Smooth particle mesh Ewald-integrated stochastic Lanczos many-body dispersion algorithm.

We derive and implement an alternative formulation of the Stochastic Lanczos algorithm to be employed in connection with the Many-Body Dispersion model (MBD). Indeed, this formulation, which is only possible due to the Stochastic Lanczos' reliance on matrix-vector products, introduces generalized dipoles and fields. These key quantities allow for a state-of-the-art treatment of periodic boundary conditions via the O(Nlog(N)) Smooth Particle Mesh Ewald (SPME) approach which uses efficient fast Fourier transforms. This SPME-Lanczos algorithm drastically outperforms the standard replica method which is affected by a slow and conditionally convergence rate that limits an efficient and reliable inclusion of long-range periodic boundary conditions interactions in many-body dispersion modelling. The proposed algorithm inherits the embarrassingly parallelism of the original Stochastic Lanczos scheme, thus opening up for a fully converged and efficient periodic boundary conditions treatment of MBD approaches.

Generalized Many-Body Dispersion Correction through Random-Phase Approximation for Chemically Accurate Density Functional Theory.

We extend our recently proposed Deep Learning-aided many-body dispersion (DNN-MBD) model to quadrupole polarizability (Q) terms using a generalized Random Phase Approximation (RPA) formalism, thus enabling the inclusion of van der Waals contributions beyond dipole. The resulting DNN-MBDQ model only relies on ab initio-derived quantities as the introduced quadrupole polarizabilities are recursively retrieved from dipole ones, in turn modeled via the Tkatchenko-Scheffler method. A transferable and efficient deep-neuronal network (DNN) provides atom-in-molecule volumes, while a single range-separation parameter is used to couple the model to Density Functional Theory (DFT). Since it can be computed at a negligible cost, the DNN-MBDQ approach can be coupled with DFT functionals, such as PBE, PBE0, and B86bPBE (dispersionless). The DNN-MBQ-corrected functionals reach chemical accuracy while exhibiting lower errors compared to their dipole-only counterparts.

Accurate Deep Learning-Aided Density-Free Strategy for Many-Body Dispersion-Corrected Density Functional Theory.

Using a deep neuronal network (DNN) model trained on the large ANI-1 data set of small organic molecules, we propose a transferable density-free many-body dispersion (DNN-MBD) model. The DNN strategy bypasses the explicit Hirshfeld partitioning of the Kohn-Sham electron density required by MBD models to obtain the atom-in-molecules volumes used by the Tkatchenko-Scheffler polarizability rescaling. The resulting DNN-MBD model is trained with minimal basis iterative Stockholder atomic volumes and, coupled to density functional theory (DFT), exhibits comparable (if not greater) accuracy to other approaches based on different partitioning schemes. Implemented in the Tinker-HP package, the DNN-MBD model decreases the overall computational cost compared to MBD models where the explicit density partitioning is performed. Its coupling with the recently introduced Stochastic formulation of the MBD equations (J. Chem. Theory Comput. 2022, 18 (3), 1633-1645) enables large routine dispersion-corrected DFT calculations at preserved accuracy. Furthermore, the DNN electron density-free features extend the MBD model's applicability beyond electronic structure theory within methodologies such as force fields and neural networks.

Variational formulation of the bond capacity charge polarization model.

We present an alternative energy formulation of the bond capacity charge polarization model to be used in molecular dynamics simulations. The energy expression consists of a Coulombic charge-charge interaction contribution as well as a quadratic Coulomb potential term, which can be seen as the electrostatic energy stored in the system's bond capacities. This formulation is shown to be variational in the potential space, although, it shares the same set of charges with the original non-variational formulation of the model. This variational formulation is compared with the non-variational one in terms of few selected observables showing the underlying distinctiveness of the two approaches. Being variational, this formulation allows for the computation of forces by invoking the classical analog of the Hellmann-Feynman theorem, which makes this approach two times faster than the non-variational one.

O(N) Stochastic Evaluation of Many-Body van der Waals Energies in Large Complex Systems.

We propose a new strategy to solve the key equations of the many-body dispersion (MBD) model by Tkatchenko, DiStasio Jr., and Ambrosetti. Our approach overcomes the original O(N3) computational complexity that limits its applicability to large molecular systems within the context of O(N) density functional theory. First, to generate the required frequency-dependent screened polarizabilities, we introduce an efficient solution to the Dyson-like self-consistent screening equations. The scheme reduces the number of variables and, coupled to a direct inversion of the iterative subspace extrapolation, exhibits linear-scaling performances. Second, we apply a stochastic Lanczos trace estimator resolution to the equations evaluating the many-body interaction energy of coupled quantum harmonic oscillators. While scaling linearly, it also enables communication-free pleasingly parallel implementations. As the resulting O(N) stochastic massively parallel MBD approach is found to exhibit minimal memory requirements, it opens up the possibility of computing accurate many-body van der Waals interactions of millions-atoms' complex materials and solvated biosystems with computational times in the range of minutes.

