J. Phys. Chem. 1987,91, 4727-4733 pairs of reactants, this energy match is sufficiently close to move the CT band into a region accessible with the irradiation sources employed here. Visible/UV absorption studies in these systems will be required to locate the positions of the CT absorptions and clarify the photochemical behavior of these complexes. Su”aQ The twin-jet deposition of C1F and Clz with a series of alkynes and alkenes has given rise to infrared absorptions that can be attributed to the 1:l complex between the two subunits. Strong
4727
shifts to lower energy were observed for the ClF stretching mode in these complexes; distinct variations in the shifts were nonetheless observed with the degree of methyl substitution. The spectra strongly support a structure in which the halogen is serving as a Lewis acid and interacting with the 7~ electron density of the alkene or alkyne in a T-shaped structure.
Acknowledgment. The author gratefully acknowledges support of this research by the National Science Foundation under Grant C H E 8400450.
-
Spectroscopy of the Transition State (Theory). 4. Absorption by HFH$ in H 4- FH’ HFHt HF -tH‘
-
J. C. Polanyi,* M. G. Prisant,t and J. S. Wrightt Department of Chemistry, University of Toronto, Toronto, Canada M5S I AI (Received: November IO, 1986; In Final Form: April IO, 1987)
+
- -
Absorption spectra of transition-state configurations have been computed for the reaction H FH’ HFHr H F + H’. The density of HFHt in configuration space was obtained from a classical trajectory study of the collinear reaction on the Williams and Wright (WW) ab-iitio *Zground-state potential surface. An upper *IIsurface was calculated for the purposes of this study by using the same MRD-CI (multiple reference doubleexcitation; con@uration interaction) method. Absorption spectra were constructed by mapping the densities in configuration space to the vertical energy difference between the upper and lower surfaces. Structured absorption is predicted in the range between 190 and 240 n m - a favorable spectral region for experimental study. The effect of increasing reagent translational and vibrational energy on the form of the transition-state spectrum is reported, the former shifts the spectral features to the red, and the latter to the blue. These shifts are associated with reaction through more compressed configurations in the first case and more extended in the second case.
Introduction The nature of molecular configurations intermediate between reagents and products is central to discussions of the molecular dynamics of chemical reactions. Direct experimental observation of intermediate configurations-termed collectively transition states-is rendered difficult by their short lifetime (61 ps). Despite these difficulties, results from several laboratories indicate that experimental techniques are emerging from the study of transition states in elementary gas-phase reacti0ns.I Further experiments on the chemiluminescence of reactive transition states: electron emission from transition states,’ and laser absorption by transition states4J have been reported since the appearance of these reviews. This experimental activity was preceded by extensive theoretical discussion of the feasibility and modality of transition-state spectroscopy.6 It has been argued that the feasibility of transition-state spectroscopy is assured, since it represents no more than the reactive analogue of the established field of far-wing line broadening.’ The present work constitutes part 4 in a series of 1D and 3D classical trajectory studies of simple exchange reactions which consider the question of the information that may be extracted from studies of transition-state spectra, and the spectral regions appropriate to the study of specific reactiom8 On the first point it was concluded that for reactions occurring with selected reagent collision energies across contrasting exothermic potential energy surfaces (PES) the intensity, breadth, and structure of the transition-state spectrum will be sensitive to the dynamics on the reactive surface and to the form of the difference potential between the pair of optically linked PES. To separate these two contributing factors one should envisage varying the reagent energies, reagent energy distributions, isotopic masses, Department of Chemistry, University of California at Berkeley, Berkeley, CA 94720. ‘Department of Chemistry, Carleton University, Ottawa, Canada K l S 5B6.
