Luke Shulenburger

Sandia National Laboratories · Radiation Effects and High Energy Density Science Research Foundation

An outstanding challenge of theoretical electronic structure is the description of van der Waals (vdW) interactions in molecules and solids. Renewed interest in resolving this is in part motivated by the technological promise of layered systems including graphite, transition metal dichalcogenides, and more recently, black phosphorus, in which the i...

The moon-forming impact and the subsequent evolution of the proto-Earth is strongly dependent on the properties of materials at the extreme conditions generated by this violent collision. We examine the high pressure behavior of MgO, one of the dominant constituents in the earth's mantle, using high-precision, plate impact shock compression experim...

X-Ray Thomson Scattering (XRTS) is an important experimental technique used to measure the temperature, ionization state, structure, and density of warm dense matter (WDM). The fundamental property probed in these experiments is the electronic dynamic structure factor (DSF). In most models, this is decomposed into three terms [Chihara, J. Phys. F:...

We apply diffusion quantum Monte Carlo (DMC) to a broad set of solids, benchmarking the method by comparing bulk structural properties (equilibrium volume and bulk modulus) to experiment and DFT based theories. The test set includes materials with many different types of binding including ionic, metallic, covalent and van der Waals. We show that, o...

van der Waals forces are notoriously difficult to account for from first principles. We have performed extensive calculations to assess the usefulness and validity of diffusion quantum Monte Carlo when predicting van der Waals forces. We present converged results for noble gas solids and clusters, archetypical van der Waals dominated systems, as we...

Argon is the most abundant noble gas on Earth and its noble, atomic fluid nature makes it an excellent candidate for comparison of experiment and theory at extreme conditions. We performed a combined computational and experimental study on shock compressed cryogenic liquid argon. Using Sandia's Z machine, we shock compressed liquid argon to 600 GPa...

The “Decel” platform at Sandia National Laboratories investigates the Richtmyer–Meshkov instability (RMI) in converging geometry under high energy density conditions [Knapp et al., Phys. Plasmas 27, 092707 (2020)]. In Decel, the Z machine magnetically implodes a cylindrical beryllium liner filled with liquid deuterium, launching a converging shock...

In recent years there has been a rapid growth in the development and application of new stochastic methods in electronic structure. These methods are quite diverse, from many-body wave function techniques in real space or determinant space to being used to sum perturbative expansions. This growth has been spurred by the more favorable scaling with...

The essential data for interior and thermal evolution models of the Earth and super-Earths are the density and melting of mantle silicate under extreme conditions. Here, we report an unprecedently high melting temperature of MgSiO 3 at 500 GPa by direct shockwave loading of pre-synthesized dense MgSiO 3 (bridgmanite) using the Z Pulsed Power Facili...

While Diffusion Monte Carlo (DMC) is in principle an exact stochastic method for ab initio electronic structure calculations, in practice, the fermionic sign problem necessitates the use of the fixed-node approximation and trial wavefunctions with approximate nodes (or zeros). This approximation introduces a variational error in the energy that pot...

We present the results of the first Charged-Particle Transport Coefficient Code Comparison Workshop, which was held in Albuquerque, NM October 4–6, 2016. In this first workshop, scientists from eight institutions and four countries gathered to compare calculations of transport coefficients including thermal and electrical conduction, electron–ion c...

Quantum Monte Carlo (QMC) methods are useful for studies of strongly correlated materials because they are many body in nature and use the physical Hamiltonian. Typical calculations assume as a starting point a wave function constructed from single-particle orbitals obtained from one-body methods, e.g., density functional theory. However, mean-fiel...

Quantum Monte Carlo (QMC) methods are some of the most accurate methods for simulating correlated electronic systems. We investigate the compatibility, strengths, and weaknesses of two such methods, namely, diffusion Monte Carlo (DMC) and auxiliary-field quantum Monte Carlo (AFQMC). The multideterminant trial wave functions employed in both approac...

While Diffusion Monte Carlo (DMC) has the potential to be an exact stochastic method for ab initio electronic structure calculations, in practice the fixed-node approximation and trial wavefunctions with approximate nodes (or zeros) must be used. This approximation introduces a variational error in the energy that potentially can be tested and syst...

