Variational principle to regularize machine-learned density functionals: The non-interacting kinetic-energy functional.

Practical density functional theory (DFT) owes its success to the groundbreaking work of Kohn and Sham that introduced the exact calculation of the non-interacting kinetic energy of the electrons using an auxiliary mean-field system. However, the full power of DFT will not be unleashed until the exact relationship between the electron density and the non-interacting kinetic energy is found. Various attempts have been made to approximate this functional, similar to the exchange-correlation functional, with much less success due to the larger contribution of kinetic energy and its more non-local nature. In this work, we propose a new and efficient regularization method to train density functionals based on deep neural networks, with particular interest in the kinetic-energy functional. The method is tested on (effectively) one-dimensional systems, including the hydrogen chain, non-interacting electrons, and atoms of the first two periods, with excellent results. For atomic systems, the generalizability of the regularization method is demonstrated by training also an exchange-correlation functional, and the contrasting nature of the two functionals is discussed from a machine-learning perspective.

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

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

Quantum Chemistry Common Driver and Databases (QCDB) and Quantum Chemistry Engine (QCEngine): Automation and interoperability among computational chemistry programs.

Community efforts in the computational molecular sciences (CMS) are evolving toward modular, open, and interoperable interfaces that work with existing community codes to provide more functionality and composability than could be achieved with a single program. The Quantum Chemistry Common Driver and Databases (QCDB) project provides such capability through an application programming interface (API) that facilitates interoperability across multiple quantum chemistry software packages. In tandem with the Molecular Sciences Software Institute and their Quantum Chemistry Archive ecosystem, the unique functionalities of several CMS programs are integrated, including CFOUR, GAMESS, NWChem, OpenMM, Psi4, Qcore, TeraChem, and Turbomole, to provide common computational functions, i.e., energy, gradient, and Hessian computations as well as molecular properties such as atomic charges and vibrational frequency analysis. Both standard users and power users benefit from adopting these APIs as they lower the language barrier of input styles and enable a standard layout of variables and data. These designs allow end-to-end interoperable programming of complex computations and provide best practices options by default.

Density Functional Model for van der Waals Interactions: Unifying Many-Body Atomic Approaches with Nonlocal Functionals.

Noncovalent van der Waals (vdW) interactions are responsible for a wide range of phenomena in matter. Popular density-functional methods that treat vdW interactions use disparate physical models for these intricate forces, and as a result the applicability of these methods is often restricted to a subset of relevant molecules and materials. Aiming towards a general-purpose density functional model of vdW interactions, here we unify two complementary approaches: nonlocal vdW functionals for polarization and interatomic methods for many-body interactions. The developed nonlocal many-body dispersion method (MBD-NL) increases the accuracy and efficiency of existing vdW functionals and is shown to be broadly applicable to molecules, soft and hard materials including ionic and metallic compounds, as well as interfaces between organic molecules and inorganic materials.

Recent developments in the PySCF program package.

PySCF is a Python-based general-purpose electronic structure platform that supports first-principles simulations of molecules and solids as well as accelerates the development of new methodology and complex computational workflows. This paper explains the design and philosophy behind PySCF that enables it to meet these twin objectives. With several case studies, we show how users can easily implement their own methods using PySCF as a development environment. We then summarize the capabilities of PySCF for molecular and solid-state simulations. Finally, we describe the growing ecosystem of projects that use PySCF across the domains of quantum chemistry, materials science, machine learning, and quantum information science.

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

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.

Robotic cochlear implantation: feasibility of a multiport approach in an ex vivo model.

PURPOSE: A recent clinical trial has shown the feasibility of robotic cochlear implantation. The electrode was inserted through the robotically drilled tunnel and an additional access through the external auditory canal was created to provide for means of visualization and manipulation. To obviate the need for this additional access, the utilization of multiple robotically drilled tunnels targeting the round window has been proposed. The objective of this study was to assess the feasibility of electrode insertion through a robotic multiport approach. METHODS: In four ex vivo human head specimens (left side), four trajectories through the facial recess (2x) and the retrofacial and suprameatal region were planned and robotically drilled. Optimal three-port configurations were determined for each specimen by analyzing combinations of three of the four trajectories, where the three trajectories were used for the electrode, endoscopic visualization and manipulative assistance. Finally, electrode insertions were conducted through the optimal configurations. RESULTS: The electrodes could successfully be inserted, and the procedure sufficiently visualized through the facial recess drill tunnels in all specimens. Effective manipulative assistance for sealing the round window could be provided through the retrofacial tunnel. CONCLUSIONS: Electrode insertion through a robotic three-port approach is feasible. Drill tunnels through the facial recess for the electrode and endoscope allow for optimized insertion angles and sufficient visualization. Through a retrofacial tunnel effective manipulation for sealing is possible.

