Tunneling splitting in a two-level system with pseudo-Jahn-Teller coupling

TUNNELING SPLITTING IN A TWO-LEVEL SYSTEM WITH PSEUDO-JAHN-TELLER COUPLING 

In this case, the corresponding APES is a two-valued function of Q expressed by the two eigenvalues of the 2x2 matrix Hamiltonian (7), 

Both have an extremum at Q = 0. For the upper curve, U+(Q), this point is a minimum at any value of k. The curvature of the lower curve, U- (0, depends on the relative value of the parameters k and A. At weak coupling, when k2 A, the curvature of U- (Q) at Q = 0 is positive, and this point is a minimum. In the opposite case of strong coupling, when k2 A, the curvature is negative at Q = 0, and this point is a maximum of U-(Q). If k2 — 4+, the two minimum points approach one another and, at k2 = A, they coalesce into one minimum at Q = 0. The symmetric double-well potential curve expressed by U-(Q) in equation (9) is shown in Fig. 1. Most important, the shape of U-(Q) is determined by one parameter, k2/A. The factor ho) in equation (9) is just a scaling coefficient. 

Let be the vibronic ground state localized in the left well of the double-well potential, and IP2 be the right-side ground state. The reference symmetry group of the undistorted molecule AB2 is D. An off-center displacement of the central atom A along the axis B - B reduces this symmetry to This means that the local symmetry 

Neglecting the overlap integral S12 as compared to ( Pl XP ) = ( I 2I T 2) = 1, and assuming that Hu = E0 = 0, the corresponding first-order energy is 

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Tunneling splitting in a two-level system with pseudo-Jahn-Teller coupling 66... 

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