# On the Use of Popular Basis Sets: Impact of the Intramolecular Basis Set Superposition Error

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## Abstract

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## 1. Introduction

- It should be experimentally operative in the gas phase, in order to avoid artifacts stemming from the effect of the environment.
- Accurate experimental data should be readily available.
- This chemistry should span a relatively wide range of energies, in order to maximize the signal/noise ratio.
- Structural changes should ideally be systematic in the sense of involving an increasing number of basis set functions without adding strong electronic or steric effects that could obscure the pure dependecy on these functions.
- Ideally, the molecular change upon reaction should be very local to have a clear locus on which the BSSE acts.
- If possible, precedents on the succesful description of the reactivity of choice by computational methods should be available.

## 2. Theoretical Background and Computational Methods

**(b0)**[36,37], 3-21G

**(b1)**[38,39,40], 6-31G(d)

**(b2)**[41,42,43,44,45], 6-31+G(d,p)

**(b3)**[46,47,48], 6-311+G(d,p)

**(b4)**[49,50] 6-311++G(3df,2pd),

**(b5)**[51,52,53,54]. The reasoning behind this choice of basis sets is both their popularity and the fact that they span a very wide range in terms of the number of functions per atom, allowing us to better highlight the BSSE and BSIE effects.

## 3. Results and Discussion

**b5**) this systematic error is greatly dilluted and the errors obtained in the calculations have a larger random component.

## 4. Conclusions

- There is no univocal way of dividing the molecule into fragments, and different partitionings would provide different corrections for the BSSE.
- The complex/monomer approach by Bernardi and Boys is based on rigid (single point) calculations whereas chemical reactions involve changes in molecular structure.
- The number of calculations needed to compute the BSSE correction depends on the number of fragments, which could easily scale up quickly to untractable numbers if fine-grain fragmentation is needed to account for the intramolecular BSSE.

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

BSSE | Basis set superposition error |

BSIE | Basis set incompleteness error |

DNA | Deoxyribonucleic acid |

ANO | Atomic Natural Orbital |

MRCI | Multi-reference configuration interactions |

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**Figure 1.**Schematic representation of the basis set superposition error (BSSE) in a single Watson–Crick base pair. Atom centered Gaussian functions are represented with like colors, atoms whose electron density is partially described by Gaussian tails of functions centered in atoms belonging to the other monomer are indicated in boldface and slanted typography.

**Figure 2.**Schematic representation of the 18 different reactions used in this study for the calculation of proton affinity (PA) and gas-phase basicity (GPB).

**Table 1.**Signed relative error values expressed as percentage with respect to the experimental reference value in the calculation of proton affinities (PAs). The results obtained with different basis sets have been colored following a conditional format and a RYG (red–yellow–green) scale in which the worst results are shown in red while the best are highlighted in green. Each density functional has been colored independently to favor the visualization and comparison of the results. The last row represents the mean signed errors (MSE) for each of the basis sets:

**(b0)**: sto-3g,

**(b1)**: 3-21g,

**(b2)**: 6-31g(d),

**(b3)**: 6-31+g(d,p),

**(b4)**: 6-311+g(d,p),

**(b5)**: 6-311++g(3df,2pd).

**Table 2.**Signed relative errors at each theoretical level and mean signed errors (MSE) for each basis set in the values obtained for the gas-phase basicities (GPBs). The color scale used, method of cell coloring, and basis set employed are the same described for PAs.

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**MDPI and ACS Style**

Vidal Vidal, Á.; de Vicente Poutás, L.C.; Nieto Faza, O.; Silva López, C.
On the Use of Popular Basis Sets: Impact of the Intramolecular Basis Set Superposition Error. *Molecules* **2019**, *24*, 3810.
https://doi.org/10.3390/molecules24203810

**AMA Style**

Vidal Vidal Á, de Vicente Poutás LC, Nieto Faza O, Silva López C.
On the Use of Popular Basis Sets: Impact of the Intramolecular Basis Set Superposition Error. *Molecules*. 2019; 24(20):3810.
https://doi.org/10.3390/molecules24203810

**Chicago/Turabian Style**

Vidal Vidal, Ángel, Luis Carlos de Vicente Poutás, Olalla Nieto Faza, and Carlos Silva López.
2019. "On the Use of Popular Basis Sets: Impact of the Intramolecular Basis Set Superposition Error" *Molecules* 24, no. 20: 3810.
https://doi.org/10.3390/molecules24203810