First-Principles Models for van der Waals Interactions in Molecules and Materials: Concepts, Theory, and Applications

Advancements and Challenges in the Integration of Indium Arsenide and Van der Waals Heterostructures

The strategic integration of low-dimensional InAs-based materials and emerging van der Waals systems is advancing in various scientific fields, including electronics, optics, and magnetics. With their unique properties, these InAs-based van der Waals materials and devices promise further miniaturization of semiconductor devices in line with Moore's Law. However, progress in this area lags behind other 2D materials like graphene and boron nitride. Challenges include synthesizing pure crystalline phase InAs nanostructures and single-atomic-layer 2D InAs films, both vital for advanced van der Waals heterostructures. Also, diverse surface state effects on InAs-based van der Waals devices complicate their performance evaluation. This review discusses the experimental advances in the van der Waals epitaxy of InAs-based materials and the working principles of InAs-based van der Waals devices. Theoretical achievements in understanding and guiding the design of InAs-based van der Waals systems are highlighted. Focusing on advancing novel selective area growth and remote epitaxy, exploring multi-functional applications, and incorporating deep learning into first-principles calculations are proposed. These initiatives aim to overcome existing bottlenecks and accelerate transformative advancements in integrating InAs and van der Waals heterostructures.

Four-Dimensional Scaling of Dipole Polarizability: From Single-Particle Models to Atoms and Molecules

Scaling laws enable the determination of physicochemical properties of molecules and materials as a function of their size, density, number of electrons or other easily accessible descriptors. Such relations can be counterintuitive and nonlinear, and ultimately yield much needed insight into quantum mechanics of many-particle systems. In this work, we show on the basis of single-particle models, multielectron atoms and molecules that the dipole polarizability of quantum systems is generally proportional to the fourth power of a characteristic length, computed from the ground-state wave function. This four-dimensional (4D) scaling is independent of the ratio of bound-to-bound and bound-to-continuum electronic transitions and applies to many-electron atoms when a correlated length metric is used. Finally, this scaling law is applied to predict the polarizability of molecules by electrostatically coupled atoms-in-molecules approach, obtaining approximately 8% absolute and relative accuracy with respect to hybrid density functional theory (DFT) on the QM7-X data set of organic molecules, providing an efficient and scalable model for the anisotropic polarizability tensors of extended (bio)molecules.

Electrocatalysis in deep eutectic solvents: from fundamental properties to applications

Electrocatalysis stands out as a promising avenue for synthesizing high-value products with minimal environmental footprint, aligning with the imperative for sustainable energy solutions. Deep eutectic solvents (DESs), renowned for their eco-friendly, safe, and cost-effective nature, present myriad advantages, including extensive opportunities for material innovation and utilization as reaction media in electrocatalysis. This review initiates with an exposition on the distinctive features of DESs, progressing to explore their applications as solvents in electrocatalyst synthesis and electrocatalysis. Additionally, it offers an insightful analysis of the challenges and prospects inherent in electrocatalysis within DESs. By delving into these aspects comprehensively, this review aims to furnish a nuanced understanding of DESs, thus broadening their horizons in the realm of electrocatalysis and facilitating their expanded application.

Studying the adsorption of emerging organic contaminants in zeolites with dispersion-corrected density functional theory calculations: From numbers to recommendations

Adsorption energies obtained from dispersion-corrected density functional theory (DFT) calculations show a considerable dependence on the choice of exchange-correlation functional and dispersion correction. A number of investigations have employed different approaches to compute adsorption energies of small molecules in zeolites, using reference values from high-level calculations and/or experiments. Such comparative studies are lacking for larger functional organic molecules such as pharmaceuticals or personal care products, despite their potential relevance for applications, e. g., in contaminant removal or drug delivery. The present study aims to fill this gap by comparing adsorption energies and, for selected cases, equilibrium structures of emerging organic contaminants adsorbed in MOR- and FAU-type all-silica zeolites. A total of 13 dispersion-corrected DFT approaches are compared, including methods using a pairwise dispersion correction as well as non-local van der Waals density functionals. While absolute values of adsorption energies vary widely, qualitative trends across the set of zeolite-guest combinations are not strongly dependent on the choice of functional. For selected cluster models, DFT adsorption energies are compared to reference values from coupled cluster (DLPNO-CCSD(T)) calculations. Although all DFT approaches deliver systematically more negative adsorption energies than the coupled cluster reference, this tendency is least pronounced for the rev-vdW-DF2 functional.

Estimating Binding Energies of π-Stacked Aromatic Dimers Using Force Field-Driven Molecular Dynamics

π-π stacking are omnipresent interactions, crucial in many areas of chemistry, and often studied using quantum chemical methods. Here, we report a simple and computationally efficient method of estimating the binding energies of stacked polycyclic aromatic hydrocarbons based on steered molecular dynamics. This method leverages the force field parameters for accurate calculation. The presented results show good agreement with those obtained through DFT at the ωB97X-D3/cc-pVQZ level of theory. It is demonstrated that this force field-driven SMD method can be applied to other aromatic molecules, allowing insight into the complexity of the stacking interactions and, more importantly, reporting π-π stacking energy values with reasonable precision.

London Dispersion Effects on the Structure and Properties of Nonlinear Optical BiB3O6 Crystal

α-BiB3O6 (BiBO) is an important nonlinear optical (NLO) material with high efficiency for applications in harmonic generations and quantum technology. Owing to its low symmetry and cooperative Bi3+ lone pair arrangement, it has also exceptional large piezoelectric and electro-optic coefficients and strong anisotropies on other material characteristics. Previous theoretical calculations on its physical (mainly optical) properties often gave confusing results. It is found here that London dispersion (LD) tends to stabilize structures with closer pack entities like lone pair heavy ion Bi3+ with large polarizabilities, which is ignored in most previous density functional theory (DFT) calculations. Present study shows that without considering the LD effect, the structure of α-BiB3O6 (BiBO) was predicted with an over-estimated (by over 10 %) unique b-axis while underestimates a and overestimates c in a less amount. Consequently it is not possible to use the calculated structure to obtain meaningful properties of this important material. By applying a modified post-DFT LD correction based on linear combination of atomic orbitals (LCAO) and B3LYP functional, the experimental structure is well reproduced with the theoretical optimized one. Many important material property tensors of BiBO crystal are calculated in unprecedented precisions, including: dielectric constants (static and in THz range), elastic and elasto-optic constants, piezoelectric constants, refractive indices, NLO and electro-optic (EO) coefficients. Among them, theoretical calculation of the refractive indices in the THz range by diagonalizing the clamped-ion dielectric constants was firstly achieved at least for BiBO crystal. The calculation also confirms that BiBO has an exceptional large piezoelectric constant d22=40 pC/N and largest free EO coefficientsγ 12 T ${{\gamma }_{12}^{T}}$ ,γ 22 T ${{\gamma }_{22}^{T}}$ ,γ 32 T ${{\gamma }_{32}^{T}}$ on the order of 10 pm/V among borate crystals. The calculation also reveals that the large free EO coefficients are largely originated from the piezoelectric induced photo-elastic effect and for practical high speed applications only the clamped-ion EO coefficients take effect. The clamped ion EO coefficient ofγ 53 S ${{\gamma }_{53}^{S}}$ =-4.17 pm/V,γ b 1 S ${{\gamma }_{{\rm b}1}^{S}}$ =-2.61 pm/V are obtained for the first time and may be consulted if one seeks to design BiBO crystal as a high-speed EO modulator. Furthermore, full tensor matrix of the elasto-optic constants was obtained on the first time. Together with the calculated elastic constants, it can help to design acoustic optic modulating devices with preferable figure of merits 10 times that of traditional quartz crystal.

