# Electron-phonon Coupling

Vibrations of atoms couple to all observables in condensed matter. We have developed improved vibrational self‐consistent field methods which provide an accurate treatment of anharmonic vibrations and coupling of vibrations to observable quantities such as the bandstructure of a crystalline solid, the stress tensor, NMR chemical shielding tensor, dielectric constant, electronic charge density, etc. Our methods can deal with the large amplitude vibrations that exist when light atoms, high temperatures, weak bonding, reduced-dimensionality, or phase transitions are present. Some examples are described below.

We have found that electron-phonon coupling arising from the zero point nuclear motion in hexagonal water ice reduces the band gap by nearly 2 eV. Our results show that other molecular crystals such as methane and ammonia exhibit reductions in their band gaps of a similar magnitude. These large band‐gap changes arise from both the lower frequency inter-molecular vibrations and the high‐frequency vibronic modes [1].

We have calculated the energies of the hexagonal and cubic forms of water ice. Our results agree with previous first-principles calculations in showing that at the static lattice and harmonic vibrational levels the hexagonal and cubic forms are degenerate. However, when we include anharmonic vibrational effects we find that the hexagonal form has a lower energy than the cubic form. This effect arises primarily from high-frequency vibronic O‐H stretching modes and is only of order a few meV, but it is a very clear effect in the calculations. This effect explains why snow and ice form hexagonal crystals [2].

The recent finding of electron‐phonon based superconductivity at 200 K in hydrogen sulfide at high pressures has attracted much interest. Experiments showed that hydrogen sulfide decomposes at high pressures, and our calculations predict that the superconducting material is H3S. Our calculations show that anharmonic vibrations are very important in the high Tc material and that they have a strong effect on both the vibrational frequencies and on the structure formed at high pressures. A proper inclusion of anharmonic vibrational effects leads to a significant improvement in agreement with experiment [3].

The resources made available through Archer have enabled us to accomplish this work, which would not have been possible using the local computing resources available to us.

**References**

- Bartomeu Monserrat, Edgar A. Engel, and Richard J. Needs

Giant electron-‐phonon coupling interactions in molecular crystals and the importance of nonquadratic coupling

Phys. Rev. B 92, 140302 (2015). - Edgar A. Engel, Bartomeu Monserrat, and Richard J. Needs

Anharmonic nuclear motion and the relative stability of hexagonal and cubic ice

Phys. Rev. X 5, 021033 (2015). - Ion Errea, Matteo Calandra, Chris J. Pickard, Joseph Nelson, Richard J. Needs, Yinwei Li, Hanyu Liu, Yunwei Zhang, Yanming Ma, and Francesco Mauri

High-pressure hydrogen sulfide from first-principles: a strongly anharmonic phonon-mediated superconductor

Phys. Rev. Lett. 114, 157004 (2015).