J . Phys. Chem. 1988, 92, 3858-3863
3858
A Surface-Hopping Quasi-Classical Trajectory Study of Li(2P) 4- H,, D, Quenching Charles W. Eaker Department of Chemistry, University of Dallas, Irving, Texas 75062-4799 (Received: October 7 , 1987)
We have studied the quenching of Li(*P) by H, and D2 with a semiclassicalsurface-hopping trajectory method. The quenching process involves two potential energy surfaces which are determined by using the optimized diatomics-in-molecules (ODIM) procedure. Using the ODIM procedure, we were able to obtain good fits to ab initio points available for these two lowest surfaces. The nonadiabatic coupling values are also in good agreement with ab initio values. We obtained the following quenching cross sections (in A2) at four different translational energies for H2 and D,, respectively: at ET = 0.039 V, 22.7 and 21.7; at ET = 0.062 eV, 19.7 and 17.5; at ET = 0.101 eV, 14.6 and 13.6; at ET= 0.140 eV, 11.0 and 10.3. These values are lower than the experimental values. We have shown that the experimental cross sections are unusually large with respect to the current models and long-range potentials for this reaction.
I. Introduction Quenching of excited alkali-metal atoms by small molecules has been studied experimentally and theoretically. The quenching of excited lithium atoms by H, and D2
+ H2 Li(2P) + D2
Li(,P)
+
+
Li(,S) Li(,S)
+ H2 + Dz
is particularly interesting from a theoretical standpoint, because the potential energy surfaces for these systems are accessible to very accurate a b initio calculations. This means that these reactions can provide a basis for testing theoretical techniques for studying quenching and nonadiabatic processes in general. Several experimental groups have determined quenching cross sections for these reactions. In the first experimental study, Jenkins,' in 1968, used flame measurements at 1400 K (ET = 0.1 19 eV) to determine the quenching cross section for H2. More recently, Lin and Weston2 applied the single-photon time-correlation method in a 1976 study of Li(,P) quenching by several gases, including H2 and D,. The quenching by H2 and D2 was studied under nonthermal conditions with translational energies of 0.10-0.17 eV for H2 and 0.13-0.28 eV for D2. In 1980 Elward-Berry and Berry3 reported Li quenching cross sections for H2 and D2 at 564 K (ET= 0.062 eV) using a dye laser excitation and interferometric fluorescence analysis technique. Unfortunately, there is not very good agreement among these research groups for the quenching cross sections or even the direction of the isotope effect. Jenkins' cross section is about 20% lower than the Lin and Weston value of 23 A2 at ET = 0.1 19 eV. At ET = 0.062 eV, the Elward-Berry and Berry cross section is 35 f 6 A' for H, and 48 f 6 A2 for D,. If the Lin and Weston cross sections are extrapolated to this energy (see ref 2 for details) by using the absorbing sphere (AS) or Langevinaioumousis-Stevenson (LGS) model, then the H2 cross section is 28 A2 (AS) or 31 A2 (LGS) and the D, value is 26 A2 (AS) or 29 A2 (LGS). Notice Lin and Weston find D2 to be a slightly less effective quenching while Elward-Berry and Berry find D2to be a significantly more effective for 2P lithium. There have been a number of theoretical studies aimed at understanding Li(,P) H, quenching. In 1968 Krauss4 calculated, at the Hartree-Fock level, the four lowest LiH, potential energy surfaces in the C,, and C2,configurations. These calculations showed that the ,B, and 2Al curves crossed in the C2, geometry as RHH increased from 1.O to 2.5 a,. Tully' used the DIM method to construct the potential energy surfaces and to calculate the nonadiabatic interactions. These calculations pro-
+
(1) Jenkins, D . R. Pror. R . Sor. London, A 1968, 306, 413. (2) Lin, S.-M.; Weston, R. E., Jr. J . Chem. Phys. 1976, 65, 1443. (3) Elward-Berry, J.; Berry, M. J. J . Chem. Phys. 1980, 72, 4510. (4) Krauss, M. J . Res. Natl. Bur. Stand., Sect. A 1968, 72. 553. (5) Tully, J. C. J . Chem. Phys. 1973, 59, 5122.
