# Electric Field and Temperature Effects on the Ab Initio Spectroscopy of Liquid Methanol
## 3 Results and Discussion  
Density functional theory (DFT) generally produces a series of shifts when evaluating and predicting the frequency of vibration of molecular modes. Nevertheless, it not only represents one of the most advanced and precise theoretical methods to deal with these predictions but is also the only one capable of determining--on firm quantum-mechanical bases--vibrational spectra of condensed-phase systems. In this way, vibrational properties of a plethora of liquids and solids have been reported in the literature by means of DFT-based approaches [74]. In condensed matter, infrared (IR) spectra carry useful information not only on the intramolecular vibrations but also on the existing intermolecular interactions. As a consequence, important properties tightly related to the presence of H-bonds have been investigated by means of IR absorption experiments [75; 76]. As shown in Figure 1, where the computational and experimental IR spectra are plotted together, all the important vibrational modes characterizing the experimental liquid methanol IR spectrum at room temperature are qualitatively caught by ab initio molecular dynamics (AIMD) simulations. As anticipated, however, significant frequency shifts are detected for almost all the allowed molecular vibrations. As an example, the OH-stretching band, whose center of frequency experimentally falls at about 3350-3400 cm\({}^{-1}\)[75; 77], is found at about 3250-3300 cm\({}^{-1}\) in our AIMD simulations. However, the CH-stretching band, which is experimentally found at 2800-3000 cm\({}^{-1}\)[75; 78], is localized at 3000 cm\({}^{-1}\) by the BLYP-D3 exchange and correlation functional used in the current AIMD simulations. Somehow surprisingly, hence, nuclear quantum effects (NQEs), believed to be important for the realistic description of the behavior of light atoms such as hydrogen, seem to only moderately affect the vibrational properties of the symmetric and asymmetric stretching of the methyl groups in liquid methanol at room temperature. In fact, the vibrational band ascribed to the CH\({}_{3}\) bending is also centered around 1400 cm\({}^{-1}\) both from laboratory experiments [75; 76] and from the first-principles molecular dynamics simulations presented here, as shown in Figure 1. Moreover, the typical frequency of vibration of the rocking mode of the methyl groups found in the simulations is in fairly good agreement with the available experimental data (i.e., \(\sim\)1100 cm\({}^{-1}\)). Finally, the low-frequency modes associated with the CO stretching and with the out-of-plane OH bending--experimentally localized around 1000 cm\({}^{-1}\) and 700 cm\({}^{-1}\), respectively--are qualitatively well reproduced by the current room-temperature AIMD simulation, in that they appear only slightly red-shifted and blue-shifted, respectively, by about 100 cm\({}^{-1}\) each, as displayed in Figure 1.  
One of the key features emerging from IR spectra of H-bonded systems is represented by the possibility of monitoring the effects induced by variations of external thermodynamic parameters such as temperature, pressure, or electric field. When a static and homogeneous electric field is applied in neat liquid methanol, a contraction of the entire  
Figure 1: Infrared (IR) absorption spectra of liquid methanol determined from AIMD simulation (black line) at room temperature and in absence of electric field. The experimental results [76] are shown as gray shading for reference. In the two panels, the intensities of the highest peaks are rigidly scaled for better comparison between computations and experiment. IR spectrum is recorded, as shown in Figure 2. In fact, whereas low-frequency modes are blue-shifted, high-frequency modes are sizably red-shifted by the electric field.