Mohan Chen

Accelerating atomic orbital-based electronic structure calculation via pole expansion and selected inversion

We describe how to apply the recently developed pole expansion and selected inversion (PEXSI) technique to Kohn-Sham density function theory (DFT) electronic structure calculations that are based on atomic orbital discretization. We give analytic expressions for evaluating the charge density, the total energy, the Helmholtz free energy and the atomic forces (including both the Hellmann-Feynman force and the Pulay force) without using the eigenvalues and eigenvectors of the Kohn-Sham Hamiltonian. We also show how to update the chemical potential without using Kohn-Sham eigenvalues. The advantage of using PEXSI is that it has a computational complexity much lower than that associated with the matrix diagonalization procedure. We demonstrate the performance gain by comparing the timing of PEXSI with that of diagonalization on insulating and metallic nanotubes. For these quasi-1D systems, the complexity of PEXSI is linear with respect to the number of atoms. This linear scaling can be observed in our computational experiments when the number of atoms in a nanotube is larger than a few hundreds. Both the wall clock time and the memory requirement of PEXSI are modest. This even makes it possible to perform Kohn-Sham DFT calculations for 10 000-atom nanotubes with a sequential implementation of the selected inversion algorithm. We also perform an accurate geometry optimization calculation on a truncated (8, 0) boron nitride nanotube system containing 1024 atoms. Numerical results indicate that the use of PEXSI does not lead to loss of the accuracy required in a practical DFT calculation.

Ab initio theory and modeling of water

Significance Water is vital to our everyday life, but its structure at a molecular level is still not fully understood from either experiment or theory. The latter is hampered by our inability to construct a purely predictive, first principles model. The difficulty in modeling water lies in capturing the delicate interplay among the many strong and weak forces that govern its behavior and phase diagram. Herein, molecular simulations with a recently proposed nonempirical quantum mechanical approach (the SCAN density functional) yield an excellent description of the structural, electronic, and dynamic properties of liquid water. SCAN (strongly constrained and appropriately normed)-based approaches, which describe diverse types of bonds in materials on an equal, accurate footing, will likely enable efficient and reliable modeling of aqueous phase chemistry. Water is of the utmost importance for life and technology. However, a genuinely predictive ab initio model of water has eluded scientists. We demonstrate that a fully ab initio approach, relying on the strongly constrained and appropriately normed (SCAN) density functional, provides such a description of water. SCAN accurately describes the balance among covalent bonds, hydrogen bonds, and van der Waals interactions that dictates the structure and dynamics of liquid water. Notably, SCAN captures the density difference between water and ice Ih at ambient conditions, as well as many important structural, electronic, and dynamic properties of liquid water. These successful predictions of the versatile SCAN functional open the gates to study complex processes in aqueous phase chemistry and the interactions of water with other materials in an efficient, accurate, and predictive, ab initio manner.

The melting point of lithium: an orbital-free first-principles molecular dynamics study

The melting point of liquid lithium near zero pressure is studied with large-scale orbital-free first-principles molecular dynamics (OF-FPMD) in the isobaric-isothermal ensemble. We adopt the Wang-Govind-Carter (WGC) functional as our kinetic energy density functional (KEDF) and construct a bulk-derived local pseudopotential (BLPS) for Li. Our simulations employ both the ‘heat-until-melts’ method and the coexistence method. We predict 465 K as an upper bound of the melting point of Li from the ‘heat-until-melts’ method, while we predict 434 K as the melting point of Li from the coexistence method. These values compare well with an experimental melting point of 453 K at zero pressure. Furthermore, we calculate a few important properties of liquid Li including the diffusion coefficients, pair distribution functions, static structure factors, and compressibilities of Li at 470 K and 725 K in the canonical ensemble. Our theoretically-obtained results show good agreement with known experimental results, suggesting that OF-FPMD using a non-local KEDF and a BLPS is capable of accurately describing liquid metals.