Phonon-Polariton Mediated Thermal Radiation and Heat Transfer among Molecules and Macroscopic Bodies: Nonlocal Electromagnetic Response at Mesoscopic Scales.

Thermal radiative phenomena can be strongly influenced by the coupling of phonons and long-range electromagnetic fields at infrared frequencies. Typically employed macroscopic descriptions of thermal fluctuations often ignore atomistic effects that become relevant at nanometric scales, whereas purely microscopic treatments ignore long-range, geometry-dependent electromagnetic effects. We describe a mesoscopic framework for modeling thermal fluctuation phenomena among molecules near macroscopic bodies, conjoining atomistic treatments of electronic and vibrational fluctuations obtained from density functional theory in the former with continuum descriptions of electromagnetic scattering in the latter. The interplay of these effects becomes particularly important at mesoscopic scales, where phonon polaritons can be strongly influenced by the objects' finite sizes, shapes, and nonlocal or many-body response to electromagnetic fluctuations. We show that, even in small but especially in elongated low-dimensional molecules, such effects can modify thermal emission and heat transfer by orders of magnitude and produce qualitatively different behavior compared to predictions based on local, dipolar, or pairwise approximations.

Unifying Microscopic and Continuum Treatments of van der Waals and Casimir Interactions.

We present an approach for computing long-range van der Waals (vdW) interactions between complex molecular systems and arbitrarily shaped macroscopic bodies, melding atomistic treatments of electronic fluctuations based on density functional theory in the former with continuum descriptions of strongly shape-dependent electromagnetic fields in the latter, thus capturing many-body and multiple scattering effects to all orders. Such a theory is especially important when considering vdW interactions at mesoscopic scales, i.e., between molecules and structured surfaces with features on the scale of molecular sizes, in which case the finite sizes, complex shapes, and resulting nonlocal electronic excitations of molecules are strongly influenced by electromagnetic retardation and wave effects that depend crucially on the shapes of surrounding macroscopic bodies. We show that these effects together can modify vdW interaction energies and forces, as well as molecular shapes deformed by vdW interactions, by orders of magnitude compared to previous treatments based on Casimir-Polder, nonretarded, or pairwise approximations, which are valid only at macroscopically large or atomic-scale separations or in dilute insulating media, respectively.

Communication: Many-body stabilization of non-covalent interactions: Structure, stability, and mechanics of Ag3Co(CN)6 framework.

Stimuli-responsive metal-organic frameworks (MOFs) and other framework materials exhibit a broad variety of useful properties, which mainly stem from an interplay of strong covalent bonds within the organic linkers with presumably weak van der Waals (vdW) interactions which determine the overall packing of the framework constituents. Using Ag3Co(CN)6 as a fundamental test case-a system with a colossal positive and negative thermal expansion [A. L. Goodwin et al., Science 319, 794 (2008)]-we demonstrate that its structure, stability, dielectric, vibrational, and mechanical properties are critically influenced by many-body electronic correlation contributions to non-covalent vdW interactions. The Ag3Co(CN)6 framework is a remarkable molecular crystal, being visibly stabilized, rather than destabilized, by many-body vdW correlations. A detailed comparison with H3Co(CN)6 highlights the crucial role of strongly polarized metallophilic interactions in dictating the exceptional properties of denser MOFs. Beyond MOFs, our findings indicate that many-body electronic correlations can substantially stabilize polarizable materials, providing a novel mechanism for tuning the properties of nanomaterials with intricate structural motifs.

A novel correction scheme for DFT: a combined vdW-DF/CCSD(T) approach.

A system-specific but very accurate density functional theory (DFT) correction scheme is proposed for precise calculations of adsorbent-adsorbate interactions by combining the non-empirical van der Waals density functional (vdW-DF) method and the empirical DFT/CC correction scheme to reach accuracy of the coupled clusters method with single, double and perturbative triple excitations (CCSD(T)). The new approach is applied to small molecules (CH4, CO2, H2, H2O, N2) interacting with silica surfaces and purely siliceous microporous solids. The vdW-DF/CC results for a perfectly reconstructed α-quartz surface are consistent with other dispersion-corrected DFT methods. Corrected for ZPVE, the vdW-DF/CC enthalpies of adsorption in pure-silica zeolite LTA (ΔHads(0 K)) of 3.6 and 5.2 kcal/mol for methane and carbon dioxide, respectively, are in excellent agreement with experimental values of 3.6 and 5.0 kcal/mol. The very high accuracy of the new scheme and its relatively easy use and numerical stability as compared to the earlier DFT/CC scheme offer a straightforward solution for obtaining reliable predictions of adsorption energies.