and PES (i.e., reacting on the upper or lower of the pair of PES). There exists, in addition, the possibility of observing quantum structure in transition-state spectra. This has been demonstrated in recent quantum scattering studies on H + HZ”I (employing the same PES as the classical studiesBbVc). These expedients are most likely to succeed if ab initio computation of the PES provides an approximate guide to its form. (1) For r a n t reviews covering exchange reactions see: (a) Brooks, P. R.; Curl, R. F.; Maguire, T. C. Eer. Bunsen-Ges.Phys. Chem. 1982,86,401. (b) Foth, H. J.; Polanyi, J. C.; Telle, H. H. J . Phys. Chem. 1982, 86, 5027. The related field of the spectroscopy of photodissociation is reviewed in (b) and in (c) Imre, D.; Kinsey, J. L.; Sinha, A.; Krenos, K. J. Phys. Chem. 1984, 88, 3956. (2) Arrowsmitb, P.; Bly, S. H. P.; Charters, P. E.; Polanyi, J. C. J . Chem. Phys. 1983, 79, 283. (3) Benz, A.; Morgner, H. Mol. Phys. 1986, 57, 319. (4) (a) Maguire, T. C.; Brooks, P. R.; Curl, R. F. Phys. Rev. Lett. 1983, 50, 1918. (b) Maguire, T. C.; Brooks, P. R.; Curl, R. F.; Spence, J. H.; Ulrich, S. J. J. Chem. Phys. 1986,85,844. ( 5 ) Kleiber, P. D.; Lyyra, A. M.; Sando, K. M.; Heneghan, S. P.; Stwalley, W. C. Phys. Rev. Lett. 1985, 54, 2003. (6) (a) For references to studies by T. F. George and co-workers see George, T. F. J . Phys. Chem. 1982,86, 10. (b) Lau, A. M. F. Phys. Rev. A 1976,13, 139; Phys. Rev. A 1976, 14, 279. Phys. Rev. Lett. 1978, 43, 1009. Phys. Rev. A 1980,22,614. (c) Duhv, V. S.;Gudzenko, L. I.; Gurvich, L. V.; Yakovlenko, S. L. Chem. Phys. Lett. 1977,45, 330. Yakovlenko, S. I. SOD. J . Quantum Electron. 1978, 8, 151. (d) Orel, A. E.; Miller, W. H. Chem. Phys. Lett. 1979, 57, 362. J . Chem. Phys. 1979, 70, 4393. (e) Light, J. C.; Altenberger-Siczek, A. J . Chem. Phys. 1979, 70, 4108. Orel, A. E. in Potential Energy Surfaces and Dynamics Calculations, Truhlar, D. G.,Ed.; Plenum: New York, 1981; p 639. (7) Polanyi, J. C. Faraday Discuss. Chem. SOC.1979, 67, 129. (8) (a) Polanyi, J. C.; Wolf, R. J. J . Chem. Phys. 1981, 75, 5951; designated part I of the present series. (b) Mayne, H. R.; Poirier, R. A.; Polanyi, J. C. J . Chem. Phys. 1984,80, 4025; part 11. (c) Mayne, H. R.; Polanyi, J. C.; Sathyamurthy, N.; Raynor, S. J . Phys. Chem. 1984, 88, 4064; part 111. (9) Engel, V.; Bacic, 2.;Schinke, R.; Shapiro, M. J . Chem. Phys. 1985, 84, 4844. (10) Agrawal, P. M.; Mohan, V.; Sathyamurthy, N. Chem. Phys. Lett. 1985, 114, 343. (11) Engle, V.; Schinke, R. Chem. Phys. Lett. 1985, 122, 103.
0022-3654/87/2091-4727$01.50/00 1987 American Chemical Society
4128
The Journal of Physical Chemistry, Vol. 91, No. 18, 1987
Consequently, work has been focussed on the systems H3 and, in the present study, FH2. These two systems have provided the proving ground for a b initio computation of PES over the past decades. An account of extensive work performed on the system FH2 (and hence on the HFH configuration, most relevant to the present study) is to be found in a review by Schaefer.Iz In the work reported here we have used a previous ab initio computation,13 based on the Buenker MRD-CI method,I4 for the HFH ground state and a (new) computation in the same approximation to obtain the first excited PES, HFH*. The transition-state H F H’. spectrum is calculated for collinear H + FH’ The approach used to simulate the electronic spectrum of the transition state is semiclassical: the Landau-Zener-Stuckelberg method. A steady-state distribution of HFH’ geometries over the 1D configuration space is obtained from a batch of classical trajectories. This is done by partitioning configuration space using a rectilinear grid. The time spent by individual trajectories in each bin is tabulated. In a second step, the accumulated time spent by all trajectories in each configuration is mapped to the vertical energy difference between the upper and lower potential at that geometry. The intensity as a function of frequency in the simulated spectrum is given by the accumulated time in a given energy interval. A fuller implementation of the semiclassical approach for simulation of electronic spectra would require specification not only of the PES on which the reaction takes place, and that of the optically coupled state, but also the transition dipole surface.I5 This was not included (see, however, ref 8b). The simulation for H H2given in our earlier worksb showed a transition-state spectrum which consisted of a wing at first falling from the Lyman-a atomic transition to the red and then rising to a satellite feature. The position of the satellite feature changed with reagent energy. The strong absorption in the Lyman-a region was due to a flattening of the difference potential in the limit of large reagent separation, and the consequent contribution of many configurations to the corresponding frequency interval. The satellite feature (or features) was due to the slowing of trajectories at turning points on the lower surface. The satellite positions for particular translational and vibrational reagent energies were determined by the vertical energy differences ( A E = E” - EL) of the turning point configurations. In the H + Hz system, these positions varied with reagent translational energy between 1500 and 2000 A. The basic features of the spectrum remained when translational averaging and a transition dipole were added to the collinear simulation.8b These same features survived the extension of the calculation to three dimensions.8c Experimental study of the H + H2 system is complicated by the positioning of transition-state structure in or near the vacuum-ultraviolet region of the spectrum. In the present study we consider the spectrum from the collinear reaction H FH’ HFH’ HF + H’. This system has a high barrier (44 kcal/mol) to reaction in the lower stateI2J3and, given the stability of HFH+, would be expected to give a deep well in the upper state HFH*. The high barrier and deep well could shift the transition-state satellite structure of the colliding H + FH system to the red of that predicted for H H2. In addition to its theoretical tractability this system could therefore represent a better prospect for experimental study.
