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In this work, we extend the selected columns of the density matrix (SCDM) methodology [ J. Chem. Theory Comput. 2015, 11, 1463-1469]─a non-iterative and real-space procedure for generating localized occupied orbitals for condensed-phase systems─to the construction of local molecular orbitals (LMOs) in systems described using non-orthogonal atomic orbital (AO) basis sets. In particular, we introduce three different theoretical and algorithmic variants of SCDM (referred to as SCDM-M, SCDM-L, and SCDM-G) that can be used in conjunction with the AO basis sets used in standard quantum chemistry codebases. The SCDM-M and SCDM-L variants are based on a pivoted QR factorization of the Mulliken and Löwdin representations of the density matrix and are tantamount to selecting a well-conditioned set of projected atomic orbitals (PAOs) and projected (symmetrically-) orthogonalized atomic orbitals, respectively, as proto-LMOs that can be orthogonalized to exactly span the occupied space. The SCDM-G variant is based on a real-space (grid) representation of the wavefunction, and therefore has the added flexibility of considering a large number of grid points (or δ functions) when selecting a set of well-conditioned proto-LMOs. A detailed comparative analysis across molecular systems of varying size, dimensionality, and saturation level reveals that the LMOs generated by these three non-iterative/direct SCDM variants are robust, comparable in orbital locality to those produced with the iterative Boys or Pipek-Mezey (PM) localization schemes, and completely agnostic toward any single orbital locality metric. Although all three SCDM variants are based on the density matrix, we find that the character of the generated LMOs can differ significantly between SCDM-M, SCDM-L, and SCDM-G. In this regard, only the grid-based SCDM-G procedure (like PM) generates LMOs that qualitatively preserve σ-π symmetry (in systems such as s-trans alkenes), and are well-aligned with chemical ( i.e. , Lewis structure) intuition. While the direct and standalone use of SCDM-generated LMOs should suffice for most chemical applications, our findings also suggest that the use of these orbitals as an unbiased and cost-effective (initial) guess also has the potential to improve the convergence of iterative orbital localization schemes, in particular for large-scale and/or pathological molecular systems.

The rational design of molecules with targeted quantum-mechanical (QM) properties requires an advanced understanding of the structure-property/property-property relationships (SPR/PPR) that exist across chemical compound space (CCS). In this work, we analyze these fundamental relationships in the sector of CCS spanned by small (primarily organic) molecules using the recently developed QM7-X dataset, a systematic, extensive, and tightly converged collection of 42 QM properties corresponding to ≈4.2M equilibrium and non-equilibrium molecular structures containing up to seven heavy/non-hydrogen atoms (including C, N, O, S, and Cl). By characterizing and enumerating progressively more complex manifolds of molecular property space-the corresponding high-dimensional space defined by the properties of each molecule in this sector of CCS-our analysis reveals that one has a substantial degree of flexibility or "freedom of design" when searching for a single molecule with a desired pair of properties or a set of distinct molecules sharing an array of properties. To explore how this intrinsic flexibility manifests in the molecular design process, we used multi-objective optimization to search for molecules with simultaneously large polarizabilities and HOMO-LUMO gaps; analysis of the resulting Pareto fronts identified non-trivial paths through CCS consisting of sequential structural and/or compositional changes that yield molecules with optimal combinations of these properties., Competing Interests: There are no conflicts to declare., (This journal is © The Royal Society of Chemistry.)

High-throughput electronic structure calculations (often performed using density functional theory (DFT)) play a central role in screening existing and novel materials, sampling potential energy surfaces, and generating data for machine learning applications. By including a fraction of exact exchange (EXX), hybrid functionals reduce the self-interaction error in semilocal DFT and furnish a more accurate description of the underlying electronic structure, albeit at a computational cost that often prohibits such high-throughput applications. To address this challenge, we have constructed a robust, accurate, and computationally efficient framework for high-throughput condensed-phase hybrid DFT and implemented this approach in the PWSCF module of Quantum ESPRESSO (QE). The resulting SeA approach (SeA = SCDM + exx + ACE) combines and seamlessly integrates: ( i ) the selected columns of the density matrix method (SCDM, a robust noniterative orbital localization scheme that sidesteps system-dependent optimization protocols), ( ii ) a recently extended version of exx (a black-box linear-scaling EXX algorithm that exploits sparsity between localized orbitals in real space when evaluating the action of the standard/full-rank V ^ xx operator), and ( iii ) adaptively compressed exchange (ACE, a low-rank V ^ xx approximation). In doing so, SeA harnesses three levels of computational savings: pair selection and domain truncation from SCDM + exx (which only considers spatially overlapping orbitals on orbital-pair-specific and system-size-independent domains) and low-rank V ^ xx approximation from ACE (which reduces the number of calls to SCDM + exx during the self-consistent field (SCF) procedure). Across a diverse set of 200 nonequilibrium (H 2 O) 64 configurations (with densities spanning 0.4-1.7 g/cm 3 ), SeA provides a 1-2 order-of-magnitude speedup in the overall time-to-solution, i.e., ≈8-26× compared to the convolution-based PWSCF(ACE) implementation in QE and ≈78-247× compared to the conventional PWSCF(Full) approach, and yields energies, ionic forces, and other properties with high fidelity. As a proof-of-principle high-throughput application, we trained a deep neural network (DNN) potential for ambient liquid water at the hybrid DFT level using SeA via an actively learned data set with ≈8,700 (H 2 O) 64 configurations. Using an out-of-sample set of (H 2 O) 512 configurations (at nonambient conditions), we confirmed the accuracy of this SeA-trained potential and showcased the capabilities of SeA by computing the ground-truth ionic forces in this challenging system containing >1,500 atoms.

Cathodic corrosion represents an enigmatic electrochemical process in which metallic electrodes corrode under sufficiently reducing potentials. Although discovered by Fritz Haber in the 19th century, only recently has progress been made in beginning to understand the atomistic mechanisms of corroding bulk electrodes. The creation of nanoparticles as the end-product of the corrosion process suggests an additional length scale of complexity. Here, we studied the dynamic evolution of morphology, composition, and crystallographic structural information of nanocrystal corrosion products by analytical and four-dimensional electrochemical liquid-cell scanning transmission electron microscopy (EC-STEM). Our operando/in situ electron microscopy revealed, in real-time, at the nanometer scale, that cathodic corrosion yields significantly higher levels of structural degradation for heterogeneous nanocrystals than bulk electrodes. In particular, the cathodic corrosion of Au nanocubes on bulk Pt electrodes led to the unexpected formation of thermodynamically immiscible Au-Pt alloy nanoparticles. The highly kinetically driven corrosion process is evidenced by the successive anisotropic transition from stable Pt(111) bulk single-crystal surfaces evolving to energetically less-stable (100) and (110) steps. The motifs identified in this microscopy study of cathodic corrosion of nanocrystals are likely to underlie the structural evolution of nanoscale electrocatalysts during many electrochemical reactions under highly reducing potentials, such as CO 2 and N 2 reduction.

In this work, we present a general framework that unites the two primary strategies for constructing density functional approximations (DFAs): nonempirical (NE) constraint satisfaction and empirical (E) data-driven optimization. The proposed method employs B-splines, bell-shaped spline functions with compact support, to construct each inhomogeneity correction factor (ICF). This choice offers several distinct advantages over traditional polynomial expansions by enabling explicit enforcement of linear and nonlinear constraints as well as ICF smoothness using Tikhonov and penalized B-splines (P-splines) regularization. As proof-of-concept, we use the so-called CASE (constrained and smoothed empirical) framework to construct a constraint-satisfying and data-driven global hybrid that exhibits enhanced performance across a diverse set of chemical properties. We argue that the CASE approach can be used to generate DFAs that maintain the physical rigor and transferability of NE-DFAs while leveraging high-quality quantum-mechanical data to remove the arbitrariness of ansatz selection and improve performance.

