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 accuracy. Advances in real space methods include techniques for accurate computation of band gaps 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

Specific Reaction Parameter Multigrid POTFIT (SRP-MGPF): Automatic Generation of Sum-of-Products Form Potential Energy Surfaces for Quantum Dynamical Calculations

We present Specific Reaction Parameter Multigrid POTFIT (SRP-MGPF), an automated methodology for the generation of global potential energy surfaces (PES), molecular properties surfaces, e.g., dipole, polarizabilities, etc. using a single random geometry as input. The SRP-MGPF workflow integrates: (i) a fully automated procedure for the global topographical characterization of a (intermolecular) PES based on the Transition State Search Using Chemical Dynamical Simulations (TSSCDS) family of methods;i (ii) the global optimization of the parameters of a semiempirical Hamiltonian in order to reproduce a given level of electronic structure theory; and (iii) a tensor decomposition algorithm which turns the resulting SRP-PES into sum of products (Tucker) form with the Multigrid POTFIT algorithm. The latter is necessary for quantum dynamical studies within the Multiconfiguration Time-Dependent Hartree (MCTDH) quantum dynamics method. To demonstrate our approach, we have applied our methodology to the cis-trans isomerization reaction in HONO in full dimensionality (6D). The resulting SRP-PES has been validated through the computation of classical on-the-fly dynamical calculations as well as calculations of the lowest vibrational eigenstates of HONO as well as high-energy wavepacket propagationsRP-B thanks the Région Hauts-de-France and the Université de Lille for a Ph.D. Fellowship. RP-B and DP thank the Région Hauts-de-France and the Ministére de l'Enseignement Supérieur et de la Recherche (CPER Climibio), and the European Fund for Regional Economic Development for their financial support. This work has been partially supported by the Agence Nationale de la Recherche through the Labex CaPPA (ANR-11-LABX-0005-01). EM-N thanks Xunta de Galicia (Research Grant No. ED431C 2017/17)S

First-principles molecular structure search with a genetic algorithm

The identification of low-energy conformers for a given molecule is a fundamental problem in computational chemistry and cheminformatics. We assess here a conformer search that employs a genetic algorithm for sampling the low-energy segment of the conformation space of molecules. The algorithm is designed to work with first-principles methods, facilitated by the incorporation of local optimization and blacklisting conformers to prevent repeated evaluations of very similar solutions. The aim of the search is not only to find the global minimum, but to predict all conformers within an energy window above the global minimum. The performance of the search strategy is: (i) evaluated for a reference data set extracted from a database with amino acid dipeptide conformers obtained by an extensive combined force field and first-principles search and (ii) compared to the performance of a systematic search and a random conformer generator for the example of a drug-like ligand with 43 atoms, 8 rotatable bonds and 1 cis/trans bond

Fixed-Node Diffusion Monte Carlo potential energy curve of the fluorine molecule F2 using selected configuration interaction trial wavefunctions

The potential energy curve of the F$_2$ molecule is calculated with Fixed-Node Diffusion Monte Carlo (FN-DMC) using Configuration Interaction (CI)-type trial wavefunctions. To keep the number of determinants reasonable (the first and second derivatives of the trial wavefunction need to be calculated at each step of FN-DMC), the CI expansion is restricted to those determinants that contribute the most to the total energy. The selection of the determinants is made using the so-called CIPSI approach (Configuration Interaction using a Perturbative Selection made Iteratively). Quite remarkably, the nodes of CIPSI wavefunctions are found to be systematically improved when increasing the number of selected determinants. To reduce the non-parallelism error of the potential energy curve a scheme based on the use of a $R$-dependent number of determinants is introduced. Numerical results show that improved FN-DMC energy curves for the F$_2$ molecule are obtained when employing CIPSI trial wavefunctions. Using the Dunning's cc-pVDZ basis set the FN-DMC energy curve is of a quality similar to that obtained with FCI/cc-pVQZ. A key advantage of using selected CI in FN-DMC is the possibility of improving nodes in a systematic and automatic way without resorting to a preliminary multi-parameter stochastic optimization of the trial wavefunction performed at the Variational Monte Carlo level as usually done in FN-DMC.Comment: 16 pages, 15 figure

Ab initio molecular dynamics of water by quantum Monte Carlo

The chapter 2, we deal with the challenge b). It focuses on the variational Monte Carlo (VMC) and the wavefunction optimization methods based on VMC. The performance of different methods are displayed through the op- timization of the Jastrow factor in our test case Beryllium dimer and the efficiency is improving surprisingly during the evolution of these methods. In chapter 3, we focus on the challenge a). It describes the wavefunc- tion ansatz used by our simulation. In this thesis, we introduce the atomic hybrid orbitals which significantly increase the compactness of our wavefunc- tion without hurting accuracy. This chapter also explain how to optimize the determinant in a way that the number of variational parameters scales only linearly with the system size. This further helps the efficiency of the wavefunction optimization. In chapters 4 and 5, the issue c) is explained in detail. In chapter 4, a second order Langevin dynamics (SLD) scheme is devised particularly for QMC and this thesis improves this scheme by developing a better integration method. Here, we also highlight the remarkable power of the force covari- ance matrix which can be defined only in QMC and is capable of accelerating the slow modes of a dynamics. In chapter 5, this SLD for QMC is validated through intensive benchmarking on the calculation of the vibrational frequen- cies of water and other small molecules. It is shown that many systematic biases in our MD scheme and QMC evaluation can be controlled so that we are confident to push forward this ab initio molecular dynamics for applica- tions on large systems. Finally in chapter 6, we perform the simulation of liquid water with all the preparation done in the previous chapters. The results are encouraging since we\u2019ve closed the discrepancy of the peak positions of RDFs between experi- ments and ab initio simulations. The power of QMC is also demonstrated by the fact that the shapes of our RDFs are much less structured than previous DFT-based ab initio simulations even if the two water molecule interaction is dealt with the same level of accuracy as the DFT/BLYP calculation. In this chapter, we have also studied the features of hydrogen bonds in our simulation of liquid water. All our results indicate that it is important to consider the quantum nature of the ions for a faithful description of liquid water. This will be left for future studies, possible in principle even within the QMC approach