Efficient Full-Frequency GW Calculations Using a Lanczos Method.

The GW approximation is widely used for reliable and accurate modeling of single-particle excitations. It also serves as a starting point for many theoretical methods, such as its use in the Bethe-Salpeter equation (BSE) and dynamical mean-field theory. However, full-frequency GW calculations for large systems with hundreds of atoms remain computationally challenging, even after years of efforts to reduce the prefactor and improve scaling. We propose a method that reformulates the correlation part of the GW self-energy as a resolvent of a Hermitian matrix, which can be efficiently and accurately computed using the standard Lanczos method. This method enables full-frequency GW calculations of material systems with a few hundred atoms on a single computing workstation. We further demonstrate the efficiency of the method by calculating the defect-state energies of silicon quantum dots with diameters up to 4 nm and nearly 2,000 silicon atoms using only 20 computational nodes.

Anisotropy and isotope effect in superconducting solid hydrogen.

Elucidating the phase diagram of solid hydrogen is a key objective in condensed matter physics. Several decades ago, it was proposed that at low temperatures and high pressures, solid hydrogen would be a metal with a high superconducting transition temperature. This transition to a metallic state can happen through the closing of the energy gap in the molecular solid or through a transition to an atomic solid. Recent experiments have managed to reach pressures in the range of 400-500 GPa, providing valuable insights. There is strong evidence suggesting that metallization via either of these mechanisms occurs within this pressure range. Computational and experimental studies have identified multiple promising crystal phases, but the limited accuracy of calculations and the limited capabilities of experiments prevent us from determining unequivocally the observed phase or phases. Therefore, it is crucial to investigate the superconducting properties of all the candidate phases. Recently, we reported the superconducting properties of theC2/c-24,Cmca-12,Cmca-4 andI41/amd-2 phases, including anharmonic effects. Here, we report the effects of anisotropy on superconducting properties using Eliashberg theory. Then, we investigate the superconducting properties of deuterium and estimate the size of the isotope effect for each phase. We find that the isotope effect on superconductivity is diminished by anharmonicity in theC2/c-24 andCmca-12 phases and enlarged in theCmca-4 andI41/amd-2 phases. Our anharmonic calculations of theC2/c-24 phase of deuterium agree closely with the most recent experiment by Loubeyreet al(2022Phys. Rev. Lett.29035501), indicating that theC2/c-24 phase remains the leading candidate in this pressure range, and has a strong anharmonic character. These characteristics can serve to distinguish among crystal phases in experiment. Furthermore, expanding our understanding of superconductivity in pure hydrogen holds significance in the study of high-Tchydrides.

Real-space solution to the electronic structure problem for nearly a million electrons.

We report a Kohn-Sham density functional theory calculation of a system with more than 200 000 atoms and 800 000 electrons using a real-space high-order finite-difference method to investigate the electronic structure of large spherical silicon nanoclusters. Our system of choice was a 20 nm large spherical nanocluster with 202 617 silicon atoms and 13 836 hydrogen atoms used to passivate the dangling surface bonds. To speed up the convergence of the eigenspace, we utilized Chebyshev-filtered subspace iteration, and for sparse matrix-vector multiplications, we used blockwise Hilbert space-filling curves, implemented in the PARSEC code. For this calculation, we also replaced our orthonormalization + Rayleigh-Ritz step with a generalized eigenvalue problem step. We utilized all of the 8192 nodes (458 752 processors) on the Frontera machine at the Texas Advanced Computing Center. We achieved two Chebyshev-filtered subspace iterations, yielding a good approximation of the electronic density of states. Our work pushes the limits on the capabilities of the current electronic structure solvers to nearly 106 electrons and demonstrates the potential of the real-space approach to efficiently parallelize large calculations on modern high-performance computing platforms.

Observation of electron orbital signatures of single atoms within metal-phthalocyanines using atomic force microscopy.

Resolving the electronic structure of a single atom within a molecule is of fundamental importance for understanding and predicting chemical and physical properties of functional molecules such as molecular catalysts. However, the observation of the orbital signature of an individual atom is challenging. We report here the direct identification of two adjacent transition-metal atoms, Fe and Co, within phthalocyanine molecules using high-resolution noncontact atomic force microscopy (HR-AFM). HR-AFM imaging reveals that the Co atom is brighter and presents four distinct lobes on the horizontal plane whereas the Fe atom displays a "square" morphology. Pico-force spectroscopy measurements show a larger repulsion force of about 5 pN on the tip exerted by Co in comparison to Fe. Our combined experimental and theoretical results demonstrate that both the distinguishable features in AFM images and the variation in the measured forces arise from Co's higher electron orbital occupation above the molecular plane. The ability to directly observe orbital signatures using HR-AFM should provide a promising approach to characterizing the electronic structure of an individual atom in a molecular species and to understand mechanisms of certain chemical reactions.