Hydrogen energy-based electrochemical energy conversion technologies offer the promise of enabling a transition of the global energy landscape from fossil fuels to renewable energy. Here, we present a comprehensive review of the fundamentals of electrocatalysis in alkaline media and applications in alkaline-based energy technologies, particularly alkaline fuel cells and water electrolyzers. Anion exchange (alkaline) membrane fuel cells (AEMFCs) enable the use of nonprecious electrocatalysts for the sluggish oxygen reduction reaction (ORR), relative to proton exchange membrane fuel cells (PEMFCs), which require Pt-based electrocatalysts. However, the hydrogen oxidation reaction (HOR) kinetics is significantly slower in alkaline media than in acidic media. Understanding these phenomena requires applying theoretical and experimental methods to unravel molecular-level thermodynamics and kinetics of hydrogen and oxygen electrocatalysis and, particularly, the proton-coupled electron transfer (PCET) process that takes place in a proton-deficient alkaline media. Extensive electrochemical and spectroscopic studies, on single-crystal Pt and metal oxides, have contributed to the development of activity descriptors, as well as the identification of the nature of active sites, and the rate-determining steps of the HOR and ORR. Among these, the structure and reactivity of interfacial water serve as key potential and pH-dependent kinetic factors that are helping elucidate the origins of the HOR and ORR activity differences in acids and bases. Additionally, deliberately modulating and controlling catalyst-support interactions have provided valuable insights for enhancing catalyst accessibility and durability during operation. The design and synthesis of highly conductive and durable alkaline membranes/ionomers have enabled AEMFCs to reach initial performance metrics equal to or higher than those of PEMFCs. We emphasize the importance of using membrane electrode assemblies (MEAs) to integrate the often separately pursued/optimized electrocatalyst/support and membranes/ionomer components. Operando/in situ methods, at multiscales, and ab initio simulations provide a mechanistic understanding of electron, ion, and mass transport at catalyst/ionomer/membrane interfaces and the necessary guidance to achieve fuel cell operation in air over thousands of hours. We hope that this Review will serve as a roadmap for advancing the scientific understanding of the fundamental factors governing electrochemical energy conversion in alkaline media with the ultimate goal of achieving ultralow Pt or precious-metal-free high-performance and durable alkaline fuel cells and related technologies.

In the previous paper of this series [Ko, H.-Y. et al. J. Chem. Theory Comput. 2020 , 16 , 3757-3785], we presented a theoretical and algorithmic framework based on a localized representation of the occupied space that exploits the inherent sparsity in the real-space evaluation of the exact exchange (EXX) interaction in finite-gap systems. This was accompanied by a detailed description of exx, a massively parallel hybrid message-passing interface MPI/OpenMP implementation of this approach in Quantum ESPRESSO (QE) that enables linear scaling hybrid density functional theory (DFT)-based ab initio molecular dynamics (AIMD) in the microcanonical/canonical ( NVE / NVT ) ensembles of condensed-phase systems containing 500-1000 atoms (in fixed orthorhombic cells) with a wall time cost comparable to semi-local DFT. In this work, we extend the current capabilities of exx to enable hybrid DFT-based AIMD simulations of large-scale condensed-phase systems with general and fluctuating cells in the isobaric-isoenthalpic/isobaric-isothermal ( NpH / NpT ) ensembles. The theoretical extensions to this approach include an analytical derivation of the EXX contribution to the stress tensor for systems in general simulation cells with a computational complexity that scales linearly with system size. The corresponding algorithmic extensions to exx include optimized routines that (i) handle both static and fluctuating simulation cells with non-orthogonal lattice symmetries, (ii) solve Poisson's equation in general/non-orthogonal cells via an automated selection of the auxiliary grid directions in the Natan-Kronik representation of the discrete Laplacian operator, and (iii) evaluate the EXX contribution to the stress tensor. Using this approach, we perform a case study on a variety of condensed-phase systems (including liquid water, a benzene molecular crystal polymorph, and semi-conducting crystalline silicon) and demonstrate that the EXX contributions to the energy and stress tensor simultaneously converge with an appropriate choice of exx parameters. This is followed by a critical assessment of the computational performance of the extended exx module across several different high-performance computing architectures via case studies on (i) the computational complexity due to lattice symmetry during NpT simulations of three different ice polymorphs (i.e., ice I h , II, and III) and (ii) the strong/weak parallel scaling during large-scale NpT simulations of liquid water. We demonstrate that the robust and highly scalable implementation of this approach in the extended exx module is capable of evaluating the EXX contribution to the stress tensor with negligible cost (<1%) as well as all other EXX-related quantities needed during NpT simulations of liquid water (with a very tight 150 Ry planewave cutoff) in ≈5.2 s ((H 2 O) 128 ) and ≈6.8 s ((H 2 O) 256 ) per AIMD step. As such, the extended exx module presented in this work brings us another step closer to routinely performing hybrid DFT-based AIMD simulations of sufficient duration for large-scale condensed-phase systems across a wide range of thermodynamic conditions.

In this work, we present NENCI-2021, a benchmark database of ∼8000 Non-Equilibirum Non-Covalent Interaction energies for a large and diverse selection of intermolecular complexes of biological and chemical relevance. To meet the growing demand for large and high-quality quantum mechanical data in the chemical sciences, NENCI-2021 starts with the 101 molecular dimers in the widely used S66 and S101 databases and extends the scope of these works by (i) including 40 cation-π and anion-π complexes, a fundamentally important class of non-covalent interactions that are found throughout nature and pose a substantial challenge to theory, and (ii) systematically sampling all 141 intermolecular potential energy surfaces (PESs) by simultaneously varying the intermolecular distance and intermolecular angle in each dimer. Designed with an emphasis on close contacts, the complexes in NENCI-2021 were generated by sampling seven intermolecular distances along each PES (ranging from 0.7× to 1.1× the equilibrium separation) and nine intermolecular angles per distance (five for each ion-π complex), yielding an extensive database of 7763 benchmark intermolecular interaction energies (E int ) obtained at the coupled-cluster with singles, doubles, and perturbative triples/complete basis set [CCSD(T)/CBS] level of theory. The E int values in NENCI-2021 span a total of 225.3 kcal/mol, ranging from -38.5 to +186.8 kcal/mol, with a mean (median) E int value of -1.06 kcal/mol (-2.39 kcal/mol). In addition, a wide range of intermolecular atom-pair distances are also present in NENCI-2021, where close intermolecular contacts involving atoms that are located within the so-called van der Waals envelope are prevalent-these interactions, in particular, pose an enormous challenge for molecular modeling and are observed in many important chemical and biological systems. A detailed symmetry-adapted perturbation theory (SAPT)-based energy decomposition analysis also confirms the diverse and comprehensive nature of the intermolecular binding motifs present in NENCI-2021, which now includes a significant number of primarily induction-bound dimers (e.g., cation-π complexes). NENCI-2021 thus spans all regions of the SAPT ternary diagram, thereby warranting a new four-category classification scheme that includes complexes primarily bound by electrostatics (3499), induction (700), dispersion (1372), or mixtures thereof (2192). A critical error analysis performed on a representative set of intermolecular complexes in NENCI-2021 demonstrates that the E int values provided herein have an average error of ±0.1 kcal/mol, even for complexes with strongly repulsive E int values, and maximum errors of ±0.2-0.3 kcal/mol (i.e., ∼±1.0 kJ/mol) for the most challenging cases. For these reasons, we expect that NENCI-2021 will play an important role in the testing, training, and development of next-generation classical and polarizable force fields, density functional theory approximations, wavefunction theory methods, and machine learning based intra- and inter-molecular potentials.

