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Ab initio study of electronic energy transfer in the quenching of CO*(a 3Π) by H2
Volume 142, number 5
CHEMICAL PHYSICS LETTERS
18 December 1987
AB INITIO STUDY OF ELECTRONIC ENERGY TRANSFER IN THE QUENCHING OF CO*(a %) BY H2
Robert F. SPERLEIN, Michael F. GOLDE and Kenneth D. JORDAN Department of Chemistry, University ofpittsburgh,
Pittsburgh, PA 15260, USA
Received 24 September 1987; in final form 30 September 1987
Potential energy calculations for the interaction of CO( a ‘IT) with Hr( X ‘C: ) are presented, both at the MC SCF level and with the inclusion of extensive configuration interaction. In C1, geometry, the lowest two 3BI surfaces exhibit a strongly avoided crossing. At the highest level of theory used, the lowest surface provides a barrier-free adiabatic pathway for energy transfer from CO(a) to Hz, the products being CO(X ‘2’) and H,(b ‘2: ), which dissociates to two H atoms. The energy transfer occurs by a two-electron exchange mechanism.
1. Introduction
Reactions of electronically excited molecules are important processes in the chemistry of the upper atmosphere, in gas lasers and in combustion flames. In many cases these reactions involve E-E emergy transfer, AB*+CD-tAB+CD*,
(1)
wherein electronic energy is transferred from the excited molecule AB* to the collision partner CD, which subsequently undergoes a unimolecular process such as dissociation into the constituent C and D atoms. Of particular interest are the collisional deactivation reactions of the lowest excited states of CO and Nz, CO(a’II) and NT(A’E:), both of which are metastable and which have similar energies, respectively 6.0 and 6.2 eV [ 11. Quenching rate constants for these two metastables have been measured in a number of experimental investigations [ 2-51 and the resulting data have intriguingly shown that a group of reagents which includes Hz, H1O and CH, quenches CO*(a 3H) at close to the collision rate while quenching Nt(A ‘II,+ ) at least four orders of magnitude more slowly. The low efficiencies for the N,(A) reactions have been ascribed [3,6,7] to the absence of accessible excited states of the reagent. For instance, the lowest excited state of Hz, Hz(b ‘2: ), lies (vertically) 10.6 eV above the
ground state. We surmised initially that the greater efficiency of the CO( a ‘II ) reactions was due to a distinct reaction channel: CO(a)+RH+HCOfR.
(2)
However, a recent investigation [ 81 of the products of the reactions with Hz, H20 and CH, showed this channel to be minor in comparison with dissociation of RH to R+H. This result implies that the potential surfaces for interaction of CO(a) with these molecules must have certain features which allow “nonvertical” access to the excited, dissociative states of RH, and should differ significantly from those of N,(A). In this work, we study the quenching of CO* (a 311) by HZ. Previous ab initio studies of relevance have addressed the quenching of electronically excited metal and rare gas atoms. In particular, attractive potential surfaces have been found for Czy approach of Na(2P) [9], Mg(‘P) [lo] and Ar(‘P) [ll] to Hz. In these systems, the reaction has been proposed to occur by a subsequent non-adiabatic transition from this surface to a product surface of differing symmetry (in the Czvpoint group), which correlates respectively with Na( 2S) +H2, MgH+H and Ar( ‘S)+2H. The present calculation of the CO(a)/H* interaction was motivated by these calculations in two ways. Firstly, the singly occupied ~3, orbital of CO has most of its weight on the C
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atom and thus may behave analogously to the p orbitals of Na(*P) and Mg( ‘P). Secondly, reagent (CO(a)+H2) and product (CO(X) +H,(b)) surfaces can be chosen to have the same symmetry, 3B2, offering the possibility of much stronger mutual coupling than in the above cases. The procedure was to calculate the lowest two states of 3B2 symmetry. In principle, in the absence of coupling, these would correspond initially to CO(a) +H2 and CO(X) + H,(b), with energies of = 6 and z 10 eV, respectively. As the Hz bond is stretched, the lower state increases in energy, while the unbound upper state decreases in energy, leading to an expected “crossing” at I( H-H) = 1.1 A. Thus, in the absence of coupling, the reaction would involve negotiation of a sizable barrier at the “crossing point”. In the present calculations, we employed a combination of multiconliguration self-consistent field (MC SCF) and singles-plus-doubles replacement configuration interaction (SDCI) methods to calculate points on the adiabatic potential surfaces. We show that a purely attractive pathway exists along the lowest 1 3Bz adiabatic surface in Czy symmetry corresponding to transfer of electronic excitation from CO*( a ‘II ) to HT( b 3CJ ) and subsequent dissociation of the latter into H atoms. The resulting MC SCF orbitals show that energy transfer is accomplished via a two-electron transfer mechanism wherein the excited R& electron on CO* is transferred to the vacant o 7, orbital on Hz and a o ,s electron is simultaneously transferred from H2 into the singly occupied 02,,, orbital on CO.
2. Theoretical approach In this work we have primarily treated the 3Bz states arising from the Czv interaction of CO* with Hz, although a number of calculations were also performed for the 1 3A’state in a computationally more cumbersome C, configuration with the Hz molecule oriented coparallel with the CO bond axis (see fig. 1). Two Gaussian basis sets were employed in these calculations. The first, which will be referred to as basis set B, consists of the Dunning [ 121 (9sSp/4s3p) contracted basis set for carbon and oxygen and his (4s/3s) contracted basis set for hydrogen. This basis set was later augmented with two d functions for car360
18 December 1987
C 2”
cs
-/ ‘X
Fig. 1.The Czvand C, (coparallel) geometrical arrangements used in this study. Some calculations in Czvsymmetry were performed with the 0 atom facing the Hz.
