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The structural characterization of proteins with a disorder requires a computational approach backed by experiments to model their diverse and dynamic structural ensembles. The selection of conformational ensembles consistent with solution experiments of disordered proteins highly depends on the initial pool of conformers, with currently available tools limited by conformational sampling. We have developed a Generative Recurrent Neural Network (GRNN) that uses supervised learning to bias the probability distributions of torsions to take advantage of experimental data types such as nuclear magnetic resonance J-couplings, nuclear Overhauser effects, and paramagnetic resonance enhancements. We show that updating the generative model parameters according to the reward feedback on the basis of the agreement between experimental data and probabilistic selection of torsions from learned distributions provides an alternative to existing approaches that simply reweight conformers of a static structural pool for disordered proteins. Instead, the biased GRNN, DynamICE, learns to physically change the conformations of the underlying pool of the disordered protein to those that better agree with experiments. [ABSTRACT FROM AUTHOR]

We developed and implemented a method-independent, fully numerical, finite difference approach to calculating nuclear magnetic resonance shieldings, using gauge-including atomic orbitals. The resulting capability can be used to explore non-standard methods, given only the energy as a function of finite-applied magnetic fields and nuclear spins. For example, standard second-order Møller-Plesset theory (MP2) has well-known efficacy for 1H and 13C shieldings and known limitations for other nuclei such as 15N and 17O. It is, therefore, interesting to seek methods that offer good accuracy for 15N and 17O shieldings without greatly increased compute costs, as well as exploring whether such methods can further improve 1H and 13C shieldings. Using a small molecule test set of 28 species, we assessed two alternatives: κ regularized MP2 (κ-MP2), which provides energy-dependent damping of large amplitudes, and MP2.X, which includes a variable fraction, X, of third-order correlation (MP3). The aug-cc-pVTZ basis was used, and coupled cluster with singles and doubles and perturbative triples [CCSD(T)] results were taken as reference values. Our κ-MP2 results reveal significant improvements over MP2 for 13C and 15N, with the optimal κ value being element-specific. κ-MP2 with κ = 2 offers a 30% rms error reduction over MP2. For 15N, κ-MP2 with κ = 1.1 provides a 90% error reduction vs MP2 and a 60% error reduction vs CCSD. On the other hand, MP2.X with a scaling factor of 0.6 outperformed CCSD for all heavy nuclei. These results can be understood as providing renormalization of doubles amplitudes to partially account for neglected triple and higher substitutions and offer promising opportunities for future applications. [ABSTRACT FROM AUTHOR]

Molecular dynamics simulations of intrinsically disordered proteins (IDPs) can provide high resolution structural ensembles if the force field is accurate enough and if the simulation sufficiently samples the conformational space of the IDP with the correct weighting of sub-populations. Here, we investigate the combined force field–sampling problem by testing a standard force field as well as newer fixed charge force fields, the latter specifically motivated for better description of unfolded states and IDPs, and comparing them with a standard temperature replica exchange (TREx) protocol and a non-equilibrium Temperature Cool Walking (TCW) sampling algorithm. The force field and sampling combinations are used to characterize the structural ensembles of the amyloid-beta peptides Aβ42 and Aβ43, which both should be random coils as shown recently by experimental nuclear magnetic resonance (NMR) and 2D Förster resonance energy transfer (FRET) experiments. The results illustrate the key importance of the sampling algorithm: while the standard force field using TREx is in poor agreement with the NMR J-coupling and nuclear Overhauser effect and 2D FRET data, when using the TCW method, the standard and optimized protein-water force field combinations are in very good agreement with the same experimental data since the TCW sampling method produces qualitatively different ensembles than TREx. We also discuss the relative merit of the 2D FRET data when validating structural ensembles using the different force fields and sampling protocols investigated in this work for small IDPs such as the Aβ42 and Aβ43 peptides. [ABSTRACT FROM AUTHOR]

