Solvent effects on dynamics of overtone-induced dissociation

Aug 20, 1992 - Y. S. Li,+ » Robert M. Whitnell,? and Kent R. Wilson* * ? ...... (90) Bergsma, J. P.; Gertner, B. J.; Wilson, K. R.; Hynes, J. T. J. C...
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J. Phys. Chem. 1993, 97, 3647-3657

3647

ARTICLES Solvent Effects on Dynamics of Overtone-Induced Dissociation Y. S. Li>g Robert M. Whitnel1,l and Kent R. Wilson'*$ Institute for Nonlinear Science and Department of Chemistry, University of California, Son Diego, La Jolla. California 92093-0339

R. D. Levine' The Fritz Haber Research Center for Molecular Dynamics, The Hebrew University, Jerusalem, 91 904 Israel Received: August 20, 1992

W e study via classical molecular dynamics simulation the overtone-excitation-induced dissociation of a model for hypochlorous acid, HOC1, in the gas phase and in fluid Ar over a large range of pressures. We find that the lifetime distribution over the first 10 ps after excitation is nonexponential, in both the gas phase and in solution, for an initial excitation of 80 kcal/mol (which, for the model we use, is >30 kcal/mol in excess of what is needed to break the OC1 bond). The presence of Ar at moderate pressures (- 100 atm) increases the initial instantaneous rate of dissociation over that in the gas phase. W e examine the time-dependent velocity power spectra of the HOC1 molecules after excitation, which gives information about the frequencies of the molecular motion as the molecules evolve, and thus about the flow of energy within the molecule. At higher pressures (- 3000 atm), recombination becomes a dominant process and the dissociation probability drops below that a t the lower pressures.

I. Introduction

Some of the earliest experimentson overtone-excitation-induced unimolecular reactions were those by Reddy and Berry, who Unimolecular reactions can be conveniently divided into two studied the isomerization of CHjNC after excitation of the C H classes: thermally activated reactions and nonthermal reactions local mode.I3 CH3NC has been of considerable interest because activated by other means. Thermal activation places energy into of the prediction of nonstatistical behavior by Bunker and cothe molecule in a manner dictated by the Boltzmann distribution. w o r k e r ~ ' ~based , ' ~ on trajectory calculations. However, Reddy Thus, nonstatisticalor non-RRKM effects arising from nonergodic and Berry found no significant deviation between experimental behavior of the energy redistribution may be difficult to detect.'v2 results and a RRKM model. On the other hand, in the case of For nonthermally activated reactions, the energy necessary to allyl isocyanide, Reddy and Berry do claim to have found drive the reaction can be in principle placed in a specific mode nonstatistical behavior for the isomerization process.'6 (Formore or coordinate molecule. Because this type of energy distribution recent workon methyl isocyanide,see ref 17 and references therein. is inherently nonstatistical, non-RRKM behvior of the dynamics The isomerization of isotopically substituted methyl isocyanide may be more readily ~ b s e r v e d . ~Our , ~ interest in this paper is to has also been studied recently,'* and the isomerization of allyl explore the dissociation and intramolecular energy flow dynamics isocyanide has also been studied again recently, and the observed of a selectively excited molecule in solution. isomerization rates have been attributed to the presence of hot Many studies of unimolecular dissociations and isomerizations bands rather than to nonstatistical effects.I9) have considered a selective activation event. Such techniques Another overtone-excitation-induced dissociation that has include chemical activation, direct photodissociation, infrared received much experimental and theoretical attention is that of multiphoton dissociation, and vibrational overtone e x c i t a t i ~ n . ~ - l ~ hydrogen peroxide, HOOH. Excitation of theOH v = 6vibration Overtone excitation, which we consider in this paper, presents provides sufficient energy to dissociate the 0-0 bond. Crim and great promise for the observation and understanding of timeco-workers10,20-z2 have studied this dissociation process using resolved energy flow dynamics and dissociation, in particular single-resonance experiments, and Luo et a1.11J**23J4have used because the excitation process is simple and the subsequent double-resonance experiments to estimate that the lower limit molecular evolution can take place on the better characterized for the lifetime of the excited molecule is 6.6 ps. Scherer and ground electronic state. Vibrational overtone excitation only ZewailZShave studied time-resolved HOOH dissociation via requires the absorption of a single photon (or more, if multiple excitation of the O H v = 5 vibration which is not sufficient in resonance techniques' are used). Thus, a very short light pulse and of itself to dissociate the bond, but with the help of thermal can be used to excite molecules essentially simultaneously, and excitation can cause dissociation. experimentally time-resolved dynamics becomes possible. In The initial experiments of Crim and co-workers led to a number addition, overtone excitation tends to place the energy in a of trajectory studies of the HOOH dissociation.2G32All of these nondissociative local mode of the molecule, thereby making the studies give qualitative agreement with the experimental lifetime. study of intramolecular energy flow important for understanding the dissociation dynamics. However, the details of the dynamics have been recently shown to be very sensitive to the intramolecular potential and, in 'Current address: Biosym Technologies, 9685 Scranton Rd, San Diego, particular, to the coupling of the 0-0 stretch with the OOH CA 92121. bend.31 8 Institute for Nonlinear Science. I Department of Chemistry. A number of other dissociations and isomerizations have been 0022-365419312097-3647$04.00/0