Advancements in nanoscale delivery systems: optimizing intermolecular interactions for superior drug encapsulation and precision release

Nanoscale preparations, such as nanoparticles, micelles, and liposomes, are increasingly recognized in pharmaceutical technology for their high capability in tailoring the pharmacokinetics of the encapsulated drug within the body. These preparations have great potential in extending drug half-life, reducing dosing frequency, mitigating drug side effects, and enhancing drug efficacy. Consequently, nanoscale preparations offer promising prospects for the treatment of metabolic disorders, malignant tumors, and various chronic diseases. Nevertheless, the complete clinical potential of nanoscale preparations remains untapped due to the challenges associated with low drug loading degrees and insufficient control over drug release. In this review, we comprehensively summarize the vital role of intermolecular interactions in enhancing encapsulation and controlling drug release within nanoscale delivery systems. Our analysis critically evaluates the characteristics of common intermolecular interactions and elucidates the techniques employed to assess them. Moreover, we highlight the significant potential of intermolecular interactions in clinical translation, particularly in the screening and optimization of preparation prescriptions. By attaining a deeper understanding of intermolecular interaction properties and mechanisms, we can adopt a more rational approach to designing drug carriers, leading to substantial advancements in the application and clinical transformation of nanoscale preparations. Moving forward, continued research in this field offers exciting prospects for unlocking the full clinical potential of nanoscale preparations and revolutionizing the field of drug delivery.

Distinction and Quantification of Noncovalent Dispersive and Hydrophobic Effects

The possibilities of comparing computational results of noncovalent interactions with experimental data are discussed, first with respect to intramolecular interactions. For these a variety of experimental data such as heats of formation, crystal sublimation heats, comparison with energy minimized structures, and spectroscopic data are available, but until now largely have not found widespread application. Early force field and QM/MP2 calculations have already shown that the sublimation heats of hydrocarbons can be predicted with an accuracy of ±1%. Intermolecular interactions in solution or the gas phase are always accompanied by difficult to compute entropic contributions, like all associations between molecules. Experimentally observed T∆S values contribute 10% to 80% of the total ∆G, depending on interaction mechanisms within the complexes, such as, e.g., hydrogen bonding and ion pairing. Free energies ∆G derived from equilibrium measurements in solution allow us to define binding increments ∆∆G, which are additive and transferable to a variety of supramolecular complexes. Data from more than 90 equilibrium measurements of porphyrin receptors in water indicate that small alkanes do not bind to the hydrophobic flat surfaces within a measuring limit of ∆G = ±0.5 kJ/mol, and that 20 functions bearing heteroatoms show associations by dispersive interactions with up to ∆G = 8 kJ/mol, roughly as a function of their polarizability. Aromatic systems display size-dependent affinities ∆G as a linear function of the number of π-electrons.

Advances and Prospects in Understanding London Dispersion Interactions in Molecular Chemistry

London dispersion (LD) interactions are the main contribution of the attractive part of the van der Waals potential. Even though LD effects are the driving force for molecular aggregation and recognition, the role of these omnipresent interactions in structure and reactivity had been largely underappreciated over decades. However, in the recent years considerable efforts have been made to thoroughly study LD interactions and their potential as a chemical design element for structures and catalysis. This was made possible through a fruitful interplay of theory and experiment. This review highlights recent results and advances in utilizing LD interactions as a structural motif to understand and utilize intra- and intermolecularly LD-stabilized systems. Additionally, we focus on the quantification of LD interactions and their fundamental role in chemical reactions.

Quantum Drude oscillators coupled with Coulomb potential as an efficient model for bonded and non-covalent interactions in atomic dimers

The quantum Drude oscillator (QDO) model has been widely used as an efficient surrogate to describe the electric response properties of matter as well as long-range interactions in molecules and materials. Most commonly, QDOs are coupled within the dipole approximation so that the Hamiltonian can be exactly diagonalized, which forms the basis for the many-body dispersion method [Phys. Rev. Lett. 108, 236402 (2012)]. The dipole coupling is efficient and allows us to study non-covalent many-body effects in systems with thousands of atoms. However, there are two limitations: (i) the need to regularize the interaction at short distances with empirical damping functions and (ii) the lack of multipolar effects in the coupling potential. In this work, we convincingly address both limitations of the dipole-coupled QDO model by presenting a numerically exact solution of the Coulomb-coupled QDO model by means of quantum Monte Carlo methods. We calculate the potential-energy surfaces of homogeneous QDO dimers, analyzing their properties as a function of the three tunable parameters: frequency, reduced mass, and charge. We study the coupled-QDO model behavior at short distances and show how to parameterize this model to enable an effective description of chemical bonds, such as the covalent bond in the H2 molecule.

Water Electric Field Induced Modulation of the Wetting of Hexagonal Boron Nitride: Insights from Multiscale Modeling of Many-Body Polarization

Understanding the behavior of water contacting two-dimensional materials, such as hexagonal boron nitride (hBN), is important in practical applications, including seawater desalination and energy harvesting. Water, being a polar solvent, can strongly polarize the hBN surface via the electric fields that it generates. However, there is a lack of molecular-level understanding about the role of polarization effects at the hBN/water interface, including its effect on the wetting properties of water. In this study, we develop a theoretical framework that introduces an all-atomistic polarizable force field to accurately model the interactions of water molecules with hBN surfaces. The force field is then utilized to self-consistently describe the water-induced polarization of hBN using the classical Drude oscillator model, including predicting the hBN-water binding energies which are found to be in excellent agreement with diffusion Monte Carlo (DMC) predictions. By carrying out molecular dynamics (MD) simulations, we demonstrate that the polarizable force field yields a water contact angle on multilayered hBN which is in close agreement with the recent experimentally reported values. Conversely, an implicit modeling of the hBN-water polarization energy utilizing a Lennard-Jones (LJ) potential, a commonly utilized approximation in previous MD simulation studies, leads to a considerably lower water contact angle. This difference in the predicted contact angles is attributed to the significant energy-entropy compensation resulting from the incorporation of polarization effects at the hBN-water interface. Our work highlights the importance of self-consistently modeling the hBN-water polarization energy and offers insights into the wetting-related interfacial phenomena of water on polarizable materials.