Accelerating the discovery of novel magnetic materials using machine learning-guided adaptive feedback.

Magnetic materials are essential for energy generation and information devices, and they play an important role in advanced technologies and green energy economies. Currently, the most widely used magnets contain rare earth (RE) elements. An outstanding challenge of notable scientific interest is the discovery and synthesis of novel magnetic materials without RE elements that meet the performance and cost goals for advanced electromagnetic devices. Here, we report our discovery and synthesis of an RE-free magnetic compound, Fe3CoB2, through an efficient feedback framework by integrating machine learning (ML), an adaptive genetic algorithm, first-principles calculations, and experimental synthesis. Magnetic measurements show that Fe3CoB2 exhibits a high magnetic anisotropy (K1 = 1.2 MJ/m3) and saturation magnetic polarization (Js = 1.39 T), which is suitable for RE-free permanent-magnet applications. Our ML-guided approach presents a promising paradigm for efficient materials design and discovery and can also be applied to the search for other functional materials.

Atomic Fingerprinting of Heteroatoms Using Noncontact Atomic Force Microscopy.

Immense strides have been made in increasing the resolution of scanning probe microscopy. Noncontact atomic force microscopy (nc-AFM) now offers one the ability to characterize and visualize single molecules with subatomic resolution. Specifically, nc-AFM with a carbon monoxide (CO) functionalized tip has the ability to discriminate functional groups (-CC-, -CH2 , -CO, …), although discriminating atomic species often remains as an ongoing challenge. Here, real-space pseudopotentials constructed within density functional theory are employed to accurately simulate nc-AFM images of molecules containing heteroatoms (S, I, and N) within dibenzothiophene (DBT), 2-iodotriphenylene (ITP), acridine (ACR) and ferrous phthalocyanine (FePc). It is found that S and I atoms can be easily identified from C based on their unique features. For N atoms, a use of tip functionalization is proposed to effectively discriminate them from C atoms.

Breaking a dative bond with mechanical forces.

Bond breaking and forming are essential components of chemical reactions. Recently, the structure and formation of covalent bonds in single molecules have been studied by non-contact atomic force microscopy (AFM). Here, we report the details of a single dative bond breaking process using non-contact AFM. The dative bond between carbon monoxide and ferrous phthalocyanine was ruptured via mechanical forces applied by atomic force microscope tips; the process was quantitatively measured and characterized both experimentally and via quantum-based simulations. Our results show that the bond can be ruptured either by applying an attractive force of ~150 pN or by a repulsive force of ~220 pN with a significant contribution of shear forces, accompanied by changes of the spin state of the system. Our combined experimental and computational studies provide a deeper understanding of the chemical bond breaking process.

Space-Filling Curves for Real-Space Electronic Structure Calculations.

Hamiltonian matrices for Kohn-Sham calculations implemented in real space are often large (millions by millions) but very sparse. This poses challenges and opportunities for iterative eigensolvers, which often require a large number of matrix-vector multiplications. As a consequence, an efficient parallel sparse matrix-vector multiplication algorithm is desired. Here, we investigate the benefits of using Hilbert space-filling curves (SFCs) in domain partitioning. We show that the use of Hilbert SFCs in grid-point partitioning brings better locality of the grid points, improves balance of communication, and reduces communication overhead. We also demonstrate an extension of Hilbert SFCs coupled with blockwise operations. The use of blockwise operations helps exploit the vector-processing units in contemporary computational platforms. We illustrate speedup and scalability improvements for an iterative eigensolver based on the Chebyshev-filtered subspace iteration method. Using blockwise Hilbert SFCs, we solve the Kohn-Sham problem for silicon nanocrystals up to 10 nm in diameter, which contain over 26,000 atoms. We illustrate how the density of states of silicon nanocrystals evolves to the bulk limit, where Van Hove singularities are clearly apparent.

Prediction of Intrinsic Ferroelectricity and Large Piezoelectricity in Monolayer Arsenic Chalcogenides.

Two-dimensional materials that exhibit spontaneous electric polarization are of notable interest for functional materials. However, despite the prediction of many two-dimensional polar materials, the number of experimentally confirmed two-dimensional ferroelectrics is far less than bulk ferroelectrics. We provide strong evidence that the Pmn21 phase of arsenic chalcogenides As2X3 (X = S, Se, and Te), which include the recently isolated monolayer orpiment, are intrinsic ferroelectrics and demonstrate strong in-plane piezoelectricity. We found the calculated energy barriers for collectively reversing the electric polarization or moving a 180° domain wall are reasonable compared to previously reported ferroelectrics. We propose a high-symmetry structure (with Pmmn space group) that transforms into the ferroelectric Pmn21 phase by a soft B2u phonon mode. By studying other soft modes of the high-symmetry Pmmn structure, we identify several undiscovered metastable polymorphs, including a polar phase (with a P21 space group) with sizable piezoelectricity.