0 1993 American Chemical Society

3648 The Journal of Physical Chemistry, Vol. 97, No. 15, 1993 studied via overtone excitation experiments, including those of tert-butyl h y d r o p e r o ~ i d e , ~various ~ - ~ ~ cyclic enes and dienes,36 nitric acid,37and HN3.3* A similarity of all these studies is that they involve molecules with at least four atoms (and, therefore, at least 6 degrees of freedom). Determining the details of the energy flow from the local mode excitation into the reaction coordinate therefore becomes difficult (although a substantial amount has been learned about the energy flow in HOOH from the trajectory studies). We are therefore interested in studying a triatomic molecule (with only three modes for intramolecular energy flow) which can be dissociated via overtone excitation. For such simple molecules, it has been suggested for some time that differences in bond frequencies may lead to bottlenecks in the intramolecular energy redistribution and hence to a nonstatistical decay.39 Model studies have since provided much evidence in s ~ p p o r t . ~ @The - ~ ~study presented herein, which uses a realistic potential energy surface, should provide further evidence on the selectivity of the intramolecular energy redistribution. However, our interest goes beyond isolated molecule studies. Schroeder and Troe have recently reviewed studies of recombination reactions and isomerizations in compressed gases and liquid^^^.^^ and have stressed the question of when gas-phase behavior of such reactions can be carried over to the same reactions in solution. A similar question has been studied in detail for a model bimolecular reaction by Li and WilsonSo(similar issues have been discussed in refs 5 1 and 52), while methods for analyzing solution-phase reactions in terms of "dressed" gas-phasevariables have been described by Charutz and L e ~ i n e . ~ )In- ~particular, ~ Schroeder and Troe have discussed when the effects of the solvent change over from those based on collision frequency (as they would in low-pressure gases) to those based on viscosity- or frequency-dependent friction (as they might in liquids). In modeling such systems, the energy can easily be placed in a localized portion of a molecule. In fact, some of the earliest simulationsof chemical reactions in solution studied exactly this type of process: the photodissociation of 12 in CC14s7and in rare gas s o l ~ e n t s .Photodissociation ~~~~~ has been the most commonly studied unimolecular process since those initial studies with, among other work, simululationsof the photodissociation of 12 in various solvent^,^^ Br2 in rare gas clusters,6sICN in rare gas solutions,& and halogen diatomics in rare gas matrices.6749 (A review of these and other related simulations is given in ref 70.) To our knowledge, no experimental or theoretical study has been done of an overtone-excitation-induceddissociation under conditions ranging from isolated molecules to liquid density solvents, although thermally activated unimolecular processes (isomerizations7'-74 and d i s s o c i a t i ~ n s ~ ~have J ~ ) indeed been previously studied in solution. (Concurrently with this work, Martens and Finney have studied the overtone-excitation-induced dissociation of HOOH in Ar clusters.32) One of our goals here is to use such a study so that wecan understand how intramolecular energy flow, dissociation dynamics, and lifetime distributionsare altered by the presence of solvent. An important complementary source of information on shorttime dynamicsof vibrationally excited molecules is high-resolution overtone ~pectroscopy.~~J~ The time-dependent approach to ~pectroscopy~~ provides the link from the absorption spectrum to thesurvival probability of the initially excited nonstationary state. Experimental or computational limitations typically restrict the information available in this way to the first 10 ps or so.47.8@83 This time range is entirely appropriate for HOCl in the energy range of present interest. However, there is another limitation. The survival probability tells whether the molecule is or is not in the initially excited region. That is enough to decide if the energy-rich molecule samples the available phase space prior to di~sociation.~~ The survival probability of the initial state does not, however, disclose where the molecule is when it is neither dissociated nor in its initial region. In principle, this information

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PC' I

Energy transfer,perhaps

Excitation (to v = 10) Figure 1. Schematic diagram of the HOCl dissociation process. The OH and OCI potential curves shown here are derived from the Schinke HOC1 potential energy surface.

