Density-Dependent Formulation of Dispersion–Repulsion Interactions in Hybrid Multiscale Quantum/Molecular Mechanics (QM/MM) Models

Extending the MST Model to Large Biomolecular Systems: Parametrization of the ddCOSMO-MST Continuum Solvation Model

Continuum solvation models such as the polarizable continuum model and the conductor-like screening model are widely used in quantum chemistry, but their application to large biosystems is hampered by their computational cost. Here, we report the parametrization of the Miertus-Scrocco-Tomasi (MST) model for the prediction of hydration free energies of neutral and ionic molecules based on the domain decomposition formulation of COSMO (ddCOSMO), which allows a drastic reduction of the computational cost by several orders of magnitude. We also introduce several novelties in MST, like a new definition of atom types based on hybridization and an automatic setup of the cavity for charged regions. The model is parametrized at the B3LYP/6-31+G(d) and PM6 levels of theory and compared to the performance of IEFPCM/MST. Then, we demonstrate the robustness of the parametrization on the SAMPL2, SAMPL4, and C10 datasets. The ddCOSMO/MST models provide errors of ~0.8 and ~3.2 kcal/mol for neutrals and ions, respectively, showing a remarkable balanced and accurate description of cations and anions.

Conical Intersection in Chemiluminescence of Cyclic Peroxides

Chemiluminescence (CL) utilizing chemiexcitation for energy transformation is one of the most highly sensitive and useful analytical techniques. The chemiexcitation is a chemical process of a ground-state reactant producing an excited-state product, in which a nonadiabatic event is facilitated by conical intersections (CIs), the specific molecular geometries where electronic states are degenerated. Cyclic peroxides, especially 1,2-dioxetane/dioxetanone derivatives, are the iconic chemiluminescent substances. In this Perspective, we concentrated on the CIs in the CL of cyclic peroxides. We first present a computational overview on the role of CIs between the ground (S₀) state and the lowest singlet excited (S₁) state in the thermolysis of cyclic peroxides. Subsequently, we discuss the role of the S₀/S₁ CI in the CL efficiency and point out misunderstandings in some theoretical studies on the singlet chemiexcitations of cyclic peroxides. Finally, we address the challenges and future prospects in theoretically calculating S₀/S₁ CIs and simulating the dynamics and chemiexcitation efficiency in the CL of cyclic peroxides.

Conical Intersections in Solution with Polarizable Embedding: Integral-Exact Direct Reaction Field

A common strategy to exploring the properties and reactivity of complex systems is to use quantum mechanics/molecular mechanics (QM/MM) embedding, wherein a QM region is defined and treated with electronic structure theory, and the remainder of the system is treated with a force field. Important to the description of electronic excited states, especially those of charge-transfer character, is the treatment of the coupling between the QM and MM subsystems. The state of the art is to use a polarizable force field for the MM region and mutually couple the QM wavefunction and MM induced dipoles, in addition to the usual electrostatic embedding, yielding a polarizable embedding (QM/MM-Pol) approach. However, we showed previously that current popular QM/MM-Pol approaches exhibit issues of root flipping and/or incorrect descriptions of electronic crossings in multistate calculations [J. Chem. Theory Comput. 14, 2137 (2018)]. Here, we demonstrate a solution to these problems with an integral-exact reformulation of the direct reaction field approach of Thole and Van Duijnen (QM/MM-IEDRF). The resulting embedding potential includes one- and two-electron operators and many-body dipole-induced dipole interactions and thus includes a natural description of the screening of electron-electron interactions by the MM induced dipoles. Pauli repulsion from the environment is mimicked by effective core potentials on the MM atoms. Inherent to the DRF approach is the assumption that MM dipoles respond instantaneously to the positions of the QM electrons; therefore, dispersion interactions are captured approximately. All electronic states are eigenfunctions of the same Hamiltonian, while the polarization induced in the environment and the associated energetic stabilization are unique to each state. This allows for a consistent definition of transition properties and state crossings. We demonstrate QM/MM-IEDRF by exploring the influence of a (polarizable) inert xenon matrix environment on the conical intersection underlying the photoisomerization of ethylene.

Method to Compute the Solute-Solvent Dispersion Contribution to the Electronic Excitation Energy in Solution

A method formulated within the polarizable continuum model of the solvent and a quantum Monte Carlo treatment of the electronic states of the solute molecule is presented for the calculation of the solute–solvent dispersion contribution to the electronic excitation energy in solution. Variational quantum Monte Carlo is exploited to measure the fluctuations of the electronic electric field of the solute molecule to compute the London’s dispersion forces with the solvent. The method previously applied to the ground state of the solute is here extended to excited states. To perform the Casimir–Polder integration, we introduce a positive parameter Ω whose value is properly chosen for this purpose. We derive a general expression that for Ω = 0 reduces to that already proposed for the ground state. For an excited state, Ω must be less than the first transition electronic energy of the solvent molecule but greater than the transition energy from the ground to excited electronic state of the solute molecule. Benchmark calculations were performed on the n → π* transition for formaldehyde, acrolein, and acetone in six solvents, including water, ethanol, cyclohexane, chloroform, carbon tetrachloride, and toluene, and the π → π* transition of acrolein in cyclohexane. Solvents are characterized by their ionization potential and the refractive index at frequency Ω. In all cases, we found that the dispersion solute–solvent interaction stabilizes the excited state of the solutes leading to red (negative) solvatochromic shifts.

