5.61 Supplement to Lecture 32: Zewail Wavepacket Experiment

MASSACHUSETTS INSTITUTE OF TECHNOLOGY 5.61 Physical Chemistry I Professor Robert W. Field Supplement to Lecture 32: Zewail Wavepacket Experiment Suggested reading: Field pp 91-97. Ahmed Zewail was awarded the 1999 Nobel Prize in Chemistry for “Femtosecond Transition State (FTS) Spectroscopy.” These experiments were described as the first time that the mechanisms of real intramolecular dynamics were ”clocked” in real time. In a pump/probe scheme, a femtosecond pump pulse creates a wavepacket on a repulsive or predissociated electronically excited V1 potential energy surface at t = 0 by excitation from the v = 0 level of the electronic ground state, V0 (ability to tune center energy of wavepacket by a small amount). After each excitation pulse, the time-evolving wavepacket is probed by a femtosecond pulse with a chosen center wavelength at a time-delay t = τ . This delay time is scanned, pulse-by-pulse, to determine the time at which the center of the wavepacket crosses through the “Optically Coupled Region (OCR).” The probe pulse excites a portion of the wavepacket from the V1 potential surface to a higher energy repulsive potential surface, V2 . The V2 potential surface is repulsive, dissociating to an electronically excited fragment. The detected signal is the time-integrated ∼ 10 nanosecond lifetime fluorescence from this excited fragment. The dynamically relevant information is encoded in the intensity vs. τ of this time-integrated fluorescence, which samples the femtosecond passage of the wavepacket through the OCR that is selected by the center wavelength of the probe pulse. The ICN photodissociation experiment shows the effect of the presence of the I atom on the frequency of the CN B2 Σ+ − X 2 Σ+ electronic transition. As the I atom moves away from the CN molecule, the energy of the CN electronic excitation increases from its value in the ICN molecule to that of the free CN molecule. Did we know this before doing the experiment? As the ICN bond stretches, the electronic structure of the CN moiety changes. This is mechanism! The photodissociation of NaI is mediated by a covalent-to-ionic curve crossing. The diabatic (crossing) potential energy curves (solid lines) are the ones for which the electronic charac- 5.61 Lecture 32S Page 2 ter does not change rapidly as the molecule traverses the internuclear distance of the curve crossing. The adiabatic curves (dashed lines), which are what “clamped nuclei” quantum chemical calculations generate, exhibit a rapid change of electronic character at the internuclear distance of the avoided crossing. As the molecule moves through the curve-crossing region, it must decide whether it is going to follow the diabatic or the adiabatic potential. Landau-Zener theory tells us the velocity-dependence of the probability of jumping across the energy gap between the ionic and the covalent adiabatic curves. If you drive too fast, you will be unable to stay on the road on a sharp curve. The sharpness of the curve is determined by the magnitude of the interaction matrix element between the diabatic potential curves. A very gentle curvature is the signature of a very large interaction matrix element. In the Zewail experiments, the velocity in the curve-crossing region can be systematically slightly adjusted by the choice of the center wavelength of the pump pulse. At an NaI energy far above that of the curve-crossing, the velocity in the crossing region is very large and the molecule stays on one of the diabatic potentials, in effect jumping the gap between adiabatic curves. At an energy near that of the curve crossing, the molecule would go through the crossing region slowly and stay on one of the adiabatic curves, with the result that the wave packet that is born covalent, is nearly 100% converted to ionic at the internuclear distance of the crossing. Zewail’s NaI experiments provide a direct experimental determination of the internuclear distance of the curve crossing and an explicit illustration of Landau-Zener theory. 5.61 Lecture 32S Page 3 Rosker, Dantus, and Zewail: Femtosecond probing of reactions. I f the dynamics of the reaction as they occur, e well-defined zero-of-time. chnique was first applied I to the reaction of " CN]h_I + CN, (2) n studied previously" with subpicosecond or the formation offree CN fragments. More was applied to studies of alkali halide reacpping resonances of photofragments en route e observed. 