bon (cy= 1.50 and 0.375) and oxygen (a= 1.70 and 0.425), which were contracted together following a scheme specified by Dunning [ 13 ] and with a single p function for hydrogen ((Y= 0.80). With this polarized basis set, which will be referred to as basis set A, we obtain a CO(X+a) adiabatic excitation energy of 6.050 eV in SDCI calculations [ 141 with the Davidson correction. This is in excellent agreement with the experimental value of 6.036 eV [ 11. SDCI excitation energies of H,(X, R=R:+b 3ZC:, R=0.74-1.4 A) were found generally to agree to within 2% with the values obtained by Kofos and Wolniewicz [ 151 in their very accurate calculations. In these and all subsequent calculations, reference equilibrium internuclear separations of 1.1283, 1.2093 and 0.7416 A were used for CO(X ‘E’), CO*( a ‘II ) and ground state H2( X ‘Z: ) respectively [ 1,161. In order to identify regions of the potential energy surface that could provide optimal pathways for energy transfer, a number of MC SCF calculations were initially performed using basis set B to characterize the Czv and C, interactions. The MC SCF program used is described by Shepard et al. [ 171. A total of four configuration state functions (CSFs) were em-
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ployed in these MC SCF calculations so as to describe the CO*(a 311)-H1 and CO-H2(b 3E: ) systems, as well as any contributions from CO--H: and CO+-H, in potential curve crossing regions. The Czv CO*-Hz geometry is shown in fig. 1; the initial C2”grid was constructed by varying the geometrical coordinates R( C-H*), the perpendicular distance between the carbon atom and the H2 bond axis, and R( H-H), the Hz internuclear separation, while maintaining R( C-O), the CO internuclear separation, at the CO(a) equilibrium value. The C, geometry with the CO and Hz bond axes set coparallel is also shown in fig. 1. The C, grid was constructed so as to maintain perpendicular hisection of the two bond axes; in this case, the coordinate R(C-Hz) was replaced by RPAR, the perpendicular distance between the two bond axes. Starting orbitals for the MC SCF calculations were obtained as necessary, directly from SCF calculations #I. However, it was generally found that more rapidly converging MC SCF solutions could be obtained if the calculations were started using the natural orbitals [ 18,191 from the converged MC SCF results for a neighboring point. The energy at each point is referenced with respect to that of the non-interacting fragments, obtained from calculations with R(C-HJ = 10.0 A. Similar MC SCF calculations were then performed using basis set A for points in the region of the surface identified in the initial calculations as most important for energy transfer. The resulting molecular orbitals from these basis set A MC SCF calculations were then used to perform SDCI calculations (using the program of Lischka et al. [ 141) to incorporate more completely electron correlation effects at each point. The SDCI configuration space was based on the four reference CSFs used in the MC SCF calculations. The two lowest energy orbitals, consisting of the 1s orbitals on carbon and oxygen were constrained to be doubly occupied in all CSFs. With the application of generalized Hartree-Fock interacting space restrictions [ 201, this O’The SCF calculations were performed with the GRNFNC program developed by G. Purvis (Quantum Theory Project, University of Florida); the molecular integrals were calculated over symmetry adapted Gaussian functions using the ARGOS integral program developed by R.M. Pitzer (Ohio State University).
18 December 1987
selection procedure resulted in 57652 CSFs for 3B2 states in Czv symmetry and 113222 CSFs for ‘A’ states in C, symmetry. Final potential energy values were then determined from the SDCI results for these points by applying a modified Langhoff-Davidson unlinked cluster correction,
as prescribed by Buenker and Peyerimhoff [ 2 1 ] and Bruna [ 221. These results are referred to as SDCI-DC.
3. Results and discussion In fig. 2 are shown the 1 3Bzand 2 ‘BZ basis set B MC SCF potential curves that result from varying R(C-Hz) from 1.0 to 3.5 A, with R( H-H) and R( C-O) respectively set at the H2 ground state and CO*( a ‘II ) equilibrium internuclear separations. The 1 3Bzand 2 ‘BZ curves respectively correlate asymptotically with the CO*( a ‘II)-H* and COH,(b ‘Z,’ ) configurations and exhibit an asymptotic energy difference of 5.133 eV which primarily
1
8-
6-
8 a > CO*- H, 138, I
2
3
4
R(CO-H2,,i Fig. 2. Calculated potential energies (basis set B, four-CSF MC SCF) as a function of CO-H, separation in Czv geometry. R(H-H) =0.7416 A;R(C-O)= 1.2093 A. Solid lines; 1 ‘B2 and 2 ‘B2 states with the C atom facing Hz: dashed line: 1 ‘BZstate with the 0 atom facing Hz.
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a lower barrier of 0.57 eV at R( C-H2) = 1.60 A and R (H-H) = 1.10 A, which could be further lowered to
results from the difference in the CO*(a ‘II) and H:(b Z: ) excitation energies, but which includes a contribution from the energy needed to stretch the CO bond length from its ground state equilibrium value of 1.1281 A. The dashed curve in the lower half of fig. 2 represents the 1 ‘Bz potential curve obtained in a CZvgeometry with the oxygen atom facing Hz, which exhibits substantially greater short-range repulsion. It was therefore decided to perform all subsequent Czvcalculations with the carbon atom facing Hz.