is available from resonance Raman ~pectroscopy.~~ In practice, one is just learning how to invert the Raman excitation spectra so as to extract the time cross-correlation functions.86 One therefore needs a practical method for determining how, in different time regimes, the excess energy of the molecule is localized in different regionsof the molecule. A possible route87*88 (a related approach is described by Martens89),and one that we adopt here, is to use the spectrum corresponding to a particular time segment. We discuss the details of this method in section 111. One practical, yet general, aspect of this method is that the spectrum wecomputeis obtained from thevelocity timecorrelation function. This tends to suppress the low-frequency end of the spectrum as compared to the spectrum of the position time correlation function. For dissociation, where the molecular fragments can separate to large distances, this use of the velocity correlation function provides a clearer picture of the changing dynamics. In a molecular dynamics simulation, it is very advantageous to have a well-defined "origin" for the time axis. This is clearly evident in earlier work on bimolecular reactions in condensed p h a ~ e s . ~ l * *For ~ ~a unimolecular reaction following pulsed optical excitation, the correspondence between experiment and simulation is direct. It is not as easy to impose experimentally such an origin for bimolecular processes in solution, although recent femtosecondexperimentson gas-phase bimolecular reactions are able to establish a zero for the time axis. (For a review, see ref 96). We have chosen to study the dissociation of a model of hypochlorous acid, HOCl, via molecular dynamics calculations. A schematic diagram of this dissociation process is shown in Figure 1. Although the overtone-excitation-induceddissociation of this molecule has to our knowledge not yet been studied experimentally, we expect that it will have many of the same qualitatively featuresas that for HOOH. The OC1 bond is similar in strength (60 k c a l / m ~ l )to~the ~ 00 bond in hydrogen peroxide ( 5 1 k c a l / m ~ l ) ?so ~ the ease of dissociation should also be roughly similar, while the smaller number of modes in HOCl makes interpretation of the dynamics simpler. In addition, an analytic potential energy surface exists for HOCI, having been derived by S ~ h i n k ebased ~ ~ on the ab initio calculations of Liu99for use in classical dynamics simulations of the O(ID2) + HCl- OH + C1 reaction. As will be discussed in section 11, the three modes of HOCl have rather distinct frequencies." There are thus no lower order resonances mixing the three modesio1 We shall find that this has clear-cut implications for the intramolecular dynamics in both the gas phase and under the perturbation by the solvent. The simplicity of HOCl makes understanding the behavior in solution easier as well. To that end, we perform molecular dynamics calculations in fluid Ar for several densities (corresponding to a pressure range of 5&3000 atm). We use several

Dynamics of Overtone-Induced Dissociation

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The Journal of Physical Chemistry, Vol. 97, No. 15, I993 3649 TABLE I: Potential Energy Parameters for Model Potential OH OCI ro, A 0.975 1.705 0, A-l 2.37 2.87 D, kcal/mol 100 43 a,A-1 1 .o 1.o V, kcal/mol 180

- Schinke Potential .._.Model Potential

eo

103.5

discuss further in section 111. Thus, the reader should keep in mind that this surface is a model which closely resembles HOCl for some properties, such as the frequencies of the fundamentals, but does not reproduce some of the properties that will be important for the dynamics, such as the dissociation energy and the vibrational anharmonicities. We expect that the qualitative results will be valid for real HOCl. In addition to using the complicated Schinke potential energy surface, we have also performed gas-phase calculations for comparison using a considerably simpler model potential energy function. This model has the form

2.0

3.0

4.0

5.0

roc1 (A) Figure 2. Minimum energy path (MEP) for OCI bond breakage of the Schinke potential and the model potential described in the text. The MEP for the Schinke potential is calculated by minimizing the potential energy in the OH and HCI coordinates while holding the OCI bond at a succession of fixed distances. The MEP for the model potential is simply the function V m ( r ~ of l ) eq 2.

different probes of the HOCl dissociation dynamics: dissociation probability as a function of solvent density, time-dependent velocity power spectra of the HOCl molecule which provide considerabledetail about the intramolecular energy flow process, and examination of individual trajectories to help delineate the recombination process in higher density solvent. Throughout, we will focus on how the presence of the Ar solvent modifies the detailed dynamics of this unimolecular dissociation. including intramolecular energy flow and solvent caging. In section 11, we describe the details of the model of HOCl and the argon solvent and the molecular dynamics calculations. Section I11 presents the results of our dynamics and describes the energy flow process that leads to dissociation and the effect of the solvent in raising the instantaneous rate of dissociation while lowering the overall yield. Section IV concludes and discusses possible models that might be used to describe the behavior observed in these calculations. 11. Potentials and Computational Methods

A. HOC1 Potential Energy Surface. For HOCl, we use the global potential energy surface which Schinkegsemployed to study 0 + HCI reaction dynamics. This surface is based on the general form for potential energy surfaces developed by Murre11 et al.IO* and is to our knowledge the only global potential energy surface currently available for HOC1. In Figure 2, we show the minimum energy path for breakage of the OC1 bond, calculated by minimizing the potential energy as a function of the O H and HC1 distances at fixed OC1 distances. The HOCl dissociation energy (for the O H + Cl channel) can be seen from Figure 2 to be 42 kcal/mol. We note that this value is considerably lower than the experimental bond strength of 60 kcal/m01.~' In addition, the Schinke potential anharmonicity of the O H bond is -200 cm-I, a value which is roughly twice as large as that given by Halonen and Ha in their determination of an anharmonic force field of HOCLio3 (The Halonen-Ha O H anharmonicity is very close to that for the O H bond in HOOH.) Both of these qualities of the Schinke surface may be expected to make the dissociation on this surface faster than what would occur experimentally, as we shall

where 0 is the angle between the OC1 and O H bonds, V,,,(r) is a Morse potential,