Polarizable charges in a generalized Born reaction potential.

The generalized Born (GB) model is a fast implicit solvent model that is used as an approximation to the Poisson equation for solutes described by point charges. Due to the simple analytical form, GB models are widely used in molecular dynamics simulations to account for (implicit) solvation effects. In this work, we extend the application of the GB model to polarizable charges by coupling it to the bond capacity (BC) model. The resulting BC-GB model is a non-variational polarization model where the reaction potential is calculated from a GB expression and included in the polarization equation to account for solvation effects. Being non-variational, the BC-GB makes use of a Lagrange formulation for an efficient evaluation of energy gradients. The stability of the algorithm in molecular dynamics simulations is tested in the microcanonical ensemble, and the results show energy conservation as well as small fluctuations. The inclusion of implicit solvation increases the computational cost by only 15% compared to vacuum. Combined with a significant reduction in system size by describing the solvent as a continuum makes the BC-GB model an interesting model for applications requiring the combination of solute polarization and extensive conformational space sampling.

Molecular, Macromolecular, and Supramolecular Glucuronide Prodrugs: Lead Identified for Anticancer Prodrug Monotherapy.

In this work, a tumor growth intervention by localized drug synthesis within the tumor volume, using the enzymatic repertoire of the tumor itself, is presented. Towards the overall success, molecular, macromolecular, and supramolecular glucuronide prodrugs were designed for a highly potent toxin, monomethyl auristatin E (MMAE). The lead candidate exhibited a fold difference in toxicity between the prodrug and the drug of 175, had an engineered mechanism to enhance the deliverable payload to tumours, and contained a highly potent toxin such that bioconversion of only a few prodrug molecules created a concentration of MMAE sufficient enough for efficient suppression of tumor growth. Each of these points is highly significant and together afford a safe, selective anticancer measure, making tumor-targeted glucuronides attractive for translational medicine.

Including implicit solvation in the bond capacity polarization model.

We derive expressions corresponding to a coupling of the recently proposed Bond Capacity polarization model with implicit solvation by means of the generalized Born and conductor-like polarizable continuum models. The original bond capacity interaction kernel is in both cases augmented with a term that accounts for the reaction potential arising from the continuum. The expressions for energy gradients are derived within the recently introduced Lagrangian formalism for the efficient evaluation of energy gradients of nonvariational force fields.

Molecular Dynamics Using Nonvariational Polarizable Force Fields: Theory, Periodic Boundary Conditions Implementation, and Application to the Bond Capacity Model.

We extend the framework for polarizable force fields to include the case where the electrostatic multipoles are not determined by a variational minimization of the electrostatic energy. Such models formally require that the polarization response is calculated for all possible geometrical perturbations in order to obtain the energy gradient required for performing molecular dynamics simulations. By making use of a Lagrange formalism, however, this computationally demanding task can be replaced by solving a single equation similar to that for determining the electrostatic variables themselves. Using the recently proposed bond capacity model that describes molecular polarization at the charge-only level, we show that the energy gradient for nonvariational energy models with periodic boundary conditions can be calculated with a computational effort similar to that for variational polarization models. The possibility of separating the equation for calculating the electrostatic variables from the energy expression depending on these variables without a large computational penalty provides flexibility in the design of new force fields.

Describing Molecular Polarizability by a Bond Capacity Model.

We propose a bond capacity model for describing molecular polarization in force field energy functions at the charge-only level. Atomic charges are calculated by allowing charge to flow between atom pairs according to a bond capacity and a difference in electrostatic potential. The bond capacity is closely related to the bond order and decays to zero as the bond distance is increased. The electrostatic potential is composed of an intrinsic potential, identified as the electronegativity, and a screened Coulomb potential from all other charges. The bond capacity model leads to integer fragment charges upon bond dissociation and displays linear scaling of the polarizability with system size. Bond capacity parameters can be derived from reference molecular polarizabilities, while electronegativity parameters can be derived from reference atomic charges or a reference molecular electrostatic potential. Out-of-plane polarization for planar systems is modeled by off-nuclei charge sites. The model is shown to be able to reproduce anisotropic reference molecular polarizabilities with an accuracy of ∼10% using a limited set of bond capacity parameters and can describe both inter- and intramolecular polarization.