Quantum Monte Carlo (QMC) methods are some of the most accurate methods for simulating correlated electronic systems. We investigate the compatibility, strengths and weaknesses of two such methods, namely, diffusion Monte Carlo (DMC) and auxiliary-field quantum Monte Carlo (AFQMC). The multi-determinant trial wave functions employed in both approac...

We present the results of the first Charged-Particle Transport Coefficient Code Comparison Workshop, which was held in Albuquerque, NM October 4-6, 2016. In this first workshop, scientists from eight institutions and four countries gathered to compare calculations of transport coefficients including thermal and electrical conduction, electron-ion c...

Pulsed power accelerators compress electrical energy in space and time to provide versatile experimental platforms for high energy density and inertial confinement fusion science. The 80-TW “Z” pulsed power facility at Sandia National Laboratories is the largest pulsed power device in the world today. Z discharges up to 22 MJ of energy stored in it...

Recently, we developed a new method for generating effective core potentials (ECPs) using valence energy isospectrality with explicitly correlated all-electron (AE) excitations and norm-conservation criteria. We apply this methodology to the 3rd-row main group elements, creating new correlation consistent ECPs (ccECPs) and also deriving additional...

Outstanding problems in the high-pressure phase diagram of hydrogen have demonstrated the need for more accurate ab initio methods for thermodynamic sampling. One promising method that has been deployed extensively above 100 GPa is coupled electron-ion Monte Carlo (CEIMC), which treats the electronic structure with quantum Monte Carlo (QMC). Howeve...

Recently, we developed a new method for generating effective core potentials (ECPs) using valence energy isospectrality with explicitly correlated all-electron (AE) excitations and norm-conservation criteria. We apply this methodology to the 3$^{rd}$-row main group elements, creating new correlation consistent effective core potentials (ccECPs) and...

Recently, we have introduced a new generation of effective core potentials (ECPs) designed for accurate correlated calculations but equally useful for a broad variety of approaches. The guiding principle has been the isospectrality of all-electron and ECP Hamiltonians for a subset of valence many-body states using correlated, nearly-exact calculati...

Very recently, we have introduced correlation consistent effective core potentials (ccECPs) derived from many-body approaches with the main target being their use in explicitly correlated methods, while still usable in mainstream approaches. The ccECPs are based on reproducing excitation energies for a subset of valence states, namely, achieving ne...

The scale and complexity of the quantum system to which real-space quantum Monte Carlo (QMC) can be applied in part depends on the representation and memory usage of the trial wavefunction. B-splines, the computationally most efficient basis set, can have memory requirements exceeding the capacity of a single computational node. This situation has...

In this work, we study the interlayer interactions between sheets of blue phosphorus with quantum Monte Carlo (QMC) methods. We find that as previously observed in black phosphorus, interlayer binding of blue phosphorus cannot be described by van der Waals (vdW) interactions alone within the density functional theory framework. Specifically, while...

We report variational and fixed-node diffusion quantum Monte Carlo (QMC) calculations of anti-ferromagnetic iron oxide (FeO) in the ground state B1 crystal structure. The goal of this study was a systematic investigation of the sensitivity of several ground state properties to a variety of QMC wave function generation techniques including advanced...

The scale and complexity of quantum system to which real-space quantum Monte Carlo (QMC) can be applied in part depends on the representation and memory usage of the trial wavefunction. B-splines, the computationally most efficient basis set, can have memory requirements exceeding the capacity of a single computational node. This situation has trad...

Recently, we have introduced a new generation of effective core potentials (ECPs) designed for accurate correlated calculations but equally useful for a broad variety of approaches. The guiding principle has been the isospectrality of all-electron and ECP Hamiltonians for a subset of valence many-body states using correlated, nearly-exact calculati...

Very recently, we have introduced correlation consistent effective core potentials (ccECPs) derived from many-body approaches with the main target being its use in explicitly correlated methods but also in mainstream approaches. The ccECPs are based on reproducing excitation energies for a subset of valence states, i.e., achieving a near-isospectra...

Forsterite (Mg2SiO4) single crystals were shock compressed to pressures between 200 and 950 GPa using independent plate-impact steady shocks and laser-driven decaying shock compression experiments. Additionally, we performed density functional theory-based molecular dynamics to aid interpretation of the experimental data and to investigate possible...

