J. Phys. Chem. A 2010, 114, 11337–11346
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Theoretical Investigations of the Time-Resolved Photodissociation Dynamics of IBr-† Samantha Horvath, Russell M. Pitzer, and Anne B. McCoy* Department of Chemistry, The Ohio State UniVersity, Columbus, Ohio 43210 ReceiVed: June 4, 2010; ReVised Manuscript ReceiVed: July 20, 2010
The role of laser pulse width as well as other quantum mechanical effects in the interpretation of the observed time-resolved photoelectron spectra (TRPES) of IBr- are investigated using conditions that are chosen to reproduce those used for the experimental study of Mabbs et al. [J. Chem. Phys. 2005, 122, 174305]. In that study, it was shown that one could correlate shifts in the frequency of the maximum in signal as a function of time to differences between the potential energies of the electronic states that are accessed by the pump and probe lasers. While this classical picture is attractive, it is based on a single trajectory with an initial I-Br separation that is ∼0.3 Å longer than the equilibrium value. In addition, it does not include the role of the pulse widths and other possible quantum effects. In the present work, the six lowest energy electronic states of IBr- were calculated at the MR-SO-CISD/aug-cc-pVDZ level of theory/basis set as a function of the I-Br distance. The TRPES of IBr- were calculated in three pulse regimes: an infinitesimally short pulse, an intermediate pulse that has a temporal full width at half-maximum (fwhm) of 300 fs, which was chosen to match the experimental value, and one that is 3 times longer than the experimental value. The resulting spectra are qualitatively different, and the sources of these differences are discussed. The intermediate pulse provides very good agreement with experiment with the introduction of no adjustable parameters. The origins of the features of the experimental signal are discussed in terms of this fully quantum mechanical picture. 1. Introduction One central goal of molecular spectroscopy has been to probe the potential energy surfaces underlying molecular transitions while a second has been to use this knowledge to explore the dynamics that takes place on these surfaces. An area where there has been much recent work is the photoinduced dissociation of homonuclear and heteronuclear dihalide anions (X2- and XY-), both in isolation and in the presence of a small number of solvating atoms or molecules.1-8 From an experimental standpoint, X2- and XY- molecules have low-lying excited electronic states, accessible by visible or near UV light. Additionally, the high electron affinities of their neutral counterparts and large polarizabilities allow for attachment of excess electrons via standard experimental methods, which in turn enables the use of time-of-flight mass spectrometry techniques in the study of size-selected clusters that incorporate these species. From a theoretical point of view, X2- and XY- species are small enough that high level ab initio calculations can be performed, and in many cases, high level calculations are necessary given the degree of coupling between electronic states and strength of the spin-orbit coupling. In these systems it is also possible to perform full quantum dynamics. Despite the fact that these systems are small, they continue to prove challenging given the density and coupling of the electronic states. Moreover, they provide a testing ground for understanding chemical physics phenomena more generally. For example, several studies have utilized the I2, Br2, or IBr chromophore to probe energy and charge transfer, vibrational dynamics, and predissociation in rare gas matrices and gas-phase clusters.1,5,7-16 The focus of the present study is on the time-resolved photoelectron spectroscopy (TRPES) of IBr-, specifically the work reported by Sanov and co-workers.17 In these experiments, an equilibrium ensemble of anions is generated at a temperature †
Part of the “Klaus Mu¨ller-Dethlefs Festschrift”.
Figure 1. Pump-probe excitation scheme utilized in the experiment modeled here.
of ∼100 K.18,19 The system is then photoexcited (or “pumped”) to a higher-lying excited electronic state of the anion. In the case of this work, the system undergoes a transition to the A′ state, which corresponds to a promotion of an electron from the antibonding π* molecular orbital to the σ* orbital. After a delay time of up to several hundred femtoseconds (∆t), an electron is detached from IBr- with a second “probe” laser pulse. The velocity and angular distribution of the ejected electrons are recorded, and these data are analyzed. In Figure 1 we illustrate the pump-probe excitation scheme utilized in these experiments while Figure 2 provides the resulting spectra, plotted as a function of pump-probe delay time.17 Related studies have been performed on complexes of IBr- with a single CO2 molecule by Lineberger and co-workers.8
10.1021/jp1051529 2010 American Chemical Society Published on Web 08/16/2010
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Horvath et al. mally short pulse that places no constraints on the excitation energy, a pulse with a temporal width that is the same as that used in the experiment,17 and a pulse that has a duration 3 times longer than experiment and consequently will excite into states over a much narrower energy range. The remainder of this paper is organized as follows. We begin by presenting our theoretical methods, which are based on the previous theoretical work on the photoinduced dissociation of I2- by Miller and co-workers,20 and then discuss our findings and relate them to the proposed mechanism of Sanov and coworkers.17 2. Theory
Figure 2. Experimental signal for the time-resolved photoelectron spectra of IBr- for different pump-probe delay time slices.17