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear-electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an "open teamware" model and an increasingly modular design.

In this work, we used finite-field derivative techniques and density functional theory (DFT) to compute the static isotropic polarizability series (αl with l = 1, 2, 3) for the C60-C84 fullerenes and quantitatively assess the intrinsic non-additivity in these fundamental response properties. By comparing against classical models of the fullerenes as conducting spherical shells (or solid spheres) of uniform electron density, a detailed critical analysis of the derived effective scaling laws (α1 ∼ N1.2, α2 ∼ N2.0, α3 ∼ N2.7) demonstrates that the electronic structure of finite-sized fullerenes-a unique dichotomy of electron confinement and delocalization effects due to their quasi-spherical cage-like structures and encapsulated void spaces-simultaneously limits and enhances their quantum mechanical response to electric field perturbations. Corresponding frequency-dependent polarizabilities were obtained by inputting the αl series into the hollow sphere model (within the modified single frequency approximation), and used to compute the molecular dispersion coefficients (Cn with n = 6, 8, 9, 10) needed to describe the non-trivial van der Waals (vdW) interactions in fullerene-based systems. Using first-order perturbation theory in conjunction with >140 000 DFT calculations, we also computed the non-negligible zero-point vibrational contributions to α1 in C60 and C70, thereby enabling a more accurate and direct comparison between theory and experiment for these quintessential nanostructures.

We introduce QM7-X, a comprehensive dataset of 42 physicochemical properties for ≈4.2 million equilibrium and non-equilibrium structures of small organic molecules with up to seven non-hydrogen (C, N, O, S, Cl) atoms. To span this fundamentally important region of chemical compound space (CCS), QM7-X includes an exhaustive sampling of (meta-)stable equilibrium structures-comprised of constitutional/structural isomers and stereoisomers, e.g., enantiomers and diastereomers (including cis-/trans- and conformational isomers)-as well as 100 non-equilibrium structural variations thereof to reach a total of ≈4.2 million molecular structures. Computed at the tightly converged quantum-mechanical PBE0+MBD level of theory, QM7-X contains global (molecular) and local (atom-in-a-molecule) properties ranging from ground state quantities (such as atomization energies and dipole moments) to response quantities (such as polarizability tensors and dispersion coefficients). By providing a systematic, extensive, and tightly-converged dataset of quantum-mechanically computed physicochemical properties, we expect that QM7-X will play a critical role in the development of next-generation machine-learning based models for exploring greater swaths of CCS and performing in silico design of molecules with targeted properties.

Alkaline anion exchange membranes (AAEMs) with high hydroxide conductivity and good alkaline stability are essential for the development of anion exchange membrane fuel cells to generate clean energy by converting renewable fuels to electricity. Polyethylene-based AAEMs with excellent properties can be prepared via sequential ring-opening metathesis polymerization (ROMP) and hydrogenation of cyclooctene derivatives. However, one of the major limitations of this approach is the complicated multi-step synthesis of functionalized cyclooctene monomers. Herein, we report that piperidinium-functionalized cyclooctene monomers can be easily prepared via the photocatalytic hydroamination of cyclooctadiene with piperidine in a one-pot, two-step process to produce high-performance AAEMs. Possible alkaline-degradation pathways of the resultant polymers were analyzed using spectroscopic analysis and dispersion-inclusive hybrid density functional theory (DFT) calculations. Quite interestingly, our theoretical calculations indicate that local backbone morphology-which can potentially change the Hofmann elimination reaction rate constant by more than four orders of magnitude-is another important consideration in the rational design of stable high-performance AAEMs., Competing Interests: There are no conflicts to declare., (This journal is © The Royal Society of Chemistry.)

Chiral nitriles and their derivatives are prevalent in pharmaceuticals and bioactive compounds. Enantioselective alkene hydrocyanation represents a convenient and efficient approach for synthesizing these molecules. However, a generally applicable method featuring a broad substrate scope and high functional group tolerance remains elusive. Here, we address this long-standing synthetic problem using dual electrocatalysis. Using this strategy, we leverage electrochemistry to seamlessly combine two canonical radical reactions-cobalt-mediated hydrogen-atom transfer and copper-promoted radical cyanation-to accomplish highly enantioselective hydrocyanation without the need for stoichiometric oxidants. We also harness electrochemistry's unique feature of precise potential control to optimize the chemoselectivity of challenging substrates. Computational analysis uncovers the origin of enantio-induction, for which the chiral catalyst imparts a combination of attractive and repulsive non-covalent interactions to direct the enantio-determining C-CN bond formation. This work demonstrates the power of electrochemistry in accessing new chemical space and providing solutions to pertinent challenges in synthetic chemistry.

The molecular dipole moment (μ) is a central quantity in chemistry. It is essential in predicting infrared and sum-frequency generation spectra as well as induction and long-range electrostatic interactions. Furthermore, it can be extracted directly-via the ground state electron density-from high-level quantum mechanical calculations, making it an ideal target for machine learning (ML). In this work, we choose to represent this quantity with a physically inspired ML model that captures two distinct physical effects: local atomic polarization is captured within the symmetry-adapted Gaussian process regression framework which assigns a (vector) dipole moment to each atom, while the movement of charge across the entire molecule is captured by assigning a partial (scalar) charge to each atom. The resulting "MuML" models are fitted together to reproduce molecular μ computed using high-level coupled-cluster theory and density functional theory (DFT) on the QM7b dataset, achieving more accurate results due to the physics-based combination of these complementary terms. The combined model shows excellent transferability when applied to a showcase dataset of larger and more complex molecules, approaching the accuracy of DFT at a small fraction of the computational cost. We also demonstrate that the uncertainty in the predictions can be estimated reliably using a calibrated committee model. The ultimate performance of the models-and the optimal weighting of their combination-depends, however, on the details of the system at hand, with the scalar model being clearly superior when describing large molecules whose dipole is almost entirely generated by charge separation. These observations point to the importance of simultaneously accounting for the local and non-local effects that contribute to μ; furthermore, they define a challenging task to benchmark future models, particularly those aimed at the description of condensed phases.

By including a fraction of exact exchange (EXX), hybrid functionals reduce the self-interaction error in semilocal density functional theory (DFT) and thereby furnish a more accurate and reliable description of the underlying electronic structure in systems throughout biology, chemistry, physics, and materials science. However, the high computational cost associated with the evaluation of all required EXX quantities has limited the applicability of hybrid DFT in the treatment of large molecules and complex condensed-phase materials. To overcome this limitation, we describe a linear-scaling approach that utilizes a local representation of the occupied orbitals (e.g., maximally localized Wannier functions (MLWFs)) to exploit the sparsity in the real-space evaluation of the quantum mechanical exchange interaction in finite-gap systems. In this work, we present a detailed description of the theoretical and algorithmic advances required to perform MLWF-based ab initio molecular dynamics (AIMD) simulations of large-scale condensed-phase systems of interest at the hybrid DFT level. We focus our theoretical discussion on the integration of this approach into the framework of Car-Parrinello AIMD, and highlight the central role played by the MLWF-product potential (i.e., the solution of Poisson's equation for each corresponding MLWF-product density) in the evaluation of the EXX energy and wave function forces. We then provide a comprehensive description of the exx algorithm implemented in the open-source Quantum ESPRESSO program, which employs a hybrid MPI/OpenMP parallelization scheme to efficiently utilize the high-performance computing (HPC) resources available on current- and next-generation supercomputer architectures. This is followed by a critical assessment of the accuracy and parallel performance (e.g., strong and weak scaling) of this approach when AIMD simulations of liquid water are performed in the canonical ( NVT ) ensemble. With access to HPC resources, we demonstrate that exx enables hybrid DFT-based AIMD simulations of condensed-phase systems containing 500-1000 atoms (e.g., (H 2 O) 256 ) with a wall time cost that is comparable to that of semilocal DFT. In doing so, exx takes us one step closer to routinely performing AIMD simulations of complex and large-scale condensed-phase systems for sufficiently long time scales at the hybrid DFT level of theory.