-
+
+
-
+
-
+
Potential Energy Surfaces A full description of the calculation of a collinear scattering surface for F H H has been given elsewhere;24 the principles by ’~ which the lower collinear HFH surface was c o n s t r ~ c t e d are similar and will be reviewed briefly here. A basis set was chosen as in ref 24, consisting of double {plus polarization (DZP) nuclear-centered AOs, and (s,p) bond functions with equal exponents located at the midpoints of the HF bonds in the triatomic system (12) Schaefer, H. F. 111J . Phys. Chem. 1985, 89, 5336. (13) Williams, R. J.; Wright, J. S., to be submitted for publication. (14) Buenker, R. J.; Peyerimhoff, S. D.; Butscher, W. Mol. Phys. 1978, 35,771. Buenker, R. J.; Peyerimhoff, S. D. Theor. Chim. Acta 1974, 35, 33. Theor. Chim. Acta 1975, 39, 217. (15) Shapiro, M.; Zeiri, Y. J . Chem. Phys., submitted for publication
Polanyi et al.
H- -F- -H. With this basis set the diatomic H F asymptote was determined to have the dissociation energy 6.16 eV (expt, 6.125 eV). The surface was constructed by the rotated Morse curvecubic spline (RMCS) choosing a “swing point” in the noninteraction region where r , = r2 = 10 bohr. Ab initio data points were generated along rays of constant swing angle 9 in the R M C coordinate system, and Morse parameters obtained by least-squares fitting along each ray were interconnected by using cubic splines (more details follow in the next section). The minimum barrier height of 44 kcal/mol occurred at 0 = 45O, with rl = r2 = 1.15 A. This barrier height is within 5 kcal/mol of other recent experimental and theoretical values.Ib2’ A contour map of the lower HFH surface created in this way is shown in Figure la, where the position of the barrier is indicated. A new potential surface for the optically coupled zIIstate was computed for the purposes of this study by using similar techniques, although some points require further explanation. The multireference double excitation configuration interaction (MRD-CI) program of Buenker and Peyerimhoff and co-workers14 was used for the calculation. The atomic basis set of Gaussian-type orbitals was obtained as follows: For hydrogen, the basis set consisted of the same DZP basis of Huzinagaz3using the Dunning22contraction (4slp/2slp). The s orbitals were scaled by 1.44 to allow for the molecular environment22and the p exponent was l.0?4 Two sets of Rydberg s and p orbitals with exponents 0.1 152 and 0.0288 were added to the D Z P basis set. Using these exponents fixed the difference between the and 2P states to agree with the experimental separation of 10.204 eV. The fluorine basis set consisted of the (9s5pld/4s2pld) DZP basis used previo~sly.’~ Finally, a bond function basis of (s,p) orbitals with exponent 0.85 was positioned at the midpoint of each H-F bond.I3sZ5 The exponent 0.85 was determined to be optimum for H F at its equilibrium internuclear distance. For the CI calculation, the lowest occupied core orbital (fluorine 1s) and highest vacant orbital were excluded from consideration; all other single and double excitations from the S C F 211reference configuration were examined. Only one reference configuration was found to be necessary, since it accounted for more than 95% of the C I wave function (Le. the square of its coefficient in the CI wave function exceeded 0.95). Test configurations which lowered the energy by more than a specified tolerance (40 Khartree) in a 2 X 2 CI calculation with the reference configuration were included in the final CI wave function. Typically, 1000-2000 configurations were included from about 10000 total configurations tested. Extrapolation of the energy to zero selection threshold gave the CI energy. Finally, the Davidson correctionz6 for quadruple excitations was applied to the CI energy to obtain the estimated full CI energy, from which the potential surface was constructed. The potential surface was constructed by using the RMCS methodz4with the swing point chosen at rl = r2 = 10 bohr. The energy of the swing point consists of the energy of the separated atoms H(*P) H(2S) + F(2P). The hydrogen atomic energies were calculated by using the DZP + double Rydberg basis described previously. For the fluorine atom, a slightly different basis set was used than the one described in the text, based on the following considerations: First, it would have been desirable to
