6470
J . Phys. Chem. 1991,95,6410-6473
Vlbratlonal Sptlttlngs for Hydrogen Atom Exchange In HOP: The Effect of 0-0 Dlsplacement and Vlbratlon Neil1 Adhikari and Ian Hamilton* Department of Chemistry, The University of Ottawa, Ottawa, Canada KIN 984 (Received: February 8,1991) Using a global potential energy surface for H02, we calculate vibrational levels up to and slightly above the energy corresponding to the potential barrier for hydrogen atom exchange for both the two-mode (excluding the G O vibration) and three-mode (including all three vibrations) cases. We examine the vibrational splittings for hydrogen atom exchange as a function of the energy; for the two-mode calculations we consider the effect on these splittings of 0 4 displacement while for the three-mode calculations we consider the effect of 0-0vibration.
Introduction The hydroperoxyl radical, H 0 2 , has been the subject of numerous experimenta11t2and theoreticalSl0 studies. The interest in H 0 2 arises primarily from its importance in combustion” reactions; it is the intermediate in the reaction H + 0, 0 OH, which initiates chain-branching ignition phenomena in the oxidation of H2 and most hydrocarbon fuels. The hydroperoxyl radical is also an intermediate in atmcsphericl2 reactions and has been detected in extraterrestrial” atmospheres. In the upper atmosphere, H 0 2 is involved in a series of reactions that result in ozone dep1eti0n.I~ In this paper we calculate vibrational levels up to and slightly above the energy corresponding to the potential barrier for hydrogen atom exchange, and we examine the vibrational splittings as a function of the energy. We have previouslyI5 calculated vibrational spacings for HOz and vibrational splittings for hydrogen atom exchange for the 0 4 3 distance fixed at its equilibrium value. That was therefore a two-mode calculation, including the 0-H stretch and bend but excluding the 0-0 stretch. This is a serious restriction, as the 0-0 stretch is a low-frequency vibration, and in this paper we consider two-mode calculations for H’60160in which the 0-0distance is displaced from its equilibrium value. However, out main purpose is to consider three-mode calculations
-
~~
+
~~
(1) Paukert T. T.; Johnston, H. J. J . Chem. Phys. 1972,56,2824. Ogilvie, J. F. Can. J . Spectrosc. 1973, 19, 171. Becker, K. H.; Fink, E. M.; Langer, P.; Schurath, U.J . Chem. Phys. 1974.60,4623. Hunzinger, H. E.; Wendt, H. R. J . Chem. Phys. 1974,60,4622. Beers, Y.; Howard, C. J. J . Chem. Phys. 1976, 64, 1541. Tuckett, R. P.; Freedman, P. A.; Jones, W. J. Mol. Phys. 1979, 37, 379. (2) Douketis, C. Ph.D. Dissertation, Indiana University, 1989; Chapter 25. (3) Farantos, S.C.; Leisegang, E. C.; Mumll. J. N.; Sorbie, K. S.;Teixeira Dias, J. J. C.; Varandas, A. J. C. Mol. Phys. 1977,34947. Dunning, T. H., Jr.; Walch, S.P.; Goodgame, M. M. J . Chem. Phys. 1%1,74,3482. Dunning, T. H., Jr.; Walch, S.P.; Wagner, A. C. In Potential Energy Surfaces and Dynumics Calculations; Truhlar, D. G., Ed.;Plenum: New York, 1981; p 329. Metz, J. T.; Lievin, J. Theor. Chim. Acra 1983, 62, 195. Murrell, J. W.; Carter, S.;Farantos, S. C.; Huxley, P.; Varandas, A. J. C. In Molecular Potential Energy Functions; Wiley: Chichester, 1984. (4) Vasquez, G.J.; Peyerimhoff, S.D.; Buenker, R. J. Chem. Phys. 1985, 99, 239. (5) Varandas, A. J. C.; Brandao, J.; Quintales, L. A. M. J . Phys. Chem. 1988, 92. 