  We study the lattice dynamics of group IV semiconductors using fully
ab-initio extended Hubbard functional. The onsite and intersite Hubbard
interactions are determined self-consistently with recently developed
pseudohybrid functionals and included in force calculations. We analyze the
Pulay forces by the choice of atomic orbital projectors and the force
contribution of the onsite and intersite Hubbard terms. The phonon dispersions,
Gruneisen parameters, and lattice thermal conductivities of diamond, silicon,
and germanium, which are most-representative covalent-bonding semiconductors,
are calculated and compared with the results using local, semilocal, and hybrid
functionals. The extended Hubbard functional produces increased phonon
velocities and lifetimes, and thus lattice thermal conductivities compared to
local and semilocal functionals, agreeing with experiments very well.
Considering that our computational demand is comparable to simple local
functionals, this work thus suggests a way to perform high-throughput
electronic and structural calculations with a higher accuracy.