In the study on the photodissociation of IBr- performed by Sanov and co-workers,17 the resulting signal (shown in Figure 2) was analyzed using a classical picture. Specifically, examination of the photoelectron signal at each time delay shows that there is a time dependence to the shape of the spectral contour as well as the energy that corresponds to the maximum in the signal. At short delay times the distribution is broad, and the signal is low at all energies. After ∼300 fs, a peak is observed at ∼0.08 eV. The position of the maximum of this peak remains at a nearly constant energy for several hundred femtoseconds before shifting to its asymptotic value of ∼0.12 eV after 1.2 ps. The shift in the position of the peak was related to the difference between the potential energy of the A′ state on which the dynamics occurs and the IBr potential energy surfaces to which the system is excited by the probe laser. These differences were related to the delay time by propagating a trajectory on the A′ surface and evaluating the difference between the potential energies as a function of R(∆t). While the agreement was generally good, it was achieved by assuming an initial I-Br separation of 3.30 Å, which is quite a bit longer than the measured equilibrium bond length of 3.01 Å.19 It is also surprising that graphs of the position of the maximum in the signal, plotted as a function of time, show a rise starting at ∼250 fs. This contrasts with the picture that would be anticipated by taking the difference between the potentials plotted in Figure 1 in which there would be a decrease in the energy of the maximum in the signal at shorter times, followed by an increase at longer times. In the present study, we take the analysis of this experiment, as well as TRPES studies more generally, one step further and focus on what effects the quantum nature of the wave packet has on the dynamics of the system. We focus on how the classical picture, described above, should be modified to account for the fact that the experiments employ lasers with finite temporal widths and consequently sample finite energy ranges. Finally, since the electronic structure of the states that are represented by these curves changes as the molecule or molecular ion dissociates, we ask if it is necessary to account for the changes in the excitation cross sections to describe the dynamics of these processes, as they are reflected in the reported spectra. In this work, we address this question by investigating how the temporal pulse width affects the TRPES signal. Specifically, we address three temporal pulse width regimes: an infinitesi-
In the present theoretical study, we model the time-resolved photodissociation experiment of IBr- by Sanov and co-workers.17 While the complete details of the experimental study are provided in ref 17, the information relevant to the present study is reported here. IBr- ions are prepared in their ground electronic state whereupon they undergo a π* f σ* photoinduced excitation to the A′ electronic state (2Π1/2) by a pump pulse with a wavelength of 780 nm (1.59 eV). This excited wave packet then evolves on the A′ surface for a length of time (∆t) before an electron is detached by a time-delayed probe pulse with a wavelength of 390 nm (3.18 eV) and most likely dissociating on the C (1Π1) and A (3Π1) states of IBr. The photoelectron spectra were collected for pump-probe delay times of approximately 50-1350 fs. The functional forms of the pulses are assumed to be Gaussian with an estimated full width at halfmaximum (fwhm) of 300 fs.17,18 Our approach is based on electronic structure and vibrational energy calculations as well as on full quantum dynamics. Multireference configuration interaction calculations that include spin-orbit terms were used to obtain the six lowest energy electronic states of the anion, and a sinc-discrete variable representation (DVR)21,22 was used to obtain the vibrational eigenstates associated with the electronic states of IBr- and IBr. 2.1. Potential Energy Surfaces. We perform ab initio calculations to obtain the electronic states of the anion using the electronic structure program package COLUMBUS.23-26 The anion surfaces were calculated as a function of the I-Br distance, R, at 29 points between 3.5 and 25.0 a0, and a list of the absolute electronic energies as a function of R can be found in the Supporting Information. These surfaces were calculated using multireference configuration interaction with single and double excitations, and spin-orbit coupling was included (MRSO-CISD).27 We employ aug-cc-pVDZ basis sets28 and relativistic core potentials (RECPs) for the atoms,29,30 where iodine has a [Kr]-like core and bromine an [Ar]-like core. The molecular orbitals (MOs) used in the MRCI calculations were determined from a multiconfiguration self-consistent field (MCSCF) calculation that optimized the averaged energy of all states obtained from placing 11 valence electrons in the six valence MOs: σ, π, π*, and σ*. All MOs were optimized. As a result six reference states were obtained. All single and double excitations out of the eight valence orbitals in these six reference states were then performed, with the MOs that correspond to the d-atomic orbitals being frozen. These calculations made use of the C*2V double group, but the CI wave functions retained their C*∞V double group symmetries. The functional forms of the potential energy surfaces for the neutral IBr electronic states were obtained from a study by Ashfold and co-workers.31 In the experiment on IBr, the energies of the electronic states are reported relative to the dissociation energy of IBr, which is set to zero. Therefore, to ensure that
Photodissociation Dynamics of IBr-
J. Phys. Chem. A, Vol. 114, No. 42, 2010 11339 (35, 55, and 75 a0) and the number of grid points (2400), and these parameters do not impact the calculated spectra. 2.3. Time-Dependent Calculations. In this study, we assume a vibrational temperature of 75 K.17-19 At this temperature, the first four vibrational states of the ground electronic state account for 99.99% of the total vibrational population with over 90% attributed to V ) 0. Each of the thermally populated Xvibrational states are propagated on the A′ excited potential surface by treating the evolving wave packet as a linear superposition of A′ vibrational states:
ψ(R,∆t) )
∑ cme-(i/p)E ∆tφm(R)
(4)
m
m
Figure 3. Electronic states of IBr- and IBr.31 The bold, black lines represent the four states relevant to the dissociation dynamics of IBr-: X and A′ states of IBr- and C and A states of IBr. Other states of IBrand IBr are plotted in red and blue lines, respectively.