We extend our recently developed quantum-mechanical/molecular mechanics (QM/MM) approach [Dziedzic et al., J. Chem. Phys. 145, 124106 (2016)] to enable in situ optimization of the localized orbitals. The quantum subsystem is described with onetep linear-scaling density functional theory and the classical subsystem – with the AMOEBA polarizable force field. The two subsystems interact via multipolar electrostatics and are fully mutually polarizable. A total energy minimization scheme is employed for the Hamiltonian of the coupled QM/MM system. We demonstrate that, compared to simpler models using fixed basis sets, the additional flexibility offered by in situ optimized basis functions improves the accuracy of the QM/MM interface, but also poses new challenges, making the QM subsystem more prone to overpolarization and unphysical charge transfer due to increased charge penetration. We show how these issues can be efficiently solved by replacing the classical repulsive van der Waals term for QM/MM interactions with an interaction of the electronic density with a fixed, repulsive MM potential that mimics Pauli repulsion, together with a modest increase in the damping of QM/MM polarization. We validate our method, with particular attention paid to the hydrogen bond, in tests on water-ion pairs, the water dimer, first solvation shells of neutral and charged species, and solute-solvent interaction energies. As a proof of principle, we determine suitable repulsive potential parameters for water, K+, and Cl−. The mechanisms we employed to counteract the unphysical overpolarization of the QM subsystem are demonstrated to be adequate, and our approach is robust. We find that the inclusion of explicit polarization in the MM part of QM/MM improves agreement with fully QM calculations. Our model permits the use of minimal size QM regions and, remarkably, yields good energetics across the well-balanced QM/MM interface. [ABSTRACT FROM AUTHOR]

The field of computational molecular sciences (CMSs) has made innumerable contributions to the understanding of the molecular phenomena that underlie and control chemical processes, which is manifested in a large number of community software projects and codes. The CMS community is now poised to take the next transformative steps of better training in modern software design and engineering methods and tools, increasing interoperability through more systematic adoption of agreed upon standards and accepted best-practices, overcoming unnecessary redundancy in software effort along with greater reproducibility, and increasing the deployment of new software onto hardware platforms from in-house clusters to mid-range computing systems through to modern supercomputers. This in turn will have future impact on the software that will be created to address grand challenge science that we illustrate here: the formulation of diverse catalysts, descriptions of long-range charge and excitation transfer, and development of structural ensembles for intrinsically disordered proteins. [ABSTRACT FROM AUTHOR]

Cesium-137 is a major byproduct of nuclear energy generation and is environmentally threatening due to its long half-life and affinity for naturally occurring micaceous clays. Recent experimental observations of illite and phlogopite mica indicate that Cs+ is capable of exchanging with K+ bound in the anhydrous interlayers of layered silicates, forming sharp exchange fronts, leading to interstratification of Cs- and K-illite. We present here a coarse-grained (CG) model of the anhydrous illite interlayer developed using iterative Boltzmann inversion that qualitatively and quantitatively reproduces features of a previously proposed feedback mechanism of ion exchange. The CG model represents a 70-fold speedup over all-atom models of clay systems and predicts interlayer expansion for K-illite near ion exchange fronts. Contrary to the longstanding theory that ion exchange in a neighboring layer increases the binding of K in lattice counterion sites leading to interstratification, we find that the presence of neighboring exchanged layers leads to short-range structural relaxations that increase basal spacing and decrease cohesion of the neighboring K-illite layers. We also provide evidence that the formation of alternating Cs- and K-illite interlayers (i.e., ordered interstratification) is both thermodynamically and mechanically favorable compared to exchange in adjacent interlayers. [ABSTRACT FROM AUTHOR]

In this work, we evaluate the accuracy of the classical AMOEBA model for representing manybody interactions, such as polarization, charge transfer, and Pauli repulsion and dispersion, through comparison against an energy decomposition method based on absolutely localized molecular orbitals (ALMO-EDA) for the water trimer and a variety of ion-water systems. When the 2- and 3-body contributions according to the many-body expansion are analyzed for the ion-water trimer systems examined here, the 3-body contributions to Pauli repulsion and dispersion are found to be negligible under ALMO-EDA, thereby supporting the validity of the pairwise-additive approximation in AMOEBA's 14-7 van derWaals term. However AMOEBA shows imperfect cancellation of errors for the missing effects of charge transfer and incorrectness in the distance dependence for polarization when compared with the corresponding ALMO-EDA terms. We trace the larger 2-body followed by 3-body polarization errors to the Thole damping scheme used inAMOEBA, and although the width parameter in Thole damping can be changed to improve agreement with the ALMO-EDA polarization for points about equilibrium, the correct profile of polarization as a function of intermolecular distance cannot be reproduced. The results suggest that there is a need for re-examining the damping and polarization model used in the AMOEBA force field and provide further insights into the formulations of polarizable force fields in general. [ABSTRACT FROM AUTHOR]

