# Comparison of Molecular Geometry Optimization Methods Based on Molecular Descriptors

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

**j**constant is the imaginary unit, $\hslash $ is the reduced Planck constant, and

**t**is time.

_{i}can be expanded in a set of known functions χ

_{k}(k = 1, 2, …, M), the basis set:

_{ki}are determined by minimizing the total energy, which by traditional methods lead to a matrix eigenvalue problem that is solved iteratively to provide a self-consistent field (SCF) solution.

**n**electrons in a molecule are assigned to a set of n molecular orbitals ψ

_{i}(i = 1, …, n), the corresponding many electron wavefunction is:

_{i}are orthonormal and α and β are spin functions.

- 6-31G → cc-pVDZ
- 6-311G → aug-cc-pVDZ
- 6-31+G(d) → cc-pVTZ
- 6-311+G(d) → aug-cc-pVTZ
- 6-31++G(d,p) → cc-pVQZ
- 6-311++G(d,p) → aug-cc-pVQZ

## 2. Materials and Methods

- Enter the PubChem
**.sdf**files to the Gaussian program. - Save the file in
**.gjf**file format (the input file format for the program). - Analyse the amino acids using the following t command: Calculate → Gaussian Calculation Setup → Job type (Optimization).
- From the Calculation Setup menu select the Gaussian Geometry Optimization Methods one after another and run the calculations.
- Save for every calculation the .out file (the output file format for the program).

## 3. Results and Discussion

^{2}X. The explained variance (R

^{2}X

_{adj}) is simply the explained variation (R

^{2}X) adjusted for the degrees of freedom.

^{2}) statistic is typically reported as a result of cross-validation and provides a qualitative measure of consistency between the predicted and original data. As we add more variables to the PCA analysis, the value of Q

^{2}increases. Large values of Q

^{2}indicates a relevant and significant analysis.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

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**Figure 2.**The explained variation (R

^{2}X) and the predictive variation (Q

^{2}X) of the PCA components.

**Figure 6.**Score plot showing the distribution of the methods in the principal components p1 and p2 and cluster analysis.

**Figure 7.**Score plot showing the distribution of the methods in the principal components p1 and p2 and cluster analysis.

**Figure 8.**Score plot showing the distribution of the methods in the principal components p1 and p2 and cluster analysis.

**Figure 9.**Score plot showing the distribution of the methods in the principal components p1 and p2 and cluster analysis.

Amino Acids (AA) | |||
---|---|---|---|

Arginine | Lysine | Methionine | Leucine |

Asparagine | Serine | Alanine | Phenylalanine |

Aspartate | Threonine | Valine | Proline |

Glutamate | Cysteine | Glycine | Tryptophan |

Glutamine | Histidine | Isoleucine | Tyrosine |

Gaussian Optimization Methods | |
---|---|

Semi-Empirical Methods (Default Spin) | 1. Parameterized Model 6 PM6 (opt-pm6)2. Austin Model 1 AM1 (opt-am1)3. Parameterized Model 3 PM3 (opt-pm3)4. Parameterized Model 3 (Molecular Mechanics correction) PM3MM (opt-pm3mm)5. Pairwise Distance Directed Gaussian function PDDG (opt-pddg) 6. Complete Neglect of Differential Overlap CNDO (opt-cndo)7. Intermediate Neglect of Differential Overlap INDO (opt-indo) |

Density Functional Theory (Default Spin) | Becke(three-parameter)–Lee–Yang–Parr (functional) B3LYP8. opt-b3lyp-sto-3g; 9. opt-b3lyp-3-21g; 10. opt-b3lyp-6-31g; 11. opt-b3lyp-6-311g; 12. opt-b3lyp-cc-pvdz;) Local Spin Density Approximation LSDA 13. opt-lsda-3-21g; 14. opt-lsda-sto-3g; 15. opt-lsda-cc-pvdz; 16. opt-lsda-6-311g; 17. opt-lsda-6-31g;)18. Perdew–Burke-Ernzerhof (functional) PBEPBE opt-pbepbe-sto-3gBVP86 19. opt-bvp86-sto-3g; 20. opt-bvp86-3-21g; 21. Opt-bvp86-6-31g; 22. opt-bvp86-6-311g;)B3PW91 23. opt-b3pw91-sto-3g; 24. opt-b3pw91-6-31g; 25. opt-b3pw91-6-311g;) |

Møller–Plesset Perturbation Theory | MP2 26. opt-mp2-sto-3g; 27. opt-mp2-3-21g; 28. opt-mp2-6-31g; 29. opt-mp2-6-311g; 30. opt-mp2-cc-pvdz;) |

Coupled-Cluster Theory | 31. Coupled Cluster single-double CCSD (opt-ccsd-sto-3g) |

Molecular Mechanics (Default Spin) | 32. Universal Force Field UFF (opt-uff)33. Dreiding (opt-dreiding) |

Hartree–Fock (Default Spin) | 34.STO-3G(opt-hf-sto-3g)35.3-21G(opt-hf-3-21g)36.3-21G*(opt-hf-3-21g*)37.6-31G(opt-hf-6-31g)38.6-311G(opt-hf-6-311g)39.CC-pvdz(opt-hf-cc-pvdz) |

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Bálint, D.; Jäntschi, L.
Comparison of Molecular Geometry Optimization Methods Based on Molecular Descriptors. *Mathematics* **2021**, *9*, 2855.
https://doi.org/10.3390/math9222855

**AMA Style**

Bálint D, Jäntschi L.
Comparison of Molecular Geometry Optimization Methods Based on Molecular Descriptors. *Mathematics*. 2021; 9(22):2855.
https://doi.org/10.3390/math9222855

**Chicago/Turabian Style**

Bálint, Donatella, and Lorentz Jäntschi.
2021. "Comparison of Molecular Geometry Optimization Methods Based on Molecular Descriptors" *Mathematics* 9, no. 22: 2855.
https://doi.org/10.3390/math9222855