Ab initio quantum chemistry with neural-network wavefunctions.

Deep learning methods outperform human capabilities in pattern recognition and data processing problems and now have an increasingly important role in scientific discovery. A key application of machine learning in molecular science is to learn potential energy surfaces or force fields from ab initio solutions of the electronic Schrödinger equation using data sets obtained with density functional theory, coupled cluster or other quantum chemistry (QC) methods. In this Review, we discuss a complementary approach using machine learning to aid the direct solution of QC problems from first principles. Specifically, we focus on quantum Monte Carlo methods that use neural-network ansatzes to solve the electronic Schrödinger equation, in first and second quantization, computing ground and excited states and generalizing over multiple nuclear configurations. Although still at their infancy, these methods can already generate virtually exact solutions of the electronic Schrödinger equation for small systems and rival advanced conventional QC methods for systems with up to a few dozen electrons.

Image-Based Planning of Minimally Traumatic Inner Ear Access for Robotic Cochlear Implantation.

Objective: During robotic cochlear implantation, an image-guided robotic system provides keyhole access to the scala tympani of the cochlea to allow insertion of the cochlear implant array. To standardize minimally traumatic robotic access to the cochlea, additional hard and soft constraints for inner ear access were proposed during trajectory planning. This extension of the planning strategy aims to provide a trajectory that preserves the anatomical and functional integrity of critical intra-cochlear structures during robotic execution and allows implantation with minimal insertion angles and risk of scala deviation. Methods: The OpenEar dataset consists of a library with eight three-dimensional models of the human temporal bone based on computed tomography and micro-slicing. Soft constraints for inner ear access planning were introduced that aim to minimize the angle of cochlear approach, minimize the risk of scala deviation and maximize the distance to critical intra-cochlear structures such as the osseous spiral lamina. For all cases, a solution space of Pareto-optimal trajectories to the round window was generated. The trajectories satisfy the hard constraints, specifically the anatomical safety margins, and optimize the aforementioned soft constraints. With user-defined priorities, a trajectory was parameterized and analyzed in a virtual surgical procedure. Results: In seven out of eight cases, a solution space was found with the trajectories safely passing through the facial recess. The solution space was Pareto-optimal with respect to the soft constraints of the inner ear access. In one case, the facial recess was too narrow to plan a trajectory that would pass the nerves at a sufficient distance with the intended drill diameter. With the soft constraints introduced, the optimal target region was determined to be in the antero-inferior region of the round window membrane. Conclusion: A trend could be identified that a position between the antero-inferior border and the center of the round window membrane appears to be a favorable target position for cochlear tunnel-based access through the facial recess. The planning concept presented and the results obtained therewith have implications for planning strategies for robotic surgical procedures to the inner ear that aim for minimally traumatic cochlear access and electrode array implantation.

Robotic Milling of Electrode Lead Channels During Cochlear Implantation in an ex-vivo Model.

Objective: Robotic cochlear implantation is an emerging surgical technique for patients with sensorineural hearing loss. Access to the middle and inner ear is provided through a small-diameter hole created by a robotic drilling process without a mastoidectomy. Using the same image-guided robotic system, we propose an electrode lead management technique using robotic milling that replaces the standard process of stowing excess electrode lead in the mastoidectomy cavity. Before accessing the middle ear, an electrode channel is milled robotically based on intraoperative planning. The goal is to further standardize cochlear implantation, minimize the risk of iatrogenic intracochlear damage, and to create optimal conditions for a long implant life through protection from external trauma and immobilization in a slight press fit to prevent mechanical fatigue and electrode migrations. Methods: The proposed workflow was executed on 12 ex-vivo temporal bones and evaluated for safety and efficacy. For safety, the difference between planned and resulting channels were measured postoperatively in micro-computed tomography, and the length outside the planned safety margin of 1.0 mm was determined. For efficacy, the channel width and depth were measured to assess the press fit immobilization and the protection from external trauma, respectively. Results: All 12 cases were completed with successful electrode fixations after cochlear insertions. The milled channels stayed within the planned safety margins and the probability of their violation was lower than one in 10,000 patients. Maximal deviations in lateral and depth directions of 0.35 and 0.29 mm were measured, respectively. The channels could be milled with a width that immobilized the electrode leads. The average channel depth was 2.20 mm, while the planned channel depth was 2.30 mm. The shallowest channel depth was 1.82 mm, still deep enough to contain the full 1.30 mm diameter of the electrode used for the experiments. Conclusion: This study proposes a robotic electrode lead management and fixation technique and verified its safety and efficacy in an ex-vivo study. The method of image-guided robotic bone removal presented here with average errors of 0.2 mm and maximal errors below 0.5 mm could be used for a variety of other otologic surgical procedures.