the electronic states of IBr- and IBr are on the same energy scale, the energies of the neutral electronic states were shifted by the electron affinity of iodine, ∼3.06 eV.32 The relevant electronic states of IBr- and IBr are shown in Figure 3. 2.2. DVR Calculations. One-dimensional variational calculations were carried out in a discrete variable representation (DVR)21,22 for the four electronic states of interest: the X and A′ states of IBr- and the C and A states of IBr. For the I-Br distance coordinate, R, the associated mass is the reduced mass (µ) of I79Br. The Hamiltonian for this system is given by
Overlaps between the wave packet and eigenstates of the neutral surface are then evaluated. The results of this treatment will be presented as the infinitesimally short pulse. It should be noted that there is no discrimination of accessible energies in this treatment, as will be discussed in more detail below. To account for the fact that the laser pulses have a finite time duration, and hence a finite spectral range, we follow an approach that is based on the study of I2- photodissociation by Zanni et al. and Batista et al.5,20 To aid in the description of the method presented here, the following two equations are identical to eqs 2.5 and 2.11 from ref 20. The probability distribution of electron kinetic energies, P(), in the long time limit is given by
P() )
∑ ∫ dE
K
K
|( ) ∫ -
i p
∞
-∞
dt
∫
t
-∞
dt′ (µK,A′ · ε(t)) × ˆ
(µA′,g · ε(t′))e(i/p)(EK+)te-(i/p)Egt′〈χEK |e-(i/p)HA′(t-t′) |χg〉 2 2 ˆ ) - p d + V(R) H 2µ dR2
B R6
(2)
where A and B are determined from the values of the potential energy at the two data points with the largest values of R. When R is smaller than the smallest available point, the potential is extrapolated using
Vsr(R) ) C exp(-γR)
2
(5)
(1)
The potential surfaces, V(R), were acquired from spline interpolations of the energies obtained from either the electronic structure calculations or from the experimental potential fit parameters31 described above. The grid points used for the DVR calculations ranged from 1 to 95 a0 with a grid spacing of 0.0294 a0 (3200 points). This grid extends over a range of R larger than that over which the potentials have been evaluated. For points at bond lengths longer than the largest available point, we extrapolate the potential using
Vlr(R) ) A -
|
(3)
and C and γ are determined from the values of the potential energy at the two data points with the smallest values of R. In using DVR basis functions, we are approximating the continuum states; however, we have varied the DVR grid length
Here P() is the sum of the manifold of IBr electronic states (K) that can be accessed upon photodetachment of the electron. The electronic transition moments, µi,j, are treated within the Condon approximation and are therefore assumed to be independent of the nuclear coordinates and the kinetic energy of the detached electron.20 The time-dependent electric field, ε(t), is given by
ε(t) ) ε01F1(t)e-iω1t + ε02F2(t - ∆t)e-iω2(t-∆t) + c.c.
(6) and is the sum of the pump and probe pulses with functional forms F1(t) and F2(t - ∆t) and characteristic frequencies ω1 and ω2, respectively. The matrix element in eq 5 accounts for the photodissociation dynamics in that the Boltzmann-populated vibrational state of the ground electronic state, |χg〉, is propagated on the excited potential surface of the anion (A′), before being projected onto eigenstates of the neutral excited electronic state, |χEK〉.20 We can obtain an expression for the photoelectron signal that depends on the pump-probe delay time (∆t) and on the electron kinetic energy () by substituting eq 6 into eq 5. We can then simplify the resulting expression by inserting the identity operator (Iˆ ) ∑m|φm〉〈φm|) twice, once on either side of ˆ A′. Making these substitutions, the exponential term containing H matrix element presented in eq 5 becomes
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∑ 〈χE |φm'〉〈φm'|e-(i/p)H (t-t')|φm〉〈φm|χg〉 ˆ A'
K
m,m'
Horvath et al.
(7)
In eq 5, there is a sum over all neutral electronic states that are accessible upon photodetachment. However, to our knowledge, the electron detachment cross sections that describe the electronic transition between the A′ state of IBr- and electronic states of IBr have not been reported. Therefore, we remove the dependence of the calculated spectra on these parameters by evaluating the dynamics that results from excitation to each of the two neutral surfaces independently. These changes make K ) 1 and |χEK〉 ) |χn〉 in eq 5, where n is the manifold of vibrational eigenstates of one of the IBr excited electronic states. The final expression for the time-resolved photoelectron signal, P(,∆t), is given by P(,∆t) ) p-4
∑ | ∑ c 〈χ |φ 〉 ∫ m
n
n
m
∞
-∞
dt F2(t - ∆t)e[i/p(En+-Eprobe-Em)t] ×
m
∫
t
-∞
dt' F1(t')e[i/p(Em-Eg-Epump)t']
|
computationally efficient to implement. Specifically, eq 8 can be rewritten by rearranging the summations to give
P(,∆t) ) p-4
∑ | ∫-∞ dt F2(t - ∆t)e[i/p(E +-E ∞
n
n
[
∑ cm〈χn|φm〉e-i/p(E t) ∫-∞ dt' F1(t')e[i/p(E -E -E m
t
m
g
ξn ) (Eg + Epump + Eprobe) - En - Eshift
(11) Because the integral over t′ is independent of , ∆t, and n, it may be evaluated for all needed values of m and t and then used in the summation over m to obtain a quantity that now depends on n and t. The resulting expression is used in the integral over t and summation over n. This provides the value of P(,∆t) for each of the desired values of and ∆t. As a way to further understand how pulse width may impact the photoelectron signal, we examine how the wave packet is dressed by the pump pulse and define the quantity
Ξd(R,∆t) )
(8)
(9)
where Eg is the energy of the Boltzmann-populated vibrational state of the X potential surface, En is the energy of the vibrational state of a given IBr surface, and Eshift ) 0.048 eV. The spectra calculated using the short pulse were discretized into a series of ∆t cuts and normalized such that the integrated signal of the time slice ∆t ) 800 fs is unity. 1. Finite Pulse Widths. For the examination of the timeresolved photoelectron spectra as calculated using pulses with finite widths, we utilized the following functional form for the laser pulses
t fδj
]|
2
2