3732. (6) Melius, C. F.; Blint, R. J. Chem. Phys. Lett. 1979, 64, 183. (7) Langhoff, S. R.; Jaffe, R. L. J . Chem. Phys. 1979, 71, 1475. (8) Varandas, A. J. C.; Brandao, J. J . Mol. Phys. 1986, 57, 387. (9) Lemon, W. J.: Hase, W. L. J . Phys. Chem. 1987, 91, 1596. (IO) Walch, S. P.; Rohlfing, C. M. J . Chem. Phys. 1989, 91, 2373. (1 1) Benson, S. W.; Nangria, P. S. Acc. Chem. Res. 1979, 12, 223. Warnatz, J. In Combustion Chemistry; Gardner, W. C., Ed.;Springer: New York, 1984: p 197. Hucknall, D. J. Chemistry of Hydrocurbon Combustion; Chapman and Hall: London, 1985. Miller, J. A. J . Chem. Phys. 1986,84, 6 170. (12) Lee, Y. P.; Howard, C. J. J . Chem. Phys. 1982,77,756. Wayne, R. P. Chemistry of Atmospheres; Oxford University Press: London, 1985. Warneck, P. Chemistry of the Natural Atmosphere; Academic Press: San Diego, 1988. (13) McElroy, M. B.; Kong, T. Y.; Ung, Y. L. J. Geophys. Res. 1977,82, 4379. McElroy, M. B.; Kong, T. Y. Planet Space Sci. 1977, 25, 839. (14) Bates, D. R.; Nicolet, M. J. Geophys. Res. 1950, 55, 301. Whitten, R. C.; Prasad, S.S.In Ozone in the Free Atmosphere; Whitten, R. C., Prasad, S.S.,Eds.; Van Nostrand Reinhold: New York, 1985; p 81. Zurer, P. S. Chem. Eng. News 1987, 65, 22. Stolarski, R. S.Sci. Am. 1988, 258, 30. (15) Adhikari, N.; Hamilton, 1. J . Chem. Phys. 1990, 93, 6111.
0022-3654191 /2095-6410$02.50/0
for both H160160and H160180(which is here equivalent to H’80160)including the 0-0 vibration. These calculations are for the 2A’’ ground electronic state only, and interactions (via spin-orbit coupling) with the low-lying 2A’ excited electronic state are neglected. The 2A’ and other excited electronic states are considered in the theoretical study of Vasquez, Peyerimhoff, and Buenker.4 It should be noted that for the 2A’’ ground electronic state of H’60160,due to nuclear spin statistics, vibrational levels corresponding to vibrational eigenfunctions that are antisymmetric with respect to oxygen atom exchange are missing for J = 0. A discussion of a b initio electronic structure calculations for the ground electronic state of H 0 2 has recently been given by Varandas, Brandao, and quint ale^,^ from which the following discussion is largely abstracted. Melius and Blint6 used a multiconfiguration self-consistent field-configuration interaction (MCSCF-CI) method to obtain electronic energies at various nuclear geometries and fitted the resulting points to an analytic form which they had developed. Their work yielded a barrier of about 800 cm-I for the H + 0 2 addition reaction. However, Langhoff and Jaffe’ used a more extensive CI method and found no barrier for this reaction. Recently, Varandas, and Brandao8 used the double many-body expansion (DMBE) method to obtain a global HOZ surface, termed DMBE I, that agreed with the calculated points of Melius and Blint but showed no barrier for the H + O2addition reaction. The DMBE I surface therefore constituted an improvement over previous surfaces, but it displayed some unsatisfactory characteristics. Several other global H 0 2 surfaces have subsequently been reported which incorporate both the calculated points of Melius and Blint and available experimental data. The switching-function surface obtained by Lemon and Hase9 is designed for the H + O2 addition but does not accurately describe hydrogen atom exchange and is therefore not suitable for our purposes. The DMBE I1 and DMBE I11 surfaces obtained by Varandas, Brandao, and Q ~ i n t a l e are s ~ both modified to give the correct thermal rate constant for the reaction 0 + OH O2+ H , and the latter is,further modified to incorporate the experimentally determined quadratic force field data. These authors believe that the DMBE I11 surface may be the most realistic global surface currently available, and in this paper we calculate the vibrational levels of H 0 2 using this surface. As expected, there are two equivalent primary minima connected by a saddle point at the T-shaped nuclear geometry. We note that very recently Walch and Rohlfing,lousing a more extensive CI method, have cast doubt on the accuracy of the points of Melius and Blint at this geometry. Unfortunately, a global surface incorporting the calculated points of Walch and Rohlfing and the experimentally determined force field data is not presently available.
