purpose of ultrafast population transfer in the presence of an environment, it is most desirable that the strong laser field suppressing the relaxation should also provide the high state selectivity of the process. This is just the case for the local OD states of the HOD molecule. C. Selective Preparation of the Local OD States. The local OD state 24(0, 7), chosen as a target, can be prepared selectively following the general strategies described above for the local OH states. The specific features of the OD states will be seen from two examples presented below. In the first example, Figure 5A-F, the local OD state 24(0, 7) is prepared selectively via the intermediate state 10(0, 4) with the overall excitation pathway

(0, 0) f (4 photons) f (0, 4) f (3 photons) f (0, 7) (60) which is accomplished by two nonoverlapping, Figure 5A-C, and by two optimally overlapping, Figure 5D-F, laser pulses, being otherwise identical to the nonoverlapping pulses. The first pulse optimized for the individual transition

(0, 0) f (4 photons) f (0, 4)

is used instead of the two-photon transition (eq 55). The overtone transition requires stronger optimal field and provides better state selectivity in the absence of relaxation: the maximal max ) 0.9978 for nonoverpopulation of the target level is P(5,0) lapping pulses, Figure 4A. Both these reasons increase the state selectivity in the presence of relaxation (Figure 4B,E), as compared to the previous case (Figure 3B,E). The maximal max ) 0.6451 for population of the target state at λ ) 0.15 is P(5,0) nonoverlapping pulses. The 0.7 ps overlap of the two pulses, which are shown in Figure 4F, decreases the maximal population of the target state by about 3% in the absence of relaxation, as max ) 0.9603, but it increases the shown in Figure 4D, where P(5,0) maximal population of the target state substantially, by about 16% in comparison with nonoverlapping pulses, in the presence of relaxation, Figure 4E. The maximal population of the target max ) 0.8172, is by about 6% state achieved in this case, P(5,0) larger than that in the case presented in Figure 3E. The 6% higher level of the population transfer may be considered as a not very important improvement if (5, 0) is the final target, but it may be rather important if (5, 0) serves as an intermediate state for selective preparation of higher target states. The second example, shown in Figure 4G-I, demonstrates selective preparation of the state (5, 0) by pumping the fivephoton transition

(0, 0) f (5 photons) f (5, 0)

(2, 0) f (2, 1) and (3, 0) f (3, 1)

(61)

in the absence of relaxation provides the maximal population max of the intermediate state P(0,4) ) 0.9927. The second laser pulse optimized separately for the individual transition

(0, 4) f (3 photons) f (0, 7)

(62)

in the absence of relaxation yields the maximal population of max ) 0.9757. The population dynamics the target state P(0,7) controlled by two nonoverlapping pulses in the absence of relaxation is shown in Figure 5A. In the presence of relaxation (λ ) 0.15) the maximal population of the intermediate state max ) 0.9674, while the maximal population of decreases to P(0,4) max ) 0.7386, as shown in Figure the target state decreases to P(0,7) 5B for nonoverlapping pulses. The 0.5 ps overlap of the pulses, which are shown in Figure 5F, decreases the maximal population max ) of the target state in the absence of relaxation to P(0,7) 0.9641, as illustrated in Figure 5D. At the same time, the overlap increases the field strength in the intermediate stage of the process, suppressing the relaxation, and increases the maximal population of the target state, in comparison to the max ) 0.8791, as shown case of nonoverlapping pulses, up to P(0,7) in Figure 5E. The 0.5 ps overlap of the two pulses is optimal with respect to maximizing the population of the target state 24(0, 7). The second example, shown in Figure 5G-I, demonstrates selective preparation of the target state (0, 7) by pumping the seven-photon transition

(0, 0) f (7 photons) f (0, 7)

(63)

with a single laser pulse, which requires a very strong optimal laser field, as shown in Figure 5I. Contrary to the local OH state 23(5, 0) considered above, the state selectivity of preparation of the local OD state 24(0, 7) by a single optimal pulse in the absence of relaxation is very high, as shown in Figure 5G. The maximal population of the target state (0, 7) achieved at max ) 0.9914, which indicates a very the end of the pulse is P(0,7)