+
(16) Bender, C. F.; Garrison, B. J.; Schaefer, H. F. J . Chem. Phys. 1975, 62, 1188. (17) Wadt, W. R.;Winter, N. W. J. Chem. Phys. 1977, 67, 3068. (18) Botschwina, P.; Meyer, W. Chem. Phys. 1977, 20, 43. (19) Bartoszek, F. E.; Manos, D. M.; Polanyi, J. C. J. Chem. Phys. 1978, 69, 933. (20) Voter, A. F.; Gcddard, W. A. J . Chem. Phys. 1981, 75, 3638. (21) Dunning, T. H. J. Chem. Phys. 1984, 88, 2469. (22) Dunning, T. H. J . Chem. Phys. 1970, 53, 2823. (23) Huzinaga, S. J. Chem. Phys. 1965, 42, 1293. (24) Wright, J. S.; Donaldson, D. J.; Williams, R. J. J . Chem. Phys. 1984, 81, 397. (25) Wright, J. S.; Williams, R. J. J . Chem. Phys. 1983, 79, 2893. (26) (a) Davidson, E. R. In The World of Quantum Chemistry, Daudel, R., Pullman, B.,Eds.; Reidel: Dordrecht, Holland, 1974; p 17. (b) Butscher, W.; Shih, S. K.; Buenker, R. J.; Peyerimhoff, S. D. Chem. Phys. Left.1977, 52, 457.
The Journal of Physical Chemistry, Vol. 91, No. 18, 1987 4729
Spectroscopy of the Transition State
TABLE I: Rotated Morse Parameters for HFH* 8, deg D, eV Po, A-I I,, A A,, A-I 0.000 10.000 20.000 30.000 35.000 37.500 40.000 42.500 45.000
25t
0.7-
,., , .
.
.
1
.
'
HFH
*
2.0
15
0.098 0.099 0.099 0.059 0.113 0.070 0.091 0.000 0.149
A2,
A-2
0.183 0.174 0.165 0.004 0.011 0.007 0.014 0.000 0.175
include Rydberg orbitals on fluorine so that the H- -F- -H system could form molecular Rydberg orbitals with contributions from all three atoms. However, direct inclusion of fluorine Rydberg orbitals caused severe linear dependence problems due to the diffuseness of such orbitals and their excessive overlap with the hydrogen Rydberg orbitals. As a result, the SCF calculation failed in the strong interaction region. This S C F failure required us to delete the Rydberg orbitals from the fluorine basis set. However, at short FH distances the F atom was able to "borrow" the Rydberg basis of the H atom, causing an overestimate of the dissociation energy of H F by 0.16 eV. These difficulties were eliminated by determining the energy of the F atom at the swing point with addition of the H-atom Rydberg orbitals to its basis set; this resulted in an improved H F dissociation energy of 6.13 eV. In the intermediate HFH region, we found that both fluorine basis sets yielded nearly identical energies, since the Rydberg character of the excited state can be correctly described by locating Rydberg orbitals on either the H or F atoms. CI data points were calculated along rays of constant 0 for 0 = 0, 30, 35, 31.5, 40, 42.5, and 45", where 10 - rl tan 0 = 10 - r2
+
where x = I - ,I @ = Po( 1 A,x + A2x2),and I, is the distance from swing point to minimum in potential. The five fitted parameters are les, D, p,, A,, and A2. At least eight points and the swing point were used in the fits of each ray; typical root mean square deviations of the fit were on the order of 0.01 eV. Values of the Morse potential parameters for the 0, 10, and 20" rays were taken from the lower surface; this ensured that upper and lower surfaces ran parallel in the asymptotic limit, with appropriate Lyman-a energy difference. The Morse potential parameters for all the rays are given in Table I. A cubic spline was used to interpolate these values and to define all points on the surface. The main features of the calculated upper surface were as follows. The well minimum is at rl = rz = 0.95 A (compared with the crest of the barrier on the lower surface which is at r , = r2 = 1.15 A). The well depth on the upper surface is 91.25 kcal/mol (3.96 eV). The vertical difference potential at the minimum of upper state well occurs at 3.2 eV. The vertical difference potential from the crest of the barrier on the lower surface is 5.49 eV. Lower surface, upper surface, and difference potential are shown as Figure la-c. The potential energies of the lower and upper states (L and U) can be compared, along the minimum energy path of the b surface, in Figure 2.