0022-3654/88/2092-3858$01.50/0
TABLE I: DIM Basis Functions A ( L i ) B (H) C ( H ) A B ( L i H )
AC(LiH)
BC (H2)
2s
Iz1+
'z,+
Izg+
3z1+
3z,+
3z,+
2 s 2 s 2 s
'n
3n
3Z"+ 9,+ 3ZU+
2 s 2 s
2 s
2 s
2P,
2 s
2Px
2 s
2P,
2s
2s
2S 'S(Li+) 2S 'S(Li+) 'S(H-)
2P,
2S IS(H-) zS
In
lZ2+ 3 ~ 2 +
'n
1z2+
3z2+
2Z+(LiH+) '2,' 'Z3+
IZ*+
2zg+(H2-)
*Z+(LiH+) 2Z,'(H2-)
vided a general understanding of the quenching process, even though there are significant errors in the surfaces. The most thorough ab initio study of the LiH, potential energy surfaces has been performed by Mizutani and co-workers. Their first paper6 in 1979 was a preliminary study of the ground-state and firstexcited-state surfaces restricted to C,, geometry using the OVC MCSCF approximation. In their 1984 paper7 they improved the calculations using a valence CASSCF method with a minimum basis set and included more geometries. Most recently, they report* MCSCF calculations on the two lowest states of LiH, using a basis set of double-{-plus-polarization quality. Each improved calculation has increased the depth of the well in the ,B2 surface and decreased the minimum energy for the intersection of the ,B2 and ,Al surfaces. Another high-quality ab initio calculation has been performed by Saxe and Y a r k ~ n y .This ~ work involves using MCSCF/CI wave functions to calculate several energies and nonadiabatic coupling matrix elements. We will compare our DIM results to these ab initio values in section I1 of this paper. 11. Potential Energy Surfaces
To use a semiclassical surface-hopping technique to study nonadiabatic processes, like quenching, we must first determine the potential energy surfaces for all surfaces involved in the reaction. The diatomics-in-molecules (DIM) method is a semiempirical technique for calculating potential energy which offers a number of advantages for nonadiabatic studies. Since it constructs a Hamiltonian matrix, a single diagonalization of that Hamiltonian gives the ground- and excited-state energies at each geometry. By use of the optimized diatomics-in-molecules (ODIM) method, the off-diagonal terms of the Hamiltonian are ( 6 ) Mizutani, K.; Yano, T.; Sekiguchi, A,; Hayashi, K.; Matsumoto, S. Bull. Chem. Sor. Jpn. 1979, 52, 2184. (7) Mizutani, K.; Yano, T.; Sekiguchi, A,; Hayashi, K.; Matsumoto, S. Bull. Chem. SOC.Jpn. 1984, 57, 3368. (8) Matsumoto, S.; Mizutani, K.; Sekiguchi, A,; Yano, T.; Toyama, M. Int. J . Quantum. Chem. 1986, 29, 689. (9) Saxe, P.; Yarkony, D. R. J . Chem. Phys. 1987, 86, 321. (10) Pedersen, L.; Porter, R. N. J . Chem. Phys. 1969, 50, 478. (11) Sharp, T. E. At. Data 1971, 2, 119. (12) Partridge, H.; Langhoff, S. R. J . Chem. Phys. 1981, 74, 2361.
0 1988 American Chemical Society
The Journal of Physical Chemistry, Vol. 92, No. 13, 1988 3859
Quenching of Li(2P) by H2 and D2
3.0
TABLE II: Diatomic Morse Functions"
state 'Z8+(H2) 3Z,,+(H,) zZ,+(H;') 2Z,+(Hz-) 'Z1+(LiH) lZ,+(LiH) IZ3+(LiH) 3ZI+(LiH) 3Zz+(LiH) 'II(LiH) 'II(LiH) %+(LiH)
De
a
Re
0.17448 0.072 30 0.03603 0.061 4 0.092 30 0.043 0 0.043 2 0.004 29 0.02095 0.001 36 0.010 38 0.003 60
1.04435 1.00012 1.07168 1.4902 0.6494 0.3648 0.2237 0.5724 0.3058 0.8941 0.8460 0.9000
1.4008 1.4008 2.0 1.4490 3.0104 4.295 1.2636 4.0 3.0 4.5251 3.6560 4.25
f
-
+ + -
-
+ + -
T, 0.0 0.0 -0.02772 -0.02772 0.0 0.06791 0.17036 0.0 0.06791 0.06791 0.06791 0.19808
ref
2.5
10 10 11 11 12 12
2.0
b, c 13 13 12 13 14
1.5 1.0 ?...
>
->
2.5 2.0 1.5
TABLE 111: Mixing Parameters"
1.0
2.4900 2.7161 1.9608 2.5296
'Zl3+
lZ23+ 3Z12+
0.6933 0.9492 1.0470 1.1844
"FI(R) = AR2 exp(-BR). parametrized, and the parameters can be adjusted to fit accurate a b initio points on the surfaces. All derivatives and nonadiabatic coupling needed in the trajectory calculation can be determined analytically. The DIM Hamiltonian for the 2A' states of LiH2 is made up of eight basis functions. These are shown in Table I. Notice that we have included the ionic terms Li+H- which are important in describing the LiH potential energies. The diatomic potential energy curves are represented as Morse functions. The parameters for the Morse functions are found in Table 11. These parameters were determined by fits to accurate ab initio curves; the references are also listed in Table 11. To determine the parameters for the 311state of LiH, we estimated the correlation energy to be given by Ce-ER,where C = 0.013 hartree and p = 0.5 a{', and lowered the ab initio values for Docken and HinzeI3 by this amount. This changed the Morse parameters (Q, a,Re) from (0.008 29,0.8645, 3.7370) to (0,010 38, 0.8460, 3.6560). We believe this gives a better approximation of the exact )ll curve and leads to more reasonable values for the long-range potential of the 2 2A' LiH2 surface. For the 'E3+ ionic state of LiH, we have included the additional terms to the Morse function to properly account for the ionic nature of this state. The parameters for this state were determined in the LiH, surface optimization procedure. What distinguishes an optimized diatomics-in-molecules calculation from the usual DIM calculation is that we consider the interaction of diatomic states with the same symmetry to be given by a mixing function ti, of the form tfj(R)-I = AR2 exp(-BR) where A and B are parameters to be determined in an optimization procedure. This then gives for the matrix elements in the fragment diatomic Hamiltonian Hij
=
Vicos2 e + 5 sinZe ( 6 -5) cos 6 sin e ( 6- 5)cos e sin e 6 sin2 e + 5 cos2 e)
(
where COS'
8=
5 ?I .2
1 + &j2
cos 6 sin 8 =
0.0 3.5 3.0
V,,,(R) = D,(exp[-2a(R -Re)] f 2 exp[-a(R - Re)]}+ T,. bThese parameters were determined in the surface optimization. V(R) = V,(R) - [1.0 - 3.5784 exp(-0.4965R)]/R.