In Silico Assessment of Safety and Efficacy of Screw Placement for Pediatric Image-Guided Otologic Surgery.

Introduction: Current high-accuracy image-guided systems for otologic surgery use fiducial screws for patient-to-image registration. Thus far, these systems have only been used in adults, and the safety and efficacy of the fiducial screw placement has not yet been investigated in the pediatric population. Materials and Methods: In a retrospective study, CT image data of the temporal region from 11 subjects meeting inclusion criteria (8-48 months at the time of surgery) were selected, resulting in n = 20 sides. These datasets were investigated with respect to screw stability efficacy in terms of the cortical layer thickness, and safety in terms of the distance of potential fiducial screws to the dura mater or venous sinuses. All of these results are presented as distributions, thickness color maps, and with descriptive statistics. Seven regions within the temporal bone were analyzed individually. In addition, four fiducial screws per case with 4 mm thread-length were placed in an additively manufactured model according to the guidelines for robotic cochlear implantation surgery. For all these screws, the minimal distance to the dura mater or venous sinuses was measured, or if applicable how much they penetrated these structures. Results: The cortical layer has been found to be mostly between 0.7-3.3 mm thick (from the 5th to the 95th percentile), while even thinner areas exist. The distance from the surface of the temporal bone to the dura mater or the venous sinuses varied considerably between the subjects and ranged mostly from 1.1-9.3 mm (from the 5th to the 95th percentile). From all 80 placed fiducial screws of 4 mm thread length in the pediatric subject younger than two years old, 22 touched or penetrated either the dura or the sigmoid sinus. The best regions for fiducial placement would be the mastoid area and along the petrous pyramid in terms of safety. In terms of efficacy, the parietal followed by the petrous pyramid, and retrosigmoid regions are most suited. Conclusion: The current fiducial screws and the screw placement guidelines for adults are insufficiently safe or effective for pediatric patients.

Coulomb interactions between dipolar quantum fluctuations in van der Waals bound molecules and materials.

Mutual Coulomb interactions between electrons lead to a plethora of interesting physical and chemical effects, especially if those interactions involve many fluctuating electrons over large spatial scales. Here, we identify and study in detail the Coulomb interaction between dipolar quantum fluctuations in the context of van der Waals complexes and materials. Up to now, the interaction arising from the modification of the electron density due to quantum van der Waals interactions was considered to be vanishingly small. We demonstrate that in supramolecular systems and for molecules embedded in nanostructures, such contributions can amount to up to 6 kJ/mol and can even lead to qualitative changes in the long-range van der Waals interaction. Taking into account these broad implications, we advocate for the systematic assessment of so-called Dipole-Correlated Coulomb Singles in large molecular systems and discuss their relevance for explaining several recent puzzling experimental observations of collective behavior in nanostructured materials.

Anisotropic Interlayer Force Field for Transition Metal Dichalcogenides: The Case of Molybdenum Disulfide.

An anisotropic interlayer force field that describes the interlayer interactions in molybdenum disulfide (MoS2) is presented. The force field is benchmarked against density functional theory calculations for both bilayer and bulk systems within the Heyd-Scuseria-Ernzerhof hybrid density functional approximation, augmented by a nonlocal many-body dispersion treatment of long-range correlation. The parametrization yields good agreement with the reference calculations of binding energy curves and sliding potential energy surfaces for both bilayer and bulk configurations. Benchmark calculations for the phonon spectra of bulk MoS2 provide good agreement with experimental data, and the calculated bulk modulus falls in the lower part of experimentally measured values. This indicates the accuracy of the interlayer force field near equilibrium. Under external pressures up to 20 GPa, the developed force field provides a good description of compression curves. At higher pressures, deviations from experimental data grow, signifying the validity range of the developed force field.

Freehand Stereotactic Image-Guidance Tailored to Neurotologic Surgery.