2 •3 aper (I) of the series discusses the technique heoretically and experimentally, and illusprobe of reaction dynamics in real time. The the FTS technique to the reaction ICN sented in detail in the second paper (II). In om this laboratory, studies of FTS of alkali methyl iodide, and "oriented" bimolecular Internuclear Separation © American Institute of Physics. All rights reserved. ... X]t*_M + X, (3a) state, which has its minimum at R = Re' At time t = 0, a pump photon of A is for absorbed, as indicated by the verticaloftransition V" The Figure 1: Pump/Probewavelength Scheme Photodissociation ICN to (Figure 1 of Ref. 24). This is I internuclear separation increases as the system evolves on this repulsive po(3b) I]t*-CH3a+reduced I, dimension representation of three singlet potential energy surfaces of ICN: the bound ground tential. At time t = r, a pulse of wavelength At (or A '2) probes the vertical electronic state, V0 with minimum at ana higher excited state, V1 , which dissociates to CN(X2 Σ+ ) and e , to PES,unbound V2 • transition fromRV, 2 I( P3/2 ), and a higher energy unbound state, which dissociates to CN(B2 Σ+ ) and I(2 P3/2 ). A t = 0 pulse (3c)with center wavelength λ , excites a vertical turning-point-to-turning-point (P = 0, from the pump laser, 1 0 P1 = 0) transition at R = R0 > Re to the V1 potential surface. The wavepacket on the V1 potential d. whichpotential causes the PI-CN momentum to increase surface a force in the increasing RI-CN direction, is structured as follows: Sec.experiences II gives an overInitially, the molecule is in its lowest surface cept of FTS. The experimental method Vo. t This represents bound of the' monotonically withused time. At = τ ,surface, a pulsewhich from the probe the laser, withstate center wavelength λ?2 or λ2∞ probes ? ∞ on ofFTS is discussed III. InofSec. molecule, have a well-defined minimum, at an (ΔR=0) and momentumfor in theSec. arrival the IV, wavepacket at Rwill =R or R . The energy occurring of the vertical I-CN ental observations conserving are presented. Sectiontransition V equilibrium internuclear separation with Re. time as the wavepacket travels outward on (ΔP=0) also increases monotonically heory of FTS andVthe interpretation of reThe FTS experiment begins with ultrafast opticaltransition in the presence of an excitation of the CNan B−X electronic 1 . This V2 −V1 transition is essentially e will consider techniques by which the FTS pulse, with=wavelength A, I =A,pump, which initiates the is reacR? Optically Coupled Region (OCR) interrogated by a probe pulse the departing I atom. The R= RI-CN ∞ ∞ used to obtain the with potential energy surfaces λ? tion. As a rule, we take all times to be relative to the temporal center wavelength > λ , where λ is the wavelength of the free CN B−X v 0 = 0 − v 00 = 0 band. 2 2 2 midpoint of this pump pulse (the "zero-of-time"). The iniThe detected signal is CN B-X spontaneous fluorescence. Reproduced with permission from Figure 1 in Ra is defined as the distance tial A. internuclear M. J. Rosker, M. Dantus, and H. Zewail,separation “Femtosecond real-time probing ofbereactions. I. The technique,” tween the fragments at t = O. In general, Roi=Re, but OF FTS J. Chem. Phys. 89, 6113–6127 (1988). Copyright 1988, AIP Publishing LLC. the excursion of the molecule within the potential well typically mics of a dissociation reaction, like all reacwill not be great. ed by the PES. In this section, we introduce Absorption of a photon involves the instantaneous, verdiscussion of the dynamical motion of fragtical transition of the molecule from a lower lying PES (in propriate PES. We adopt a classical mechanthis case, Va) to an excited PES (here, VI)' The absorption but later (Sec. V), we will extend the discusof the photon is appreciable only if at Ro the difference in the e a quantum mechanical (wave packet) potentials of the two surfaces is nearly equal to the energy of ynamics. the pump photon, CH3 ••• tential energy surfaces al energy surfaces can be quite complicated, xample, van der Waals wells, avoided level resonances. We will initially assume, howPES's for the molecule being studied (say, icularly simple, as pictured in Fig. 1. Such t typical of many real molecules undergoing king, and have been invoked to describe thessociation. 12 We further assume that the only urational parameter is R, the internuclear he fragments in the center-of-mass frame. S's are taken to have no angular dependence, case for a diatomic molecule. In paper II, we nsequences of an angular dependence. VI (Ro) - Vo(Ro) -;::::,hclA, I • (4) The excited molecules prepared by the pump pulse at t = 0 will evolve for t> O. The subsequent time evolution of the system wave packet is entirely determined by the details of the excited-state PES. Classically, the molecule falls down VI' with R - 00 as t --+ 00. After the molecule is allowed to evolve for some time delay, t = T, it is irradiated by the second femtosecond (probe) pulse, with wavelength ,.1,2 A, probe • The probe pulse will only be absorbed if the configuration of the system at time T is appropriate for a vertical transition from VI to a highly excited PES, V2 • Those configurations which allow for absorption of the probe photon are called the optically coupled region (OCR) of the PES by the probe. The OCR will depend on: (1) the difference between = J. Chem. Phys., Vol. 89, No. 10,15 November 1988 5.61 Lecture 32S Page 4 FS p r o b e( t , λ) … ‡ …… ‡ NaI *[ Na I ]* [ Na I ]* t 0 t * Na+I+Etr t R + – I ONI CNa +I 35 FS p u mp( λ) 30 COVALENTNa+I 25 20 En e r g y( 1 0c m) 3 –1 15 10 5 0 4 0 02 © American Institute of Physics. All rights reserved. Rx=6 . 