'%2+
0.5
sin2 6 =
1 1
+ Sit
Sij
1
+ ti;
(13) Docken, K. K.; Hinze, J. J . Chem. Phys. 1972, 57, 4928. (14) Lin, C. S. J . Chem. Phys. 1969, 50, 2787.
0.5
Figure 1. Potential energy curves for perpendicular-bisectorapproach ( x = 90') of Li + H2 as functions of Li-to-Hz distance, RLi-H2:(top) RHH = 1.4 a,; (bottom) RHH = 2.0 ao. 4.0
3.5 3.0 2.5 2.0 1.5 c
0
1.0
- 04 .. 50 2 3 . 5 3.0
2.5 2.0 1.5 1.0
-
0.5 2 S
3.5
4.5
5.5
6.5
RLi-H2(a01
Figure 2. Potential energy contours for the two lowest energy surfaces for x = 90': (top) ZAlsurface; (bottom) 2B2 surface. The values of the contours are in eV. The dashed line is the seam of intersection. and and v/ are the potential energies of diatomic states i and j at internuclear separation R. The parameters A and B are determined by fitting known features of the polyatomic surface or surfaces. To determine the optimal parameters for LiH,, we chose a set of 50 points: 18 on the 1 ,A', 18 on the 2 ,A', and 14 on the 3 'A' surfaces. We used a simplex algorithm to obtain from these points the eight mixing function parameters found in Table I11 and the five diatomic curve parameters shown in Table 11. The energies relative to Li(2S) + H2(X IZg+)of the four lowest potential energy surfaces at x = 90' and fixed RHH are graphed in Figure 1 as a function of RLi-H,. We will describe the geometry of LiH2 in terms of RLi-H2, the distance from Li to the center of mass of H2, RHH, the separation of the two H atoms, and x,the angle between the vectors corresponding to RLi-H2 and RHH. The top panel is for RHH = 1.4 a. and the bottom panel for R H H = 2.0 a,. For x = 90° there is an actual crossing of the ,A, and ,B2 surfaces. Notice how the location of the crossing of two lowest states changes as RHH increases. The highest 'B2 state is a little
3860 The Journal of Physical Chemistry, Vol. 92, No. 13, 1988
Eaker
TABLE I V Comparison of DIM and ab Initio Nonadiabatic Coupling
" AE
3.OO
1.814
90.0 89.95 89.9 89.5 89.0 85.0 75.0 60.0
0.00682 0.00683 0.00687 0.00783 0.0103 0.0391 0.119 0.276
-0.0037 -3.842 -7.576 -29.041 -3 3.74 1 -1 1.453 -3.133 -0.496
0.0069 5.408 10.646 40.770 47.390 16.372 5.245 1.967
10.968 10.934 10.834 8.394 4.980 0.572 0.297 0.264
3 .OO
1.89
90.0 89.95 89.9 89.5 89.0 85.0 75.0 60.0
Ab Initio 0.00693 0.00695 0.00699 0.008 15 0.01 10 0.0434 0.129 0.262
0.000 -4.186 -8.277 -30.413 -33.262 -10.645 -3.375 -1.210
0.000 7.394 14.622 53.732 58.779 18.959 6.429 3.016
11.735 11.690 11.558 8.479 4.611 0.240 -0.039 -0.092
= E ( 2 2A') - E( 1 2A').
q2is actually q2/RLi-H2.