Evaluation of molecular photophysical and photochemical properties using linear response time-dependent density functional theory with classical embedding: Successes and challenges

Time-dependent density functional theory (TDDFT) based approaches have been developed in recent years to model the excited-state properties and transition processes of the molecules in the gas-phase and in a condensed medium, such as in a solution and protein microenvironment or near semiconductor and metal surfaces. In the latter case, usually, classical embedding models have been adopted to account for the molecular environmental effects, leading to the multi-scale approaches of TDDFT/polarizable continuum model (PCM) and TDDFT/molecular mechanics (MM), where a molecular system of interest is designated as the quantum mechanical region and treated with TDDFT, while the environment is usually described using either a PCM or (non-polarizable or polarizable) MM force fields. In this Perspective, we briefly review these TDDFT-related multi-scale models with a specific emphasis on the implementation of analytical energy derivatives, such as the energy gradient and Hessian, the nonadiabatic coupling, the spin-orbit coupling, and the transition dipole moment as well as their nuclear derivatives for various radiative and radiativeless transition processes among electronic states. Three variations of the TDDFT method, the Tamm-Dancoff approximation to TDDFT, spin-flip DFT, and spin-adiabatic TDDFT, are discussed. Moreover, using a model system (pyridine-Ag20 complex), we emphasize that caution is needed to properly account for system-environment interactions within the TDDFT/MM models. Specifically, one should appropriately damp the electrostatic embedding potential from MM atoms and carefully tune the van der Waals interaction potential between the system and the environment. We also highlight the lack of proper treatment of charge transfer between the quantum mechanics and MM regions as well as the need for accelerated TDDFT modelings and interpretability, which calls for new method developments.

A simplified charge projection scheme for long-range electrostatics in ab initio QM/MM calculations

In a previous work [Pan et al., Molecules 23, 2500 (2018)], a charge projection scheme was reported, where outer molecular mechanical (MM) charges [>10 Å from the quantum mechanical (QM) region] were projected onto the electrostatic potential (ESP) grid of the QM region to accurately and efficiently capture long-range electrostatics in ab initio QM/MM calculations. Here, a further simplification to the model is proposed, where the outer MM charges are projected onto inner MM atom positions (instead of ESP grid positions). This enables a representation of the long-range MM electrostatic potential via augmentary charges (AC) on inner MM atoms. Combined with the long-range electrostatic correction function from Cisneros et al. [J. Chem. Phys. 143, 044103 (2015)] to smoothly switch between inner and outer MM regions, this new QM/MM-AC electrostatic model yields accurate and continuous ab initio QM/MM electrostatic energies with a 10 Å cutoff between inner and outer MM regions. This model enables efficient QM/MM cluster calculations with a large number of MM atoms as well as QM/MM calculations with periodic boundary conditions.

Combining multilevel Hartree–Fock and multilevel coupled cluster approaches with molecular mechanics: a study of electronic excitations in solutions

We present the coupling of different quantum-embedding approaches with a third molecular-mechanics layer, which can be either polarizable or non-polarizable.

A Many-Body, Fully Polarizable Approach to QM/MM Simulations

We present a new development in quantum mechanics/molecular mechanics (QM/MM) methods by replacing conventional MM models with data-driven many-body (MB) representations rigorously derived from high-level QM calculations. The new QM/MM approach builds on top of mutually polarizable QM/MM schemes developed for polarizable force fields with inducible dipoles and uses permutationally invariant polynomials to effectively account for quantum-mechanical contributions (e.g., exchange-repulsion and charge transfer and penetration) that are difficult to describe by classical expressions adopted by conventional MM models. Using the many-body MB-pol and MB-DFT potential energy functions for water, which include explicit two-body and three-body terms fitted to reproduce the corresponding CCSD(T) and PBE0 two-body and three-body energies for water, we demonstrate a smooth energetic transition as molecules are transferred between QM and MM regions, without the need of a transition layer. By effectively elevating the accuracy of both the MM region and the QM/MM interface to that of the QM region, the new QM/MB-MM approach achieves an accuracy comparable to that obtained with a fully QM treatment of the entire system.