I
3.0
(a) 2.5
2.0
!O
n
oa
Y
IO
P 1.5
0 '0
0
8
0
1.0 0.7
1.0
1.5
r,
2.0
2.5
3.0
[il-;~
Figure 1. (a) The potential energy surface of the lower state, HFH 22. Contours are given in kcal/mol relative to the potential minimum of asymptotic H(*S) + FH. (b) T h e potential energy surface of the upper state, HFH* 211. Contours are given in kcal/mol relative to the potential minimum of asymptotic H('P) + HF. (c) The energy difference between the upper and lower state as a function of molecular geometry. Contours are given 10' cm-I.
4.377 4.445 4.658 5.056 5.349 5.532 5.748 5.969 6.140
V(1) = D[(1 - exp(@x))*- 11
0.7
07
2.28395 2.24918 2.14619 1.98424 1.85763 1.82550 1.72912 1.60629 1.53826
The ray at 45" corresponds to rl = rz, where the potential minimum occurs in the upper state. The data were fitted to a fiveparameter generalized Morse function defined by2'
1.0
T
6.162 6.162 6.162 6.436 6.708 7.027 7.803 9.026 10.117
Classical Trajectory Calculations Collinear classical trajectory calculations were carried out on the lower potential surface. The vibrational eigenvalues of the H F molecule at the asymptotes were determined by a Numerov-Cooley procedure. Turning points for vibrational levels 0-5 were determined by examining a single trajectory with appropriate vibrational energy and zero translational energy. (27) Whitten, W. N.; Kuntz, P.J. J . Chem. Phys. 1976,64, 3624.
4730 The Journal of Physical Chemistry, Vol. 91, No. 18. 1987 lo
5r---r
, -
7 H+FH ( v = O )
-230 -220
I
-210
- 200 190
2 0-
15-
IO-
O
4L
'-27
-21
-15
-09
L
-03
03
R X N COORD
09
15
21
L
27
[ & 4
Figure 2. Potential energy of upper and lower states along the minimum energy path of the lower state: the bottom axis labels distance from the barrier col along the minimum energy path in mass weighted coordinates.
The passage of trajectories was considered over the square region 0.7 A < rl < 2.7 A and 0.7 8, < r2 < 2.7 A. This region was uniformly divided into 2.25 X lo4 smaller boxes each having a length of 0.0133 A. For this mesh resolution, the maximum variation of the vertical energy difference between upper and lower potentials between neighboring boxes was smaller than lo00 cm-I. The position of a trajectory at the end of each time step of 0.5 X s was determined and a count was added to the appropriate box in configuration space. The choice of time step was tied to the mesh resolution: over the range of energies considered in this study at least four steps were required for a trajectory to traverse a box. Trajectories were chosen to be uniformly distributed over the initial phase of reagent vibration. A sufficient number of trajectories were taken to ensure (by trial and error) that the separation between trajectory paths was less than the box dimension of the mesh. The counts accumulated over all trajectories determined a density map which gave the time spent in a particular region of configuration space and, therefore, the relative concentration of each intermediate geometry. Spectra were calculated from the density map produced by the classical trajectory calculation as follows. The central point of each box in configuration space was used to fix the difference potential for that box. The counts in each box in configuration space were then mapped according to the assigned difference potential to a bin of 1000 cm-' width in frequency space. The frequency bin width for the spectral histogram was dictated by the mesh resolution of the trajectory calculation and was chosen to be greater than the maximum variation of the difference potential over neighboring boxes of the configuration space mesh. The final spectra histogram represented counts accumulated in each frequency box after scanning over all the boxes in configuration space. Appropriate choice of mesh resolution and time step were the crucial determinants of noise in the simulated spectrum. By contrast, for a given mesh resolution and time step the noise was insensitive to the number of trajectories. Results Dependence of the Spectrum on Collision Energy. Figure 3 shows the dependence of the transition-state spectra on reagent
' 3b0 250 200 I50 Figure 3. Variation of transition-state spectrum with changing collision energy; transition-state absorption spectra for colliding H + FH at energies of 0.5, 1.0, 1.5, and 2.0 eV at a resolution of 1000 cm-'. The vibrational energy of the reagent is kept constant at u = 0 (0.26 eV). The top axis gives the frequency displacement in IO' cm-' from the L, line. The scales on the bottom axis give the absolute position in lo3cm-' and in nanometers. The left-hand axis gives the average time spent by a single trajectory in each frequency interval. The right-hand axis gives the number of counts in each frequency bin compiled over 40 trajectories s. Small letters denote features discussed with a time step of 0.5 X in the text. collision energy a t the zero point vibrational energy of 0.26 eV. The units on the left-hand ordinate give the average time spent by each trajectory in particular frequency interval. The units on the right-hand ordinate give the total number of trajectory steps accumulated over 40 trajectories in each frequency interval. Because these calculations do not encompass the asymptotic configurations of separated reagents and product, they yield no information on the intensity of the Lyman-a atomic absorption relative to the collision-induced "wing" absorption. The total time spent by HFHt in traversing the spectral region shown is
-
S.
