J. Phys. Chem. 1987, 91, 312-314
312
Deactlvatlon of Vlbrationally Exclted Nitrogen Molecules by Colllslon with Nitrogen Atoms A. Lagan&,*E. Garcia, and L. Ciccarelli Dipartimento di Chimica, Uniuersitd degli Studi, Perugia, Italy (Received: March 5, 1986; In Final Form: July 24, 1986)
A classical trajectory study of the title reaction has been carried out at T = 1000 K on a tentative LEPS surface. Reactivity was found to be small at low vibrational states and to increase exponentially at higher vibrational energies. Nonreactive collisions were found to be strongly adiabatic, while no bias toward a given final vibrational state was shown by reactive processes.
1. Introduction Processes involving nitrogen atom-nitrogen molecule collisions are thought to be important in determining the complex mechanism of energy transfers in N 2 under electrical discharge. Vibrational excitation and deexcitation mechanisms in nitrogen plasmas have been discussed recently.' The modeling of these processes is usually based upon the assumption that the conversion between translational and vibrational energy is the least effective step of the complex mechanism leading to vibrational excitation of nitrogen molecules and, as a consequence, to its ionization and dissociation.* Due to a lack of both experimental and theoretical information, sometimes, rate constants for the process N
+ N,(u)
+
N ~ ( u ' )+ N
(1)
have been assumed to coincide with rates of relaxation in collisions between nitrogen molecules. The aim of this paper is to present values of rate constants obtained from a theoretical investigation of process 1 performed for a wide range of initial vibrational states of the target molecule. The paper is organized as follows: in section 2 we report the construction of a reasonable potential energy surface; in section 3 the computational technique as well as global and detailed rate constants calculated for process 1 are described.
than the reactants' ground state. This well correlates with the first excited state of the reactants, which has a 2D, lZg+symmetry and is located about 55 kcal/mol above the ground state of the reactants. As a consequence, the two lowest potential energy surfaces of the N N2 system cross when the nitrogen atom approaches the nitrogen molecule. Nonetheless, starting from reactants in the ground electronic state, no radical formation occurs. This fact implies that the spin-forbidden transition from the surface tied to the ground-state asymptotes to that supporting the intermediate complex is unlikely. That means that, in both the reactive and nonreactive cases, collisions can be assumed to occur on a single adiabatic surface connecting the N(4S,) NZ(lXg+)asymptotic state via the 142[ intermediate barrier. Using this information, we modeled a LEPS potential so as to yield a barrier height of 36 kcal/mol. Due to the symmetry of the system, only one Sato parameter needed to be adjusted. The resulting value of this parameter is -0.023. The remaining LEPS parameters were determined, as usual, from spectroscopic datas (re = 1.0977 A, De = 228.4 kcal/mol, fl = 2.689 A-'). A graphical analysis of this LEPS surface is given in Figure 1 where cuts of the surface taken every 10 kcal/mol are reported. Contour maps for the collinear approach (angle of encounter ( 0 ) of 180O) and for a 9 value of 135' are reported respectively in the left and right panels of the figure. The figure shows the smoath behavior of the surface, its strong curvature in the saddle region, and both the location and height of the barrier to reaction. From collinearity to lower angles of approach, the saddle height increases quite smoothly (only a few kcal/mol) for the first 45O, whereas it increases more rapidly, to above 70 kcal/mol, in the range between 45' and 90'.
+
+
+
2. Potential Energy Surface Information about the N + N2interaction was derived in the early 1960s from experimental studies of isotope-exchange processes. In the temperature range between 300 and 1300 K the experiment was unable to detect isotope exchange between I4N and '5N2.3 The authors of ref 3 indicated an upper bound of 0.66 X cm3/(molecule.s) for the rate constant of the global exchange process and suggested, as a reasonable lower limit for the activation energy, a value falling in the range between 14 and 3 1 kcal/mol. Similar conclusions were reached also by Bauer and T ~ a n g . In ~ addition, nitrogen molecules have been found to be quite stable in the presence of N atoms even when vibrationally excited.* The ground energy asymptote of the N 3 system is N(4S,) + N2('Zg+). In the strong interaction region this level correlates with the collinear 148; state. As suggested by experimental data reported above, the energy of the transition state of the 14Z; triatomic surface is quite large (this information is confirmed also by preliminary results of an accurate quantum calculation6). We have assumed for the potential energy barrier a tentative value of 36 kcal/mol. The ground state of the N 3 radical is known to be stabilized by a well7 about 12 4 kcal/mol lower in energy
3. Calculations and Results Calculations were carried out on this model surface using the same vectorized computer code adopted for calculating rate constants of the hydrogen atom-hydrogen molecule reaction? The main features of this program are described in ref 10. The initial conditions were selected by means of the importance sampling technique." Calculations were carried out by starting from reactants thermalized at 1000 K. Odd reactant vibrational numbers included in the interval ranging from 1 to 15 were used. As a reasonable compromise between the amount of time needed for integrating the chosen sample of trajectories and the degree of convergence obtainable for calculated rate constants, we adopted a maximum impact parameter of 2 A. We found, in fact, that for all u values considered the opacity function becomes zero at b > 1.8 A.
