Development of Hessian calculation using the combined plane wave and localized basis sets method and its application to adsorption of a water molecule on Pt(111) surface

Hydrogen is the lightest element and is strongly affected by nuclear quantum effects. We have developed the Hessian calculation with the combined plane wave and localized basis sets (CPLB) method to efficiently analyze an adsorbed molecule on metal surfaces. To validate the effectiveness of the CPLB Hessian, we conducted test calculations for the H2O dimer and applied it to the surface system of an H2O molecule adsorbed on the Pt(111) surface. The adsorption energy of the H2O molecule without zero-point energy correction is 0.603 eV, while the adsorption energy with ZPE correction is 0.444 eV This suggests that the zero-point energy correction reduces the adsorption energy. We also estimated the adsorption energy of a heavy water D2O molecule as 0.471 eV, which is consistent with the experimental trends. Such vibrational estimation with the CPLB method enables us to perform efficient low-cost calculations, even in large-scale systems such as metal surfaces.