Large-Z atoms in the strong-interaction limit of DFT: Implications for gradient expansions and for the Lieb-Oxford bound.

We numerically study the strong-interaction limit of the exchange-correlation functional for neutral atoms and Bohr atoms as the number of electrons increases. Using a compact representation, we analyze the second-order gradient expansion, comparing it with the one for exchange (weak interaction limit). The two gradient expansions, at strong and weak interaction, turn out to be very similar in magnitude but with opposite signs. We find that the point-charge plus continuum model is surprisingly accurate for the gradient expansion coefficient at strong coupling, while generalized gradient approximations, such as Perdew-Burke-Ernzerhof (PBE) and PBEsol, severely underestimate it. We then use our results to analyze the Lieb-Oxford bound from the point of view of slowly varying densities, clarifying some aspects on the bound at a fixed number of electrons.

Regularized and Opposite Spin-Scaled Functionals from Møller-Plesset Adiabatic Connection─Higher Accuracy at Lower Cost.

Noncovalent interactions (NCIs) play a crucial role in biology, chemistry, material science, and everything in between. To improve pure quantum-chemical simulations of NCIs, we propose a methodology for constructing approximate correlation energies by combining an interpolation along the Møller-Plesset adiabatic connection (MP AC) with a regularization and spin-scaling strategy applied to MP2 correlation energies. This combination yields cosκos-SPL2, which exhibits superior accuracy for NCIs compared to any of the individual strategies. With the N4 formal scaling, cosκos-SPL2 is competitive or often outperforms more expensive dispersion-corrected double hybrids for NCIs. The accuracy of cosκos-SPL2 particularly shines for anionic halogen bonded complexes, where it surpasses standard dispersion-corrected DFT by a factor of 3 to 5.

Electronic Excited States in Extreme Limits via Ensemble Density Functionals.

Density functional theory (DFT) has greatly expanded our ability to affordably compute and understand electronic ground states, by replacing intractable ab initio calculations by models based on paradigmatic physics from high- and low-density limits. But, a comparable treatment of excited states lags behind. Here, we solve this outstanding problem by employing a generalization of density functional theory to ensemble states (EDFT). We thus address important paradigmatic cases of all electronic systems in strongly (low-density) and weakly (high-density) correlated regimes. We show that the high-density limit connects to recent, exactly solvable EDFT results. The low-density limit reveals an unnoticed and most unexpected result-density functionals for strictly correlated ground states can be reused directly for excited states. Nontrivial dependence on excitation structure only shows up at third leading order. Overall, our results provide foundations for effective models of excited states that interpolate between exact low- and high-density limits, which we illustrate on the cases of singlet-singlet excitations in H_{2} and a ring of quantum wells.

Gradient Expansions for the Large-Coupling Strength Limit of the Møller-Plesset Adiabatic Connection.

The adiabatic connection that has, as weak-interaction expansion, the Møller-Plesset perturbation series has been recently shown to have a large coupling-strength expansion, in terms of functionals of the Hartree-Fock density with a clear physical meaning. In this work, we accurately evaluate these density functionals and we extract second-order gradient coefficients from the data for neutral atoms, following ideas similar to the ones used in the literature for exchange, with some modifications. These new gradient expansions will be the key ingredient for performing interpolations that have already been shown to reduce dramatically MP2 errors for large noncovalent complexes. As a byproduct, our investigation of neutral atoms with large number of electrons N indicates that the second-order gradient expansion for exchange grows as N log(N) rather than as N, as often reported in the literature.

Dispersion without Many-Body Density Distortion: Assessment on Atoms and Small Molecules.