The shock Hugoniot for full-density and porous CeO2 was investigated in the liquid regime using ab initio molecular dynamics (AIMD) simulations with Erpenbeck's approach based on the Rankine-Hugoniot jump conditions. The phase space was sampled by carrying out NVT simulations for isotherms between 6000 and 100 000 K and densities ranging from ρ=2.5...

QMCPACK is an open source quantum Monte Carlo package for ab-initio electronic structure calculations. It supports calculations of metallic and insulating solids, molecules, atoms, and some model Hamiltonians. Implemented real space quantum Monte Carlo algorithms include variational, diffusion, and reptation Monte Carlo. QMCPACK uses Slater-Jastrow...

QMCPACK has enabled cutting-edge materials research on supercomputers for over a decade. It scales nearly ideally but has low single-node efficiency due to the physics-based abstractions using array-of-structures objects, causing inefficient vectorization. We present a systematic approach to transform QMCPACK to better exploit the new hardware feat...

We outline ideas on desired properties for a new generation of effective core potentials (ECPs) that will allow valence-only calculations to reach the full potential offered by recent advances in many-body wave function methods. The key improvements include consistent use of correlated methods throughout ECP constructions and improved transferabili...

B-spline based orbital representations are widely used in Quantum Monte Carlo (QMC) simulations of solids, historically taking as much as 50% of the total run time. Random accesses to a large four-dimensional array make it challenging to efficiently utilize caches and wide vector units of modern CPUs. We present node-level optimizations of B-spline...

Titanium dioxide, TiO2, has multiple applications in catalysis, energy conversion and memristive devices because of its electronic structure. Most of these applications utilize the naturally existing phases: rutile, anatase and brookite. Despite the simple form of TiO2 and its wide uses, there is long-standing disagreement between theory and experi...

An understanding of the mechanical and optical properties of lithium fluoride (LiF) is essential to its use as a transparent tamper and window for dynamic materials experiments. In order to improve models for this material, we applied iterative Lagrangian analysis to ten independent sets of data from magnetically driven planar shockless compression...

In these proceedings, we show that time-dependent density functional theory is capable of stopping calculations at the extreme conditions of temperature and pressure seen in warm dense matter. The accuracy of the stopping curves tends to be up to about 20% lower than empirical models that are in use. However, TDDFT calculations are free from fittin...

We lay the foundation for a benchmarking methodology for assessing current and future quantum computers. We pose and begin addressing fundamental questions about how to fairly compare computational devices at vastly different stages of technological maturity. We critically evaluate and offer our own contributions to current quantum benchmarking eff...

The Magn\'eli phase Ti$_4$O$_7$ is an important transition metal oxide with a wide range of applications because of its interplay between charge, spin, and lattice degrees of freedom. At low temperatures, it has non-trivial magnetic states very close in energy, driven by electronic exchange and correlation interactions. We have examined three low-l...

We performed diffusion Monte Carlo (DMC) calculations of the spectroscopic properties of a large set of molecules, assessing the effect of different approximations. In systems containing elements with large atomic numbers, we show that the errors associated with the use of nonlocal mean-field-based pseudopotentials in DMC calculations can be signif...

We present density functional theory (DFT) + quasiparticle self-energy (G(0)W(0)) + Bethe-Salpeter calculations of the real and imaginary parts of the long-wavelength dielectric function of LiF between ambient pressure and P = 5 Mbars. While the optical absorption spectrum is predicted to show dramatic pressure-dependent features above the optical...

We lay the foundation for a benchmarking methodology for assessing current and future quantum computers. We pose and begin addressing fundamental questions about how to fairly compare computational devices at vastly different stages of technological maturity. We critically evaluate and offer our own contributions to current quantum benchmarking eff...

Motivated by the disagreement between recent diffusion Monte Carlo calculations and experiments on the phase transition pressure between the ambient and beta-Sn phases of silicon, we present a study of the HCP to BCC phase transition in beryllium. This lighter element provides an oppor- tunity for directly testing many of the approximations require...

