We then proceeded to estimate the number of water molecules that flip their dipole orientations. To this end, we employ the molecular hyperpolarizability for a liquid water model Speelman and Geiger page 8 estimated by Gubskaya and Kusalik at the MP2 and MP4 level of theory (a (2) =5.3 x 10 -52 C m 3 V - 2 ) (41). This value was used recently by the Roke group to estimate the non-resonant thirdorder nonlinear susceptibility, c (3) , of liquid water, which is in good agreement with the experimental value reported by the Wen group . Dividing the ∆𝜒 (;) values shown in Fig. by a (2) and multiplying by a Stern layer water permittivity estimate of 1.9 (the mean of e =1.77, the square of water's index of refraction at 515 nm, and e =2.0, from recent experiments ) and the vacuum permittivity, e0, according to 𝒩↓= |∆𝜒 (;) | . e . e0/(10 4 cm 2 m -2. a (2) ) yields the number of water molecules per cm 2 that point their oxygen atoms down towards the electrode. Fig. shows that at the most positive applied potential (+0.9 V), ca. 1.1 x 10 15 water molecules per square cm have a net orientation with their oxygen atoms pointing towards the electrode. Larger values for 𝒩↓ would arise from larger values for the Stern layer relative permittivity. In addition, the angular orientation distribution of the Stern layer water molecules relative to the surface normal is not known and could very well be multimodal. Yet, under the s-in/p-out polarization combination employed here, our estimate for 𝒩↓, max=1.1 x 10 15 cm -2 matches the geometric number density of water molecules on the surface of a 1 cm 3 cube of liquid water at standard temperature and pressure