J. PhyS, Chem. 1982, 86, 862-885
862
Photodissociation of Ozone in the Hartley Band. Exploratory Potential Energy Surfaces and Molecular Dynamics P. J. Hay,' R. T. Pack, R. B. Walker, and E. J. Heller Lo6 Akms Netknal Laboratory, UniversRy of CaNfwnk,Los Alamos, New Maxieo 87545
(Recehred: November 12, 198i;
I n Final Form: Jenuary 2 1, 1982)
Potential energy surfaces for the four 'A' states of ozone involved in photodissociation by UV radiation (22G280 nm) have been computed by ab initio techniques. Preliminary molecular dynamics studies on two of these surfaces are reported by usihg the Gaussian wavepacket photodissociation method to obtain a theoretical 'Bz 'Al absorption spectrum. +
Introduction Photodissociation of ozone in the Hartley band (220-310 nm) 03 + hv ---+ 02 + 0 provides the dominant source of O(lD) and the principal absorbance of solar W radiation in the atmosphere. The wavelength dependence of the quantum yield and the final electronic states of O2 and 0 have been extensively explored.1*2 Although the dominant proceee for X < 300 nm in the Hartley band of Osis production of 02('AJ + O(lD), recent work- has shown the quantum yield of 02(32,-) O(aP)to be significant (4 = 0.15). In an effort to understand (1)photodissociation of O3in the Hartley band, (2) the role of vibrational excitation on UV dissociation, and (3) the distribution of f d electronic and rovibrational states we have undertaken an ab initio study of the potential energy surfaces and molecular dynamics of ozone. In this Letter we report preliminary resulta which include (1)a description of the four lowest 'A' surfaces of Osfrom configuration interaction calculatione and (2) the calculated 'B2 'A1 absorption spectrum arising from two of these surfaces obtained by using the wavepacket photodissociation method. Full dynamid studies and the role of w e crossings will be treated in future papers.
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Ckneral Theoretical Coneideratione The electronic states of 03 have been the subject of numerous theoretical studiesw and several studies of the ground-state potential energy surface have been carried out.612 The Hartley band arises from the 'B2 X'A1 electronic abrption. The ground (X'A ) state of Os,with an equilibrium geometry of R = 1.271 and 6 = 116.8O, dissociates to 02(*E-1 + O(8p). The 'B2 state (R = 1.405 A and B 3: 108O in d2,symmetry) correlates with 02(1Ag) + O(lD) and is dissociative in nature. Both states have 'A' symmetry along the C, dissociation path. The 21A1 state liea below the 'B2 state and also dissociates to 02('A1) + O(lD). This state, corresponding to a two-electron transition from the ground state, is expected to play a lesser role in the photochemistry since its absorption cross section is several orders of magnitude smaller than the 'B2 state. Its equilibrium geometry (R = 1.449 A, 6 = 60°)6 is the "ring" form of ozone, and lies about 1.2 eV above the "open" form of 03.The structure at lower energy (Huggins band) in the Hartley band has been variously attributed to the 2'A1 stat@ or portions of the 'Bzsurface that are bound relative to products.14 The final state of 'A' symmetry which must be included in any realistic
k
'Theoretical Chemistry/Mol&
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Physics Group, Mail Stop 569. QO22-3654f82/2088-0862$0 1 . 2 s0
TABLE I: Comparison of Calculated (POL-CI and POL-CI-Bk)and Experimental Spectroscopic Constants for the 0,Molecule CI CI-BK expt 3z g-
Re,ao
2.34 4.60 1640
De, e V
w e , cm-
'*P
Re,ao
2.36 3.68 1.02 1464
De,eV Te,e V w e , cm-l
2.34 4.79 1566
2.28 5.21 1580
2.36 3.76
2.30 4.23
1.06
0.98
1480
1609
treatment of O8 photodissociation is the repulsive state which dissociates to ground-state products but is energetically inaccessible in the Franck-Condon region. These four 'A' states are shown for one cut of the O2+ 0 surface in Figure 1. Since the relative ordering of the states can vary along the potential energy surface, we shall use the letters X, A, B, and R to designate the "diabatic" states. At the ground-state eometry they have the relative ordering X('A,) < A(2 A,) < B('B2) < R(repulsive).