ˆ A′|φm〉 ) Em|φm〉. Epump represents the where cm ) 〈φm|χg〉 and H energy of the pump pulse and is equal to pω1 with a value of 1.589 55 eV. For the probe pulse, Eprobe ) pω2 and has a value of 3.179 11 eV.17,20 As noted above for the infinitesimally short pulse, the electron kinetic energy () is not well-defined because there is no central frequency. To facilitate comparisons with the results of calculations that model the use of laser pulses with finite pulse durations, we define the energy value, ξn, which is shifted to ensure that the maximum in the signal at long times is at the same energy as that obtained from the calculations that employed pulses with finite width. Thus, ξn is defined as
( )
pump)t']
m
| ∑ cle-i/p(E ∆t)φl(R) ∫-∞ dt' F1(t')e[i/p(E -E -E l
∆t
l
g
pump)t']
l
Fj(t) ) sech2
×
probe)t]
(10)
where δj is the fwhm and has a value of either 300 or 900 fs, and cosh[1/(2f)] ) 2. While we follow the derivation discussed in ref 20 for the work presented here, our expressions for Fj(t) and f differ slightly from those noted in ref 20 due to inconsistencies between these definitions in ref 20. The intermediate pulse, δj ) 300 fs, has the same fwhm as that determined in the experiment. While eq 8 follows from the derivation presented in ref 20, there is an alternate form for eq 8 that we found to be more
|
2
(12)
The definition for Ξd(R,∆t) is the expression for P(,∆t) when F2(t - ∆t) ) δ(t - ∆t) projected onto R. We can obtain a related quantity by multiplying the term that is squared in eq 12 by φm(R) and integrating over R:
|
Ξe(m,∆t) ) cme-i/p(Em∆t)
∫-∞∆t dt' F1(t')e[i/p(E -E -E m
g
pump)t']
|
2
(13)
The corresponding quantity of Ξe(m,∆t) for the wave packet prepared by the infinitesimally short pulse is straightforward to obtain as this quantity is independent of time and is simply cm2 from eq 4. 2. Numerical Details. For the study presented here, the timeresolved photoelectron signal of IBr- was calculated over a range of electron kinetic energies from 0.00 to 0.31 eV in increments of 0.01 eV and over a range of pump-probe delay times from 0 to 1350 fs in increments of 10 fs. The time step for the numerical integration is 1.0 fs for the long pulse (δj ) 900 fs) and 0.2 fs for the intermediate pulse (δj ) 300 fs). The integral over t is defined for -14 000 fs e t e +14 000 fs and for -5000 fs e t e +5000 fs for the 900 and 300 fs pulses, respectively. These time steps and ranges of t were chosen to ensure that all of the oscillations in the integrands in eq 11 were captured within the envelope of Fj(t), and the value of Fj(t) was vanishingly small outside these ranges. The spectra calculated with the finite pulse widths were normalized in two ways. First, the spectra were normalized such that the integrated signal for the ∆t ) 800 fs time slice is unity. Second, to aid in comparison with experiment, the spectra were discretized into a series of slices in ∆t, convoluted with a Gaussian with a hwhm of 15 meV, and normalized such that the integrated area of each time slice is unity. The spectra were convoluted to account for several sources of broadening in the experiment that were not included in the calculations. Most notable of these are the effects of velocity spread in the molecular beam, the fact that the laser pulses are not Fouriertransform limited, and the energy resolution of the detector.18,33-35
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TABLE 1: Calculated and Derived Parameters from the Electronic Structure Calculations of the Six IBr- Electronic States in Order of Increasing Energya state
label
Re (Å)b
X A A′ a a′ B
2 + Σ1/2 2 Π3/2 2 Π1/2 2 Π3/2 2 Π1/2 2 + Σ1/2
3.105 4.071 5.131 5.172 4.897 4.943
De (eV)b,c 0.8586 0.0397 0.0450 0.0015 0.0264 0.0401
SO splitting of I: 0.9327 eV SO splitting of Br: 0.4676 eV ∆EA of I and Br: 0.3352 eV a Relevant electronic properties, such as spin-orbit (SO) splittings and differences in electron affinities (∆EA), are given as well. Re is the equilibrium bond length and De is the dissociation energy, calculated as the difference between the interpolated potential energies at 25 a0 and Re. b Obtained from a cubic spline interpolation of the ab initio points. c De obtained using V(R ) 95 a0) differs from the listed value by 500 fs. The shift in the photoelectron signal with time is also present in the A state dynamics, but it is much less pronounced. Overall, the agreement between calculation and experiment is very good, and we obtain this level of agreement without introducing any adjustable parameters. There are small quantitative differences between the calculated and experimental spectra, which could be due to the fact that the C and A state dynamics are calculated separately whereas the experiment samples both of those surfaces as well as others, including the Y state. In the absence of detachment cross sections, we were not able to fully model the spectra. However, the fact that the calculated spectra for the C and A states each exhibit many of the features in the experimental spectra gives us confidence as we move to addressing the origin of these features. 3.3. Photodissociation Dynamics of IBr-. As we begin our discussion of the origins of the spectral features observed in the experiment, we revisit the classical model discussed above and investigate how we would expect the spectra to look if we assume that the signal is a convolution of the energy differences between the A′ potential of IBr- and IBr neutral C and A state surfaces with the evolving wave packet (∆E(R) from eq 14). Figure 5a shows the value of eKE when the photoelectron signal is at a maximum for each measured (blue circles) and calculated C state (black curve) and A state (red curve) time slice. For Figure 5a, the first point plotted for the experimental results is for 200 fs. While the data were recorded for earlier times, there are low signal-to-noise ratios in the experiment,18 as evidenced by the spectra plotted in Figure 2, making identification of the maximum in the signal difficult. In Figure 5a, we can more clearly see the shift in the maximum of the eKE distribution with time as compared to
Photodissociation Dynamics of IBr-
Figure 5. Illustration of estimated electron kinetic energy available to the system and that obtained from solving eq 8 with a pulse width of 300 fs and from the experiment:17 (a) value of the electron kinetic energy (eKE) that corresponds to the maximum in the signal for a given ∆t time slice; (b) value of the average ∆E(∆t) (defined as ∆E(R) over |ψ(R,∆t)|2 from eqs 14 and 4, respectively) with error bars providing the width of the distribution. In (a) and (b) the black curves correspond to C state dynamics; red, A state dynamics; and the blue, open points correspond to the experimental data. Note that in (b) only every fifth point is shown for clarity.