In fig. 3 are shown the basis set B MC SCF potential curves that were calculated by varying R(H-H) from 0.7416 to 1.50 A for values of R(C-HZ) equal to 1.50, 2.00 and 2.50 A. For each value of R(C-H,), the 1 ‘B, and 2 3Bz curves show a strongly avoided crossing between the CO*-H, and CO-HI configurations. The lower curve for R( C-HZ) =2.50 8, clearly reveals the expected barrier to dissociation of the HZ, occurring at the expected R(H-H) distance of 1.1 A. As R(C-HZ) decreases, the barrier height decreases. The effect arises from the increased coupling between the 1 3B2 and 2 3Bz surfaces: at R(H-H) = 1.1 A, the energy splitting increases from approximately 0.45 to 4.55 eV as R(C-HZ) is reduced from 2.50 to 1.50 A. A grid of potential energy points calculated for the 1 ‘Bz state is shown in table 1, where it can be seen that CO*-HZ to CO-H? energy transfer and subsequent H atom production might proceed by stretching of the Hz bond as CO* approaches, with a reaction barrier (at this level of theory) of approximately 0.6 1 eVatR(C-H,)=1.50AandR(H-H)=l.lOA.Additional MC SCF calculations over a more refined grid in the immediate vicinity of this point produced
0.43 eV by reducing the CO bond length to 1.1593 A, which is approximately midway between the CO( X ‘C ’ ) and CO*( a 31T) bond lengths. A barrier height of 0.43 eV exceeds the total energy available for reaction at 300 K, which, based on the sum of the thermal and Hz zero-point vibrational energies, is approximately 0.30 eV. The basis set B MC SCF calculations for the C, coparallel configuration showed a generally similar although less favorable pathway for energy transfer with a barrier of approximately 1.26 eV at R PAR = 1.50AandR(H-H)=l.lOA.Thuswechose to perform combined MC SCNSDCI calculations using basis set A in CZvgeometry along a series of points chosen from table 1 as constituting the most energetically favorable pathway for the energy transfer reaction. The results of these calculations are presented in table 2, which sequentially shows the basis set A MC SCF, MC SCF/SDCI and MC SCF/ SDCI-DC results for the 1 3BZstate. The MC SCF results show that adding polarization functions to the basis set gives a barrier at the same location as seen in table 1 but with the height lowered to 0.45 eV. The combined MC SCF/SDCI results show that electron correlation shifts the barrier to a smaller R(H-H) distance and lowers its height to 0.0223 eV. Electron correlation effects also increase with decreasing R( C-HZ), as might be expected. The MC SCF/SDCI barrier height is now below the total energy available for reaction. Finally, the lowest panel of table 2 shows that applying the Davidson correction to the SDCI results produces a pathway for energy transfer and H atom production that is purely attractive with re-
Table 1 MC SCF potential energy grid (eV) for the 1 3B2state, using basis set B ‘)
NH-H)
0.7416 0.900 1.100 1.300 1.500
(A)
R(C-Hz)
(A)
1.00
1.50
2.00
2.50
3.00
3.50
4.736 3.74 2.93 2.400 2.039
0.739 0.590 0.607 0.512 0.342
0.198 0.457 0.911 0.494 0.010
0.021 0.393 1.343 0.502 -0.117
- 0.024 0.353 1.315 0.491 -0.153
-0.006 0.351 1.315 2.397” 3.426 b’
a) Energies referenced to the asymptotic value at R(C-H,) = 10.0 A,with R( H-H) =0.7416 A. ‘) Convergence on the CO(X)-H,(b) configuration was not achieved.
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Table 2 Potential energy grids (eV) for the I ‘B2 state using basis set A”’ R(H-H)
(A)
R(C-Hz) (A) 1.50
MC SCF
MC SCF/SDCI
MC SCF/SCDI-DC
0.7416 0.900 1.100 1.300 1.500
0.45 1 0.449 0.358
0.7416 0.900 1.100 1.300 1.500
0.023 0.014 -0.036
0.7416 0.900 1.100 1.300 1.500
- 0.040 -0.058 -0.104
2.00
2.50
3.00
3.50
0.170 0.412 0.794 0.341 -0.133
- 0.004
-0.047
-0.051
0.019 0.203 0.542 0.236 -0.174
- 0.063
-0.080
-0.076
-0.007 0.152 0.484 0.229 -0.161
- 0.072
-0.083
-0.078
-0.274
-0.195
1 -0.335
a) Energies referenced to the appropriate asymptotic values at R( C-H,) = 10.0 A and R(H-H) ~0.7416
spect to the CO*(a ‘II)-HZ asymptote. It is expected that optimizing the CO internuclear separation as R(H-H) is increased would provide an even more energetically favorable reaction pathway. By comparing the 2 3B,/1 3B2 energy splittings at the MC SCF and SDCI levels of theory, we conclude that the observed lowering of the energy barrier in this sequence of calculations did not arise solely from increased coupling of the CO(a) + Hz and CO + H2( b) configurations. For the less favorable C, coparallel geometry, combined MC SCF/SDCI calculations with basis set A were performed at the 1 ‘A’ basis set B saddle points to determine the effect of electron correlation, which was expected to be more important in this conliguration than in the CZvorientation due to the closer proximity of all atoms. The MC SCF and MC SCF/SDCI potential energies, again referenced to the asymptotic CZvenergy, are respectively 1.199 and 0.672 eV. Electron correlation indeed has a somewhat greater effect in the C, than in CZv geometry. Adding the Davidson correction tot he SDCI result produces a potential energy of 0.53 eV, and thus although the overall effect of electron correlation is greater than in the CZvcase, it is not sufficient
A.
to produce a barrier lower than the total available reaction energy in this geometry. The favorable pathway for energy transfer in CZv geometry arises principally from strong coupling of the CO(a3D)+Hz(X ‘El) and H2(b3G,‘) +CO( X ‘C ’ ) configurations, which persists over a wide range of geometries, as shown in fig. 3. The MC SCF orbital coefficients give insight into the origin of the strong coupling and on the mechanism of energy transfer. At early and late stages of the reaction path, the system has the electron configuration
Initially, the 5a, and 6a, orbitals consist essentially of the Hz ols and CO crzP,orbitals respectively, while the 2b2 and 3bz similarly constitute the CO R$,, and orbitals; this corresponds to the HZ o:, CO( a ‘II ) + H2( X) state. (The relevant CO and Hz orbitals are illustrated in fig. 4.) Late on the reaction path, the identities of the 5a, and 6a, orbitals are reversed, with similar behavior by the 2b2 and 3b2 orbitals. The final state is thus clearly identified as CO(X)+H,(b 3Z$).Theoriginofthisbehaviorcan be traced to the H2 ts,, and 07, orbitals, which re363
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R(c-H,)
0.7
0.9
q
2.5% -
I#
=2.oA
II
=
(JH
1.1 R(H-H),
-----
1.3
co%pr
-
1.5
i
Fig. 3. Calculated potential energies (basis set B, fourCSF MC SCF) of the 1 ‘Bz and 2 3Bzand 2 )B2 states as a function of H-H bond length in Gv geometry. NC-O) = 1.2093 A; R(C-H,)=1.5,2.0,2.5 A. rise and fall in energy as the H-H bond is stretched. Close to the MC SCF saddle point, each of the 5a, and 6a, orbitals contains approximately equal contributions of Hz o,, and CO o,, character, and the 2bz and 3bz orbitals similarly reflect mixed Hz a:, and CO RF,”character. The strongly avoided crossing (fig. 3)‘thus arises from the strong coupling of the component orbitals, which happen to have similar energies in this region of the reaction path. This symmetry-induced mixing and orbital energy reordering causes smooth transfer of the CO n* electron to the Hz o T, orbital and back transfer from Hz o IS to CO ozp,. The energy transfer thus occurs by a classic electron exchange mechanism [ 23,241. A similar orbital mixing process might be presumed to arise in the coparallel case, as illustrated in fig. 4. As shown above, the mixing is somewhat weaker than in the perpendicular case. In addition, the basis set B MC SCF orbitals show a less clearly defined orbital mixing and conversion pattern for the 1 3A’state. This is due in part to the larger number of orbitals with the correct symmetry to interact. Better mixing and a more attractive pathway may be achieved by modifications to the geometry, such as a decrease in the CO bond length or tilting or disspecti)rely
I8 December I987
co
Qzpr
co
cpy
Fig. 4. Schematic representation of the most strongly interacting orbitals in Czv and C, (coparallel) geometries. In Czv symmetry, the CO(al,,) and H,(o,,) orbitals contribute strongly to the 5a, and 6a, molecular orbitals; CO(r$,, ) and H2(ots)contribute strongly to the 2b, and 3b2molecular orbitals - see text for details.