f
Method of Calculation Ab Initio Potential Energy Surfaces. Within a (3s2pld) contracted Gaussian basis set,16the 12 a' and 3 a'' valence orbitals were obtained self-consistently at each point on the surface with the "perfect pairing" generalized valence bond (GVB-PP) multiconfiguration SCF technique,18 (1)W. B. DeMore and 0. F. Raper, J. Chem. Phys., 44, 1780 (1966). (2)H. I. Schiff, Ann. Geophys., 28,67 (1972). (3) C.E.Fairchild, E. J. Stone, and G. M. Lawrence,J.Chem. Phys., 69,3632 (1978). (4)S.T.Amimoto. A. P. Force. J. R. Wiesenfeld. and R. H. Young. J . Chem. Phvs.., 23. --, 1244 (19801. ' (6)R.K.fipnrh, L. R. Carbon, K. Shobatake, M. L. Kowalczyk,and Y.T.Lee, J. Chem. Phys., 72,1401(1980). (6) P. J. Hay and T.H. Dunning,Jr., J. Chem. Phys., 67,2290 (1977). (7)K.H.Thunemann. 9. D. Peverimhoff.and R. J. Buenker, J. Mol. Spectrosc., 70, 432 (1978). (8)c. W. Wilson. Jr., and D. G. HoDDer. J. Chem. Phvs.. - . 74.. 696 (1981). (9)J. 5.Wright, S. Shih, and R. J. Buenker, Chem. Phys. Lett., 76, 613 (1980). (10)J. N. Mwell, K. 9. Sorbie, and A. J. C. Varandas, Mol. Phys., 32, 1369 (1976). (11)J. N. Murrell and 5. Farantoe, Mol. Phys., 34, 1185 (1977). (12) G. D. Carney, L. A. Curtiss, and S. R. Langhoff, J . Mol. Spectrosc., 61,371 (1976). (13)J. C. D. Brand, K. J. Cross, and A. R. Hoy, Can. J . Phys., 66,327 ~
__
11 8).. ~1-17-_,.
(14)J. W. Simons, R. J. Paw, H. A. Webster, 111, and E. J. Bair, J. Chem. Phys., 59, 1203 (1973). (16)T.H. Dunning, Jr., and P. J. Hay, 'Gaussian Basis Seta for Molecular Calculations",in 'Methods of Electronic Structure Theory", H. F . Schaefer, 111, Ed., Plenum Press, New York, 1977,pp 1-27. (16) See ref 6 for details of GVB-PP calculations on 03.
0 1982 American Chemical Society
The Journal of Physical Chemistry, Vol. 86, No. 6, 1982 889
Letters I
I
I
I
II
I
I
I
X
I
40
325
3.20
35
0"
330
u N30 K
25
1
\ 2 c
"20
I 3
2
I 4 Rp(a0)
I
I J
5
6
-
25
30
35
40
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Figurr 1. Calculated potential energy curves for O3 0, 0 by varying one bond kngth (R,) and flxlng the other geometrical parameters at R , = 2.5 a,, and 0 = 110'. Insert shows a blowup of the curve-crosslng region.
Both ground-state (lA') and triplet-state (3A') orbitals, corresponding to llAl and lag2states at the equilibrium geometry, were tested. Preliminary CI calculations at representative points on the O2 + 0 surface were used to identify 18 "reference configurations" that spanned the dominant configurations of the lowest four lA' states. Triplet-state orbitals resulted in small differences from singlet orbitals near equilibrium, but led to a more compact representation near O2 + 0 and hence were then used throughout. All single and double excitations were generated with respect to these 18 spatial configurations with the following restrictions: (1)no excitations were included from the first six a' orbitals; (2)at most one electron was permitted outside the valence space (POL-CI) restriction)." This led to 10638 spin eigenfunctions. The CI matrix was constructed and the lowest four (or more) roots were extracted within the BKscheme.18 In the BKscheme the matrix is partitioned into H,, and Hbb, and only diagonal elements are retained in Hbb while H, and are evaluated rigorously. In this case the size of H, was 729 spin eigenfunctions, which included all excitations in the valence space. The "full" CI matrix was also constructed at representative points to compare to the BK results and relative differences of at most 0.1-0.2 eV were noted. Results on the two lowest states of O2obtained by using identical procedures and basis sets are shown in Table I. These procedures were carried out for a grid of points described by 95O < 8 < 135O,2.1 < R2< 10.0 %, 1.9 < R1 < 3.1 a,,, where R1 IR2. Analytic Potential Energy Surfaces. For convenience in studying the dynamics of ozone photodissociation, we fit each of the four computed surfaces to an analytic form. For the purposes of this study only the "diabatic" surfaces were fit, where each surface was defined as having the same orbital makeup throughout and where curve-crossing regions were neglected in the fitting process. The functional form choeen was ewentially that of Murrell, Sorbie, and Varandas,1° except that we included terms up to seventh order in the symmetry adapted three-body polynomial expreesion (eq 8 of ref 11). Although we have fit all four ab initio surfaces, only the X and B surfaces were involved in the dynamical calculations to be reported here. The quality of the surface fib can be summarized in general terms by the number of ab initio points (N)and the rma -~ ~~
(17) P. J. Hay and T. H. Dunning, Jr., J. Chem. Phys., 64,6077 (1976). (18) Z. Gemhgorn and I. Shavitt, Znt. J. Quantum Chem., 2, 761 (1968).
