We provide a perspective on the role of non-integer electron number in the density functional theory approach to chemical reactivity (conceptual DFT), emphasizing that it is important to not only treat reagents as open systems, but also as non-isolated systems, in contact with their surroundings. The special case of well-separated reagents is treated in some detail, as is the case where reagents interact strongly. The resulting expressions for the chemical potential of an acid, μ_acid = −(αI + A)/(1 + α), and a base, μ_base = −(I + αA)/(1 + α), elucidate and generalize the assumptions inherent in the chemical potential models of Mulliken (α = 1) and Gazquez, Cedillo, and Vela (α = 3). In the strongly-interacting limit, it is appropriate to model the effects of the environment as a state-specific effective temperature, thereby providing a rigorous justification for the phenomenological effective-temperature model one of the authors previously proposed. The framework for the strongly interacting limit subsumes our model for weakly-interacting subsystems at nonzero temperature, the case of open but otherwise noninteracting subsystems, and the zero-temperature limit.

Molecular dynamics (MD) is a core methodology of molecular modeling and computational design for the study of the dynamics and temporal evolution of molecular systems. MD simulations have particularly benefited from the rapid increase of computational power that has characterized the past decades of computational chemical research, being the first method to be successfully migrated to the GPU infrastructure. While new-generation MD software is capable of delivering simulations on an ever-increasing scale, relatively less effort is invested in developing postprocessing methods that can keep up with the quickly expanding volumes of data that are being generated. Here, we introduce a new idea for sampling frames from large MD trajectories, based on the recently introduced framework of extended similarity indices. Our approach presents a new, linearly scaling alternative to the traditional approach of applying a clustering algorithm that usually scales as a quadratic function of the number of frames. When showcasing its usage on case studies with different system sizes and simulation lengths, we have registered speedups of up to 2 orders of magnitude, as compared to traditional clustering algorithms. The conformational diversity of the selected frames is also noticeably higher, which is a further advantage for certain applications, such as the selection of structural ensembles for ligand docking. The method is available open-source at https://github.com/ramirandaq/MultipleComparisons.

Despite being a central concept in cheminformatics, molecular similarity has so far been limited to the simultaneous comparison of only two molecules at a time and using one index, generally the Tanimoto coefficent. In a recent contribution we have not only introduced a complete mathematical framework for extended similarity calculations, (i.e. comparisons of more than two molecules at a time) but defined a series of novel idices. Part 1 is a detailed analysis of the effects of various parameters on the similarity values calculated by the extended formulas. Their features were revealed by sum of ranking differences and ANOVA. Here, in addition to characterizing several important aspects of the newly introduced similarity metrics, we will highlight their applicability and utility in real-life scenarios using datasets with popular molecular fingerprints. Remarkably, for large datasets, the use of extended similarity measures provides an unprecedented speed-up over “traditional” pairwise similarity matrix calculations. We also provide illustrative examples of a more direct algorithm based on the extended Tanimoto similarity to select diverse compound sets, resulting in much higher levels of diversity than traditional approaches. We discuss the inner and outer consistency of our indices, which are key in practical applications, showing whether then-ary and binary indices rank the data in the same way. We demonstrate the use of the newn-ary similarity metrics ont-distributed stochastic neighbor embedding (t-SNE) plots of datasets of varying diversity, or corresponding to ligands of different pharmaceutical targets, which show that our indices provide a better measure of set compactness than standard binary measures. We also present a conceptual example of the applicability of our indices in agglomerative hierarchical algorithms. The Python code for calculating the extended similarity metrics is freely available at:https://github.com/ramirandaq/MultipleComparisons

Quantification of the similarity of objects is a key concept in many areas of computational science. This includes cheminformatics, where molecular similarity is usually quantified based on binary fingerprints. While there is a wide selection of available molecular representations and similarity metrics, there were no previous efforts to extend the computational framework of similarity calculations to the simultaneous comparison of more than two objects (molecules) at the same time. The present study bridges this gap, by introducing a straightforward computational framework for comparing multiple objects at the same time and providing extended formulas for as many similarity metrics as possible. In the binary case (i.e. when comparing two molecules pairwise) these are naturally reduced to their well-known formulas. We provide a detailed analysis on the effects of various parameters on the similarity values calculated by the extended formulas. The extended similarity indices are entirely general and do not depend on the fingerprints used. Two types of variance analysis (ANOVA) help to understand the main features of the indices: (i) ANOVA of mean similarity indices; (ii) ANOVA of sum of ranking differences (SRD). Practical aspects and applications of the extended similarity indices are detailed in the accompanying paper: Miranda-Quintana et al. J Cheminform. 2021. 10.1186/s13321-021-00504-4. Python code for calculating the extended similarity metrics is freely available at: https://github.com/ramirandaq/MultipleComparisons.