placing the CO molecule relative to the Hz molecular axis. The discovery of an attractive adiabatic pathway constitutes an important first step towards explaining the highly efficient quenching of CO(a) by Hz and the observed dominance of the dissociation channel for reaction [ 81. It should be stressed that this could be considered an unfavorable situation for strong coupling in that, at the equilibrium H2 bond length, the H,(b) +-CO state lies 4 eV above CO(a) +H2. Many molecules have considerably lower-lying excited triplet states and are found to be efficient quenchers of N2( A 3Z: ) as well as of CO( a) [ 71. Extremely strong coupling may be expected in these cases (assuming that the relevant orbitals have the appropriate symmetry), offering a possible explanation for a large number of observed efficient energy transfer processes involving dissociation of small molecules by N,(A) [ 25,261, CO(a) [ 81 and the metastable ‘PO,*states of Ar, ISr and Xe [ 27,281. It is important to understand the origin of the in-
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eflcient quenching of N2(A) by molecules such as Hz, HI0 and CH,; weak coupling of for instance N2(A)+H2 and H2(b)+N2 may arise either because of the different orbital sizes and energies in N2 and CO, or because of their different symmetries, since N2( A) contains a hole in the nU2Porbital rather than in the oB2,, orbital. Calculations on the N2(A) + Hz system are underway.
Acknowledgement This work was carried out with the support of AFOSR (MFG, RFS) and the National Science Foundation (KDJ). The calculations were performed on the Chemistry Department’s Harris HlOOO superminicomputer, funded by NSF and Harris Corporation. We wish to thank Dr. ILK. Sunil for many helpful discussions during the course of this study.
References [ 1] K.P. Huber and G. Herzberg, Molecular spectra and molecular structure, Vol. 4. Constants of diatomic molecules (Van Nostrand Reinhold, New York, 1979). [ 21 K. Schofield, J. Phys. Chem. Ref. Data 8 (1979) 723. [ 31 A.B. Callear and P.M. Wood, Trans. Faraday Sot. 67 ( 1971) 272, 598. [4] T.G. Slanger, B.J. Wood and G. Black, J. Photochem. 2 (1973/74) 63. [ 51D. Lcvron and A.V. Phelps, J. Chem. Phys. 69 (1978) 2260.
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[ 61 W.G. Clark and D.W. Setser, J. Phys. Chem. 84 (1980) 2225.
[ 71 M.F. Golde, Intern. J. Chem. Kinetics, to be published. [ 81 M.F. Golde and G.H. Ho, unpublished data. [ 91 P. Botschwina, W. Meyer, I.V. Hertel and W. Reiland, J. Chem. Phys. 75 (1981) 5438. [lo] R.P. Blickensderfer, K.D. Jordan, N. Adams and W.H. Breckenridge, J. Phys. Chem. 86 (1982) 1930. [ 111 R.P. Blickensderfer, K.K. Sunil and K.D. Jordan, J. Phys. Chem. 87 (1983) 1488. [ 121 T.H. Dunning, J. Chem. Phys. 53 (1970) 2823. [ 131 T.H. Dunning, J. Chem. Phys. 55 (1971) 3959. [ 141 H. Lischka, R. Shepard, F.B. Brown and I. Shavitt, Intern. J. Quantum Chem. Symp. 15( 1981) 9 1. [ 151 W. Kolos and L. Wolniewicz, J. Chem. Phys. 43 (1965) 2429. [ 16] G. Herzberg, Molecular spectra and molecular structure, Vol. 1, Spectra of diatomic molecules (Van Nostrand, Princeton, 1950). [ 171 R. Shepard, J. Simons and I. Shavitt, J. Chem. Phys. 76 (1982) 543. [ 181 P.O. Liiwdin, Phys. Rev. 97 (1955) 1474. [ 191 A. Szabo and N.S. Ostland, Modem quantum chemistry (Macmillan, New York, 1982). [ 201 B.R. Brooks and H.F. Schaefer III, J. Chem. Phys. 70 (1979) 5092. [ 211 R.J. Buenker and S.D. Peyerimhoff, in: Excited states in quantum chemistry, eds. C.A. Nicolaides and D.R. Beck (Reidel, Dordrecht, 1978). [22] P.J. Bruna, Gazz. Chim. Ital. 108 (1978) 395. [23] D.L. Dexter, J. Chem. Phys. 21 (1953) 836. [24] Th. Fijrster, Discussions Faraday Sot. 27 (1959) 7. [25] M.F. Golde and A.M. Moyle, Chem. Phys. Letters 117 (1985) 375. [26] W. Tao, M.F. Golde, G.H. Ho and A.M. Moyle, J. Chem. Phys. 87 (1987) 1045. [ 27 ] J. Balamutaand M.F. Golde, J. Chem. Phys. 76 (1982) 2430. [28] J. Balamuta, M.F. Golde and Y.-S. Ho, J. Chem. Phy. 79 (1983) 2822.
