  Jahn-Teller (JT) systems with strong and intermediate vibronic coupling are
described in terms of local JT active vibrational modes. In JT crystals, the
elastic interaction of these modes at different JT centers plays a crucial
role, for instance, in determining critical temperature of structural phase
transitions. Despite their importance, the parameters of elastic interaction
between JT centers have not been accessed yet by first-principles calculations.
In this paper, we develop an effective Hamiltonian methodology for the thorough
description of the elastic interactions in cooperative Jahn-Teller problems,
which treats the interactions with both phonons and uniform strains. All the
microscopic parameters, such as lattice Green's functions, elastic modulus, can
be obtained or calculated based on first-principles the calculation. The method
has been applied to a series of 5d1 double perovskites. Such effective
Hamiltonian methodology can be, in general, used to investigate the APES of any
type of the local distortions, such as impurities, defects, etc.