too low, but the other states are in good agreement with ab initio calculations. Figure 2 gives a contour plot of the 2A, surface (top panel) and the 2B2surface (bottom panel) for x = 90°. The dashed line indicates where the surfaces cross. The minimumenergy crossing point (RLi-H2, R H H , x) occurs at (3.0, 1.75, 90') with energy 1.27 eV. The minimum in the 2B2surface is found at (3.27, 1.5, 90') with energy 1.10 eV, giving a well depth of 0.74 eV. In the most recent calculation by Matsumoto et aL8 the 2Bzminimum (3.3, 1.5, 90') has energy 1.46 eV and depth 0.46 eV. Our 2B2 minimum is in better agreement with the more accurate ab initio calculation of Hobza and S ~ h l e y e r ,who ' ~ determine the well depth to be 0.71 eV. The Matsumoto 2B2-2A, minimum crossing geometry is (2.93, 1.91, 90') with energy 1.77 eV. This crossing minimum in the MCSCF/CI calculation of Saxe and Yarkony9 was located at (3.0, 1.9, 90°) with energy 1.50 eV. Saxe and Yarkony did not calculate the 2B2minimum-energy point, and Hobza and Schleyer did not calculate the crossing minimum. The MCSCF/CI value should be closer to the exact value since their absolute energy, -8.544 hartrees is lower than the value of -8.530 hartrees of Matsumoto et al. Our DIM value is 0.21 eV lower than the MCSCF/CI energy and is perhaps a little low. However, we found that if we increased the energy of this crossing point to the Saxe and Yarkony value of 1 S O eV with a ZB2well depth of 0.59 eV (with a different set of parameters), our quenching cross sections decreased by about 25% for H2 at E, = 0.039 eV. It is certainly possible that the ab initio value could be too high by 0.1-0.2 eV. Overall, we are pleased with the agreement of our surfaces with ab initio points. It would be beneficial if we had further information at the MCSCF/CI level of the location of the 2B2minimum. Since the Saxe and Yarkony paper calculate nonadiabatic coupling matrix elements, we can compare these to the DIM values. The DIM and ab initio results are shown in Table IV. In order to compare the two methods in a similar region, we adjusted the R H H distance to 1.75 ao. This placed the 'Bz state below the 2Atstate by the same amount in the DIM calculation (0.006 82 eV) as in the ab initio calculation (0.006 93 eV) at x = 90'. The nonadiabatic coupling matrix elements between states i and j along direction M are defined as df = ( S i l V & P j ) In our DIM calculation we consider only changes in the coefficients of the basis functions and do not include changes in the basis functions themselves.I6 With this assumption, these matrix elements can be determined analytically in DIM as df = (VM%)jj/(Ej- E[) (15) Hobza, P.; Schleyer, P. v. R. Chem. Phys. Lett. 1984, 105, 630 (16) Eaker, C. W. J . Chem. Phys. 1987,87,4532. (17) Preston, K.; Tully, J. C. J . Chem. Phys. 1971, 54, 4297.
TABLE V Quenching Cross Sections (A2) E T , LW-AS" LW-LGS" quencher eV (exptl) (exptl) H2 0.039 35 36 Hz 0.062 28 31 H, 0.101 24 26 H2 0.140 22 24 D2 D2 D2
D2
0.039 0.062 0.101 0.140
Reference 2.
33 26 22 20
34 29 25 22
EBBb (exptl) 35 f 6
48 f 6
this work (calcd) 22.7 f 0.7 19.7 f 0.7 14.6 f 0.6 11.0 f 0.6 21.7 f 1.0 17.5 f 1.0 13.6 f 0.8 10.3 f 0.7
Reference 3
where Vu% is the derivative of the DIM Hamiltonian and Eiis the energy of state i. As can be seen in Table IV, the DIM results are in good agreement in magnitudes and angular dependence with the ab initio values of Saxe and Yarkony. The best agreement is for d q p and df2. The DIM values for dfyH are a little lower than the ab initio values. The DIM and a b initio nonadiabatic coupling terms were found also to be in good agreement in our studyt6of Na(2P) H2 quenching.
+
111. Trajectory Calculations In order to account for surface hopping, we use a classical path technique developed by Blais and Truhlar.18 In this method the probability of being on a particular surface i is given by ]ail2where the ai's are given by integrating
ul = -CaJ(Q.dlJ)exp[-(i/h)J'(E,
-
E,) dt]19
J#I
where Q is the time derivative of the nuclear coordinates, d, is the nonadiabatic coupling matrix elements, and E,, E, are the adiabatc energies. During each trajectory, the value of 1aIl2is monitored. If it drops below 0.5, we generate a random number to determine the surfacej on which the trajectory will proceed. The a,'s are then reset to .6, I f j corresponds to a different surface (Le., a "hop" has occurred), then the momentum must be adjusted. We use a formula derived by Miller and George.20 We choose the direction of the new momentum vector to be that of the coupling vector d,,. We only allow hops between surfaces 1 and 2. For this trajectory study we focused on studying the dependence of quenching as a function of translational energy for H2 and D2. Initially, the diatom is in its ground vibrational state, v = 0, and (18) Blais, N . C.; Truhlar, D. G. J . Chem. Phys. 1983, 79, 1334. (19) Tully, J. C. In Dynamics ofMolecular Collisiom, Part B; Miller, W. H., Ed.; Plenum: New York, 1976. (20) Miller, W. H.; George, T. J. J . Chem. Phys. 1978, 68, 185.