Flgurr 2. Contour maps of the X, A, B, and R potential energy surfaces of Osfor ked bond angle of 118'. R , and R , are the 0-0 bond lengths.
error (u) as follows: X(N = 93,u = 0.02 eV), B(N = 93, u = 0.06 eV), A(N = 91,u = 0.07 eV), and R(N = 75,u = 0.13 eV). Photodissociation Dynamics and Spectra. For preliminary photodissociation dynamics and spectra, we made several simplifying assumptions: (1)The ground vibrational state of the ground XIA1 electronic energy surface was fit to a quadratic about the equilibrium geometry, and the resulting harmonic vibrational eigenstate was used in the photodissociation dynamics (see below). (2) The electronic transition dipole was assumed to be a constant, independent of nuclear coordinates. (3)Although all three internal coordinates were employed in the dynamics, the molecule was initially placed in a space-fixed orientation, not an angular momentum eigenstate. All three of these simplifications will be removed in future work. For the absorption out of the ground vibrational state, these simplifications are expected to play a minor role. The theoretical spectrum was computed by the wavepacket photodissociation method of Kulander and Heller,ls with the modification that the "frozen" Gaussian approximation (FGA) was used.M This simplified the calculation somewhat, but the "thawed" Gaussian routines (TGA)21will be used in future work on this problem. Briefly, the basic procedure of the wavepacket approach to photodissociation spectra (or absorption) spectra is as follows: (1)The initial Franck-Condon state 4 = p# ( p is the transition moment and # the initial vibrational state) is represented as a superposition of Gaussians. The Gaussians involve all the coordinates of the problem and can accurately represent any state.22 (2)The Gaussians are propagated independently on the upper electronic potential energy surface. Collectively, these Gausaians add up to $ ( t ) ,the approximate dynamical evolving out of 4 on the upper potential surface. (3)The frequency dependence (absorption spectrum) is then obtained from the Fourier transform of the overlap function (dlt$(t)) (apart (19) K. C. Kulander and E. J. Heller, J. Chem. Phys., W2.439 (1978). (20) E. J. Heller, J. Chem. Phys., in prew. (21) E. J. Heller, J. Chem. Phys., 64,63 (1976); 611,4979 (1976). (22) M.J. Davis and E. J. Heller, J. Chem. Phys., 71, 3383 (1979).
