J. Phys. Chem. 1983, 87, 1488-1490
1488
Attractive Nature of Ar"('P) f H, Interaction and the Ar*(3P,,2) H Process
+
R.
+ H2
-
Ar('S)
+H
P. Bllckensderfer,t K. K. Sunll, and K. D. Jordan'
Department of Chemistry, Unlvwslty of Plttsburgh, Pittsburgh, Pennsyhranle 15260 (Recelved: February 25, 1983)
The SCF-CIprocedure is utilized to study the Czointeraction of Ar*(3P)with H2.The lowest energy 3A, surface is found to have a deep (-13 kcal/mol) minimum and is intersected by the lowest 3B2surface. Since the 3B2 surface dissociates to Ar('S) + H H, this suggests that the Ar*?P) + Hz Ar(lS) + H + H reaction may proceed in part by surface hopping in the vicinity of the 3B2/3A1surface crossing.
+
Electronically excited inert gas atoms may be quenched by molecules via a variety of mechanisms including electronic energy transfer, vibrational excitation, dissociation, chemi-ionization,and chemiluminescent reaction. Various models including long-range energy transfer via multipole interactions, crossing of entrance and exit surfaces, and formation of charge-transfer intermediates have been postulated to explain the quenching reactions. l4 Unfortunately, in most cases it has proven difficult to determine the validity of the various models due to the absence of high-quality information on the relevant potential energy surfaces. In the present study we utilize the selfconsistent field (SCF) and configuration interaction (CI) methods to calculate potential energy surfaces for the Ar*(3P) H2 system. This system was chosen due to its theoretical "tractability" and due to the fact hat it has been the subject of several experimental investigation^.'^^^^ A correlation diagram giving the experimental energies of the relevant states of argon and of H2is given in Figure 1. The 3p54sconfiguration of Ar gives rise to 3P2,3P1,3P0, and 'PI states at 11.55, 11.62, 11.72, and 11.83 eV, re~pectively.~ The quenching of the 3P1and 'P, states is dominated by near-resonant excitation of the B1& state of Ha. Although excitation of the 3Zg+and c311ustates of H2by the 3P0and 3P, levels of Ar is endothermic, their u = 0 levels are accessible for triplet quenching due to thermal energy spreads; a 32g+ b3ZU+H2 emission acand formation of counts for 5-10% of the total 3P2/3P0 c3HUH2 is expected to contribute at most a few percent to the total quenching cross section. Since direct vibrational excitation of XIZg+ H2 should also be relatively unimportant, the dominant quenching process is expected to be dissociative, producing Ar + H + H.lv7 This suggests that nonradiative formation of the repulsive b3Z,+ state of H2 is involved. In this Letter we report the results of calculations for Czuinteraction of Ar*t3P) with H,, which is expected to be the favored approach at large separations.8 For CzU approach and neglect of spin-orbit interaction, 3A1,3B1, and 3B2surfaces are possible depending on the orientation of the singly occupied p orbital. We focus here on the 3B2 and 3A1surfaces. Some possible consequences of sph-orbit coupling will be considered in the concluding section of the paper. The geometry of ArH2 with Czusymmetry is specified by using the internal coordinates RHH (H-H separation) and RAr(distance of Ar along the Czvaxis from the midpoint of the H2 bond). An effective core potentiallo was utilized for the argon atom, reducing the Ar* + Hz system from a 20- to a 10-
+
-
Permanent address: Department of Chemistry and Physical Sciences, Quinnipiac College, Hamden, C T 26518. *Camille and Henry Dreyfus Teacher Scholar; John Simon Guggenheim Foundation Fellow.