the results in Figure 4. In Figure 5b we show the time-dependent average of ∆E(R), 〈∆E(∆t)〉, where the average is over |ψ(R,∆t)|2 as defined in eq 4. The error bars in Figure 5b provide the width of the distribution. An important feature of Figure 5b is that at long delay times, ∆t > 500 fs, 〈∆E(∆t)〉 values for the C and A states are nearly identical. This delay time corresponds to an I-Br distance of ∼8 Å, indicating the asymptotic region of the potential where the C and A states are isoenergetic. This is also the approximate time after which the calculated and experimental maxima in eKE are the same in Figure 5a. A second important feature of Figure 5b is the range of ∆E(R) sampled by the wave packet over time. For delay times up to 300 fs, the range of 〈∆E(∆t)〉 is inconsistent with the experimental signal in Figure 5a. Specifically, due to conservation of energy, energies above ∼0.12 eV will not be accessible in the experiment. However, all energies below ∼0.12 eV should be energetically accessible by the pump and probe lasers used in the experiment. Comparison of the energies of the maxima in the experimental and calculated peaks in Figure 5a to 〈∆E(∆t)〉 in Figure 5b shows large deviations for times smaller than ∼300 fs. This difference leads us to conclude that some of the short time features of the spectra involve processes that are not accounted for by the classical model. Before looking for this, we examine what one would have to do from an experimental standpoint to obtain spectra that follow the curves plotted in Figure 5b. Such a picture implies instantaneous excitation and does not include pulse information; this would be akin to using an infinitesimally short pulse in the experiment. The
J. Phys. Chem. A, Vol. 114, No. 42, 2010 11343 results of such a treatment are presented in Figure 6a,d. We also overlay the curves from Figure 5b for comparison. Note that the data presented in Figure 6 are truncated to ∆t ) 800 fs. This is because the spectra change very little past ∆t ) 800 fs. When the spectra calculated with the infinitesimally short pulse are compared to the experimental signal in Figure 4a, the largest difference is the fwhm of the spectra at ∆t ) 800 fs. The increased width along the energy axis reflects the fact that no energy window has been imposed on the system, so a much broader range of ξ will be accessible, where ξ provides the energy sampled upon detachment, as shown in eq 9. In Figure 6a,d, the signal is strongest for ξ > 0.12 eV at ∆t < 200 fs. In panel d the strength of the signal for ∆t < 200 fs is off the scale of the plot and extends to ξ ∼ 0.7 eV, and the patterns in the signal in this energy region reflect the large overlap of the wave packet with the bound vibrational states of the A potential surface. (Plots similar to Figure 6a,d with a larger range in ξ are given in the Supporting Information.) Both of these observations reflect the range sampled by 〈∆E(∆t)〉 and will not contribute when the pulses are included. Again since the calculated spectra in Figure 6a,d do not look like the experimental spectra shown in Figure 4a, the source of the underlying shape of the experimental signal at short times requires knowledge of more than the energy differences between the A′ state of IBr- and C or A states of IBr. Since we know that by utilizing a pulse width that is the same as the one used in the experiment, we can obtain very good agreement with the experimental spectra, we then pose the question of how does the pulse width impact the visualization of the dynamics through the spectra? To address this, we calculate the time-resolved photoelectron spectra using a pulse that has a duration 3 times longer than experiment. Panels b and e of Figure 6 represent the data that were obtained using the pulse with a fwhm of 300 fs. These data were also presented in Figure 4b,c. The differences in the two pairs of plots reflect the fact that in Figure 6 we present the data without convolution with a Gaussian and using a different normalization scheme. Panels c and f of Figure 6 show the spectra calculated using a pulse with a fwhm of 900 fs. All four of these plots show bimodal distribution in the photoelectron spectra with time. In the case of the longer duration pulse (Figure 6c,f), the peak at ∼0.08 eV persists for pump-probe delay times beyond 800 fs, although the strength of the signal in this region is substantially weaker than in Figure 6b,e. If we focus on the peak at ∼0.12 eV, this feature is very similar in all four calculated spectra, plotted in Figure 6b,c,e,f, for delay times longer than 500 fs. To understand how and why the spectral features change with pulse width, we turn to an analysis of the wave packet that has been prepared by the pump pulse as described by eqs 12 and 13 for V ) 0. In Figure 7b,c we plot Ξd(R,∆t) from eq 12, and in panel a we show |ψ(R,∆t)|2 evaluated using eq 4 for comparison. The most notable difference between the three pulse widths (short, intermediate, and long) is how the width of Ξd(R,∆t) changes with time. In Figure 7a |ψ(R,∆t)|2, which has no pulse information included, is symmetric and its amplitude broadens with time. For Ξd(R,∆t) in panels b and c at ∆t ) 0 fs, Ξd(R,∆t) is bimodal with a sharp rise at small values of R and a slowly decaying tail as compared to |ψ(R,∆t)|2. More specifically, as apparent by the insets in Figure 7b,c, Ξd(R,∆t) is bimodal for at least the first 100 fs. If one estimates the R values that correlate to the centers of the two peaks at ∆t ) 0 fs for either the intermediate or long pulse, the maxima of the two peaks are located at ∼3.06 Å (Re for the X state) and at a slightly longer R value, ∼3.19 Å,
