2 III. RESULTS AND DISCUSSION A. Equilibrium geometries choosing energy cut-off values up to 1000eV. The cut- off energy of 550eV was chosen for NC-PP to ensure reliable convergence of predicted optical data. Choice of pseudopotentials (ultrasoft or norm-conserving) does not significantly affect the results. Exchange and cor- relation (XC) interaction is modeled using the Perdew- Burke-Ernzerhof formalism $^{15}$. A Monkhorst Pack grid of 6 × 6 × 1 was used to sample the Brillouin zone, just like for DMol $^{3}$, yielding well converged results. Calculated self-consistent eigen energies and eigen functions are used as inputs for optical calculations. Within its penetration depth beneath the surface, the incident light field ( E ( ω )), at frequency ω , induces a lin- ear optical susceptibility function χ $^{(1)}$: Realistic modeling of optical functions of solid surfaces and interfaces still remains challenging for the first prin- ciple theories $^{17}$. As a first step it requires reliable re- production of the ground state of the material (equilib- rium atomic geometry) by minimizing the free energy. As a next step optical properties could be calculated us- ing the optimized geometry as an input. Description of excited states, which could be in good agreement with experiment, normally requires inclusion of local field, many-body (excitons) effects, and probably other non- local contributions $^{18,19}$. This makes theory much more complicated than frequently used independent particles approach (or Random Phase Approximation, RPA). In this work we focus on relative changes of electron en- ergy structure and optical response caused by molecular adsorption on Ag (111) surface, which could be realis- tically described without inclusion of many-body effects in optics $^{18,20}$. As such we chose to calculate the dielec- tric function spectra within the RPA employing norm- conserving pseudopotentials $^{21}$. The function χ (1) is then used to determine the com- plex dielectric function ( ε = ε$_{1}$ + iε$_{2}$ ) through the linear optical susceptibility: ε = 1 + 4 πχ $^{(1)}$. Within the Ran- dom Phase Approximation (RPA) the function ε is given by $^{16}$: where indices c , v run over conduction (empty) and va- lence (filled) electron states, respectively. The spectral function F$_{cv}$ ( ω, k ) at the incident light frequency ω is given by $^{16}$: Table I lists the adsorption energies E$_{ads}$ , per molecule, as calculated by Eqn. 4 and the optimized structural pa- rameters of the adsorbates on the surface. Atomic re- laxation of water on transition metals has been studied both theoretically and experimentally $^{1–3,22,23}$. Two dif- ferent atomic geometries of water molecules physisorbed on Ag (111) surface are predicted: with hydrogen up and down. Our predicted geometries of physisorbed water molecules on Ag (111) surface agree, for the most part, well with those reported in Refs. 3 and 22 where a similar theoretical framework was used. The H$_{2}$O-up and H$_{2}$O- down geometries are shown in Fig. 1a and b, respectively. We also studied the effect of water molecule dissocia- tion on optical properties of silver. At room temperature the reaction H$_{2}$O − ⇀ ↽ HO – + H + occurs spontaneously. The proton is then free to enter into reaction with the surface. For a single water molecule adsorbed on a closed- packed Ag (111) surface the distance between the oxygen and the host Ag atoms, the O − Ag distance, of 2.78 ˚ A was reported in Ref. 22. Once enough H$_{2}$O molecules are added to the system to form hexamers on the surface, the molecules form an ice-like structure. For a single bi- layer of H$_{2}$O adsorbed on the surface, the zig-zag config- uration of ice isn’t as pronounced, as for water molecules not in contact with the surface. Our oxygen-silver surface distances can be found in Table I. The water hexagons are slightly irregular as can be seen in Figs. 1a,b. The shift is much more pronounced in the H$_{2}$O-up configura- tion. This asymmetry of the hexagonal structure of water molecules was previously reported for Ru { 0001 } $^{22}$. Once one of the hydrogen is desorbed, see Fig. 1c, the remain- ing OH molecule shifts much closer to the surface and the The normalization quantity Ω$_{0}$ has dimension of vol- ume in direct space. The ε represents the local part of the dielectric function. In this study we did not include non-localities due to the local field effect. Note that Eqs. (2) and (3) represent an effective value for the dielectric function averaged over different tensor component of ε$_{α,β}$ (where α, β = x, y, z ) in direct space. A more detailed explanation can be found in $^{16}$. The stability of various equilibrium configurations is judged by the adsorption energy. The adsorption energy per molecule is defined as the difference between the total energy of the adsorption system and the energies of the isolated components, namely the clean substrate and the adsorbate, divided by the number of adsorbed molecules N per unit cell: P$_{i}$ ( ω ) = χ (1) ij E$_{j}$ ( ω ) (1) ε ( ω ) = 1 − 8 π Ω$_{0}$ 1 N ∑ k ∑ c,v p$_{cv}$ ( k ) p ∗ $_{cv}$( k ) [ E$_{c}$ ( k ) − E$_{v}$ ( k )] $_{2}$F$_{cv}$ ( ω, k ) (2) F$_{cv}$ ( ω, k ) = 1 ω + iη − E$_{c}$ ( k ) + E$_{v}$ ( k ) + 1 − ω − iη − E$_{c}$ ( k ) + E$_{v}$ ( k ) (3) E$_{ads}$ = E$_{tot}$ − ( E$_{substrate}$ + N · E$_{adsorbate}$ ) N (4)