A review of carbon nanomaterials/bacterial cellulose composites for nanomedicine applications

Carbon nanomaterials (CNMs) mainly include fullerene, carbon nanotubes, graphene, carbon quantum dots, nanodiamonds, and their derivatives. As a new type of material in the field of nanomaterials, it has outstanding physical and chemical properties, such as minor size effects, substantial specific surface area, extremely high reaction activity, biocompatibility, and chemical stability, which have attracted widespread attention in the medical community in the past decade. However, the single use of carbon nanomaterials has problems such as self-aggregation and poor water solubility. Researchers have recently combined them with bacterial cellulose to form a new intelligent composite material to improve the defects of carbon nanomaterials. This composite material has been widely synthesized and used in targeted drug delivery, biosensors, antibacterial dressings, tissue engineering scaffolds, and other nanomedicine fields. This paper mainly reviews the research progress of carbon nanomaterials based on bacterial cellulose in nanomedicine. In addition, the potential cytotoxicity of these composite materials and their components in vitro and in vivo was discussed, as well as the challenges and gaps that need to be addressed in future clinical applications.

Molecules in Environments: Toward Systematic Quantum Embedding of Electrons and Drude Oscillators

We develop a quantum embedding method that enables accurate and efficient treatment of interactions between molecules and an environment, while explicitly including many-body correlations. The molecule is composed of classical nuclei and quantum electrons, whereas the environment is modeled via charged quantum harmonic oscillators. We construct a general Hamiltonian and introduce a variational Ansatz for the correlated ground state of the fully interacting molecule-environment system. This wave function is optimized via the variational Monte Carlo method and the ground state energy is subsequently estimated through the diffusion Monte Carlo method. The proposed scheme allows an explicit many-body treatment of electrostatic, polarization, and dispersion interactions between the molecule and the environment. We study solvation energies and excitation energies of benzene derivatives, obtaining excellent agreement with explicit ab initio calculations and experiments.

Frontiers of molecular crystal structure prediction for pharmaceuticals and functional organic materials

The reliability of organic molecular crystal structure prediction has improved tremendously in recent years. Crystal structure predictions for small, mostly rigid molecules are quickly becoming routine. Structure predictions for larger, highly flexible molecules are more challenging, but their crystal structures can also now be predicted with increasing rates of success. These advances are ushering in a new era where crystal structure prediction drives the experimental discovery of new solid forms. After briefly discussing the computational methods that enable successful crystal structure prediction, this perspective presents case studies from the literature that demonstrate how state-of-the-art crystal structure prediction can transform how scientists approach problems involving the organic solid state. Applications to pharmaceuticals, porous organic materials, photomechanical crystals, organic semi-conductors, and nuclear magnetic resonance crystallography are included. Finally, efforts to improve our understanding of which predicted crystal structures can actually be produced experimentally and other outstanding challenges are discussed.

Universal Pairwise Interatomic van der Waals Potentials Based on Quantum Drude Oscillators

Repulsive short-range and attractive long-range van der Waals (vdW) forces play an appreciable role in the behavior of extended molecular systems. When using empirical force fields, the most popular computational methods applied to such systems, vdW forces are typically described by Lennard-Jones-like potentials, which unfortunately have a limited predictive power. Here, we present a universal parameterization of a quantum-mechanical vdW potential, which requires only two free-atom properties─the static dipole polarizability α1 and the dipole-dipole C6 dispersion coefficient. This is achieved by deriving the functional form of the potential from the quantum Drude oscillator (QDO) model, employing scaling laws for the equilibrium distance and the binding energy, and applying the microscopic law of corresponding states. The vdW-QDO potential is shown to be accurate for vdW binding energy curves, as demonstrated by comparing to the ab initio binding curves of 21 noble-gas dimers. The functional form of the vdW-QDO potential has the correct asymptotic behavior at both zero and infinite distances. In addition, it is shown that the damped vdW-QDO potential can accurately describe vdW interactions in dimers consisting of group II elements. Finally, we demonstrate the applicability of the atom-in-molecule vdW-QDO model for predicting accurate dispersion energies for molecular systems. The present work makes an important step toward constructing universal vdW potentials, which could benefit (bio)molecular computational studies.

From ab initio to continuum: Linking multiple scales using deep-learned forces

We develop a deep learning-based algorithm, called DeepForce, to link ab initio physics with the continuum theory to predict concentration profiles of confined water. We show that the deep-learned forces can be used to predict the structural properties of water confined in a nanochannel with quantum scale accuracy by solving the continuum theory given by Nernst-Planck equation. The DeepForce model has an excellent predictive performance with a relative error less than 7.6% not only for confined water in small channel systems (L < 6 nm) but also for confined water in large channel systems (L = 20 nm) which are computationally inaccessible through the high accuracy ab initio molecular dynamics simulations. Finally, we note that classical Molecular dynamics simulations can be inaccurate in capturing the interfacial physics of water in confinement (L < 4.0 nm) when quantum scale physics are neglected.

libMBD: A general-purpose package for scalable quantum many-body dispersion calculations

Many-body dispersion (MBD) is a powerful framework to treat van der Waals (vdW) dispersion interactions in density-functional theory and related atomistic modeling methods. Several independent implementations of MBD with varying degree of functionality exist across a number of electronic structure codes, which both limits the current users of those codes and complicates dissemination of new variants of MBD. Here, we develop and document libMBD, a library implementation of MBD that is functionally complete, efficient, easy to integrate with any electronic structure code, and already integrated in FHI-aims, DFTB+, VASP, Q-Chem, CASTEP, and Quantum ESPRESSO. libMBD is written in modern Fortran with bindings to C and Python, uses MPI/ScaLAPACK for parallelization, and implements MBD for both finite and periodic systems, with analytical gradients with respect to all input parameters. The computational cost has asymptotic cubic scaling with system size, and evaluation of gradients only changes the prefactor of the scaling law, with libMBD exhibiting strong scaling up to 256 processor cores. Other MBD properties beyond energy and gradients can be calculated with libMBD, such as the charge-density polarization, first-order Coulomb correction, the dielectric function, or the order-by-order expansion of the energy in the dipole interaction. Calculations on supramolecular complexes with MBD-corrected electronic structure methods and a meta-review of previous applications of MBD demonstrate the broad applicability of the libMBD package to treat vdW interactions.

First-Principles Study of the Dispersion Effects in the Structures and Keto-Enol Tautomerization of Curcumin

Noncovalent interactions, such as dispersion, play a significant role in the stability of flexible molecules, such as curcumin. This study revealed the importance of dispersion correction in the structure and keto-enol tautomerization of curcumin, which has rarely been addressed in computational studies. We rigorously constructed all possible unique curcumin conformers in the enol and keto forms within the first-principles framework. Regardless of the different environments, we carefully explained the agreement between the computational geometry (in the gas phase) and the experimental measurement (in the polymorph) by using dispersion correction. The calculation results for the aqueous solution of conformational abundance, thermochemistry, and reaction kinetics support the experimental observations after considering the dispersion correction. The study also suggests a water-catalyzed mechanism for keto-enol tautomerization, where dispersion correction plays a role in decreasing the energy barrier and making the keto form thermochemically and kinetically favorable. Our results could be helpful in future computational studies to find a method for increasing the aqueous solubility of curcumin; hence, the potential of curcumin as a multifunctional medicine can be fully achieved.

