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10.1146/annurev.physchem.57.032905.104601

Annu. Rev. Phys. Chem. 2006. 57:555–92
doi: 10.1146/annurev.physchem.57.032905.104601
c 2006 by Annual Reviews. All rights reserved
Copyright 

FEMTOSECOND TIME-RESOLVEDPHOTOELECTRON IMAGING
Toshinori Suzuki
Chemical Dynamics Laboratory, RIKEN (Institute of Physical and Chemical Research),
Wako 351-0198, Japan; email: toshisuzuki@riken.jp

Key Words ultrafast spectroscopy, wave-packet dynamics,
photoionization-differential cross sections, photoelectron-angular distribution■ Abstract Femtosecond time-resolved photoelectron imaging (TRPEI) is a variantof time-resolved photoelectron spectroscopy used in the study of gas-phase photoinduced dynamics. A new observable, time-dependent photoionization-differential crosssection provides useful information on wave-packet motions, electronic dephasing,and photoionization dynamics. This review describes fundamental issues and the mostrecent works involving TRPEI.

INTRODUCTION AND OVERVIEW
The fine details of bimolecular chemical–reaction dynamics have been experimentally studied using the crossed-molecular beam method (1, 2). This sophisticatedmethod measures the (state-resolved) differential cross sections (DCSs), i.e., thescattering and quantum-state distributions of reaction products (3–5), for welldefined initial states of reagents at controlled collision energies. The DCS andexcitation function (the collision energy dependence of the reaction) are valuable
in elucidating a reaction mechanism (6, 7), especially when compared with accurate theoretical predictions (8–10). On the other hand, the crossed-molecularbeam method observes asymptotic states of products, not the dynamics at shortinterparticle distances, as in the case of elementary particle physics. The quest for
direct experimental observation of electron and nuclear motions in reaction is adriving factor behind the development of ultrafast-laser spectroscopy (11).
According to the Born-Oppenheimer approximation, which is widely applicable to various molecular problems, chemical reactions are driven primarily byelectrons. Real-time observation of a nonstationary electronic state or electron orbitals in chemical transformation is essential for elucidation of the reaction mechanism. From this viewpoint, femtosecond time-resolved photoelectron spectroscopy(TRPES), which probes electronic states with femtosecond time resolution, is extremely useful. Furthermore, ionization can occur from any electronic state andin any nuclear geometry, provided the ionization wavelength is sufficiently short.
0066-426X/06/0505-0555$20.00

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Therefore, TRPES serves as a versatile means to probe dynamics along the entire
reaction pathway.
Photoionization is inherently an electron-scattering process, in which the mostdetailed observable is the photoionization DCS. Conventional photoelectron spectroscopy has employed photoelectron-angular distribution (PAD) to investigate
the ionization continuum, including such features as the autoionization resonance(12), shape resonance (13), and Cooper minimum (14, 15). However, TRPES did
not fully exploit time-dependent PAD as an observable until recently. In 1999,
two research groups presented femtosecond time-resolved photoelectron imaging(TRPEI) to visualize time-dependent photoionization DCS (16–20). Since then
TRPEI has been applied to various molecular systems including large molecularaggregates (21, 22).
The characteristics of TRPEI—or more generally TRPES—may be understoodin comparison with other means of probing electronic states or electron orbitals.
The X-ray free-electron lasers that are planed or under construction in several
countries (23) will enable ultrafast X-ray diffraction (and scattering) with femtosecond time resolution (24, 25). Because X-ray diffraction depends on the total
electron-density distribution in a molecule, it is utilized for the direct determinationof nuclear positions. Ultrafast X-ray diffraction is expected to significantly impact
studies of complex systems including biological molecules (26), and its development is anticipated to progress considerably over the next 5 years. For an analogous
approach of ultrafast-electron diffraction, see the review by Zewail in this volume(26a). On the other hand, chemical dynamics often require information on a specificelectron orbital that plays a key role in the reaction. The (e, 2e) momentum spectroscopy (27, 28) can observe distribution functions of various electron orbitals in
the momentum space, even in the frame of a molecule in its most advanced form
(29). However, its signal level is extremely low and an ultrafast pump-probe experiment has not been realized with (e, 2e). Itatani et al. (30) have presented a novel
approach to realize tomographic imaging of a molecular orbital using high harmonic generation in an intense laser field (31–33). This method utilizes recollisionof an electron that is tunnel-ionized from a molecule and accelerated in a laser field
to facilitate the 1D Fourier transform of the function rψHOMO (r ) (HOMO is ther ) can be reconstructed.
highest occupied molecular orbital), from which ψHOMO (The applicability of this method to chemical dynamics is to be studied further.
An important consideration in the ultrafast pump-probe experiment is whether the
probing step selectively monitors the photoexcited molecules. This is importantfrom a practical viewpoint because a pump pulse does not typically excite all themolecules in the target volume; in fact, most of the molecules remain unexcited. If
the probing step is nonselective, the observed signal will be overwhelmed by theunexcited ground-state molecules. Although the signal of interest can be extracted
by taking the difference between the data obtained with and without the pumppulses, this procedure is not always accurate. TRPES of neutral molecules withvisible and UV probe light selectively observes an ensemble of molecules excitedby the pump pulses, thus making this approach sensitive and straightforward.

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This review focuses on TRPEI, the time-dependent PAD, and related subjects
with examples from works in the last few years. The reader is referred to otherexcellent articles from the Annual Review of Physical Chemistry (34–38) andelsewhere (39–43) for a general historical background on TRPES and the literatureup until 2003.

PHOTOELECTRON IMAGING
In this section, I provide only a brief explanation of photoelectron imaging (PEI)
because the technical details of TRPEI are beyond the scope of this review. PEI
involves the 2D multiplex detection of the velocity vectors of electrons. Althoughmultiplex detection takes place in many other experiments in various disciplines,
PEI has essentially been derived from cold target–recoil ion-momentum spectroscopy in atomic physics (44, 45) and 2D photofragment ion–imaging in physicalchemistry (46, 47). The ion-imaging apparatus reported by Chandler & Houston(46) is largely the same as the Wiley-McLaren time-of-flight mass spectrometer(48), except that an electron multiplier at the end of the flight tube is replacedwith a 2D position-sensitive detector. Helm, Jung, and their coworkers (49–51)
performed PEI with nanosecond lasers in the mid-1990s. The acceleration electrodes modified by Eppink & Parker (52) provided an immersion lens for 2D spacefocusing of charged-particle trajectories; the arrival positions of particles depend
only on their velocity and not the initial position (the velocity map imaging). Further modification of the electrodes by Wrede et al. (53) minimized chromatic andspherical aberrations in charged-particle trajectories, thus improving the imaging
resolution. Magnification and contraction of electron images is possible by either
changing the time-of-flight or by bending the electron trajectories with an electrostatic lens placed in the middle of the flight tube (54–56): Garcia et al. (56) observed
electrons having kinetic energies of up to 14 eV with an energy resolution of 6%.
Weber et al. (57) combined a retarding electric field with a solenoidal-magnetic
guiding field to achieve resolution of <1eV at 300 eV.
A camera-based system and a delay line detector (58) are commonly employedas 2D position-sensitive detectors in PEI. Both comprise a microchannel plate as
the front surface, and each photoelectron that impinges upon the detector induces
the secondary electron amplification in a 5–12-μm microchannel. The amplified
electron pulses are emitted from the back of the microchannel plate. However, themethod of obtaining 2D positions of amplified electron pulses differs between thetwo systems. In the camera-based system, electron pulses are accelerated towarda phosphor screen at kinetic energies up to 2–4 keV. Light spots on the screen are
observed by a charge-coupled device or a complementary metal-oxide semiconductor camera. The latter can capture images at a high-frame rate comparable withthe repetition rate of amplified femtosecond laser systems. The delay line detector
places finely spaced wires (delay lines) on the back of the microchannel plate andmeasures the transmission times of the electric pulses through these lines. The

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2D positions are then calculated using these measurements. The delay line detector registers both the arrival position and the arrival time; however, it can handle
only up to 4 to 5 electrons in a response time of approximately 10 ns. In contrast,
there is virtually no limit to the number of electrons that the camera-based system can detect simultaneously; however, the camera-based system cannot record
the arrival times of electrons. This system is mainly used in photoionization experiments with lasers where many electrons are created. Another advantage ofthe camera-based system is the realization of high-fidelity measurements, as described below. Moreover, imaging resolution is improved to subpixel resolution(59) by real-time image processing (centroiding of each light spot) of each frame(59–61). A drawback of camera-based TRPEI is that a cylindrical symmetry of
the 3D distribution is required to reconstruct a single image, which restricts thepump and probe laser polarization to be parallel to each other. The reconstruction
is usually performed by an inverse Abel transform, although basis-set expansion
methods are more robust to numerical noises in image data (62, 63). A monographdescribes useful tutorials (47), and some more recent approaches can be found in
the literature (63–65).