Hypothesis: The use of freehand stereotactic image-guidance with a target registration error (TRE) of µTRE + 3σTRE < 0.5 mm for navigating surgical instruments during neurotologic surgery is safe and useful. Background: Neurotologic microsurgery requires work at the limits of human visual and tactile capabilities. Anatomy localization comes at the expense of invasiveness caused by exposing structures and using them as orientation landmarks. In the absence of more-precise and less-invasive anatomy localization alternatives, surgery poses considerable risks of iatrogenic injury and sub-optimal treatment. There exists an unmet clinical need for an accurate, precise, and minimally-invasive means for anatomy localization and instrument navigation during neurotologic surgery. Freehand stereotactic image-guidance constitutes a solution to this. While the technology is routinely used in medical fields such as neurosurgery and rhinology, to date, it is not used for neurotologic surgery due to insufficient accuracy of clinically available systems. Materials and Methods: A freehand stereotactic image-guidance system tailored to the needs of neurotologic surgery-most importantly sub-half-millimeter accuracy-was developed. Its TRE was assessed preclinically using a task-specific phantom. A pilot clinical trial targeting N = 20 study participants was conducted (ClinicalTrials.gov ID: NCT03852329) to validate the accuracy and usefulness of the developed system. Clinically, objective assessment of the TRE is impossible because establishing a sufficiently accurate ground-truth is impossible. A method was used to validate accuracy and usefulness based on intersubjectivity assessment of surgeon ratings of corresponding image-pairs from the microscope/endoscope and the image-guidance system. Results: During the preclinical accuracy assessment the TRE was measured as 0.120 ± 0.05 mm (max: 0.27 mm, µTRE + 3σTRE = 0.27 mm, N = 310). Due to the COVID-19 pandemic, the study was terminated early after N = 3 participants. During an endoscopic cholesteatoma removal, a microscopic facial nerve schwannoma removal, and a microscopic revision cochlear implantation, N = 75 accuracy and usefulness ratings were collected from five surgeons each grading 15 image-pairs. On a scale from 1 (worst rating) to 5 (best rating), the median (interquartile range) accuracy and usefulness ratings were assessed as 5 (4-5) and 4 (4-5) respectively. Conclusion: Navigating surgery in the tympanomastoid compartment and potentially in the lateral skull base with sufficiently accurate freehand stereotactic image-guidance (µTRE + 3σTRE < 0.5 mm) is feasible, safe, and useful. Clinical Trial Registration: www.ClinicalTrials.gov, identifier: NCT03852329.

Deep-neural-network solution of the electronic Schrödinger equation.

The electronic Schrödinger equation can only be solved analytically for the hydrogen atom, and the numerically exact full configuration-interaction method is exponentially expensive in the number of electrons. Quantum Monte Carlo methods are a possible way out: they scale well for large molecules, they can be parallelized and their accuracy has, as yet, been only limited by the flexibility of the wavefunction ansatz used. Here we propose PauliNet, a deep-learning wavefunction ansatz that achieves nearly exact solutions of the electronic Schrödinger equation for molecules with up to 30 electrons. PauliNet has a multireference Hartree-Fock solution built in as a baseline, incorporates the physics of valid wavefunctions and is trained using variational quantum Monte Carlo. PauliNet outperforms previous state-of-the-art variational ansatzes for atoms, diatomic molecules and a strongly correlated linear H10, and matches the accuracy of highly specialized quantum chemistry methods on the transition-state energy of cyclobutadiene, while being computationally efficient.

Nonlocal Electronic Correlations in the Cohesive Properties of High-Pressure Hydrogen Solids.

High-pressure hydrogen exhibits remarkable phenomena including the insulator-to-metal (IM) transition; however, a complete resolution of its phase diagram is still an elusive goal despite many efforts and much controversy. Theoretical modeling is typically based on density functional theory (DFT) with a mean-field description of electronic correlations, which is known to be rather limited in describing IM transitions. Herein, we show that nonlocal electron correlations play a central role in the relative stability of solid hydrogen phases, and that DFT-correcting for these correlations by the many-body dispersion (MBD) model reaches the accuracy of quantum Monte Carlo (QMC) simulations and predicts the same C2/c-24 → Cmca-12 → Cs(IV) IM transition. In contrast with the conventional assumption that many-body electronic correlations become localized in metallic systems because of exponential screening with interelectronic distance, we find that the anisotropy of the electronic response of hydrogen solids under pressure leads to longer-ranged many-body effects in metallic phases relative to insulating ones. This refines our understanding of phase diagram of hydrogen solids as well as anisotropic many-body correlations.