J. Phys. Chem. 1988, 92,4352-4358
4352
Vibronic Symmetry Correlation Theory for Proton Scattering from Hydrocarbons with Degenerate Valence Orbltald Ying-Nan Cbiu Center for Molecular Dynamics and Energy Transfer, Department of Chemistry, The Catholic University of America, Washington, D.C. 20064, and Max-Planck-Institus fur Stromungsforschung, Bunsenstrasse I O , 3400 Gottingen, Federal Republic of Germany (Received: July 31, 1987; In Final Form: February 9, 1988)
A chemical reaction Jahn-Teller effect is discussed. It is proposed that the impact of a proton on a molecule serves as the driving force for the molecule's incipient distortion. The distortion happens as the proton abstracts an electron from the completely filled degenerate molecular orbitals of the target molecule to create degenerate states of the latter. Two examples of proton scattering from hydrocarbons are cited. One deals with methane, where the proton abstracts an electron from the degenerate t2 orbitals to yield the 'T2 state of CH4+. One deals with a linear molecule, acetylene, for which the conventional Jahn-Teller effect is not operative, and the proton abstracts an electron from the degenerate II, orbitals to yield the 211u state of C2H2+. It is shown that charge-transfer interaction with the unique degenerate component promotes vibration of a special symmetry in a 'vibronic resonance" in which the electron oscillates between charge-transferred and non-chargetransferred states of the same vibronic symmetry. In the case of methane this special vibration can distort CH4+to Dzdsymmetry and explains the experimental observation of a v2(E) vibration. In the case of acetylene, the special vibrations can cause the protonated acetylene C2H3+to undergo merry-go-round motion of the hydrogen atoms in the isomeric transformation between a nonclassical ring structure and a classical vinyl cation structure H2C=C+H. It also help to explain the experimental observation of valence dilution excitation of vibration and the planar orbit of H-atom motion. In either case the continuing vibrational distortion is shown to serve as a symmetry trap to polarize the degenerate components and preserve the phase coherence of the selected degenerate electronic as well as vibrational component. The preference of this selected component is attributed to the unique approach of the proton, which makes it orthogonal to other components. Compatibility of nuclear spin symmetry and rovibronic symmetry is proposed as one way to help verify the energy-transfer and charge-transfer reaction mechanisms.
Introduction It is well-known that molecules with degenerate electronic states are unstable and tend to distort toward a geometry with lower symmetry and nondegenerate states. This is the well-known Jahn-Teller effect',* due to first-order vibronic interaction. As Ballhausen3 puts it, it is not that the molecule is first formed in a degenerate state, discovers itself to be in an untenable situation and immediately proceeds to adjust itself by distortion. It is just a result of our approximation that artificially separates nuclear and electronic motions. However, in this work we impose perturbation in the form of an approaching proton, and the molecule finds itself in incipient danger of being pushed into an untenable degenerate state. We then ask how the molecule responds to this situation. We consider two examples: (1) when a proton approaches the ground-state CHI in the 'Al state with (2a1)2(lt2)6configuration and abstracts one electron from it to give CH4+in the 2T2state with (2al)2(lt2)s configuration; (2) when a proton approaches the ground state of acetylene in 'Eg+state with (1l-1,)~configuration and abstracts one electron from it to give a zl-Iu state with (1l-1,)~ configuration. When the target molecule is initially vibrationally excited, the vibration, through vibronic interaction, might prepare a special excited orbital of the target molecule with which the proton can *) of methane might interact. For example, the V ~ , ~ ( Tvibration by vibronic interaction mix the first excited IT2 state into the ground 'A, state. This is because the vibronic state of CHI('A1~3,4(T2))and CH4('T2) are identical in vibronic symmetry and are connected by the vibronic operator C,.,,(aH/aQ(T,))Q(T2i), which is totally symmetric. This mixed-in IT2state will have a configuration (2al)2(lt2)'(3al) with a lone electron in the excited 3al molecular orbital, which may be abstracted by the proton. Furthermore, the x , y , and z directions of this degenerate vibration v(T2), as well as of the degenerate electronic state 2Tzmay combine to give a unique (1 11) direction for charge transfer to the proton along a given C-H bond, which points to the center of one of the tetrahedron faces. But what if the target molecules initially have no vibrational motion? Then, vibrational 'Presented in part at the 1987 International Conference on the Dynamics of Molecular Collisions, Wheeling, WV.
motion must derive from the incoming proton, which attacks the degenerate highest occupied molecular orbitals. What are the proton's options? What are the consequences of its actions, and what is the special role played by this degeneracy?
