Raman Chirped Adiabatic Passage Probed by X-ray Spectroscopy

Raman Chirped Adiabatic Passage Probed by X‑ray SpectroscopySelma Engin, Nicolas Sisourat,* Patricia Selles, Richard Taïeb, and Stephane Carniato

Laboratoire de Chimie Physique Matière et Rayonnement, Université Pierre et Marie Curie - CNRS (UMR 7614), Paris, France

ABSTRACT: We report a theoretical study of the selective vibrational excitation of a HClmolecule achieved by Raman chirped adiabatic passage (RCAP) and probed by X-rayphotoelectron spectroscopy (XPS). It is demonstrated that HCl can be prepared in anyvibrational level up to ν = 9 with nearly complete population inversion. We explore the effectsof both the rotation of the molecule and of the temperature on the RCAP process, which isproved to be very robust. Furthermore, we emphasize that XPS spectra at the chlorine K-shellthreshold show characteristic signatures of the populated vibrational level, allowing us to followthe RCAP process.

I. INTRODUCTION

Spectroscopic studies of molecules are generally limited to theFranck−Condon region, and thus only a small portion of thepotential energy surfaces (PESs) can be probed. Informationbeyond this region can be obtained by preparing the moleculesin some intermediate state that has a larger interatomicdistribution, by, for example, laser pumping1 or core excitation.2

In the former case, the laser pump prepares a coherentsuperposition of vibrational eigenstates that is probed with adelayed pulse. In the latter case, one uses the nuclear dynamicson the core-excited PES to explore far from the Franck−Condon region. A better control can be achieved if the systemis prepared in a well-defined excited vibrational eigenstate. Inthe case of core-excitation, this can be done by fine-tuning ofthe X-ray photon energies.3 In a pump−probe scheme, anintense specially designed laser pump field allows a selectivevibrational excitation. Furthermore, such preparation ofmolecules in excited vibrational levels leads to a coherentcontrol of chemical reactions.4

Selective vibrational excitation by laser pulses can beachieved by climbing the corresponding ladder by successiveone-level transitions.5 Adiabatic passage techniques have beenused successfully for climbing electronic, vibrational, androtational ladders.6 Among these techniques, the Ramanchirped adiabatic passage (RCAP)7 is a very promising schemeusing two superimposed laser pulses (pump and Stokes). Onthe basis of Raman two-photon resonant transitions (see Figure1), population inversion between two successive vibrationallevels is achieved. Furthermore, one or both laser pulses arefrequency chirped such that the frequency difference of the twolaser pulses smoothly decreases in time, adjusting to theanharmonicity of the molecular potential and ensuring theadiabatic evolution of the system. Efficiency of RCAP has beentheoretically demonstrated on H2, H2

+,8,9 O2, and Cl210 and has

been experimentally achieved on CO2 molecule.11

In a previous paper,12 we showed that RCAP technique is anefficient method to prepare fixed-in-space HCl molecules in a

given ν vibrational level with nearly complete populationinversion. It was also demonstrated that XPS is an appropriatetool to probe the quantum state of a molecule following thepopulation transfer because of the so-called chemical shifts. Inthe present paper, we report on the RCAP process, taking intoaccount the molecular rotation and the effects of thetemperature to simulate present day experimental conditions.We show that efficient population transfer can still be achievedup to ν = 9 with rotating molecules because of optimized laserpulses parameters. Higher selectivity of the RCAP process isobtained at lower temperatures. We then demonstrate that the

Special Issue: Stereodynamics Symposium

Received: January 31, 2013Revised: April 3, 2013Published: April 3, 2013

Figure 1. Schematic view of the RCAP process. Two lasers (pump andStokes) are used to climb the vibrational ladder by successive one-leveltransitions. One of the two laser pulses is frequency chirped such thatthe frequency difference of the two laser pulses smoothly decreases intime, adjusting to the anharmonicity of the molecular potential.

Article

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© 2013 American Chemical Society 8132 dx.doi.org/10.1021/jp401125a | J. Phys. Chem. A 2013, 117, 8132−8138

pubs.acs.org/JPCA

vibrational state of the molecule during the RCAP process canbe probed by XPS at the chlorine K-shell threshold. Effects ofthe temperature on the XPS spectra are finally discussed.Atomic units are used in the following, unless otherwise

stated.