Increasing the collision energy from 0.5 to 2.0 eV decreases the integrated intensity of the absorption spectrum and shifts the position of the principal satellite feature to the red. The first effect is due to the decreasing time of collision with increasing collision energy. The second effect is caused by the shift of the translational turning points to regions of smaller reagent separation, higher potential energy, and reduced vertical energy difference between upper and lower surface. We now consider the collision dynamics in greater detail. Figure 4 a - d shows the density plots corresponding to collision energies of 0.5, 1.0, 1.5, and 2.0 eV superimposed on the difference potential contour plot of the H F H system. The peak densities have been normalized to 1.0. The filled areas indicate densities of 30.5, whereas the lines have a density of 0.1. The curves that resemble those in Figure IC are the difference potential contours. At 0.5 eV the transition-state spectrum exhibits a single satellite peak at 63 000 cm-' with an intensity corresponding to total time of 0.005 ps spent between 62 500 and 63 500 cm-I. This satellite peak may be identified as originating from the regions of highdensity labeled a' and a" in Figure 4a. These regions of high density correspond to the vibrational turning points of the FH' reagent at the H atom distance of closest approach (the "translational turning point"). The scattering at this collision energy is entirely elastic. At 1.0 eV, the satellite peak has shifted to 54000 cm-' and diminished by a factor of 60% in intensity. The satellite peak
The Journal of Physical Chemistry, Vol. 91, No. 18, 1987 4731
Spectroscopy of the Transition State
(d) 2 7
(b) 2,7
l-----4 T.20
T= 1.0 V.0.26
2.2
n
oa
I
V.0.26
22-
L-1
N
(c) 27
I 26 T= I 5 V=O
22
Figure 4. Variation of transition-state density with changing collision energy: the density plots show just high-density regions (filled areas, density 2 0.5) and a 0.1 density contour line, as determined from the time spent in each region of configuration space in the classical trajectory calculation. The density distributions are normalized to the point of highest density. The difference potential contours, labeled in lo3 cm-I, are superimposed on the plot. Small letters refer to features in Figure 4, discussed in the text. The collision energies are (a) 0.5 eV, (b) 1.0 eV, (c) 1.5 eV, and (d) 2.0 eV
originates from the regions of high density shown in Figure 4b, corresponding to the vibrational turning points in the r2 coordinate, a t the translational turning point rl = 1.37 A. The vibrational amplitude in the strong interaction region is marginally larger than that of the reagent. Scattering, however, remains totally elastic and nonreactive. At 1.5 eV, the translational turning point satellite moves to 46000 cm-I. A shoulder c begins to appear on the red side of the satellite maximum. Figure 4c shows that the translational turning points (a’ and a”) of the elastically scattered trajectories occurs at rl = 1.25 A. In addition to the elastic scattering, the trajectory calculations show that approximately 20% of the collisions undergo nonreactive inelastic scattering. These vibrationally inelastic collisions transfer approximately one quantum of vibration to the scattered FH’. The distortion in the strong interaction region gives rise to this inelastic scattering. This can be seen on the density map, since region b lies at a more extended vibrational amplitude, corresponding to HF (0’ = 1). Regions a’ and b contribute to the broadening of the satellite peak. The penetration of trajectories to higher points on the barrier hill (region c, with r , = 1.2 A, lies farthest up the barrier, see Figure la) gives rise
to a band of density parallel to the difference contour. This contributes to the formation of the shoulder between 40 000 and 44 000 cm-l in the transition-state spectrum. At a collision energy of 2.0 eV the primary satellite peak has shifted to 40000 cm-I. The peak has diminished fourfold in intensity from the 0.5-eV spectrum. The satellite peak is broadened to the blue and the red of its maximum. A secondary satellite c appears to the red at 35 000 cm-’. Figure 4d shows the density plot for this collision energy. The primary satellite feature may again be identified with the turning point of r vibration (points a’ and a”) in the collision complex, at rl = 1.16 Turning point a’ and the large amplitude vibration (forming HF ( u ‘ = 1))in the strong interaction region b at rl = 1.05 8, contribute to broadening the primary satellite to the blue. The translational energy in this case is sufficient to surmount the barrier: approximately half of the collisions at this energy are reactive. The reactive encounters traverse the col in the region of the minimum barrier energy (symbolized + in the figure), since the total reagent energy is 52 kcal/mol as compared with the barrier height of 44.3 kcal/mol. After traversing the col in region c the system forms products with little vibrational excitation. The density in region
A.
4732 The Journal of Physical Chemistry, Vol. 91, No. 18, 1987 6p
(b)
5,O
4p
3p
2,O
Polanyi et ai.
