Relative alchemical binding free energy calculations are routinely used in drug discovery projects to optimize the affinity of small molecules for their drug targets. Alchemical methods can also be used to estimate the impact of amino acid mutations on protein:protein binding affinities, but these calculations can involve sampling challenges due to the complex networks of protein and water interactions frequently present in protein:protein interfaces. We investigate these challenges by extending a graphics processing unit (GPU)-accelerated open-source relative free energy calculation package (Perses) to predict the impact of amino acid mutations on protein:protein binding. Using the well-characterized model system barnase:barstar, we describe analyses for identifying and characterizing sampling problems in protein:protein relative free energy calculations. We find that mutations with sampling problems often involve charge-changes, and inadequate sampling can be attributed to slow degrees of freedom that are mutation-specific. We also explore the accuracy and efficiency of current state-of-the-art approaches─alchemical replica exchange and alchemical replica exchange with solute tempering─for overcoming relevant sampling problems. By employing sufficiently long simulations, we achieve accurate predictions (RMSE 1.61, 95% CI: [1.12, 2.11] kcal/mol), with 86% of estimates within 1 kcal/mol of the experimentally determined relative binding free energies and 100% of predictions correctly classifying the sign of the changes in binding free energies. Ultimately, we provide a model workflow for applying protein mutation free energy calculations to protein:protein complexes, and importantly, catalog the sampling challenges associated with these types of alchemical transformations. Our free open-source package (Perses) is based on OpenMM and is available at https://github.com/choderalab/perses.

Linear response time-dependent density functional theory (TDDFT) is widely applied to valence, Rydberg, and charge-transfer excitations but, in its current form, makes large errors for core-electron excitations. This work demonstrates that the admixture of nonlocal exact exchange in atomic core regions significantly improves TDDFT-predicted core excitations. Exact exchange admixture is accomplished using projected hybrid density functional theory [ J. Chem. Theory Comput. 2023, 19, 837−847]. Scalar relativistic TDDFT calculations using core-projected B3LYP accurately model core excitations of second-period elements C–F and third-period elements Si–Cl, without sacrificing performance for the relative shifts of core excitation energies. Predicted K-edge X-ray near absorption edge structure (XANES) of a series of sulfur standards highlight the value of this approach. Core-projected hybrids appear to be a practical solution to TDDFT’s limitations for core excitations, in the way that long-range-corrected hybrids are a practical solution to TDDFT’s limitations for Rydberg and charge-transfer excitations.

We report the development and benchmark of multireference algebraic diagrammatic construction theory (MR-ADC) for the simulations of core-excited states and X-ray absorption spectra (XAS). Our work features an implementation that incorporates core-valence separation into the strict and extended second-order MR-ADC approximations (MR-ADC(2) and MR-ADC(2)-X), providing efficient access to high-energy excited states without including inner-shell orbitals in the active space. Benchmark results on a set of small molecules indicate that at equilibrium geometries, the accuracy of MR-ADC is similar to that of single-reference ADC theory when static correlation effects are not important. In this case, MR-ADC(2)-X performs similarly to single- and multireference coupled cluster methods in reproducing the experimental XAS peak spacings. We demonstrate the potential of MR-ADC for chemical systems with multiconfigurational electronic structure by calculating the K-edge XAS spectrum of the ozone molecule with a multireference character in its ground electronic state and the dissociation curve of core-excited molecular nitrogen. For ozone, the MR-ADC results agree well with the data from experimental and previous multireference studies of ozone XAS, in contrast to the results of single-reference methods, which underestimate relative peak energies and intensities. The MR-ADC methods also predict the correct shape of the core-excited nitrogen potential energy curve, and are in good agreement with accurate calculations using driven similarity renormalization group approaches. These findings suggest that MR-ADC(2) and MR-ADC(2)-X are promising methods for the XAS simulations of multireference systems and pave the way for their efficient computer implementation and applications.