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Figure 5. (A-F) Selective preparation of the local OD state 24(0, 7) in the absence of relaxation (A, D) and in the presence of relaxation (B, E) by two nonoverlapping 1 ps laser pulses (C) and by two overlapping 1 ps pulses (F) with the optimal overlap of 0.5 ps. The excitation pathway opt opt opt -1 is defined by eq 60. The optimal parameters of the laser pulses are opt 1 ) 219.6 MV/cm, ω1 ) 2648.9 cm , 2 ) 75.55 MV/cm, and ω2 ) -1 2315.6 cm . (G-I) Selective preparation of the state (0, 7) in the absence (G) and in the presence (H) of relaxation by a single 1 ps laser pulse opt -1 (I) with the excitation pathway 63. The optimal pulse parameters are opt 1 ) 512.7 MV/cm and ω1 ) 2498.2 cm .

small competition of any “side transitions”. At the same time, the large optimal field strength efficiently suppresses the relaxation, as demonstrated in Figure 5H for λ ) 0.15. The maximal population of the target state achieved in the presence max ) 0.9687, is only by about 2% smaller than of relaxation, P(0,7) in the absence of relaxation. The local OD state 24(0, 7), prepared with high selectivity by a very strong optimal laser pulse as shown in Figure 5H, may serve as the intermediate state for state-selective preparation of higher local OD states

by straightforward prolongation of the excitation pathway 63. Therefore, efficient population transfer along the local OD bond and state-selective preparation of higher local OD states are still possible even in the presence of strong coupling of the HOD molecule to the environment (results will be reported elsewhere). D. Selective Preparation of Symmetric States. It has been shown previously,43 within the Schro¨dinger wave function formalism, that even in the absence of relaxation the symmetric


J. Phys. Chem., Vol. 100, No. 33, 1996 13937

Figure 6. Selective preparation of the symmetric state 26(3, 3) in the absence of relaxation (A, D) and in the presence of relaxation (B, E) by two nonoverlapping 1 ps laser pulses (C) and by two overlapping 1 ps pulses (F) with the optimal overlap of 0.4 ps. The excitation pathway is defined opt opt -1 opt -1 by eq 65. The optimal parameters of the laser pulses are opt 1 ) 188.2 MV/cm, ω1 ) 3606.9 cm , 2 ) 135.0 MV/cm, and ω2 ) 2696.1 cm .

states of the HOD molecule, (m, n ) m), which have equal number of vibrational quanta in each bond, cannot be prepared selectively by directly pumping the respective multiphoton or overtone transition

(0, 0) f (m, m)

local OD state 7(0, 3), as demonstrated below in Figures 6 and 7, correspondingly. Figure 6 illustrates the state-selective preparation of the state (3, 3) by two nonoverlapping (A-C) and by two optimally overlapping (D-F) 1 ps laser pulses with the excitation pathway

(64)

The optimal approach to the problem is to make use of the local OH or OD states as the intermediate states. The symmetric state 26(3, 3), which is chosen as a target, for example, can be prepared selectively via the local OH state 11(3, 0) or via the

(0, 0) f (3 photons) f (3, 0) f (3 photons) f (3, 3) (65) where the local OH state (3, 0) serves as the intermediate state. Each laser pulse is optimized individually to yield the maximal population transfer for the respective transition in the absence

13938 J. Phys. Chem., Vol. 100, No. 33, 1996

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Figure 7. Selective preparation of the symmetric state 26(3, 3) in the absence (A, D) and in the presence (B, E) of relaxation by two nonoverlapping 1 ps laser pulses (C) and by two overlapping 1 ps pulses (F) with the optimal overlap of 0.7 ps. The excitation pathway is defined by eq 66. The opt opt opt -1 -1 optimal parameters of the laser pulses are opt 1 ) 144.8 MV/cm, ω1 ) 2696.9 cm , 2 ) 184.9 MV/cm, and ω2 ) 3602.4 cm .

