This thesis investigates the effects of 2D mode coupling in solid crystal structures by using the Numerov method. The structures of interest are Ice XI and Lithium Imide. The goal is to create more accurate predictions of infrared spectra and to explore the effect of mode coupling on the infrared frequencies.
First, a geometry optimization is performed using CRYSTAL followed by a frequency analysis using the harmonic oscillator approximation to extract the normal modes. Then the atoms are moved along the normal coordinates and an energy calculation is performed at each step. This yields an equidistant energy grid of the potential energy surface. Afterwards, this 1D grid is used to conduct the Numerov calculation,
which yields the eigenvalues of the system. By using the eigenvalues the frequencies of the system are calculated.
The atoms are subsequently moved simultaneously along two normal coordinates to calculate a 2D potential energy grid. Applying the 2D Numerov method derives the 2D eigenvalues, which again can be used to calculate the 2D frequencies.
All accumulated frequencies are compared to experimental data as well as each other. By comparing the computed values to external data the accuracy of the prediction can be quantified. For Ice XI, the predictions acquired by the 2D Numerov approach are closer to the experimental values than the predictions attained by the harmonic oscillator approximation. The coupling effect proves to be significantly different, depending on the modes coupled.
For Lithium Imide, approximations of the unit cell have to be made as the crystal structure is not easy to simulate. As a result, the shift in frequency deviates further from the experimental data than the harmonic oscillator approximation. Valuable information is acquired about the effects of normal mode coupling.