ROTATIONAL WAVE-PACKET AND
PHOTOELECTRON-ANGULAR ANISOTROPY
Various dynamics in the neutral state affect PAD. For instance, when the system
undergoes a nonadiabatic transition, ionization transition–dipole moments to thecontinuum wave functions vary with the wave-packet motion, creating a timedependent PAD (66, 67). However, nonadiabatic transitions in isolated moleculesand clusters are generally associated with a change in the vibrational wave function, which can be observed in the time-dependent photoelectron kinetic energy
distribution (PKED). Although TRPEI offers the most efficient measurement ofa time-dependent PKED via the ultimate collection efficiency (100%) of photoelectrons, PKED is measurable with conventional TRPES. Therefore, to illustrate
the unique features of TRPEI, we concentrate on a time-dependent PAD and the
directional properties of a molecule in this section.
A molecular orbital is inherently anisotropic, and ejection of an electron fromthe molecular orbital creates a complex molecular-frame photoelectron-angular
distribution (MF-PAD). However, the laboratory-frame photoelectron-angular distribution (LF-PAD) is averaged over the molecular-axis distribution at the instantof ionization; thus the LF-PAD is generally less structured than the MF-PAD.
Assuming that molecules are in the J = 0 state, this ensemble has no specificdirection of the molecular axes in space, and it appears to be an isotropic target
for ionization light. Such an isotropic ensemble provides only a weakly polarized
LF-PAD from which hardly any detailed information on the molecular frame (MF)can be obtained.
In TRPEI, one-photon electronic transition in the pump step coherently excites
the P(J = –1), Q(0), and R(+1) branch lines. This creates a nonstationary

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superposition of the molecular rotational eigenstates or a rotational wave packet(68, 69). The wave packet provides a time-dependent molecular-axis distributionthat revives at characteristic time intervals determined by rotational constants.
The time-dependent molecular-axis distribution is generally expressed in terms ofspherical harmonics (and the multipole moments):P(t, θz , φz ) =AKQ (t)YKQ (θz , φz ),1.
KQ

where θz and φz are the polar and azimuthal angles of the molecular axis, respectively, measured in the laboratory frame (LF). The odd K terms discriminate themolecular axes in the upward and downward directions and are referred to as theorientation terms, whereas the even K terms are referred to as the alignment terms.
The orientation is not created by linearly polarized light. In one-photon photoexcitation of randomly oriented molecules by linearly polarized light, the highest
rank K is 2, and the terms with Q = 0 vanish as a result of a cylindrical symmetryaround the polarization of light:
P(t, θz , φz ) = A00 (t)Y00 (θz , φz ) + A20 (t)Y20 (θz , φz ).

2.

The highest rank (K ) in the equation is K max = 2n in the n-photon absorption
process.
PAD is the flux distribution of the outgoing electrons as a function of their angle
from the symmetry axis (the polarization direction of linearly polarized light or
the propagation direction of circularly polarized light). In one-photon ionizationof a randomly oriented ensemble of molecules with linearly polarized light, the
LF-PAD is expressed by the following equation:σdσ
3.
[1 + βP2 (cos θk )],
 =
dk
4π
where θk is the polar angle of the photoelectron k-vector with respect to the ionization laser polarization, and Pn (x) is a Legendre polynomial. When the ensembleof molecules is polarized as expressed by Equation 2, one-photon ionization ofthis ensemble with the probe-laser polarization parallel to that of the pump laser
provides the following LF-PAD:dσ (t)σ (t)[1 + β2 (t)P2 (cos θk ) + β4 (t)P4 (cos θk )].
 =
dk
4π

4.

Comparing Equations 3 and 4, the P4 term in the (1 + 1 ) resonance-enhanced multiphoton ionization (REMPI) appears only when the ionized target is anisotropic.
In fact, σ(t) · β 4 (t) is proportional to A20 (t) in the (1 + 1 ) REMPI. In generalcases, including the pump and the probe laser not polarized in parallel, the PAD
is expressed by (70)dσ (t) =βLQ (t)YLQ (θk , φk ),
5.
dk
LQ
where the maximum value of L is 2(m + n) in (m + n) REMPI.

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The photoelectron-anisotropy parameters can be expanded by the axis-alignment
parameters as follows (71):βLQ (t) =A K −Q (t) aKLQ ,6.
K

where the expansion coefficients aKLQ carry all the information of photoionization
dynamics. The detailed form of aKLQ has been obtained by Underwood & Reid
(71). In 2005, Suzuki & Seideman (57) presented a general quantum-mechanicalexpression for TRPEI, in which they show the relation between the time-dependentalignment moments and the rotational wave-packet revivals for various pump intensities. Under certain (realistic) conditions, the general expression (72) can be
reduced to Equation 6. Several important points are noted for Equation 6. First,
following AKQ (t), β LQ (t) also exhibits rotational wave-packet revival structures,provided aKLQ are not too small. Second, if β LQ are measured for known AKQ ,aKLQ (or the ionization-dynamical parameters) can be determined. Finally, if aKLQ
are known and β LQ are measured, AKQ or the axis distribution can be determined.
Because photoelectron-scattering wave functions in the ionization continuum
are degenerate, ionization is induced via various transition-dipole moments in
MF: For instance, ionization can occur with comparable efficiencies via paralleland perpendicular transitions in linear molecules. Consequently, the ionization
intensity (an integral cross section) in the (1 + 1 ) scheme is rather insensitive
to the rotational wave-packet motion, except that ionization is mediated by the
autoionization resonance or shape resonance.
Rotational coherence spectroscopy monitors the periodic motion of a rotational
wave packet through polarized fluorescence or transient absorption to higher electronic states: Other variants of rotational coherence spectroscopy, although notincluding TRPEI, have been considered by Felker & Zewail (73). An advantageof TRPEI in detecting rotational wave-packet dynamics is that photoionization
is more sensitive than fluorescence. Bragg et al. (74) demonstrated the (1 + 1 )TRPEI detection of a rotational wave packet of C−
2 whose density in the ion beam
is small. TRPEI can also observe wave packets in the triplet state, as described in
the section below.

ROTATIONAL DYNAMICS IN ELECTRONIC DEPHASING
Polyatomic molecules hardly exhibit the unit fluorescence quantum yield becauseradiationless transitions (75) such as spin-allowed internal conversion and spinforbidden intersystem crossing (ISC) are ubiquitous. The S1 −T1 ISC in pyrazine
is the best-known example for the intermediate coupling case in molecular radiationless transition (76–83). Strong spin-orbit coupling of the S1 B3u (nπ ∗ ) vibronic
state with moderately dense triplet vibronic states results in a complex energy
structure of molecular eigenstates. Coherent excitation of these eigenstates createsa nonstationary state that rapidly evolves with time. The evolution has previously