Accelerating Time-Dependent Density Functional Theory and GW Calculations for Molecules and Nanoclusters with Symmetry Adapted Interpolative Separable Density Fitting.

Computing integrals over orbital pairs is one of the most costly steps in many popular first-principles methods used by the quantum chemistry and condensed matter physics community. Here, we employ a recently proposed interpolative separable density fitting method (ISDF) to significantly reduce the cost of steps involving orbital pairs in linear response time-dependent density functional theory and GW calculations. In our implementation, we exploit the symmetry property of a system to effectively reduce the number of interpolation points and thus the computational cost. The performance of ISDF is illustrated with calculations on the GW100 set and silicon nanoclusters. We demonstrate the cost for constructing auxiliary basis and interpolation coefficients are negligible compared to the total cost. Compared to the conventional brute-force approach, the computation cost for evaluating all kernel matrix elements is reduced by nearly 3 orders of magnitude. The total cost for GW calculations can be reduced by four to eight times, depending on the system size.

Optically Driven Magnetic Phase Transition of Monolayer RuCl3.

Strong light-matter interactions within nanoscale structures offer the possibility of optically controlling material properties. Motivated by the recent discovery of intrinsic long-range magnetic order in two-dimensional materials, which allow for the creation of novel magnetic devices of unprecedented small size, we predict that light can couple with magnetism and efficiently tune magnetic orders of monolayer ruthenium trichloride (RuCl3). First-principles calculations show that both free carriers and optically excited electron-hole pairs can switch monolayer RuCl3 from a proximate spin-liquid phase to a stable ferromagnetic phase. Specifically, a moderate electron-hole pair density (on the order of 1 × 1013 cm-2) can significantly stabilize the ferromagnetic phase by 10 meV/f.u. in comparison to the competing zigzag phase, so that the predicted ferromagnetism can be driven by optical pumping experiments. Analysis shows that this magnetic phase transition is driven by a combined effect of doping-induced lattice strain and itinerant ferromagnetism. According to Ising-model calculations, we find that the Curie temperature of the ferromagnetic phase can be increased significantly by raising carrier or electron-hole pair density. This enhanced optomagnetic effect opens new opportunities to manipulate two-dimensional magnetism through noncontact, optical approaches.

Real-Space Based Benchmark of G0W0 Calculations on GW100: Effects of Semicore Orbitals and Orbital Reordering.

Using an implementation based on real-space wave functions, we perform G0W0 calculations of the HOMO and LUMO energies of molecules and atoms in the GW100 set. Our main conclusions are as follows: (1) Different implementations of the G0W0 approximation show much better agreements for HOMO (highest occupied molecular orbital) energies than for LUMO (lowest unoccupied molecular orbital) energies. The mean absolute differences between the results calculated with different pseudopotential codes range from 100 to 200 meV. For delocalized LUMOs, all-electron codes that use local orbital basis tend to predict much higher energies than those calculated with plane-wave basis or real-space methods. (2) The effects of semicore electrons in pseudopotentials can explain some of the large discrepancies between results calculated with different GW implementations. For molecules or atoms that include I, Xe, and Ga, pseudopotential-based calculations that exclude semicore electrons produce results that agree better with all-electron calculations. For polar molecules such as NaCl and BrK, however, it is necessary to include semicore electrons for alkaline metal elements to get correct LUMO energies. (3) More than 20 molecules show rearrangement of the order between LUMO (or HOMO) with other orbitals due to GW corrections. Such orbitals that switch order with LUMO are unbound and delocalized in space. The predicted LUMO GW levels (or electron affinity) can be corrected by 2.0 eV if we consider the rearrangement of orbitals in GW calculations. In all, our work clarifies some of the discrepancies between different GW codes and sets a benchmark for real-space implementations of the G0W0 approximation.

Discrimination of Bond Order in Organic Molecules Using Noncontact Atomic Force Microscopy.

Noncontact atomic force microscopy (nc-AFM) with a CO-functionalized tip can image submolecular structures through high-resolution images with the possibility of discriminating bond order. We employ real-space pseudopotential calculations to simulate nc-AFM images of molecules containing double (dibenzo(cd,n)naphtho(3,2,1,8-pqra)perylene (DBNP), hexabenzo(bc,ef,hi,kl,no,qr)coronene (HBC)) and triple (1,2-bis[2-(2-ethynylphenyl)ethynyl]-benzene (BEEB), 6-phenylhexa-1,3,5-triynylbenzene (PHTB)) bonds. We find (1) triple bonds can be unambiguously distinguished from other interatomic interactions based on a characteristic image and (2) the degree of double bond character can be directly determined from the image. We propose that large lateral forces acting on the tip may induce specific image distortions in the cases of DBNP and BEEB.