The Journal of Physical Chemistry, Vol. 92, No. 13, 1988 3861
Quenching of Li(2P) by H2 and D2
TABLE VI: Orbiting Impact Parameters and Long-Range Potentials dispersion“ ab initiob DIM ET. eV borbrao Sorb: A2 barb, ao S o r b l C A2 barb, ao Sorb: A2 0.039 0.062 0.101 0.140
o.zll 1
1
22.2 18.8 16.1 14.4
8.7 8.0 7.4 7.0
“Reference 2. bReference8.
10.0 9.4 8.7 8.2
24.8 21.2 17.4 15.6
9.2 8.5 7.7 7.3
29.3 25.9 22.2 19.7
= (1/3)rborb2
‘Sorb
l
0.0
2
0
4 b
6
8 1 0
(a01
-> >
Figure 3. Probability of Li + H2 quenching as a function of impact parameter. ET = 0.039 (-), 0.062 (---), 0.101 and 0.140 eV (---). (e-),
0
t h e j = 1 rotational state. The translational energies used were 0.039, 0.062, 0.101, and 0.140 eV. The maximum impact parameters were 10.5, 10.0, 9.1, and 9.0 ao, respectively. The equations of motion and a,’s were integrated by using a standard Adams-Mouton predictor-corrector algorithm with a time step of 1.2 X s. At each translational energy, we analyzed 400 trajectories with H2 and 200 trajectories with D2.
IV. Results The quenching cross sections are listed in Table V. The values calculated by the trajectory method include a factor of to account for the equal distribution of Li(2P) + H2 or D2 collisions among the three surfaces: 2 2Ar,3 2Ar,and 1 2Ar’. Our results are all lower than the experimental values of Lin and Weston2 and of Elward-Berry and Berry.3 The experimental values listed for Lin and Weston correspond to their results in the region 0.10-0.17 eV fit to either the absorbing sphere (AS) model or the Langevin-Gioumousis-Stevenson (LGS) model.21 The A S quenching cross sections are given by Sts(E,) = ~ R 2 [ 1 V(R,)/E,] where R, is the capture radius that leads to quenching and V(R,) is a potential energy term. Fitting the experimental cross sections to this equation gives for H2 (D2) R, = 2.33 (2.22) A and V(R,) = -0.040 (-0.043) eV. Another model, the LGS model, predicts quenching to occur for all trajectories that overcome the effective potential barrier arising from the long-range attractive potential and the repulsive centrifugal potential. If we assume the longrange potential is due to dispersion forces, V(R)= -C6/R6, then the LGS cross sections will be
sbGs(ET)= w( 3T / 2) (2c6 / E T ) where w is the quenching efficiency. Lin and Weston found w to be 0.55 (0.52) for Li H2 (D2) where c 6 is the Slater-Kirkwood value of 53.7 eV A6. Our results show little or no difference in quenching for H2 and D2, similar to Lin and Weston results and unlike the finding of Elward-Berry and Berry where D2 has a significantly higher quenching cross section a t ET = 0.062 eV. To understand what the magnitude of quenching cross sections can tell us about this reaction, consider the opacity function plotted in Figure 3. This graph indicates how the probability of quenching varies with impact parameter, b. We notice that this function for E T = 0.039 eV has oscillations around 80% out to a fairly large value of b and then drops off suddenly. This is the same type of opacity function as found previously by Blais and TruhlarIs for Na(2P) H2 quenching. This is consistent with the LGS model, which assumes a constant probability of quenching out to a maximum impact parameter equal to the orbiting impact parameter, bo& As the translational energy increases to 0.140 eV, the average quenching probability starts off around 70% for low impact parameters and then more gradually goes to zero as the
+
+
(21) Gioumousis, G . ; Stevenson, D. P. J . Chem. Phys. 1958, 29, 294.
-. 020
-. 0 3 0
t’ I
r 8
10
12
14
RLi -HJaO1
Figure 4. Long-range Li-H2 potentials for x = 90°, RHH = 1.4 ao: DIM (-),
ab initio*
(-a),
dispersion2 (---).
