The Interacting Quantum Atoms (IQA) energy partitioning scheme has been applied to a set of liquid water largely spherical clusters (henceforth called spheres) of up to 9 Å radius, with a maximum cluster size of 113 molecules. This constitutes half of the commonly used 216 molecules in a typical simulation box of a liquid water box, and to our knowledge is the largest analysis of this kind ever undertaken. As well as demonstrating the topological analysis of large systems, which has only recently become computationally feasible, important long range properties of liquid water are obtained. The full topological partitioning of each sphere into atomic basins is used to consider the long-range convergence of the energetic and multipolar properties of the water molecule at the centre of each sphere. It is found that the total molecular energy converges to its 9 Å value after 7 Å, which corresponds to approximately the first three solvation shells, while the molecular dipole and quadrupole moments approximately converge after 5.5 Å, which corresponds to approximately the first two solvation shells. The effect of water molecule flexibility is also considered.

Here, we extend the system energy prediction approach used in the force field FFLUX (Maxwell et al. Theor Chem Acc 135:195, 2016) to complexes bound by weak intermolecular interactions. The investigation features the first application of the approach to bound complex systems, additionally challenged by investigating complexes held together only weakly, through either a predominant dispersion contribution, or through mixed dispersion and hydrogen-bonding. Our approach uses the interacting quantum atoms (IQA) energy partitioning scheme to obtain the intra-atomic, \( {E}_{\mathrm{intra}}^{\mathrm{A}} \), and interatomic, \( {V}_{\mathrm{inter}}^{{\mathrm{AA}}^{\hbox{'}}} \), energies, which when summed, compose the molecular energy, \( {E}_{\mathrm{IQA}}^{\mathrm{system}} \). The \( {E}_{\mathrm{intra}}^{\mathrm{A}} \) and \( {V}_{\mathrm{inter}}^{{\mathrm{AA}}^{\hbox{'}}} \) energies are mapped to the positions of the nuclear coordinates through the machine learning method kriging to build atomic energy models. A model’s quality is established through its ability to accurately predict the atomic and molecular energies of atoms in an external test set. Mean absolute error percentages (MAE%) of 1.5, 1.5, 1.6, 1.0, 2.6 and 1.7% are obtained in recovering the molecular energy for ammonia…benzene, water…benzene, HCN…benzene, methane…benzene, stacked-benzene (C2h) dimer and T-benzene (C2v) dimer complexes, respectively.

The machine learning method kriging is an attractive tool to construct next-generation force fields. Kriging can accurately predict atomistic properties, which involves optimization of the so-called concentrated log-likelihood function (i.e., fitness function). The difficulty of this optimization problem quickly escalates in response to an increase in either the number of dimensions of the system considered or the size of the training set. In this article, we demonstrate and compare the use of two search algorithms, namely, particle swarm optimization (PSO) and differential evolution (DE), to rapidly obtain the maximum of this fitness function. The ability of these two algorithms to find a stationary point is assessed by using the first derivative of the fitness function. Finally, the converged position obtained by PSO and DE is refined through the limited-memory Broyden–Fletcher–Goldfarb–Shanno bounded (L-BFGS-B) algorithm, which belongs to the class of quasi-Newton algorithms. We show that both PSO and DE are able to come close to the stationary point, even in high-dimensional problems. They do so in a reasonable amount of time, compared to that with the Newton and quasi-Newton algorithms, regardless of the starting position in the search space of kriging hyperparameters. The refinement through L-BFGS-B is able to give the position of the maximum with whichever precision is desired.

The proposed AIBLHiCoS method predicts a given compound’s pKa in aqueous solution from a single ab initio bond length only, after geometry optimization in the gas phase. Here we provide simple and predictive equations for naphthols and chemically similar biomolecules. Each linear equation corresponds to a High-Correlation Subset (HiCoS) that expresses the novel type of linear free energy relationship discovered here. The naphthol family exhibits a clear and strong relationship with the phenol family, with the “active” C–O bond always producing the highest correlations. The proposed method can isolate erroneous experiments and operate in non-aqueous solution and at different temperatures. Moreover, the existence of “active fragments” is demonstrated in a variety of sizable biomolecules for which the pKa is successfully predicted.

An interaction between two atoms, bonded or non-bonded, consists of interatomic contributions: electrostatic energy, exchange energy and electronic correlation energy. Together with the intra-atomic energy of an atom, these contributions are the basic components of the Interacting Quantum Atom (IQA) energy decomposition scheme. Here, we investigate IQA's proper use in conjunction with an explicit implementation of the B3LYP functional. The recovery of the total molecular energy from the IQA components is emphasised, for the first time. A systematic study of three model systems of biological relevance, N-methylacetamide (NMA), the doubly capped tripeptide GlyGlyGly and an alloxan dimer, shows the stabilization effect of B3LYP on most of the interatomic exchange energies (VABX) compared to their Hartree–Fock values. Diagrams of exchange energies versus interatomic distance show the clustering of interactions, one cluster for each 1,n (n = 1 to 6 where the atoms are separated by n − 1 bonds). The positioning of some VABX values outside their expected cluster marks interesting interactions.

