• Accepted manuscript •

### Quantification of Molecular Basicity for Amines: a Combined Conceptual Density Functional Theory and Information-Theoretic Approach Study

Xuezhu Xiao1, Xiaofang Cao1, Dongbo Zhao2, Chunying Rong1, Shubin Liu3

1. 1 College of Chemistry and Chemical Engineering, Hunan Normal University, Changsha 410081, P. R. China;
2 School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, P. R. China;
3 Research Computing Center, University of North Carolina, Chapel Hill, NC 27599-3420, USA
• Received:2019-06-06 Revised:2019-07-01 Accepted:2019-07-12 Published:2019-07-17
• Contact: Chunying Rong, Shubin Liu E-mail:rongchunying@aliyun.com;shubin@email.unc.edu
• Supported by:
The project was supported by the National Natural Science Foundation of China (21503076) and the Hunan Provincial Natural Science Foundation of China (2017JJ3201).

Abstract: The pair of molecular acidity and basicity is one of the most widely used chemical concepts in chemistry, biology, and other related fields. Nevertheless, quantitative determination of these intrinsic physical properties from the perspective of theory and computation is still an unresolved task at present. Earlier, we proposed to utilize the molecular electrostatic potential and natural atomic orbital from conceptual density functional theory for this purpose. Later, we also proposed utilizing quantities from the information-theoretic approach in the density functional reactivity theory such as Shannon entropy, Fisher information, and information gain to quantify electrophilicity, nucleophilicity, regioselectivity, and stereoselectivity. The latter was successfully applied later to five series of molecular systems for determining the molecular acidity, including singly and doubly substituted benzoic acids, benzenesulfonic acids, benzeneseleninic acids, phenols, and alkyl carboxylic acids, whose validity and effectiveness have been sufficiently corroborated. As a continuation of our recent efforts along this line, in this work, we generalize our previous approaches by combining these two approaches together as a new set of descriptors to quantify the molecular basicity. The applicability and usefulness of our new approach are demonstrated hereby by three types of amines, namely, primary, secondary, and tertiary amines, with a total of 179 systems. We show that this new set of descriptors, including the molecular electrostatic potential or its equivalence, the natural valence atomic orbital energy, and quantities from information-theoretic approach such as Shannon entropy, Fisher information, Ghosh-Berkowitz-Parr entropy, information gain, Onicescu information energy, and relative Rényi entropy, is able to accurately predict the experimental pKa values for the three types of amines. Our findings confirm that each of these quantities possesses strong linear correlation with the experimental pKa value, though less significantly than expected. Moreover, when combined, these quantities can yield accurate and quantitative models for determining the molecular basicity of all the three types of amines. The reason behind this is that all these descriptors are simple electron density functionals. According to the basic theorem of density functional theory, they should contain adequate information for the determination of all the physio-chemical properties in the ground state of molecular systems, including molecular acidity and basicity. Our present results predict that this new approach should be readily applicable to many other molecular species, thereby providing an effective and robust approach to appreciate chemical concepts such as acidity and basicity.

MSC2000:

• O641