9 3 Å 5 10 R( Å) 15 Figure 2: Wavepacket Transit through an Ionic∼Covalent Potential Energy Curve Crossing in NaI (Figure 1 of Ref. 26). The diabatic (solid lines) Na+ ,I− and Na,I potential energy curves cross ˚ The avoided crossing between the adiabatic potential curves is shown as dashed lines. At at Rx = 6.93A. t = t0 the 310 nm pump pulse creates a wavepacket at the inner turning point of the covalent (Na 2 S, I2 P3/2 ) potential curve at R≈Re (X1 Σ+ ) and P= 0. By adjusting the center wavelength of the pump pulse, the center total-energy (electronic plus vibrational) of the wavepacket can be adjusted between 30,000 and 34,000 cm−1 . The excitation energy of the ionic∼covalent curve crossing is ∼ 26, 000 cm−1 . The wavepacket is accelerated outward, passes through the curve-crossing region at t? , and bifurcates, one part traveling on the bound ionic potential and the other part traveling irreversibly outward on the unbound covalent potential. The ionic part is reflected at tR at the outer turning point of the ionic potential, passes with P< 0 through the R= 6.93 Å curve crossing region where it bifurcates again, and the resultant ionic and covalent parts are reflected outward at the inner turning points of the ionic and covalent potential curves, respectively. Each outward passage of a wavepacket through the curve crossing region results in a wavepacket traveling irreversibly outward on the unbound covalent potential, eventually forming free Na(2 S) and I(2 P3/2 ) atoms. The probe pulse (not shown) interrogates the dynamics by exciting Na(2 S),I(2 P3/2 ) weakly-bound molecules to a higher energy repulsive electronic state that dissociates to Na(2 P) + I(2 P3/2 ) atoms. Excitation at centerwavelength longer than 589 nm samples NaI molecules en route to full dissociation. Excitation centered at 589 nm provides what is essentially a time-integrated sample of the accumulation of the free Na(2 S) atoms. Reproduced with permission from Figure 1 in T. S. Rose, M. J. Rosker, and A. H. Zewail, “Femtosecond real-time observations of wave packet oscillations (resonance) in dissociation reactions,” J. Chem. Phys. 88, 6672–6673 (1988). Copyright 1988, AIP Publishing LLC. 5.61 Lecture 32S Page 5 I I I I I © American Institute of Physics. All rights reserved. ∆t( f s ) 5 0 0f s Figure 3: Clocking of the Photodissociation of NaI (and NaBr) as the Nuclear Wavepacket Repeatedly Traverses the Ionic/Covalent Curve Crossing (Figure 2 of Ref. 26). The wavepacket, illustrated in Fig. 6.5, is created at t = t0 at the inner turning point on the covalent excited electronic state. At each outward-bound traversal of the curve-crossing region, part of the wavepacket follows the covalent adiabatic curve irreversibly outward to separated Na(2 S)+I(2 P3/2 ) atoms. If the probe laser centerwavelength is tuned slightly to the red of the 589 nm free Na atom 2 P←2 S transition, each time a wavepacket of incompletely separated Na,I molecules passes through the Optically Coupled Region, some not quite free Na atoms are excited to the 2 P state, from which spontaneous fluorescence is detected. The series of Na atom fluorescence pulses shown in Spectrum I samples each outward passage of a wavepacket through the curve-crossing region. The temporal spacing of the pulses corresponds to a 36 cm−1 vibrational frequency. When the center-wavelength of the probe laser is tuned to 589 nm, the arrivals of free Na atom wavepackets are displayed in Spectrum II as a periodic series of upward steps. Spectrum III shows that the (upper) adiabatic potential curve for NaBr is shallower and “leakier” than that for NaI. Reproduced with permission from Figure 2 in T. S. Rose, M. J. Rosker, and A. H. Zewail, “Femtosecond real-time observations of wave packet oscillations (resonance) in dissociation reactions,” J. Chem. Phys. 88, 6672–6673 (1988). Copyright 1988, AIP Publishing LLC. 5.61 Lecture 32S Page 6 Landau-Zener References R. K. Preston, C. Sloane, and W. H. Miller, J. Chem. Phys. 60, 4961 (1974). G. C. Schatz and M. A. Ratner, Quantum Mechanics in Chemistry, Dover, 2002 (page 76). H. Lefebvre-Brion and R. W. Field, Spectra and Dynamics of Diatomic Molecules, pp. 510514 and 536 (Landau-Zener) and pp. 163-177 (Diabatic vs. Adiabatic).