Despite possessing an interesting chemical nature and tuneable physicochemical properties, ionic liquids (ILs) must have their ecotoxicity tested in order to be commercialized. The water solubility of ILs allows their easy access to the aquatic compartment of the ecosystem creating a potential hazard to aquatic organisms. Hence, it is relevant to design ionic liquids with lower toxicity while keeping the desired properties of interest. Considering the possibility of an enormous number of combinations of different cations and anions, a rational guidance for the structural design of ionic liquids is essential in order to prioritize the synthesis as well as testing of selected molecules only. Predictive in silico models, such as quantitative structure–activity relationship (QSAR) models, can play a pivotal role in exploring the important chemical attributes contributing to the response activity. These models may then lead to the design of novel ionic liquids. The present study aims at developing predictive QSAR models for the ecotoxicity of ionic liquids using the bacteria Vibrio fischeri as an indicator response species. Instead of a single model, here we have used multiple models to capture more complete structural information of ionic liquids for toxicity towards Vibrio fischeri. The derived chemical attributes have been implemented in designing new analogues, some of which have been synthesized and had their ecotoxicity tested for the same model organism. The predictive QSAR models reported here can be used for ecotoxicity prediction of new IL chemicals and for data-gap filling. Moreover, the synthesized low-toxic ILs could be considered for evaluation as well as for application in suitable processes serving the purpose of industry and academia.

The Raman optical activity spectra of the epimers β-d-glucose and β-d-galactose, two monosaccharides of biological importance, have been calculated using molecular dynamics combined with a quantum mechanics/molecular mechanics approach. Good agreement between theoretical and experimental spectra is observed for both monosaccharides. Full band assignments have been carried out, which has not previously been possible for carbohydrate epimers. For the regions where the spectral features are opposite in sign, the differences in the vibrational modes have been noted and ascribed to the band sign changes.

Explicit formulas are derived analytically for the first derivatives of a (i) polarizable, (ii) high-rank multipolar electrostatic potential energy function for (iii) flexible molecules. The potential energy function uses a machine learning method called Kriging to predict the local-frame multipole moments of atoms defined via the Quantum Chemical Topology (QCT) approach. These atomic multipole moments then interact via an interaction tensor based on spherical harmonics. Atom-centered local coordinate frames are used, constructed from the internal geometry of the molecular system. The forces involve derivatives of both this geometric dependence and of the trained kriging models. In the near future, these analytical forces will enable molecular dynamics and geometry optimization calculations as part of the QCT force field.

An interaction between two atoms, bonded or non-bonded, consists of interatomic contributions: electrostatic energy, exchange energy and electronic correlation energy. Together with the intra-atomic energy of an atom, these contributions are the basic components of the Interacting Quantum Atom (IQA) energy decomposition scheme. Here, we investigate IQA's proper use in conjunction with an explicit implementation of the B3LYP functional. The recovery of the total molecular energy from the IQA components is emphasised, for the first time. A systematic study of three model systems of biological relevance, N-methylacetamide (NMA), the doubly capped tripeptide GlyGlyGly and an alloxan dimer, shows the stabilization effect of B3LYP on most of the interatomic exchange energies (VABX) compared to their Hartree–Fock values. Diagrams of exchange energies versus interatomic distance show the clustering of interactions, one cluster for each 1,n (n = 1 to 6 where the atoms are separated by n − 1 bonds). The positioning of some VABX values outside their expected cluster marks interesting interactions.

Histidine is a key component of a number of enzymatic mechanisms, and undertakes a myriad of functionalities in biochemical systems. Its computational modelling can be problematic, as its capacity to take on a number of distinct formal charge states, and tautomers thereof, is difficult to capture by conventional techniques. We demonstrate a means for recovering the experimental Raman optical activity (ROA) spectra of histidine to a high degree of accuracy. The resultant concordance between experiment and theory is of particular importance in characterising physically insightful quantities, such as band assignments. We introduce a novel conformer selection scheme that unambiguously parses snapshots from a molecular dynamics trajectory into a smaller conformational ensemble, suitable for reproducing experimental spectra. We show that the “dissimilarity” of the conformers within the resultant ensemble is maximised and representative of the physically relevant regions of molecular conformational space. In addition, we present a conformer optimisation strategy that significantly reduces the computational costs associated with alternative optimisation strategies. This conformer optimisation strategy yields spectra of equivalent quality to those of the aforementioned alternative optimisation strategies. Finally, we demonstrate that microsolvated models of small molecules yield spectra that are comparable in quality to those obtained from ab initio calculations involving a large number of solvent molecules.