Ion-π interactions between the face of a molecular π-system and a cation or anion are among the strongest noncovalent interactions known, with applications throughout biochemistry and structural biology, molecular recognition and host-guest chemistry, as well as enzyme kinetics and organocatalysis. In this work, we examine the competing notions of selectivity and flexibility in this class of noncovalent interactions by investigating how certain π-systems can be promiscuous ion-π binders with the versatility to form favorable cation- and anion-π complexes. We focus our efforts on a detailed theoretical case study of the DNA/RNA nucleobases by first demonstrating that these π-systems are promiscuous ion-π binders with the biologically relevant Li + /Na + cations and F - /Cl - anions via benchmark-quality quantum-mechanical binding energy curves computed at the CCSD(T)/CBS level of theory. Using a symmetry-adapted perturbation theory (SAPT)-based energy decomposition analysis, we explore the different physicochemical driving forces underlying the formation of cation- and anion-π complexes, as well as the crucial role played by charge penetration effects in determining the nontrivial (and often counterintuitive) electrostatics in anion-π systems. In doing so, a unified view of these rather distinct noncovalent binding motifs emerges with the finding that both cation- and anion-π complexes are strongly stabilized by an essentially ring-independent potential that can only be overcome by substantially unfavorable electrostatics. This work furnishes a more comprehensive explanation for decades of observed correlations between the equilibrium binding energy and the electrostatic potential above the ring and provides new insight into the nature of selectivity and flexibility in this important class of noncovalent interactions. Quite interestingly, the analysis presented herein demonstrates that π-systems have an inherent propensity to bind both cations and anions, thereby implying that promiscuous ion-π binding is not an exotic property of the nucleobases and should be common in nature.

Coordination compounds of the lanthanide ions (Ln 3+ ) have important applications in medicine due to their photophysical, magnetic, and nuclear properties. To effectively use the Ln 3+ ions for these applications, chelators that stably bind them in vivo are required to prevent toxic side effects that arise from localization of these ions in off-target tissue. In this study, two new picolinate-containing chelators, a heptadentate ligand OxyMepa and a nonadentate ligand Oxyaapa, were prepared, and their coordination chemistries with Ln 3+ ions were thoroughly investigated to evaluate their suitability for use in medicine. Protonation constants of these chelators and stability constants for their Ln 3+ complexes were evaluated. Both ligands exhibit a thermodynamic preference for small Ln 3+ ions. The log K LuL = 12.21 and 21.49 for OxyMepa and Oxyaapa, respectively, indicating that the nonadentate Oxyaapa forms complexes of significantly higher stability than the heptadentate OxyMepa. X-ray crystal structures of the Lu 3+ complexes were obtained, revealing that Oxyaapa saturates the coordination sphere of Lu 3+ , whereas OxyMepa leaves an additional open coordination site for a bound water ligand. Solution structural studies carried out with NMR spectroscopy revealed the presence of two possible conformations for these ligands upon Ln 3+ binding. Density functional theory (DFT) calculations were applied to probe the geometries and energies of these conformations. Energy differences obtained by DFT are small but consistent with experimental data. The photophysical properties of the Eu 3+ and Tb 3+ complexes were characterized, revealing modest photoluminescent quantum yields of <2%. Luminescence lifetime measurements were carried out in H 2 O and D 2 O, showing that the Eu 3+ and Tb 3+ complexes of OxyMepa have two inner-sphere water ligands, whereas the Eu 3+ and Tb 3+ complexes of Oxyaapa have zero. Lastly, variable-temperature 17 O NMR spectroscopy was performed for the Gd-OxyMepa complex to determine its water exchange rate constant of k ex 298 = (2.8 ± 0.1) × 10 6 s -1 . Collectively, this comprehensive characterization of these Ln 3+ chelators provides valuable insight for their potential use in medicine and garners additional understanding of ligand design strategies.

In this work, we have explored the use of a third species during chemical vapor deposition (CVD) to direct thin-film growth to occur exclusively on one surface in the presence of another. Using a combination of density functional theory (DFT) calculations and experiments, including in situ surface analysis, we have examined the use of 4-octyne as a coadsorbate in the CVD of ZrO 2 thin films on SiO 2 and Cu surfaces. At sufficiently high partial pressures of the coadsorbate and sufficiently low substrate temperatures, we find that 4-octyne can effectively compete for adsorption sites, blocking chemisorption of the thin-film precursor, Zr[N(CH 3 C 2 H 5 )] 4 , and preventing growth on Cu, while leaving growth unimpeded on SiO 2 . The selective dielectric-on-dielectric (DoD) process developed herein is fast, totally vapor phase, and does not negatively alter the composition or morphology of the deposited thin film. We argue that this approach to area-selective deposition (ASD) should be widely applicable, provided that suitable candidates for preferential binding can be identified.

While density functional theory (DFT) is often an accurate and efficient methodology for evaluating molecular properties such as energies and multipole moments, this approach often yields larger errors for response properties such as the dipole polarizability (α), which describes the tendency of a molecule to form an induced dipole moment in the presence of an electric field. In this work, we provide static α tensors (and other molecular properties such as total energy components, dipole and quadrupole moments, etc.) computed using quantum chemical (QC) and DFT methodologies for all 7,211 molecules in the QM7b database. We also provide the same quantities for the 52 molecules in the AlphaML showcase database, which includes the DNA/RNA nucleobases, uncharged amino acids, several open-chain and cyclic carbohydrates, five popular pharmaceutical molecules, and 23 isomers of C 8 H n . All QC calculations were performed using linear-response coupled-cluster theory including single and double excitations (LR-CCSD), a sophisticated approach for electron correlation, and the d-aug-cc-pVDZ basis set to mitigate basis set incompleteness error. DFT calculations employed the B3LYP and SCAN0 hybrid functionals, in conjunction with d-aug-cc-pVDZ (B3LYP and SCAN0) and d-aug-cc-pVTZ (B3LYP).

The molecular dipole polarizability describes the tendency of a molecule to change its dipole moment in response to an applied electric field. This quantity governs key intra- and intermolecular interactions, such as induction and dispersion; plays a vital role in determining the spectroscopic signatures of molecules; and is an essential ingredient in polarizable force fields. Compared with other ground-state properties, an accurate prediction of the molecular polarizability is considerably more difficult, as this response quantity is quite sensitive to the underlying electronic structure description. In this work, we present highly accurate quantum mechanical calculations of the static dipole polarizability tensors of 7,211 small organic molecules computed using linear response coupled cluster singles and doubles theory (LR-CCSD). Using a symmetry-adapted machine-learning approach, we demonstrate that it is possible to predict the LR-CCSD molecular polarizabilities of these small molecules with an error that is an order of magnitude smaller than that of hybrid density functional theory (DFT) at a negligible computational cost. The resultant model is robust and transferable, yielding molecular polarizabilities for a diverse set of 52 larger molecules (including challenging conjugated systems, carbohydrates, small drugs, amino acids, nucleobases, and hydrocarbon isomers) at an accuracy that exceeds that of hybrid DFT. The atom-centered decomposition implicit in our machine-learning approach offers some insight into the shortcomings of DFT in the prediction of this fundamental quantity of interest., Competing Interests: The authors declare no conflict of interest.

