An Extended Mixed Quantum/Classical Approach for Quantitative Calculation of Complex Refractive Index

TL;DR

The paper tackles the challenge of achieving quantitative spectral intensities and the real part of the IR refractive index for water using Skinner's mixed quantum/classical approach. It develops a linear-response formulation to compute the complex dielectric constant $\,\epsilon_r(req)$ directly, incorporating a Lorentzian broadening and time-averaging, and applies a local-field correction to obtain $\,\epsilon_{cor}(req)$ and the complex refractive index $\,\hat{n}(req)=n(req)+ik(req)$. Applied to the liquid-water OH stretching region, the method reproduces both line shapes and intensities with the local-field correction proving essential for accurate magnitudes, and yields related quantities such as the absorption cross-section $\,\sigma(req)$, molar absorptivity $\,\epsilon_M(req)$, and band strength $\beta$ that agree well with experiment. This approach enables efficient, quantitative analysis of bulk, thin-film, and cluster water spectra and can be extended to other phases and isotopologues, offering a versatile tool for evaluating optical properties in condensed-phase systems.

Abstract

The mixed quantum/classical approach of Skinner and co-workers has been widely used to calculate the line shapes of the infrared spectra of water (H2O), but less attention has been paid to the use of this approach in quantitatively calculating spectral intensity, thereby limiting direct comparisons of calculated and experimental spectra. Here, we extend this theoretical framework to facilitate direct computation of the full complex refractive index of water, replacing the normalized ordinate used in previous studies. Our results for the OH stretching region of H2O capture both the shapes and intensities of the experimental spectra. They reveal that inclusion of the local field effect is crucial to the accurate reproduction of spectral intensity. This extended approach enables new areas of analysis of the bulk, thin-film, and cluster spectra of water.

Figures (5)

• Figure 1: Theoretical (red) and experimental (black) OH stretching spectra of H2O. The upper and lower plots respectively show the imaginary ($k$) and real ($n$) parts of the complex refractive index.
• Figure 2: Second derivatives of the theoretical (red) and experimental (black) spectra in Figure \ref{['fig:n-k']}, showing the (a) imaginary ($k$) and (b) real ($n$) parts of the complex refractive index.Pink, blue, and orange areas represent regions I, II, and III, respectively. The original spectra are included in the lower part of each plot.
• Figure 3: Theoretical and experimental values of absorption cross-section $\sigma$ (left vertical axis) and molar absorption coefficient $\epsilon_\text{M}$ (right vertical axis).
• Figure 4: (a, c) Comparison of theoretical spectra of $k$ (a) and $n$ (c) before (blue) and after (red) the application of LFC. Top and middle spectra represent the second-derivative and original spectra, respectively. The second-derivative spectra of $k$ are calculated using normalized spectra of $k$ to have the same height. (b, d) Ratio of the corresponding theoretical spectra after LFC to that before LFC.
• Figure :