Deciphering second harmonic generation signals

Abstract

Second harmonic generation is one of the most powerful techniques used to selectively probe interfaces of all types. The direct ab initio method developed here allows predicting the signal and highlights the importance of local and non-local effects.

Why local and non-local terms are essential for second harmonic generation simulation?

“…Those oscillations have already been reported in the literature when a water/air interface was studied at ambient temperatures. 33,34,39 The average number density of 33.24 nm À3 in the water bulk (zone I) corresponded to a density of 0.9946 g cm À3 , which was in very good agreement with the experimental measured density of water. 71 Second, considering the significant importance of the molecular orientational structure for SHG, we computed the two order parameters P 1 and P 2 , which represent the first and second Legendre moment variations defined as:…”

“…This indicated that the molecules were oriented with their dipole moment, i.e., their hydrogen atoms, pointing towards the water bulk when they were near the interface, which was in agreement with the works reported in the literature. 33,34,38,39,72 Just outside the interface (zone III), P 1 (z) changed sign to become positive, which meant that the water molecules were oriented with their dipole moment pointing towards the gas phase. This could be attributed to the fact that molecules were ejected from the slab only when they were in a disfavored configuration, i.e., with their dipole moment pointing away from the water slab.…”

“…Interestingly, b zyy E b yyz and b zxx E b xxz , especially with BLYP, which indicated that the Kleinman symmetry 76 was valid for an isolated water molecule in vacuo albeit it was no more valid for a slab containing a larger number of water molecules. 39 This could be attributed to the local electric fields, represented by each molecule, that probably locally modify the intensity of the electric field. Besides, 25 fields are enough to obtain accurate values of a and b since we covered all the domain of fields (see Table S5, ESI †): two electric fields (the zero field and the 0.005 a.u.…”

“…(2),D s,xzx (z), 85,86 which was not in accordance with the values found here albeit the absolute values of w (2),D s,zzz (z), w (2),D s,zxx (z), and w (2),D s,xzx (z) were in very good agreement with the values calculated by a direct ab initio method, where they vary between 0.5 and 2 a.u. 39 When we integrated w (2),D s,zzz (z), w ¼ 0:98. While the former was in good agreement with our experimental and the reported values, the latter was much higher compared to those values (Table 4).…”

First hyperpolarizability of water in bulk liquid phase: long-range electrostatic effects included via the second hyperpolarizability

“…2 for condensed phases is very useful for the interpretation of S-SHG of aqueous solutions, and the values of β and γ for water in liquid water become parameters of the equation. To obtain values of β and γ for water in liquid water, one can use Quantum Mechanical/Molecular Mechanic (QM/MM) calculations 9,24,26,31,32 . In such approaches, the electrostatic effect of the environment is included within the QM calculations of a molecular hyperpolarizability β env for a given electrostatic environment, so that…”