Vm(r) D(e-a(r-r'J) - I)* - D while @ is given by

(2)

(3) Finally,fa is an attenuation or "switching" function which is given by

The exponential decay of the attenuation function is present to guarantee that the OH can rotate freely after dissociation has taken place. In eq 4, U O H and am1 are adjustable parameters. The parameters of this model are given in Table I and have been adjusted to give approximate agreement with the experimental HOCl normal mode frequencies.lwIM In Figure 2, we plot Vm(roc,),the minimum energy path for OC1 bond breakage in this potential. Note that in this minimum energy path, fOH = @OH and B = Bo, which is most certainly not the case for the Schinke surface. The forces needed to perform molecular dynamics calculations are determined from analytic derivatives of the Schinke or the model potential energy functions. Examination of the resonance conditionsIo7 for this simpler model potential suggests that intramolecular energy transfer out of a highly vibrationally excited OH stretch will be inefficient. Such redistribution of energy that does take place will probably involve the HOCl bend motion. The reason is that, a t the total energy of interest here, there are very few low-order resonances involving the high-frequency O H motion. The mismatch in frequencies between O H and the bend or the OC1 stretch is so extreme that one O H vibrational quantum exchanges against three or four other quanta. Most notably, there is a (-1,1,2) resonance corresponding to one OH quantum exchange to one OC1 stretch and two quanta of the bend. The only other loworder resonance is (-1,2,1). Higher order resonances affecting IVR are (-2,3,3), (-2,4,2), and (-2,2,4). However, once energy does get out of the O H stretch and into the two other modes, there are many low-order resonances that can affect the further exploration of phase space. The prediction of nonlinear dynamics is thus that there is a bottleneck for energy flow out of the OH stretch. B. Solvent. Our calculations in solution have been done with a fluid Ar solvent. The solvent is modeled as Lennard-Jones particles with parameters as given in Table 11. The interaction

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3650 The Journal of Physical Chemistry, Vol. 97, No. 15, 1993

TABLE II: Lennard-Jones Parameters for Interatomic Interactions atom Ar

CI 0

H

e,

kcal/mol

0.238 0656 0.344 7178 0.122 41 IO 0.017 0898

Q,

A

3.41 3.35 2.95 2.81

n CI)

0 r X

choosing new velocities from a Maxwell-Boltzmann distribution at 298 K. Every 5 ps, the positions of the atoms are written out into an initial configuration file. The configurations taken from these runs should be statistically independent because of theshort correlation times in this system. However, in order to obtain an even better sampling of configuration space, we perform this entire procedure for 10 initial random boxes of atoms. In this way, 100 initial configurations are produced at each density. (A similar procedure is used for the p* = 0 pure HOCl case to produce 2000 initial configurations, although no periodic boundary conditions are used so that the single HOCl in each trajectory sees no other molecules.) Each HOCl trajectory is generated by selecting velocities from the Maxwell-Boltzmann distribution for one of the initial configuration files. The excitation energy in the O H bond is introduced as vibrational kinetic energy in that local mode. To be specific, we first calculate the total vibrational energy in this O H vibrational mode,

In this equation, p is the reduced mass, P=

P Figure 3. Pressure of the Ar solvent as a function of reduced density p* foreachofthefivevaluesofp*usedin this work. Thepressureiscalculated from 60-ps equilibrium molecular dynamics simulations at 298 K. The curve is drawn as an aid to the eye.

between the solvent and the HOCl molecule is described by a Lennard-Jones potential with parameters for H, 0,and C1 given in Table I1 and the values of E and u for the Ar-H, Ar-0, and Ar-Cl interactions determined from standard combining rules:

and ui g=-

+ uj

2 The density dependence of the dissociation dynamics is determined by using Ar fluids at five densities (in addition to the case of pure HOCl at the limit of zero density with no Ar). The values of the reduced densities used are p* = 0.059.0.1 19,0.237, 0.475, and 0.830 (where p* = 1 corresponds to a density p = 1.68 g/cm3 and p* = 0 corresponds to pure HOCl at the limit of zero Ar pressure). In order to express these densities in more familiar terms, we have used molecular dynamics to calculate the pressure of these fluids.”J* We show those pressures in Figure 3 and find that the pressures range from -60 atm for the lowest density used here to -3000 atm for the highest density. As we shall show, this range of pressures leads to a wide variety of solvent effects on the unimolecular dissociation process. C. Molecular Dynamics. The molecular dynamics of the dissociation process are calculated in the following manner. To construct initial configurations, we randomly place 100Ar atoms and 1 HOCl molecule in a unit cell of periodic truncated octahedron boundary conditions. The size of the unit cell is chosen to give the desired density. A minimization procedure is applied to the potential energy of this (high-energy) configuration. Long runs for molecular dynamics are then performed on this system, with the velocities of all atoms being randomized every 250 fs by

