Insights from the Absorption Coefficient for the Development of Polarizable (Multipole) Force Fields

Abstract

We present a detailed examination of the absorption coefficients in the THz region for different water models using different types of potentials: the non-polarizable SPC/E, the Drude-polarizable SWM4-NDP and OPC3-pol, IPOL-0.13 and the multipole AMOEBA14 water. The primary focus is on understanding the interplay between permanent and induced dipole moments and their influence on the THz spectrum. Although the induced dipoles strongly contribute to the peak at 200 cm^-1, merely increasing the induced dipole moments does not improve the agreement with experiments. We aim to investigate the behavior of the intensity at 200 cm^-1 depending on the water model. Furthermore, we dissect the THz spectra of the water models into distinct contributions to gain more insight into the inter- and intramolecular interactions. Intermolecular interactions significantly contribute to the low-frequency peak, while the peak observed at 600 cm^-1 can be adequately attributed to intramolecular dipole-dipole interactions.

Keywords: computational spectroscopy; induced dipoles; terahertz spectroscopy; water.

Figure 3

Local frames for the AMOEBA [66,69] atomic dipoles ${\overrightarrow{\mu }}_{i\beta }$: (a) The z axis for the local oxygen frame is the bisector of the H-O-H angle. The x axis is in the plane of the atoms and perpendicular to the z axis, which is not necessarily in the same direction as the HH vector (e.g., two different bond lengths). (b) The z axis is always in the direction from the respective hydrogen to the oxygen. The x axis is in the plane of the atoms and pointing inwards. The y axis for oxygen and H1 points up, and for H2 points down.

Figure 1

Decomposition of the collective rotational dipole moment ${\overrightarrow{M}}_D\left(t\right)$ into molecular dipole contributions indicated by the molecular index i. The permanent and induced components of the molecular dipole moments consist of atomic contributions (indicated by the index $\beta$), which depend on the polarizable force field type: AMOEBA or Drude.

Figure 2

Polarizable Drude water models: (a) Drude oscillator pair (gray circles) attached to a polarizable oxygen (red). (b) Three-site polarizable water model (IPOL-0.13, OPC3-pol). (c) Four-site polarizable water model SWM4-NDP. The black circles indicate the position of the partial charges $q_{i\beta }$. Please note that O in SWM4-NDP has no partial charge but hosts the Drude pair.

Figure 4

Simple model of a water dimer and its predicted THz spectrum. Partial charges and dipole moments are given in Table 2.

Figure 5

Scaled absorption coefficient of the water models: The solid lines represent $\alpha ·n^{\prime }$ for the respective water model. The dotted lines are the contributions of the induced dipole interactions. The gray dots are experimental values and were taken from Bertie and Lan [82].

Figure 6

(Top): Histograms of the total (SWM4: red, orange, yellow with increasing polarizability, AMOEBA: black) and induced dipole moments (SWM4: blue, turquoise, green with increasing polarizability, AMOEBA: gray). (Middle): THz contribution of the induced dipoles ${\alpha }^{\mathrm{ind}}·n^{\prime }$ of SWM4-NDP and AMOEBA with the same color code as above. (Bottom): The total THz spectrum $\alpha ·n^{\prime }$ of the polarizable SWM4-NDP and multipole AMOEBA14. The gray dots depict the experimental data.

Figure 7

Absorption spectrum of the multipole AMOEBA water model with and without atomic quadrupoles ${\Theta }_{i\beta }$.

Figure 8

(Top left): AMOEBA14, (top right): SWM4-NDP, (bottom left): AIMD, (bottom right): SPC/E. The green lines represent the cross-terms, and the red lines represent the self-terms. The blue lines are the sum of the two contributions and yield the total spectra. The gray dots depict the experimental data from Bertie and Lan [82]. The data from AIMD simulations were kindly provided by Shane Carlson and Roland Netz and are published in Carlson et al. [21].