Operando Modeling of Zeolite-Catalyzed Reactions Using First-Principles Molecular Dynamics Simulations

Within this Perspective, we critically reflect on the role of first-principles molecular dynamics (MD) simulations in unraveling the catalytic function within zeolites under operating conditions. First-principles MD simulations refer to methods where the dynamics of the nuclei is followed in time by integrating the Newtonian equations of motion on a potential energy surface that is determined by solving the quantum-mechanical many-body problem for the electrons. Catalytic solids used in industrial applications show an intriguing high degree of complexity, with phenomena taking place at a broad range of length and time scales. Additionally, the state and function of a catalyst critically depend on the operating conditions, such as temperature, moisture, presence of water, etc. Herein we show by means of a series of exemplary cases how first-principles MD simulations are instrumental to unravel the catalyst complexity at the molecular scale. Examples show how the nature of reactive species at higher catalytic temperatures may drastically change compared to species at lower temperatures and how the nature of active sites may dynamically change upon exposure to water. To simulate rare events, first-principles MD simulations need to be used in combination with enhanced sampling techniques to efficiently sample low-probability regions of phase space. Using these techniques, it is shown how competitive pathways at operating conditions can be discovered and how broad transition state regions can be explored. Interestingly, such simulations can also be used to study hindered diffusion under operating conditions. The cases shown clearly illustrate how first-principles MD simulations reveal insights into the catalytic function at operating conditions, which could not be discovered using static or local approaches where only a few points are considered on the potential energy surface (PES). Despite these advantages, some major hurdles still exist to fully integrate first-principles MD methods in a standard computational catalytic workflow or to use the output of MD simulations as input for multiple length/time scale methods that aim to bridge to the reactor scale. First of all, methods are needed that allow us to evaluate the interatomic forces with quantum-mechanical accuracy, albeit at a much lower computational cost compared to currently used density functional theory (DFT) methods. The use of DFT limits the currently attainable length/time scales to hundreds of picoseconds and a few nanometers, which are much smaller than realistic catalyst particle dimensions and time scales encountered in the catalysis process. One solution could be to construct machine learning potentials (MLPs), where a numerical potential is derived from underlying quantum-mechanical data, which could be used in subsequent MD simulations. As such, much longer length and time scales could be reached; however, quite some research is still necessary to construct MLPs for the complex systems encountered in industrially used catalysts. Second, most currently used enhanced sampling techniques in catalysis make use of collective variables (CVs), which are mostly determined based on chemical intuition. To explore complex reactive networks with MD simulations, methods are needed that allow the automatic discovery of CVs or methods that do not rely on a priori definition of CVs. Recently, various data-driven methods have been proposed, which could be explored for complex catalytic systems. Lastly, first-principles MD methods are currently mostly used to investigate local reactive events. We hope that with the rise of data-driven methods and more efficient methods to describe the PES, first-principles MD methods will in the future also be able to describe longer length/time scale processes in catalysis. This might lead to a consistent dynamic description of all steps-diffusion, adsorption, and reaction-as they take place at the catalyst particle level.

A transferable double exponential potential for condensed phase simulations of small molecules

The Lennard-Jones potential is the most widely-used function for the description of non-bonded interactions in transferable force fields for the condensed phase. This is not because it has an optimal functional form, but rather it is a legacy resulting from when computational expense was a major consideration and this potential was particularly convenient numerically. At present, it persists because the effort that would be required to re-write molecular modelling software and train new force fields has, until now, been prohibitive. Here, we present Smirnoff-plugins as a flexible framework to extend the Open Force Field software stack to allow custom force field functional forms. We deploy Smirnoff-plugins with the automated Open Force Field infrastructure to train a transferable, small molecule force field based on the recently-proposed double exponential functional form, on over 1000 experimental condensed phase properties. Extensive testing of the resulting force field shows improvements in transfer free energies, with acceptable conformational energetics, run times and convergence properties compared to state-of-the-art Lennard-Jones based force fields.

Accurate prediction of global-density-dependent range-separation parameters based on machine learning

In this work, we develop an accurate and efficient XGBoost machine learning model for predicting the global-density-dependent range-separation parameter, ωGDD, for long-range corrected functional (LRC)-ωPBE. This ωGDDML model has been built using a wide range of systems (11 466 complexes, ten different elements, and up to 139 heavy atoms) with fingerprints for the local atomic environment and histograms of distances for the long-range atomic correlation for mapping the quantum mechanical range-separation values. The promising performance on the testing set with 7046 complexes shows a mean absolute error of 0.001 117 a0-1 and only five systems (0.07%) with an absolute error larger than 0.01 a0-1, which indicates the good transferability of our ωGDDML model. In addition, the only required input to obtain ωGDDML is the Cartesian coordinates without electronic structure calculations, thereby enabling rapid predictions. LRC-ωPBE(ωGDDML) is used to predict polarizabilities for a series of oligomers, where polarizabilities are sensitive to the asymptotic density decay and are crucial in a variety of applications, including the calculations of dispersion corrections and refractive index, and surpasses the performance of all other popular density functionals except for the non-tuned LRC-ωPBE. Finally, LRC-ωPBE (ωGDDML) combined with (extended) symmetry-adapted perturbation theory is used in calculating noncovalent interactions to further show that the traditional ab initio system-specific tuning procedure can be bypassed. The present study not only provides an accurate and efficient way to determine the range-separation parameter for LRC-ωPBE but also shows the synergistic benefits of fusing the power of physically inspired density functional LRC-ωPBE and the data-driven ωGDDML model.

Challenges in modelling dynamic processes in realistic nanostructured materials at operating conditions

The question is addressed in how far current modelling strategies are capable of modelling dynamic phenomena in realistic nanostructured materials at operating conditions. Nanostructured materials used in applications are far from perfect; they possess a broad range of heterogeneities in space and time extending over several orders of magnitude. Spatial heterogeneities from the subnanometre to the micrometre scale in crystal particles with a finite size and specific morphology, impact the material's dynamics. Furthermore, the material's functional behaviour is largely determined by the operating conditions. Currently, there exists a huge length-time scale gap between attainable theoretical length-time scales and experimentally relevant scales. Within this perspective, three key challenges are highlighted within the molecular modelling chain to bridge this length-time scale gap. Methods are needed that enable (i) building structural models for realistic crystal particles having mesoscale dimensions with isolated defects, correlated nanoregions, mesoporosity, internal and external surfaces; (ii) the evaluation of interatomic forces with quantum mechanical accuracy albeit at much lower computational cost than the currently used density functional theory methods and (iii) derivation of the kinetics of phenomena taking place in a multi-length-time scale window to obtain an overall view of the dynamics of the process. This article is part of a discussion meeting issue 'Supercomputing simulations of advanced materials'.

Optimized Quantum Drude Oscillators for Atomic and Molecular Response Properties

The quantum Drude oscillator (QDO) is an efficient yet accurate coarse-grained approach that has been widely used to model electronic and optical response properties of atoms and molecules as well as polarization and dispersion interactions between them. Three effective parameters (frequency, mass, and charge) fully characterize the QDO Hamiltonian and are adjusted to reproduce response properties. However, the soaring success of coupled QDOs for many-atom systems remains fundamentally unexplained, and the optimal mapping between atoms/molecules and oscillators has not been established. Here we present an optimized parametrization (OQDO) where the parameters are fixed by using only dipolar properties. For the periodic table of elements as well as small molecules, our model accurately reproduces atomic (spatial) polarization potentials and multipolar dispersion coefficients, elucidating the high promise of the presented model in the development of next-generation quantum-mechanical force fields for (bio)molecular simulations.