Proton Attack on the Degenerate Orbitals of Methane: Chemically Induced Jabn-Teller Effect and Vibronic Resonance When the proton approaches the methane tetrahedron, it can attack any point on the four faces and six edges. However, only attacks on points with correct symmetry will yield more orbital overlap between the proton's acceptor 1s orbital and the methane orbitals. This means the center of faces or center of edges. The attack on the center of one of the faces or one of the four vertices is interesting in itself. This is because of the uniqueness of the axis along a C-H bond and the threefold symmetry thus created for the remaining three vertices (corresponding to the other three C-H bonds). It is also the direction for substitution with inversion of configuration. However, to explore the special role of the degeneracy, we wish to consider the attack along the centers of a pair of perpendicular edges (Figure 1). There are three such pairs corresponding to the three directions of the degenerate molecular orbitals. Other reasons for this choice are as follows: (1) This is the direction for the formation of a trigonal bipyramid complex CHS+,leading to electrophilic substitution and inversion of configuration in parallel to the Berry p~eudorotation~ for pentacoordinated PH5. (2) This is the direction favored over face or vertex attack by calculation.' (3) This complex, when dissociated, will lead to p2(E) vibration of the target methane molecule, as is actually observed in proton scattering. (1) Herzberg, G. Electronic Structure ond Spectra of Polyatomic Molecules; D. Van Nostrand: Princeton, NJ, 1966. (2) Jahn, H. A.; Teller, E. Pmc. R. Sac. London, A 1937, 161, 220. (3) Ballhausen, C. J. Introduction to Ligand Field Theory; McGraw-Hill: New York, 1962. (4) Berry, R. S. J. Chem. Phys. 1960, 32, 933. Hoffmann, R.; Howell, J. M.; Muetterties, E. L. J. Am. Chem. Sac. 1972, 94, 3047. ( 5 ) Dyczmons, V.;Staemmler, V.; Kutzelnigg, W. Chem. Phys. Lett. 1970, 5 , 361. Dyczmons, V.; Kutzelnigg, W. Theor. Chim. Acta 1974, 33, 239. Paddon-Row, M. N.; Fox,D. J.; Pople, J. A,; Houk, K. N.; Pratt, D. W . J . Am. Chem. SOC.1985, 107, 7697.
0 1988 American Chemical Society
The Journal of Physical Chemistry, Vol. 92, No. 15, 1988 4353
Vibronic Symmetry Correlation Theory
0 4
Figure 1. Approach of the proton along one (tZy)of the degenerate orbitals and at the centers of two perpendicular and opposite edges (13 and 2 5 ) of the methane tetrahedron. Abstraction of one electron from tzYresults in distortion to Dty. The correlation between the molecular orbitals of tetrahedral methane versus its distorted cation is shown.
V(A,).
GV
m,)’c3v
~(A,)B
$
v(A1). $6
Figure 2. Vibrations of the methane tetrahedron (T,)and their correlation to the vibrations of distorted structures of lower symmetry (Cay, C,,, D2y and DJ).
As shown in Figure 1, approach of proton no. 4 is along the y direction. Its orbital will have overlap interaction with the t2
molecular orbital but will be orthogonal to the other two (tk, t z j orbitals. If charge transfer is to take place, it will most likely be from this tzy orbital to result in a 2T2state of CH4+. In an equilibrium situation for the formation of CH4+ with nascent configuration (2al)2(lt2)5,the molecule may distort to C,, or C, if ~3,4(T2)vibration is the driving force or may distort to DZdor D2 if v2(E) is the driving force (Figure 2). Both are possible because in the first-order Jahn-Teller vibranic energy correction
L
5 Yb (E‘)
2
5
Y7 ( E ’ )
2
-
Y‘
the direct self-product of the electronic state, T2 X T2 (=A, + E [TI] T2) contains both T2and E. Therefore, the vibrational coordinate Qi can come from u(T2) as well as v(E). In either case, the molecule strives to put the largest number of electrons in the lowest energy orbitals that are created by distortion splitting. In the case of C,, symmetry, T2splits to e and a, the (1t2)5configuration becomes (le)4(3al),where the 3al is significantly higher, and little stabilization results? In case of DMsymmetry it becomes ( le)4(1b2), where significant stabilization results. Whereas the Jahn-Teller splitting is driven by the vibrations, here the incipient distortion splitting is driven indirectly by an approaching proton. The question is, what vibration of the target methane can be promoted by this proton impact? The resultant distortion due to this reaction with the proton is what we will term the chemical reaction Jahn-Teller effect. We distinguish this vibration from the usual excitation by the (electric dipole) radiation which is due to the field of an accelerating (proton) charge. Our vibration
+
+
( 6 ) Pearson, R.G . Symmetry Rules for Chemical Reactions; Wiley: New York, 1976.
IT1
5 (A;]
y [Ail
Figure 3. Vibrations of the trigonal bipyramid (D,,,) CH5+complex and their correlation to the vibrations of the methane tetrahedron. The v6,,(E’) is more readily mixed into the ground IAl state of CH5+because of the first excited electronic state IE’. The ~,,~(A2/1) is not as readily mixed in because ‘A? state is of higher energy. See Figure 1 for formation of this complex and labeling of H atoms.
comes from electronic-vibrational energy transfer in the collisional interaction. Not only the IR-active but also the IR-inactive mode in the target can be excited. We may visualize such excitation through the intermediate complex. The allowed vibrational mode of the quasimolecular complex, however, must be consistent with the motion of the incoming proton. For example, the centerof-edge attack (along y ) leads to a trigonal bipyramid CH5+ complex with the incident proton on the equatorial position (Figures 1 and 3), which is the usual labile position. The ground-state IC.o of this complex of D3hsymmetris is as follows: = (2a’J2( la”& le’)4(3a’,)0 = llA’l) (2)
4354 The Journal of Physical Chemistry, Vol. 92, No. 15, 1988
The first low-lying excited state #, is
IC.,
= (2a’1)2(la’’2)2(le’)3(3a’l)1 = IIE’)