The "fixed diagonal matrices" (FDM) dispersion formalism [Kooi, D. P.; et al. J. Phys. Chem. Lett. 2019, 10, 1537] is based on a supramolecular wave function constrained to leave the diagonal of the many-body density matrix of each monomer unchanged, reducing dispersion to a balance between kinetic energy and monomer-monomer interaction. The corresponding variational optimization leads to expressions for the dispersion energy in terms of the ground-state pair densities of the isolated monomers only, providing a framework to build new approximations without the need for polarizabilities or virtual orbitals. Despite the underlying microscopic real space mechanism being incorrect, as in the exact case there is density relaxation, the formalism has been shown to give extremely accurate (or even exact) dispersion coefficients for H and He. The question we answer in this work is how accurate the FDM expressions can be for isotropic and anisotropic C6 dispersion coefficients when monomer pair densities are used from different levels of theory, namely Hartree-Fock, MP2, and CCSD. For closed-shell systems, FDM with CCSD monomer pair densities yield a mean average percent error for isotropic C6 dispersion coefficients of about 7% and a maximum absolute error within 18%, with a similar accuracy for anisotropies. The performance for open-shell systems is less satisfactory, with CCSD pair densities performing sometimes worse than Hartree-Fock or MP2. In the present implementation, the computational cost on top of the monomer's ground-state calculations is O(N4). The results show little sensitivity to the basis set used in the monomer's calculations.

Large coupling-strength expansion of the Møller-Plesset adiabatic connection: From paradigmatic cases to variational expressions for the leading terms.

We study in detail the first three leading terms of the large coupling-strength limit of the adiabatic connection that has as weak-interaction expansion the Møller-Plesset perturbation theory. We first focus on the H atom, both in the spin-polarized and the spin-unpolarized cases, reporting numerical and analytical results. In particular, we derive an asymptotic equation that turns out to have simple analytical solutions for certain channels. The asymptotic H atom solution for the spin-unpolarized case is then shown to be variationally optimal for the many-electron spin-restricted closed-shell case, providing expressions for the large coupling-strength density functionals up to the third leading order. We also analyze the H2 molecule and the uniform electron gas.

London dispersion forces without density distortion: a path to first principles inclusion in density functional theory.

We analyse a path to construct density functionals for the dispersion interaction energy from an expression in terms of the ground state densities and exchange-correlation holes of the isolated fragments. The expression is based on a constrained search formalism for a supramolecular wavefunction that is forced to leave the diagonal of the many-body density matrix of each fragment unchanged, and is exact for the interaction between one-electron densities. We discuss several aspects: the necessary features of a density functional approximation for the exchange-correlation holes of the monomers, the optimal choice of the one-electron basis (named "dispersals"), and the functional derivative with respect to monomer density variations.

A Variational Approach to London Dispersion Interactions without Density Distortion.

We introduce a class of variational wave functions that captures the long-range interaction between neutral systems (atoms and molecules) without changing the diagonal of the density matrix of each monomer. The corresponding energy optimization yields explicit expressions for the dispersion coefficients in terms of the ground-state pair densities of the isolated systems, providing a clean theoretical framework to build new approximations in several contexts. As the individual monomer densities are kept fixed, we can also unambiguously assess the effect of the density distortion on London dispersion interactions; for example, we obtain virtually exact dispersion coefficients between two hydrogen atoms up to C10 and relative errors below 0.2% in other simple cases.

Local and global interpolations along the adiabatic connection of DFT: a study at different correlation regimes.

Interpolating the exchange-correlation energy along the density-fixed adiabatic connection of density functional theory is a promising way to build approximations that are not biased toward the weakly correlated regime. These interpolations can be performed at the global (integrated over all spaces) or at the local level, using energy densities. Many features of the relevant energy densities as well as several different ways to construct these interpolations, including comparisons between global and local variants, are investigated here for the analytically solvable Hooke's atom series, which allows for an exploration of different correlation regimes. We also analyze different ways to define the correlation kinetic energy density, focusing on the peak in the kinetic correlation potential.

eTOX ALLIES: an automated pipeLine for linear interaction energy-based simulations.