Reliable prediction of the polymorphic energy landscape of a molecular crystal would yield profound insight into drug development in terms of the existence and likelihood of late-appearing polymorphs. However, the computational prediction of molecular crystal polymorphs is highly challenging due to the high dimensionality of conformational and crystallographic space accompanied by the need for relative free energies to within 1 kJ/mol per molecule. In this study, we combine the most successful crystal structure sampling strategy with the most successful first-principles energy ranking strategy of the latest blind test of organic crystal structure prediction methods. Specifically, we present a hierarchical energy ranking approach intended for the refinement of relative stabilities in the final stage of a crystal structure prediction procedure. Such a combined approach provides excellent stability rankings for all studied systems and can be applied to molecular crystals of pharmaceutical importance.

In this work, we investigate how geometric changes influence the static dipole polarizability ( α ) of a water molecule by explicitly computing the corresponding dipole polarizability surface (DPS) across 3125 total (1625 symmetry-unique) geometries using linear response coupled cluster theory including single, double, and triple excitations (LR-CCSDT) and the doubly augmented triple- ζ basis set (d-aug-cc-pVTZ). Analytical formulae based on power series expansions of this ab initio surface are generated using linear least-squares analysis and provide highly accurate estimates of this quantity as a function of molecular geometry (i.e., bond and angle variations) in a computationally tractable manner. An additional database, which consists of 25 representative molecular geometries and incorporates a more thorough treatment of both basis sets and core electron effects, is provided as a current benchmark for this quantity and the corresponding leading-order C 6 dispersion coefficient. This database has been utilized to assess the importance of these effects as well as the relative accuracy that can be obtained using several quantum chemical methods and a library of density functional approximations. In addition to high-level electron correlation methods (like CCSD) and our analytical least-squares formulae, we find that the SCAN0, PBE0, MN15, and B97-2 hybrid functionals yield the most accurate descriptions of the molecular polarizability tensor in H 2 O. Using first-order perturbation theory, we compute the zero-point vibrational correction to α at the CCSDT/d-aug-cc-pVTZ level and find that this correction contributes approximately 3% to the isotropic ( α iso ) and nearly 50% to the anisotropic ( α aniso ) polarizability values. In doing so, we find that α iso = 9.8307 bohr 3 , which is in excellent agreement with the experimental value of 9.83 ± 0.02 bohr 3 provided by Russell and Spackman. The DPS reported herein provides a benchmark-quality quantum mechanical estimate of this fundamental quantity of interest and should find extensive use in the development (and assessment) of next-generation force fields and machine-learning based approaches for modeling water in complex condensed-phase environments.

Converting biomass-based feedstocks into polymers not only reduces our reliance on fossil fuels, but also furnishes multiple opportunities to design biorenewable polymers with targeted properties and functionalities. Here we report a series of high glass transition temperature (T g up to 184 °C) polyesters derived from sugar-based furan derivatives as well as a joint experimental and theoretical study of substituent effects on their thermal properties. Surprisingly, we find that polymers with moderate steric hindrance exhibit the highest T g values. Through a detailed Ramachandran-type analysis of the rotational flexibility of the polymer backbone, we find that additional steric hindrance does not necessarily increase chain stiffness in these polyesters. We attribute this interesting structure-property relationship to a complex interplay between methyl-induced steric strain and the concerted rotations along the polymer backbone. We believe that our findings provide key insight into the relationship between structure and thermal properties across a range of synthetic polymers.

Classical intermolecular potentials typically require an extensive parametrization procedure for any new compound considered. To do away with prior parametrization, we propose a combination of physics-based potentials with machine learning (ML), coined IPML, which is transferable across small neutral organic and biologically relevant molecules. ML models provide on-the-fly predictions for environment-dependent local atomic properties: electrostatic multipole coefficients (significant error reduction compared to previously reported), the population and decay rate of valence atomic densities, and polarizabilities across conformations and chemical compositions of H, C, N, and O atoms. These parameters enable accurate calculations of intermolecular contributions-electrostatics, charge penetration, repulsion, induction/polarization, and many-body dispersion. Unlike other potentials, this model is transferable in its ability to handle new molecules and conformations without explicit prior parametrization: All local atomic properties are predicted from ML, leaving only eight global parameters-optimized once and for all across compounds. We validate IPML on various gas-phase dimers at and away from equilibrium separation, where we obtain mean absolute errors between 0.4 and 0.7 kcal/mol for several chemically and conformationally diverse datasets representative of non-covalent interactions in biologically relevant molecules. We further focus on hydrogen-bonded complexes-essential but challenging due to their directional nature-where datasets of DNA base pairs and amino acids yield an extremely encouraging 1.4 kcal/mol error. Finally, and as a first look, we consider IPML for denser systems: water clusters, supramolecular host-guest complexes, and the benzene crystal.

We report a method for tuning the domain spacing ( D sp ) of self-assembled block copolymer thin films of poly(styrene- block-methyl methacrylate) (PS- b-PMMA) over a large range of lamellar periods. By modifying the molecular weight distribution (MWD) shape (including both the breadth and skew) of the PS block via temporal control of polymer chain initiation in anionic polymerization, we observe increases of up to 41% in D sp for polymers with the same overall molecular weight ( M n ≈ 125 kg mol -1 ) without significantly changing the overall morphology or chemical composition of the final material. In conjunction with our experimental efforts, we have utilized concepts from population statistics and least-squares analysis to develop a model for predicting D sp based on the first three moments of the MWDs. This statistical model reproduces experimental D sp values with high fidelity (with mean absolute errors of 1.2 nm or 1.8%) and provides novel physical insight into the individual and collective roles played by the MWD moments in determining this property of interest. This work demonstrates that both MWD breadth and skew have a profound influence over D sp , thereby providing an experimental and conceptual platform for exploiting MWD shape as a simple and modular handle for fine-tuning D sp in block copolymer thin films.

Proton transfer via hydronium and hydroxide ions in water is ubiquitous. It underlies acid-base chemistry, certain enzyme reactions, and even infection by the flu. Despite two centuries of investigation, the mechanism underlying why hydroxide diffuses slower than hydronium in water is still not well understood. Herein, we employ state-of-the-art density-functional-theory-based molecular dynamics-with corrections for non-local van der Waals interactions, and self-interaction in the electronic ground state-to model water and hydrated water ions. At this level of theory, we show that structural diffusion of hydronium preserves the previously recognized concerted behaviour. However, by contrast, proton transfer via hydroxide is less temporally correlated, due to a stabilized hypercoordination solvation structure that discourages proton transfer. Specifically, the latter exhibits non-planar geometry, which agrees with neutron-scattering results. Asymmetry in the temporal correlation of proton transfer leads to hydroxide diffusing slower than hydronium.

Nuclear quantum effects (NQE), which include both zero-point motion and tunneling, exhibit quite an impressive range of influence over the equilibrium and dynamical properties of molecules and materials. In this work, we extend our recently proposed perturbed path-integral (PPI) approach for modeling NQE in molecular systems [I. Poltavsky and A. Tkatchenko, Chem. Sci. 7, 1368 (2016)], which successfully combines the advantages of thermodynamic perturbation theory with path-integral molecular dynamics (PIMD), in a number of important directions. First, we demonstrate the accuracy, performance, and general applicability of the PPI approach to both molecules and extended (condensed-phase) materials. Second, we derive a series of estimators within the PPI approach to enable calculations of structural properties such as radial distribution functions (RDFs) that exhibit rapid convergence with respect to the number of beads in the PIMD simulation. Finally, we introduce an effective nuclear temperature formalism within the framework of the PPI approach and demonstrate that such effective temperatures can be an extremely useful tool in quantitatively estimating the "quantumness" associated with different degrees of freedom in the system as well as providing a reliable quantitative assessment of the convergence of PIMD simulations. Since the PPI approach only requires the use of standard second-order imaginary-time PIMD simulations, these developments enable one to include a treatment of NQE in equilibrium thermodynamic properties (such as energies, heat capacities, and RDFs) with the accuracy of higher-order methods but at a fraction of the computational cost, thereby enabling first-principles modeling that simultaneously accounts for the quantum mechanical nature of both electrons and nuclei in large-scale molecules and materials.