-
DMBE 111 Surface To calculate the vibrational levels of H02, we employ a combination of the discrete variable representationt6 (DVR) and distributed Gaussian basis” (DGB) methods. This DVR-DBG Method and
~~
~
(16) Lill, J . V.; Parker, G. A.; Light, J. C. Chem. Phys. Lett. 1982, 89, 483. Light, J. C.; Hamilton, I. P.; Lill, J. V. J . Chem. Phys. 1985, 82, 1400.
0 1991 American Chemical Society
Vibrational Splittings for Hydrogen Atom Exchange in H 0 2 method, developed by Bacic and Light,ls has been shown to be very efficient and accurate for variational calculations on triatomia such as HCN and LiCN for which there is largeamplitude motion of the light atom, as in H02. In essence, this large-amplitude motion is divided into an angular part (treated by using the DVR) and a radial part (treated by using the DGB). In this calculation we use Jacobi coordinates (r,R,B) in which the triatomic ( J = 0) Hamiltonian, in atomic units, is
:(=+s)zzi + a
sin 8 :e)
=
mop01 mo, + mo2
and
+ mol) mH + mo,+ mol mH(mOl
The Hamiltonian matrix elements are then
where he, and Vel are the kinetic and potential matrix elements of the corresponding terms in eq 1 and Weal is a transformed angular momentum matrix element responsible for the angleangle coupling in the DVR. Rays are superscripted by DVR angles, B,, which are specified by Gauss-Legendre points. Because the DGB on any given ray is not orthogonal, the overlap matrix S is not diagonal and hence must be evaluated in order to solve the generalized eigenvalue problem. The overlap, kinetic, and angle-angle coupling matrix elements are calculated analytically, while the potential matrix elements are determined by using 5-point Gauss-Hermite quadrature. For the two-mode calculations, in which r is fixed and the matrix element of the first term in eq 1 is zero, we use Gaussian basis functions of the form
4p = (~A?/T)'/~exp[-Ap(R
geometry. The primary minima are located at r = 2.512 UO, R = 2.469 a, and 3I = 46.405' or 133,595' with energy 2332.4 cm-I (since we report vibrational spacings only, we have not adjusted the energy of the primary minima to zero). For r = 2.512 a, the saddle point is located a t R = 1.79 a. (and B = 90°), with energy 8030 cm-I. For this value of r, the potential barrier for hydrogen exchange is therefore approximately 6000 cm-I while for the relaxed T-shaped geometry it is somewhat lower. There is a secondary potential minimum which, for this value of r, is located at R = 4.74 (and B = 90°), but its energy is 19 557 cm-I, which is much higher than the energies considered in this paper. The asymptotic energy of H O2 is 22095 cm-' for r = re, and consequently, the difference between the saddle point and asymptotic energies is approximately 16 000 cm-'. Although this difference is somewhat lower for the relaxed T-shaped geometry, it is still much greater than that found by Walch and Rohlfing.'O Of course, of crucial importance for the vibrational splittings for hydrogen atom exchange is the difference between the saddle point and primary potential minima energies, and this may be accurate for the DMBE 111 surface.