Systematically improvable optimized atomic basis sets for ab initio calculations

We propose a unique scheme to construct fully optimized atomic basis sets for density-functional calculations. The shapes of the radial functions are optimized by minimizing the spillage of the wavefunctions between the atomic orbital calculations and the converged plane wave results for dimer systems. The quality of the bases can be systematically improved by increasing the size of the bases within the same framework. We show that the spillage can describe the convergency of the total energy very well and the cutoff radii of the atomic orbitals are extremely important for the quality of the atomic orbitals. The scheme is easy to implement and very flexible. We have performed extensive tests of this scheme for a wide variety of systems, including semiconductors, oxides, metals, clusters, etc. The results show that the obtained atomic bases are very satisfactory for both accuracy and transferability.

Petascale Orbital-Free Density Functional Theory Enabled by Small-Box Algorithms

Orbital-free density functional theory (OFDFT) is a quantum-mechanics-based method that utilizes electron density as its sole variable. The main computational cost in OFDFT is the ubiquitous use of the fast Fourier transform (FFT), which is mainly adopted to evaluate the kinetic energy density functional (KEDF) and electron-electron Coulomb interaction terms. We design and implement a small-box FFT (SBFFT) algorithm to overcome the parallelization limitations of conventional FFT algorithms. We also propose real-space truncation of the nonlocal Wang-Teter KEDF kernel. The scalability of the SBFFT is demonstrated by efficiently simulating one full optimization step (electron density, energies, forces, and stresses) of 1,024,000 lithium (Li) atoms on up to 65,536 cores. We perform other tests using Li as a test material, including calculations of physical properties of different phases of bulk Li, geometry optimizations of nanocrystalline Li, and molecular dynamics simulations of liquid Li. All of the tests yield excellent agreement with the original OFDFT results, suggesting that the OFDFT-SBFFT algorithm opens the door to efficient first-principles simulations of materials containing millions of atoms.

Hydroxide diffuses slower than hydronium in water because its solvated structure inhibits correlated proton transfer

Proton transfer via hydronium and hydroxide ions in water is ubiquitous. It underlies acid-base chemistry, certain enzyme reactions, and even infection by the flu. Despite two-centuries of investigation, the mechanism underlying why hydronium diffuses faster than hydroxide in water is still not well understood. Herein, we employ state of the art Density Functional Theory based molecular dynamics, with corrections for nonlocal van der Waals interactions, and self-interaction in the electronic ground state, to model water and the hydrated water ions. At this level of theory, structural diffusion of hydronium preserves the previously recognized concerted behavior. However, by contrast, proton transfer via hydroxide is dominated by stepwise events, arising from a stabilized hyper-coordination solvation structure that discourages proton transfer. Specifically, the latter exhibits non-planar geometry, which agrees with neutron scattering results. Asymmetry in the temporal correlation of proton transfer enables hydronium to diffuse faster than hydroxide.Proton transfer via hydronium and hydroxide ions in water is ubiquitous. It underlies acid–base chemistry, certain enzyme reactions, and even infection by the flu. Despite two centuries of investigation, the mechanism underlying why hydroxide diffuses slower than hydronium in water is still not well understood. Herein, we employ state-of-the-art density-functional-theory-based molecular dynamics—with corrections for non-local van der Waals interactions, and self-interaction in the electronic ground state—to model water and hydrated water ions. At this level of theory, we show that structural diffusion of hydronium preserves the previously recognized concerted behaviour. However, by contrast, proton transfer via hydroxide is less temporally correlated, due to a stabilized hypercoordination solvation structure that discourages proton transfer. Specifically, the latter exhibits non-planar geometry, which agrees with neutron-scattering results. Asymmetry in the temporal correlation of proton transfer leads to hydroxide diffusing slower than hydronium.Even though the Grotthuss mechanism was proposed two centuries ago, it is still unclear why proton transfer via the hydroxide ion is slower than that via hydronium. Advanced ab initio molecular dynamics simulations now show that it is because proton transfer via hydroxide is less temporally correlated than transfer via hydronium.