864
Letters
The Journal of Physical Chemistty, Vol. 86, No. 6, 1982
L
Floun 3. Comparison of the experbnentelabsorption spectrum of ozone (left) wlth the calculated spectrum for absorptbn from the (O,O,O) vibrational state of the ground electronic state of O3to the 'B, (B)state. The calculated spectrum has been shifted as discussed In the text. TABLE 11: Ozone Ground-State Prooerties properts bond length, a, bond angle, deg u 2 (bend), cm-' u 3 (AS),cm-' u1
(SS),cm-'
exptl value
fitted surface value
2.42 116.8 705 1042 1110
2.46 115.7 725 1041 1110
from an overall constant which depends on the magnitude of the dipole matrix element). Results and Discussion Potential Energy Surfaces. The potential energy surfaces for the four lowest 'A' states of O3 (designated as X, A, B, and R) are shown as a function of R1and R2(for 0 = l l O o ) in Figure 2. The surfaces depicted here have the same electronic character for all nuclear confiiations and do not reflect the avoided crossings that will occur between these "diabatic" surfaces. The ground-state (X) surface shows the characteristic well corresponding to the stable O3 species at R1 = R2 = 2.42 %. In Table I1 we compare experimental to fitted properties of the ozone equilibrium ground state. The agreement between the fitted surface and the measured normal mode frequencies is surprisingly good, especially considering that the errors are less than the rms error of the analytic fit to the ab initio surface. This agreement is especially surprising for the antisymmetric stretch frequency (Y& which corresponds initially to the dissociative mode, since the calculated well depth relative to O2 + 0 is only 0.38 eV (compared to 1.1 eV experimentally). In addition, we obtain a slight barrier (0.3 eV) to 02(31: -) + O(3P)recombination. At this point we do not ascrike much significance to this barrier, and there doeg not appear to be any experimental evidence to support its existence. Rather it is probably an artifact of the MC-SCF wave function (GVB-PP) used to obtain the orbitals for the subsequent CI calculations. While the CI wave functions do dissociate properly to 02(3E,-) + O(3P),the MC-SCF function contains admixtures of 02('A ) and O(lD) and may not give the ideal orbital space at fmge internuclear separation. The B surface, corresponding to the 'B2 state of the Hartley band in the Franck-Condon region, is generally
characterized by a barrier along the R1 = R2 diagonal relative to its dissociation limit 02('Ae) + O(lD). Excursions perpendicular to the diagonal are monotonically downhill toward dissociation. The minimum barrier height is found to be 1.14 eV relative to O&AJ + O(lD) at a geometry of R1 = R2 2.75 a,, and 0 = 111'. At this point the lB2 state is 5.01 eV above the calculated ground-state minimum. The avoided curve crossings are shown in detail in the insert in Figure 1. For the particular slice through the surfaces in Figure 1, the A, B, and R surfaces all converge near Rz = 3.3 a,. The interactions between the surfaces lead to the avoided crossings as the surfaces approach to within 0.1 eV in this region. The dynamics in this region, which will be addressed in future studies, determine the branching ratio of excited-state to ground-state photofragments. Of the molecules initially excited to the B surface, those that remain on this surface will produce O2('4) + O('D) while those that cross over to the R surface (above 15% according to recent measurements)3a will yield 02(3z,-)+ 0 ( 3 ~ ) . Absorption Spectra. Figure 3 shows the experimental and present theoretical 'Bz 'A, absorption spectrum out of the ground vibrational state computed by using the fitted B and X surfaces. The theoretical absorption curve was shifted by about 4000 cm-' to lower frequency; this represents the error in the computed vertical energy separating the XIA1and lB2 surfaces. Also, since the computed transition moment was assumed constant in this calculation, we have plotted the spectral intensity in arbitrary units. Generally the agreement is excellent. The fwhm is in very good accord, as is the shape of the absorption band, being slightly skewed toward higher energy. These features suggest that the shape and slope of the calculated and fitted upper potential surface in the Franck-Condon region are in good agreement with nature. We did not reproduce the very detailed, small amplitude oscillations seen in the experimental spectrum. These could arise out of a recurrence in the autocorrelation function ( & ( t ) ) at something on the order of few vibrational periods.23a Our experience suggests that such structures are extremely +
(23) R. T.Pack, J . Chem. Phys., 65,4765 (1976). (24) E.J. Heller, J. Chem. Phys., 68, 3891 (1978).
J. Phys. Chem. 1982, 86, 865-807
sensitive to the potential energy surface and the accuracy of the dynamics. We hope that improved potential surfaces and dynamicsz1(which relax the "frozen" Gaussian approximationm) will reveal the source of the structure
865
seen in the spectrum. Future studies will also concentrate on (1)the effect of initial vibration on absorption as well as (2) the final electronic vibrational and rotational state distributions in photodissociation.
A Mass Spectrometric Study of the Reactions of Acetone Ion Clusters A. J. Stace' and A.
K. Shuklat
Depertment of Chemistry, The Unhntfy, Soufhampton, SO9 5NH United K l w m (Received: November 19, 198 1)
A combined molecular beam-mass spectrometer system has been used to study the fragmentation routes of acetone ion clusters. Apart from the production of protonated ion clusters, (CH3COCH3),H+,the fragmentation pattern is similar to that observed for the monomer ion. However, for large ion clusters the relative intensities of the fragments are found to be independent of cluster size. The implication of this in radiolysis experiments is discussed.