Molecular spectroscopy of aqueous solutions: a theoretical perspective

Computational spectroscopy is an invaluable tool to both accurately reproduce the spectra of molecular systems and provide a rationalization for the underlying physics. However, the inherent difficulty to accurately model systems in aqueous solutions, owing to water's high polarity and ability to form hydrogen bonds, has severely hampered the development of the field. In this tutorial review we present a technique developed and tested in recent years based on a fully atomistic and polarizable classical modeling of water coupled with a quantum mechanical description of the solute. Thanks to its unparalleled accuracy and versatility, this method can change the perspective of computational and experimental chemists alike.

Absorption spectra of xanthines in aqueous solution: a computational study

We present a detailed computational analysis of the UV/Vis spectra of caffeine, paraxanthine and theophylline in aqueous solution. A hierarchy of solvation approaches for modeling the aqueous environment have been tested, ranging from the continuum model to the non-polarizable and polarizable quantum mechanical (QM)/molecular mechanics (MM) models, with and without the explicit inclusion of water molecules in the QM portion. The computed results are directly compared with the experimental data, thus highlighting the role of electrostatic, polarization and hydrogen boding solute-solvent interactions.

Polarizable embedding QM/MM: the future gold standard for complex (bio)systems?

We provide a perspective of the induced dipole formulation of polarizable QM/MM, showing how efficient implementations will enable their application to the modeling of dynamics, spectroscopy, and reactivity in complex biosystems.

Electronic transitions for a fully polarizable QM/MM approach based on fluctuating charges and fluctuating dipoles: Linear and corrected linear response regimes

The fully polarizable Quantum Mechanics/Molecular Mechanics (QM/MM) approach based on fluctuating charges and fluctuating dipoles, named QM/FQFμ [T. Giovannini et al., J. Chem. Theory Comput. 15, 2233 (2019)], is extended to the calculation of vertical excitation energies of solvated molecular systems. Excitation energies are defined within two different solvation regimes, i.e., linear response (LR), where the response of the MM portion is adjusted to the QM transition density, and corrected-Linear Response (cLR) in which the MM response is adjusted to the relaxed QM density, thus being able to account for charge equilibration in the excited state. The model, which is specified in terms of three physical parameters (electronegativity, chemical hardness, and polarizability) is applied to vacuo-to-water solvatochromic shifts of aqueous solutions of para-nitroaniline, pyridine, and pyrimidine. The results show a good agreement with their experimental counterparts, thus highlighting the potentialities of this approach.

SAMPL6 host-guest challenge: binding free energies via a multistep approach

In this effort in the SAMPL6 host-guest binding challenge, a combination of molecular dynamics and quantum mechanical methods were used to blindly predict the host-guest binding free energies of a series of cucurbit[8]uril (CB8), octa-acid (OA), and tetramethyl octa-acid (TEMOA) hosts bound to various guest molecules in aqueous solution. Poses for host-guest systems were generated via molecular dynamics (MD) simulations and clustering analyses. The binding free energies for the structures obtained via cluster analyses of MD trajectories were calculated using the MMPBSA method and density functional theory (DFT) with the inclusion of Grimme's dispersion correction, an implicit solvation model to model the aqueous solution, and the resolution-of-the-identity (RI) approximation (MMPBSA, RI-B3PW91-D3, and RI-B3PW91, respectively). Among these three methods tested, the results for OA and TEMOA systems showed MMPBSA and RI-B3PW91-D3 methods can be used to qualitatively rank binding energies of small molecules with an overbinding by 7 and 37 kcal/mol respectively, and RI-B3PW91 gave the poorest quality results, indicating the importance of dispersion correction for the binding free energy calculations. Due to the complexity of the CB8 systems, all of the methods tested show poor correlation with the experimental results. Other quantum mechanical approaches used for the calculation of binding free energies included DFT without the RI approximation, utilizing truncated basis sets to reduce the computational cost (memory, disk space, CPU time), and a corrected dielectric constant to account for ionic strength within the implicit solvation model.

Exchange-repulsion energy in QM/EFP

The effective fragment potential (EFP) is a quantum mechanics (QM)-based model designed to accurately describe intermolecular interactions. Hybrid QM/EFP calculations combine quantum mechanical methods with an EFP embedding to study complex systems in which many-body effects are relevant. As in EFP-only calculations, non-bonded interactions between the QM region and EFP fragments are computed as a sum of electrostatic, polarization, dispersion, and exchange-repulsion energies. The exchange-repulsion term is a computational bottleneck of the EFP calculations. Here, we present a general procedure for computing the QM/EFP exchange-repulsion interactions based on one-electron contributions to the QM Hamiltonian, by using Gaussian functions to represent localized molecular orbitals of the effective fragments. The accuracy of the exchange-repulsion and total QM/EFP interaction energies is evaluated on a diverse set of dimers, including complexes from the S22 dataset of non-covalent interactions. In most cases, the QM/EFP energies are at least as accurate as corresponding EFP energies. A simple and computationally efficient form of the introduced QM/EFP exchange-repulsion term will facilitate further developments and applications of QM/EFP methods.