Accuracy of Partial Core Corrections Using Fourier Transforms in Pseudopotential-Density Functional Theory.

Partial core corrections can be important in obtaining an accurate description of nonlinear exchange-correlation functionals and improving the transferability of pseudopotentials. We show that a widely used procedure, which calculates partial core charge density, ρ core partial, in Fourier space and then converts it to real space with fast Fourier transforms, can lead to sizable numerical errors of exchange-correlation potentials in the vacuum region. Such errors occur in modeling low-dimensional materials or surfaces with supercells. The loss of accuracy originates from the slow-decaying feature of core charge density in reciprocal space. Numerical errors on the order of 1 eV in the Kohn-Sham energies of unoccupied states can occur in pseudopotential-density functional calculations. The direct calculation of the partial core charge in real space can avoid the numerical errors caused by Fourier transforms.

The stability, electronic structure, and optical absorption of boron-nitride diamondoids predicted with first-principles calculations.

Although diamondoids are broadly studied for their fundamental properties and applications, boron-nitride-based diamondoids are scarcely explored. Here we predict the stability, electronic structure, and optical absorption spectra of six boron-nitride (BN) diamondoids with first-principles methods based on pseudopotential density functional theory and many-body perturbation methods implemented with a real-space formalism. We find that four of them are thermodynamically stable at room temperature, while B10N8H24 and B6N4H16 show thermodynamic instability in molecular dynamics simulations. With the GW approximation, we predicted the ionization energies and electron affinities of BN-diamondoids and find that the evolution of the electronic structure with size does not follow the same trend as diamondoids, owing to the unbalanced numbers of boron and nitrogen atoms. We show strong photoabsorption of BN-triamantane and BN-adamantane in the infrared and visible ranges and analyze the features of low-energy absorption by examining the characteristics of related orbitals.

Orientation dependence of the work function for metal nanocrystals.

Work function values measured at different surfaces of a metal are usually different. This raises an interesting question: What is the work function of a nano-size crystal, where differently oriented facets can be adjacent? Work functions of metallic nanocrystals are also of significant practical interest, especially in catalytic applications. Using real space pseudopotentials constructed within density functional theory, we compute the local work function of large aluminum and gold nanocrystals. We investigate how the local work function follows the change of the surface plane orientation around multifaceted nanocrystals, and we establish the importance of the orbital character near the Fermi level in determining work function differences between facets.

Atomically precise graphene nanoribbon heterojunctions from a single molecular precursor.

The rational bottom-up synthesis of atomically defined graphene nanoribbon (GNR) heterojunctions represents an enabling technology for the design of nanoscale electronic devices. Synthetic strategies used thus far have relied on the random copolymerization of two electronically distinct molecular precursors to yield GNR heterojunctions. Here we report the fabrication and electronic characterization of atomically precise GNR heterojunctions prepared through late-stage functionalization of chevron GNRs obtained from a single precursor. Post-growth excitation of fully cyclized GNRs induces cleavage of sacrificial carbonyl groups, resulting in atomically well-defined heterojunctions within a single GNR. The GNR heterojunction structure was characterized using bond-resolved scanning tunnelling microscopy, which enables chemical bond imaging at T = 4.5 K. Scanning tunnelling spectroscopy reveals that band alignment across the heterojunction interface yields a type II heterojunction, in agreement with first-principles calculations. GNR heterojunction band realignment proceeds over a distance less than 1 nm, leading to extremely large effective fields.

Real-space pseudopotential method for computing the vibrational Stark effect.

The vibrational Stark shift is an important effect in determining the electrostatic environment for molecular or condensed matter systems. However, accurate ab initio calculations of the vibrational Stark effect are a technically demanding challenge. We make use of density functional theory constructed on a real-space grid to expedite the computation of this effect. Our format is especially advantageous for the investigation of small molecules in finite fields as cluster boundary conditions eliminate spurious supercell interactions and allow for charged systems, while convergence is controlled by a single parameter, the grid spacing. The Stark tuning rate is highly sensitive to the interaction between anharmonicity in a vibrational mode and the applied field. To ensure this subtle interaction is fully captured, we apply three parallel approaches: a direct finite field, a perturbative method, and a molecular dynamics method. We illustrate this method by applying it to several small molecules containing C-O and C-N bonds and show that a consistent result can be obtained.