Manipulation of the Magnetic State of a Porphyrin-Based Molecule on Gold: From Kondo to Quantum Nanomagnet via the Charge Fluctuation Regime

By moving individual Fe-porphyrin-based molecules with the tip of a scanning tunneling microscope in the vicinity of the elbow of the herringbone-reconstructed Au(111) containing a Br atom, we reversibly and continuously control their magnetic state. Several regimes are obtained experimentally and explored theoretically: from the integer spin limit, through intermediate magnetic states with renormalized magnetic anisotropy, until the Kondo-screened regime, corresponding to a progressive increase of charge fluctuations and mixed valency due to an increase in the interaction of the molecular Fe states with the substrate Fermi sea. Our study demonstrates the potential of utilizing charge fluctuations to generate and tune quantum magnetic states in molecule-surface hybrids.

Modeling coarse-grained van der Waals interactions using dipole-coupled anisotropic quantum Drude oscillators

The Quantum Drude Oscillator (QDO) model is a promising candidate for accurately calculating the van der Waals (vdW) interaction. Anisotropic QDO models have recently been used to represent quantum fluctuations of molecular fragments rather than that of single atoms. While this model promises accurate calculation of vdW energy, there is significant room for improvements, such as incorporating a proper fragmentation method, higher-order dispersion corrections, and so forth. The present work attempts to gauge dipole-dipole interactions' ability without fragmentation. A suitable anisotropic damping function is also introduced to work with anisotropic QDO. This revised model accurately predicts the binding energies of vdW complexes for most of the systems considered. This work indicates the limit of dipole approximation for an anisotropic QDO-based model.

clay with enhanced affinity for per- and polyfluoroalkyl substances

Motivated by the need for enhancing sorbent affinity for per- and polyfluoroalkyl substances (PFAS), we demonstrate the possibility of rationally designing clay-based material (FluoroClay) with a pre-selected intercalant and predicting sorbent performance using all-atom molecular dynamics simulation coupled with density functional theory-based computation. Perfluorohexyldodecane quaternary ammonium (F6H12A) as the selected intercalant revealed significant enhancement in adsorption affinity for hard-to-remove compounds, including perfluorobutane sulfonate (PFBS) and polyfluoroalkylethers (GenX and ADONA). The adsorption is thermodynamically entropy-driven and dominated by the hydrophobic effect. The incorporation of fluorine atoms into clay intercalants gave rise to a hydrophobic and fluorophilic "cavity" structure for targeted PFAS. The self-assembly of intercalant-PFAS under the negative electric field of clay sheets created a unique configuration that significantly enlarged the contact surface area between PFAS and F6H12A and was quantitatively driven by their intermolecular interactions, e.g., CF chain-CH chain, CF chain-CF chain, and charge-CH chain interactions. Collectively, our work demonstrated a new approach to select fluorinated functionality for designing a new adsorbent and estimating its performance via molecular simulation. It also provided an in-depth understanding of the underlying fundamental physics and chemistry in the adsorption of PFAS, suggesting a new strategy for PFAS removal, particularly for short-chain PFAS and new chemical alternatives.

Machine Learning Interatomic Potentials and Long-Range Physics

Advances in machine learned interatomic potentials (MLIPs), such as those using neural networks, have resulted in short-range models that can infer interaction energies with near ab initio accuracy and orders of magnitude reduced computational cost. For many atom systems, including macromolecules, biomolecules, and condensed matter, model accuracy can become reliant on the description of short- and long-range physical interactions. The latter terms can be difficult to incorporate into an MLIP framework. Recent research has produced numerous models with considerations for nonlocal electrostatic and dispersion interactions, leading to a large range of applications that can be addressed using MLIPs. In light of this, we present a Perspective focused on key methodologies and models being used where the presence of nonlocal physics and chemistry are crucial for describing system properties. The strategies covered include MLIPs augmented with dispersion corrections, electrostatics calculated with charges predicted from atomic environment descriptors, the use of self-consistency and message passing iterations to propagated nonlocal system information, and charges obtained via equilibration schemes. We aim to provide a pointed discussion to support the development of machine learning-based interatomic potentials for systems where contributions from only nearsighted terms are deficient.

Casimir Self-Interaction Energy Density of Quantum Electrodynamic Fields

Quantum electrodynamic fields possess fluctuations corresponding to transient particle-antiparticle dipoles, which can be characterized by a nonvanishing polarizability density. Here, we extend a recently proposed quantum scaling law to describe the volumetric and radial polarizability density of a quantum field corresponding to electrons and positrons and derive the Casimir self-interaction energy (SIE) density of the field, E[over ¯]_{SIE}, in terms of the fine-structure constant. The proposed model obeys the cosmological equation of state w=-1 and the magnitude of the calculated E[over ¯]_{SIE} lies in between the two recent measurements of the cosmological constant Λ obtained by the Planck Mission and the Hubble Space Telescope.

A theoretical framework for the design of molecular crystal engines

Photomechanical molecular crystals have garnered attention for their ability to transform light into mechanical work, but difficulties in characterizing the structural changes and mechanical responses experimentally have hindered the development of practical organic crystal engines. This study proposes a new computational framework for predicting the solid-state crystal-to-crystal photochemical transformations entirely from first principles, and it establishes a photomechanical engine cycle that quantifies the anisotropic mechanical performance resulting from the transformation. The approach relies on crystal structure prediction, solid-state topochemical principles, and high-quality electronic structure methods. After validating the framework on the well-studied [4 + 4] cycloadditions in 9-methyl anthracene and 9-tert-butyl anthracene ester, the experimentally-unknown solid-state transformation of 9-carboxylic acid anthracene is predicted for the first time. The results illustrate how the mechanical work is done by relaxation of the crystal lattice to accommodate the photoproduct, rather than by the photochemistry itself. The large ∼10⁷ J m^-3 work densities computed for all three systems highlight the promise of photomechanical crystal engines. This study demonstrates the importance of crystal packing in determining molecular crystal engine performance and provides tools and insights to design improved materials in silico.

Synthesis, crystal structure, DFT, Hirshfeld surface analysis, energy framework, docking and molecular dynamic simulations of (E)-4-(4-methylbenzyl)-6-styrylpyridazin-3(2H)-one as anticancer agent

In this work, a novel crystal, (E)-4-(4-methylbenzyl)-6-styrylpyridazin-3(2H)-one (E-BSP) was synthesized via Knoevenagel condensation of benzaldehyde and (E)-6-(4-methoxystyryl)-4,5-dihydropyridazin-3(2H)-one. The molecular structure of E-BSP was confirmed by using FT-IR, 1H-NMR, 13C-NMR, UV-vis, ESI-MS, TGA/DTA thermal analyses and single crystal X-ray diffraction. The DFT/B3LYP methods with the 6-311++G(d,p) basis set were used to determine the vibrational modes over the optimized structure. Potential energy distribution (PED) and the VEDA 4 software were used to establish the theoretical mode assignments. The same approach was used to compute the energies of frontier molecular orbitals (HOMO-LUMO), global reactivity descriptors, and molecular electrostatic potential (MEP). Additionally, experimental and computed UV spectral parameters were determined in methanol and the obtained outputs were supported by FMO analysis. Molecular docking and molecular dynamics (MD) simulation analyses of the E-BSP against six proteins obtained from different cancer pathways were carried out. The proteins include; epidermal growth factor receptor (EGFR), Estrogen receptor (ERα), Mammalian target of rapamycin (mTOR), Progesterone receptor (PR) (Breast cancer), Human cyclin-dependent kinase 2 (CDK2) (Colorectal cancer), and Survivin (Squamous cell carcinoma/Non-small cell lung cancer). The results of the analyses showed that the compound had less binding energies ranging between -6.30 to -9.09 kcal/mol and formed stable complexes at the substrate-binding site of the proteins after the 50 ns MD simulation. Therefore, E-BSP was considered a potential inhibitor of different cancer pathways and should be used for the treatment of cancer after experimental validation and clinical trial.Communicated by Ramaswamy H. Sarma.