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been monitored by fluorescence from the S1 state, which exhibited a biexponential
decay; the fast component is a result of pure dephasing between the component
eigenstates, whereas the slow component is a result of depopulation of these eigenstates through deactivation down to S0 . On the other hand, there has been no direct
detection of the dark manifold with ultrafast lasers.
The real-time observation of the S1 decay and the T1 formation was performedby TRPEI as shown in Figure 1. These images are doubly differential ionization
cross section at specified pump-probe time delays. Because ionization occurs fromthe S1 zero vibrational level to the low vibrational states of the cation due to theFranck-Condon overlap, the singlet component of the nonstationary state creates
well-resolved concentric rings in the outer part of the photoelectron images (Figure 1b). On the other hand, as the origin of T1 is located 0.5 eV (4055 cm−1 )lower than S1 , T1 vibronic levels isoenergetic to the S1 zero level are highly vibrationally excited. Consequently, ionization occurs from the T1 vibronic levels
to highly vibrationally excited levels of the cation at longer time delays, creating
slow electrons that appear at the center of the images. The S1 decay and the T1 formation were found to occur with the identical time constant of 110 ps. Integrationof the images for the angular part provides the time-dependent PKEDs displayedin Figure 1c. An isosbestic point was identified in the PKEDs at approximately
200 meV, illustrating that ISC is an exclusive decay process from S1 in this time
range. Vibrational structures in the PKED are attributed to progressions of totallysymmetric vibrational modes. The PAD at individual photoelectron kinetic energies (PKEs) can be extracted from the images; for instance, the PADs associatedwith ionization from the S1 zero level to the 6a1 level of the cation (the second
outermost ring in Figure 1b) are presented as a function of the pump-probe timedelay in Figure 1a. The PAD exhibits time dependence—it is slightly enhanced atθk = 90◦ only when t = 0 and at 82 ps (the first full revival time of the rotational
wave packet). Correspondingly, the β 4 coefficients extracted from a series of thephotoelectron images clearly exhibited the wave-packet revivals (42).
Although (1 + 1 ) TRPEI is useful for probing rovibronic dynamics, a lowenergy tail of the PKED from S1 overlaps the PKED from T1 in the (1 + 1 ) REMPI(Figure 1c). An alternative way to selectively observe ionization from different
electronic states is (1 + 2 ) REMPI, where ionization occurs using Rydberg states
as stepping stones (20, 84). As a result of the v = 0 propensity rule in ionizationfrom the Rydberg states to the cation, this ionization scheme creates well-separated
PKEDs for ionization from S1 and T1 . Ionization from S1 was observed through thesinglet 3pz (n−1 ) (TR = 55 000 cm−1 ) and 3s(n−1 ) (TR = 50 700 cm−1 ) Rydberg
states, and ionization from T1 occurred via the triplet 3s(n−1 ) (TR = 50 200 cm−1 )(Figure 2) (85). The z-axis of pyrazine in D2h point group is along the N-N axis.
The ionization intensities from the singlet state diminish with τ = 110 ± 5 ps,
whereas that from the triplet grows accordingly. The rotational revival features inthe singlet and triplet manifold are seen as rapid modulations in the intensities andanisotropy parameters. As the S1 (1 B3u ) ← S0 (1 Ag ) transition-dipole moment isparallel to the top axis of this near oblate-top molecule, the axis distributes as cos2 θz

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Figure 1 Time-resolved photoelectron images, photoelectron-angular distributions,and photoelectron kinetic energy distributions in (1 + 1 ) resonance-enhanced multiphoton ionization via the S1 zero vibrational level. The pump-laser wavelength was
fixed to the (0, 0) band of the S1 (1 B3u ) ← S0 (1 Ag ) transition (324 nm), and the probelaser wavelength was 197 nm. (a) Polar plots of the photoelectron-angular distributions
associated with ionization from the S1 zero vibrational level to the cation 6a1 vibrational level at specified time delays. (b) Inverse Abel transforms of the time-resolved
photoelectron images corresponding to the slices through the 3D photoelectron velocity distributions at specified time delays. (c) Photoelectron kinetic energy distributions
obtained by angular integration of the inverse Abel transforms of the time-resolved
photoelectron images. Structured distribution in the high energy side is a result of
ionization from the S1 state, whereas a low energy distribution appearing at long
pump-probe time delays is ionization from T1 .

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Int. (arb. units)

(a)

563

A
B
C

1.0

0.5

0.0

(b)

β2
β4

1.5
1.0
0.5
0.0
1.0

(c)
A20/A00

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0

20

40

60

80

100

Pump-probe delay /ps
Figure 2 (a) Temporal profiles of the energy-selected photoelectron intensities in the (1 +2 ) resonance-enhanced multiphoton ionization of pyrazine via the S1 zero vibrational levelwith the pump (324 nm) and probe (401 nm) lasers. A and B indicate S1 detected via the
3pz Rydberg state and S1 via the 3s Rydberg state, respectively. C indicates T1 detected
via the 3s Rydberg state. (b) Time evolution of√the anisotropy parameters, β 2 and β 4 , ofthe photoelectron-angular distributions: β L = 2L + 1β L0 . (c) The alignment parameter,
A20 /A00 , in the S1 state calculated for the rotational temperature of 20 K.

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with respect to the laser polarization at t = 0 and the full revival times. The revival
features in the ionization intensities via 3s(n−1 ) and 3pz (n−1 ) are out of phase,in which the former takes the maximum at t = 0. This unambiguously indicatesthat the transition-dipole moments for 3s ← S1 and 3pz ← S1 are parallel andperpendicular to the top axis, respectively. The 3pz ← S1 transition is vibronicallyinduced, as it is an ungerade-ungerade electronic transition. The revival features inanisotropy parameters are also out of phase in ionization via 3s(n−1 ) and 3pz (n−1 );however this is for a different reason. The time-dependent anisotropy parametersindicate that the MF-PAD has a sharper peak in the parallel than in the perpendicular
ionization transition from 3s, whereas this relation is reversed in ionization from
3pz . The analysis of the time dependencies of anisotropy parameters provided the
LF-PADs expected for the axis alignment of cos4 θz and sin4 θz , which exhibited
dramatic differences from each other (86).
The revival feature appears quite strongly in the singlet signal, both in the intensities and the photoelectron-angular anisotropies, whereas the revival feature
is considerably smaller for the triplet. In 2004 Tsubouchi et al. (86) theoreticallyexamined the rotational revival feature in ionization from the T1 state. In the analysis, pyrazine was approximated as an oblate symmetric top because the asymmetry
parameter is 0.985 in the 00 level in S1 (87). The triplet state—with a small spin
splitting—was described by Hund’s coupling case b, whereas the singlet state wasdescribed by case a. The basis sets for these two cases are denoted as |NJKSM and|JPM |S , respectively (88). The quantum numbers are as follows: N denotes
the rotational angular momentum, J the total angular momentum, K the projectionof N on the top axis, S the spin-angular momentum, M the projection of J on thespace-fixed axis, P the projection of J on the top axis, and the projection of S
on the top axis. The analogy with the diatomic case is such that J, N, K, and P
correspond to J, N, , and , where and  are the projection quantum numbersof the electronic orbital and the total angular momenta onto the internuclear axis,
respectively. The molecular eigenstates of the effective Hamiltonian, including thespin-orbit coupling, are expressed by a linear combination of the zero-order S1 andT1 states:|n JS PS MS = anJS PS MS | S , 0 |JS PS MS |0, 0bni NT K T MS  T , vTi |NT JS K T 1MS ,+7.

i NT K T

where v i represents the vibrational quantum number of the i-th mode, and i includes all other quantum numbers. The zero-order eigenenergies of the S1 states
were constructed from the spectroscopic constants in the literature (87), whereas
those of the T1 states remained unknown. Accordingly, the T1 vibronic levels wererandomly distributed around the S1 00 level with a state density of ρ that reproduces the observed dephasing time. The weighting factors, anJS PS MS and bni NT K T MS ,and the eigenenergies, E nJS PS MS , were obtained by diagonalizing the Hamiltonian
matrix.

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The time-dependent wave function of the nonstationary state is expressed by( ; t; J0 P0 M0 ) ∝I (JS PS MS ; J0 P0 M0 )JS PS MS

×





anJS PS MS |n JS PS MS exp −i E nJS PS MS t h̄ ,8.

nwhere I (JS PS MS ; J0 P0 M0 ) denotes the excitation strength from a rotational state|J0 P0 M0 in the S0 zero vibrational level to each |JS PS MS . The singlet and triplet
components of the nonstationary state areS ( ; t; J0 P0 M0 ) =| S , 0 |JS P0 M0 |0, 0
JS

×
and


S , 0 | JS P0 M0 | 0, 0|( ; t; J0 P0 M0 )

T ( ; t; J0 P0 M0 ) =9.

|NT JS K T 1M0  T , vTi

i JS NT K T

× NT JS K T 1M0 |iT , vT ( ; t; J0 P0 M0 ) ,10.

respectively. The distribution function of the top axes in the S1 and T1 states areP S (θz ; t; Trot ) =exp −E rot
J0 K 0 M0 k B Trot
J0 K 0 M0and
P T (θz ; t; Trot ) =×dφdχ  S∗ ( ; t; J0 P0 M0 )S ( ; t; J0 P0 M0 )






exp −E rot
J0 K 0 M0 k B Trot

11.