Ligand design problems involve searching chemical space for a molecule with a set of desired properties. As chemical space is discrete, this search must be conducted in a pointwise manner, separately investigating one molecule at a time, which can be inefficient. We propose a method called “Flexible Topology”, where a ligand is composed of a set of shapeshifting “ghost” atoms, whose atomic identities and connectivity can dynamically change over the course of a simulation. Ghost atoms are guided toward their target positions using a translation-, rotation-, and index-invariant restraint potential. This is the first step toward a continuous model of chemical space, where a dynamic simulation can move from one molecule to another by following gradients of a potential energy function. This builds on a substantial history of alchemy in the field of molecular dynamics simulation, including the Lambda dynamics method developed by Brooks and co-workers [X. Kong and C.L. Brooks III, J. Chem. Phys. 105, 2414 (1996)], but takes it to an extreme by associating a set of four dynamical attributes with each shapeshifting ghost atom that control not only its presence but also its atomic identity. Here, we outline the theoretical details of this method, its implementation using the OpenMM simulation package, and some preliminary studies of ghost particle assembly simulations in vacuum. We examine a set of 10 small molecules, ranging in size from 6 to 50 atoms, and show that Flexible Topology is able to consistently assemble all of these molecules to high accuracy, beginning from randomly initialized positions and attributes.

We present a novel method for the automatic detection of pockets on protein molecular surfaces. The algorithm is based on an ad hoc hierarchical clustering of virtual probe spheres obtained from the geometrical primitives used by the NanoShaper software to build the solvent-excluded molecular surface. The final ranking of putative pockets is based on the Isolation Forest method, an unsupervised learning approach originally developed for anomaly detection. A detailed importance analysis of pocket features provides insight into which geometrical (clustering) and chemical (amino acidic composition) properties characterize a good binding site. The method also provides a segmentation of pockets into smaller subpockets. We prove that subpockets are a convenient representation to pinpoint the binding site with great precision. SiteFerret is outstanding in its versatility, accurately predicting a wide range of binding sites, from those binding small molecules to those binding peptides, including difficult shallow sites.

Similarity-transformed equation-of-motion coupled-cluster theory (STEOM-CC) is an alternative approach to equation-of-motion coupled-cluster theory for excited states (EOMEE-CC), which uses a second similarity transformation of the Hamiltonian, followed by diagonalization in a small (CI singles-like) excitation space, even when single and double excitations are included in the transformation. In addition to vertical excitation energies, transition moments measure the strength of the interactions between states determining absorption, emission, and other processes. In STEOM-CCSD, transition moments are calculated in a straightforward manner as biorthogonal expectation values using both the left- and right-hand solutions, with the main difference from EOMEE-CC being the inclusion of the transformation operator. We recently developed an extension of STEOM-CCSD to core excitations, CVS-STEOM-CCSD+cT, which includes triple excitations and the well-known core-valence separation for the core ionization potential calculations. In this work, we derived transition moments for core-excited states with core triple excitations, including both ground-to-core-excited and valence-to-core-excited transitions. The improvement of the computed transition moments of the CVS-STEOM-CCSD+cT method is compared to standard CVS-STEOMEE-CCSD and CVS-EOMEE-CCSD for our previously published small-molecule benchmark set.

The study of the interactions of chemical systems in a cavity and the ability to control the reactions inside the cavities become an evolving and hot field of research. Despite that, there is still a significant gap between experiment and theory. Herein, we aim to bridge this gap by starting with the analysis of solvable analytical models for reactions inside a cavity, then continuing to realistic models for many molecules inside a single mode and in a multimode cavity. In addition, we investigate different ways to control the strength of the molecule–cavity coupling term, which in turn allows controlling chemical reactions. Our analysis can benefit the development of ab initio computational methods to simulate molecular systems in polariton cavities; in addition, we show how to parameterize the model Hamiltonians in order to simulate a specific molecular system. Finally, we demonstrate the possibility of achieving isomerization, in case it is prohibited out of the cavity, by placing the reaction inside a cavity.

Simulating the conformations and functions of biological macromolecules by using all-atom (AA) models is a challenging task due to expensive computational costs. One possible strategy to solve this problem is to develop hybrid all-atom and ultra-coarse-grained (AA/UCG) models of the biological macromolecules. In the AA/UCG scheme, the interest regions are described by AA models, while the other regions are described in the UCG representation. In this study, we develop the hybrid AA/UCG models and apply them to investigate the conformational changes of microtubule-bound tubulins. The simulation results of the hybrid models elucidated the mechanism of why the taxol molecules selectively bound microtubules but not tubulin dimers. In addition, we also explore the interactions of the microtubules and dyneins. Our study shows that the hybrid AA/UCG model has great application potential in studying the function of complex biological systems.

