Theoretical calculations of thermal shifts and thermal broadenings of sharp lines and zero-field splitting for ruby. Part I. Thermal shifts of R1 and R2 lines Original Research Article

A new theory of spectral thermal shifts (TS) has been developed. For the first time, by taking into account all the irreducible representations and their components in the electron–phonon interaction (EPI), all the levels and the admixtures of wavefunctions within d3 electronic configuration, the microscopic expressions for all the parameters in Raman, neighbor-level and optical-branch terms of TS due to EPI have been derived; their values for the R1, R2 and ground levels of ruby have been evaluated; the contributions to TS from thermal expansion have also been calculated; and then, the unified calculation of the TS of R1 and R2 lines and zero-field splitting (ZFS) for the ground state and the thermal broadenings of R, R′ and B line-groups have successfully been accomplished. It is found that the contributions from the second-order term of EPI Hamiltonian H(2) are dominant in Raman terms of R1 and R2 lines; the optical-branch terms play an important role in TS and increase rapidly with temperature and the ones of R1 and R2 lines have opposite signs due to the effects of neighbor levels; the neighbor-level terms are very important and it is the admixtures of wavefunctions caused by Coulomb interaction between d electrons and/or trigonal-field and/or spin–orbit interactions that make them nonzero; the contributions to TS from thermal expansion are also important.