Enhanced Twist-Averaging Technique for Magnetic Metals: Applications Using Quantum Monte Carlo.

We propose an improved twist-averaging (TA) scheme for quantum Monte Carlo methods that use converged Kohn-Sham or Hartree-Fock orbitals as the reference. This TA technique is tailored to sample the Brillouin zone of magnetic metals, although it naturally extends to nonmagnetic (NM) conducting systems. The proposed scheme aims to reproduce the reference magnetization and achieves charge neutrality by construction, thus avoiding the large energy fluctuations and the postprocessing needed to correct the energies. It shows the most robust convergence of total energy and magnetism to the thermodynamic limit (TDL) when compared to four other TA schemes. Diffusion Monte Carlo applications are shown on NM Al and ferromagnetic α-Fe. The cohesive energy of Al in the TDL shows an excellent agreement with the experimental result. Furthermore, the magnetic moments in α-Fe exhibit rapid convergence with an increasing number of twists.

A new generation of effective core potentials: Selected lanthanides and heavy elements.

We construct correlation-consistent effective core potentials (ccECPs) for a selected set of heavy atoms and f elements that are currently of significant interest in materials and chemical applications, including Y, Zr, Nb, Rh, Ta, Re, Pt, Gd, and Tb. As is customary, ccECPs consist of spin-orbit (SO) averaged relativistic effective potential (AREP) and effective SO terms. For the AREP part, our constructions are carried out within a relativistic coupled-cluster framework while also taking into account objective function one-particle characteristics for improved convergence in optimizations. The transferability is adjusted using binding curves of hydride and oxide molecules. We address the difficulties encountered with f elements, such as the presence of large cores and multiple near-degeneracies of excited levels. For these elements, we construct ccECPs with core-valence partitioning that includes 4f subshell in the valence space. The developed ccECPs achieve an excellent balance between accuracy, size of the valence space, and transferability and are also suitable to be used in plane wave codes with reasonable energy cutoffs.

Emergent Magnetism with Continuous Control in the Ultrahigh-Conductivity Layered Oxide PdCoO2.

The current challenge to realizing continuously tunable magnetism lies in our inability to systematically change properties, such as valence, spin, and orbital degrees of freedom, as well as crystallographic geometry. Here, we demonstrate that ferromagnetism can be externally turned on with the application of low-energy helium implantation and can be subsequently erased and returned to the pristine state via annealing. This high level of continuous control is made possible by targeting magnetic metastability in the ultrahigh-conductivity, nonmagnetic layered oxide PdCoO2 where local lattice distortions generated by helium implantation induce the emergence of a net moment on the surrounding transition metal octahedral sites. These highly localized moments communicate through the itinerant metal states, which trigger the onset of percolated long-range ferromagnetism. The ability to continuously tune competing interactions enables tailoring precise magnetic and magnetotransport responses in an ultrahigh-conductivity film and will be critical to applications across spintronics.

A new generation of effective core potentials from correlated and spin-orbit calculations: Selected heavy elements.

We introduce new correlation consistent effective core potentials (ccECPs) for the elements I, Te, Bi, Ag, Au, Pd, Ir, Mo, and W with 4d, 5d, 6s, and 6p valence spaces. These ccECPs are given as a sum of spin-orbit averaged relativistic effective potential (AREP) and effective spin-orbit (SO) terms. The construction involves several steps with increasing refinements from more simple to fully correlated methods. The optimizations are carried out with objective functions that include weighted many-body atomic spectra, norm-conservation criteria, and SO splittings. Transferability tests involve molecular binding curves of corresponding hydride and oxide dimers. The constructed ccECPs are systematically better and in a few cases on par with previous effective core potential (ECP) tables on all tested criteria and provide a significant increase in accuracy for valence-only calculations with these elements. Our study confirms the importance of the AREP part in determining the overall quality of the ECP even in the presence of sizable spin-orbit effects. The subsequent quantum Monte Carlo calculations point out the importance of accurate trial wave functions that, in some cases (mid-series transition elements), require treatment well beyond a single-reference.

Binding and excitations in SixHy molecular systems using quantum Monte Carlo.

We present high-accuracy correlated calculations of small SixHy molecular systems in both the ground and excited states. We employ quantum Monte Carlo (QMC) together with a variety of many-body wave function approaches based on basis set expansions. The calculations are carried out in a valence-only framework using recently derived correlation consistent effective core potentials. Our primary goal is to understand the fixed-node diffusion QMC errors in both the ground and excited states with single-reference trial wave functions. Using a combination of methods, we demonstrate the very high accuracy of the QMC atomization energies being within ≈0.07 eV or better when compared with essentially exact results. By employing proper choices for trial wave functions, we have found that the fixed-node QMC biases for total energies are remarkably uniform ranging between 1% and 3.5% with absolute values at most ≈0.2 eV across the systems and several types of excitations such as singlets and triplets as well as low-lying and Rydberg-like states. Our results further corroborate that Si systems, and presumably also related main group IV and V elements of the periodic table (Ge, Sn, etc), exhibit some of the lowest fixed-node biases found in valence-only electronic structure QMC calculations.

QMCPACK: Advances in the development, efficiency, and application of auxiliary field and real-space variational and diffusion quantum Monte Carlo.