of relaxation, Figure 6A. The first pulse provides the maximal max ) 0.9999, while the population of the intermediate state P(3,0) max second pulse yields P(3,3) ) 0.9877 for the target state (3, 3). In the presence of relaxation at λ ) 0.15, and without overlap of the pulses, Figure 6B, the maximal population of the intermedimax ) 0.9440, and the maximal ate state decreases to P(3,0) max ) 0.6607, is rather small. population of the target state, P(3,3) To increase the field strength between the two pulses and to compete efficiently against relaxation, the optimal 0.4 ps overlap of the pulses is introduced, as shown in Figure 6F. This overlap

decreases the maximal population of the target state in the max absence of relaxation to P(3,3) ) 0.9758, Figure 6D, but increases the maximal population of the target state (3, 3) in max ) 0.8091 at λ ) 0.15, the presence of relaxation, yielding P(3,3) as shown in Figure 6E. The second example for selective preparation of the symmetric state is given in Figure 7, presenting the case where the target state (3, 3) is prepared selectively by two nonoverlapping (A-C) and by two optimally overlapping (D-F) laser pulses via the intermediate local OD state (0, 3) with the excitation

Dissipative Vibrational Dynamics of HOD pathway

(0, 0) f (3 photons) f (0,3) f (3 photons) f (3,3) (66) It is instructive to compare two different excitation pathways 66 and 65 for selective preparation of the same target state (3, 3). The comparison of the population dynamics and the optimal laser fields presented in Figure 7 with the corresponding results of Figure 6 reveals the following. The excitation pathway 66 is less selective than its counterpart, eq 65, in the absence of relaxation and yields, for nonoverlapping pulses, Figure 7A, max ) 0.9547, the maximal population of the target state P(3,3) which is smaller than its counterpart presented in Figure 6A. At the same time, the second laser pulse used in the excitation pathway 66, Figure 7C, is substantially stronger than its counterpart in Figure 6C. The stronger laser pulse is more efficient in suppressing the relaxation, Figure 7B, and the maximal population of the target state in the presence of max ) 0.7114, is larger than its counterpart of relaxation, P(3,3) Figure 6B at the same coupling of HOD to the environment at λ ) 0.15. The optimal overlap of the two pulses for the excitation pathway 66 is 0.7 ps, Figure 7F, and it is almost 2 times larger than its counterpart in Figure 6F. The larger overlap results in stronger decrease of the state selectivity in the absence of relaxation, Figure 7D, as compared to smaller overlap corresponding to Figure 6D. At the same time, the larger overlap provides a stronger laser field in the middle stage of the process, as seen from Figure 6F. The stronger laser field suppresses the relaxation more efficiently, Figure 7E, and provides better overall population transfer, with the maximal max ) 0.8370, which is population of the target state being P(3,3) larger than its counterpart in Figure 6E. The comparative analysis given above emphasizes the role of the laser field strength in suppressing the relaxation and reveals that the excitation pathway, which is optimal in the absence of relaxation, may prove not to be optimal in the presence of relaxation. 5. Conclusion The main conclusions that can be drawn from the results of this work are the following. The strong laser field can efficiently compete against relaxation, and the ultrafast state-selective preparation of a molecule coupled to an environment is still possible if the laser field is properly shaped and optimized. The series of shaped laser pulses, which have already proven to be an efficient and flexible tool for controlling the dynamics of isolated molecules, for example in the first simulations of stateselective isomerization reactions50-55 and multiphoton dissociation of the rotating HF molecule,45 are also very suitable for controlling the dissipative dynamics of molecules coupled to an environment. The overlap of sequential laser pulses, which has been introduced previously42,43 in order to diminish the overall time of the state-selective preparation of isolated molecules, is a very important optimization parameter for the laser-controlled dissipative dynamics of molecules coupled to the environment. The optimally chosen overlap of the laser pulses extends the controllable stage of the process by suppressing the relaxation and increases significantly the selective population transfer to the target state. This emphasizes the importance of explicitly defined laser-molecule time-dependent interactions for developing the optimal control schemes. Our simulations have been carried out beyond a Markovtype approximation within the reduced density matrix formalism for a two-dimensional model of stretching vibrations of a nonrotating and nonbending HOD molecule coupled to a quasiresonant environment. The maximal strength of the moleculeenvironment interaction has been assumed to correspond to all

