Chebyshev polynomial filtered subspace iteration in the discontinuous Galerkin method for large-scale electronic structure calculations.

The Discontinuous Galerkin (DG) electronic structure method employs an adaptive local basis (ALB) set to solve the Kohn-Sham equations of density functional theory in a discontinuous Galerkin framework. The adaptive local basis is generated on-the-fly to capture the local material physics and can systematically attain chemical accuracy with only a few tens of degrees of freedom per atom. A central issue for large-scale calculations, however, is the computation of the electron density (and subsequently, ground state properties) from the discretized Hamiltonian in an efficient and scalable manner. We show in this work how Chebyshev polynomial filtered subspace iteration (CheFSI) can be used to address this issue and push the envelope in large-scale materials simulations in a discontinuous Galerkin framework. We describe how the subspace filtering steps can be performed in an efficient and scalable manner using a two-dimensional parallelization scheme, thanks to the orthogonality of the DG basis set and block-sparse structure of the DG Hamiltonian matrix. The on-the-fly nature of the ALB functions requires additional care in carrying out the subspace iterations. We demonstrate the parallel scalability of the DG-CheFSI approach in calculations of large-scale two-dimensional graphene sheets and bulk three-dimensional lithium-ion electrolyte systems. Employing 55 296 computational cores, the time per self-consistent field iteration for a sample of the bulk 3D electrolyte containing 8586 atoms is 90 s, and the time for a graphene sheet containing 11 520 atoms is 75 s.

Carbon Kagome nanotubes-quasi-one-dimensional nanostructures with flat bands.

In recent years, a number of bulk materials and heterostructures have been explored due their connections with exotic materials phenomena emanating from flat band physics and strong electronic correlation. The possibility of realizing such fascinating material properties in simple realistic nanostructures is particularly exciting, especially as the investigation of exotic states of electronic matter in wire-like geometries is relatively unexplored in the literature. Motivated by these considerations, we introduce in this work carbon Kagome nanotubes (CKNTs)-a new allotrope of carbon formed by rolling up Kagome graphene, and investigate this material using specialized first principles calculations. We identify two principal varieties of CKNTs-armchair and zigzag, and find both varieties to be stable at room temperature, based on ab initio molecular dynamics simulations. CKNTs are metallic and feature dispersionless states (i.e., flat bands) near the Fermi level throughout their Brillouin zone, along with an associated singular peak in the electronic density of states. We calculate the mechanical and electronic response of CKNTs to torsional and axial strains, and show that CKNTs appear to be more mechanically compliant than conventional carbon nanotubes (CNTs). Additionally, we find that the electronic properties of CKNTs undergo significant electronic transitions-with emergent partial flat bands and tilted Dirac points-when twisted. We develop a relatively simple tight-binding model that can explain many of these electronic features. We also discuss possible routes for the synthesis of CKNTs. Overall, CKNTs appear to be unique and striking examples of realistic elemental quasi-one-dimensional materials that may display fascinating material properties due to strong electronic correlation. Distorted CKNTs may provide an interesting nanomaterial platform where flat band physics and chirality induced anomalous transport effects may be studied together.

The Biological Qubit: Calcium Phosphate Dimers, Not Trimers.

The Posner molecule (calcium phosphate trimer, Ca9(PO4)6) has been hypothesized to function as a biological quantum information processor due to its supposedly long-lived entangled 31P nuclear spin states. This hypothesis was challenged by our recent finding that the molecule lacks a well-defined rotational axis of symmetry─an essential assumption in the proposal for Posner-mediated neural processing─and exists as an asymmetric dynamical ensemble. Following up, we investigate here the spin dynamics of the molecule's entangled 31P nuclear spins within the asymmetric ensemble. Our simulations show that entanglement between two nuclear spins prepared in a Bell state in separate Posner molecules decays on a subsecond time scale─much faster than previously hypothesized, and not long enough for supercellular neuronal processing. Calcium phosphate dimers (Ca6(PO4)4) however, are found to be surprisingly resilient to decoherence and are able to preserve entangled nuclear spins for hundreds of seconds, suggesting that neural processing might occur through them instead.

A Chirality-Based Quantum Leap.

There is increasing interest in the study of chiral degrees of freedom occurring in matter and in electromagnetic fields. Opportunities in quantum sciences will likely exploit two main areas that are the focus of this Review: (1) recent observations of the chiral-induced spin selectivity (CISS) effect in chiral molecules and engineered nanomaterials and (2) rapidly evolving nanophotonic strategies designed to amplify chiral light-matter interactions. On the one hand, the CISS effect underpins the observation that charge transport through nanoscopic chiral structures favors a particular electronic spin orientation, resulting in large room-temperature spin polarizations. Observations of the CISS effect suggest opportunities for spin control and for the design and fabrication of room-temperature quantum devices from the bottom up, with atomic-scale precision and molecular modularity. On the other hand, chiral-optical effects that depend on both spin- and orbital-angular momentum of photons could offer key advantages in all-optical and quantum information technologies. In particular, amplification of these chiral light-matter interactions using rationally designed plasmonic and dielectric nanomaterials provide approaches to manipulate light intensity, polarization, and phase in confined nanoscale geometries. Any technology that relies on optimal charge transport, or optical control and readout, including quantum devices for logic, sensing, and storage, may benefit from chiral quantum properties. These properties can be theoretically and experimentally investigated from a quantum information perspective, which has not yet been fully developed. There are uncharted implications for the quantum sciences once chiral couplings can be engineered to control the storage, transduction, and manipulation of quantum information. This forward-looking Review provides a survey of the experimental and theoretical fundamentals of chiral-influenced quantum effects and presents a vision for their possible future roles in enabling room-temperature quantum technologies.