Rock-salt structure lithium deuteride formation in liquid lithium with high-concentrations of deuterium: a first-principles molecular dynamics study

Because of lithium’s possible use as a first wall material in a fusion reactor, a fundamental understanding of the interactions between liquid lithium (Li) and deuterium (D) is important. We predict structural and dynamical properties of liquid Li samples with high concentrations of D, as derived from first-principles molecular dynamics simulations. Liquid Li samples with four concentrations of inserted D atoms (LiD�, � = 0.25, 0.50, 0.75, and 1.00) are studied at temperatures ranging from 470 to 1143 K. Densities, diffusivities, pair distribution functions, bond angle distribution functions, geometries, and charge transfer between Li and D atoms are calculated and analyzed. The analysis suggests liquid–solid phase transitions can occur at some concentrations and temperatures, forming rock-salt LiD within liquid Li. We also observe formation of some D2 molecules at high D concentrations.

Effect of Temperature on the Desorption of Lithium from Molybdenum(110) Surfaces: Implications for Fusion Reactor First Wall Materials

Determining the strength of Li binding to Mo is critical to assessing the survivability of Li as a potential first wall material in fusion reactors. We present the results of a joint experimental and theoretical investigation into how Li desorbs from Mo(110) surfaces, based on what can be deduced from temperature-programmed desorption measurements and density functional theory (DFT). Li desorption peaks measured at temperatures ranging from 711 K (1 monolayer, ML) to 1030 K (0.04 ML), with corresponding desorption onsets from 489 to 878 K, follow a trend similar to predicted Gibbs free energies for Li adsorption. Bader charge analysis of DFT densities reveals that repulsive forces between neighboring positively charged Li atoms increase with coverage and thus reduce the bond strength between Mo and Li, thereby lowering the desorption temperature as the coverage increases. Additionally, DFT predicts that Li desorbs at higher temperatures from a surface with vacancies than from a perfect surface, offering an explanation for the anomalously high desorption temperatures for the last Li to desorb from Mo(110). Analysis of simulated local densities of states indicates that the stronger binding to the defective surface is correlated with enhanced interaction between Li and Mo, involving the Li 2s electrons and not only the Mo 4d electrons as in the case of the pristine surface, but also the Mo 5s electrons in the case with surface vacancies. We suggest that steps and kinks present on the Mo(110) surface behave similarly and contribute to the high desorption temperatures. These findings imply that roughened Mo surfaces may strengthen Li film adhesion at higher temperatures.

Electronic structure interpolation via atomic orbitals

We present an efficient scheme for accurate electronic structure interpolation based on systematically improvable optimized atomic orbitals. The atomic orbitals are generated by minimizing the spillage value between the atomic basis calculations and the converged plane wave basis calculations on some coarse k-point grid. They are then used to calculate the band structure of the full Brillouin zone using the linear combination of atomic orbitals algorithms. We find that usually 16-25 orbitals per atom can give an accuracy of about 10 meV compared to the full ab initio calculations, and the accuracy can be systematically improved by using more atomic orbitals. The scheme is easy to implement and robust, and works equally well for metallic systems and systems with complicated band structures. Furthermore, the atomic orbitals have much better transferability than Shirleys basis and Wannier functions, which is very useful for perturbation calculations.

Potential Functional Embedding Theory at the Correlated Wave Function Level. 1. Mixed Basis Set Embedding

Embedding theories offer an elegant solution to overcome intrinsic algorithmic scaling and accuracy limitations of simulation methods. These theories also promise to achieve the accuracy of high-level electronic structure techniques at near the computational cost of much less accurate levels of theory by exploiting positive traits of multiple methods. Of crucial importance to fulfilling this promise is the ability to combine diverse theories in an embedding simulation. However, these methods may utilize different basis set and electron-ion potential representations. In this first part of a two-part account of implementing potential functional embedding theory (PFET) at a correlated wave function level, we discuss remedies to basis set and electron-ion potential discrepancies and assess the performance of the PFET scheme with mixed basis sets.