(1) Capitelli, M.; Gorse, C.; Ricard, A. Top. Curr. Phys. 1986, 39, 5 . (2) Polak, L. S.; Sergeev, P. A,; Slovetsky, D. I. High Temp. 1977, 15, 13. Golubovskii, Y. B.; Telezko, V. M. High Temp. 1984, 22, 340. (3) Back, R. A,; Mui, J. Y. P. J. Phys. Chem. 1962, 66, 1362. (4) Bauer, S. H.; Tsang, S. C. Phys. Fluids 1963, 6, 182. (5) Morgan, J. E.; Schiff, H. I. Can. J. Chem. 1963, 41, 903. (6) Petrongolo, C., private communication.
(7) Brunning, J.; Clyne, M. A. A. Chem. Phys. Lett. 1984, 106, 337. (8) Huber, K. P.; Herzberg, G. Molecular Spectra and Molecular Structure; Van Nostrand: New York, 1979. (9) Lagan;, A. Gazz. Chim. Ital. 1986, 116, 143. (10) Novak, M. M. Newsletter on Heauy Parricle Dynamics 1985, 7 , 1. ( 1 1 ) Faist, M. B.; Muckerman, J. T.; Schubert, F. E. J. Phys. 1978, 69, 4087. Muckerman, J. T.; Faist, M. B. J. Phys. Chem. 1979, 83, 79.
*
0022-3654/87/2091-0312$01 .50/0
0 1987 American Chemical Society
The Journal of Physical Chemistry, Vol. 91. No. 2, 1987 313
Deactivation of Nitrogen Molecules
3c c v) r
-m3 -u
2c
P 0
0
J --
2
i
i
,
I
4
0
2
4
rNa/
s!
-
\
A
10
8
Figure 1. Contour maps for the LEPS surface derived for the nitrogen atom-nitrogen molecule system at 0 = 180’ (collinear) (left panel) and 0 = 135’ right panel. Isoenergetic levels have been cut every 10 kcal/mol starting from 5 kcal/mol.
-yr o 6
i
3 0
0
-
12
6 n
Figure 3. Fixed u detailed rate constants k(u,u’=u-n) of the N + N2(u) N2(u’) N processes reported as a function of n. Triangles ( u = 15); circles (u = 13); squares (u = 11). Reactive values are shown in the
+
upper panel, nonreactive ones are reported in the lower panel. Typical error bars are given as dotted lines. reactive rate of the process rises from 5.8% at u = 7 to about 80% at larger u values. A marginal role is played by excitation to higher product vibrational states. It contributes to reactivity only at large u values ( u = 11, 13, and 15) and with a percentage never exceeding 2%. We have also analyzed the behavior of detailed state (u) to state (u? rate constants (k(u,u’)). A systematic investigation of the dependence of detailed rate constants upon the initial vibrational energy for the corresponding H H2 reaction is given in ref 13. For this reaction, it has already been seen that an appropriate way of reporting such a dependence is to consider the evolution of the rate constant value as a function of the gap n between the initial and the final vibrational state (n = u’- v). In this case, curves originated at fiied initial vibrational energy tend to group together and to have a similar shape. For the N + N,reaction, plots of the state to state rate constants are reported as a function of n in the upper panel of Figure 3 at u = 11, 13, and 15. The area covered by all these curves decreases with u in analogy with the behavior of the corresponding hydrogen system. Also the shape of these curves is similar to that of plots obtained for the H + H2 system. At negative values of n, they show, at first, a sharp increase. Then, after a maximum at about n = 0, they show a decrease to zero. A difference between the results for the nitrogen and hydrogen systems is the different interval of u spanned by the rate constant plots. This is due to the narrower spacing of the vibrational levels associated with the N, molecule. Another difference is, as expected from what is found for the global reactive rate constant, the smaller absolute value of the N N2detailed rate constants. This is not only associated with the higher barrier to reaction but also related to the heavier mass of the colliding partners. The trend is, in fact, in line with what happens when moving from a three hydrogen system to its isotopic variants.I4 In contrast with the strong vibrational diabaticity of reactive events, the dynamic behavior of nonreactive trajectories is dominated by vibrationally adiabatic events. This is well illustrated by the fact that for the first five u values no trajectory returns to the reactants’ asymptote in a vibrational state different from
+
V
Figure 2. Rate constants for reactive (circles) and nonreactive (triangles) vibrational deactivation and rate constants for reactive vibrationally adiabatic processes (squares) of the N + N2system reported as a function of the initial vibrational state.