We use Sandia's Z machine and magnetically accelerated flyer plates to shock compress liquid krypton to 850 GPa and compare with results from density-functional theory (DFT) based simulations using the AM05 functional. We also employ quantum Monte Carlo calculations to motivate the choice of AM05. We conclude that the DFT results are sensitive to t...

We have performed quantum Monte Carlo (QMC) simulations and density functional theory (DFT) calculations to study the equations of state of $MgSiO_3$ perovskite (Pv) and post-perovskite (PPv), up to the pressure and temperature conditions of the base of Earth's lower mantle. The ground state energies were derived using QMC and the temperature depen...

We present an improved first-principles description of melting under pressure based on thermodynamic integration comparing Density Functional Theory (DFT) and quantum Monte Carlo (QMC) treatments of the system. The method is applied to address the longstanding discrepancy between density functional theory (DFT) calculations and diamond anvil cell (...

We describe the challenges involved when using time-dependent density functional theory (TDDFT) to describe warm dense matter (WDM) within a plane-wave, real-time formulation. WDM occurs under conditions of temperature and pressure (over 1000 K and 1 Mbar) where plasma physics meets condensed matter physics. TDDFT is especially important in this re...

A challenging application for any electronic structure method is the calculation of solid-solid phase transitions under pressure. Due to stringent requirements on accuracy imposed by the sensitivity of such transitions on small changes in free energy these calculations are exquisitely sensitive to any systematic errors in the calculations. In this...

With advances in algorithms and growing computing powers, quantum Monte Carlo (QMC) methods have become a leading contender for high accuracy calculations for the electronic structure of realistic systems. The performance gain on recent HPC systems is largely driven by increasing parallelism: the number of compute cores of a SMP and the number of S...

Van der Waals forces are as ubiquitous as infamous. While post-Hartree-Fock methods enable accurate estimates of these forces in molecules and clusters, they remain elusive for dealing with many-electron condensed phase systems. We present Quantum Monte Carlo [1,2] results for condensed van der Waals systems. Interatomic many-body contributions to...

Diffusion quantum Monte Carlo (DMC) has been applied to solids under pressure in several different contexts a high degree of success.ootnotetextJ. Kolorenc and L. Mitas. Rep. Prog. Phys. 74 026502 (2011) All of these calculations must address three errors present in DMC calculations of solids: the fixed node approximation, the pseudopotential appro...

Continuum quantum Monte Carlo (QMC) methods are a leading contender for high accuracy calculations for the electronic structure of realistic systems, especially on massively parallel high-performance computers (HPC). The performance gain on recent HPC systems is largely driven by increasing parallelism: the number of compute cores of a SMP and the...

X-ray diffraction experiments on postperovskite (ppv) with compositions (Mg0.9Fe0.1)SiO3 and (Mg0.6Fe0.4)SiO3 at Earth core-mantle boundary pressures reveal different crystal structures. The former adopts the CaIrO3-type structure with space group Cmcm, whereas the latter crystallizes in a structure with the Pmcm (Pmma) space group. The latter has...

More accurate than mean-field methods and more scalable than quantum chemical methods, continuum quantum Monte Carlo (QMC) is an invaluable tool for predicting the properties of matter from fundamental principles. Because QMC algorithms offer multiple forms of parallelism, they're ideal candidates for acceleration in the many-core paradigm.

Magnesium Oxide (MgO) is a highly stable material that melts at temperatures above 3000 K at ambient pressure. It is abundantly found in the Earth's mantle and is likely to be an important constituent of exo-planets, including ``super earths'' with higher inner pressures. However, little data exist at extreme pressures and temperatures and the curr...

The principal Hugoniot for CO2 is known up to 75 GPa and it displays a plateau in shock pressure interpreted as the result of dissociation [1]. To confidently model the structure of gas-giant planets and the deep carbon cycle of the earth it is important to accurately know the properties of CO2 at even higher pressures. We present results from flye...

Ab initio calculations based on density functional theory (DFT) have proven a valuable tool in understanding the properties of materials at extreme conditions. However, there are entire classes of materials where the current limitations of DFT cast doubt upon the predictive power of the method. These include so called strongly correlated systems an...

Quantitative knowledge of the thermo-physical properties of CO2 at high pressure is required to confidently model the structure of gas-giants like Neptune and Uranus and the deep carbon cycle of the earth. DFT based molecular dynamics has been established as a method capable of yielding high fidelity results for many materials, including shocked ga...

