Linear Jahn-Teller effect: A connected-moments approach

Abstract

The ground-state energy of the linear E ⑀ Jahn-Teller effect is obtained using a connected-moments expansion. The calculation is straightforward and leads to a set of simple algebraic expressions for the connected moments of the Hamiltonian. This is then compared to a recent calculation wherein a coupled-cluster scheme has been applied resulting in a set of thirteen nonlinear coupled algebraic equations.

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“…Now following Refs. 15 and 16 we perform the following unitary displacement transformation on the Hamiltonian operator with T = k ( a − a 2 )/. We then arrive at where we have defined the renormalized coupling constant η = k /, S = (ħ/2)σ, and S ± = S x ± iS y .…”

“…As a practical matter, the calculational effort reported in Ref. 16 was orders of magnitude simpler than those of Wong and Lo 15.…”

“…In a more recent calculation of the ground‐state energy of the linear E ⊗ ε Jahn–Teller effect, Mancini et al 16 applied the connected moments expansion (CMX) of Cioslowski 17–21. The CMX scheme is attractive for a number of reasons, including the fact that it is size extensive (as it is in fact related to the cummulants), usually convergent and calculationally trivial to program.…”