+
V(r,R,B) (1)
where r is the 0-0 distance, R is the distance between H a n d the center of mass of 0-0,B is the angle between the R and r axes, and the reduced masses are PI
The Journal of Physical Chemistry, Vol. 95, NO. 17, 1991 6471
- Rle,)2]
(3)
For the three-mode calculations we use products of these basis functions and Gaussian basis functions of the same form but dependent on r (rather than R ) . The parameter A, determines the degree of overlap between adjacent Gaussians and was chosen such that the maximum overlap was 0.65;the results were found to be insensitive to this choice for S,,. In both the two- and three-mode calculations, the centers of the Gaussians were distributed semiclassically along a ray through the potential surface at each DVR angle. The region of the potential surface on which basis functions were placed corresponds to energies below a total energy cutoff, Em,. In addition, minimum and maximum values of R (dependent on e) were specified to delimit the physical region of the potential surface. In particular, we selected Rminto avoid those artas where V is negative, and R , to match the maximum of the potential beyond the minimum (except for those 0, close to the minimum energy path for the H O2 reaction where a large value of R , was arbitrarily chosen). The matrix elements were evaluated and used to find the eigenfunctions for each ray Hamiltonian (rather than the complete Hamiltonian), that is, for each DVR angle. The resulting set of ray basis functions was then truncated, and therefore made smaller than the total number of Gaussian basis functions, by including only those eigenvectors corresponding to eigenvalues below a ray energy cutoff, Eray. Hence this compact ray basis generated a smaller Hamiltonian matrix which was then diagonalized to give the vibrational levels. For the DMBE I11 surface there are two equivalent primary minima connected by a saddle point at the T-shaped nuclear
+
(17) Hamilton, 1. P.; Light, J. C. J . Chem. Phys. 1986, 84, 306. (18) Bacic, Z.; Light, J. C. J . Chem. Phys. 1986, 85, 4594. Ibid. 1987, 86, 3065. Bacic, 2.;Light, J. C. Annu. Rev. Phys. Chem. 1989, 40, 469.
Results We first consider two-mode calculations (which include the 0-H stretch and 0-H bend vibrations but exclude the 0-0 stretch vibration) in which the 0-0 distance is displaced from its equilibrium value. In particular, the 0-0 distance is varied parametrically from r = 2.49 to 2.55 ao, which is a range of r values that is easily accessed in the three-mode calculations for the energy range considered in this paper. We then consider three-mode calculations which include all three vibrational modes. Unless otherwise noted, all distances are in a, and all energies are in cm-l. Two-ModeCalculations. The calculations used 35 DVR angles with energy cutoffs of 0.161 au for E , and 0.160 au for Emy,which gave rise to 701 (for r = 2.49)to 707 (for r = 2.55)compact ray basis functions. Table I shows the first 20 vibrational spacings (energies are tabulated to 0.1 an-')for five r values (one of which, r = 2.51,is very close to re). In Table I, column 1 gives the number of the vibrational spacing while column 2 gives the zeroth-order assignment for some of these levels: the first label is the 0-H stretch while the second label is the 0-H bend. The +(-) vibrational eigenfunctions are symmetric (antisymmetric) with respect to oxygen atom exchange. It may be seen from Table I that as r increases from 2.49 to 2.55,the 0-H stretch fundamental increases from 3199.1 to 3225.7 (0.8% larger) while the 0-H bend fundamental decreases from 1315.3 to 1299.5 (1.2% smaller). This is reasonable since, as the oxygen atoms separate, the 0-H stretch fundamental tends to that for OH, while the 0-H bend fundamental tends to zero as the bend vibration becomes a free rotation. We now consider progressions in the 0-H stretch and bend (which are calculated from the average of the + and - spacings in Table 1). For the 0-H stretch progression, the first two successive spacings increase from 3199 and 3053 to 3226 and 3082 while for the 0-H bend progression the first four successive spacings decrease from 