Epitaxy forms the basis of modern electronics and optoelectronics. We report coherent atomically thin superlattices in which different transition metal dichalcogenide monolayers-despite large lattice mismatches-are repeated and laterally integrated without dislocations within the monolayer plane. Grown by an omnidirectional epitaxy, these superlattices display fully matched lattice constants across heterointerfaces while maintaining an isotropic lattice structure and triangular symmetry. This strong epitaxial strain is precisely engineered via the nanoscale supercell dimensions, thereby enabling broad tuning of the optical properties and producing photoluminescence peak shifts as large as 250 millielectron volts. We present theoretical models to explain this coherent growth and the energetic interplay governing the ripple formation in these strained monolayers. Such coherent superlattices provide building blocks with targeted functionalities at the atomically thin limit., (Copyright © 2018 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works.)

Quantum EXPRESSO is an integrated suite of open-source computer codes for quantum simulations of materials using state-of-the-art electronic-structure techniques, based on density-functional theory, density-functional perturbation theory, and many-body perturbation theory, within the plane-wave pseudopotential and projector-augmented-wave approaches. Quantum EXPRESSO owes its popularity to the wide variety of properties and processes it allows to simulate, to its performance on an increasingly broad array of hardware architectures, and to a community of researchers that rely on its capabilities as a core open-source development platform to implement their ideas. In this paper we describe recent extensions and improvements, covering new methodologies and property calculators, improved parallelization, code modularization, and extended interoperability both within the distribution and with external software.

Noncovalent van der Waals (vdW) or dispersion forces are ubiquitous in nature and influence the structure, stability, dynamics, and function of molecules and materials throughout chemistry, biology, physics, and materials science. These forces are quantum mechanical in origin and arise from electrostatic interactions between fluctuations in the electronic charge density. Here, we explore the conceptual and mathematical ingredients required for an exact treatment of vdW interactions, and present a systematic and unified framework for classifying the current first-principles vdW methods based on the adiabatic-connection fluctuation-dissipation (ACFD) theorem (namely the Rutgers-Chalmers vdW-DF, Vydrov-Van Voorhis (VV), exchange-hole dipole moment (XDM), Tkatchenko-Scheffler (TS), many-body dispersion (MBD), and random-phase approximation (RPA) approaches). Particular attention is paid to the intriguing nature of many-body vdW interactions, whose fundamental relevance has recently been highlighted in several landmark experiments. The performance of these models in predicting binding energetics as well as structural, electronic, and thermodynamic properties is connected with the theoretical concepts and provides a numerical summary of the state-of-the-art in the field. We conclude with a roadmap of the conceptual, methodological, practical, and numerical challenges that remain in obtaining a universally applicable and truly predictive vdW method for realistic molecular systems and materials.

The sixth blind test of organic crystal structure prediction (CSP) methods has been held, with five target systems: a small nearly rigid molecule, a polymorphic former drug candidate, a chloride salt hydrate, a co-crystal and a bulky flexible molecule. This blind test has seen substantial growth in the number of participants, with the broad range of prediction methods giving a unique insight into the state of the art in the field. Significant progress has been seen in treating flexible molecules, usage of hierarchical approaches to ranking structures, the application of density-functional approximations, and the establishment of new workflows and `best practices' for performing CSP calculations. All of the targets, apart from a single potentially disordered Z' = 2 polymorph of the drug candidate, were predicted by at least one submission. Despite many remaining challenges, it is clear that CSP methods are becoming more applicable to a wider range of real systems, including salts, hydrates and larger flexible molecules. The results also highlight the potential for CSP calculations to complement and augment experimental studies of organic solid forms.

Recent experiments on noncovalent interactions at the nanoscale have challenged the basic assumptions of commonly used particle- or fragment-based models for describing van der Waals (vdW) or dispersion forces. We demonstrate that a qualitatively correct description of the vdW interactions between polarizable nanostructures over a wide range of finite distances can only be attained by accounting for the wavelike nature of charge density fluctuations. By considering a diverse set of materials and biological systems with markedly different dimensionalities, topologies, and polarizabilities, we find a visible enhancement in the nonlocality of the charge density response in the range of 10 to 20 nanometers. These collective wavelike fluctuations are responsible for the emergence of nontrivial modifications of the power laws that govern noncovalent interactions at the nanoscale., (Copyright © 2016, American Association for the Advancement of Science.)

An accurate treatment of the long-range electron correlation energy, including van der Waals (vdW) or dispersion interactions, is essential for describing the structure, dynamics, and function of a wide variety of systems. Among the most accurate models for including dispersion into density functional theory (DFT) is the range-separated many-body dispersion (MBD) method [A. Ambrosetti et al. , J. Chem. Phys. , 2014, 140 , 18A508], in which the correlation energy is modeled at short-range by a semi-local density functional and at long-range by a model system of coupled quantum harmonic oscillators. In this work, we develop analytical gradients of the MBD energy with respect to nuclear coordinates, including all implicit coordinate dependencies arising from the partitioning of the charge density into Hirshfeld effective volumes. To demonstrate the efficiency and accuracy of these MBD gradients for geometry optimizations of systems with intermolecular and intramolecular interactions, we optimized conformers of the benzene dimer and isolated small peptides with aromatic side-chains. We find excellent agreement with the wavefunction theory reference geometries of these systems (at a fraction of the computational cost) and find that MBD consistently outperforms the popular TS and D3(BJ) dispersion corrections. To demonstrate the performance of the MBD model on a larger system with supramolecular interactions, we optimized the C 60 @C 60 H 28 buckyball catcher host-guest complex. In our analysis, we also find that neglecting the implicit nuclear coordinate dependence arising from the charge density partitioning, as has been done in prior numerical treatments, leads to an unacceptable error in the MBD forces, with relative errors of ∼20% (on average) that can extend well beyond 100%.

In order to carry out a detailed analysis of the molecular static polarizability, which is the response of the molecule to a uniform external electric field, the molecular polarizability was computed using the finite-difference method for 21 small molecules, using density functional theory. Within nine charge population schemes (Löwdin, Mulliken, Becke, Hirshfeld, CM5, Hirshfeld-I, NPA, CHELPG, MK-ESP) in common use, the charge fluctuation contribution is found to dominate the molecular polarizability, with its ratio ranging from 59.9% with the Hirshfeld or CM5 scheme to 96.2% with the Mulliken scheme. The Hirshfeld-I scheme is also used to compute the other contribution to the molecular polarizability coming from the induced atomic dipoles, and the atomic polarizabilities in eight small molecules and water pentamer are found to be highly anisotropic for most atoms. Overall, the results suggest that (a) more emphasis probably should be placed on the charge fluctuation terms in future polarizable force field development and (b) an anisotropic polarizability might be more suitable than an isotropic one in polarizable force fields based entirely or partially on the induced atomic dipoles.

How strong is the effect of van der Waals (vdW) interactions on the electronic properties of molecules and extended systems? To answer this question, we derived a fully self-consistent implementation of the density-dependent interatomic vdW functional of Tkatchenko and Scheffler [Phys. Rev. Lett. 102, 073005 (2009)]. Not surprisingly, vdW self-consistency leads to tiny modifications of the structure, stability, and electronic properties of molecular dimers and crystals. However, unexpectedly large effects were found in the binding energies, distances, and electrostatic moments of highly polarizable alkali-metal dimers. Most importantly, vdW interactions induced complex and sizable electronic charge redistribution in the vicinity of metallic surfaces and at organic-metal interfaces. As a result, a substantial influence on the computed work functions was found, revealing a nontrivial connection between electrostatics and long-range electron correlation effects.

