Pump-Probe Photoionization Study of the Passage and Bifurcation of a Quantum Wave Packet Across an Avoided Crossing

Abstract

The application of femtosecond pump-probe photoelectron spectroscopy to directly observe vibrational wave packets passing through an avoided crossing is investigated using quantum wave packet dynamics calculations. Transfer of the vibrational wave packet between diabatic electronic surfaces, bifurcation of the wave packet, and wave packet construction via nonadiabatic mixing are shown to be observable as time-dependent splittings of peaks in the photoelectron spectra. DOI: 10.1103/PhysRevLett.90.248303 PACS numbers: 82.20.Gk, 33.60.-q, 82.53.Eb, 82.53.Kp The concept of nonadiabatic transitions is fundamental to an understanding of chemical phenomena [1,2]. A typical example, and the one of interest here, is intramolecular electron transfer induced by vibrational motion in the excited state of alkali halides such as the NaI molecule. Pump-probe studies of this system have demonstrated the decrease of wave packet population on the excited adiabatic surface due to dissociation at the avoided crossing [3,4]. Oscillations in the population of the dissociative products (Na and I) due to the interference of wave packets on the covalent and ionic potentials merging at the avoided crossing have also been observed [3]. Although bifurcation of wave packets must be invoked to explain these observations, no real-time evidence of the instance of wave packet bifurcation has yet been experimentally observed. Such direct observation, if possible, would be interesting in itself, but also quite significant to studies of electron transfer, wave packet engineering, and reaction control through wave packet splitting and mixing. Also, from the perspective of quantum measurement, wave packet bifurcation corresponding to an intramolecular double-slit experiment will shed light on the evolution of quantum entanglement between electronic and nuclear motion [5]. Bifurcation and merging of wave packets are important as an intrinsic mechanism of ''quantum chaos,'' which has no simple classical counterpart [6 -8].Pump-probe photoelectron spectroscopy has been demonstrated to be a powerful means to monitor real-time reaction dynamics [9][10][11][12][13][14]. We here show theoretically that the method permits real-time observations of a wave packet passing through an avoided crossing, using excited-state dynamics of NaI as an example.The pump-probe spectroscopy of NaI has been studied extensively [3,4,[15][16][17][18][19][20][21]. Figure 1 depicts the pump-probe scheme and the relevant potential curves for femtosecond photoelectron spectroscopy of the excited-state wave packet dynamics. The adiabatic excited state features an extended well whose character changes from covalent at shorter distances to ionic at larger distances due to an avoided crossing with the ground state at 7 A [22,23]. In the diabatic representation, the same system is viewed as an ionic curve (here called V 1 ) intersecting a covalent curve (V 2 ), with an associated nonadiabatic interaction (V 12 ). The diabatic curves are shown in Fig. 1.The excited-state wave packet...

Applied Bohmian mechanics

“…Multiconfiguration schemes, such as Tully's surface hopping, are in general required to account for bifurcation paths with entaglement [45,46]. Although the undeniable success of these mixed approaches to describe many nonadiabatic phenomena, some limitations arise when quantum nuclear effects such as tunneling [47], decoherence [48] or interferences [49] occur. Only the so-called quantum wave packet methods [50][51][52] provide a complete description of nuclear quantum effects, although their computational cost becomes rapidly unaffordable with the size of the system.…”

Time-resolved photoelectron spectroscopy of wavepackets through a conical intersection in NO2

“…We also report the photoelectron angular distributions for these timeresolved spectra. We have previously demonstrated the utility of such time-resolved photoelectron angular distributions and the need to incorporate geometry-and energy-dependent photoionization matrix elements in studies of time-resolved photoelectron spectra in a series of papers tracking funda-mental wavepacket dynamics in different scenarios: vibrational motion across a one-dimensional double-well potential in an excited state of Na 2 , [24][25][26][27][28] wavepacket bifurcation at an avoided crossing in NaI, 29,30 and proton transfer in the ground state of chloromalonaldehyde. [31][32][33] The scheme for our studies of the pump-probe photoelectron spectra in NO 2 is illustrated in Fig.…”

Monitoring the effect of a control pulse on a conical intersection by time-resolved photoelectron spectroscopy

“…Our formulation of time-resolved pump-probe photoelectron spectroscopy has been fully discussed in earlier papers 24,28 and here we present just a brief outline with emphasis on the use of geometry-and energy-dependent photoionization matrix elements. The wavefunction of the total system, C(r,R,t), is expanded in the electronic wavefunctions relevant to the pump-probe arrangement,…”

“…In fact, internal conversion in polyatomic molecules was among the earliest suggested application of this technique, 21 which was subsequently realized experimentally. 22 We have also previously demonstrated the utility of time-resolved photoelectron spectra, along with the need to incorporate geometry-and energy-dependent photoionization matrix elements in such studies, in a series of papers tracking wavepacket dynamics in different scenarios: vibrational motion across a one-dimensional double-well potential in an excited state of Na 2 , [23][24][25][26][27] wavepacket bifurcation at an avoided crossing in NaI, 28,29 and proton transfer in the ground state of chloromalonaldehyde. [30][31][32] Anticipating that advances in ultrashort pulse shaping technology may also well enable the observation of wavepacket dynamics through a CI on the actual time scale of the nonadiabatic transition, we recently studied the photoelectron energy and angular distributions expected in and around the CI between the lowest 2 A 0 states of the NO 2 molecule 33,34 and showed that the photoelectron signals, particularly the angular distributions, provide a valuable window on wavepacket dynamics there.…”