1315,1225,1150,and 1097 to 1300, 1195, 1097, and 1060 (as r increases from 2.49 to 2.55). The first measurable (that is, for the two-mode calculations, greater than 0.1 cm-I) splitting is for the (0,3)level. The splitting for the (0,4)level is much larger and that for (0,5) is too large for this level to be assigned. The splitting for the (2,O)level is much smaller than that for the (0,4)level although the energy of this level is much greater. However, energy in the 0-H stretch vibration is important in promoting hydrogen atom exchange [for example, the splitting is measurable for the (1,l) level], as found for r = re in our previous study.15 Of greater interest is the behavior of the splittings as a function of the 0-0 displacement. As r increases from 2.49 to 2.55,the splitting of the (2,O)level decreases from 6.2 to 0.0, which is reasonable since, as the oxygen atoms separate, hydrogen atom exchange must ultimately become more difficult. However, as r increases from 2.49 to 2.55,the splitting of all other vibrational levels increases and the rate of increase is greater for the (1,l) level than for either the (0,3)or
6412 The Journal of Physical Chemistry, Vol. 95, No. 17, 1991
Adhikari and Hamilton
TABLE I: Two-Mode Cdcuhtiu"
no. I
2 3 4 5 6 7 8 9 IO 11
12 13 14 15 16 17 18 19 20
assignment
2.49 0.0 1315.3 1315.3 2539.8 2539.8 3199.1 3199.1 3689.2 3689.5 4497.6 4498.8 4782.6 4791 .O 5501.7 5567.5 5823.1 5886.1 6213.9 6248.9 6255.1
S
0.0 O'O O'O
0.3
6'2
2.51 0.0 1310.0 1310.0 2524.6 2524.6 3209.9 3209.9 3656.6 3657.2 4487.2 4490.4 4729.6 4743.3 5384.7 5504.9 5775.3 5855.1 6101.7 6271.7 6272.6
S
0.0 0.0 0.0
0.6 3.2 13.7
0.9
2.53 0.0 1304.7 1304.7 2509.7 2509.7 3218.7 3218.7 3624.0 3625.0 4465.2 4473.7 4680.2 4700.7 5249.9 5434.3 5728.9 5830.2 6013.2 6291.1 6291.6
S
0.0 0.0 0.0 1.o
8.5
20.5
0.5
2.55 0.0 1299.5 1299.5 2494.9 2494.9 3225.7 3225.7 3591.0 3592.6 4425.4 4446.5 4637.5 4665.1 5111.4 5359.4 5678.9 5808.5 5948.4 6307Ab 6307.8b
5
0.0 0.0 0.0 1.6 21.1 27.6
0.0
#The number of the vibrational spacing (column I), the zeroth-order assignment for some of these levels (column 2), the vibrational spacings for
HI6O160 for four values of the 0-0 distance (columns 3, 5, 7, and 9),and the vibrational splittings. s, for the assigned levels (columns 4, 6,8,and IO) are given. Distances are in h,and energies are in cm-l. bFor r = 2.55,the 19th vibrational spacing is 6273.5 (unassigned) but for simplicity it has been omitted. TABLE 11: Thm-Mode Calculrtio~tu~ no. assignment 16-16 1 0 2 1038 3 1038 4 1303 1303 5 2064 6 2064 7 2334 8 2334 9 2506 IO 2506 II 3078 I2 3078 13 3207 14 3207 15 3350 16 3350 17 3503 18 3505 19 3630 20 3632 21
s
O
16-18 0 1009 1009 1299 1300 2007 2008 2301 2302 2497 2500 2993 2996 3197 3207 3288 3293 3472 3476 3607 3620
s
0 1 1
I 3
3
IO 5 4
no. 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
assignment
16-16 4078 4078 4202 4219 4250 4332 4353 4382 4502 4505 4566 4622 4708 4745 4784 5062 5062 5114 5212
s
17 21
16-18 3966 3971 4172 4188 4220 4259 4277 4351 4459 4462 4538 4590 4664 4714 4766 4924 493 1 5082 5154
5
16 18
25
@Thenumber of the vibrational spacing (columns 1 and 7), the zeroth-order assignment for some of these levels (columns 2 and 8), the vibrational spacings for HI6Ol6O(columns 3 and 9) and H1Q1*0 (columns 5 and 1 I), and the vibrational splittings, s, for the assigned levels (columns 4, 6, 10, and 12) are given. Energies are in cm-I. (0,4) level. A qualitative explanation for these results is given
in the next section. Three-Mode cpladrtiorrn The calculations used 45 DVR angles with energy cutoffs of 0.18 au for both Eta and E,,, which gave rise to 1011 (for HI60l60)and 1040 (for H160190)compact ray basis functions. Table I1 shows the first 40 vibrational spacings (energies are tabulated to 1 cm-I). In Table 11, columns 1 and 7 give the number of the vibrational spacing while columns 2 and 8 give the zeroth-order assignment for some of these levels: the first, second, and third labels are the 0-H stretch, 0-H bend, and 0-0 stretch, respectively. We first consider results for H'60'60. It may be seen from Table I1 that the calculated 0-H stretch and bend fundamentals are 3207 and 1303. These are very close to those for the two-mode calculation at r = re (3211 and 1309, from ref 15) and no closer to the experimental's values, which are 3410 and 1389. The C%O stretch fundamental is 1038, which is also much smaller than the experimentall*2value (1095). For the 0-H stretch progression, the first two successive spacings are 3207 and 3071 (the latter number is calculated by using the 63rd and 64th vibrational spacings, which are not shown in Table 11). These are very close