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Figure 6. Calculated time-resolved photoelectron spectra of IBr- for the (a)-(c) C state and (d)-(f) A state dynamics in the three pulse width regimes: (a) and (d) infinitesimally short pulse; (b) and (e) intermediate pulse with a fwhm of 300 fs; (c) and (f) long pulse with a fhwm of 900 fs. The average ∆E(∆t) curves from Figure 5b are overlaid on the spectra in (a) and (d). The data presented in (b) and (e) are the same as that shown in Figure 4a,b but for a different normalization scheme, as discussed in the text. The color indicates signal strength: red (weak signal) to blue (strong signal).
Figure 7. Wave packet as dressed by the pump pulse as a function of the I-Br distance. In (a) |ψ(R,∆t)|2 for the infinitesimally short pulse from eq 4. In (b) and (c) Ξd(R,∆t) from eq 12 for the finite pulse widths: (b) fwhm ) 300 fs; (c) fwhm ) 900 fs. The main panels show the first 800 fs in increments of 100 fs, and the insets in each panel show the first 100 fs in increments of 20 fs. The colors show the progression of time, from red (shortest delay times) to blue (longest delay times). (d) Ξe(m,∆t) from eq 13 plotted as a function of the corresponding energy eigenvalue, Em. The black curve (cm2 from eq 4) is for the infinitesimally short pulse, and the two red curves (solid and dashed) are for the 300 and 900 fs finite pulses, respectively, at ∆t ) 0 fs.
respectively. As time increases, the bimodal character of Ξd(R,∆t) is lost for the intermediate pulse after ∼300 fs; however, this bimodality persists for the longer pulse, so amplitude continues to build up at small R over the entire time
range of interest. The times over which there is significant amplitude at small values of R are the same as the times over which the low electron kinetic energy peak is seen in the spectra. Specifically, the low energy peak centered between 0.05 and
Photodissociation Dynamics of IBr0.10 eV is seen for times less than ∼300 fs for the 300 fs pulse and persists beyond 800 fs for the 900 fs pulse. Lastly, the two sets of calculated spectra in Figure 6b,c,e,f look similar in the long time region, ∆t > 500 fs, because the wave packet has reached the dissociation region of the potential, where eKE is constant, and has larger overlap with the continuum neutral eigenstates that are less affected by the characteristics of the potential surface. Both of these observations of the spectra calculated using finite pulse widths are consistent with the narrowing of the photoelectron spectra with time as shown in Figure 2. The correlation between the bimodal character of the spectra and the bimodal character of the dressed wave packets, plotted as functions of R, can be better illustrated by examining the range of A′ vibrational eigenstates accessed by the pump pulse, shown in Figure 7d. The black curve in Figure 7d shows the broad distribution of contributing eigenstates when the infinitesimally short pulse is used (cm2 from eq 4). In the case of the finite pulse widths (red curves), we plot Ξe(m,∆t) from eq 13 as a function of Em, where m is the A′ vibrational state quantum number, and Em is the corresponding energy eigenvalue. Not surprisingly, the number of energetically accessible vibrational states decreases and the distribution narrows dramatically as the pulse width increases. These different ranges of energetically accessible A′ vibrational states overlap with very different ranges of neutral eigenstates upon detachment, and this is manifested in the spectra, especially for short delay times. In light of the results presented here, we conclude by commenting on the analysis of the time-resolved photoelectron spectra of IBr- using the classical model mentioned above. In general, the observed signal increase in electron kinetic energy with time is dominated by the energy difference between the A′ state of IBr- and the C or A states of IBr, for times longer than ∼300 fs. For shorter delay times, quantum effects are seen in the calculations. The quantum effects arise from the fact that the wave packet is prepared in a very specific manner by the pump pulse and leads to excitation of a small fraction of the states that have nonvanishing cm2 values. This leads to the bimodal character of the dressed wave packet when it is plotted as a function of R. This bimodality can persist for up to 800 fs for the long pulse and leads to the two peaks seen in the experimental spectra. Once the calculated spectra are convoluted by a Gaussian to account for the experimental resolution, the two peaks become difficult to distinguish and appear as a shift in the intensity within a single peak, as seen in Figure 4. 