Efficient Method for Electron-Phonon Coupling in Molecules and Nanoscale Systems

The coupling between electrons and phonons plays important roles in physics, chemistry and biology. However, the accurate calculation of the electron-phonon coupling constants is computationally expensive as it can involve solving the Schr\"odinger equation for ${\cal O}(3N)$ nuclear configurations, where $N$ is the number of nuclei. In analogy to the efficient field-induced extraction of IR and Raman spectra in molecules,[1] consideration of charge-induced changes in Hellman-Feynman forces as a function of electronic charge allows determination of all HOMO and LUMO electron-phonon coupling constants, including isotope dependencies, with only two SCF calculations {\it regardless of system size}.[2] The approach can also be used for electron-phonon interactions associated with other electronic states. The relation of this method to Janak's theorem[3] is discussed. This ${\cal O}(1)$ approach is numerically very stable and produces accurate results for electron-phonon coupling constants in tests on approximately 15-20 molecules ranging in size from H$_2$ to C$_{60}$. Adiabatic ionization potentials and relaxed Hubbard U parameters are presented as an example of the method. \newline [1]D.V. Porezag and M.R. Pederson, Phys. Rev. B {\bf 54}, 7830 (1996). \newline [2]B.J. Powell, M.R. Pederson and T. Baruah (submitted). \newline [3] J.F. Janak, Phys. Rev. B {\bf 18}, 7165 (1978).