J0 K 0 M0×dφdχ T∗ ( ; t; J0 P0 M0 )T ( ; t; J0 P0 M0 ),12.

respectively, where kB is the Boltzmann constant, Trot is the rotational temperaturein the molecular beam, and E rot
J0 K 0 M0 is the rotational energy of the |J0 P0 M0 state.
The experimental result was well reproduced by the calculations (Figure 3).
The mechanism that reduces the revival signal in the dark state was explained
as follows (Figure 4). For simplicity, we first discuss the case of intramolecularvibrational redistribution via anharmonic coupling. The rotational selection rule isJ = K = 0 between the bright and the dark states. In this case, if a dark state
has the same rotational constant as the bright state (type I), the mixing strengths
between these states become equal for all J states. This provides the ratios of theexcitation probabilities for the J − 1, J, and J + 1 state in the dark manifold
to be equal to those of the bright states, thus maximizing alignment in the dark

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obs. T1
calc. T1
calc. S1

A20/A00

0.8
0.6
0.4
0.2
0.0
0

25

50

70

100

Pump-probe delay / ps
Figure 3 Time evolution of the molecular-axis alignment A20 /A00 . Open circles represent
observed data points for the T1 state populated via intersystem crossing from the S1 zerovibrational state. The solid and dashed lines show the calculated time profiles for the T1 andS1 states, respectively (see text).

state. On the other hand, if the rotational constants in the bright and dark states
differ (type II), the ratios of the excitation probabilities for the J − 1, J, and J +1 state in the dark state deviate from those in the bright state, reducing alignment
in the dark state. The case of ISC in pyrazine is different from the intramolecularvibrational–redistribution case because although the rotational constants are essentially the same in the bright and dark states, alignment diminishes in the darkstate. The key difference of intersystem crossing from intramolecular vibrational
redistribution is that the spin-orbit interaction provides the selection rule (N =J − 1, J, J + 1, K = P ± 1) that allows three different rotational ladders in T1
to be involved in the ISC. We term them types A (N = J), B (N = J + 1), andC (N = J − 1). Type A is analogous to type I of the intramolecular vibrational–
redistribution case, whereas types B and C are analogous to type II. The type A
scheme provides rotational revival in the dark state with the same strength as thebright state, in contrast with the cases of types B and C. Therefore, types B and C
contribute to the sources of reduced alignment in the dark state.
In general, appearance of the rotational wave-packet dynamics in the dark state
depends on the ratio between a coupling strength and an energy difference between
the bright and dark states. When the coupling strength increases, the rotational

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TIME-RESOLVED PHOTOELECTRON IMAGING(a)Type I

567

Type IIJ + 1, P

2 B( J + 1)

2 B ( J + 1)

2 B( J + 1)

2 B ' ( J + 1)

2 BJ

2 BJ

2 BJ

2 B' J

Type A

Type B

Type CJ, P

J − 1, P(b)
J + 1, P

2 B ( J + 1)

2 B( J + 1)

2 BJ

2 BJ

2 B( J + 2)

2 BJ

J, P

2 B( J + 1)

2 B( J − 1)

J − 1, P

N=J

N = J +1

N = J −1

Figure 4 A picture of the rotational energy–level structure of the interacting brightand dark states in the case of (a) intramolecular vibrational redistribution and (b)intersystem crossing. In type I, the rotational constants of the bright and dark states
are the same, whereas they differ in type II. In intersystem crossing, type A, B, and C
ladders of the rotational states in the dark state can be coupled with a bright state. Even
if the rotational constant in the dark state is the same as that in the bright state, theladder spacings of types B and C are different from that in the bright state. The shaded
area around each bright state indicates the magnitude of the interaction strength withthe dark states.

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wave-packet revivals in the dark state can appear for larger differences in therotational constants from the bright state.

PHOTOIONIZATION DYNAMICS VIA TIME-RESOLVEDPHOTOELECTRON IMAGING
A rotational wave packet affects LF-PAD primarily because MF-PADs generally
differ for different ionization-dipole moments. When LF-PADs are analyzed indetail via Equation 6, TRPEI serves as a means to probe ionization dynamics.

Extraction of Photoionization-Dynamical Parameters from
Photoelectron-Angular Distribution
Experimental studies of ionization dynamics ultimately aim at the observation of
the MF-PAD expressed by (13, 89–100)
2l
max

dσ
=
αlm Ylm (θk , φk ),
dk
l=0

13.

where lmax is the largest orbital-angular momentum of the outgoing photoelectron,and θ k and φ k are the polar and azimuthal angles, respectively, of the photoelectron k-vector measured in the MF. Following intricate analysis, the MF-PAD yields
photoionization-dynamical parameters such as transition-dipole moments to individual partial waves and the phase shifts. The MF-PAD can be observed by angleresolved photoelectron-photoion coincidence, which simultaneously observes thevelocities of the photoelectron and the daughter ion in dissociative photoionization.
From this observation, the angular correlation between the molecular axis and thephotoelectron k-vector is determined. Reference 101 summarizes recent advancesin coincidence techniques. As a result of its nature, photoelectron-photoion coincidence can provide MF-PADs only for dissociative ionization in the axial recoil
limit. An alternative approach presented by Zare and coworkers (102–109) was tomeasure LF-PADs for the state-to-state ionization process with various polarization combinations of the pump and probe lasers, from which ionization-dynamicalparameters were extracted.
In TRPEI, time-dependent LF-PAD provides the aKL0 parameters via Equation 6, which can be solved, in principle, to obtain the photoionization-dynamicalparameters. Here I present an example of (1 + 1 ) REMPI of NO via the A(2 + ) state (110). The NO+ ion has a closed shell with the electron configuration 1σ2 2σ2 3σ2 4σ2 1π 4 5σ2 . Nitric oxide is the benchmark system for studies ofmolecular photoionization (111, 112) and Rydberg states (113–117). It has been
the only molecule for which photoionization-dynamical parameters have been determined experimentally (102–109); however, these experiements have only been
for PKE = 0.18 eV. This fact illustrates the limited understanding of ionization
dynamics of molecules near the threshold. Figure 5 shows the overview of the7 Mar 2006

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time-dependent anisotropy parameters observed in the (1 + 1 ) TRPEI of NO via
the v  = 0 level in the A (2 + ) state. The data points shown here are from our
new measurements performed after the 2004 report (110). In the experiment, a
femtosecond 226-nm pump pulse created a rotational wave packet in the A stateof NO, and a time-delayed femtosecond probe pulse ionized the molecules fromthe A state. Because the A state is the 3sσ Rydberg state, the v = 0 propensity
rule holds in photoionization, and the PKE associated with the single vibrational
state (v + = 0) of NO+ was continuously varied with the ionization wavelength.
The rotational wave-packet revivals are clearly identified in β 2 and β 4 , although
the time-dependent variations are less than 0.1 at some PKEs (Figure 5). The full
revival time of the rotational wave packet is 8.2 ps. Both β 2 and β 4 show a clear
trend against PKE: Anisotropy parameters at the full revival time exhibit the minima at the lowest PKE, whereas they exhibit the maxima at the largest PKE. The
phase reversal at PKEs of approximately 0.3 eV (β 2 ) and 0.5 eV (β 4 ) clearly indicates that the MF-PADs vary with the PKE. Because the molecular axis of NO in
the A state is primarily perpendicular to the laser polarization at t = 0 and 8.2 ps,
ionization at these moments occurs predominantly via the perpendicular transition
to create a kπ scattering wave. Conversely, at 4.2 ps, ionization mainly occurs via
the parallel transition to the kσ ionization continuum. Therefore, Figure 5 indicatesthat MF-PAD exhibits a sharper peak for the σ-ionization channel than for the πchannel near the threshold, whereas this relation is reversed at PKE > 0.5 eV.
Because an electron wave function of a molecule is referenced to the MF, theone-electron scattering wave in the LF is expressed as∗l∗|ψ − (k , r ; R) =i l e−iσl Ylm(k̂  )Dmλ( R̂)ϕlλ (r ; k, R),
14.
lmλwhere variables with and without the prime correspond to the LF and MF, respectively. k = k k̂  is a wave vector of the photoelectron with k̂  as the unit vector
along the direction of ejection, and r = r r̂  is a similar relation for the positionof the photoelectron; l is the orbital angular momentum, and m is its projection
quantum number onto the LF z-axis, σl is the Coulomb phase shift of a partial
wave with l, R is the internuclear distance, and R̂ is the Euler angle that relates
the MF to LF. As the orbital-angular momentum l is not a good quantum number
for molecules, the partial waves ϕlλ (r ; k, R) are generally not the eigenfunctions.
Because mixing between the sσ and dσ Rydberg orbitals (s,d supercomplexes)
have been identified for NO by extensive spectroscopic and theoretical analyses(113–115), similar mixing is anticipated for the sσ and dσ scattering waves. The
origin of this mixing has been speculated to be a result of interactions with the
HOMO(5σ) of NO+ , which has a mixed sσ + dσ character. To account for thiss-d mixing, Park & Zare (108, 109) employed the electronic eigenchannel wave
functions ξiλλ (r ; k, R) composed of partial waves with the same λ. Each partial
wave in Equation 14 is then expressed by
ϕlλ (
r ; k, R) =Uliλλ exp −iπ τiλλ ξiλλ (r ; k, R),
15.
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1.7