We have recently constructed compact, CNOT-efficient, quantum circuits for Fermionic and qubit excitations of arbitrary many-body rank [Magoulas, I.; Evangelista, F. A. J. Chem. Theory Comput. 2023, 19, 822]. Here, we present approximations of these circuits that substantially reduce the CNOT counts even further. Our preliminary numerical data, using the selected projective quantum eigensolver approach, show up to a 4-fold reduction in CNOTs. At the same time, there is practically no loss of accuracy in the energies compared to the parent implementation, while the ensuing symmetry breaking is essentially negligible.

Induced dipole models have proven to be effective tools for simulating electronic polarization effects in biochemical processes, yet their potential has been constrained by energy conservation issue, particularly when historical data is utilized for dipole prediction. This study identifies error outliers as the primary factor causing this failure of energy conservation and proposes a comprehensive scheme to overcome this limitation. Leveraging maximum relative errors as a convergence metric, our data demonstrates that energy conservation can be upheld even when using historical information for dipole predictions. Our study introduces the multi-order extrapolation method to quicken induction iteration and optimize the use of historical data, while also developing the preconditioned conjugate gradient with local iterations to refine the iteration process and effectively remove error outliers. This scheme further incorporates a “peek” step via Jacobi under-relaxation for optimal performance. Simulation evidence suggests that our proposed scheme can achieve energy convergence akin to that of point-charge models within a limited number of iterations, thus promising significant improvements in efficiency and accuracy.

Redox-active organic molecules, i.e., molecules that can relatively easily accept and/or donate electrons, are ubiquitous in biology, chemical synthesis, and electronic and spintronic devices, such as solar cells and rechargeable batteries, etc. Choosing the best candidates from an essentially infinite chemical space for experimental testing in a target application requires efficient screening approaches. In this Review, we discuss modern in silico techniques for predicting reduction and oxidation potentials of organic molecules that go beyond conventional first-principles computations and thermodynamic cycles. Approaches ranging from simple linear fits based on molecular orbital energy approximation and energy difference approximation to advanced regression and neural network machine learning algorithms employing complex descriptors of molecular compositions, geometries, and electronic structures are examined in conjunction with relevant literature examples. We discuss the interplay between ab initio data and machine learning (ML), i.e., whether it is better to base predictions on low-level quantum-chemical results corrected with ML or to bypass first-principles computations entirely and instead rely on elaborate deep learning architectures. Finally, we list currently available data sets of redox-active organic molecules and their experimental and/or computed properties to facilitate the development of screening platforms and rational design of redox-active organic molecules.

Coarse-grained (CG) simulations are an important computational tool in chemistry and materials science. Recently, systematic “bottom-up” CG models have been introduced to capture electronic structure variations of molecules and polymers at the CG resolution. However, the performance of these models is limited by the ability to select reduced representations that preserve electronic structure information, which remains a challenge. We propose two methods for (i) identifying important electronically coupled atomic degrees of freedom and (ii) scoring the efficacy of CG representations used in conjunction with CG electronic predictions. The first method is a physically motivated approach that incorporates nuclear vibrations and electronic structure derived from simple quantum chemical calculations. We complement this physically motivated approach with a machine learning technique based on the marginal contribution of nuclear degrees of freedom to electronic prediction accuracy using an equivariant graph neural network. By integrating these two approaches, we can both identify critical electronically coupled atomic coordinates and score the efficacy of arbitrary CG representations for making electronic predictions. We leverage this capability to make a connection between optimized CG representations and the future potential for “bottom-up” development of simplified model Hamiltonians incorporating nonlinear vibrational modes.

Grand canonical ensemble (GCE) modeling of electrochemical interfaces, in which the electrochemical potential is converged to a preset constant, is essential for understanding electrochemistry and electrocatalysis at the electrodes. However, it requires developing efficient and robust algorithms to perform practical and effective GCE modeling with density functional theory (DFT) calculations. Herein, we developed an efficient and robust fully converged constant-potential (FCP) algorithm based on Newton’s method and a polynomial fitting to calculate the necessary derivative for DFT calculations. We demonstrated with the constant-potential geometry optimization and Born–Oppenheimer molecular dynamics (BOMD) calculations that our FCP algorithm is resistant to the numerical instability that plagues other algorithms, and it delivers efficient convergence to the preset electrochemical potential and renders accurate forces for updating the nuclear positions of an electronically open system, outperforming other algorithms. The implementation of our FCP algorithm enables flexibility in using various computational codes and versatility in performing advanced tasks including the constant-potential enhanced-sampling BOMD simulations that we showcased with the modeling of the electrochemical hydrogenation of CO, and it is thus expected to find a wide spectrum of applications in the modeling of chemistry at electrochemical interfaces.