II. METHODSA. RCAP. The RCAP process (see Figure 1) was simulated

by solving the time-dependent Schroedinger equation in theadiabatic elimination approximation.13 Within this model, thenuclear dynamics in the excited electronic states can beeliminated because they are weakly populated. We thus onlyneed to consider the nuclear wave function in the electronicground state (GS). The interactions with the electronic excitedstates are implicitly included in an effective coupling operator.The total Hamiltonian is then given by

μ μα θ

α θ

= − ∂∂

+ + −

−

Σ

Π

HR

V RJR

R t

R t

12

( )2

12

( ) ( ) cos

12

( ) ( ) sin

2

2 0

2

22 2

2 2(1)

where V0 is the potential energy curve of the HCl electronicGS, J2 is the squared angular momentum operator, and θ is theangle between the molecular axis and the laser electric field.The effective coupling operators α∑(R) and αΠ(R) are given by

∑α =| |

−Σ Π∈Σ Π

Rd R

V R V R( )

( )( ( ) ( ))i

i

i( )

( )

02

0 (2)

where di0(R) is the dipole transition moment between theelectronic GS and excited state i and Vi(R) is the potentialenergy curve of the excited state. The two laser fields arechosen to be linearly polarized and parallel. The electric field

(t) is thus defined as

ω ω = − +t U t t c t t( ) ( )[sin( ( /2) ) sin( )]io r2

s (3)

The parameters ωs, ωi, and cr are the Stokes pulsation, theinitial pump pulsation, and the chirp rate, respectively. Thecarrier envelope U(t) is trapezoidal.The adiabatic elimination approximation is valid as long as

the excited electronic states are far above the electronic GScompared with the photon energy because this approximationbreaks down when the excited states are strongly populated.Note that the RCAP technique is efficient only when theexcited states are also weakly populated and control isotherwise lost. We have evaluated that for HCl the adiabaticelimination approximation is valid and the RCAP is efficient upto ν = 9. Above this vibrational level, the first excited state isclose in energy to the GS and starts to be significantlypopulated. Therefore, we simulated the RCAP process only upto this level.For each initial rotational state (J0, M0), the time-dependent

2-D nuclear wave function is written as

∑θ χ θ ϕΨ =ν

ν νε− νR t c t R( , , ) ( ) ( , , )eJ M

JJ M

J MJ M

GS i t,

,, ,,

, ,J0 0

f

f 00 0

f 0

, f

(4)

where χν,Jf,M0(R,θ,ϕ), and εν,Jf are the eigenvectors and

eigenvalues of the field-free Hamiltonian in eq 1, respectively.Inserting eq 4 into the time-dependent Schroedinger equationresults in a system of first-order coupled differential equations

for the time-dependent expansion coefficients, which wassolved with the Adams−Bashforth−Moulton predictor−corrector integrator.14

To simulate the RCAP process in HCl, we considered theX1Σ+ GS and a collection of low-lying (2−4)1Σ+ and (1−6)1Πspin-singlet excited states in the energy range up to the firstionization potential (Ip = 12.75 eV15). For each state, the PESand the dipole transition moment were calculated using an aug-cc-pCVQZ and an aug-cc-pVQZ atomic Cartesian−Gaussianbasis set16 centered on the Cl and H atoms, respectively, andthe post Hartree−Fock configuration interaction methodincluding up to quadruple electronic excitations (CI-SDTQ),as implemented in GAMESS(US) ab initio package.17 We hadto perform the calculations in C1 symmetry group to obtain thetransition dipole moments from Σ+ to Π states. Owing to thelarge numbers of configurations in such symmetry, we includedonly excited configurations up to triple excitations.The PESs of the ground and low-lying excited states of HCl

