## 3 Application
Figure 1: Visual vibrations of water (**a**) O-H symmetric stretch, (**b**) H-O-H bend and (**c**) O-H asymmetric stretch. \begin{table}
\begin{tabular}{c c c c c c} \hline Calculated & **2803** & **1749** & **1502** & **2819** & **1168** & **1246** \\ \hline Experimental & 2783 & 1746 & 1500 & 2843 & 1167 & 1249 \\ \hline Error & 0.71 \% & 0.17\% & 0.13\% & 0.85\% & 0.08\% & 0.24\% \\ \hline \end{tabular}
\end{table} 
Table 2: Formaldehyde fundamental frequencies (cm\({}^{-1}\)) calculated from a 2160-geometry surface with comparisons with observed values [19]. Figure 2: The six fundamental transitions corresponding to formaldehyde are depicted. (**a**) H-C-H Symmetric stretch (**b**) C=O stretch (**c**) H-C-H Scissoring (**d**) H-C-H Asymmetric stretch (**e**) CH\({}_{2}\) out of plane wagging (**f**) H-C-H Rock. calculated using a PES comprised of 2160 geometries generated using _MolecGeom_. In Table 2, the calculated value of 2803 cm\({}^{-1}\) corresponds to CH\({}_{2}\) symmetric stretch, meaning the H-C-H bonds are stretched equally. The following value reported of 1749 cm\({}^{-1}\) corresponds to C=O stretch, meaning the double bond is stretched upwards. In continuation, 1502 cm\({}^{-1}\) corresponds to the CH\({}_{2}\) scissoring; this is the movement of two atoms toward and away from each other. Furthermore, the 2819 cm\({}^{-1}\) value reported resembles the CH\({}_{2}\) asymmetric stretching, where the C-H bond is contracted, and the other C-H bond is stretched and vice versa. Additionally, 1168 cm\({}^{-1}\) relates to the CH\({}_{2}\) wagging motion; this motion can be described as a \"v\" shape moving side to side. Lastly, 1246 cm\({}^{-1}\) corresponds to the CH\({}_{2}\) rocking; this motion can be pictured as a \"v\" opening and closing. Following the analysis of the vibrational-rotational transitions, quantum mechanical averages (expectation values) of molecular properties, such as dipole moments and electric field gradients, can also be calculated using _Survibtm_, as well as other codes such as SPECTRO [20]. These are based on surfaces for these properties analogous to the PESs. Additionally, transition intensities among vibrational levels can be calculated using dipole moment surfaces [21]. Lastly, in order to show the robustness of _MolecGeom_ for larger molecules, vinyl alcohol and ascorbic acid (vitamin C) were selected as examples. In the case of vinyl alcohol, shown in Figure 3, there are six equilibrium bond lengths (B), along with five bond angles(A) and three dihedral angles (D) for this molecule. More specifically: B1 = 1.07 A, B2 = 1.07 A, B3 = 1.35 A, B4 = 1.07 A, B5 = 1.43 A, B6 = 0.96 A, A1 = 120.0\({}^{\circ}\), A2 = 120.0\({}^{\circ}\), A3 = 120.0\({}^{\circ}\), A4 = 120\({}^{\circ}\), A5 = 109.0\({}^{\circ}\), D1 = 180.0\({}^{\circ}\), D2 = 180.0\({}^{\circ}\), and D3 = 150.0\({}^{\circ}\). These equilibrium values were generated using _Gaussview 16_; the structure can be seen below [22]. The equilibrium values generated are used as a starting point to select a range of geometric distortions of 0.20 A above and below the range start of 1.00 A and the range end of 1.10 A, for B1, B2 and B4. The range start for B3 is 1.34 A and the range end is set at 1.37 A with the same 0.20 A incrementation. Next, the distortions of the five angles were calculated. The range start begins at 115.0\({}^{\circ}\) and the range ends at 120.0\({}^{\circ}\), with 5.0\({}^{\circ}\) increments for A1, A2, A3 and A4. For the last distortion, A5, the range start begins at 106.0\({}^{\circ}\) and the range ends at 112.0\({}^{\circ}\), with 5.0\({}^{\circ}\) increments. The _MolecGeom_ code calculated a new geometry at every incrementation within each range start and end, thus creating a comprehensive geometric list for vinyl alcohol, containing 1458 unique geometries for follow-on implementation into _Survibtm_ for the calculation of its vibrational-rotational spectrum.