Gauge invariance is a fundamental symmetry connected to charge conservation and is widely accepted as indispensable for any electronic structure method. Hence, the gauge variance of the time-dependent kinetic energy density τ used in many meta-generalized gradient approximations (MGGAs) to the exchange-correlation (XC) functional presents a major obstacle for applying MGGAs within time-dependent density functional theory (TDDFT). Replacing τ by the gauge-invariant generalized kinetic energy density τ̂ significantly improves the accuracy of various functionals for vertical excitation energies [R. Grotjahn, F. Furche, and M. Kaupp. J. Chem. Phys. 2022, 157, 111102]. However, the dependence of the resulting current-MGGAs (cMGGAs) on the paramagnetic current density gives rise to new exchange-correlation kernels and hyper-kernels ignored in previous implementations of quadratic and higher-order response properties. Here we report the first implementation of cMGGAs and hybrid cMGGAs for excited-state gradients and dipole moments, as well as an extension to quadratic response properties including dynamic hyperpolarizabilities and two-photon absorption cross sections. In the first comprehensive benchmark study of MGGAs and cMGGAs for two-photon absorption cross sections, the M06-2X functional is found to be superior to the GGA hybrid PBE0. Additionally, two case studies from the literature for the practical prediction of nonlinear optical properties are revisited and potential advantages of hybrid (c)MGGAs compared to hybrid GGAs are discussed. The effect of restoring gauge invariance varies depending on the employed MGGA functional, the type of excitation, and the property under investigation: While some individual excited-state equilibrium structures are significantly affected, on average, these changes result in marginal improvements when compared against high-level reference data. Although the gauge-variant MGGA quadratic response properties are generally close to their gauge-invariant counterparts, the resulting errors are not bounded and significantly exceed typical method errors in some of the cases studied. Despite the limited effects seen in benchmark studies, gauge-invariant implementations of cMGGAs for excited-state properties are desirable from a fundamental perspective, entail little additional computational cost, and are necessary for response properties consistent with cMGGA linear response calculations such as excitation energies.

Bolapolyphiles constitute a versatile class of materials with a demonstrated potential to form a wide variety of complex ordered mesophases. In particular, cubic network phases (like the gyroid, primitive, and diamond phases) have been a target of many studies for their ability to create percolating 3D nanosized channels. In this study, molecular simulations are used to explore the phase behavior of bolapolyphiles containing a rigid rodlike core, associating hydrophilic core ends and a hydrophobic side chain with a multident architecture, i.e., where the branching pattern can vary from bident (two branches) to hexadent (six branches). Upon network phase formation, its skeleton is made up of “nodes” populated by the core ends and “struts” populated by the cores. It is shown that, by varying the side chain length, branching pattern, and attachment point to the core, one can alter the crowding around the cores and hence tune the nodal size and nodal valence (i.e., number of connecting struts) which lead to different types of network morphologies. For example, for a fixed total side chain length, having more branches generates a stronger crowding around the molecular core, driving them to form bundlelike domains with curvier interfaces that result in thinner struts. Also, attaching the lateral chain closer to one core end breaks the symmetry between the environments around the two core ends, leading to networks with bimodal nodal sizes. Importantly, since the characterization of (ordered or partially ordered) network phases is challenging given the potential incompatibilities between the simulation box size with the structure’s space group periodic symmetry and the effect of morphological defects, a detailed framework is presented to analyze and fully characterize the unit cell parameters and structure factor of such systems.

An overview of the approximations in the explicitly correlated local coupled cluster methods PNO-LCCSD(T)-F12 in Molpro and DLPNO-CCSD(T)F12 in ORCA is given. Options to select the domains of projected atomic orbitals (PAOs), pair natural orbitals (PNOs), and triples natural orbitals (TNOs) in both programs are described and compared in detail. The two programs are applied to compute isomerization and conformational energies of the ISOL24 and ACONFL test sets, where the former is part of the GMTKN55 benchmark suite. Thorough studies of basis set effects are presented for selected systems. These revealed large intramolecular basis set superposition effects that make it practically impossible to reliably determine the complete basis set (CBS) limits without including explicitly correlated terms. The latter strongly reduce the basis set dependence and at the same time also errors caused by the local domain approximations. On the basis of these studies, the PNO-LCCSD(T)-F12 method is applied to determine new reference energies for the above-mentioned benchmark sets. We are confident that our results should agree within a few tenths of a kcal mol–1 with the (unknown) CCSD(T)/CBS values, which therefore allowed us to define computational settings for accurate explicitly correlated local coupled cluster methods with moderate computational effort. With these protocols, especially PNO-LCCSD(T)-F12b/AVTZ′, reliable reference values for comprehensive benchmark sets can be generated efficiently. This can significantly advance the development and evaluation of the performance of approximate electronic structure methods, especially improved density functional approximations or machine learning approaches.