Graphene at Liquid Copper Catalysts: Atomic-Scale Agreement of Experimental and First-Principles Adsorption Height

Liquid metal catalysts have recently attracted attention for synthesizing high-quality 2D materials facilitated via the catalysts' perfectly smooth surface. However, the microscopic catalytic processes occurring at the surface are still largely unclear because liquid metals escape the accessibility of traditional experimental and computational surface science approaches. Hence, numerous controversies are found regarding different applications, with graphene (Gr) growth on liquid copper (Cu) as a prominent prototype. In this work, novel in situ and in silico techniques are employed to achieve an atomic-level characterization of the graphene adsorption height above liquid Cu, reaching quantitative agreement within 0.1 Å between experiment and theory. The results are obtained via in situ synchrotron X-ray reflectivity (XRR) measurements over wide-range q-vectors and large-scale molecular dynamics simulations based on efficient machine-learning (ML) potentials trained to first-principles density functional theory (DFT) data. The computational insight is demonstrated to be robust against inherent DFT errors and reveals the nature of graphene binding to be highly comparable at liquid Cu and solid Cu(111). Transporting the predictive first-principles quality via ML potentials to the scales required for liquid metal catalysis thus provides a powerful approach to reach microscopic understanding, analogous to the established computational approaches for catalysis at solid surfaces.

Mapping the Binding Energy of Layered Crystals to Macroscopic Observables

Van der Waals (vdW) integration of two dimensional (2D) crystals into functional heterostructures emerges as a powerful tool to design new materials with fine-tuned physical properties at an unprecedented precision. The intermolecular forces governing the assembly of vdW heterostructures are investigated by first-principles models, yet translating the outcome of these models to macroscopic observables in layered crystals is missing. Establishing this connection is, therefore, crucial for ultimately designing advanced materials of choice-tailoring the composition to functional device properties. Herein, components from both vdW and non-vdW forces are integrated to build a comprehensive framework that can quantitatively describe the dynamics of these forces in action. Specifically, it is shown that the optical band gap of layered crystals possesses a peculiar ionic character that works as a quantitative indicator of non-vdW forces. Using these two components, it is then described why only a narrow range of exfoliation energies for this class of materials is observed. These findings unlock the microscopic origin of universal binding energy in layered crystals and provide a general protocol to identify and synthesize new crystals to regulate vdW coupling in the next generation of heterostructures.

Systematic Evaluation of Counterpoise Correction in Density Functional Theory

A widespread belief persists that the Boys-Bernardi function counterpoise (CP) procedure "overcorrects" supramolecular interaction energies for the effects of basis-set superposition error. To the extent that this is true for correlated wave function methods, it is usually an artifact of low-quality basis sets. The question has not been considered systematically in the context of density functional theory, however, where basis-set convergence is generally less problematic. We present a systematic assessment of the CP procedure for a representative set of functionals and basis sets, considering both benchmark data sets of small dimers and larger supramolecular complexes. The latter include layered composite polymers with ∼150 atoms and ligand-protein models with ∼300 atoms. Provided that CP correction is used, we find that intermolecular interaction energies of nearly complete-basis quality can be obtained using only double-ζ basis sets. This is less expensive as compared to triple-ζ basis sets without CP correction. CP-corrected interaction energies are less sensitive to the presence of diffuse basis functions as compared to uncorrected energies, which is important because diffuse functions are expensive and often numerically problematic for large systems. Our results upend the conventional wisdom that CP "overcorrects" for basis-set incompleteness. In small basis sets, CP correction is mandatory in order to demonstrate that the results do not rest on error cancellation.

Simple Exchange-Correlation Energy Functionals for Strongly Coupled Light-Matter Systems Based on the Fluctuation-Dissipation Theorem

Recent experimental advances in strongly coupled light-matter systems have sparked the development of general ab initio methods capable of describing interacting light-matter systems from first principles. One of these methods, quantum-electrodynamical density-functional theory (QEDFT), promises computationally efficient calculations for large correlated light-matter systems with the quality of the calculation depending on the underlying approximation for the exchange-correlation functional. So far no true density-functional approximation has been introduced limiting the efficient application of the theory. In this Letter, we introduce the first gradient-based density functional for the QEDFT exchange-correlation energy derived from the adiabatic-connection fluctuation-dissipation theorem. We benchmark this simple-to-implement approximation on small systems in optical cavities and demonstrate its relatively low computational costs for fullerene molecules up to C_{180} coupled to 400 000 photon modes in a dissipative optical cavity. This Letter now makes first principle calculations of much larger systems possible within the QEDFT framework effectively combining quantum optics with large-scale electronic structure theory.

Evaluating fast methods for static polarizabilities on extended conjugated oligomers

Given the importance of accurate polarizability calculations to many chemical applications, coupled with the need for efficiency when calculating the properties of sets of molecules or large oligomers, we present a benchmark study examining possible calculation methods for polarizable materials. We first investigate the accuracy of the additive model used in GFN2, a highly-efficient semi-empirical tight-binding method, and the D4 dispersion model, comparing its predicted additive polarizabilities to ωB97XD results for a subset of PubChemQC and a compiled benchmark set of molecules spanning polarizabilities from approximately 3 ų to 600 ų, with some compounds in the range of approximately 1200-1400 ų. Although we find additive GFN2 polarizabilities, and thus D4, to have large errors with polarizability calculations on large conjugated oligomers, it would appear an empirical quadratic correction can largely remedy this. We also compare the accuracy of DFT polarizability calculations run using basis sets of varying size and level of augmentation, determining that a non-augmented basis set may be used for large, highly polarizable species in conjunction with a linear correction factor to achieve accuracy extremely close to that of aug-cc-pVTZ.