We compare two standard replica exchange methods using temperature and dielectric constant as the scaling variables for independent replicas against two new corresponding enhanced sampling methods based on non-equilibrium statistical cooling (temperature) or descreening (dielectric).We test the four methods on a rough 1D potential as well as for alanine dipeptide in water, for which their relatively small phase space allows for the ability to define quantitative convergence metrics. We show that both dielectric methods are inferior to the temperature enhanced sampling methods, and in turn show that temperature cool walking (TCW) systematically outperforms the standard temperature replica exchange (TREx) method. We extend our comparisons of the TCW and TREx methods to the 5 residue met-enkephalin peptide, in which we evaluate the Kullback-Leibler divergence metric to show that the rate of convergence between two independent trajectories is faster for TCW compared to TREx. Finally we apply the temperature methods to the 42 residue amyloid-ß peptide in which we find non-negligible differences in the disordered ensemble using TCW compared to the standard TREx. All four methods have been made available as software through the OpenMM Omnia software consortium (http://www.omnia.md/). [ABSTRACT FROM AUTHOR]

We present a novel quantum mechanical/molecular mechanics (QM/MM) approach in which a quantum subsystem is coupled to a classical subsystem described by the AMOEBA polarizable force field. Our approach permits mutual polarization between the QM and MM subsystems, effected through multipolar electrostatics. Self-consistency is achieved for both the QM and MM subsystems through a total energy minimization scheme. We provide an expression for the Hamiltonian of the coupled QM/MM system, which we minimize using gradient methods. The QM subsystem is described by the ONETEP linear-scaling DFT approach, which makes use of strictly localized orbitals expressed in a set of periodic sinc basis functions equivalent to plane waves. The MM subsystem is described by the multipolar, polarizable force field AMOEBA, as implemented in TINKER. Distributed multipole analysis is used to obtain, on the fly, a classical representation of theQMsubsystem in terms of atom-centered multipoles. This auxiliary representation is used for all polarization interactions between QM and MM, allowing us to treat them on the same footing as in AMOEBA.We validate our method in tests of solute-solvent interaction energies, for neutral and charged molecules, demonstrating the simultaneous optimization of the quantum and classical degrees of freedom. Encouragingly, we find that the inclusion of explicit polarization in the MM part of QM/MM improves the agreement with fully QM calculations. [ABSTRACT FROM AUTHOR]

Recently developed density functionals have good accuracy for both thermochemistry (TC) and non-covalent interactions (NC) if very large atomic orbital basis sets are used. To approach the basis set limit with potentially lower computational cost, a new self-consistent field (SCF) scheme is presented that employs minimal adaptive basis (MAB) functions. The MAB functions are optimized on each atomic site by minimizing a surrogate function. High accuracy is obtained by applying a perturbative correction (PC) to the MAB calculation, similar to dual basis approaches. Compared to exact SCF results, using this MAB-SCF (PC) approach with the same large target basis set produces <0.15 kcal/mol root-mean-square deviations for most of the tested TC datasets, and <0.1 kcal/mol for most of the NC datasets. The performance of density functionals near the basis set limit can be even better reproduced. With further improvement to its implementation, MAB-SCF (PC) is a promising lower-cost substitute for conventional large-basis calculations as a method to approach the basis set limit of modern density functionals. [ABSTRACT FROM AUTHOR]

We have adapted a hybrid extended Lagrangian self-consistent field (EL/SCF) approach, developed for time reversible Born Oppenheimer molecular dynamics for quantum electronic degrees of freedom, to the problem of classical polarization. In this context, the initial guess for the mutual induction calculation is treated by auxiliary induced dipole variables evolved via a time-reversible velocity Verlet scheme. However, we find numerical instability, which is manifested as an accumulation in the auxiliary velocity variables, that in turn results in an unacceptable increase in the number of SCF cycles to meet even loose convergence tolerances for the real induced dipoles over the course of a 1 ns trajectory of the AMOEBA14 water model. By diagnosing the numerical instability as a problem of resonances that corrupt the dynamics, we introduce a simple thermostating scheme, illustrated using Berendsen weak coupling and Nose-Hoover chain thermostats, applied to the auxiliary dipole velocities. We find that the inertial EL/SCF (iEL/SCF) method provides superior energy conservation with less stringent convergence thresholds and a correspondingly small number of SCF cycles, to reproduce all properties of the polarization model in the NVT and NVE ensembles accurately. Our iEL/SCF approach is a clear improvement over standard SCF approaches to classical mutual induction calculations and would be worth investigating for application to ab initio molecular dynamics as well. [ABSTRACT FROM AUTHOR]