are shown in Figure 2. They agree well with the previous results

of Bettendorff et al.18 The PES of the electronic GS has aminimum located at around R = 1.27 Å, which is ∼4.46 eVbelow the dissociation limit. We found that 1H35Cl in thiselectronic state has 20 vibrational bound levels, which haveenergy spacing from 0.35 eV between ν = 0 and 1 to 0.03 eVbetween ν = 19 and 20. The first electronic excited state has aΠ symmetry and is ∼7.85 eV above the GS at the equilibriumgeometry. The PES of this state is repulsive and presents thesame dissociation limit as the GS. Therefore, as the internucleardistance increases, the two curves get closer in energy. Asalready previously mentioned, this is a limitation in theapplication of RCAP method for controlling the vibrationalstate of the molecule. The dipole transition moments used tocompute the effective operators αΣ(R) and αΠ(R) are shown inFigure 3. PES and dipole transition moments of HCl arediscussed in more detail in ref 19. The nature of the low-lyingexcited states of HCl is discussed in refs 18 and 20−22.

B. XPS Spectra. The inner-shell single ionization cross-section associated with the XPS spectrum can be computed at atime τ as

Figure 2. Ab initio PES of the first low-lying states of HCl used in thisstudy. The solid lines represent the Σ states while the dashed lines areused for the Π states. These PESs were used to compute the effectivecoupling operators (eq 2).

The Journal of Physical Chemistry A Article

dx.doi.org/10.1021/jp401125a | J. Phys. Chem. A 2013, 117, 8132−81388133

∑

∑

σ τ

τ

ε ε

∝

| | |⟨ ′ ′ | | ⟩|

− + ′ ′ − + Γν ν

ν ν ν

ν ν

− +

′ ′

c R

(BE, ) e

( ) ( )

(BE IP ) /4

T

J

BJ J kT

j J J M

J MJ M

J Mj

j J M

j Jj

J

( 1)/

, , , , ,

, ,, 2

, , , ,GS 2

, ,GS 2

c2

0

0 0

0

00 0

0 0

(5)

where B is the rotational constant of HCl taken equal to 10.2cm−1, T is the temperature, and k is the Boltzmann constant.The ionization potential of the adiabatic transition to the core-ionized state j is denoted IPj and the binding energy BE = ℏωX− EP is introduced as the difference between the X-ray photon(ℏωX) and the photoelectron (EP) energies. The width (Γc ≈0.65 eV) corresponds to the Cl 1s−1 core hole lifetime (∼1fs).23 The electronic dipole transition moment j is evaluatedwithin the sudden approximation24

ϕ= ⟨ | | ⟩⟨Ψ |Ψ ⟩− −R E z( ) ( ) 1sj jN Nc 1

GS1

(6)

where the first term corresponds to the transition dipolemoment from inner shell 1s to continuum ϕc(E) orbital. It isassumed constant over the energy range. The second term isthe overlap between (N − 1) electronic wave functions of theGS and of the jth state of the 2Σ core-ionized manifold.The PESs of the core-ionized electronic states and the

corresponding dipole transition moments were computed as inref 12. In brief, they were computed at the post Hartree−Fock

configuration interaction level including up to double electronicexcitations (CI-SD) using a homemade package. To account forrelaxation of the valence orbitals and to obtain accuratetransition moments, we included a set of 75 Hartree−Fockorthogonal orbitals optimized for the Cl 2s−1 σ*(2s−1) core-excited state in the CI active space to describe simultaneouslythe 1s−1 core-ionized states and the GS. Calculations wereperformed using a large aug-cc-pCVQZ atomic Cartesian−Gaussian basis set limited to s, p, and d waves centered on theCl and H atoms.25

The PESs of the three Σ core-ionized states (X, 2, and 3 2Σ+)are shown in Figure 4. The PES of the X2Σ+ state has a

minimum located at around R = 1.27 Å, which is ∼4.46 eVbelow the dissociation limit. This PES is similar to that of theelectronic GS. In the infinite atomic distance limit, the X2Σ+

corresponds to H+ + Cl(1s−1 3p6). The PESs of the two higherstates (2 and 3 2Σ+) are repulsive. These states correspond inthe asymptotic limit to H + Cl+ (1s−1, 1P) and H + Cl+ (1s−1,3P), respectively. The dipole transition moments of these states,shown in Figure 5, exhibit different behavior as a function of

Figure 3. Ab initio electronic dipole transition moments as functionsof the interatomic distance for the transitions between the groundstate and the Σ excited states (lower panel) and between the groundstate and the Π excited states (top panel). These dipole transitionmoments were used to compute the effective coupling operators (eq2).