Magnetoresponsive Functionalized Nanocomposite Aggregation Kinetics and Chain Formation at the Targeted Site during Magnetic Targeting

Drug therapy for vascular disease has been promoted to inhibit angiogenesis in atherosclerotic plaques and prevent restenosis following surgical intervention. This paper investigates the arterial depositions and distribution of PEG-functionalized magnetic nanocomposite clusters (PEG_MNCs) following local delivery in a stented artery model in a uniform magnetic field produced by a regionally positioned external permanent magnet; also, the PEG_MNCs aggregation or chain formation in and around the implanted stent. The central concept is to employ one external permanent magnet system, which produces enough magnetic field to magnetize and guide the magnetic nanoclusters in the stented artery region. At room temperature (25 °C), optical microscopy of the suspension model’s aggregation process was carried out in the external magnetic field. According to the optical microscopy pictures, the PEG_MNC particles form long linear aggregates due to dipolar magnetic interactions when there is an external magnetic field. During magnetic particle targeting, 20 mL of the model suspensions are injected (at a constant flow rate of 39.6 mL/min for the period of 30 s) by the syringe pump in the mean flow (flow velocity is Um = 0.25 m/s, corresponding to the Reynolds number of Re = 232) into the stented artery model. The PEG_MNC clusters are attracted by the magnetic forces (generated by the permanent external magnet) and captured around the stent struts and the bottom artery wall before and inside the implanted stent. The colloidal interaction among the MNC clusters was investigated by calculating the electrostatic repulsion, van der Waals and magnetic dipole-dipole energies. The current work offers essential details about PEG_MNCs aggregation and chain structure development in the presence of an external magnetic field and the process underlying this structure formation.

Modeling of Structure H Carbon Dioxide Clathrate Hydrates: Guest-Lattice Energies, Crystal Structure, and Pressure Dependencies

We performed first-principles computations to investigate the complex interplay of molecular interaction energies in determining the lattice structure and stability of CO₂@sH clathrate hydrates. Density functional theory computations using periodic boundary conditions were employed to characterize energetics and the key structural properties of the sH clathrate crystal under pressure, such as equilibrium lattice volume and bulk modulus. The performance of exchange-correlation functionals together with recently developed dispersion-corrected schemes was evaluated in describing interactions in both short-range and long-range regions of the potential. Structural relaxations of the fully CO₂-filled and empty sH unit cells yield crystal structure and lattice energies, while their compressibility parameters were derived by including the pressure dependencies. The present quantum chemistry computations suggest anisotropy in the compressibility of the sH clathrate hydrates, with the crystal being less compressible along the a-axis direction than along the c-axis one, in distinction from nearly isotropic sI and sII structures. The detailed results presented here give insight into the complex nature of the underlying guest-host interactions, checking earlier assumptions, providing critical tests, and improving estimates. Such entries may eventually lead to better predictions of thermodynamic properties and formation conditions, with a direct impact on emerging hydrate-based technologies.

Multistate Density Functional Theory of Excited States

We report a rigorous formulation of density functional theory for excited states, providing a theoretical foundation for a multistate density functional theory. We prove the existence of a Hamiltonian matrix functional H[D] of the multistate matrix density D(r) in the subspace spanned by the lowest N eigenstates. Here, D(r) is an N-dimensional matrix of state densities and transition densities. Then, a variational principle of the multistate subspace energy is established, whose minimization yields both the energies and densities of the individual N eigenstates. Furthermore, we prove that the N-dimensional matrix density D(r) can be sufficiently represented by N² nonorthogonal Slater determinants, based on which an interacting active space is introduced for practical calculations. This work establishes that the ground and excited states can be treated on an equal footing in density functional theory.

Long-range dispersion-inclusive machine learning potentials for structure search and optimization of hybrid organic-inorganic interfaces

The computational prediction of the structure and stability of hybrid organic-inorganic interfaces provides important insights into the measurable properties of electronic thin film devices, coatings, and catalyst surfaces and plays an important role in their rational design. However, the rich diversity of molecular configurations and the important role of long-range interactions in such systems make it difficult to use machine learning (ML) potentials to facilitate structure exploration that otherwise requires computationally expensive electronic structure calculations. We present an ML approach that enables fast, yet accurate, structure optimizations by combining two different types of deep neural networks trained on high-level electronic structure data. The first model is a short-ranged interatomic ML potential trained on local energies and forces, while the second is an ML model of effective atomic volumes derived from atoms-in-molecules partitioning. The latter can be used to connect short-range potentials to well-established density-dependent long-range dispersion correction methods. For two systems, specifically gold nanoclusters on diamond (110) surfaces and organic π-conjugated molecules on silver (111) surfaces, we train models on sparse structure relaxation data from density functional theory and show the ability of the models to deliver highly efficient structure optimizations and semi-quantitative energy predictions of adsorption structures.

Efficient Crystal Structure Prediction for Structurally Related Molecules with Accurate and Transferable Tailor-Made Force Fields

Crystal structure prediction (CSP) his generally used to complement experimental solid form screening and applied to individual molecules in drug development. The fast development of algorithms and computing resources offers the opportunity to use CSP earlier and for a broader range of applications in the drug design cycle. This study presents a novel paradigm of CSP specifically designed for structurally related molecules, referred to as Quick-CSP. The approach prioritizes more accurate physics through robust and transferable tailor-made force fields (TMFFs), such that significant efficiency gains are achieved through the reduction of expensive ab initio calculations. The accuracy of the TMFF is increased by the introduction of electrostatic multipoles, and the fragment-based force field parameterization scheme is demonstrated to be transferable for a family of chemically related molecules. The protocol is benchmarked with structurally related compounds from the Bromodomain and Extraterminal (BET) domain inhibitors series. A new convergence criterion is introduced that aims at performing only as many ab initio optimizations of crystal structures as required to locate the bottom of the crystal energy landscape within a user-defined accuracy. The overall approach provides significant cost savings ranging from three- to eight-fold less than the full-CSP workflow. The reported advancements expand the scope and utility of the underlying CSP building blocks as well as their novel reassembly to other applications earlier in the drug design cycle to guide molecule design and selection.

Triple electron-electron-proton excitations and second-order approximations in nuclear-electronic orbital coupled cluster methods

The accurate description of nuclear quantum effects, such as zero-point energy, is important for modeling a wide range of chemical and biological processes. Within the nuclear-electronic orbital (NEO) approach, such effects are incorporated in a computationally efficient way by treating electrons and select nuclei, typically protons, quantum mechanically with molecular orbital techniques. Herein, we implement and test a NEO coupled cluster method that explicitly includes the triple electron-proton excitations, where two electrons and one proton are excited simultaneously. Our calculations show that this NEO-CCSD(eep) method provides highly accurate proton densities and proton affinities, outperforming any previously studied NEO method. These examples highlight the importance of the triple electron-electron-proton excitations for an accurate description of nuclear quantum effects. Additionally, we also implement and test the second-order approximate coupled cluster with singles and doubles (NEO-CC2) method, as well as its scaled-opposite-spin (SOS) versions. The NEO-SOS$'$-CC2 method, which scales the electron-proton correlation energy as well as the opposite-spin and same-spin components of the electron-electron correlation energy, achieves nearly the same accuracy as the NEO-CCSD(eep) method for the properties studied. Because of its low computational cost, this method will enable a wide range of chemical and photochemical applications for large molecular systems. This work sets the stage for a wide range of developments and applications within the NEO framework.