The Dynamical Ensemble of the Posner Molecule Is Not Symmetric.

The Posner molecule, Ca9(PO4)6, has long been recognized to have biochemical relevance in various physiological processes. It has found recent attention for its possible role as a biological quantum information processor, whereby the molecule purportedly maintains long-lived nuclear spin coherences among its 31P nuclei (presumed to be symmetrically arranged), allowing it to function as a room temperature qubit. The structure of the molecule has been of much dispute in the literature, although the S6 point group symmetry has often been assumed and exploited in calculations. Using a variety of simulation techniques (including ab initio molecular dynamics and structural relaxation), rigorous data analysis tools, and by exploring thousands of individual configurations, we establish that the molecule predominantly assumes low-symmetry structures (Cs and Ci) at room temperature, as opposed to the higher-symmetry configurations explored previously. Our findings have important implications for the viability of this molecule as a qubit.

Two-Level Chebyshev Filter Based Complementary Subspace Method: Pushing the Envelope of Large-Scale Electronic Structure Calculations.

We describe a novel iterative strategy for Kohn-Sham density functional theory calculations aimed at large systems (>1,000 electrons), applicable to metals and insulators alike. In lieu of explicit diagonalization of the Kohn-Sham Hamiltonian on every self-consistent field (SCF) iteration, we employ a two-level Chebyshev polynomial filter based complementary subspace strategy to (1) compute a set of vectors that span the occupied subspace of the Hamiltonian; (2) reduce subspace diagonalization to just partially occupied states; and (3) obtain those states in an efficient, scalable manner via an inner Chebyshev filter iteration. By reducing the necessary computation to just partially occupied states and obtaining these through an inner Chebyshev iteration, our approach reduces the cost of large metallic calculations significantly, while eliminating subspace diagonalization for insulating systems altogether. We describe the implementation of the method within the framework of the discontinuous Galerkin (DG) electronic structure method and show that this results in a computational scheme that can effectively tackle bulk and nano systems containing tens of thousands of electrons, with chemical accuracy, within a few minutes or less of wall clock time per SCF iteration on large-scale computing platforms. We anticipate that our method will be instrumental in pushing the envelope of large-scale ab initio molecular dynamics. As a demonstration of this, we simulate a bulk silicon system containing 8,000 atoms at finite temperature, and obtain an average SCF step wall time of 51 s on 34,560 processors; thus allowing us to carry out 1.0 ps of ab initio molecular dynamics in approximately 28 h (of wall time).

Adaptively Compressed Exchange Operator for Large-Scale Hybrid Density Functional Calculations with Applications to the Adsorption of Water on Silicene.

Density functional theory (DFT) calculations using hybrid exchange-correlation functionals have been shown to provide an accurate description of the electronic structures of nanosystems. However, such calculations are often limited to small system sizes due to the high computational cost associated with the construction and application of the Hartree-Fock (HF) exchange operator. In this paper, we demonstrate that the recently developed adaptively compressed exchange (ACE) operator formulation [J. Chem. Theory Comput. 2016, 12, 2242-2249] can enable hybrid functional DFT calculations for nanosystems with thousands of atoms. The cost of constructing the ACE operator is the same as that of applying the exchange operator to the occupied orbitals once, while the cost of applying the Hamiltonian operator with a hybrid functional (after construction of the ACE operator) is only marginally higher than that associated with applying a Hamiltonian constructed from local and semilocal exchange-correlation functionals. Therefore, this new development significantly lowers the computational barrier for using hybrid functionals in large-scale DFT calculations. We demonstrate that a parallel planewave implementation of this method can be used to compute the ground-state electronic structure of a 1000-atom bulk silicon system in less than 30 wall clock minutes and that this method scales beyond 8000 computational cores for a bulk silicon system containing about 4000 atoms. The efficiency of the present methodology in treating large systems enables us to investigate adsorption properties of water molecules on Ag-supported two-dimensional silicene. Our computational results show that water monomer, dimer, and trimer configurations exhibit distinct adsorption behaviors on silicene. In particular, the presence of additional water molecules in the dimer and trimer configurations induces a transition from physisorption to chemisorption, followed by dissociation on Ag-supported silicene. This is caused by the enhanced effect of hydrogen bonds on charge transfer and proton transfer processes. Such a hydrogen bond autocatalytic effect is expected to have broad applications for silicene as an efficient surface catalyst for oxygen reduction reactions and water dissociation.