We review recent advances in the capabilities of the open source ab initio Quantum Monte Carlo (QMC) package QMCPACK and the workflow tool Nexus used for greater efficiency and reproducibility. The auxiliary field QMC (AFQMC) implementation has been greatly expanded to include k-point symmetries, tensor-hypercontraction, and accelerated graphical processing unit (GPU) support. These scaling and memory reductions greatly increase the number of orbitals that can practically be included in AFQMC calculations, increasing the accuracy. Advances in real space methods include techniques for accurate computation of bandgaps and for systematically improving the nodal surface of ground state wavefunctions. Results of these calculations can be used to validate application of more approximate electronic structure methods, including GW and density functional based techniques. To provide an improved foundation for these calculations, we utilize a new set of correlation-consistent effective core potentials (pseudopotentials) that are more accurate than previous sets; these can also be applied in quantum-chemical and other many-body applications, not only QMC. These advances increase the efficiency, accuracy, and range of properties that can be studied in both molecules and materials with QMC and QMCPACK.

Accurate Atomic Correlation and Total Energies for Correlation Consistent Effective Core Potentials.

Very recently, we introduced a set of correlation consistent effective core potentials (ccECPs) constructed within full many-body approaches. By employing significantly more accurate correlated approaches, we were able to reach a new level of accuracy for the resulting effective core Hamiltonians. We also strived for simplicity of use and easy transferability into a variety of electronic structure methods in quantum chemistry and condensed matter physics. Here, as a reference for future use, we present exact or nearly exact total energy calculations for these ccECPs. The calculations cover H-Kr elements and are based on the state-of-the-art configuration interaction (CI), coupled-cluster (CC), and quantum Monte Carlo (QMC) calculations with systematically eliminated/improved errors. In particular, we carry out full CI/CCSD(T)/CCSDT(Q) calculations with cc-pVnZ with up to n = 6 basis sets and we estimate the complete basis set limits. Using combinations of these approaches, we achieved an accuracy of ≈1-10 mHa for K-Zn atoms and ≈0.1-0.3 mHa for all other elements-within about 1% or better of the ccECP total correlation energies. We also estimate the corresponding kinetic energies within the feasible limit of full CI calculations. In order to provide data for QMC calculations, we include fixed-node diffusion Monte Carlo energies for each element that give quantitative insights into the fixed-node biases for single-reference trial wave functions. The results offer a clear benchmark for future high-accuracy calculations in a broad variety of correlated wave function methods such as CI and CC as well is in stochastic approaches such as real space sampling QMC.

A new generation of effective core potentials from correlated calculations: 4s and 4p main group elements and first row additions.

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 ECPs to complete the ccECP table for H-Kr. For K and Ca, we develop Ne-core ECPs, and for the 4p main group elements, we construct [Ar]3d10-core potentials. Scalar relativistic effects are included in their construction. Our ccECPs reproduce AE spectra with significantly better accuracy than many existing pseudopotentials and show better overall consistency across multiple properties. The transferability of ccECPs is tested on monohydride and monoxide molecules over a range of molecular geometries. For the constructed ccECPs, we also provide optimized DZ-6Z valence Gaussian basis sets.

A new generation of effective core potentials from correlated calculations: 3d transition metal series.

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 calculations. Here we present such ECPs for the 3d transition series Sc to Zn with Ne-core, i.e., with semi-core 3s and 3p electrons in the valence space. Besides genuine many-body accuracy, the operators are simple, being represented by a few gaussians per symmetry channel with resulting potentials that are bounded everywhere. The transferability is checked on selected molecular systems over a range of geometries. The ECPs show a high overall accuracy with valence spectral discrepancies typically ≈0.01-0.02 eV or better. They also reproduce binding curves of hydride and oxide molecules typically within 0.02-0.03 eV deviations over the full non-dissociation range of interatomic distances.

A new generation of effective core potentials from correlated calculations: 2nd row elements.

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 near-isospectrality between the original and pseudo Hamiltonians. In addition, binding curves of dimer molecules were used for refinement and overall improvement of transferability over a range of bond lengths. Here we apply similar ideas to the 2nd row elements and study several aspects of the constructions in order to find the high accuracy solutions within the chosen ccECP forms with 3s, 3p valence space (Ne-core). Our new constructions exhibit accurate low-lying atomic excitations and equilibrium molecular bonds (on average within ≈0.03 eV and 3 mÅ); however, the errors for Al and Si oxide molecules at short bond lengths are notably larger for both ours and existing effective core potentials. Assuming this limitation, our ccECPs show a systematic balance between the criteria of atomic spectra accuracy and transferability for molecular bonds. In order to provide another option with much higher uniform accuracy, we also construct He-core ccECPs for the whole 2nd row with typical discrepancies of ≈0.01 eV or smaller.

A new generation of effective core potentials for correlated calculations.

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 transferability as required for an accurate description of molecular systems over a range of geometries. The guiding principle is the isospectrality of all-electron and ECP Hamiltonians for a subset of valence states. We illustrate these concepts on a few first- and second-row atoms (B, C, N, O, S), and we obtain higher accuracy in transferability than previous constructions while using semi-local ECPs with a small number of parameters. In addition, the constructed ECPs enable many-body calculations of valence properties with higher (or same) accuracy than their all-electron counterparts with uncorrelated cores. This implies that the ECPs include also some of the impacts of core-core and core-valence correlations on valence properties. The results open further prospects for ECP improvements and refinements.