We develop a coarse-grained parametrization strategy for lipid membranes that we illustrate for a dipalmitoylphosphatidylcholine bilayer. Our coarse-graining approach eliminates the high cost of explicit solvent but maintains more lipid interaction sites. We use a broad attractive tail-tail potential and extract realistic bonded potentials of mean force from all-atom simulations, resulting in a model with a sharp gel to fluid transition, a correct bending modulus, and overall very reasonable dynamics when compared with experiment. We also determine a quantitative stress profile and correct breakdown of contributions from lipid components when compared with detailed all-atom simulation benchmarks, which has been difficult to achieve for implicit membrane models. Such a coarse-grained lipid model will be necessary for efficiently simulating complex constructs of the membrane, such as protein assembly and lipid raft formation, within these nonaqueous chemical environments. [ABSTRACT FROM AUTHOR]

Here we investigate a family of isotropic waterlike glass-forming liquids, in which each thermodynamic state point corresponds to a different potential energy surface which is prescribed to reproduce the gOO(r;T,ρ) of the reference TIP4P-Ew water model potential. Although each isotropic potential is simulated separately, together the family of isotropic potentials displays anomalous dynamics with density and fragile diffusivity with temperature. By removing a common energy landscape, and therefore expected thermodynamic trends with temperature within a single potential, we can more rigorously evaluate whether various entropic measures used in popular phenomenological thermodynamic theories can quantitatively predict the diffusivity or viscosity. We find that the Adam–Gibbs relation between diffusion (or viscosity) and the temperature scaled configurational entropy, Sc, is a poor predictor of fragility trends and density anomalies when necessary anharmonic corrections are added. By contrast the Dzugutov scaling relationship that uses the pair correlation approximation to Sexcess∼S2 provides excellent agreement for diffusion anomalies and for fragile dynamics for weakly supercooled states for the family of isotropic potentials, within a single isotropic potential, and for the TIP4P-Ew model, but deviates strongly in all three cases at more deeply supercooled temperatures. By studying the microscopic dynamics at these low temperatures, we find an increased heterogeneity in the mobility of particle populations reflected in a highly non-Gaussian distribution of particle displacements, even at very long time scales. We conclude that after the onset of dynamical heterogeneity, new consideration of higher structural correlations and/or more complex connectivity paths between basins through barriers appear to be critical for the formulation of a predictive theory for dynamics. [ABSTRACT FROM AUTHOR]

The solvation of large hydrophobic solutes, modeled as repulsive and attractive Gay–Berne oblate ellipsoids, is characterized in several modified water liquids using the SPC/E model as the reference water fluid. We find that small amounts of attraction between the Gay–Berne particle and any model fluid result in wetting of the hydrophobic surface. However, significant differences are found among the modified and SPC/E water models and the critical distances in which they dewet the hydrophobic surfaces of pairs of repulsive Gay–Berne particles. We find that the dewetting trends for repulsive Gay–Berne particles in the various model liquids correlate directly with their surface tensions, the widths of the interfaces they form, and the openness of their network structure. The largest critical separations are found in liquids with the smallest surface tensions and the broadest interfaces as measured by the Egelstaff–Widom length. [ABSTRACT FROM AUTHOR]

We have conducted extensive molecular dynamics simulations to study the single particle and collective dynamics of water in solutions of N-acetyl-glycine-methylamide, a model hydrophilic protein backbone, and N-acetyl-leucine-methylamide, a model (amphiphilic) hydrophobic peptide, as a function of peptide concentration. Various analytical models commonly used in the analysis of incoherent quasielastic neutron scattering (QENS), are tested against the translational and rotational intermediate scattering function, the mean square displacement of the water molecule center of mass, and fits to the second-order rotational correlation function of water evaluated directly from the simulation data. We find that while the agreement between the model-free analysis and analytical QENS models is quantitatively poor, the qualitative feature of dynamical heterogeneity due to caging is captured well by all approaches. The center of mass collective and single particle intermediate scattering functions of water calculated for these peptide solutions show that the crossover from collective to single particle-dominated motions occurs at a higher value of Q for high concentration solutions relative to low concentration because of the greater restriction in movement of water molecules due to confinement. Finally, we have shown that at the same level of confinement of the two peptides, the aqueous amphiphilic amino acid solution shows the strongest deviation between single particle and collective dynamics relative to the hydrophilic amino acid, indicating that chemical heterogeneity induces even greater spatial heterogeneity in the water dynamics. [ABSTRACT FROM AUTHOR]

