First-principles theory of infrared absorption spectra at surfaces and interfaces: Application to the $\text{Si}\left(100\right):{\text{H}}_2\text{O}$ surface

We calculate the transverse and the longitudinal infrared absorption spectra of the hydrated silicon surface using a first-principles approach. The absorption spectra are computed for two different configurations of water molecules dissociatively chemisorbed on the $\text{Si}\left(100\right)\text{−}\left(2\times 1\right)$ surface at full coverage. Our calculations compare favorably with the experimental spectra for both the frequency and the intensity of the absorption peaks. Our results suggest the possibility of combining infrared spectroscopy and first-principles theoretical modeling to investigate the phase diagram of the $\text{Si}\left(100\right):{\text{H}}_2\text{O}$ surface and similar systems. We also provide a detailed discussion of the underlying formalism, already introduced by Giustino and Pasquarello [Phys. Rev. Lett. 95, 187402 (2005)]. The methods described here are of general validity and provide a basis for the theoretical modeling of infrared spectroscopy at surfaces and interfaces.

Figure 1

(Color online) Ball-and-stick representation of the two structural models for the $\text{Si}\left(100\right):{\text{H}}_2\text{O}$ surface considered in this work: (a) checkerboard phase and (b) stripe phase. The left (right) panels correspond to an oblique (top) view of the uppermost Si layer with the dissociated water molecules. Gray balls represent Si atoms, red (black) balls O atoms, and yellow (light gray) balls the H atoms. The dashed lines in (b) represent the hydrogen bonds. The structural parameters for the checkerboard model are as follows: $d\left(\text{Si-O}\right)=1.64\text{Å}$, $d\left(\text{O-H}\right)=0.97\text{Å}$, $d\left(\text{Si-H}\right)=1.51\text{Å}$, $\angle \text{HOSi}=118°$, $\angle \text{HSiSi}=109°$, and $\angle \text{OSiSi}=113°$. The corresponding structural parameters for the stripe model are essentially the same (within $0.01\text{Å}$) except for the O-H bond length which in the stripe model is $d\left(\text{O-H}\right)=1.00\text{Å}$.

Figure 2

(Color online) IR absorption corresponding to the checkerboard model of the $\text{Si}\left(100\right):{\text{H}}_2\text{O}$ surface, spatially resolved along the longitudinal coordinate (vertical axis). (a) Density of the IR absorption obtained from Eq. (27) by replacing the delta function in the frequency domain with a Lorentzian of width $5{\text{cm}}^{-1}$ and the delta function in the longitudinal coordinate with a Gaussian of width $1\text{Å}$. (b) Local density of vibrational states for comparison. Arbitrary units are used for the density of IR absorption and for the density of vibrational states. The ball-and-stick models on the left indicate the spatial location of the absorption peaks across the slabs. In the frequency range $0–500{\text{cm}}^{-1}$ the interior of the slab exhibits a significant density of states corresponding to the vibrational modes of bulk Si [panel (b)], which do not contribute to the IR absorption to first order in the electric-field strength [panel (a)].

Figure 3

(Color online) Infrared absorption strengths of the $\text{Si}\left(100\right):{\text{H}}_2\text{O}$ surface at full coverage: [(a) and (c)] strength of the transverse absorption function [from the strength of the peaks in Eq. (14)] and [(b) and (d)] strength of the longitudinal absorption function [from the strength of the peaks in Eq. (22)]. Panels (a) and (b) correspond to the checkerboard model, while (c) and (d) are for the stripe model. The characteristic vibrational modes involved are indicated. The symbols $s$ and $b$ indicate stretching and bending, respectively.