mHmO

mli + m0 ur is the relative velocity along the OH bond, and VO&) is the potential energyin the OH bond. We then introduce theexcitation energy to this OH bond by rescaling the relative velocity to a value u; such that the total vibrational energy in this OH bond is equal to a particular excitation energy; Le., 1 &ib = jp(v,‘ I2 + vOH(r) = Eexcitation (9) For most of the calculations presented here, Ecxcitation = 80 kcal/ mol. This introduction of energy defines t = 0. For each trajectory, 10 ps of dynamics is run using a Verlet algorithmwithaO.1-fs timestep. Thisshort timestepisnecessary because of the high-frequency OH stretch and provides a good balance between energy conservation and computational effort. We monitor a number of quantities during the course of these trajectories including the HOCl atomic positions and thus the OC1 bond distance. We will describe the analysis of the resulting data in the following section. 111. Results

A. Dissociation Probability. As a first question, one might ask how many HOCl molecules dissociate in a given time period after the initial overtone excitation. Figure 4 displays the percentage of molecules that dissociate within 10 ps of excitation as a function of Ar density for the pure HOCl and for the five densities of Ar solvent. For the purposes of this figure, we define dissociation as the 0-C1 separation being at least 3rOml or -7 A at t = 10 ps. In solution, this separation is more than sufficient for solvent atoms to intervene between the 0 and C1 atoms and thereby make recombination on the 10-ps time scale unlikely. In pure HOCI, as we shall discuss presently, it is possible to use a much tighter criterion for dissociation. Figure 4 shows that the dissociation probability increases from the pure HOCl value until p* 0.19 and then decreases monotonically and rapidly for higher densities. At first glance, there might be a temptation to treat this turnover behavior as resulting from a Kramers-like picture of the dissociation process. Such pictures have been applied to a number of bimolecular, isomerization, and recombination reactions. (For reviews, see the articles by Hynes,Io9 Schroeder and Tr0e,4~and HPnggi et al.lIO) We urge caution in the application of such a picture here. The Kramers treatment of isomerization reactions assumes thermal activation of the reactants as well as a well-defined transition state at which all velocities and all coordinates (except

-

Dynamics of Overtone-Induced Dissociation

The Journal of Physical Chemistry, Vol. 97, No. 15, 1993 3651

1

0.8

.-

fn

0.6

L

.nu

0.4

0.2

1 0.1

Figure 4. Fraction of HOC1 molecules (Schinke potential) that have dissociated within 10 ps after a r = 0 excitation of 80 kcal/mol as a function of Ar density. The dissociation criterion is that roc1 > 3r”oci at f = 10 ps. The curve is a cubic spline fit to the data points.

for the reaction coordinate) are in thermal equilibrium. However, the HOC1 overtone-induced dissociation is clearly not a thermally activated process, and the substantial excess energy in this system indicates that it is quite likely that the condition of thermal equilibrium at a transition state cannot be met either (assuming that one can indeed even define a transition state for this system). We do not wish to imply that models with some features of the Kramers picture cannot be applied to this dissociation reaction. In order to determine what models will be useful, however, it is first necessary to delineate the physical processes which lead to the behavior shown in Figure 4. While sections IIIC and IIID explore that question in greater detail, we shall find it useful to discuss first the time dependence of the dissociation probability. B. Lifetimes for Nascent Dissociation. In order to determine the lifetime of the HOCl molecule, we must have a precise definition of that quantity. This causes some problem in the solution case because of the possibility of recombination. Thus, we will limit our discussion in this section only to the question of when the OC1 bond obtains enough extension to dissociate. Whether it in fact dissociates will depend on the details of the HOCI-solvent dynamics as we shall discuss shortly. We therefore define the lifetime as the time at which the OC1 extension first reaches a particular value. From our studies of pure HOCl dissociation, we have found that the OC1 distance reaching a value of 3 A is a sufficient criterion for dissociation in the gas phase (i.e., once the OCI distance reaches this value, it always continues to increase and the molecule dissociates), We therefore adopt the definition that the HOCl lifetime is determined by the first time at which the OCI distance is at least 3 A. In the liquid, this criterion only represents a nascent dissociation, because recombination may occur. (We note that this nascent dissociation criterion is very similar to the ‘critical configuration” criterion used by Slater in his theory of unimolecular reactions1I1) In Figure 5 , we present decay curves N ( t ) representing the fraction of trajectories that have not achieved the nascent dissociation criterion by time t as a function o f t for an initial excitation of 80 kcal/mol (which corresponds to v = 10 in the Schinke model). Since we are only concerned with when the OC1 bond first has enough energy to dissociate, we do not consider recombination in constructing these curves-as soon as the OCI