Wavefunction embedding for molecular polaritons

Polaritonic chemistry relies on the strong light-matter interaction phenomena for altering the chemical reaction rates inside optical cavities. To explain and to understand these processes, the development of reliable theoretical models is essential. While computationally efficient quantum electrodynamics self-consistent field (QED-SCF) methods, such as quantum electrodynamics density functional theory (QEDFT) needs accurate functionals, quantum electrodynamics coupled cluster (QED-CC) methods provide a systematic increase in accuracy but at much greater cost. To overcome this computational bottleneck, herein we introduce and develop the QED-CC-in-QED-SCF projection-based embedding method that inherits all the favorable properties from the two worlds, computational efficiency and accuracy. The performance of the embedding method is assessed by studying some prototypical but relevant reactions, such as methyl transfer reaction, proton transfer reaction, as well as protonation reaction in a complex environment. The results obtained with the new embedding method are in excellent agreement with more expensive QED-CC results. The analysis performed on these reactions indicate that the electron-photon correlation effects are local in nature and that only a small region should be treated at the QED-CC level for capturing important effects due to cavity. This work sets the stage for future developments of polaritonic quantum chemistry methods and it will serve as a guideline for development of other polaritonic embedding models.

The contribution of intermolecular spin interactions to the London dispersion forces between chiral molecules

Dispersion interactions are one of the components of van der Waals (vdW) forces that play a key role in the understanding of intermolecular interactions in many physical, chemical, and biological processes. The theory of dispersion forces was developed by London in the early years of quantum mechanics. However, it was only in the 1960s that it was recognized that for molecules lacking an inversion center, such as chiral and helical molecules, there are chirality-sensitive corrections to the dispersion forces proportional to the rotatory power known from the theory of circular dichroism and with the same distance scaling law R^-6 as the London energy. The discovery of the chirality-induced spin selectivity effect in recent years has led to an additional twist in the study of chiral molecular systems, showing a close relation between spin and molecular geometry. Motivated by it, we propose in this investigation to describe the mutual induction of charge and spin-density fluctuations in a pair A-B of chiral molecules by a simple physical model. The model assumes that the same fluctuating electric fields responsible for vdW forces can induce a magnetic response via a Rashba-like term so that a spin-orbit field acting on molecule B is generated by the electric field arising from charge density fluctuations in molecule A (and vice versa). Within a second-order perturbative approach, these contributions manifest as an effective intermolecular exchange interaction. Although expected to be weaker than the standard London forces, these interactions display the same R^-6 distance scaling.

Small-Basis Set Density-Functional Theory Methods Corrected with Atom-Centered Potentials

Density functional theory (DFT) is currently the most popular method for modeling noncovalent interactions and thermochemistry. The accurate calculation of noncovalent interaction energies, reaction energies, and barrier heights requires choosing an appropriate functional and, typically, a relatively large basis set. Deficiencies of the density-functional approximation and the use of a limited basis set are the leading sources of error in the calculation of noncovalent and thermochemical properties in molecular systems. In this article, we present three new DFT methods based on the BLYP, M06-2X, and CAM-B3LYP functionals in combination with the 6-31G* basis set and corrected with atom-centered potentials (ACPs). ACPs are one-electron potentials that have the same form as effective-core potentials, except they do not replace any electrons. The ACPs developed in this work are used to generate energy corrections to the underlying DFT/basis-set method such that the errors in predicted chemical properties are minimized while maintaining the low computational cost of the parent methods. ACPs were developed for the elements H, B, C, N, O, F, Si, P, S, and Cl. The ACP parameters were determined using an extensive training set of 118655 data points, mostly of complete basis set coupled-cluster level quality. The target molecular properties for the ACP-corrected methods include noncovalent interaction energies, molecular conformational energies, reaction energies, barrier heights, and bond separation energies. The ACPs were tested first on the training set and then on a validation set of 42567 additional data points. We show that the ACP-corrected methods can predict the target molecular properties with accuracy close to complete basis set wavefunction theory methods, but at a computational cost of double-ζ DFT methods. This makes the new BLYP/6-31G*-ACP, M06-2X/6-31G*-ACP, and CAM-B3LYP/6-31G*-ACP methods uniquely suited to the calculation of noncovalent, thermochemical, and kinetic properties in large molecular systems.

Comprehensive Basis-Set Testing of Extended Symmetry-Adapted Perturbation Theory and Assessment of Mixed-Basis Combinations to Reduce Cost

Hybrid or "extended" symmetry-adapted perturbation theory (XSAPT) replaces traditional SAPT's treatment of dispersion with better performing alternatives while at the same time extending two-body (dimer) SAPT to a many-body treatment of polarization using a self-consistent charge embedding procedure. The present work presents a systematic study of how XSAPT interaction energies and energy components converge with respect to the choice of Gaussian basis set. Errors can be reduced in a systematic way using correlation-consistent basis sets, with aug-cc-pVTZ results converged within <0.1 kcal/mol. Similar (if slightly less systematic) behavior is obtained using Karlsruhe basis sets at much lower cost, and we introduce new versions with limited augmentation that are even more efficient. Pople-style basis sets, which are more efficient still, often afford good results if a large number of polarization functions are included. The dispersion models used in XSAPT afford much faster basis-set convergence as compared to the perturbative description of dispersion in conventional SAPT, meaning that "compromise" basis sets (such as jun-cc-pVDZ) are no longer required and benchmark-quality results can be obtained using triple-ζ basis sets. The use of diffuse functions proves to be essential, especially for the description of hydrogen bonds. The "δ(Hartree-Fock)" correction for high-order induction can be performed in double-ζ basis sets without significant loss of accuracy, leading to a mixed-basis approach that offers 4× speedup over the existing (cubic scaling) XSAPT approach.

Molecular Interactions Induced by a Static Electric Field in Quantum Mechanics and Quantum Electrodynamics

By means of quantum mechanics and quantum electrodynamics applied to coupled harmonic Drude oscillators, we study the interaction between two neutral atoms or molecules subject to a uniform static electric field. Our focus is to understand the interplay between leading contributions to field-induced electrostatics/polarization and dispersion interactions, as considered within the employed Drude model for both non-retarded and retarded regimes. For the first case, we present an exact solution for two coupled oscillators obtained by diagonalizing the corresponding quantum-mechanical Hamiltonian and demonstrate that the external field can control the strength of different intermolecular interactions and relative orientations of the molecules. In the retarded regime described by quantum electrodynamics, our analysis shows that field-induced electrostatic and polarization energies remain unchanged (in isotropic and homogeneous vacuum) compared to the non-retarded case. For interacting species modeled by quantum Drude oscillators, the developed framework based on quantum mechanics and quantum electrodynamics yields the leading contributions to molecular interactions under the combined action of external and vacuum fields.

Cavity-Modulated Proton Transfer Reactions

Proton transfer is ubiquitous in many fundamental chemical and biological processes, and the ability to modulate and control the proton transfer rate would have a major impact on numerous quantum technological advances. One possibility to modulate the reaction rate of proton transfer processes is given by exploiting the strong light-matter coupling of chemical systems inside optical or nanoplasmonic cavities. In this work, we investigate the proton transfer reactions in the prototype malonaldehyde and Z-3-amino-propenal (aminopropenal) molecules using different quantum electrodynamics methods, in particular, quantum electrodynamics coupled cluster theory and quantum electrodynamical density functional theory. Depending on the cavity mode polarization direction, we show that the optical cavity can increase the reaction energy barrier by 10-20% or decrease the reaction barrier by ∼5%. By using first-principles methods, this work establishes strong light-matter coupling as a viable and practical route to alter and catalyze proton transfer reactions.