+
electron problem. The argon basis set was generated by augmenting the 3s3p primitive Gaussian basis set of Topiol'O with s and p functions, with exponents chosen to be one third those of Topiol's most diffuse functions, together with a primitive Gaussian d function with an exponent of 0.92, chosen to minimize the energy of Ar*(3P) in a single-plus-double excitation (SDCI) calc~lation.~ The two innermost p functions of the argon basis set were contracted together, introducing less than 0.1-eV changes in the Ar 'S lp3Pexcitation energies. The hydrogen basis set was formed by adding two diffuse 3 functions (a = 0.05, 0.02) and three p functions (a = 0.80, 0.30, and 0.09) to the [4s/2s] contracted basis of Pople and co-workers." Calculations on the 32g+, lZ +,and 3&+ states of H2 indicated that the two outer cfiffuse s functions as well as the two innermost p functions could be contracted together with little degradation of the vertical excitation energies. The [4&pld/4s3pld] argon and the [6s3p/3s2p] hydrogen basis sets thus derived were utilized in all calculations on the Ar* H2 system. The molecular orbitals for the CI calculations on the ArH2*states were obtained from SCF calculations on the ArH, ground state. The orbital space was divided into an extended valence space consisting of the lal-5al, lbl-2bl, and lbz-2b2 molecular orbitals and a secondary space containing the remaining virtual orbitals. In terms of the
-
+
(1) J. Balamuta and M. F. Golde, J . Chem. Phys., 76, 2430 (1982). (2) J. E. Velazco, J. H. Kolts, and D. W. Setser, J . Chem. Phys., 69, 4357 (1978). (3) M. F. Golde in 'Reaction Kinetics", Vol. 2, Specialist Periodical Reports, The Chemical Society, London, 1976, p 121. (4) R. J. Donovan, B o g . React. Kinet., 10, 253 (1979). ( 5 ) D. H. Stedman and D. W. Setser, B o g . React. Kinet., 6,193 (1971). L. G. Piper, W. C. Richardson, G. N. Taylor, and D. W. Setser, J. Chem. SOC.,Faraday Discuss., 53, 100 (1972). (6) E. H. Fink, D. Wallach, and C. B. Moore, J. Chem. Phys., 56,3608 (1972). (7) It is possible that the Ar* + H2 reaction gives rise to ArH*(A22) + H since ArH* is sufficiently stron ly bound that this channel opens at nearly the same energy as the H2*(a Zg+and c311,) excitations. However, since the A X emission of ArH should be detected together with the Ht a32 emission, this should also be a relatively minor process. Theoretica! studies on ArH* have been published by R. L. Vance and G. A. Gallup, J.Chem. Phys., 74,894 (1980);R. E. Olson and B. Liu, Phys. Reu. A , 17, 1568 (1978). (8) Ar*(3p54ssP) like Mg*(3s3p 3P)has unpaired s and p electrons. , approach has been found to be favored for Mg*(3P)+ H,: R. P. The C Blickensderfer, K. D. Jordan, N. Adams, and W. H. Breckenridge, J. Phys. Chem., 86, 1930 (1982). (9) The integrals over symmetry-adapted Gaussian functions were performed with the program developed by R. Pitzer at Ohio State University; the SCF calculations were performed with the GRNFNC program of G. Purvis of the Quantum Theory Project, University of Florida; and the CI calculations utilized the unitary group CI programs developed by Ron Shepard at the University of Utah. The local potential integrals were calculated by using the codes of L. Kahn of Battelle Memorial Laboratory. (10) S. Topiol, J. W. Moskowitz, C . F. Melius, M. D. Newton, and J. Jafri, Courant Institute of Mathematical Sciences Report COO-3077-105. (11) W. J. Hehre, R. Dichtfield, and J. A. Pople, J. Chem. Phys., 56, 2257 (1972).
-
f
+
0022-3654/83/2087-1488$01.50/00 1983 American Chemical Society
The Journal of Physlcal Chemistry, Vol. 87, No. 9, 1983 1480
Letters
Ar+H7
A
-
97
3
tI
2.
I
0%
3?
C W
93-
3P 2
-
?
L;
4-
aJ
0
5-
'5 t P
- -22.08-
1-
-22.10
-
0-
u , 1 2 3 4 5 1 2 3
3-
R
R
4
5
(8)
Flgure 2. 3A1and 3B, potential energy curves for the C l v approach of Ar to H2 for R H H = 0.735 and 0.85 A.
2-
22.065 91
l -
Ar*
B'Z,,*
c311,
a311
F W r e 1. Correlation diagram giving the experimental energles of Ar' Hdv' = 0) and Ar iH2*(v) relative to Ar 4- H,(v' = 0). The repulsive b3Zu+state of H, which is not included in the diagram lies at 83 800 cm-' for I?+,, = 0.735 A, the equilibrium bond length of the ground state. In the vertical excitation limit the a3Z,+ state lies about 1500 cm-' below the c3nUstate and both states lie several thousand cm-' above the adlabatic values given in the figure.