1.6 β 2
1.5
1
1.4
1
1.25
0

1.00
2

0.75

4
0.50

6

Pump-probe delay/ps

Excess energy/eV

0.25

8
10 0.00

0.2
0.1
0.0 β 4
-0.1
-0.2
1.25
0

1.00
2

0.75

4
0.50

6

Pump-probe delay/ps

0.25

8

Excess energy/eV

10 0.00

Figure 5 Experimentally observed variation of the photoelectron-anisotropy parameters β 2 and β 4 as functions of the pump-probe time delay and the probe√ wavelength
in one-photon ionization from the A state v  = 0 level of NO. β L = 2L + 1β L0 .

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where τiλλ is the dynamical phase shift due to the interaction of an electron with
the ion core in the short range, and Uliλλ is an element of the transformation matrix that diagonalizes the scattering K matrix (109, 114). The running index i λ isfor numbering the eigenchannel wave functions with the same λ. Considerable
configuration mixing occurs only for the sσ and dσ waves in NO.
When the scattering wave function is described by Equations 14 and 15, theaKL0 coefficients for NO+ X (1 + ) ← NOA(2 + ) are expressed as follows (110):
aKL0 ∝(2L + 1)(2K + 1)



(2P + 1)P×



(2l + 1)(2l  + 1)

lλl  λ

λ

1

P

P

K

L

0

0

0

0

0

0





P

1
−λ

λ −λ

P
λ−λ

K


0

l
L
,


−λ λ − λ





 
× (−i)l−l ei(σi −σl  )Uiλλ Uiλ λ Miλλ Miλ λ exp iπ τiλλ − τiλ  ,
×

l l
0 0

1

1

L
0

L


λ −λ

l
λ

i λ i  λλ16.

where Miλλ =  + ; ξiλλ (k M , r)|μλ |3s is the magnitude of the matrix element of
the ionization transition–dipole moment. Because the ionized orbital is 3sσ (λ =0), partial waves are restricted to the σ (λ = 0) and the π wave (λ = ± 1). In
addition, because the s character of this orbital is as high as 94.0% (111), thecontribution of high angular momentum (l > 3) to partial waves is neglected,
which is supported by the fact that Zare and coworkers have not detected N ≥4 transitions in the state-to-state ionization from the A state to the cation (102–109). With these restrictions, there still remain 7 partial waves with 12 dynamicalparameters (4 transition-dipole moments and 3 relative phase-shift differences forthe σ wave, 3 transition-dipole moments and 2 relative phase-shift differences forλthe π waves) to account for in the analysis, other than the matrix Ul,i
. On theλother hand, the aKL0 parameters determinable in the (1 + 1 ) REMPI are only 4,i.e., relative values of a000 , a020 , a200 , a220 , and a240 , at each ionization wavelength.
Therefore, extraction of the dynamical parameters from TRPEI is not possible
from a measurement performed at a single ionization wavelength.
However, as anticipated from the smooth energy dependence of the anisotropy
parameters shown in Figure 5, the aKL0 parameters determined from these experimental data also vary monotonically with the PKE. This fact suggests thatthe dynamical parameters can be approximated to vary linearly with PKE. Explicit assumption of this fact facilitates the analysis because the aKL0 parametersat each PKE can be employed altogether to determine the dynamical parameters
and their first derivatives against the PKE at the ionization threshold. Furthermore, the dynamical phase shift at low energies connects smoothly to the quantum
defect of a high Rydberg state through the Levinson-Seaton theorem (118–122).

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Therefore, the dynamical phase shifts of the partial waves were estimated by extrapolating the quantum defects in high Rydberg states of NO, and they wereλexcluded from the least-squares fitting. Similarly, Ul,iwere taken from the results
λfor Rydberg states (113–115). In this way, the energy-dependent transition-dipole
strengths for each partial wave Miλλ (E) were determined from the aKL0 parameters(110).
Nonlinear least-squares fitting of the second-order Equation 16 generally
provides multiple numerical solutions. This is similar to the multiple solutions
always encountered in the extraction of dynamical parameters from MF-PAD
observed by photoelectron-photoion coincidence (123, 124). However, all the obtained solutions exhibited a major contribution of the p wave; this is in agreementwith the l = ± 1 propensity rule in ionization from the 3sσ state. The MF-PADs
calculated from the different sets of dynamical parameters are similar to each other,thus only one example is shown in Figure 6.
In 2004, Guérout et al. (116, 117) reported the ab initio multichannel quantumdefect theory to calculate electronic wave functions of highly excited Rydberg
states and the continuum. Further experimental and theoretical investigations arenecessary to elucidate the ionization dynamics of this benchmark system, and theyshould be extended to other molecules.

Figure 6 Molecular-frame photoelectron-angular distributions in one-photon ionization ofNO from the A state v  = 0 level calculated using one set of Miλλ (E) determined by theleast-squares fitting of Equation 16. The dynamical phase shifts τiλλ were estimated from theλquantum defects in high Rydberg states. The matrix elements of Ul,ito describe the sσ-dσλmixing were taken from those for high Rydbeg states. See the text for details.

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573

Strategies for Narrower Axis Distribution
If a strongly aligned ensemble of molecules is prepared prior to photoionization,
LF-PAD will be identical to MF-PAD. However, such strong alignment cannot
be created by one-photon excitation because the unit spin–angular momentumof a photon restricts the rotational wave-packet components to only the J − 1,
J, and J + 1 eigenstates. This leads to a molecular-axis distribution of cos2 θz orsin2 θz at most. Because of the uncertainty principle, a narrower axis distribution
requires the superposition of a large number of J states. A pendular state of apolar molecule in a static electric field (125–127) or a polarizable molecule ina (quasi-)stationary laser field (128–131) is also a way of achieving alignment
or orientation; however, the presence of strong external fields is inconvenient forphotoelectron spectroscopy. The employment of an intense laser field is considered
to be a more promising method. Interaction of an intense laser pulse with a molecule
induces rapid Rabi-cycling in which rotational ladder climbing and superpositionof a broad J distribution occur (132). In addition, when the laser turn-on and turnoff times are considerably shorter than the rotational time period, the rotational
dynamics are nonadiabatic in that a rotational wave packet persists even after thealignment laser field vanishes, thus providing field-free molecular-axis alignment.
Although a wave packet can be created via resonant and nonresonant interaction ofa laser field with a molecule (132), the latter can be implemented more easily with
an amplified titanium sapphire laser (800 nm) (133). The nonresonant scheme isessentially multiple rotational–Raman scattering (134).
As an example, Figure 7 shows a calculated molecular-axis distribution of N2 in
the ground-electronic state after interaction with a nonresonant-femtosecond laser
pulse (800 nm) (135). The distribution becomes narrow at particular time delays.
Dooley et al. have verified the time-dependent axis distributions of N2 and O2
created by multielectron-dissociative ionization and imaging of the daughter-ion
recoil directions (136). Figure 8 shows the observed alignment moment cos2 θzand the axis distributions measured at specified time delays. The LF-PAD measurement using such transient molecular axis alignment has not yet been realized: Onlya theoretical prediction has been reported for the LF-PADs from the aligned N2
molecules for the 2σg -shell photoionization (hv = 58.2 eV) and (2 + 1) REMPI
via the a (1 g+ ) state at 205 nm (135). The calculated LF-PAD clearly exhibiteda characteristic nodal pattern of the MF-PAD when ionized at the maximal axis
alignment.
In general, a single pulse–alignment scheme meets saturation when the alignment is no longer enhanced by the laser intensity. For squeezing the axis distribution beyond the saturation limit, employment of multiple laser pulses has been
proposed (137–139). In the multiple-pulse schemes, the first pulse creates transientalignment of the molecular axis in the harmonic region of the angular-interaction
potential (sin θ ≈ θ ), where the subsequent pulse provides the angular velocity(ω∞ sin θ ) linearly proportional to the angle between the molecular axis and the7 Mar 2006