BACKGROUND: Computational methods to predict binding affinities of small ligands toward relevant biological (off-)targets are helpful in prioritizing the screening and synthesis of new drug candidates, thereby speeding up the drug discovery process. However, use of ligand-based approaches can lead to erroneous predictions when structural and dynamic features of the target substantially affect ligand binding. Free energy methods for affinity computation can include steric and electrostatic protein-ligand interactions, solvent effects, and thermal fluctuations, but often they are computationally demanding and require a high level of supervision. As a result their application is typically limited to the screening of small sets of compounds by experts in molecular modeling. RESULTS: We have developed eTOX ALLIES, an open source framework that allows the automated prediction of ligand-binding free energies requiring the ligand structure as only input. eTOX ALLIES is based on the linear interaction energy approach, an efficient end-point free energy method derived from Free Energy Perturbation theory. Upon submission of a ligand or dataset of compounds, the tool performs the multiple steps required for binding free-energy prediction (docking, ligand topology creation, molecular dynamics simulations, data analysis), making use of external open source software where necessary. Moreover, functionalities are also available to enable and assist the creation and calibration of new models. In addition, a web graphical user interface has been developed to allow use of free-energy based models to users that are not an expert in molecular modeling. CONCLUSIONS: Because of the user-friendliness, efficiency and free-software licensing, eTOX ALLIES represents a novel extension of the toolbox for computational chemists, pharmaceutical scientists and toxicologists, who are interested in fast affinity predictions of small molecules toward biological (off-)targets for which protein flexibility, solvent and binding site interactions directly affect the strength of ligand-protein binding.

Fermionic Statistics in the Strongly Correlated Limit of Density Functional Theory.

Exact pieces of information on the adiabatic connection integrand, Wλ[ρ], which allows evaluation of the exchange-correlation energy of Kohn-Sham density functional theory, can be extracted from the leading terms in the strong coupling limit (λ → ∞, where λ is the strength of the electron-electron interaction). In this work, we first compare the theoretical prediction for the two leading terms in the strong coupling limit with data obtained via numerical implementation of the exact Levy functional in the simple case of two electrons confined in one dimension, confirming the asymptotic exactness of these two terms. We then carry out a first study on the incorporation of the Fermionic statistics at large coupling λ, both numerical and theoretical, confirming that spin effects enter at orders ∼e-√λ.

Improving the iterative Linear Interaction Energy approach using automated recognition of configurational transitions.

Recently an iterative method was proposed to enhance the accuracy and efficiency of ligand-protein binding affinity prediction through linear interaction energy (LIE) theory. For ligand binding to flexible Cytochrome P450s (CYPs), this method was shown to decrease the root-mean-square error and standard deviation of error prediction by combining interaction energies of simulations starting from different conformations. Thereby, different parts of protein-ligand conformational space are sampled in parallel simulations. The iterative LIE framework relies on the assumption that separate simulations explore different local parts of phase space, and do not show transitions to other parts of configurational space that are already covered in parallel simulations. In this work, a method is proposed to (automatically) detect such transitions during the simulations that are performed to construct LIE models and to predict binding affinities. Using noise-canceling techniques and splines to fit time series of the raw data for the interaction energies, transitions during simulation between different parts of phase space are identified. Boolean selection criteria are then applied to determine which parts of the interaction energy trajectories are to be used as input for the LIE calculations. Here we show that this filtering approach benefits the predictive quality of our previous CYP 2D6-aryloxypropanolamine LIE model. In addition, an analysis is performed of the gain in computational efficiency that can be obtained from monitoring simulations using the proposed filtering method and by prematurely terminating simulations accordingly.

Integrative Modeling Strategies for Predicting Drug Toxicities at the eTOX Project.

Early prediction of safety issues in drug development is at the same time highly desirable and highly challenging. Recent advances emphasize the importance of understanding the whole chain of causal events leading to observable toxic outcomes. Here we describe an integrative modeling strategy based on these ideas that guided the design of eTOXsys, the prediction system used by the eTOX project. Essentially, eTOXsys consists of a central server that marshals requests to a collection of independent prediction models and offers a single user interface to the whole system. Every of such model lives in a self-contained virtual machine easy to maintain and install. All models produce toxicity-relevant predictions on their own but the results of some can be further integrated and upgrade its scale, yielding in vivo toxicity predictions. Technical aspects related with model implementation, maintenance and documentation are also discussed here. Finally, the kind of models currently implemented in eTOXsys is illustrated presenting three example models making use of diverse methodology (3D-QSAR and decision trees, Molecular Dynamics simulations and Linear Interaction Energy theory, and fingerprint-based QSAR).