In this work, we report the results of a series of density functional theory (DFT) based ab initio molecular dynamics (AIMD) simulations of ambient liquid water using a hierarchy of exchange-correlation (XC) functionals to investigate the individual and collective effects of exact exchange (Exx), via the PBE0 hybrid functional, non-local van der Waals/dispersion (vdW) interactions, via a fully self-consistent density-dependent dispersion correction, and an approximate treatment of nuclear quantum effects, via a 30 K increase in the simulation temperature, on the microscopic structure of liquid water. Based on these AIMD simulations, we found that the collective inclusion of Exx and vdW as resulting from a large-scale AIMD simulation of (H2O)128 significantly softens the structure of ambient liquid water and yields an oxygen-oxygen structure factor, SOO(Q), and corresponding oxygen-oxygen radial distribution function, gOO(r), that are now in quantitative agreement with the best available experimental data. This level of agreement between simulation and experiment demonstrated herein originates from an increase in the relative population of water molecules in the interstitial region between the first and second coordination shells, a collective reorganization in the liquid phase which is facilitated by a weakening of the hydrogen bond strength by the use of a hybrid XC functional, coupled with a relative stabilization of the resultant disordered liquid water configurations by the inclusion of non-local vdW/dispersion interactions. This increasingly more accurate description of the underlying hydrogen bond network in liquid water also yields higher-order correlation functions, such as the oxygen-oxygen-oxygen triplet angular distribution, POOO(θ), and therefore the degree of local tetrahedrality, as well as electrostatic properties, such as the effective molecular dipole moment, that are in much better agreement with experiment.

This work reviews the increasing evidence that many-body van der Waals (vdW) or dispersion interactions play a crucial role in the structure, stability and function of a wide variety of systems in biology, chemistry and physics. Starting with the exact expression for the electron correlation energy provided by the adiabatic connection fluctuation-dissipation theorem, we derive both pairwise and many-body interatomic methods for computing the long-range dispersion energy by considering a model system of coupled quantum harmonic oscillators within the random-phase approximation. By coupling this approach to density functional theory, the resulting many-body dispersion (MBD) method provides an accurate and efficient scheme for computing the frequency-dependent polarizability and many-body vdW energy in molecules and materials with a finite electronic gap. A select collection of applications are presented that ascertain the fundamental importance of these non-bonded interactions across the spectrum of intermolecular (the S22 and S66 benchmark databases), intramolecular (conformational energies of alanine tetrapeptide) and supramolecular (binding energy of the 'buckyball catcher') complexes, as well as molecular crystals (cohesive energies in oligoacenes). These applications demonstrate that electrodynamic response screening and beyond-pairwise many-body vdW interactions--both captured at the MBD level of theory--play a quantitative, and sometimes even qualitative, role in describing the properties considered herein. This work is then concluded with an in-depth discussion of the challenges that remain in the future development of reliable (accurate and efficient) methods for treating many-body vdW interactions in complex materials and provides a roadmap for navigating many of the research avenues that are yet to be explored.

An accurate determination of the electron correlation energy is an essential prerequisite for describing the structure, stability, and function in a wide variety of systems. Therefore, the development of efficient approaches for the calculation of the correlation energy (and hence the dispersion energy as well) is essential and such methods can be coupled with many density-functional approximations, local methods for the electron correlation energy, and even interatomic force fields. In this work, we build upon the previously developed many-body dispersion (MBD) framework, which is intimately linked to the random-phase approximation for the correlation energy. We separate the correlation energy into short-range contributions that are modeled by semi-local functionals and long-range contributions that are calculated by mapping the complex all-electron problem onto a set of atomic response functions coupled in the dipole approximation. We propose an effective range-separation of the coupling between the atomic response functions that extends the already broad applicability of the MBD method to non-metallic materials with highly anisotropic responses, such as layered nanostructures. Application to a variety of high-quality benchmark datasets illustrates the accuracy and applicability of the improved MBD approach, which offers the prospect of first-principles modeling of large structurally complex systems with an accurate description of the long-range correlation energy.

Noncovalent interactions are ubiquitous in molecular and condensed-phase environments, and hence a reliable theoretical description of these fundamental interactions could pave the way toward a more complete understanding of the microscopic underpinnings for a diverse set of systems in chemistry and biology. In this work, we demonstrate that recent algorithmic advances coupled to the availability of large-scale computational resources make the stochastic quantum Monte Carlo approach to solving the Schrödinger equation an optimal contender for attaining "chemical accuracy" (1 kcal/mol) in the binding energies of supramolecular complexes of chemical relevance. To illustrate this point, we considered a select set of seven host-guest complexes, representing the spectrum of noncovalent interactions, including dispersion or van der Waals forces, π-π stacking, hydrogen bonding, hydrophobic interactions, and electrostatic (ion-dipole) attraction. A detailed analysis of the interaction energies reveals that a complete theoretical description necessitates treatment of terms well beyond the standard London and Axilrod-Teller contributions to the van der Waals dispersion energy.

Interatomic pairwise methods are currently among the most popular and accurate ways to include dispersion energy in density functional theory calculations. However, when applied to more than two atoms, these methods are still frequently perceived to be based on ad hoc assumptions, rather than a rigorous derivation from quantum mechanics. Starting from the adiabatic connection fluctuation-dissipation (ACFD) theorem, an exact expression for the electronic exchange-correlation energy, we demonstrate that the pairwise interatomic dispersion energy for an arbitrary collection of isotropic polarizable dipoles emerges from the second-order expansion of the ACFD formula upon invoking the random-phase approximation (RPA) or the full-potential approximation. Moreover, for a system of quantum harmonic oscillators coupled through a dipole-dipole potential, we prove the equivalence between the full interaction energy obtained from the Hamiltonian diagonalization and the ACFD-RPA correlation energy. This property makes the Hamiltonian diagonalization an efficient method for the calculation of the many-body dispersion energy. In addition, we show that the switching function used to damp the dispersion interaction at short distances arises from a short-range screened Coulomb potential, whose role is to account for the spatial spread of the individual atomic dipole moments. By using the ACFD formula, we gain a deeper understanding of the approximations made in the interatomic pairwise approaches, providing a powerful formalism for further development of accurate and efficient methods for the calculation of the dispersion energy.

Van der Waals (vdW) interactions are ubiquitous in molecules and condensed matter, and play a crucial role in determining the structure, stability, and function for a wide variety of systems. The accurate prediction of these interactions from first principles is a substantial challenge because they are inherently quantum mechanical phenomena that arise from correlations between many electrons within a given molecular system. We introduce an efficient method that accurately describes the nonadditive many-body vdW energy contributions arising from interactions that cannot be modeled by an effective pairwise approach, and demonstrate that such contributions can significantly exceed the energy of thermal fluctuations--a critical accuracy threshold highly coveted during molecular simulations--in the prediction of several relevant properties. Cases studied include the binding affinity of ellipticine, a DNA-intercalating anticancer agent, the relative energetics between the A- and B-conformations of DNA, and the thermodynamic stability among competing paracetamol molecular crystal polymorphs. Our findings suggest that inclusion of the many-body vdW energy is essential for achieving chemical accuracy and therefore must be accounted for in molecular simulations.

An efficient method is developed for the microscopic description of the frequency-dependent polarizability of finite-gap molecules and solids. This is achieved by combining the Tkatchenko-Scheffler van der Waals (vdW) method [Phys. Rev. Lett. 102, 073005 (2009)] with the self-consistent screening equation of classical electrodynamics. This leads to a seamless description of polarization and depolarization for the polarizability tensor of molecules and solids. The screened long-range many-body vdW energy is obtained from the solution of the Schrödinger equation for a system of coupled oscillators. We show that the screening and the many-body vdW energy play a significant role even for rather small molecules, becoming crucial for an accurate treatment of conformational energies for biomolecules and binding of molecular crystals. The computational cost of the developed theory is negligible compared to the underlying electronic structure calculation.