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Figure 7 Calculated time-dependent molecular-axis distribution in the ground state of N2
created by interaction with an intense laser field. The initial rotational temperature was assumed to be 20 K. The intensity and pulse width of the alignment-laser light in the calculation
are I = 100 TW/cm2 and talign = 100 fs, respectively.

laser polarization, thereby squeezing the angular distribution. The suggested enhanced alignment by the two-pulse scheme has been experimentally observed (140,141). These calculations and experiments were performed for linear molecules.
In the case of asymmetric top molecules, maximal alignment occurs initiallybecause complex rotational energy structures prevent the complete revival of theinitially aligned state. Péronne et al. (142) aligned iodobenzene with a 2.2-ps-longalignment pulse and observed strong alignment at a time delay of approximately
2 ps. Asymmetric top molecules provide another interesting problem of the fieldfree 3D alignment of molecules, for which several strategies have been proposed(143–145).
For application of MF-PAD measurements by TRPEI considered here, it is important to precisely characterize the axis distribution created by a laser pulse prior
to LF-PAD measurement. The creation of a strongly aligned molecular ensemble without contamination from weakly aligned molecules is more difficult thanthe observation of the revival features on top of a background. In the weak-field

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Figure 8 (a) Variation of the molecular-axis alignment moment cos2 θ of N2 with a timedelay between the alignment and explosion (dissociative-ionization) pulse. Prior to the alignment pulse, the molecular ensemble of N2 is isotropic. (b–d) Plots of measured (dots) andsimulated (lines) N2 -axis distributions. Polarization of the alignment pulse is in the horizontal
direction; anti-alignment is seen at the half revival time in panel c. For clarity, the areas ofthe simulated plots are two-thirds those of the measured distributions.

.

case discussed in the above section, the alignment is mild but is completely characterized (and predictable). Molecular-axis alignment also attracts attention in laser
physics as it can be used for quasi-phase matching in high-harmonic generation
and attosecond pulse shaping (146).

IONIZATION CONTINUA OF POLYATOMICS: POORLYUNDERSTOOD FINAL STATEIn TRPEI, if the final state for ionization, rovibronic wave functions of a cation andphotoelectron-scattering waves, were well understood, the ionization continuum
would serve as an ideal screen to project complex dynamics in the neutral state. In
reality, the rovibronic states of cations are poorly understood, especially those oflarge molecules that exhibit interesting dynamics, and virtually nothing is known
about electron-scattering wave functions. The latter is particularly problematicfor interpretation of the absolute values of anisotropy parameters and is briefly
discussed in this section.

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Using conventional photoelectron spectroscopy, a number of mechanisms havebeen elucidated as origins for energy-dependent photoelectron-angular anisotropyβ(E ): (a) For instance, in photoionization from the inner p subshells of rare gases(Ar 2p, Kr 3p, and Xe 3p and 4p), anisotropy parameters vary with the ionizationenergy due to the Coulomb phase shifts of the s and d partial waves (147). β(E )drops sharply with an excess energy above the ionization threshold and then increases smoothly to reach an asymptotic value of approximately 1.5. (b) Interactionof the ionization continuum with superexcited states exhibits resonances, such as
the Beutler-Fano type, and provides a β(E ) that varies sharply around the energyof the superexcited state (12). (c) Photoionization from the subshells of l < n −1 exhibits the Cooper minimum in that a transition-dipole moment to a particularpartial wave vanishes at a certain energy; β(E ) varies in a wide energy range (14).
The Cooper minimum observed in molecular photoionization is generally ascribedto the atomic character of the molecular orbital, in which the effect is much lesspronounced than in the atomic case. (d ) In molecular photoioinzation, the PAD isaffected by shape resonance due to excitation to an unoccupied molecular orbitalthat rapidly decays into the continuum (148).
Photoionization from various orbitals exhibits a characteristic β(E ). Piancastelli
et al. (149) have assigned the π−1 and n−1 bands in photoelectron spectra of azabenzenes based on the experimental evidence that π−1 generally exhibits a β(E )that increases with excess energy, whereas n−1 shows a much lower anisotropy andweak energy dependence. We have examined this phenomenon using continuummultiple scattering (CMS)-Xα calculations (150, 151). Figure 9 shows the calculated β(E ) for ionization of π electrons in benzene, pyridine, and pyrazine. The
molecules are assumed to be randomly oriented. The experimental values (149,
152) (filled circles and triangles) and calculations (solid and dotted lines) are inexcellent agreement. The smooth variation with excess energy seen in all cases
is a result of the energy-dependent Coulomb phase shifts of the partial waves.
Conversely, photoionization of the σ and n electrons exhibits completely different
features (Figure 10). The circles and diamonds represent the experimental β(E )values (149, 152, 153). The calculated β(E ) for ionization from the 3e1u (σ) orbital
in benzene are in reasonable agreement with the experimental result, which is thesame as that obtained by Carlson et al. (153). The partial cross section to the ke2g ,ka1g , and ka2g continua is also shown in the same panel. The enhanced cross sections around 6 eV and 12 eV indicate the shape resonances with the a2g (σ), a1g (σ),
and e2g (σ) unoccupied orbitals. A close comparison of the anisotropy parameterand the cross section reveals that β(E ) is indeed influenced by shape resonances.
The result of the pyridine 6b2 (σ) orbital that correlates with the benzene 3e1u one issimilar. For pyrazine, calculations are shown for 4b2u (σ) and 5b1u (n). Again, β(E )is determined by shape resonances. A close examination of Figure 9 reveals the effect of shape resonance on the σ∗ orbital in ionization from π as dips in the curves;
however, this effect is negligible. These results support the argument by Piancastelli
et al. (149) and illustrate that the shape resonance is a crucial factor in determining
the PAD, particularly in ionization from the nonbonding and σ orbitals.

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Benzene
β (E)

1

1e1g

0

Pyridine

2b1
1a2

β (E)

1

N

0

Pyrazine

1b1g

1

β (E)

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N

0

N
0

10

20

Photoelectron kinetic energy / eV
Figure 9 (left) Photoelectron-anisotropy parameter as a function of photoelectron kinetic
energy calculated for orbitals 1e1g of benzene, 1a2 (solid line) and 2b1 (dashed line) of
pyridine, and 1b1g (solid line) and 1b2g (dashed line) of pyrazine. Experimental data are indicated by open circles (153) and filled circles for benzene (152), and filled circles and triangles
for pyridine (pyrazine) 1a2 (1b1g ) and 2b1 (1b2g ), respectively (149). (right) Isosurfaces of
HF/4-31G molecular orbitals. Benzene 1e1g (xz), pyridine 1a2 , and pyrazine 1b1g orbitals areshown.