1,o
H + FH'(v.5)
21
300 250
200
150
'
lnml
Figure 5. Variation of transition-state spectrum with changing reagent vibrational energy (translational energy held constant at 1.0 eV). The arrow indicates the peak position in the u = 0 spectrum of Figure 3, at 1.0 eV. The format is identical with Figure 3. Small letters label features discussed in the text. In (a) the vibrational energy is 1.2 eV (HF ( u = 2)); and in (b) the vibrational energy is 2.6 eV (HF ( u = 5)).
c runs virtually along the 35 000-cm-' difference potential and consequently accounts for the secondary satellite seen at this frequency. Dependence of the Spectrum on Reagent Vibrational Energy, Figure 5 shows the dependence of the transition-state spectra on reagent vibrational energy at a collision energy of 1.0 eV, with Figure 5a showing u = 2 reagent vibrational excitation and Figure 5b showing u = 5. The spectral resolution, trajectory time step, mesh resolution, and axis labels are in accordance with the spectra previously presented. Increasing the reagent vibrational excitation from u = 0 (0.26 eV) to u = 2 (1.2 eV) both moderately shifts the position of the 54000-cm-' satellite (shown in Figure 3) to the red and increases its intensity. Figure 6 shows the density map for the trajectory calculation. The satellite feature is due to the vibrational turning regions a' and arr at the H atom distance of rl = 1.3 A. Though widely separated these two turning points lie virtually on the same difference potential and are not resolved in the transition-state spectrum. A third region of high density b corresponds to larger displacement motion in the strong interaction region en route to reaction. The presence of this feature broadens the satellite to the blue. Approximately 30% of the collisions are reactive. Reaction occurs by corner cutting as seen from the region labeled c on the density plot. The density originating from corner-cutting trajectories runs parallel to the 50 0 0 0 - ~ m -difference ~, potential contour and accounts for the red shoulder on the spectral peak (Figure 5a). Doubling the vibrational energy to u = 5 (2.6 eV) significantly erodes the peak structure in the transition-state spectrum (Figure 5b). A primary satellite a of much diminished intensity relative to the "wing" background appears between 55000 and 57000 cm-I. The red shoulder of this feature extends to 50000 cm-' terminating in a secondary satellite b at 50000 em-'. Past this point, the spectral intensity rapidly falls to a background of weak intensity extending to 40000 cm-I. Figure 6b shows the density plot compiled over 80 trajectories for this energy combination. The erosion of satellite structure is due to the smearing of trajectory density over a greater range of configuration geometries in the presence of high translation and vibration in the reagents. The buildup of intensity at the trajectory turning points is diminished relative to the average
" '07
1'2
2'2
27
Figure 6. Variation of transition-state densities with changing reagent vibrational energy. The format is that of Figure 4. Small letters refer to features labeled in Figure 5 and discussed in the text. (a) Vibrational energy = 1.2 eV ( u = 2) accumulated over 40 trajectories. (b) Vibrational energy = 2.5 eV (u = 5) accumulated over 80 trajectories.
density. The vibrational turning points a' and a" account for the primary satellite feature. A buildup of density in region b due to the vibration of the distorted complex contributes to the presence of a secondary satellite. Fully two-thirds of the trajectories are reactive. The reactive trajectories cut the corner of the potential surface in an extreme fashion, along density ridge c. The corner cutting contributes to the spectrum in the region indicated in Figure 5b, since c runs along the 67 000-cm-' difference potential. The corner cutting leads to high vibrational excitation in the new bond (oscillation in r i r Figure 6b). Conclusion
According to this collinear computation the system H + H F is well-suited to studies of transition-state spectroscopy. Atomic H can be readily formed experimentally (by photolysis of hydrides) with velocities corresponding to centre-of-mass collision energies in the 1-2-eV range employed here. Under these conditions, according to the present calculation, collisions of H with the F end of HF wiIl form compressed HFHI transition states that exhibit maxima in their absorption spectra in the region 190-250 nm. This is a region in which there exist intense excimer laser sources. The most serious limitation of the present computation is the we found that restriction to collinear collisions. For H + H28b.c
J. Phys. Chem. 1987, 91, 4733-4743 relaxation of this restriction had only a minor effect on the predicted spectral features. This had to do with the fortunate circumstance that the altered density distribution for bent configurations mapped onto altered difference potentials in such a way that similar spectra were predicted for bent as for collinear configurations. There will be other systems, and H F H * may be one, in which collisions in variously bent configurations give rise to spectral features that are markedly displaced from one another. It does not follow, even in such a case, that the observed spectrum averaged over bent configurations will be featureless, but it would lack the relatively sharp features that we report here. As in line-broadening experiments it is not only the location of satellite features, but also the breadth and shape of the far-wing, that yields information as to the nature of the interaction. Questions of central interest to the understanding of molecular motions in chemical reactions include the duration of the reactive encounter (reflected here in the relative intensity of the “wing” 20000-60000 cm-’ to the red of the atomic H absorption), the complexity of the encounter (the spectrum is broadened and flattened by increasing ergodicity), the configuration of highest potential energy en route from reagent to product (often indicated in the spectrum by a feature reflecting accumulated density of absorbers in the neighbourhood of the energy barrier), and the related question of the direction from which nascent reaction products approach the exit valley of the PES. On this last point, we have noted in a number of previous theoretical and experimental studiesZ*that enhanced reagent (28) Ding, A. M. G.; Kirsch, L. J.; Perry, D. S.; Polanyi, J. C.; Schreiber, J. L. Faraday Discuss. Chem. SOC.1973, 55, 252. Polanyi, J. C.; Schreiber, J. L. Faraday Discuss. Chem. SOC.1977, 62, 261, and references therein.