Molecular force fields have been approaching a generational transition over the past several years, moving away from well-established and well-tuned, but intrinsically limited, fixed point charge models toward more intricate and expensive polarizable models that should allow more accurate description of molecular properties. The recently introduced AMOEBA force field is a leading publicly available example of this next generation of theoretical model, but to date, it has only received relatively limited validation, which we address here. We show that the AMOEBA force field is in fact a significant improvement over fixed charge models for small molecule structural and thermodynamic observables in particular, although further fine-tuning is necessary to describe solvation free energies of drug-like small molecules, dynamical properties away from ambient conditions, and possible improvements in aromatic interactions. State of the art electronic structure calculations reveal generally very good agreement with AMOEBA for demanding problems such as relative conformational energies of the alanine tetrapeptide and isomers of water sulfate complexes. AMOEBA is shown to be especially successful on protein-ligand binding and computational X-ray crystallography where polarization and accurate electrostatics are critical.

The 1,4-phenylenediisocyanide (PDI) dimer serves as an intriguing case of the substituted benzene dimer, as well as a prototype system for self-assembled monolayers of organic isocyanide complexes. Structures and binding energies are explored using recently developed dual-basis second-order Møller-Plesset perturbation theory energies and gradients. The structures are dictated by a combination of dispersion and electrostatics, a combination not properly treated with local or gradient-corrected density functionals. The PDI dimer binds more than twice as strongly as unsubstituted benzene dimers in several configurations, and greater directional specificity between parallel-displaced and T-shaped structures is observed. A rotated-parallel structure is the predicted lowest-energy, gas-phase configuration, in which the isocyanide ligands are staggered on the monomers. Relevant potential energy curves of the dimer are also presented, and insights into PDI monolayer formation on metal surfaces are explored via simple two-body models. Based on the adsorbate interaction alone, a high-coverage configuration and non-vertical tilt are predicted to be favorable, although the total binding for PDI in these configurations is still insufficient to form ordered monolayers, a result consistent with previous experimental findings. Additional phenyl rings (biphenyldiisocyanide, triphenyldiisocyanide) significantly stabilize the interaction and provide the additional dispersion necessary for an ordered monolayer.

We show that the often unsatisfactory performance of Møller-Plesset second-order perturbation theory (MP2) for the dispersion interaction between closed-shell molecules can be rectified by adding a correction Delta C(n)/R(n), to its long-range behavior. The dispersion-corrected MP2 (MP2 + Delta vdW) results are in excellent agreement with the quantum chemistry "gold standard" [coupled cluster theory with single, double and perturbative triple excitations, CCSD(T)] for a range of systems bounded by hydrogen bonding, electrostatics and dispersion forces. The MP2 + Delta vdW method is only mildly dependent on the short-range damping function and consistently outperforms state-of-the-art dispersion-corrected density-functional theory.

Basis set pairings for dual-basis calculations are presented for the aug-cc-pVXZ (X = D, T, Q) series of basis sets. Fidelity with single-basis results is assessed at the second-order Møller-Plesset perturbation theory (MP2) level within the resolution-of-the-identity (RI) approximation, using the S22 set of noncovalent interactions and a series of electron affinities from the G3 set. Root-mean-squared errors for the S22 set are 0.019 kcal mol(-1) or lower, with a maximum deviation of 0.44%, and errors in nuclear structures are 0.09% or lower. Cost savings of 60-93% (RI-MP2 energies) and 50-88% (RI-MP2 gradients) are demonstrated. Spin-component-scaled MP2 [SCS(MI)-MP2] scaling parameters are provided for the aug-cc-pVXZ series, and dual-basis results are shown to be consistent without reoptimization of the single-basis parameters. Explicit handling of linear dependence in the basis set projection scheme is also provided. These dual-basis pairings will be helpful for accelerating accurate Hartree-Fock, density functional theory (DFT), MP2 and scaled MP2, and so-called doubly hybrid DFT calculations of intermolecular interactions (and other systems), where augmented basis sets are physically important.

The recently proposed new family of "double-hybrid" density functionals [Grimme, S. J. Chem. Phys. 2006, 124, 34108] replaces a fraction of the semi-local correlation energy by a non-local correlation energy expression that employs the Kohn-Sham orbitals in second-order many-body perturbation theory. These functionals have provided results of high accuracy over a wide range of properties but fail to accurately describe long-range van der Waals interactions. In this work, a distance-dependent scaling factor for the non-local correlation energy is introduced to address this problem, and two new double-hybrid density functionals are proposed. The new functionals are optimized with the finite cc-pVTZ basis on training sets of atomization energies and intermolecular interaction energies. They are compared against (scaled) second-order Møller-Plesset perturbation theories and popular density functionals including the hybrid-GGA functional B3-LYP and the first double-hybrid functional (B2-PLYP). Tests are performed on an extensive set including reaction energies, barrier heights, weakly interacting complexes, transition-metal systems, molecular geometries, and harmonic vibrational frequencies. Within the cc-pVTZ atomic orbital basis, we have demonstrated the ability to find a parametrization scheme which is simultaneously able to describe thermochemistry and weakly bound systems with a satisfactory degree of accuracy.

We present a new algorithm for analytical gradient evaluation in resolution-of-the-identity second-order Møller-Plesset perturbation theory (RI-MP2) and thoroughly assess its computational performance and chemical accuracy. This algorithm addresses the potential I/O bottlenecks associated with disk-based storage and access of the RI-MP2 t-amplitudes by utilizing a semi-direct batching approach and yields computational speed-ups of approximately 2-3 over the best conventional MP2 analytical gradient algorithms. In addition, we attempt to provide a straightforward guide to performing reliable and cost-efficient geometry optimizations at the RI-MP2 level of theory. By computing relative atomization energies for the G3/99 set and optimizing a test set of 136 equilibrium molecular structures, we demonstrate that satisfactory relative accuracy and significant computational savings can be obtained using Pople-style atomic orbital basis sets with the existing auxiliary basis expansions for RI-MP2 computations. We also show that RI-MP2 geometry optimizations reproduce molecular equilibrium structures with no significant deviations (>0.1 pm) from the predictions of conventional MP2 theory. As a chemical application, we computed the extended-globular conformational energy gap in alanine tetrapeptide at the extrapolated RI-MP2/cc-pV(TQ)Z level as 2.884, 4.414, and 4.994 kcal/mol for structures optimized using the HF, DFT (B3LYP), and RI-MP2 methodologies and the cc-pVTZ basis set, respectively. These marked energetic discrepancies originate from differential intramolecular hydrogen bonding present in the globular conformation optimized at these levels of theory and clearly demonstrate the importance of long-range correlation effects in polypeptide conformational analysis., ((c) 2007 Wiley Periodicals, Inc.)

Analytic gradients of dual-basis Hartree-Fock and density functional theory energies have been derived and implemented, which provide the opportunity for capturing large basis-set gradient effects at reduced cost. Suggested pairings for gradient calculations are 6-31G/6-31G**, dual[-f,-d]/cc-pVTZ, and 6-311G*/6-311 + +G(3df,3pd). Equilibrium geometries are produced within 0.0005 A of large-basis results for the latter two pairings. Though a single, iterative SCF response equation must be solved (unlike standard SCF gradients), it may be obtained in the smaller basis set, and integral screening further reduces the cost for well-chosen subsets. Total nuclear force calculations exhibit up to 75% savings, relative to large-basis calculations.