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Benzene
3e1u

0
ke2g

ka1g

ka2g

Pyridine
β (E)

1

6b2
0
kb2

ka1

Pyrazine
β (E)

1

4b2u

0
kag

kb3g

Pyrazine

5b1u(n)

β (E)

1

0

kb3g
kag

0

10

20

Photoelectron kinetic energy / eV
Figure 10 (left) Photoelectron-anisotropy parameter as a function of photoelectron kinetic
energy calculated for the orbitals, benzene 3e1u , pyridine 6b2 , and pyrazine 4b2u and 5b1u .
Experimental data are shown by open circles (153), filled circles (152), and diamonds (149).
Partial cross sections are plotted for benzene using green (ke2g , C = C∗ ), blue (ka1g , C-H∗ ),and red lines (ka2g , C = C∗ ), respectively. For pyridine and pyrazine, cyan lines indicate
partial cross sections for the waves correlated with the benzene ke2g (x2 − y2 ) and ka1g thatare no longer separable in lower symmetry. Orange lines are for the waves correlated with thebenzene ke2g (xy) and kag waves. (right) Isosurfaces of ionized molecular orbitals calculated
at the level of HF/4-31G.

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Bellm & Reid (154) observed the photoelectron anisotropy parameter that varies
with the PKE in nanosecond (1 + 1 ) REMPI of jet-cooled paradifluorobenzene via
the S1 (B2u ) state; β 20 /β 00 diminished from 0.5 to −0.2 within PKE < 1 eV. In 2005,
Bellm et al. (155) reported CMS-Xα calculations that qualitatively reproduced thegradual depression of the anisotropy parameter in the first 1 eV above the threshold. The energy dependence was attributed to a kb2g shape resonance centered at
PKE = 2 eV. The calculations predict that the anisotropy parameter increases
again in PKE > 3 eV, which, however, has not been experimentally confirmed. As
for the region of PKE < 1 eV, several notable disagreements remain between theexperiment and the theory. The observed PAD was insensitive to the alignmentin S1 , whereas calculations predicted an alignment dependence. Furthermore, theexperimental PADs best agreed with those predicted by CMS-Xα, when ionization
is assumed to occur from the maximally aligned ensemble of molecules in the S1state contradicting the experimental conditions when using nanosecond lasers. It
is also interesting that the observed photoelectron spectra exhibited no variation of
the vibrational structure with the excess energy, whereas shape resonances in othersystems normally provide it. These interesting features should be explored further
both experimentally and theoretically. Although Bellm et al. (155) have employeda time-of-flight photoelectron spectrometer, similar measurements could be carriedout more easily using a photoelectron imaging method.
Theoretical calculations of PAD using the random-phase approximation (156),
the Schwinger variational method (157), and the R-matrix method (158) are moreaccurate than using CMS-Xα. However, these methods are computationally demanding, and applications to large molecules are scarce (159). Time-dependent
density functional theory (160, 161) is a promising approaches to large systems.
Further development of theoretical methods sufficiently accurate for large polyatomic molecules, especially those to examine ionization from the excited states,
is of great importance for TRPEI.
Photoelectron-angular anisotropy in photodetachment of anions is generally
more easily interpreted than the neutral case. Sanov and coworkers (162, 163)
have studied energy dependence of photoelectron-angular anisotropy in photodetachment of solvated atomic anions. They analyzed the PAD using a Cooper-Zareformula (164, 165) analogously with the works on bare atomic anion (166, 167).
As the Coulomb phase shift is absent in photodetachment of anions, the phaseshift difference between the two partial waves is fixed over the excess energy. The
photoelectron anisotropy is influenced by the ratio of the two transition dipoles tothe l + 1 and l – 1 outgoing waves, and these tend to vary linearly with the excessenergy, as predicted by Wigner’s threshold law (168). The observed trend of β(E )was reproduced fairly well by the Cooper-Zare formula.

LONG-RANGE INTERACTION AND INTERFERENCE
Photodissociation of I−
2 has been studied in detail using TRPES (169, 170). Photoexcitation of I−
atapproximately
800 nm creates a wave packet on the dissociative
2
2
g,1/2 potential curve, which rapidly moves toward the asymptote of I (2 P3/2 ) and7 Mar 2006

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P1: KUVSUZUKII− (1 S0 ). The wave-packet motion from the molecular to the atomic region is almost
completed within the first 200 fs, which is represented by the PKED that narrows
down to an atomic line of I− . Within 300–600 fs, the wave packet travels through ashallow basin (0.0017 eV) due to the charge-induced dipole interactions between
I(2 P3/2 ) and I− , centered at an internuclear distance of 6.2 Å, which results in aslight reverse shift in the PKED. In the subsequent range of 600–3000 fs, the bondlength increases further from approximately 10 Å to 40 Å, during which no further
change in the PKED is discernible. In 2003, Davis et al. (171) reexamined this system by TRPEI using pump- and probe-laser wavelengths of 793 nm and 265 nm,
respectively, and found an interesting feature of PAD. The anisotropy parameterβ 2 initially decreased from approximately −0.1 near t = 0 to −0.55 near t = 200−
fs, as a result of the wave-packet motion from the molecular (I−2 ) to the atomic (I )region; however, the β 2 value increased to −0.44 near 580 fs and declined again
after 800 fs. Davis et al. (171) ascribed the increase of β 2 to the wave-packet motion
from the shallow basin, whereas they attributed the slight decrease after 800 fs tothe process in which an electron distribution changes from a delocalized one withthe same amplitude on each I atom to a localized one at an iodine atom due to thegerade/ungerade mixing between the 2 g,1/2 and 2 u+ state induced by hyperfine
coupling or an external field. In 2005, Mabbs et al. (172) repeated the same experiment with slightly different wavelengths of the pump (780 nm) and probe (390nm) lasers. They observed that the β 2 parameter varied from approximately −0.2
at t = 0 to −0.36 at 1.5 ps, and it increased to −0.17 at approximately 3 ps. Such avariation was not observed for IBr− , indicating that this phenomenon is related to
the nature of homonuclear diatomic molecules. Mabbs et al. (172) interpreted thetime dependence of β 2 as the interference in a photodetached electron from two
equivalent sites in the homonuclear diatomic molecule I−
2 . The difference in thetimescale of the variation in the β 2 parameter between Davis et al. and Mabbs et al.
was ascribed to the different de Broglie wavelengths of photoelectrons—10 Å in
the former and 35 Å in the latter. A quantitative analysis yielded the best agreementwith the experiment performed by Mabbs et al. when the de Broglie wavelength
was assumed to be 43 Å. Although further theoretical analysis seems necessary
for completely elucidating the physics behind time-dependent anisotropy, theseworks demonstrated that the PAD can serve as a sensitive probe for understanding
the dynamics in regions where the PKED no longer provides useful information.

TOWARD DYNAMICS IN THE CONDENSED PHASE
Liquid electron spectroscopy for chemical analysis pioneered by K. Siegbahn, H.
Siegbahn, and coworkers (173, 174) has been extended more recently by Faubel
et al. (175–181). Because the mean free path of an electron in the bulk is generally short, especially at low energies, photoelectron spectroscopy is essentially asurface-sensitive method. However, if nanoscale aggregates that mimic the bulk
properties are targeted, TRPEI in the gas phase may become a powerful tool in
disentangling complex dynamics in the condensed phase.

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In 2004, Neumark et al. (21, 22) applied TRPEI to large water-cluster anions.
The hydrated electron in the condensed phase is a trapped electron in the cavity
defined by six OH bonds in bulk water. Its property may be regarded as analogous
to a color center or a quantum dot in the solid phase; however, a hydrated electron
experiences a considerably more flexible environment. Consequently, photoexcitation of a hydrated electron from the ground-state s orbital to an excited p orbital
may induce reorganization of a solvation shell upon a sudden change of the electron cloud. Alternatively, it might lead to an ultrafast internal conversion down
to the s state as a result of a strong interaction between the p and s states. Thus,
photophysics of a hydrated electron has been controversial (182–188). Figure 11
shows the TRPEI of (D2 O)−
25 . A pump pulse at 1250 nm excites a hydrated electronfrom the s state to the p state, and the probe pulse at 400 nm detaches the electron.

Figure 11 Time-resolved photoelectron imaging of water cluster anions. (a) Photoelectron
image of (D2 O)−
25 collected at the 1250 nm + 400 nm pump-probe temporal overlap. Features
I and II arise from the two-color resonant and direct 400-nm photodetachment processes. (b)Time-resolved photoelectron spectra of (D2 O)−
25 . Features highlighted in part a are displayedwith the corresponding pump-probe delays. (c) Integrated intensities of features I and II
versus pulse delay (circles represent experiment; lines represent fit). The fit curves produce
a 398 ± 50-fs electronic lifetime for the excited cluster.