to but smaller and larger thafi those for the two-mode calculation at r = re (321 1 and 3063). For the 0-H bend progression, the first three successive spacings are 1303,1203, and 1 125, very close to but in all cases smaller than those for the two-mode calculation at this r value (1309, 1214, and 1130). For the 0-0 stretch progression, the first five successive spacings are 1038,1026,1014, 1O00, and 984. These successive spacings show that the potential surface is strongly anharmonic (although the 0-0 stretch is the least anharmonic vibrational mode). For the 0-H bend progression the first measurable (that is, for the three-mode calculations, greater than 1 cm-') splitting is for the (0,3,0) level (2 cm-I), and that for (0,4,0) is too large for this level to be assigned. The splittings are too small to be measurable for either the 0-H or 0-0stretch progressions for the energy range considered in this paper. However, energy in the 0-H or 0-0 stretch vibration is important in promoting hydrogen atom exchange in combination with the CkH bend. As examples for the 0-0 stretch vibration, the splitting is 2 for the (0,2,1) level and 21 for the (0,1,3) level. In fact, energy in the 0-H and 0-0 stretch vibrations is significant in promoting hydrogen atom exchange in combination with one another. As an
J. Phys. Chem. 1991, 95,6473-6481 example, the splitting for the (l,O,l) level is 17. Note that the splitting for the (0,3,0)level, in the three.-mode calculation, is 2 while that for the (0,3)level, in the two-mode calculation at r = re, is 0.6 (from ref 15). In part, the larger splitting for the three-mode calculation may be attributed to the greater zero-point energy for the three-mode Hamiltonian and the correspondingly lower adiabatic potential barrier for hydrogen atom exchange. We now consider results for H'60'80, which we compare to those for H " W 6 0 . As expected, the 0-0 stretch fundamental is smaller by a factor approximately equal to the square root of the relative reduced masses of the oxygen atoms, and the 0-H stretch and bend fundamentals are both slightly smaller. The splitting for the 0-0stretch fundamental is not measurable, but it is measurable for all other vibrational levels and, in particular, for both the 0-H stretch and bend fundamentals (10 and 1, respectively). Summary and Discussion
In this paper we have calculated vibrational levels for H 0 2 using the DMBE 111 surface of Varandas, Brandao, and Q~intales.~ We have considered vibrational levels up to and slightly above the potential barrier for hydrogen atom exchange. The calculated fundamentals for all three vibrational modes are significantly smaller than the experimentally determined fundamentals, and the calculated successive spacings for progressions in all three vibrations show that the potential surface is strongly anharmonic. It would Seem that, in incorporating the experimentally determined force field data into the DMBE I11 surface, this strong anharmonicity has not been taken into account. For the two-mode calculations, except for the (2,O) level, the splittings of all vibrational levels increase as the 0-0distance increases. However, as the oxygen atoms separate, hydrogen atom exchange must ultimately become more difficult, and these results must therefore be specific to the range of r values that have been considered in this paper. These results must also be specific to the potential surface and are evidently a consequence of the fact that the saddle point region is located at a small R value that is
6473