Accuracy of the integration of the classical equations of motion was tested, as usual, against the constancy of the total energy, total angular momentum, and collision time. Random back-integrations were also performed. A step size of 0.1 fs was found to be satisfactory. About 47 000 trajectories were computed. The number of trajectories run a t a given initial vibrational state decreased from 5950 a t u = 1 to 5750 at u = 15. Among calculated trajectories no reactive outcomes were obtained a t u = 1 and 3. At larger u values (u = 5, 7, 9, 11, 13, and 15) the number of reactive events increased to 1, 5, 16, 41, 93, and 184, respectively. The corresponding values of the reactive (6.8 rate constants are (2.9 f 2.9) X lO-I5, (1.9 f 0.9) X f 1.7) X 10-14, (2.3 f 0.4) X (6.1 f 0.7) X lO-I3, and (1.4 f 0.1) X cm3/(molecule.s). A plot is given in Figure 2. The curve is a quite sensitive function of the vibrational energy available to the reactants. Its rate of increase is quite similar to that found for the corresponding curve of the H H2 reaction at low vibrational states. However, as shown in ref 12, the absolute value of the reactive rate constant for reaction 1 is almost 2 orders of magnitude smaller. Most of the rate constant increase with u is due to the contribution of collisions not conserving the initial vibrational number. In fact, as shown by Figure 2, the fraction of events leading to deactivated products increases quite dramatically with the amount of vibrational energy available to reactants. Accordingly, the contribution of deactivation to the
+
(12) Garcia, E.; Laganl, A. Chem. Phys. Letr. 1986, 123, 365.
+
(13) Garcia, E.; Lagan& A. J . Phys. Chem. 1986, 90, 987. (14) Ciccarelli, L.; Laganl, A,, unpublished results.
314
J. Phys. Chem. 1987, 91, 314-317
the initial one. Only at quite large v values does the deviation from adiabatic behavior becomes appreciable. Nonreactive deactivation rates have a value of 2.9 X 6.0 X lO-I4, 1.4 X and 4.9 X cm3/(molecule-s) respectively at v = 9, 11, 13, and 15. The importance of deactivation mechanisms is reflected also by the shape of the plots of detailed rate constants when reported as a function of n. Apart from the sharp peak for the elastic (n = 0) rate constants not reported in the figure, these plots have no definite trend with n. This is clearly illustrated by the lower panel of Figure 3, where the nonreactive k(v,u’ = ~ n ) rate constant values are reported at fixed v values. Although we did not carry out a graphical analysis of individual trajectories, we expect that the dynamics of nonreactive vibrational deactivation is determined by those events that spend most of their life in the strong interaction region before finding their way out. In fact, the dynamical outcome of these trajectories is known to have a sensitive dependence on even small variations of the initial conditions and, therefore, to lead to a substantially random population of final states.15
4. Conclusions Rate constants calculated for the N + N, reaction using a classical trajectory approach show that the system is scarcely reactive for reactions thermalized at 1000 K even when the initial vibrational number is large. The nitrogen system is less reactive than the similar hydrogen system, although the vibrational energy dependence of the reactive rate constants was found to be similar to that for the H H2reaction. Nonreactive collisions were found to be strongly biased toward vibrationally adiabatic behavior, in contrast with the dynamics of reactive collisions.
+
Acknowledgment. We thank M. Capitelli for stimulating the systematic investigation of the kinetics of vibrationally excited nitrogen molecules colliding with nitrogen atoms and for useful discussions. Registry No. N2, 7727-37-9; N, 17778-88-0. (15) Lagan& A.; Hernandez, M. L.; Alvarifio, J. M. Chem. Phys. Lett. 1984, 106, 41 and references therein.