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Figure 11a is the photoelectron image observed at t = 0, in which a two-color
signal appears as a thin outermost ring denoted as I. The direct photodetachmentfrom the ground state by the probe pulse results in a broader distribution denoted
as II. Figure 11b shows the time evolution of the signals I and II that represent
the population in the p and s states, respectively. The integrated intensities of thefeatures I and II are also plotted (Figure 11c), in which the decay of the p state andthe recovery of the s state exhibit the identical time constant (21). When the time
constant measured for various cluster sizes were extrapolated to the bulk, it agreed
quite well with the time constant, approximately 50 fs, observed for the dynamics
immediately after the photoexcitation of a hydrated electron in bulk water. Paik
et al. (189) have drawn similar conclusions. Neumark and coworkers (22) have also
addressed whether an excess electron in the anion thus observed is indeed inside
the cluster or on the surface. They found one species with a long lifetime in the pstate and weak dependence of the vertical detachment energy on the cluster size
under the molecular beam conditions where the clusters have a low temperature.
Conversely, the conditions for higher temperatures provided another species withmuch shorter lifetimes and larger vertical detachment energies that varied morestrongly with the cluster size. The former species was assigned to a surface electron on an ice nanocrystal whereas the latter was assigned to the hydrated electronin the cluster. It was confirmed that their earlier TRPEI experiment was indeed
for an internal state, thereby strongly suggesting that the ultrafast dynamics in aphotoexcited hydrated electron in the p state is a direct internal conversion to thes state. Conversely, interpretation of the observed PADs has not been reported andit awaits future work.

BRIEF SUMMARY AND OUTLOOKThis review presents general aspects of TRPEI and time-dependent photoionization
DCSs in application to the studies of wave-packet dynamics, electronic dephasing, and photoionization dynamics. Molecular-axis alignment in perturbative andnonperturbative regimes is also described. Although discussion on ultrafast-laser
technology is omitted, it is essential for successful TRPEI experiments and coherent control. Whereas pyrazine and NO were the first systems studied by TRPEI
using a 10-Hz ultrafast-laser system in 1998 (17), extensive and efficient measurements for obtaining detailed information were made possible by a stable 1-kHz
laser system with optical parametric amplifiers to generate tunable pump- andprobe-laser pulses.
Future efforts include a better understanding of the ionization continuum forlarge polyatomic molecules that exhibit interesting photoinduced dynamics. For
quantitative analysis of time-dependent photoionization DCSs, development oftheoretical methods to calculate continuum wave functions of polyatomic molecules is crucial. Such theoretical efforts need assistance from detailed experimental studies on photoionization dynamics. Only a few experimental studies
have been conducted on molecular photoionization dynamics near the ionization

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583

threshold at the level of photoionization-dynamical parameters, and further studies
with TRPEI and other experimental methods are indispensable for elucidation ofionization dynamics. TRPEI experiments will be revolutionized by developmentof a particle detector that registers the arrival positions and arrival times for tens ofelectrons in a short response time. Creation of strongly aligned or oriented molecular ensemble will be useful for studying stereodynamics of photoinduced reactions
and photoionization, although the rotational degrees of freedom cannot always be
decoupled from vibronic dynamics. Sharpness will not be the most important characteristic of the axis distribution; the homogenuity and precise characterization of
the distrbution determine the quality of information extracted for photoionization.
Linear and nonlinear excitation processes of a molecule can create superpositionof multiple vibronic states with different rotational dynamics, which may create
interesting interferences in the TRPEI observables.
ACKNOWLEDGMENTS
Financial support from the Ministry of Education, Culture, Sports, Science, andTechnology of Japan and the Japan Science and Technology Agency are gratefully
acknowledged. I am indebted to M. Tsubouchi and Y. Suzuki for their contributions
to the experimental and theoretical studies on TRPEI at RIKEN.
The Annual Review of Physical Chemistry is online at
http://physchem.annualreviews.org
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AR272-FM

Annual Review of Physical Chemistry
Volume 57, 2006

CONTENTS
Annu. Rev. Phys. Chem. 2006.57:555-592. Downloaded from www.annualreviews.org
Access provided by Kyoto University - Multi-site on 11/17/15. For personal use only.

REFLECTIONS ON PHYSICAL CHEMISTRY: SCIENCE AND SCIENTISTS,
Joshua Jortner

1

ON A RESEARCH ROLLERCOASTER WITH FRIENDS,
Robin M. Hochstrasser

4D ULTRAFAST ELECTRON DIFFRACTION, CRYSTALLOGRAPHY,
AND MICROSCOPY, Ahmed H. Zewail
HETEROGENEOUS CHEMISTRY OF CARBON AEROSOLS,
Amanda M. Nienow and Jeffrey T. Roberts

PROGRESS IN THE THEORY OF MIXED QUANTUM-CLASSICALDYNAMICS, Raymond Kapral
STARK DECELERATION AND TRAPPING OF OH RADICALS,
Sebastiaan Y.T. van de Meerakker, Nicolas Vanhaecke,
and Gerard Meijer

37
65
105
129

159

ATMOSPHERIC FIELD MEASUREMENTS OF THE HYDROXYL RADICALUSING LASER-INDUCED FLUORESCENCE SPECTROSCOPY,
Dwayne E. Heard

EXCITONS IN CONJUGATED OLIGOMER AGGREGATES, FILMS,
AND CRYSTALS, Frank C. SpanoLASER PROBING OF SINGLE-AEROSOL DROPLET DYNAMICS,
Jonathan P. Reid and Laura Mitchem

191
217
245

CONNECTING CHEMICAL DYNAMICS IN GASES AND LIQUIDS,
Christopher G. Elles and F. Fleming Crim

NEAR-FIELD OPTICAL MICROSCOPY AND SPECTROSCOPY WITH
POINTED PROBES, Lukas Novotny and Stephan J. Stranick
ON THE NATURE OF IONS AT THE LIQUID WATER SURFACE,
Poul B. Petersen and Richard J. Saykally

CORRELATED ELECTRONIC STRUCTURE NONLINEAR RESPONSE
METHODS FOR STRUCTURED ENVIRONMENTS, Kurt V. Mikkelsen
COHERENT EXCITATION OF VIBRATIONAL MODES IN METALLIC
NANOPARTICLES, Gregory V. Hartland

273
303
333
365
403

ix

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CONTENTS

Annual Reviews

AR272-FMION PAIR DISSOCIATION: SPECTROSCOPY AND DYNAMICS,
Arthur G. Suits and John W. Hepburn

REACTIVITY OF THE GERMANIUM SURFACE: CHEMICAL PASSIVATION
AND FUNCTIONALIZATION, Paul W. Loscutoff and Stacey F. Bent
SCANNING TUNNELING MICROSCOPY MANIPULATION OF COMPLEXORGANIC MOLECULES ON SOLID SURFACES, Roberto Otero,Annu. Rev. Phys. Chem. 2006.57:555-592. Downloaded from www.annualreviews.org
Access provided by Kyoto University - Multi-site on 11/17/15. For personal use only.

Federico Rosei, and Flemming Besenbacher

RAMAN CRYSTALLOGRAPHY AND OTHER BIOCHEMICALAPPLICATIONS OF RAMAN MICROSCOPY, Paul R. Carey
FEMTOSECOND TIME-RESOLVED PHOTOELECTRON IMAGING,
Toshinori Suzuki

431
467

497
527
555

SINGLE-MOLECULE ELECTRICAL JUNCTIONS, Yoram Selzer
and David L. Allara

593

DYNAMICAL STUDIES OF THE OZONE ISOTOPE EFFECT: A STATUSREPORT, R. Schinke, S. Yu. Grebenshchikov, M.V. Ivanov,and P. Fleurat-Lessard

625

INDEXES
Subject Index
Cumulative Index of Contributing Authors, Volumes 53–57
Cumulative Index of Chapter Titles, Volumes 53–57

ERRATA
An online log of corrections to Annual Review of Physical Chemistry
chapters may be found at http://physchem.annualreviews.org/errata.shtml

663
683
685