not easily accessed by the zeroth-order 0 - H bend motion. Our results indicate that the zeroth-order 0 - H bend motion more effectively acceSSeS the saddle point region for slightly larger 0-0 distances. Apparently, the zeroth-order 0 - H stretch motion (in combination with the zeroth-order 0-H bend motion) is even more effective in accessing this region for slightly larger r values since the rate of increase of the splitting is greater for the (1,l) level than for either the (0,3)or (0,4) levels. Complicating a definitive statement in this regard is the existence of a secondary potential minimum at the linear O-H-O geometry for significantly larger 0-0distances. It is clear from eq 1 that there is a singularity in the triatomic ( J = 0) Hamiltonian for R = 0. For the three-mode calculations, the calculated splittings are not measurable for any of the fundamentals for H'60'60, but for H ' 6 0 ' 8 0 they are measurable for the 0 - H stretch and bend fundamentals (10 and 1 cm-', respectively). The larger splittings for H'60180at low energies may be qualitatively understood as resulting from the dynamical nonequivalence of the 160-H and I80-H stretch and bend vibrations. As expected, energy in the 0-H bend vibration is of primary importance in promoting hydrogen atom exchange. However, energy in the 0 - H or 0-0 stretch vibration is also important in combination with the 0-H bend vibration (and in combination with one another). On the basis of the two-mode calculations, we infer that the 0-0stretch vibration is important in promoting hydrogen atom exchange primarily because it creates nuclear geometries in which the saddle point region is more effectively accessed by the zeroth-order ( F H bend motion.
Acknowledgment. We thank NSERC (Canada) for partial funding of this work and McGill University and the University of Ottawa for grants of computer time. We thank Herong Yang (McGill University Computer Centre) for program modifications that made these calculations possible for the total number of basis functions used. Regis@ NO. HOZ, 3170-83-0;H,12385-13-6.
Cluster Beam Analysis via Photoionization J. R. Grover,* Department of Chemistry, Brookhaven National Laboratory, Upton, New York 11973
W . J. Herron, M. T. Coolbaugh, W. R. Peifer, and J. F. Garvey Department of Chemistry, State University of New York at Buffalo, Buffalo, New York 14214 (Received: February 12, 1991; In Final Form: April 9, 1991)
A photoionization method for quantitatively analyzing the neutral products of free jet expansions is described. The basic principle is to measure the yield of an ion characteristic of each component cluster at a photon energy just below that at which production of the same ion from larger clusters can be detected. Since there is then no problem with fragmentation, the beam density of each neutral cluster can be measured in the presence of larger clusters. Although these measurements must be done in the test ions' onset regions where their yields are often quite small, the technique is made highly practicable by the large intensities of widely tunable vacuum-ultraviolet synchrotron light now available at electron storage rings. As an example, the method is applied to the analysis of cluster beams collimated from the free jet expansion of a 200:l ammonia-chlorobenzene mixture.
Introduction Syntheses of neutral clusters in jet expansions are now widely used in research, hause the method is very convenient and applicable to a tremendous range of compositions. A serious drawback, however, is that such expansions always produce mixtures of clusters, so that for many experiments a knowledge of the relative amounts of the different cluster species becomes necessary. Analysis is usually attempted via mass spectrometry
following electron impact ionization, although results obtained by this method are subject to distortions, often ruinous, due to extensive dissociative ionization of the clusters (fragmentation).'-' (1) Henka. W. 2.Narurforsch. A 1962, 17, 786-789. Acra (2)19,8, Herrmann, 61, 453-487. A,; Leutwylcr, S.; Schumacher, E.;Woste,
L. Hefu. Chim.
(3) Lee, N.; Fenn, J. B. Rev. Sci. Insfrum. 1918,19, 1269-1272. Fenn, J. B.; Lea, N. Reu. Sci. Instrum. 1982.53. 1494-1495.
0022-36S4/91/209S-6473302.50/00 1991 American Chemical Society
