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.

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.

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.

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 3, 3 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.

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 also derive 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]3d 10 -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.2. We use a simple and minimal parameterization for the ECP. The ccECPs are expressed in a wellestablished functional form [12] that is captured by arXiv:1907.08658v1 [cond-mat.mtrl-sci]