Introduction In recent years a number of studies have been made of the gas-phase ion-molecule chemistry of acetone.'* Through these experiments the nature and rates of formation of many of the reaction products have become reasonably well established, although the decomposition routes for some ions are not completely Like many ionic species, the ion-molecule chemistry of acetone centers around the formation of ion clusters, and these species play an important role as stable intermediates in many of the reactions.'* In previous studies the ionmolecule reactions have been initiated either by elect r ~ n ' - ~or* ~photon4i6 impact ionization of the acetone monomer. Recently, however, it has been realized that through the ionization of neutral clusters it is possible to form ions which closely resemble many of the intermediates found in ion-molecule reactions.'* This behavior is particularly well established in the case of aliphatic alcohols! where it has been found that ionization of neutral alcohol clusters can result in the formation of ions which decompose in a manner identical with that observed for ion clusters formed in ion cyclotron resonance experiments.'*12 In this paper we report the results of a study made of the decomposition processes of acetone ion clusters, formed as the result of electron impact ionization of neutral clusters. It has now become recognized that cluster formation is an important intermediate stage in the passage of a gaseous system through a phase boundary to the J ~this respect, therefore, the study condensed ~ t a t e . ' ~ In of acetone ion cluster reactions could provide data which would be of use in the interpretation of radiolysis experiments on liquid a ~ e t o n e . ~ In J ~particular, the degree of reactivity in large acetone ion clusters may provide information on the extent of energy transfer to the local environment of an ion in a liquid. Experimental Section The neutral acetone clusters are generated by expanding a mixture of acetone and argon through a 0.005-cmorifice into a chamber maintained at a pressure of 1 X torr. 'Department of Chemistry, University of Warwick, Coventry,
CV4 7AL England. 0022-3654/82/2086-0865$0 1.2510
After passing through a skimmer the cluster beam is modulated at 110 Hz by an electrically driven tuning fork. The clusters are then ionized by electron impact and mass analyzed on a modified A.E.I. MS 12 mass spectrometer. After preamplification the modulated ion current is fed into a lock-in amplifier (Brookdeal 9503SC) which is synchronized with a reference signal from the beam chopper. The beam is maintained by passing the argon at a pressure of approximately 3000 torr through a small reservoir filled with acetone heated almost to ita boiling point. The saturated carrier gas is then expanded through the nozzle which is held at a temperature 10 "C above the boiling point of acetone. This technique provides a stable beam of clusters and avoids the use of large gas reservoirs or the excessive heating of liquid samples. In studying the ion cluster decomposition processes we have made use of two established techniques in mass spectrometry; these are metastable peak analysis and collisional activation. Transitions arising as metastable peaks are designated m* and those resulting from collisional activation are designated m*/CA. (1) M. S. B. Munson, J. Am. Chem. SOC.,87, 5313 (1965). (2) J. 0. Terry and T. 0. Tiernan, 'Proceedings of the 16th Annual Conference on Maas Spectrometry and Applied Topics", Pittsburg,PA, 1968, p 33. (3) K. A. G. MacNeil and J. H. Futrell, J. Phys. Chem., 76,409 (1972). (4) I. W. Sieck and P. Ausloos, Radiat. Res., 52, 47 (1972). (5) A. S. Blair and A. G. Harrison, Can J. Chem., 51, 703 (1973). (6) 2.Luczynaki and H. Wincel, Znt. J.Mass Spectrom. Zon Phys., 23, 37 (1977). (7) T. A. Milne, J. E. Beachey, and F. T. Greene, J.Chem. Phys., 56, 3007 (1972). (8) S. T. Ceyer, P. W. Tiedemann, C. Y. Ng, B. H. Mahan, and Y. T. Lee, J. Chem. Phys., 70, 2138 (1979). (9) A. K. Shukla and A. J. Stace, submitted for publication. (10) J. L. Beauchamp and R. C. Dunbar, J.Am. Chem. SOC.,92,1477 (1970). (11) J. L. Beauchamp and M. C. Caserio, J.Am. Chem. SOC.,94,2638
.--(12) J. L. Beauchamp, M. C. Caserio, and T. B. McMahan, J. Am.
(1972). .-,-
Chem. SOC.,96,6243 (1974). (13) A. W. Castleman, Jr., in 'Kinetics of Ion Molecule Reactions",P. Ausloos, Ed., Plenum Press, New York, 1979, p 295. (14) P. Kebarle in 'Ion Molecule Reactions",Vol. 1, J. L. Franklin, ed., Plenum Press, New York, 1972, p 315. (15) M. A. J. Rodgers, Trans. Faraday SOC.,67, 1029 (1971).
0 1982 American Chemical Society