The use of an effective intermolecular potential often involves a compromise between more accurate, complex functional forms and more tractable simple representations. To study this choice in detail, we systematically derive coarse-grained isotropic pair potentials that accurately reproduce the oxygen-oxygen radial distribution function of the TIP4P-Ew water model at state points over density ranges from 0.88 to 1.30 g/cm3 and temperature ranges from 235 to 310 K. Although by construction these effective potentials correctly represent the isothermal compressibility of TIP4P-Ew water, they do not accurately resolve other thermodynamic properties such as the virial pressure, the internal energy, or thermodynamic anomalies. Because at a given state point the pair potential that reproduces the pair structure is unique, we have therefore explicitly demonstrated that it is impossible to simultaneously represent the pair structure and several key equilibrium thermodynamic properties of water with state-point dependent radially symmetric pair potentials. We argue that such representability problems are related to, but different from, more widely acknowledged transferability problems and discuss in detail the implications this has for the modeling of water and other liquids by coarse-grained potentials. Nevertheless, regardless of thermodynamic inconsistencies, the state-point dependent effective potentials for water do generate structural and dynamical anomalies. [ABSTRACT FROM AUTHOR]

A re-parameterization of the standard TIP4P water model for use with Ewald techniques is introduced, providing an overall global improvement in water properties relative to several popular nonpolarizable and polarizable water potentials. Using high precision simulations, and careful application of standard analytical corrections, we show that the new TIP4P-Ew potential has a density maximum at ∼1 °C, and reproduces experimental bulk-densities and the enthalpy of vaporization, DHvap , from -37.5 to 127 °C at 1 atm with an absolute average error of less than 1%. Structural properties are in very good agreement with x-ray scattering intensities at temperatures between 0 and 77 °C and dynamical properties such as self-diffusion coefficient are in excellent agreement with experiment. The parameterization approach used can be easily generalized to rehabilitate any water force field using available experimental data over a range of thermodynamic points. [ABSTRACT FROM AUTHOR]

This work develops a statistical mechanical perturbation theory for understanding and quantifying the role of directional hydrogen bonding in pure water at any given temperature or density. A reference fluid has been defined with no orientational preferences, but which reproduces the short-ranged oxygen order as determined by x-ray or neutron diffraction. The orientational anisotropy can be reintroduced by perturbing the reference potential toward a fully coupled water potential; we have developed a new water model, ST4, which provides some noticeable structural improvements over its predecessor, ST2, to provide these anisotropic interactions. Monte Carlo simulations at 25 °C and 1 kg/l mass density have been implemented for various values of the coupling parameter to determine the importance of directed hydrogen bonds at various strengths in dictating energetic and structural features of liquid water. We find that virtually full hydrogen bond strength is required to recover the basic structural features of liquid water. We have also evaluated and contrasted the inherent structures (potential energy minima) for the reference fluid and the ST4 model, where we find that hydrogen bonding provides significant structural rigidity to resist vibrational distortion. Furthermore, we show that the ST4 model exhibits bifurcated hydrogen bonds which only occur in local regions of high density, i.e., they are found as tetrahedral network defects. These high density clusters also include tetrahedral oxygen triplets, sometimes linearly hydrogen-bonded, which may well serve as low energy intermediates for flow processes in liquid water. [ABSTRACT FROM AUTHOR]