Figure 4. Ab initio PES of the core-ionized HCl states. Only Σ statesare reached within the sudden approximation (eq 6). The lowest stateconverges to H+ + Cl (1s−1, 3p6) in the infinite atomic distance, andthe corresponding PES is nearly parallel to that of the groundelectronic state. The two higher states converge asymptotically to H +Cl+ (1s−1, 3P) and H + Cl+ (1s−1, 1P). The corresponding PESs areboth repulsive.

Figure 5. Electronic dipole transition moments as a function of theinteratomic distance for the transition between the ground state andthe Σ core-ionized states computed within the sudden approximation.



the interatomic distance. Around the equilibrium distance ofHCl, the dipole transition moment of the X2Σ+ is maximumand decreases to zero in the asymptotic limit. On the contrary,the dipole transition moments of the two other states are smallaround the equilibrium distance and increase at larger distances.We can already anticipate that as the molecule climbs thevibrational ladder, the contribution of the X2Σ+ state to the XPSspectra should decrease and that of 2 and 3 2Σ+ states shouldincrease.

III. RESULTS AND DISCUSSION

Laser parameters must be chosen carefully such that efficientpopulation transfer is achieved. We fixed both laser intensitiesto I = 5 × 1012 W·cm−2 and the Stokes photon energy to ωs =1.17 eV. Such an intensity can be experimentally reached and islow enough for the multiphoton ionization to be negligible.The chosen Stokes photon energy corresponds to a Nd:YAGlaser wavelength. The two last parameters, chirp rate cr andinitial pulsation of the pump pulse ωi, must be optimized.The RCAP process is based on two-photon transitions and

leads to the selection rule on the rotational quantum numberΔJ = 0,±2. In our lasers configuration, there is no transitionbetween different M quantum numbers ΔM = 0. Owing to thechirp of the pump pulse, the first resonant transition reached isΔJ = +2. To keep selectivity in the RCAP process, it isnecessary to optimize the chirp rate cr such that completepopulation inversion is achieved between (ν,J) and (ν + 1,J +2) states before the next resonant transition ΔJ = 0 isapproached. If the population transfer is not complete between(ν,J) and (ν + 1,J + 2) states, a transition between (ν,J) and (ν+ 1,J) at later time may happen simultaneously with a transitionbetween (ν + 1,J + 2) and (ν + 2,J + 4). This situation leads toa loss of control on the vibrational level.The second laser parameter to be optimized, that is, the

initial pulsation of the pump pulse, ωi, must be chosen suchthat initially the energy difference between the two photons(Stokes and pump) is larger than the energy spacing between(ν = 0, J0) and (ν = 1, J0 + 2) states. Furthermore, ωi must befixed such that this criterion is verified for all J0 initial statespopulated at the temperature T considered in the present study.We simulated the RCAP process at different temperatures up to300 K for which population of states above J0 = 10 (see Figure6) are negligible. We therefore optimized the ωi parameter forJ0 = 10, which ensures that RCAP remains efficient for lower J0values.We found that ωi = 1.574 eV and cr = 1.12 × 10−6 eV fs−1 are

the optimal parameters.A. RCAP for T = 0K. In the limit of T = 0 K, the only

populated rovibrational level is (ν = 0,J0 = 0). This situation isclose to what is encountered in supersonic gas jet experiments.We simulated the RCAP process starting from this rovibrationallevel. The population of all rovibrational levels were computedas a function of time. Only the most populated ones, whichcorrespond to (ν, J = 2ν, for ν = 0,9), are shown in Figure 7.There is a long plateau up to t = 40 ps, where the system staysin the (ν = 0, J = 0) level. This is due to the choice of ωi =1.574 eV, which was optimized for a J0 = 10 initial level. Theplateau can be shortened by choosing a smaller ωi such that theresonance between (ν = 0, J = 0) and (ν = 1, J = 2) is reachedfaster. After the long plateau, transitions between (ν,J) and (ν +1, J + 2) take place up to (ν = 9, J = 18) with a probability of∼60%. As discussed above, for higher excited levels, the first