4. Conclusions In this study we have investigated the sources of the spectral shift in the TRPES of IBr- that was reported by Sanov and co-workers17 by treating the system in a fully quantum mechanical manner. We find that while the experimental signal contains contributions from the detachment cross sections, the good agreement between the results of the present calculations and the experimental signal, where our calculations do not include this dependence, leads us to conclude that the detachment cross sections do not change significantly with internuclear distance. We have also examined the effects of temporal pulse width on the photoelectron signal, particularly the effects of finite pulse width, using a width that is the same as in the experiment and one 3 times longer. In the limit of the infinitesimally short pulse, there are no constraints on the excitation energy, yielding a very broad distribution in the photoelectron spectra. For the other pulses, many of the features found in the spectra calculated with the short pulse disappear,
J. Phys. Chem. A, Vol. 114, No. 42, 2010 11345 and in particular, there is a shift in the signal of the photoelectron spectra from ∼0.08 to 0.12 eV over a time interval from 250 to 600 fs. This observation is derived from how the pulses prepare the time-evolving wave packet and from the features of the potential surfaces at various internuclear distances. We find that while there are some effects that can be rationalized by pulse width, especially for short delay times (∆t < 300 fs), these effects are subtle, and the majority of the structure in the spectra reflects the difference in potential energies between the anion and neutral surfaces as described by the classical model that was proposed by Mabbs et al.17 Overall, the calculated spectra are in very good agreement with experiment and give insights into the mechanism for the spectral structure. Acknowledgment. We gratefully acknowledge the Office of Naval Research for support of this work as well as the Graduate School at The Ohio State University for fellowship support. We also recognize the Ohio Supercomputer Center for an allocation of computing resources. We thank R. Mabbs and A. Sanov for their helpful scientific discussions and for clarifying details of their experiment. Finally, we thank A. Sanov for his generosity in providing us with the experimental IBr- time-resolved photoelectron spectra in electronic form. Supporting Information Available: List of the absolute electronic energies for the six calculated electronic states of IBr-, time-resolved photoelectron spectra as calculated using data from the unshifted potential surfaces, waterfall plots of the timeresolved photoelectron spectra as calculated using the 300 fs pulse, and graphs of the calculated spectra from the infinitesimally short pulse for a larger range of ξ values than that presented in Figure 6. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Papanikolas, J. M.; Gord, J. R.; Levinger, N. E.; Ray, D.; Vorsa, V.; Lineberger, W. C. J. Phys. Chem. 1991, 95, 8028. (2) Nadal, M. E.; Kleiber, P. D.; Lineberger, W. C. J. Chem. Phys. 1996, 105, 504. (3) Greenblatt, B. J.; Zanni, M. T.; Neumark, D. M. Chem. Phys. Lett. 1996, 258, 523. (4) Zanni, M. T.; Taylor, T. R.; Greenblatt, B. J.; Soep, B.; Neumark, D. M. J. Chem. Phys. 1997, 107, 7613. (5) Zanni, M. T.; Batista, V. S.; Greenblatt, B. J.; Miller, W. H.; Neumark, D. M. J. Chem. Phys. 1999, 110, 3748. (6) Nandi, S.; Sanov, A.; Delaney, N.; Faeder, J.; Parson, R.; Lineberger, W. C. J. Phys. Chem. A 1998, 102, 8827. (7) Dribinski, V.; Barbera, J.; Martin, J. P.; Svendsen, A.; Thompson, M. A.; Parson, R.; Lineberger, W. C. J. Chem. Phys. 2006, 125, 133405. (8) Sheps, L.; Miller, E. M.; Horvath, S.; Thompson, M. A.; Parson, R.; McCoy, A. B.; Lineberger, W. C. Science 2010, 328, 220. (9) Bihary, Z.; Zadoyan, R.; Karavitis, M.; Apkarian, V. A. J. Chem. Phys. 2004, 120, 7576. (10) Davis, A. V.; Zanni, M. T.; Frischkorn, C.; Neumark, D. M. J. Electron Spectrosc. Relat. Phenom. 2000, 108, 203. (11) Greenblatt, B. J.; Zanni, M. T.; Neumark, D. M. J. Chem. Phys. 1999, 111, 10566. (12) Zadoyan, R.; Almy, J.; Apkarian, V. A. Faraday Discuss. 1997, 108, 255. (13) Gu¨hr, M.; Schwentner, N. Phys. Chem. Chem. Phys. 2005, 7, 760. (14) Bardeen, C. J.; Che, J.; Wilson, K. R.; Yakovlev, V. V.; Apkarian, V. A.; Martens, C. C.; Zadoyan, R.; Kohler, B.; Messina, M. J. Chem. Phys. 1997, 106, 8486. (15) Thompson, M. A.; Martin, J. P.; Darr, J. P.; Lineberger, W. C.; Parson, R. J. Chem. Phys. 2008, 129, 224304. (16) Greenblatt, B. J.; Zanni, M. T.; Neumark, D. M. Science 1997, 276, 1675. (17) Mabbs, R.; Pichugin, K.; Sanov, A. J. Chem. Phys. 2005, 122, 174305. (18) Sanov, A. Private communication. Department of Chemistry and Biochemistry, University of Arizona, Tucson, Arizona 85721. (19) Sheps, L.; Miller, E. M.; Lineberger, W. C. J. Chem. Phys. 2009, 131, 064304.