impact parameter increases. The orbiting impact parameter can be determined from an effective potential of the form VefdR) = V(R)
+ ETb2/R2
by requiring at the centrifugal barrier Veff(Rmax)
We have determined, as shown in Table VI, borbfor three different Li(2P) H2 potentials. The values labeled Sorb, which are given by (1/3)?rbOrb2,provide an upper limit to the quenching by assuming that all collisions with b < barb quench. The factor of is included, as discussed previously, to account for the distribution of collisions among the three Li(2P) H2 surfaces. The dispersion potential gives maximum cross sections lower than observed experimentally. This is interesting, because Lin and Weston fit their data to the LGS model, assuming a dispersion potential
+
+
SkGS(E,) = W?rborb2= w(3T/2)(2C,/ET)1/3 For H2, they determined w, the quenching efficiency, to be 0.55, which at first thought seems reasonable. However, if we properly include the factor of then w would have to be 1.65, which is not reasonable. This is not this case for Na(2P) + H2 quenching, where w = 0.2, since w is “corrected” to give a 60% probability of quenching with the dispersion potential and the LGS model. Therefore, it seems that if we want to invoke the LGS model for Li(2P) H2 quenching, the long-range potential must be more attractive to give a larger value for barb. Figure 4 gives three different long-range potentials for the perpendicular approach of Li(2P) to H2 in the region 8.0-15.0 a,,. The ab initio and our DIM potentials are more attractive than the dispersion potential, with the DIM potential being much more attractive for RLi-H2 less than 10 a@ This is reflected in the larger values of barb and S o r b in Table VI. Only in the case of the DIM potential are the Sorb values close to the Lin and Weston experimental cross sections. In making this comparison, we have made the assumption that all trajectories with b < barb quench, whereas in our trajectory study at most 80% of our trajectories quench. Our conclusion from this analysis is that the experimental Li(2P) + H2 quenching cross sections are large considering the best estimates of the long-range potentials involved. There are three possible theoretical resolutions: (1) the assumption that the fraction of collisions that can possibly quench
+
3862 The Journal of Physical Chemistry, Vol. 92, No. 13, 198'8 1801
I
i
I
I
I
I
I
1
I
I
Eaker TABLE VII: Diatomic Excitation followine Ouenchine
ET,eV
E,,,, eV
i 35
Li(*S)
90 m
0"'"''' 0 2 4 b
8 1 0
6 [aBl
Figure 5. Average scattering angle as a function of impact parameter and 0.140 eV for Li H2. ET = 0.039 (-), 0.062 (---), 0.101
+
(e-),
(- -).
-,251.0
2.16 2.18 2.22 2.26
0.039 0.062 0.101 0.140
2.07 2.10 2.14 2.17
Li(*S)
4s
-
0.039 0.062 0.101 0.140
C
I I
l I
l I
I I
I
l I
l I
Eyj, eV
(u')
ci')
0.85 0.83 0.79 0.82
0.88 0.82 0.74 0.74
3.60 3.72 3.74 4.08
1.24 1.18 1.07 1.15
4.70 5.83 5.70 6.13
+ H2(u'j?
+ D2(v'j? 0.76 0.80 0.75 0.78
tional quantum numbers are fairly constant with ( u ' ) = 0.8 and (j') ii: 3.8 for H2 and ( u ' ) = 1.2 and ( j ' ) ii: 5.6 for D ,. The percentage distribution of u'is similar for all translational energies with 39:42:16:4:0% for H2 and 31:35:22:11:2% for D, with u ' = 0:1:2:3:4 at ET = 0.062 eV. We have also analyzed the surface-hopping behavior of these trajectories. We will discuss the results for the Li(,P) + H2 trajectories at ET = 0.062 eV. Of these 400 trajectories, 273 (68%) quenched and 127 (32%) exited on the 2 *A' surface. The average number of times per trajectory that a surface-hopping decision was made was three for quenching trajectories and two for nonquenching trajectories. Most trajectories that reach surface 1 exit on that surface; only 7% of these trajectories leave surface 1 and exit on surface 2. About 5% of the quenching trajectories have multiple hops between surfaces 1 and 2. The amount of surface hopping is much less than we found previously in our Na H2 studyI6 and by Blais and Truhlar.'* This is largerly due to the absence of hopping to surface 3 for Li + H2. We believe the Na H2results would be substantially different with a corrected set of potential energy surfaces in which the upper 'B2 (surface 3) is raised. The average geometry (RLi-H2, R H H , x) for the first hop from surface 2 to 1 was (3.0 ao, 1.7 a,, 81'). The x distribution was localized around 90' (66% were 80' and 90°, 91% between 70' and 90') for first hops from surface 2 to surface 1.
+
I 0.0' 0
'
'
90
1
90
180
+
1
180
B IDegI
Figure 6. Weighted differential cross sections for Li + H2: (a) ET = 0.039 eV, (b) ET = 0.062 eV, (c) ET = 0.101 eV, (d) ET = 0.140 eV. Solid lines are the histogram results, and the dotted lines are Legendre smoothed results.
+
is greater than (2) the 2 'A' Li H2 long-range potential must actually be more attractive than even our DIM values; or (3) the trajectory results are wrong, and all collisions for 6 less than barb do in fact quench. The factor of seems reasonable since the 3 ,A' surface is repulsive and the 1 ,A'' is only weakly attractive. The separation in energies of the 1 'A' and the 1 'A" surfaces is always large, which gives low quenching probabilities. It also seems unlikely that the actual long-range potentials are significantly more attractive than the DIM potentials used in this study. Finally, the trajectory quenching probabilities calculated by this method ma be too small. Recall that the DIM nonadiabatic coupling d I y H is smaller than the ab initio values. Larger values of d f y H would be expected to increase quenching. However, H2 studyI6 calculated the same method used in our N a quenching cross sections larger than the experimental results. Of course, the other possibility is that the experimental results are too high. Next let us look at the angular behavior of the trajectory results. Figure 5 plots the average scattering angle, 8, as a function of impact parameter, b, for quenching Li + H2 trajectories at the four different translational energies. The correlation of 8 and b indicates a direct reaction. The minimum scattering angle decreases as ET increases. The quenching differential cross sections weighted by the sine function, u(0) sin 8, are shown in Figure 6. Forward scattering is more likely a t all translational energies studied; however, the difference between forward and backward scattering decreases as translational energy increases. This is consistent with Figure 5 where we see the increase in scattering angle at larger impact parameters becomes more pronounced as ET increases. Following quenching, the H2 or D2 molecule absorbs about 37% of the total available energy in internal degrees of freedom. This is shown in Table VII. The average final vibrational and rota-
2.