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AB INITIO STUDY OF ELECTRONIC ENERGY TRANSFER IN THE QUENCHING OF CO*(a %) BY H2
Robert F. SPERLEIN, Michael F. GOLDE and Kenneth D. JORDAN Department of Chemistry, University ofpittsburgh,
Pittsburgh, PA 15260, USA
Received 24 September 1987; in final form 30 September 1987
Potential energy calculations for the interaction of CO( a ‘IT) with Hr( X ‘C: ) are presented, both at the MC SCF level and with the inclusion of extensive configuration interaction. In C1, geometry, the lowest two 3BI surfaces exhibit a strongly avoided crossing. At the highest level of theory used, the lowest surface provides a barrier-free adiabatic pathway for energy transfer from CO(a) to Hz, the products being CO(X ‘2’) and H,(b ‘2: ), which dissociates to two H atoms. The energy transfer occurs by a two-electron exchange mechanism.
1. Introduction
Reactions of electronically excited molecules are important processes in the chemistry of the upper atmosphere, in gas lasers and in combustion flames. In many cases these reactions involve E-E emergy transfer, AB*+CD-tAB+CD*,
(1)
wherein electronic energy is transferred from the excited molecule AB* to the collision partner CD, which subsequently undergoes a unimolecular process such as dissociation into the constituent C and D atoms. Of particular interest are the collisional deactivation reactions of the lowest excited states of CO and Nz, CO(a’II) and NT(A’E:), both of which are metastable and which have similar energies, respectively 6.0 and 6.2 eV [ 11. Quenching rate constants for these two metastables have been measured in a number of experimental investigations [ 2-51 and the resulting data have intriguingly shown that a group of reagents which includes Hz, H1O and CH, quenches CO*(a 3H) at close to the collision rate while quenching Nt(A ‘II,+ ) at least four orders of magnitude more slowly. The low efficiencies for the N,(A) reactions have been ascribed [3,6,7] to the absence of accessible excited states of the reagent. For instance, the lowest excited state of Hz, Hz(b ‘2: ), lies (vertically) 10.6 eV above the
ground state. We surmised initially that the greater efficiency of the CO( a ‘II ) reactions was due to a distinct reaction channel: CO(a)+RH+HCOfR.
(2)
However, a recent investigation [ 81 of the products of the reactions with Hz, H20 and CH, showed this channel to be minor in comparison with dissociation of RH to R+H. This result implies that the potential surfaces for interaction of CO(a) with these molecules must have certain features which allow “nonvertical” access to the excited, dissociative states of RH, and should differ significantly from those of N,(A). In this work, we study the quenching of CO* (a 311) by HZ. Previous ab initio studies of relevance have addressed the quenching of electronically excited metal and rare gas atoms. In particular, attractive potential surfaces have been found for Czy approach of Na(2P) [9], Mg(‘P) [lo] and Ar(‘P) [ll] to Hz. In these systems, the reaction has been proposed to occur by a subsequent non-adiabatic transition from this surface to a product surface of differing symmetry (in the Czvpoint group), which correlates respectively with Na( 2S) +H2, MgH+H and Ar( ‘S)+2H. The present calculation of the CO(a)/H* interaction was motivated by these calculations in two ways. Firstly, the singly occupied ~3, orbital of CO has most of its weight on the C
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atom and thus may behave analogously to the p orbitals of Na(*P) and Mg( ‘P). Secondly, reagent (CO(a)+H2) and product (CO(X) +H,(b)) surfaces can be chosen to have the same symmetry, 3B2, offering the possibility of much stronger mutual coupling than in the above cases. The procedure was to calculate the lowest two states of 3B2 symmetry. In principle, in the absence of coupling, these would correspond initially to CO(a) +H2 and CO(X) + H,(b), with energies of = 6 and z 10 eV, respectively. As the Hz bond is stretched, the lower state increases in energy, while the unbound upper state decreases in energy, leading to an expected “crossing” at I( H-H) = 1.1 A. Thus, in the absence of coupling, the reaction would involve negotiation of a sizable barrier at the “crossing point”. In the present calculations, we employed a combination of multiconliguration self-consistent field (MC SCF) and singles-plus-doubles replacement configuration interaction (SDCI) methods to calculate points on the adiabatic potential surfaces. We show that a purely attractive pathway exists along the lowest 1 3Bz adiabatic surface in Czy symmetry corresponding to transfer of electronic excitation from CO*( a ‘II ) to HT( b 3CJ ) and subsequent dissociation of the latter into H atoms. The resulting MC SCF orbitals show that energy transfer is accomplished via a two-electron transfer mechanism wherein the excited R& electron on CO* is transferred to the vacant o 7, orbital on Hz and a o ,s electron is simultaneously transferred from H2 into the singly occupied 02,,, orbital on CO.
2. Theoretical approach In this work we have primarily treated the 3Bz states arising from the Czv interaction of CO* with Hz, although a number of calculations were also performed for the 1 3A’state in a computationally more cumbersome C, configuration with the Hz molecule oriented coparallel with the CO bond axis (see fig. 1). Two Gaussian basis sets were employed in these calculations. The first, which will be referred to as basis set B, consists of the Dunning [ 121 (9sSp/4s3p) contracted basis set for carbon and oxygen and his (4s/3s) contracted basis set for hydrogen. This basis set was later augmented with two d functions for car360
18 December 1987
C 2”
cs
-/ ‘X
Fig. 1.The Czvand C, (coparallel) geometrical arrangements used in this study. Some calculations in Czvsymmetry were performed with the 0 atom facing the Hz.
