  The nuclear-electronic orbital (NEO) method is a well-established approach
for treating nuclei quantum mechanically in molecular systems beyond the usual
Born-Oppenheimer approximation. In this work, we present a strategy to
implement the NEO method for periodic electronic structure calculations,
particularly focused on multicomponent density functional theory (DFT). The
NEO-DFT method is implemented in an all-electron electronic structure code,
FHI-aims, using a combination of analytical and numerical integration
techniques as well as a resolution of the identity scheme to enhance
computational efficiency. After validating this implementation,
proof-of-concept applications are presented to illustrate the effects of
quantized protons on the physical properties of extended systems such as
two-dimensional materials and liquid-semiconductor interfaces. Specifically,
periodic NEO-DFT calculations are performed for a trans-polyacetylene chain, a
hydrogen boride sheet, and a titanium oxide-water interface. The zero-point
energy effects of the protons, as well as electron-proton correlation, are
shown to noticeably impact the density of states and band structures for these
systems. These developments provide a foundation for the application of
multicomponent DFT to a wide range of other extended condensed matter systems.