+
V. Conclusions
+
Our results for Li('P) H2quenching show that there is a high probability of quenching for collisions which can overcome the centrifugal barrier. This agrees with the predictions of the Langevin-Gioumousis-Stevenson model, particularly for relative translational energies less than 0.062 eV. However, we find that the region of constant quenching probability is less than 100% and that it is dependent on the translational energy. We found for ET = 0.039 and 0.062 eV about 80% probability of quenching. We find a decrease in quenching as ET increases to 0.140 eV. Given the expected long-range dispersion potential, the experimental quenching cross sections seem to be unusually large. If we assume a reasonable potential with a 100% quenching probability for all impact parameters less than the orbiting impact parameter, we get cross sections lower than the experimental values. Our DIM potential is more attractive than the dispersion potential, but our cross sections are still smaller than the experimental values, since we do not observe a 100% quenching of our trajectories. Our potential energy surfaces may need to be modified. Lowering the minimum in the *B2 surface and the 'B2-'Al minimum crossing energy would increase the quenching probabilities. However, these minimums are currently lower than the best available ab initio calculations, and we are hesitant to lower our DIM surfaces any further. Another possibility might be that the classical path method we use might underestimate the probability of hopping from the excited surface to the ground surface. A final possibility is that the experimental values are high. We would like to see some new experiments performed on this system. We are encouraged by the results of these calculations. Even though our quenching cross sections are lower than the experimental values, they seem reasonable. We reproduce the experimental trend of a decrease in quenching cross sections with an increase in translational energy. We find that D2 is a slightly less
J. Phys. Chem. 1988, 92, 3863-3869 effective quencher than H2, as found experimentally by Lin and Weston; however, the experiments of Elward-Berry and Berry at 0.062 eV show the opposite result. W e have found that the nonadiabatic coupling matrix elements are in good agreement with the ab initio results of Saxe and Yarkony. Overall, the method used in this paper looks promising for studying and understanding
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nonadiabatic processes.
Acknowledgment. The support of this research by the Robert A. Welch Foundation through Grant BA-957 is gratefully acknowledged. Registry No. Li, 7439-93-2; D,, 7782-39-0; H1,1333-74-0.
Excimer Laser Photolysis of Gas-Phase W(CO),+ Yo-ichi Ishikawa,t Peter A. Hackett,* and David M. Rayner* Laser Chemistry Group, Division of Chemistry, National Research Council of Canada, Ottawa, Canada K1A OR6 (Received: October 27, 1987; In Final Form: January 26, 1988)
Laser-based time-resolved infrared absorption spectroscopy was performed to investigate the excimer laser, XeF (35 1 nm), XeCl (308 nm), and KrF (248 nm), photolysis of W(CO)6 in the gas phase. The spectra observed in the wavenumber region between 1700 and 2033 cm-’ show the primary production of coordinatively unsaturated tungsten carbonyls through a single-photon mechanism. The extent of the fragmentation depends strongly on the absorbed photon energy. Infrared assignments for W(CO), and W(CO)5 are determined unambiguously from the stoichiometry revealed by the kinetics of the reactions with added CO. These assignments suggest that W(CO)5 is the only primary product in the XeF and XeCl laser photolysis while W(CO)4 is the main product from KrF laser photolysis. For W(CO)5 the C-0 stretching bands are at around 1942 and 1980 cm-I, and those of W(CO)4 are at around 1909 and 1957 cm-I. The infrared absorption spectra lead to low-symmetry structure assignments of C4, for W(CO)5 and C, for W(CO)4. This is consistent with the assignment from low-temperature inert gas matrices. These coordinatively unsaturated tungsten carbonyls react with CO about once in every 10 collisions.