Dynamics of Charge Recombination Processes in the Singlet Electron-Transfer State of Pyrene-Pyromeilitic Dianhydride Systems in Various Solvents. Picosecond Laser Photolysis Studies Noboru Mataga,* Hiroshi Shioyama, and Yu Kanda Department of Chemistry, Faculty of Engineering Science, Osaka University, Toyonaka, Osaka 560, Japan (Received: April 14, 1986; In Final Form: August 26, 1986)
In order to elucidate the underlying mechanisms showing that no dissociated ion radicals are produced even in acetonitrile solution when some complexes of the strong electron donors and acceptors with CT absorption bands in the visible region are photoexcited, we have made detailed time-resolved transient absorption spectral measurements and timeresolved fluorescence measurements upon the pyrenepyromellitic dianhydride (PMDA) system in various solvents with picosecond laser spectroscopy. A weakly fluorescent electron-transfer (ET) state with 400-pslifetime is formed by photoexcitation in benzene solution, while nonfluorescent geminate ion pairs with much shorter lifetimes due to the charge recombination (CR) deactivation are formed in more polar solvents. In all solutions examined, dissociation into free ions from the geminate pair cannot compete with the CR deactivation which becomes faster in more polar solvents due to the decrease of the energy gap between the ion pair and neutral ground state. Moreover, it has been demonstrated that ion pairs produced by encounter between excited pyrene and unexcited PMDA in acetonitrile have more loose structure and show a smaller CR rate constant than those produced by exciting the ground-state complex.
The photoinduced electron transfer (ET) and charge separation (CS) in solution take place through the encounter between excitedand ground-state molecules or excitation of the ground-state EDA (electron donor-acceptor) complex.’ Fairly detailed studies on behaviors of the ET state have been made for the systems with a relatively large energy gap between the E T and ground state such as typical exciplexes and weak EDA complexes.’ However, such studies on the systems with stronger electron donors and acceptors or with considerably smaller energy gaps between the ET and ground state were scarce, mainly because of the very rapid nonradiative degradation of the E T state to the ground state. Investigations on the dynamics of such short-lived ET states have become possible by the picosecond laser photolysis method.Ic” (1) See for example: (a) Mataga, N.; Ottolenghi, M. In Molecular Assocation; Foster, R., Ed.; Academic: New York, 1979; Vol. 2, p 1. (b) Mataga, N . In Molecular Interactions; Ratajczak, H., Orville-Thomas, W. J., Eds.; Wiley: Chichester, 1981; Vol. 2, p 509. (c) Mataga, N. Pure Appl. Chem. 1984, 56, 1255. (2) Mataga, N.; Karen, A.; Okada,T.; Nishitani, S.; Kurata, N.; Sakata, Y.; Misumi, S . J. Am. Chem. Soc. 1984,106,2442. (b) Mataga, N.; Karen, A.; Okada, T.; Nishitani, S.; Sakata, Y.; Misumi, S. J. Phys. Chem. 1984, 88, 4650. (c) Mataga, N.; Karen, A,; Okada, T.; Nishitani, S.; Kurata, N.; Sakata, Y.; Misumi, S. J . Phys. Chem. 1984, 88, 5138. (d) Mataga, N. THEOCHEM. 1986, 135, 279. (e) Mataga, N.; Okada, T.; Kanda, Y.; Shioyama, H. Tetrahedron, in press.
0022-365418712091-0314$01.50/0
Nevertheless, systematic picosecond laser photolysis studies on various factors affecting the dynamic behaviors of such systems are rather scarce. In the previous papers, we have reported the detection of the short-lived exciplex state of porphyrin-quinone systems by means of the picosecond laser photolysis method in nonpolar solvent and its solvation-induced ultrafast deactivation in polar solvents.2a,b In contrast to the case of typical exciplexes like the pyrene-N,N-dimethylaniline (DMA) and pyrene-p-dicyanobenzene CpDCNB) systems or weak EDA complexes like the 1,2,4,5-tetracyanobenzene (TCNB)-toluene system which are fluorescent in nonpolar or less polar solvents and undergo the dissociated ion radical formation in strongly polar solvents, the porphyrinquinone exciplex is practically nonfluorescent even in nonpolar solvents and does not show any dissociated radical ion formation even in strongly polar solvents due to the overwhelming ultrafast charge recombination (CR) deactivation. Since the porphyrin-quinone systems have much smaller energy gaps between ET and ground state compared to the typical exciplexes and weak EDA complexes, the above result is a demonstration of the strong energy gap (3) (a) Hilinski, E. F.; Masnovi, J. M.; Amatore, C.; Kochi, J. K.; Rentzepis, P. M. J. Am. Chem. Soc. 1983, 105, 6167. (b) Hilinski, E. F.; Masnovi, J. M.; Kochi, J. K.; Rentzepis, P. M. J . Am. Chem. SOC.1984, 106, 8071.
0 1987 American Chemical Society