+
separated Ar and H2 species the valence space consists of the 4s and 3p orbitals of Ar and the lag, 2ag, and la, orbitals of H2.12 The CI calculations are based on four references, corresponding at RA = to Ar* to H2, Ar + H2*, Ar+ + H2-, and Ar- Hz+.All single and double excitations are allowed from the reference configurations with the restriction that the lal (Ar 3s) orbital is kept doubly occupied and that only one electron is allowed out of the extended valence space. This procedure gives rise to spaces containing 1382 and 2132 configurations for the 3A1 and 3B2states, respectively. To establish the suitability of this first-order type of CI procedure, we checked the excitation energies of Ar and H2 by performing calculations on a system made up of the noninteracting fragments. For RHH = 0.735 A (the equilibrium H2separation) and R h = 10 A excitation energies of 11.34 and 12.5 eV were obtained for argon 3Pand a 3Zg+ H2,respectively, in good agreement with the corresponding experimental values of 11.55 (3P2)and 12.4 eV. To obtain the C2"surfaces we calculated a grid of points with RHH ranging from 0.70 to 1.2 A and Rh ranging from 1.3 to 10
+
A.
The lowest two 3A1and 3B2potential energy curves obtained for fixed HH distances (RHH = 0.735 8,and RHH = 0.85 A) are shown in Figure 2. For Rm = 0.735 A the 13A1 and the 23B2states correlate with the Ar* H2 limit. The 23B2state is repulsive while the 13A1state has a shallow minimum (near R = 4.1 A), a small (=2 kcal/mol) barrier near 3 A, and a deep minimum (=llkcal/mol) at Rh = 1.8 A. The 23A1 surface, correlating with Ar + H2(a3Z+), is repulsive, and the 13B2surface has a minimum near hh = 2.1 A. For RHH = 0.85 A,the Ar* + H2 and Ar Hz* asymptotes have switched, so that the 13A1curve now dissociates to Hz*(3Zg+)+ Ar. (Actually, the 13A1surface should now correlate with the c3nU state of H2 However, with the basis
+
+
(12) Actually a somewhat smaller configuration space was employed for the 3A1problem since the 2bl orbital was not retained in this case.
22.075
t 0.00
0.82
R
0.84
(A)
Figure 3. 3A1 potentlal energy surfaces of ArH,, for variable H-H distance and fixed Ar-H, dlstances, in the avoided crossing region. Resuits are presented for R, = 6 (-), 5 (- -), 4 (- -), and 3.5 A (- -).
-
sets and configuration lists used here the c3nU state lies several tenths of an electronvolt above the a3Z,+state.) At this HH distance the 13A1 curve no longer has a barrier, and the depth of its minimum is increased to nearly 13 kcal/mol. Examination of the corresponding curves for other values of RHH reveals that the barrier in the 13A1curve is absent for Rm > 0.78 A and that the 13A1and 23A1 curves are essentially degenerate for large values of RArwhen Rm = 0.82 A. Along the minimum energy 3A1pathway, RHH varies from 0.735 %I at large values of Rh, increases to a maximum of 1.0 for RAr = 3 A,and then decreases to 0.84 A for Rh = 1.8 A, i.e., near the minimum in the surface. The minimum in the lower 3A1 surface arises from an avoided crossing between Ar* H2 and Ar + H2* configurations. The behavior of the curves in the vicinity of the crossing is examined in Figure 3, where the 3A, energies are plotted as a function of RHH for various fixed values of R h For R h = 6 I%,the minimum splitting between the two 3A1curves occurs at Rm = 0.8085 A and is only 9 cm-'. As expected, this value of Rm is close to that at which the X'Zg+ curve, shifted upward by the Ar 'S 3P excitation energy, crosses the a3Z,+ curve. The splitting increases to 70 and 430 cm-' for Rh = 5 and 4 A,respectively. From Figure 2 it may be seen that the 13A1 and 13Bz surfaces intersect at small values of R h and that this intersection lies energetically below the Ar* + Hz(X'Zg+) reactants. Thus a trajectory for which Ar*(3P)approaches Hz on the 3A1surface could switch to the 3B2surface in the vicinity of this crossing,13providing a mechanism for the
+
-
(13) If the Ar atom moves off the C,, axis, the 3A1 and 3B2surfaces adopt A' symmetry and avoid. It would be of interest to map out the surfaces near their avoided crossing and to address the question concerning the relative importance of Czu and C, trajectories.