The slope of the melting temperature as a function of pressure yields, via the Clausius-Clapeyron equation, important information regarding the changes in density, energy, and entropy. It is therefore crucial to resolve the long-standing differences in melt lines under pressure between Diamond Anvil Cell data (low/flat melt line) and other methods,...

Quantum Monte Carlo (QMC) simulations are among the most accurate ab initio methods describing the many-particle systems properties. Computations perform accesses to an ensemble data structure describing the system quantum state. The ensemble data grows rapidly with the system size and desired resolution. For leadership-scale simulations, this stru...

Discovery of a high-pressure post-perovskite phase transition of MgSiO3 opened a new paradigm for understanding the deepest region of the core-mantle boundary and the D'' region. The structure was found to be Cmcm space group as same structure as CaIrO3. However, we discovered a new structure for the post-perovskite phase of iron rich magnesium sil...

Material Resource Planning (MRP) is a common production system used by many of today's manufacturing facilities. When interactions between a manufacturer and supplier become complex, MRP systems sometimes become chaotic, an event called MRP Nervousness. MRP Nervousness occurs when small scheduling updates lead to very large changes in the finished...

LDA+U and LDA+DMFT are successful methods for determining the electronic structure of FeO under pressure, but they suffer from two deficiencies. The extreme sensitivity of the spin collapse in MnO on the parameters U and J casts doubt upon the predictive power of the methods^1. Additionally, the symmetry of the occupation matrix has a profound effe...

We perform first-principles linear response computations within LDA+U and GGA+U to systematically investigate the pressure dependence of magnetic exchange interactions for archetypal transition metal oxides (TMOs): MnO, FeO, CoO, and NiO. We obtain the Neel temperatures (TN) using Monte Carlo simulations. We find that the magnitude of the next near...

We are using a variety of methods, including density functional theory, dynamical mean field theory, and quantum Monte Carlo, to better understand the behavior of FeO in particular, and ferrous iron and other transition metal oxides in general, under compression. We have computed the spin-wave dispersion and effective Heisenberg couplings for FeO u...

The crystal field splitting and d bandwidth of the 3d transition metal monoxides MnO, FeO, CoO and NiO are analyzed as a function of pressure within density functional theory. In all four cases the 3d bandwidth is significantly larger than the crystal field splitting over a wide range of compressions. The bandwidth actually increases more as pressu...

FeO has a rich behavior under pressure, exhibiting a structural phase transition as well as an insulator-metal transition and a spin collapse. The electronic transitions have been particularly difficult to explain because of the failure of Density Functional Theory (DFT) to capture the electronic state of FeO. We present results from three differen...

By carrying out extensive lattice regularized diffusion Monte Carlo calculations, we study the spin and density dependence of the ground state energy for a quasi-one-dimensional electron gas, with harmonic transverse confinement and long-range $1/r$ interactions. We present a parametrization of the exchange-correlation energy suitable for spin dens...

We have performed Quantum Monte Carlo (QMC) computations for silica, FeO, and c-BN as functions of compression. QMC uses no approximate density functional, and the many-body, correlated, Schrödinger equation is effectively solved stochastically. In spite of the great success of DFT there are still some fundamental problems that need improvement. Fi...

The nature of the magnetic collapse in transition metal oxides under pressure has been a source of recent theoretical interest with multiple explanations presented in the literature[1,2]. In order to better understand this phenomenon we present the results of two sets of calculations utilizing different electronic structure methods. We perform quan...

We explore the role of electron correlation in quasi-one-dimensional quantum wires as the range of the interaction potential is changed and their thickness is varied by performing exact quantum Monte Carlo simulations at various electronic densities. In the case of unscreened interactions with a long-range 1/x tail there is a crossover from a liqui...

Since the post-perovskite (ppv) phase in MgSiO3 was discovered to be similar structure of CaIrO3 (Cmcm Z=4) under the conditions of near Earth's core-mantle boundary, many investigations have provided explanations for the presence of low seismic velocity. However, precise experimental structure analysis of ppv-(Mg1-xFex)SiO3 has never been reported...