Excited State Specific Multi-Slater Jastrow Wave Functions

We combine recent advances in excited state variational principles, fast multi-Slater Jastrow methods, and selective configuration interaction to create multi-Slater Jastrow wave function approximations that are optimized for individual excited states. In addition to the Jastrow variables and linear expansion coefficients, this optimization includes state-specific orbital relaxations in order to avoid the compromises necessary in state-averaged approaches. We demonstrate that, when combined with variance matching to help balance the quality of the approximation across different states, this approach delivers accurate excitation energies even when using very modest multi-Slater expansions. Intriguingly, this accuracy is maintained even when studying a difficult chlorine-anion-to-$\pi^{*}$ charge transfer in which traditional state-averaged multi-reference methods must contend with different states that require drastically different orbital relaxations.Comment: 16 pages, 6 figures, 2 table

Reduced Scaling Hilbert Space Variational Monte Carlo

We show that for both single-Slater-Jastrow and Jastrow geminal power wave functions, the formal cost scaling of Hilbert space variational Monte Carlo can be reduced from fifth to fourth order in the system size, thus bringing it in line with the long-standing scaling of its real space counterpart. While traditional quantum chemistry methods can reduce costs related to the two-electron integral tensor through resolution of the identity and Cholesky decomposition approaches, we show that such approaches are ineffective in the presence of Hilbert space Jastrow factors. Instead, we develop a simple semi-stochastic approach that can take similar advantage of the near-sparsity of this four-index tensor. Through demonstrations on alkanes of increasing length, we show that accuracy and overall statistical uncertainty are not meaningfully affected and that a total cost crossover is reached as early as 50 electrons.Comment: 8 pages, 7 figure

Continuum variational and diffusion quantum Monte Carlo calculations

This topical review describes the methodology of continuum variational and diffusion quantum Monte Carlo calculations. These stochastic methods are based on many-body wave functions and are capable of achieving very high accuracy. The algorithms are intrinsically parallel and well-suited to petascale computers, and the computational cost scales as a polynomial of the number of particles. A guide to the systems and topics which have been investigated using these methods is given. The bulk of the article is devoted to an overview of the basic quantum Monte Carlo methods, the forms and optimisation of wave functions, performing calculations within periodic boundary conditions, using pseudopotentials, excited-state calculations, sources of calculational inaccuracy, and calculating energy differences and forces

Quantum Monte Carlo for large chemical systems: Implementing efficient strategies for petascale platforms and beyond

Various strategies to implement efficiently QMC simulations for large chemical systems are presented. These include: i.) the introduction of an efficient algorithm to calculate the computationally expensive Slater matrices. This novel scheme is based on the use of the highly localized character of atomic Gaussian basis functions (not the molecular orbitals as usually done), ii.) the possibility of keeping the memory footprint minimal, iii.) the important enhancement of single-core performance when efficient optimization tools are employed, and iv.) the definition of a universal, dynamic, fault-tolerant, and load-balanced computational framework adapted to all kinds of computational platforms (massively parallel machines, clusters, or distributed grids). These strategies have been implemented in the QMC=Chem code developed at Toulouse and illustrated with numerical applications on small peptides of increasing sizes (158, 434, 1056 and 1731 electrons). Using 10k-80k computing cores of the Curie machine (GENCI-TGCC-CEA, France) QMC=Chem has been shown to be capable of running at the petascale level, thus demonstrating that for this machine a large part of the peak performance can be achieved. Implementation of large-scale QMC simulations for future exascale platforms with a comparable level of efficiency is expected to be feasible

Generalized effective hamiltonian for graphene under non-uniform strain

We use a symmetry approach to construct a systematic derivative expansion of the low energy effective Hamiltonian modifying the continuum Dirac description of graphene in the presence of non-uniform elastic deformations. We extract all experimentally relevant terms and describe their physical significance. Among them there is a new gap-opening term that describes the Zeeman coupling of the elastic pseudomagnetic field and the pseudospin. We determine the value of the couplings using a generalized tight binding model.Comment: 13 pages, 1 figure. Matches published version + 1 footnote added, typos correcte