bon (cy= 1.50 and 0.375) and oxygen (a= 1.70 and 0.425), which were contracted together following a scheme specified by Dunning [ 13 ] and with a single p function for hydrogen ((Y= 0.80). With this polarized basis set, which will be referred to as basis set A, we obtain a CO(X+a) adiabatic excitation energy of 6.050 eV in SDCI calculations [ 141 with the Davidson correction. This is in excellent agreement with the experimental value of 6.036 eV [ 11. SDCI excitation energies of H,(X, R=R:+b 3ZC:, R=0.74-1.4 A) were found generally to agree to within 2% with the values obtained by Kofos and Wolniewicz [ 151 in their very accurate calculations. In these and all subsequent calculations, reference equilibrium internuclear separations of 1.1283, 1.2093 and 0.7416 A were used for CO(X ‘E’), CO*( a ‘II ) and ground state H2( X ‘Z: ) respectively [ 1,161. In order to identify regions of the potential energy surface that could provide optimal pathways for energy transfer, a number of MC SCF calculations were initially performed using basis set B to characterize the Czv and C, interactions. The MC SCF program used is described by Shepard et al. [ 171. A total of four configuration state functions (CSFs) were em-
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ployed in these MC SCF calculations so as to describe the CO*(a 311)-H1 and CO-H2(b 3E: ) systems, as well as any contributions from CO--H: and CO+-H, in potential curve crossing regions. The Czv CO*-Hz geometry is shown in fig. 1; the initial C2”grid was constructed by varying the geometrical coordinates R( C-H*), the perpendicular distance between the carbon atom and the H2 bond axis, and R( H-H), the Hz internuclear separation, while maintaining R( C-O), the CO internuclear separation, at the CO(a) equilibrium value. The C, geometry with the CO and Hz bond axes set coparallel is also shown in fig. 1. The C, grid was constructed so as to maintain perpendicular hisection of the two bond axes; in this case, the coordinate R(C-Hz) was replaced by RPAR, the perpendicular distance between the two bond axes. Starting orbitals for the MC SCF calculations were obtained as necessary, directly from SCF calculations #I. However, it was generally found that more rapidly converging MC SCF solutions could be obtained if the calculations were started using the natural orbitals [ 18,191 from the converged MC SCF results for a neighboring point. The energy at each point is referenced with respect to that of the non-interacting fragments, obtained from calculations with R(C-HJ = 10.0 A. Similar MC SCF calculations were then performed using basis set A for points in the region of the surface identified in the initial calculations as most important for energy transfer. The resulting molecular orbitals from these basis set A MC SCF calculations were then used to perform SDCI calculations (using the program of Lischka et al. [ 141) to incorporate more completely electron correlation effects at each point. The SDCI configuration space was based on the four reference CSFs used in the MC SCF calculations. The two lowest energy orbitals, consisting of the 1s orbitals on carbon and oxygen were constrained to be doubly occupied in all CSFs. With the application of generalized Hartree-Fock interacting space restrictions [ 201, this O’The SCF calculations were performed with the GRNFNC program developed by G. Purvis (Quantum Theory Project, University of Florida); the molecular integrals were calculated over symmetry adapted Gaussian functions using the ARGOS integral program developed by R.M. Pitzer (Ohio State University).
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selection procedure resulted in 57652 CSFs for 3B2 states in Czv symmetry and 113222 CSFs for ‘A’ states in C, symmetry. Final potential energy values were then determined from the SDCI results for these points by applying a modified Langhoff-Davidson unlinked cluster correction,
as prescribed by Buenker and Peyerimhoff [ 2 1 ] and Bruna [ 221. These results are referred to as SDCI-DC.
3. Results and discussion In fig. 2 are shown the 1 3Bzand 2 ‘BZ basis set B MC SCF potential curves that result from varying R(C-Hz) from 1.0 to 3.5 A, with R( H-H) and R( C-O) respectively set at the H2 ground state and CO*( a ‘II ) equilibrium internuclear separations. The 1 3Bzand 2 ‘BZ curves respectively correlate asymptotically with the CO*( a ‘II)-H* and COH,(b ‘Z,’ ) configurations and exhibit an asymptotic energy difference of 5.133 eV which primarily
1
8-
6-
8 a > CO*- H, 138, I
2
3
4
R(CO-H2,,i Fig. 2. Calculated potential energies (basis set B, four-CSF MC SCF) as a function of CO-H, separation in Czv geometry. R(H-H) =0.7416 A;R(C-O)= 1.2093 A. Solid lines; 1 ‘B2 and 2 ‘B2 states with the C atom facing Hz: dashed line: 1 ‘BZstate with the 0 atom facing Hz.
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a lower barrier of 0.57 eV at R( C-H2) = 1.60 A and R (H-H) = 1.10 A, which could be further lowered to
results from the difference in the CO*(a ‘II) and H:(b Z: ) excitation energies, but which includes a contribution from the energy needed to stretch the CO bond length from its ground state equilibrium value of 1.1281 A. The dashed curve in the lower half of fig. 2 represents the 1 ‘Bz potential curve obtained in a CZvgeometry with the oxygen atom facing Hz, which exhibits substantially greater short-range repulsion. It was therefore decided to perform all subsequent Czvcalculations with the carbon atom facing Hz.