We derive an expression for resonance energy transfer between a pair of chromophores embedded in a condensed medium by considering the energy splitting of the chromophores from their resonant excited states. We employ time-dependent density functional response theory in our derivation. The linear response theory treatment is rigorous within the framework of time-dependent density functional theory, while in obtaining the energy transfer coupling, the standard first-order approximation is used. The density response function for the medium, which can be replaced by the macroscopic dielectric susceptibility, enables the inclusion of the medium influence on the energy transfer coupling between the donor and acceptor. We consider the Coulomb coupling, and determine that our result is isomorphic to the Coulomb interaction between two charge densities inside a dielectric medium. The isomorphism we found not only provides a general and useful expression for applications, but additionally offers a basis for the extension of the dielectric response model to energy transfer coupling, which has been implicitly used earlier. An illustrative model shows that for two separated molecules, the medium adds a dielectric screening effect to the Coulomb coupling of their transitions. However, if the two molecules are so closely spaced that they effectively reside in a single cavity, the medium can enhance or reduce the strength of the coupling depending on the orientation and the alignment of the two chromophores. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We report a new, high-quality x-ray scattering experiment on pure ambient water using a synchrotron beam line at the Advanced Light Source at Lawrence Berkeley National Laboratory. Several factors contribute to the improved quality of our intensity curves including use of a highly monochromatic source, a well-characterized polarization correction, a Compton scattering correction that includes electron correlation, and more accurate intensities using a modern charge coupled device (CCD) detector. We provide a comprehensive description of the data processing that we have used for correcting systematic errors, and we provide an estimate of our remaining random errors. The resulting error estimates of our data are smaller then the discrepancies between data sets collected in past x-ray experiments. We find that the older x-ray curves support a family of g[sub OO](r)'s that exhibit a smaller first peak (∼2.2), while the current data is better fit with a family of g[sub OO](r)'s with a first peak height of 2.8, and systematic shifts in all peak positions to smaller r. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We present an analysis of the Advanced Light Source (ALS) x-ray scattering experiment on pure liquid water at ambient temperature and pressure described in the preceding article. The present study discusses the extraction of radial distribution functions from the x-ray scattering of molecular fluids. It is proposed that the atomic scattering factors used to model water be modified to include the changes in the intramolecular electron distribution caused by chemical bonding effects. Based on this analysis we present a g[sub OO](r) for water consistent with our recent experimental data gathered at the ALS, which differs in some aspects from the g[sub OO](r) reported by other x-ray and neutron scattering experiments. Our g[sub OO](r) exhibits a taller and sharper first peak, and systematic shifts in all peak positions to smaller r. Based on experimental uncertainties, we discuss what features of g[sub OO](r) should be reproduced by classical simulations of nonpolarizable and polarizable water models, as well as ab initio simulations of water, at ambient conditions. We directly compare many water models and simulations to the present data, and discuss possible improvements in both classical and ab initio simulation approaches in the future. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

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.

Iterative energy minimization with the aim of achieving self-consistency is a common feature of Born-Oppenheimer molecular dynamics (BOMD) and classical molecular dynamics with polarizable force fields. In the former, the electronic degrees of freedom are optimized, while the latter often involves an iterative determination of induced point dipoles. The computational effort of the self-consistency procedure can be reduced by re-using converged solutions from previous time steps. However, this must be done carefully, as not to break time-reversal symmetry, which negatively impacts energy conservation. Self-consistent schemes based on the extended Lagrangian formalism, where the initial guesses for the optimized quantities are treated as auxiliary degrees of freedom, constitute one elegant solution. We report on the performance of two integration schemes with the same underlying extended Lagrangian structure, which we both employ in two radically distinct regimes-in classical molecular dynamics simulations with the AMOEBA polarizable force field and in BOMD simulations with the Onetep linear-scaling density functional theory (LS-DFT) approach. Both integration schemes are found to offer significant improvements over the standard (unpropagated) molecular dynamics formulation in both the classical and LS-DFT regimes.

Recently developed density functionals have good accuracy for both thermochemistry (TC) and non-covalent interactions (NC) if very large atomic orbital basis sets are used. To approach the basis set limit with potentially lower computational cost, a new self-consistent field (SCF) scheme is presented that employs minimal adaptive basis (MAB) functions. The MAB functions are optimized on each atomic site by minimizing a surrogate function. High accuracy is obtained by applying a perturbative correction (PC) to the MAB calculation, similar to dual basis approaches. Compared to exact SCF results, using this MAB-SCF (PC) approach with the same large target basis set produces <0.15 kcal/mol root-mean-square deviations for most of the tested TC datasets, and <0.1 kcal/mol for most of the NC datasets. The performance of density functionals near the basis set limit can be even better reproduced. With further improvement to its implementation, MAB-SCF (PC) is a promising lower-cost substitute for conventional large-basis calculations as a method to approach the basis set limit of modern density functionals.