Intrinsically disordered proteins (IDPs) play a critical role in many biological processes. Due to the inherent structural flexibility of IDPs, experimental methods present significant challenges for sampling their conformational information at the atomic level. Therefore, molecular dynamics (MD) simulations have emerged as the primary tools for modeling IDPs whose accuracy depend on force field and water model. To enhance the accuracy of physical modeling of IDPs, several force fields have been developed. However, current water models lack precision and underestimate the interaction between water molecules and proteins. Here, we used Monte-Carlo re-weighting method to re-parameterize a three-point water model based on OPC3 for IDPs (named OPC3-B). We benchmarked the performance of OPC3-B compared with nine different water models for 10 IDPs and three ordered proteins. The results indicate that the performance of OPC3-B is better than other water models for both IDPs and ordered proteins. At the same time, OPC3-B possess the power of transferability with other force field to simulate IDPs. This newly developed water model can be used to insight into the research of sequence-disordered-function paradigm for IDPs.

Defining a theoretical model systematically delivering accurate ab initio predictions of the fluorescence quantum yields of organic dyes is highly desirable for designing improved fluorophores in a systematic rather than trial-and-error way. To this end, the first required step is to obtain reliable radiative rates (kr), as low kr typically precludes effective emission. In the present contribution, using a series of 10 substituted phenyls with known experimental kr, we analyze the impact of the computational protocol on the kr determined through the thermal vibration correlation function (TVCF) approach on the basis of time-dependent density functional theory (TD-DFT) calculations of the energies, structures, and vibrational parameters. Both the electronic structure (selected exchange–correlation functional, application or not of the Tamm–Dancoff approximation) and the vibronic parameters (line-shape formalism, coordinate system, potential energy surface model, and dipole expansion) are tackled. Considering all possible combinations yields more than 3500 cases, allowing to extract statistically-relevant information regarding the impact of each computational parameter on the magnitude of the estimated kr. It turns out that the selected vibronic model can have a significant impact on the computed kr, especially the potential energy surface model. This effect is of the same order of magnitude as the difference noted between B3LYP and CAM-B3LYP estimates. For the treated compounds, all evaluated functionals do deliver reasonable trends, fitting the experimental values.

Understanding frictional phenomena is a fascinating fundamental problem with huge potential impact on energy saving. Such an understanding requires monitoring what happens at the sliding buried interface, which is almost inaccessible by experiments. Simulations represent powerful tools in this context, yet a methodological step forward is needed to fully capture the multiscale nature of the frictional phenomena. Here, we present a multiscale approach based on linked ab initio and Green’s function molecular dynamics, which is above the state-of-the-art techniques used in computational tribology as it allows for a realistic description of both the interfacial chemistry and energy dissipation due to bulk phonons in nonequilibrium conditions. By considering a technologically relevant system composed of two diamond surfaces with different degrees of passivation, we show that the presented method can be used not only for monitoring in real-time tribolochemical phenomena such as the tribologically induced surface graphitization and passivation effects but also for estimating realistic friction coefficients. This opens the way to in silico experiments of tribology to test materials to reduce friction prior to that in real labs.

We introduce a novel three-body correlation factor that is designed to vanish in the core region around each nucleus and approach a universal two-body correlation factor for valence electrons. The transcorrelated Hamiltonian is used to optimize the orbitals of a single Slater determinant within a biorthonormal framework. The Slater–Jastrow wave function is optimized on a set of atomic and molecular systems containing both second-row elements and 3d transition metal elements. The optimization of the correlation factor and the orbitals, along with an increase in the basis set, results in a systematic lowering of the variational Monte Carlo energy for all systems tested. Importantly, the optimal parameters of the correlation factor obtained for atomic systems can be transferred to molecules. Additionally, the present correlation factor is computationally efficient and uses a mixed analytical–numerical integration scheme that reduces the costly numerical integration from R6${\mathbb{R}}^6$ to R3${\mathbb{R}}^3$.