electronic excited state can be populated via one-photontransition and the RCAP process breaks down.Populations of the rovibrational levels are shown while the

laser pulses are still on. We checked that turning off the laserpulses within a few femtoseconds at a given time does notsignificantly affect the populations. At low temperature, it istherefore possible to prepare selectively HCl in any vibrationallevel up to ν = 9 by choosing appropriately the laser pulseduration.

B. RCAP for Different Temperatures. In the case of gas-phase experiments performed at liquid nitrogen (T ≈ 80 K) orroom (T ≈ 300 K) temperature, several rovibrational levels arepopulated initially. Assuming a Maxwell−Boltzmann distribu-tion, the populations at T = 80 and 300 K of the firstrovibrational levels are shown in Figure 6. At T = 80 K, thedistribution is maximal for J = 1 and is negligible for J greaterthan 6. At the highest temperature considered (T = 300 K), thedistribution is maximal for J = 3 and is negligible for J greaterthan 10. We, therefore, performed the RCAP simulation fordifferent initial rovibrational levels from (ν = 0, J0 = 0) to (ν =0, J0 = 10). The populations of the rovibrational levels (ν, J = 2ν+ J0, for ν = 0, 9) were computed as a function of time. Resultsfor M0 = 0 are first shown in Figures 8 and 9.

Figure 6. Maxwell−Boltzmann distributions of the first rovibrationallevels of HCl at T = 80 and 300 K.

Figure 7. Rovibrational level population of HCl as a function of timeduring the RCAP process for (ν = 0, J0 = 0) initial level.



It is seen that RCAP is efficient for all initial rovibrationallevels, but owing to the rovibrational structure of the molecule,

transitions between the successive levels take place at differenttimes depending on the initial rovibrational level. For example,for (ν = 0, J = 0), the first transition occurs at t = 40 ps, whereasit takes only ∼20 ps for (ν = 0, J = 5) to undergo the firsttransition. It is then clear that due to the initial rovibrationaldistribution, there is at any time a distribution of differentexcited rovibrational levels and the selectivity on the rovibra-tional state is partially lost at high temperature.However, for high vibrational levels (ν = 8 to 9), it is possible

to find laser pulse durations (indicated by dashed lines inFigure 8) such that selectivity is regained because there is onepreferentially populated level at these times. Results fordifferent M0 values are now discussed.For a given J0 rotational quantum number there are (2J0 + 1)

equally populated M0 states. The transition energies betweensuccessive rovibrational levels are M-independent, but thecoupling between the levels through the lasers does depend onthis quantum number.26 The population of the rovibrationallevels during the RCAP process for J0 = 3 and M0 = 0−3 isshown in Figure 10. The transitions from a given (ν,J) to (ν +

1, J + 2) states take place at the same time for all M0 values, butit is seen that the larger M0, the less efficient the populationtransfer. For example, for J0 = M0 = 3, the population transfer isonly ∼40% from (ν = 0, J = 3) to (ν = 1, J = 5) compared with90% for M0 = 0.Note that after the first (ν = 0, J = 3) to (ν = 1, J = 5)

transition the population of the former drops again. Forinstance, for J0 = M0 = 3, the population of the level (ν = 0, J =3) decreases from 0.6 to 0.4 at ∼50 ps. This decreasecorresponds to transition to (ν = 1, J = 3). Indeed, as discussedabove, when the population transfer is not complete for thetransitions (ν,J) → (ν + 1, J + 2), other transitions like (ν,J) →(ν + 1,J) can take place at a later time. The populations of (ν,J0)are shown in dashed lines in the Figure, demonstrating suchtransitions.

Figure 8. Rovibrational level population of HCl as a function of timeduring the RCAP process for different (ν = 0, J0) initial levels.

Figure 9. Rovibrational level population of HCl as a function of timeduring the RCAP process for different (ν = 0, J0) initial levels.