In fig. 3 are shown the basis set B MC SCF potential curves that were calculated by varying R(H-H) from 0.7416 to 1.50 A for values of R(C-HZ) equal to 1.50, 2.00 and 2.50 A. For each value of R(C-H,), the 1 ‘B, and 2 3Bz curves show a strongly avoided crossing between the CO*-H, and CO-HI configurations. The lower curve for R( C-HZ) =2.50 8, clearly reveals the expected barrier to dissociation of the HZ, occurring at the expected R(H-H) distance of 1.1 A. As R(C-HZ) decreases, the barrier height decreases. The effect arises from the increased coupling between the 1 3B2 and 2 3Bz surfaces: at R(H-H) = 1.1 A, the energy splitting increases from approximately 0.45 to 4.55 eV as R(C-HZ) is reduced from 2.50 to 1.50 A. A grid of potential energy points calculated for the 1 ‘Bz state is shown in table 1, where it can be seen that CO*-HZ to CO-H? energy transfer and subsequent H atom production might proceed by stretching of the Hz bond as CO* approaches, with a reaction barrier (at this level of theory) of approximately 0.6 1 eVatR(C-H,)=1.50AandR(H-H)=l.lOA.Additional MC SCF calculations over a more refined grid in the immediate vicinity of this point produced
0.43 eV by reducing the CO bond length to 1.1593 A, which is approximately midway between the CO( X ‘C ’ ) and CO*( a 31T) bond lengths. A barrier height of 0.43 eV exceeds the total energy available for reaction at 300 K, which, based on the sum of the thermal and Hz zero-point vibrational energies, is approximately 0.30 eV. The basis set B MC SCF calculations for the C, coparallel configuration showed a generally similar although less favorable pathway for energy transfer with a barrier of approximately 1.26 eV at R PAR = 1.50AandR(H-H)=l.lOA.Thuswechose to perform combined MC SCNSDCI calculations using basis set A in CZvgeometry along a series of points chosen from table 1 as constituting the most energetically favorable pathway for the energy transfer reaction. The results of these calculations are presented in table 2, which sequentially shows the basis set A MC SCF, MC SCF/SDCI and MC SCF/ SDCI-DC results for the 1 3BZstate. The MC SCF results show that adding polarization functions to the basis set gives a barrier at the same location as seen in table 1 but with the height lowered to 0.45 eV. The combined MC SCF/SDCI results show that electron correlation shifts the barrier to a smaller R(H-H) distance and lowers its height to 0.0223 eV. Electron correlation effects also increase with decreasing R( C-HZ), as might be expected. The MC SCF/SDCI barrier height is now below the total energy available for reaction. Finally, the lowest panel of table 2 shows that applying the Davidson correction to the SDCI results produces a pathway for energy transfer and H atom production that is purely attractive with re-
Table 1 MC SCF potential energy grid (eV) for the 1 3B2state, using basis set B ‘)
NH-H)
0.7416 0.900 1.100 1.300 1.500
(A)
R(C-Hz)
(A)
1.00
1.50
2.00
2.50
3.00
3.50
4.736 3.74 2.93 2.400 2.039
0.739 0.590 0.607 0.512 0.342
0.198 0.457 0.911 0.494 0.010
0.021 0.393 1.343 0.502 -0.117
- 0.024 0.353 1.315 0.491 -0.153
-0.006 0.351 1.315 2.397” 3.426 b’
a) Energies referenced to the asymptotic value at R(C-H,) = 10.0 A,with R( H-H) =0.7416 A. ‘) Convergence on the CO(X)-H,(b) configuration was not achieved.
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Table 2 Potential energy grids (eV) for the I ‘B2 state using basis set A”’ R(H-H)
(A)
R(C-Hz) (A) 1.50
MC SCF
MC SCF/SDCI
MC SCF/SCDI-DC
0.7416 0.900 1.100 1.300 1.500
0.45 1 0.449 0.358
0.7416 0.900 1.100 1.300 1.500
0.023 0.014 -0.036
0.7416 0.900 1.100 1.300 1.500
- 0.040 -0.058 -0.104
2.00
2.50
3.00
3.50
0.170 0.412 0.794 0.341 -0.133
- 0.004
-0.047
-0.051
0.019 0.203 0.542 0.236 -0.174
- 0.063
-0.080
-0.076
-0.007 0.152 0.484 0.229 -0.161
- 0.072
-0.083
-0.078
-0.274
-0.195
1 -0.335
a) Energies referenced to the appropriate asymptotic values at R( C-H,) = 10.0 A and R(H-H) ~0.7416
spect to the CO*(a ‘II)-HZ asymptote. It is expected that optimizing the CO internuclear separation as R(H-H) is increased would provide an even more energetically favorable reaction pathway. By comparing the 2 3B,/1 3B2 energy splittings at the MC SCF and SDCI levels of theory, we conclude that the observed lowering of the energy barrier in this sequence of calculations did not arise solely from increased coupling of the CO(a) + Hz and CO + H2( b) configurations. For the less favorable C, coparallel geometry, combined MC SCF/SDCI calculations with basis set A were performed at the 1 ‘A’ basis set B saddle points to determine the effect of electron correlation, which was expected to be more important in this conliguration than in the CZvorientation due to the closer proximity of all atoms. The MC SCF and MC SCF/SDCI potential energies, again referenced to the asymptotic CZvenergy, are respectively 1.199 and 0.672 eV. Electron correlation indeed has a somewhat greater effect in the C, than in CZv geometry. Adding the Davidson correction tot he SDCI result produces a potential energy of 0.53 eV, and thus although the overall effect of electron correlation is greater than in the CZvcase, it is not sufficient
A.
to produce a barrier lower than the total available reaction energy in this geometry. The favorable pathway for energy transfer in CZv geometry arises principally from strong coupling of the CO(a3D)+Hz(X ‘El) and H2(b3G,‘) +CO( X ‘C ’ ) configurations, which persists over a wide range of geometries, as shown in fig. 3. The MC SCF orbital coefficients give insight into the origin of the strong coupling and on the mechanism of energy transfer. At early and late stages of the reaction path, the system has the electron configuration
Initially, the 5a, and 6a, orbitals consist essentially of the Hz ols and CO crzP,orbitals respectively, while the 2b2 and 3bz similarly constitute the CO R$,, and orbitals; this corresponds to the HZ o:, CO( a ‘II ) + H2( X) state. (The relevant CO and Hz orbitals are illustrated in fig. 4.) Late on the reaction path, the identities of the 5a, and 6a, orbitals are reversed, with similar behavior by the 2b2 and 3b2 orbitals. The final state is thus clearly identified as CO(X)+H,(b 3Z$).Theoriginofthisbehaviorcan be traced to the H2 ts,, and 07, orbitals, which re363
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R(c-H,)
0.7
0.9
q
2.5% -
I#
=2.oA
II
=
(JH
1.1 R(H-H),
-----
1.3
co%pr
-
1.5
i
Fig. 3. Calculated potential energies (basis set B, fourCSF MC SCF) of the 1 ‘Bz and 2 3Bzand 2 )B2 states as a function of H-H bond length in Gv geometry. NC-O) = 1.2093 A; R(C-H,)=1.5,2.0,2.5 A. rise and fall in energy as the H-H bond is stretched. Close to the MC SCF saddle point, each of the 5a, and 6a, orbitals contains approximately equal contributions of Hz o,, and CO o,, character, and the 2bz and 3bz orbitals similarly reflect mixed Hz a:, and CO RF,”character. The strongly avoided crossing (fig. 3)‘thus arises from the strong coupling of the component orbitals, which happen to have similar energies in this region of the reaction path. This symmetry-induced mixing and orbital energy reordering causes smooth transfer of the CO n* electron to the Hz o T, orbital and back transfer from Hz o IS to CO ozp,. The energy transfer thus occurs by a classic electron exchange mechanism [ 23,241. A similar orbital mixing process might be presumed to arise in the coparallel case, as illustrated in fig. 4. As shown above, the mixing is somewhat weaker than in the perpendicular case. In addition, the basis set B MC SCF orbitals show a less clearly defined orbital mixing and conversion pattern for the 1 3A’state. This is due in part to the larger number of orbitals with the correct symmetry to interact. Better mixing and a more attractive pathway may be achieved by modifications to the geometry, such as a decrease in the CO bond length or tilting or disspecti)rely
I8 December I987
co
Qzpr
co
cpy
Fig. 4. Schematic representation of the most strongly interacting orbitals in Czv and C, (coparallel) geometries. In Czv symmetry, the CO(al,,) and H,(o,,) orbitals contribute strongly to the 5a, and 6a, molecular orbitals; CO(r$,, ) and H2(ots)contribute strongly to the 2b, and 3b2molecular orbitals - see text for details.