J. Phys. Chem., Vol. 100, No. 33, 1996 13939 molecular frequencies, which is the most unfavorable situation for the state-selective population transfer. Nevertheless, the local OH state 23(5, 0), the local OD state 24(0, 7), and the symmetric state 26(3, 3), exemplarily chosen as targets, have been prepared selectively with probabilities of 80-90%. An evident extension of the sequential-pulses control schemes used in the present work should make it possible to prepare selectively higher vibrational states of HOD and similar dihydride molecules coupled to the environment. The optimal laser carrier frequencies used in our control schemes correspond to near-infrared and mid-infrared domains, where generation of ultrashort laser pulses is practically feasible with the available experimental techniques.75,76 The optimal laser field strengths range from 54.7 to 512.7 MV/cm. A brief discussion on the field strength used is in order. It is sometimes argued now that strong infrared laser fields can ionize a real molecule, as has been observed experimentally77 for HCl under nonresonant excitation with 10 µm radiation. On the basis of the barrier suppression model for atomic ionization, the following expression has been derived in ref 77 for the threshold intensity for ionization of molecules:

Ithr ) (0c/2) [4π0/e3]2(ES4/16Z2)

(67)

For the initially neutral HOD molecule Z ) 1, the ionization HOD ) potential ES ) 12.612 eV, and from eq 67 we obtain Ithr 14 2 1.01 × 10 W/cm , which corresponds to the threshold electric HOD ) 276 MV/cm. All optimal field strengths field strength thr used in our control schemes are below this threshold limit except for two examples, shown in Figures 4I and 5I, which in practice can be avoided by making use of other alternatives presented therein. Nevertheless, in our opinion, the problem of ionization of molecules by resonant infrared radiation is not clear now. Complete theoretical analysis should include explicitly timedependent laser-molecule interactions, which is beyond the scope of this work. Several results of our simulations for a one-electron model system, similar to that used in ref 77, are in disagreement with eq 67 (details will be reported elsewhere64). Ionization and dissociation78 and coupling to higher electronic states, if they take place with a remarkable probability, are sure to reduce the fraction of molecules prepared selectively at the target vibrational levels of the electronic ground state. On the other hand, it is demonstrated in this work that the state selectivity is depleted by relaxation, and one has to employ strong laser fields to compete against relaxation. Therefore, in a realistic situation, one has to look for a compromise with respect to the field strengths used. Acknowledgment. The present research has been supported by the Volkswagen-Stiftung, Project I/69 348, which is gratefully acknowledged. The computer simulations have been carried out on HP 9000/S 750 workstations at the Freie Universita¨t Berlin. J.M. also thanks the Fonds der Chemischen Industrie for continuous support. References and Notes (1) Ben-Shaul, A.; Haas, Y.; Kompa, K. L.; Levine, R. D. Lasers and Chemical Change; Springer: Berlin, 1981. (2) Bloembergen, N.; Zewail, A. H. J. Phys. Chem. 1984, 88, 5459. (3) Crim, F. F. Annu. ReV. Phys. Chem. 1984, 35, 647. (4) Lupo, D. W.; Quack, M. Chem. ReV. 1987, 87, 181. (5) Khundkar, L. R.; Zewail, A. H. Annu. ReV. Phys. Chem. 1990, 41, 15. (6) Crim, F. F. Science 1990, 249, 1387. (7) Levine, R. D.; Zewail, A. H.; El-Sayed, M. A. J. Phys. Chem. 1991, 95, 7961. (8) Brumer, P.; Shapiro, M. Annu. ReV. Phys. Chem. 1992, 43, 257. (9) Potter, E. D.; Herek, J. L.; Pedersen, S.; Liu, Q.; Zewail, A. H. Nature 1992, 355, 66.

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JP960930Y

State-Selective Control for Dissipative Vibrational Dynamics of HOD

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