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(20) Batista, V. S.; Zanni, M. T.; Greenblatt, B. J.; Neumark, D. M.; Miller, W. H. J. Chem. Phys. 1999, 110, 3736. (21) Bacˇic´, Z.; Light, J. C. Annu. ReV. Phys. Chem. 1989, 40, 469. (22) Colbert, D. T.; Miller, W. H. J. Chem. Phys. 1992, 96, 1982. (23) Lischka, H.; Shepard, R.; Shavitt, I.; Pitzer, R. M.; Dallos, M.; Mu¨ller, T.; Szalay, P. G.; Brown, F. B.; Ahlrichs, R.; Bo¨hm, H. J.; Chang, A.; Comeau, D. C.; Gdanitz, R.; Dachsel, H.; Ehrhardt, C.; Ernzerhof, M.; Ho¨chtl, P.; Irle, S.; Kedziora, G.; Kovar, T.; Parasuk, V.; Pepper, M. J. M.; Scharf, P.; Schiffer, H.; Schindler, M.; Schu¨ler, M.; Seth, M.; Stahlberg, E. A.; Zhao, J.-G.; Yabushita, S.; Zhang, Z.; Barbatti, M.; Matsika, S.; Schuurmann, M.; Yarkony, D. R.; Brozell, S. R.; Beck, E. V.; Blaudeau, J.-P. COLUMBUS, an ab initio electronic structure program, release 5.9.1; http://www.univie.ac.at/columbus/, 2006. (24) Lischka, H.; Shepard, R.; Brown, F. B.; Shavitt, I. Int. J. Quantum Chem., Quantum Chem. Symp. 1981, 15, 91. (25) Shepard, R.; Shavitt, I.; Pitzer, R. M.; Comeau, D. C.; Pepper, M.; Lischka, H.; Szalay, P. G.; Ahlrichs, R.; Brown, F. B.; Zhao, J. Int. J. Quantum Chem., Quantum Chem. Symp. 1988, 22, 149. (26) Lischka, H.; Shepard, R.; Pitzer, R. M.; Shavitt, I.; Dallos, M.; Mu¨ller, T.; Szalay, P. G.; Seth, M.; Kedziora, G. S.; Yabushita, S.; Zhang, Z. Phys. Chem. Chem. Phys. 2001, 3, 664. (27) Yabushita, S.; Zhang, Z.; Pitzer, R. M. J. Phys. Chem. A 1999, 103, 5791. (28) Pitzer, R. M. “Br and I basis sets”, see http://web.chemistry. ohio-state.edu/∼pitzer/basis_sets.html. (29) Hurley, M. M.; Pacios, L. F.; Christiansen, P. A.; Ross, R. B.; Ermler, W. C. J. Chem. Phys. 1986, 84, 6840. (30) LaJohn, L. A.; Christiansen, P. A.; Ross, R. B.; Atashroo, T.; Ermler, W. C. J. Chem. Phys. 1987, 87, 2812.
Horvath et al. (31) Wrede, E.; Laubach, S.; Schulenburg, S.; Brown, A.; Wouters, E. R.; Orr-Ewing, A. J.; Ashfold, M. N. R. J. Chem. Phys. 2001, 114, 2629. (32) Miller, T. M. Electron Affinities. In CRC Handbook of Chemistry and Physics, 90th ed., Internet Version 2010 ed.; Lide, D. R., Ed.; CRC Press: Boca Raton, FL, 2009. (33) Chandler, D. W.; Houston, P. L. J. Chem. Phys. 1987, 87, 1445. (34) Eppink, A. T. J. B.; Parker, D. H. ReV. Sci. Instrum. 1997, 68, 3477. (35) Paschotta, R. Encyclopedia of Laser Physics and Technology; Wiley-VCH Verlag GmbH & Co.: KGaA, Weinheim, Federal Republic of Germany, 2008. (36) Stoll, H.; Metz, B.; Dolg, M. J. Comput. Chem. 2002, 23, 767. (37) Thompson, M. A. From Femtoseconds to Nanoseconds: Simulation of IBr- Photodissociation Dynamics in CO2 Clusters. Thesis, University of Colorado, Boulder, 2007. (38) Werner, H.-J.; Knowles, P. J.; Lindh, R.; Manby, F. R.; Schu¨tz, M.; Celani, P.; Korona, T.; Mitrushenkov, A.; Rauhut, G.; Adler, T. B.; Amos, R. D.; Bernhardsson, A.; Berning, A.; Cooper, D. L.; Deegan, M. J. O.; Dobbyn, A. J.; Eckert, F.; Goll, E.; Hampel, C.; Hetzer, G.; Hrenar, T.; Knizia, G.; Ko¨ppl, C.; Liu, Y.; Lloyd, A. W.; Mata, R. A.; May, A. J.; McNicholas, S. J.; Meyer, W.; Mura, M. E.; Nicklass, A.; Palmieri, P.; Pflu¨ger, K.; Pitzer, R.; Reiher, M.; Schumann, U.; Stoll, H.; Stone, A. J.; Tarroni, R.; Thorsteinsson, T.; Wang, M.; Wolf, A. MOLPRO, a package of ab initio programs, version 2002.6; see http://www.molpro.net, 2002. (39) Sansonetti, J. E.; Martin, W. C. Basic Atomic Spectroscopic Data. In NIST Standard Reference Database, Electronic Version; National Institute for Standards and Technology (NIST): Gaithersburg, MD, 2005; Vol. 108. (40) Heller, E. J. J. Chem. Phys. 1978, 68, 2066.
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