0

2

4 6 Time (ps)

8

10

Figure 5. Decay curves N(r),defined as the fraction of undissociated molecules at time r after excitation, for “nascent” HOC1 dissociation on the Schinke potential after an initial excitation of 80 kcal/mol a t I 5 0. The decay curves for pure HOC1 and for two Ar solvent densities, p*, are shown. Each liquid-phase curve is calculated from 100 10-ps trajectories, while the curve for pure HOC1 ( p * = 0) is computed from 800 10-ps trajectories. The scale for N(r) is logarithmic. The nascent dissociation criterion is that roc1 > 3 A.

1

Schinke E = 70.5 0 E=80

oOOOOOO@

A

“““O“““Ow,,

Model

A

E = 70.5 E=80

Time (ps) Figure 6. Decay curves N(r). defined as in Figure 5 , on the Schinke surface and on the model potential in the gas phase after two different initial excitations (70.5 and 80 kcal/mol) at r = 0. These curves have been computed from 2000 trajectories for the model potential and lo00 trajectories for the Schinke surface at each excitation. The scale for N ( I ) is logarithmic. The dissociation criterion is the same as in Figure 5.

bond reaches 3 A, the trajectory is removed from consideration. These curves are calculated from the 800 pure HOCl trajectories and the 100 trajectories for both of the Ar densities shown. Note that the lifetime distribution is the (negative) derivative of the decay function N(t).’i2.113 We first note that the decay, and therefore the lifetime distribution, is in general nonexponential both in the pure HOCl

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3652 The Journal of Physical Chemistry, Vol. 97, No. IS, 1993

8.0

I

t

4.0

2.0

UI

I

v (cm-') Figure 7. Equilibrium velocity power spectrumS(v) of Schinke potential HOC1 in p* = 0.830 Ar solvent. The spectrum is calculated from 65 ps of equilibrium molecular dynamics at 298 K as described in the text. The power spectrum has been multiplied by the speed of light, c, so that the integral of cS(u) over the frequencyin wavenumbers will be dimensionless. The resolution of the spectrum is 1 cm-I.

and in solution. Over the 10-ps time scale displayed in Figure 5, and with the statistics we have obtained, we see evidence of exponential decay only in the case of p* = 0.1 19, while the pure HOCl and the higher density results are clearly not exponential. This short-time dramatically nonexponential behavior does not continue for all times in pure HOCl. We have calculated pure HOCl lifetime distributions from trajectories that were 100 ps in length using both theschinkepotential and themodel potential. The resulting decay curves are shown in Figure 6 for two different initial energies (correspondingly roughly to v = 8 and v = 10 on the Schinke potential). The nonexponential behavior for times less that 20 ps is again evident. However, at times greater than 30 ps, the distribution becomes much closer to exponential for both initial excitations. In the remainder of this work, we will concentrate on times less than 10 ps during which much of the interesting dynamics occurs. We now consider the similarities in and differences between the pure HOCl and solution lifetimes. For the first picosecond, all decay curves are essentially identical. This result indicates that the dissociation process for these short times is dominated by the HOCl isolated molecule forces which then lead to dynamics similar to the pure HOCl even with solvent present. This demonstration of the similarity of isolated molecule and solutionphase dynamics at short times is similar to that reached in several recent computational studies of bimolecular chemical reactions in rare gas sol~tion.50~5~-~3.l l4 At longer times, the picture changes substantially. For the highest density, p* = 0.830, N ( t ) rapidly (on the order of 3 ps) reaches a plateau, as seen in Figure 5 . If the OC1 bond does not have enough energy to dissociate in this solution within 3 ps after excitation, it never will (unless the highly unlikely event of thermal reactivation takes place). But note that the probability of nascent dissociationin thehigh-density A r a t lops, 1 -N(lOps) isgreater than the dissociation probability of Figure 4. This difference is a measure of how many HOCl molecules had sufficient energy in the dissociative mode to dissociate at some point during the IO ps of dynamics but did not satisfy the stricter dissociation criterion of Figure 4. It is therefore a rough measure of how

much recombination occurs in this high-density solvent. Note that, in the pure HOCl and in the low-density solvent, the dissociation probability from Figure 4 and the quantity 1 - N(10 ps) are essentially identical, indicating that recombination is nonexistent in these systems. We will discuss recombination further in section IIID. C. Time-DependentVelocity Power Spectra and Energy Flow. The excitation of modes which are anharmonic changes the frequencies of those modes. In the overtone-induced dissociation process, a large amount of energy is placed into the system, and we therefore expect the frequency shifts to be substantial. Those frequency shifts will change as a function of time after the initial excitation as the energy migrates among modes. The initial energy is placed solely into the O H stretch, and we therefore expect that, a t very short times, only that mode will show a significant frequency shift. As the energy begins to flow into other modes, the frequencies of all the modes will be altered from their thermal equilibrium values. By monitoring these changes in frequencies as a function of time, we can map out the energy flow in this system. In particular, we shall see the important effects that the solvent has in changing the character of the intramolecular energy flow. Our main tool in this enterprise is thevelocity power spectrum. This quantity S(u) is related to the spectral density operator D by"5 3N

where the sum is over all the Cartesian velocity component of the N atoms and B is equal to l / k T with T being the temperature of the system. The mass of the atom corresponding to the j t h velocity component is given by m, and D is a functional that can be calculated from the Fourier transform of the velocity component:

D[uj(t)](u)= ( 2 ~ ) - lim ' -1S'df 1 e-i2nu*uj(t)12 r-m 27 -' An important feature of the velocity power spectrum in an equilibrium system is that its integral over frequency is simply 3 times the number of atoms in the system:l15

A corollary of eq 12 is that, in a truly harmonic system, the peaks of the velocity power spectrum are at the normal mode frequencies and the area under each peak is equal to the number of normal modes contributing to that peak. But in general, eq 12 is independent of the anharmonicity of the underlying potential. However, its derivation relies on an assumption of thermal equilibrium.II5 In particular, if the energy in the system is greater than that expected from thermal equilibrium, the power spectrum can be larger than its equilibrium value and the integral of the power spectrum over frequency can be larger than 3N. The velocity power spectrum defined in this fashion contains information about the frequencies in the system. To demonstrate this, we display the equilibrium velocity power spectrum a t 298 K for HOCl in the p* = 0.830 Ar solvent in Figure 7. The spectrum is calculated from only the HOCl atomic velocities in a 65-ps trajectory in thermal equilibrium. (Equation 12 then holds with N = 3.) The spectrum shows three peaks at 600, 1300, and 3500 cm-I corresponding to the OC1 stretch, the HOCl bend, and the O H stretch, respectively. In addition, there is a large, broad peak near zero frequency which corresponds to the diffusive and rotational motions of the molecule in the solvent. While power spectra are normally calculated from long trajectories, shorter trajectories can be used at the price of some loss of resolution in the spectrum. This is particularly valuable for nonequilibrium systems where the spectrum is itself a function

Dynamics of Overtone-Induced Dissociation

The Journal of Physical Chemistry, Vol. 97, No. 15, 1993 3653

2*ol

v (cm”) (cm-’) (cm-’) Figure 8. Time-dependent velocity power spectra for overtone-excited HOCl in Ar. Calculations as described in the text. For all panels, the spectra calculated during the first, second, third, and ninth picosecond after excitation of the OH bond are displayed. The resolution of the spectra in this figure and in Figure 9 is 65 cm-I. (a, left) Gas phase, p* = 0; (b, middle) p* = 0.1 19; (c, right) p* = 0.830. \I

of time. To apply this idea to the current system, we compute the power spectrum during each picosecond after the overtone excitation. Thus, rather than eq 11, we use

In the following, we have taken 72 - T I = 1.024 ps, and we can therefore determine nine power spectra from our nonequilibrium simulations. In evaluating eq 13, a Parzen window is used in conjunction with standard FFT techniques’ l 6 so that the resulting power spectrum does not show any extraneous wings. We calculate the average is eq 10 over 100 trajectories. In the results presented here, we show velocity power spectra for 72 = 1,2, 3, and 9 ps at 298 K. Figure 8 displays these time-dependent spectra for pure HOCl (p* = 0) and for p* = 0.1 19 and 0.830. It is immediately evident that all these spectra differ substantially from the equilibrium power spectrum shown in Figure 7, as well as differing from each other. Through molecular dynamics calculations of the isolated O H fragment in Ar, we have found that the initial excitation of the fragment O H stretch to 80 kcal/mol creates a relatively narrow peak at -1400 cm-I, consistent with the frequency of the OH u = 10 level for the Schinke surface.Ii7 However, this peak is not the only feature evident in the pure HOCl spectrum of Figure 8a corresponding to the first picosecond after excitation. Instead, a broad feature between 2000 and 3000 cm-I has appeared (and is evident both in pure HOCl and in Ar solution). The appearance of this broad feature indicates that there has been substantial energy flow out of the O H bond in the first picosecond. Where does the energy go? Concentrating on the pure HOCl power spectrum first, Figure 8a, we note a broad feature at 500800 cm-i as well as sharper features at 1100 and 1400 cm-I. The spectra at later times show both of these latter features steadily disappearing. The broad feature steadily moves to higher frequencies, becoming a sharp peak at 900 cm-1 by the end of the ninth picosecond. This shift to higher frequencies is consistent with energies being lost out of an excited mode which then settles down into a more harmonic region of its potential. A closer examination of the pure HOC1 data shows a rise in the power at very low frequencies (2500 cm-I, as the O H vibration drops in excitation and becomes more harmonic. That this energy travels rapidly to other modes is evident in the