Introduction Transition-metal carbonyls have photocatalytic properties under mild conditions in a variety of liquid-phase organic reactions including hydrogenation, isomerization, and hydrosilation of olefins.’-3 Recently, analogous homogeneous photoinduced reactions have been observed in the gas-phase. photolysis of mixtures containing metal carbonyl^.^-^ In these catalytic systems, photoproduced coordinatively unsaturated metal carbonyls are thought to play a central role in a homogeneous catalytic mechanism consisting of the following general processes: (1) photoproduction of coordinatively unsaturated metal carbonyls; (2) addition of reactants to the coordinatively unsaturated metal species, which may be regarded as akin to an adsorption process at a catalytic site; (3) reaction on the metal carbonyl; and (4) substitution of products by reactants, which may be regarded as akin to a desorption process. Kinetic information about the reactions of coordinatively unsaturated metal carbonyls therefore provides an approach to reactions at the surface of metals as well as an elucidation of homogeneous catalysis mechanisms. The photochemistry of group VI metal carbonyls has been extensively studied in low-temperature glasses and matrices, in the liquid phase, and in the gas phase, and has been widely re~ i e w e d . ’ - ~ The , ~ primary photoprocess in condensed phases is generally thought to be single CO ligand elimination and subsequent occupation of the sixth coordination site with an appropriate ligand L. M(CO)6 + hv M(CO), + C O (1) M(CO),
+ L
M(CO),(L)
(2)
The UV-vis and IR absorption spectra obtained after the photolysis of M(CO)6 in low-temperature matrices seem to depend sensitively upon the matrix, even in ‘Ynert” gas matrices.1° This phenomenon can be interpreted as a formation of M(CO),(L). The production of this complex has also been reported to be very fast in the liquid For example, a rise time for the ‘Issued as NRCC No. 28177 ‘Research Associate 1986-1988. On leave from The Institute of Physical and Chemical Research, Wako, Saitama 351-01, Japan.
0022-3654/88/2092-3863$01.50/0
formation of Cr(CO)5(cyclohexane)has been observed to be less ~ high reactivity of than 0.8 ps in cyclohexane s o l ~ t i o n . ’ The M(CO), makes is difficult to obtain spectroscopic and kinetic data on “naked” W(CO)5. The similarity of visible absorption spectra of Cr(C0)5(perflu~r~methylcyclohexane)produced in the UV flash photolysis of Cr(C0)6 in perfluoromethylcyclohexane sol u t i o ~ ~Cr(CO),(Ne) ,’~ in the UV photolysis of Cr(C0)6 in Ne and Cr(CO)5 in the 355-nm pulse laser matrices at 20 K,10c915 photolysis of Cr(C0)6 with Ar or CH4 buffer gasesI6 suggests that Cr(CO)5 does not make a strong bond with these molecules and that “naked” Cr(CO)5 has a visible absorption band at around 620 nm. Recent UV photolysis studies of Cr(C0)6 in the gas phase have revealed the characteristics of its initial photodecomposition processes and the structure and the reactivity of the primary fragments.16-20 The extent of fragmentation in the gas-phase (1) Wrighton, M. S. Chem. Rev. 1974, 74, 401. (2) Geoffroy, G. L.; Wrighton, M. S.Organometallic Photochemistry; Academic: New York, 1979. (3) Wrighton, M. S.; Graff, J. L.; Kazlansleas, R. L.; Mitchener, J. C.; Reichel, C. L. Pure Appl. Chem. 1982, 54, 161. (4) Whetten, R. L.; Fu,K.4.; Grant, E. R. J. Chem. Phys. 1982, 77, 3769; J. Am. Chem. SOC.1982, 104, 4270. (5) Tumas, W.; Gitlin, B.; Rosan, A. M.; Yardley, J. T. J . Am. Chem. SOC. 1982, 104, 55. (6) Miller, M. E.; Grant, E. R. J. Am. Chem. SOC.1984, 106, 4635. (7) Teng, P. A.; Lewis, F. D.; Weitz, E. J . Phys. Chem. 1984, 88, 4895. (8) Miller, M. E.; Grant, E. R. J . Am. Chem. SOC.1985, 107, 3386. (9) Poliakoff, M.; Weitz, E. Adu. Organomet. Chem. 1986, 25, 277. (10) (a) Burdett, J. K.; Graham, M. A.; Perutz, R. N.; Poliakoff, M.; Rest, A. J.; Turner, J. J.; Turner, R . E. J . Am. Chem. SOC.1975, 97, 4805. (b) Perutz, R. N.; Turner, J. J. Zbid. 1975, 97, 4800. (c) Perutz, R. N.; Turner, J. J. Zbid. 1975, 97, 4791. (d) Perutz, R. N.; Turner, J. J. Znorg. Chem. 1975, 14, 262. (e) Graham, M. A.; Poliakoff, M.; Turner, J. J. J . Chem. SOC.A 1971, 2939. (11) Welch, J. A,; Peters, K. S.; Vaida, V. J. Phys. Chem. 1982, 86, 1941. (12) Simon, J. D.; Peters, K. S. Chem. Phys. Lett. 1983, 98, 53. (13) Simon, J. D.; Xie, X . J. Phys. Chem. 1986, 90, 6751. (14) (a) Kelly, J. M.; Long, C.; Bonneau, R. J . Phys. Chem. 1983, 87, 3344. (b) Bonneau, R.; Kelly, J. M. J . Am. Chem. SOC.1980, 102, 1220. (15) Turner, J. J.; Burdett, J. K.; Perutz, R. N.; Poliakoff, M. Pure Appl. Chem. 1977,49, 271. (16) Breckenridge, W. H.; Stewart, G. M. J . Am. Chem. SOC.1986, 108, 364.
Published 1988 by the American Chemical Society