J. Phys. Chem. 1983, 87, 1490-1493
1490
+
formation of the Ar('S) H + H products. The existence of the 3A1potential well is important because it enables the 3A1/3B2crossing to occur at energetically accessible geometries. Whether it is also important because some trajectoriers are trapped in the region of the well enhancing either the probability of the 3A1/3B2surface hopping or a3Zg+excitation cannot be answered at present. Although the attractive nature of the 3A1 surface and the accessible 3Al/3B2surface crossing are probably responsible for the much higher total quenching cross section for the 3P2level of Ar compared to that of Xe or Kr,2,3,5the magnitude (3.6-5.7 A2) of the Art3P) quenching cross section suggests that either relatively few trajectories make it into the region of the deep well or that of those that do only a small fraction go on to react. Both these possibilities are consistent with the finding that the 3A1 surface has a barrier for RHH= Re: The barrier could turn back those trajectories for which the H2 bond length remains close to Re, and if the H2 bond stretches appreciably near R h = 3.3 A (resulting in an attractive rather than a repulsive interaction) and remains stretched as the collision proceeds to small Rh, then the 3B2and 3A1surfaces would no longer cross in an energetically accessible region. Experimentally it has been found that the total cross section for quenching of Ar(3P0)by H2is 1.2-1.6 times that of Ar(3P2).2,14The larger cross section for the 3P0state
may be due in part to its greater energy. However, part of the difference in the 3P2and 3P0quenching rates may arise from differences in the potential energy surfaces for the individual sublevels. In particular when spin-orbit interactions are included, it is found in C2, symmetry that there are five surfaces correlating with Ad3P2)+ H2,three to Ar(3Pl) H2, and one to Ad3Po)+ H2. The attractive 13A1surface correlates with the 3P2limit, while the surface correlating to the 3P0limit (assuming RHH = 0.735 A) is derived from the repulsive 23B2surface. Hence, the larger quenching cross section for the 3P0case may indicate involvement of additional potential energy surfaces, in particular the 3B1surfaces arising from Ar(3P) H2 and Ar + H2(c3II,,)or one or more of the surfaces arising from the Ar('P,) + H2 limit. In order to establish the detailed mechanisms for the quenching of the individual sublevels we plan to extend the present study to include these additional surfaces and to include the effects of spin-orbit interactions.
+
+
Acknowledgment. This work has been supported by the National Science Foundation. It is a pleasure to acknowledge stimulating discussions with Professors M. Golde and P. Siska. (14)J. Balamuta and M. F. Golde, unpublished results.
ARTICLES Transfer of Excitation Energy from Zinc to Copper Porphyrln in Methylcyclohexane Rigid Solution S. Konishl,' M. Hoshlno, and M. Imamura The Institute of Physical and Chemical Research, Wako-shi, Saitama 35 1, Japan (Received: July 29, 1982; I n Final Form: November 1, 1982)
The emission spectrum of methylcyclohexane (MCH) rigid solutions of a mixture of zinc(I1) and copper(I1) mesoporphyrin dimethyl ester (ZnMPDE and CuMPDE) consists of two components at 77 K: the fluorescence of ZnMPDE and the phosphorescence of the CuMPDE aggregate. The excitation spectrum of the zinc fluorescence is in good agreement with the absorption spectrum of solutions of only ZnMPDE, whereas that of the copper phosphorescence corresponds to the sum of the absorption spectra of solutions of the separate components. On the other hand, no aggregation of the solute(s), nor contribution from the zinc porphyrin to the excitation spectrum of the copper phosphorescence, was observed for 2-methyltetrahydrofuran (MTHF) rigid solutions of the mixed components. These results are interpreted in terms of transfer of excitation energy from ZnMPDE to CuMPDE in MCH rigid solutions,which provide favorable conditions for the energy transfer.
(1) Birks, J. B. In 'Photophysics of Aromatic Molecules"; Wiley-Interscience: New York, 1970; Chapter 11.
0022-3654/83/2087- 1490$0 1.50/0
(2) Govindjee, Ed. "Bioenergetics of Photosynthesis"; Academic Press: New York, 1975.
0 1983 American Chemical Society