placing the CO molecule relative to the Hz molecular axis. The discovery of an attractive adiabatic pathway constitutes an important first step towards explaining the highly efficient quenching of CO(a) by Hz and the observed dominance of the dissociation channel for reaction [ 81. It should be stressed that this could be considered an unfavorable situation for strong coupling in that, at the equilibrium H2 bond length, the H,(b) +-CO state lies 4 eV above CO(a) +H2. Many molecules have considerably lower-lying excited triplet states and are found to be efficient quenchers of N2( A 3Z: ) as well as of CO( a) [ 71. Extremely strong coupling may be expected in these cases (assuming that the relevant orbitals have the appropriate symmetry), offering a possible explanation for a large number of observed efficient energy transfer processes involving dissociation of small molecules by N,(A) [ 25,261, CO(a) [ 81 and the metastable ‘PO,*states of Ar, ISr and Xe [ 27,281. It is important to understand the origin of the in-
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eflcient quenching of N2(A) by molecules such as Hz, HI0 and CH,; weak coupling of for instance N2(A)+H2 and H2(b)+N2 may arise either because of the different orbital sizes and energies in N2 and CO, or because of their different symmetries, since N2( A) contains a hole in the nU2Porbital rather than in the oB2,, orbital. Calculations on the N2(A) + Hz system are underway.
Acknowledgement This work was carried out with the support of AFOSR (MFG, RFS) and the National Science Foundation (KDJ). The calculations were performed on the Chemistry Department’s Harris HlOOO superminicomputer, funded by NSF and Harris Corporation. We wish to thank Dr. ILK. Sunil for many helpful discussions during the course of this study.
References [ 1] K.P. Huber and G. Herzberg, Molecular spectra and molecular structure, Vol. 4. Constants of diatomic molecules (Van Nostrand Reinhold, New York, 1979). [ 21 K. Schofield, J. Phys. Chem. Ref. Data 8 (1979) 723. [ 31 A.B. Callear and P.M. Wood, Trans. Faraday Sot. 67 ( 1971) 272, 598. [4] T.G. Slanger, B.J. Wood and G. Black, J. Photochem. 2 (1973/74) 63. [ 51D. Lcvron and A.V. Phelps, J. Chem. Phys. 69 (1978) 2260.
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[ 61 W.G. Clark and D.W. Setser, J. Phys. Chem. 84 (1980) 2225.
[ 71 M.F. Golde, Intern. J. Chem. Kinetics, to be published. [ 81 M.F. Golde and G.H. Ho, unpublished data. [ 91 P. Botschwina, W. Meyer, I.V. Hertel and W. Reiland, J. Chem. Phys. 75 (1981) 5438. [lo] R.P. Blickensderfer, K.D. Jordan, N. Adams and W.H. Breckenridge, J. Phys. Chem. 86 (1982) 1930. [ 111 R.P. Blickensderfer, K.K. Sunil and K.D. Jordan, J. Phys. Chem. 87 (1983) 1488. [ 121 T.H. Dunning, J. Chem. Phys. 53 (1970) 2823. [ 131 T.H. Dunning, J. Chem. Phys. 55 (1971) 3959. [ 141 H. Lischka, R. Shepard, F.B. Brown and I. Shavitt, Intern. J. Quantum Chem. Symp. 15( 1981) 9 1. [ 151 W. Kolos and L. Wolniewicz, J. Chem. Phys. 43 (1965) 2429. [ 16] G. Herzberg, Molecular spectra and molecular structure, Vol. 1, Spectra of diatomic molecules (Van Nostrand, Princeton, 1950). [ 171 R. Shepard, J. Simons and I. Shavitt, J. Chem. Phys. 76 (1982) 543. [ 181 P.O. Liiwdin, Phys. Rev. 97 (1955) 1474. [ 191 A. Szabo and N.S. Ostland, Modem quantum chemistry (Macmillan, New York, 1982). [ 201 B.R. Brooks and H.F. Schaefer III, J. Chem. Phys. 70 (1979) 5092. [ 211 R.J. Buenker and S.D. Peyerimhoff, in: Excited states in quantum chemistry, eds. C.A. Nicolaides and D.R. Beck (Reidel, Dordrecht, 1978). [22] P.J. Bruna, Gazz. Chim. Ital. 108 (1978) 395. [23] D.L. Dexter, J. Chem. Phys. 21 (1953) 836. [24] Th. Fijrster, Discussions Faraday Sot. 27 (1959) 7. [25] M.F. Golde and A.M. Moyle, Chem. Phys. Letters 117 (1985) 375. [26] W. Tao, M.F. Golde, G.H. Ho and A.M. Moyle, J. Chem. Phys. 87 (1987) 1045. [ 27 ] J. Balamutaand M.F. Golde, J. Chem. Phys. 76 (1982) 2430. [28] J. Balamuta, M.F. Golde and Y.-S. Ho, J. Chem. Phy. 79 (1983) 2822.
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