Using Reduced Dimensional Models to Interpret Spectral Signatures of Large Amplitude Motions of OH Bonds

Abstract

Understanding the spectral signatures of hydrogen bonding is an ongoing topic of study inphysical chemistry. Determining the origins of these spectral signatures will lead to increased understanding of the underlying physics and couplings associated with hydrogen bonding. This work provides insights into the manifestation of large amplitude motions involving OH bonds in various regions of the vibrational spectrum in order to understand the spectral signatures of hydrogen bonding, using small, gas-phase molecular and protonated clusters of water. Additionally, multiple methods for solving the vibrational Schr ̈odinger equation are used to extract meaningful conclusions from reduced dimensional models. To start, an adiabatic separation is employed to create a two-dimensional model in order to study the two quanta transition of an OH stretch with the corresponding OO stretch- ing vibration between a hydrogen bonded pair in protonated water clusters with 2-4 water molecules (H + (H 2 O) 2 - H + (H 2 O) 4 ). The results of this method are then compared to a full two-dimensional model to assess the validity of the approximation. Both models are used to better understand the origins of the intensity. Experimentally, in this two quanta transition, H + (H 2 O) 2 has the largest relative intensity, followed by H + (H 2 O) 4 , while H + (H 2 O) 3 shows no intensity. This work showed that the relative intensity of the OH stretching and OO stretching vibrations reflects the changes in the frequency and anharmonicity of the OH vi-bration with OO stretch excitation. A conclusion that could only be drawn from the ability to decompose the components of the intensity, allowed by the use of the adiabatic approxi- mation, which shows qualitative agreement with the full two-dimensional model. Ultimately it is found that the direction of the change in the OO stretching frequency upon excitation of the OH stretching frequency is associated with the strength of the ionic hydrogen bond, similar to the effects seen in the frequency of the OH stretching fundamental transition. Elaborating on this idea, the origins of the intensity of the two quanta transition involving the OH stretch and HOH bend (stretch-bend) within one water molecule are investigated. When looking at the experimental band profiles of the OH stretch and stretch-bend tran- sition, initially they look quite different. The OH stretch transition feature has a strong intensity and its corresponding band contour is symmetric. The stretch-bend band contour is less intense, and has a more constant intensity across the frequency range. Keeping this in mind, the experimental vibrational spectrum of the H + (H 2 O) 21 cluster was analyzed. Within this cluster it was found the symmetry of the OH stretch transition feature is caused by com- peting effects. The intensity decreases with hydrogen bond strength, but there is a larger density of transitions in the higher frequency range. Therefore, if one divides the profile of the OH stretch by the calculated intensity of the individual OH stretch transitions within the cluster, the resulting profile is in good agreement with the stretch-bend transition. Further investigation into the origin of the stretch-bend transition intensity shows that it is driven by electrical anharmonicity, or higher order terms of the dipole moment sur- face. More specifically, it is found that the quadratic bilinear term of the dipole expansion (∂ 2 μ/∂θ HOH ∂r OH ) is the largest contributor to the intensity of the transition. To better understand the origin of the intensity, the change in charge distribution with r OH and θ HOH displacement was investigated. This study showed that when θ HOH is extended the partial charges on the hydrogen atoms generally increase, but this effect is partially cancelled by a decrease in the charge of hydrogen atoms when a hydrogen bond is broken. The extent ofthis cancellation increases with hydrogen bond strength, creating the more constant inten- sity across the stretch-bend transition band contour. Additionally, the mixing of vibrational modes causes near degeneracy splittings therefore leading to the breadth of the stretch-bend region seen in large water clusters and the bulk, but overall it is found that excluding this mixing leads to a similar integrated intensity across the region. Finally, the assignments of the OH-stretching fundamental and overtone regions (∆v OH = 1–5) of the vibrational spectra of gas phase tert-butyl hydroperoxide (TBHP) are assigned using a reduced dimensional reaction path model. A comparison between theory and experi- ment illustrates the necessity for treatments that include OH-stretch and COOH torsion (τ ) explicitly in order to unravel the spectral features observed in the OH-stretching overtones (∆v OH = 1-5) of TBHP. A linear treatment of the transition dipole moment fails in capturing the intensity of the OH-stretch-torsion features, requiring the incorporation of higher order terms in the expansion of the dipole surface used in reduced dimensions to obtain intensities that agree with experimental findings. This model was extended to the carbon-centered hydroperoxyalkyl radical, becoming a three-dimensional model including the rotation of the CH 2 group (φ), which is a result of the loss of the hydrogen atom in the formation of the molecule. Both molecules have a double well potential in the torsion coordinate, and excita- tion of the OH stretching overtones is complicated by this potential landscape. For TBHP, it was found that the tunneling splitting of the torsion states was large enough to produce multiple transitions to the OH excited states that carried intensity, therefore leading to some of the breadth seen in the spectral regions of these transitions. Although, in the carbon- centered hydroperoxyalkyl radical the torsion potential is no longer symmetric, the tunneling splitting decreases and no evidence was found that the tunnelling doublets were leading to the breadth of the feature.