## 4 Conclusions  
The _MolecGeom_ code reported here allows for the rapid and efficient generation of geometric data for PESs. _Mathematica_ provides an ideal programming environment for addressing the algebraic manipulations required to define such PESs. Additionally, depending on the required application of the PES generated, the parameters of _MolecGeom_ can be adjusted as needed. In this study, the code is applied to water, formaldehyde, vinyl alcohol and ascorbic acid molecules; however, it can be used to generate a PES for any polyatomic system, while also recognizing the molecular point group symmetry relations. By applying the results of _MolecGeom_, accurate vibrational-rotational spectra are attainable. The errors in the calculations of fundamental frequencies for water and formaldehyde are shown to be less than 1% in comparison with the published literature values for PESs, based on accurate ab initio electronic energy and properties calculations. The _MolecGeom_ code provides an effective means by which accurate PESs for vibrational analyses of polyatomic molecules may be realized.  
**Supplementary Materials:** The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/a16010006/s1](https://www.mdpi.com/article/10.3390/a16010006/s1)]([https://www.mdpi.com/article/10.3390/a16010006/s1](https://www.mdpi.com/article/10.3390/a16010006/s1)), File S1: The notebook (.nb) files for water, formaldehyde, vinyl alcohol and ascorbic acid have been provided. Additionally, File S2: The text (.txt) files containing the unique geometric points for each molecule are also provided.  
**Author Contributions:** Conceptualization, A.R.C. and W.C.E.; methodology, A.R.C. and W.C.E.; software, A.R.C. and W.C.E.; validation, A.R.C. and W.C.E.; formal analysis, A.R.C. and W.C.E.; investigation, A.R.C. and W.C.E.; resources, A.R.C. and W.C.E.; data curation, A.R.C. and W.C.E.; writing--original draft preparation, A.R.C. and W.C.E.; writing--review and editing, A.R.C. and W.C.E.; visualization, A.R.C. and W.C.E.; supervision, W.C.E.; project administration, W.C.E.; funding acquisition, A.R.C. and W.C.E. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This work is supported by the RISE PhD program at UTSA funded by NIH/NIGMS RISE GM60655. Additionally, this research was supported in part by the National Science Foundation under grant CHE-1853477.  
**Institutional Review Board Statement:** Not Applicable.  
**Informed Consent Statement:** Not Applicable.  
**Data Availability Statement:** Data available in a publicly accessible repository. The data presented in this study are openly available at [[[https://www.mdpi.com/article/10.3390/a16010006/s1](https://www.mdpi.com/article/10.3390/a16010006/s1)]([https://www.mdpi.com/article/10.3390/a16010006/s1](https://www.mdpi.com/article/10.3390/a16010006/s1))].  
**Acknowledgments:** This work received computational support from UTSA's HPC cluster Arc, operated by the university technology solutions research computing support group. Lastly, we are grateful to Wolfram Technology Support Services for their troubleshooting help.  
**Conflicts of Interest:** The authors declare no conflict of interest.  
Figure 4: Ascorbic acid (C\({}_{6}\)H\({}_{8}\)O\({}_{6}\)) image generated in _Gaussview 16_[22].