4733
translation tends to give rise to reaction through more-compressed intermediate configurations, which in turn leads to acceleration along the exit valley, as evidenced in enhanced product translation. By contrast enhanced reagent vibration leads to reaction through more-extended intermediates (the so-called “corner cutting” on the PES) so that the characteristic acceleration is ucross the exit valley, with efficient vibrational excitation of the newly formed chemical bond. These contrasting dynamics are evident in the calculated density distributions shown here in Figures 4b and 6, a and b. They evidence themselves in the corresponding transition-state spectra by shifts (of 10 000-30 000 cm-I) in features a and c with changing reagent energy distribution; in the present system compressed transition states absorb at much longer wavelengths (i.e., to the red) as compared with extended transition states. The extent of these redistributions in spectral intensity with altered reagent energy should, when taken together with the measurements of redistribution of product excitation, advance our understanding of the details of the process by which chemical reagents evolve into products.
Acknowledgment. We thank Professor R. J. Buenker for the use of his MRD-CI program and for helpful discussions. We are grateful for the computer time made available to us by the University of Ottawa and the C M S development project at the University of Toronto. M.G.P. thanks the Department of Chemistry at Carleton University for the generous hospitality extended to him during his stay there. This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC). Registry No. H atomic, 12385-13-6;HF, 7664-39-3;H2, 1333-74-0.
Photophysical and Theoretical Studies of Photoisomerism and Rotamerism of trans-Styrylphenanthrened C. Bartocci, F. Masetti, U. Mazzucato,* A. Spalletti, Dipartimento di Chimica, Universitri di Perugia, I-061 00 Perugia, Italy
I. Baraldi, and F. Momicchioli Dipartimento di Chimica, Universitd di Modena, I-41 100 Modena, Italy (Received: December 18, 1986; In Final Form: April 1, 1987)
The photophysical and photochemicalproperties and the ground-state conformational equilibrium of trans-n-styrylphenanthrene (n-StPh, with n = 1, 2, 3,4, 9) have been studied in inert solvents. The kinetic parameters of the competitive radiative and reactive decay processes have been obtained. A detailed analysis of the fluorimetric behavior as a function of the excitation wavelength and temperature has allowed the distinct decay parameters and the ground-state energy difference of the two rotamers of trans-3-StPh to be obtained. Parallel theoretical calculations of the potential energy curves for the internal rotation of the phenanthryl group in the ground state, of the energies and oscillator strengths of the lowest transitions, and of the activation energies for trans cis isomerization in the ground and lowest excited singlet states have been carried out with a modified (CS) INDO method. The results of the experimental and theoretical studies are in satisfactory agreement and provide a general description of the photophysical and photochemical behavior of this class of compounds.
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Introduction The luminescence properties, photochemical reactivity, and ground-state conformational equilibrium of diarylethylenes have been thoroughly investigated in the past years in our and other laboratories.’ Recently, we reported an extensive description of the behavior of trans-n-styrylnaphthalene (n-StN, with n = 1, 2), based on a Paper presented at the XI IUPAC Symposium on Photochemistry, Lisboa, July 1986; Abstract 2P-27.
0022-3654/87/2091-4733$01.50/0
fluorimetric analysis and CNDO/S calculations of the electronic properties of the conformers.2 The interpretation of the trans cis photoisomerization mechanism indicated the coexistence of an activated singlet Pathway, which Prevails above room ternperature, and an intersystem crossing (ISC) followed by isom-
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( I ) For a review, see: Mazzucato, and references cited therein.
U.Pure Appl. Chem. 1982, 54, 1705
(2) Bartocci, G.; Masetti, F.; Mazzucato, U.; Marconi, G. J . Chem. Sor., Faraday Trans. 2 1984, 80, 1093.
0 1987 American Chemical Society