Figure 10. Rovibrational level population of HCl as a function of timeduring the RCAP process for (ν = 0, J0 = 3, M0 = 0−3) initial levels.



C. XPS Spectra. We first discuss the XPS spectra for T = 0K, which are shown in Figures 11 and 12. The XPS spectra

were computed at different times during the RCAP processwhen the population of one vibrational level was maximum (t =0, 43, 45, 51, 56, 63, 69, 76, 86, and 100 ps). The XPS of HCl inthe Cl(1s−1) region (2820−2850 eV) presents two bands: (i)the narrow main peak (denoted M) corresponds to the X1Σ+ →X2Σ ionization threshold energy (BE = 2829.8 eV27); (ii) thebroader and less intense satellite band (denoted B) at a BEabove 2832 eV is assigned to X1Σ+ → (2,3)2Σ transitions. For ν= 0, it is located at BE = 2844 eV. In Figure 12, for clarity weshow only the region of the satellite band. The two XPS bandsdisplay significantly different evolutions. The main peakposition (M) is roughly independent of the vibrational levelof electronic GS, while the satellite band is red-shifted towardlow binding energies when increasing the vibrational level,converging to ∼2835 eV, close to the peak M. It should also benoted that the intensity of the peak (M) decreases whenincreasing ν, while the band (B) exhibits opposite behavior.This behavior is a direct consequence of the R dependence ofthe dipole transition moments, discussed above, and has beenexplained in ref 12. The band B is therefore characteristic of thevibrational level of the GS. The position of the maximum of the

band B can therefore be used to determine the populatedvibrational level.At T = 80 and 300 K, we have a distribution of rovibrational

levels; it is therefore not possible to select times when thepopulation of one vibrational level is maximum. To comparewith XPS at T = 0 K, we computed XPS spectra at the sametimes as those selected for the T = 0 K case. XPS spectra in theregion of the satellite band, which is characteristic of therovibrational level, at T = 80 and 300 K are shown in Figures 13and 14, respectively.

At T = 80 K, the evolution of the spectra as a function oftime is similar to that obtained at T = 0 K. However, themaximum of the band at a given time is red-shifted. What isactually observed is mainly the population transfer during theRCAP process for (ν = 0, J0 = 1) because the Maxwell−Boltzmann distribution is dominated by this rotational level.For the initial (ν = 0, J0 = 1) level, the population transferbetween successive levels takes place at earlier time comparedwith (ν = 0, J = 0).At T = 300 K, the characteristic band B is blurred. The

selectivity with respect to the time and consequently to thevibrational level is partially lost. It is, however, regained forhigher vibrational levels (t = 86 and 100 ps).

Figure 11. XPS spectra at different times in the main peak region for T= 0 K. From bottom to top, the times are 0, 43, 45, 51, 56, 63, 69, 76,86, and 100 ps. The choice for these values is explained in the text.

Figure 12. Same as in Figure 11 but in the region of the satellite band(2832−2846 eV).

Figure 13. Same as in Figure 12 for T = 80 K.

Figure 14. Same as in Figure 13 for T = 300 K.



IV. CONCLUSIONSIn conclusion, we presented results on a new schemecombining RCAP technique with XPS. We discussed in detailthe RCAP process in the HCl molecule. It was shown thatusing this technique HCl molecule can be prepared in a well-defined vibrational level up to ν = 9. Effects of the temperatureon the RCAP process were investigated. It was demonstratedthat higher selectivity is obtained at lower temperatures.XPS during the RCAP process was computed. It was shown

that XPS is a powerful tool to probe the rovibrational state ofHCl molecule and can be used to follow the population transferduring the RCAP process. Influence of the temperature on theXPS spectra was also investigated. It should be noted that X-rayspectroscopies can be used as diagnostic tools not only foradiabatic passage methods but also for any coherent or optimalcontrol schemes. These spectroscopies should exhibit highercapabilities than other probes for large molecules where thechemical site selectivity will be a great advantage.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: [email protected]. Tel: 0033144276626.NotesThe authors declare no competing financial interest.

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Raman Chirped Adiabatic Passage Probed by X-ray Spectroscopy