OC1 spectrum of Figure 9b, in which at the end of the first picosecond, the peaks corresponding to the OC1stretch and HOCl bend are substantially red shifted compared to their equilibrium values. As the dynamics progress, two effects can be observed. First, these stretch and bend peaks shift to the blue and become closer to their equilibrium values. In addition, a close examination of the OC1 spectrum shows that the zero-frequency component is increasing as a function of time as more HOCl molecules dissociate. Moving on to the p* = 0.830 solvent, we find that the O H component spectrum becomes more blue shifted with increasing time. This indicates that the initial energy transfer of energy out of the O H bond is even faster in the dense solvent than in the pure HOCl case. By the end of the calculated dynamics, almost all

The Journal of Physical Chemistry, Vol. 97, No. 15, 1993 3655

Dynamics of Overtone-Induced Dissociation

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l i m e (ps) Time (ps) Figure 10. OC1 and OH internuclear distances (in A) and HOC1 bond angle (in rad) as a function of time for several individual trajectories in the p* = 0.830 solvent. (a, left) Dissociativetrajectory. (b, middle) Dissociativerecombiningtrajectory. (c, right) A trajectory that undergo a dissociativerecombination-dissociativecycle. the power in this mode is near the frequency of the equilibrium O H stretch. The initial high-energy bend peak steadily shifts to higher frequencies as the bend loses energy. Although it is not immediately evident from this spectrum alone where the energy in this system goes, the relatively small dissociation probability suggests that what we observe here is energy loss into the solvent from highly excited bound molecules. As the energy is lost, the frequency of the various HOCl modes become much closer to their equilibrium values. We will conclude this section with a discussion of what happens in the higher density solvents to prevent dissociation from taking place. D. Dissociation and Recombination. We have found that, in the p* = 0.830 system, 10% of the trajectories recombine. We define a recombining trajectory as one that satisfies the nascent dissociation criterion (roc, 2 3 A) a t a time t , but at some later time T > t , the HOC1 molecule is again bound (roc1 < 3 A).This type of geminate recombination has been extensively studied for I2 photodissociation in liquids (see Haris et al.’’* for a review). In this section, we willdescribe the typeof recombination processes we have observed for HOCl in the high-density Ar solvent. Figure 10 displays a representative trajectory for each of three different kinds of dissociative or recombination processes in the p* = 0.830 solvent. In these figures, we plot the OCI and OH internuclear distances and the HOCl bond angle as a function of time after OH excitation. Figure 10a shows a dissociative trajectory. Dissociation is marked by an unperturbed excursion of several angstroms into the solvent followed by diffusive, randomwalk behavior for the remainder of the trajectory.’19 The energy in the OC1 stretch can be seen to slowly increase over the first 2 ps of thedynamics. The actual dissociative event is accompanied by a loss of energy both from the OH stretch and the bend, which up to this time, have been simply exchanging energy. Figure 1Obdisplays a dissociative-recombining trajectory. This trajectory shows an excursion into the solvent where approximately 1 ps is spent in apparent random-walk behavior before recombination occurs. In this trajectory, the dissociative event is marked by a sudden drop in the O H stretch energy. After recombination takes place, the O H stretch regains much of its vibrational energy, while very little energy remains in the OC1 stretch. Finally, Figure 1Oc displays an interesting trajectory that shows a dissociation-recombination-dissociation event. There is one recombination event of the type shown in Figure lob; however, the molecule in this trajectory eventually dissociates. This type of behavior is in part due to the large excitation energy initially

-

placed in the O H bond. Thus, even after recombination, there is enough energy left in the O H fragment to help fuel another dissociation event. Each of the dissociation events shows an increase in the HOC1 bending motion followed by a rapid decrease in the O H stretch energy. We make two general points about the recombination events. First, Figure 10b,c shows that the interactions of the fragments with the solvent that leads to recombination can occur fairly far into the solvent. If one were to try to interpret this process in a caging picture, it would be necessary to extend the notion of cage to one that includes more than one solvent shell. Second, many of the trajectories we have examined show a highly excited, but nondissociative, OCI bond. (“Highly excited” is signified by a value of roc1 greater than 2.5 A. Figure 2 shows that this is equivalent to a potential energy of at least 25 kcal/mol above the HOC1 minimum.) It is quite likely, given the high density of this solvent, that the lack of dissociation might result from HOClsolvent collisions rather than some intrinsic feature of the HOCl energy flow. If this is indeed the case, models of this process will have to take into account the important role of solvent interaction well before the OC1 bond has enough energy to dissociate. IV. Discussion and Conclusions

Our initial studies into the overtone-induced dissociation of HOCl have revealed some quite interesting behavior. The lowpressure p* = 0 pure HOC1 dissociation (see Figures 5 and 6) shows a distinctly nonexponential decay at short times (