# Features of QMCPACK¶

Note that besides direct use, most features are also available via Nexus, an advanced workflow tool to automate all aspects of QMC calculation from initial DFT calculations through to final analysis. Use of Nexus is highly recommended for research calculations due to the greater ease of use and increased reproducibility.

## Real-space Monte Carlo¶

The following list contains the main production-level features of QMCPACK for real-space Monte Carlo. If you do not see a specific feature that you are interested in, check the remainder of this manual or ask if that specific feature can be made available.

Variational Monte Carlo (VMC).

Diffusion Monte Carlo (DMC).

Reptation Monte Carlo.

Single and multideterminant Slater Jastrow wavefunctions.

Wavefunction updates using optimized multideterminant algorithm of Clark et al.

Backflow wavefunctions.

One, two, and three-body Jastrow factors.

Excited state calculations via flexible occupancy assignment of Slater determinants.

All electron and nonlocal pseudopotential calculations.

Casula T-moves for variational evaluation of nonlocal pseudopotentials (non-size-consistent and size-consistent variants).

Spin-orbit coupling from relativistic pseudopotentials following the approach of Melton, Bennett, and Mitas.

Support for twist boundary conditions and calculations on metals.

Wavefunction optimization using the “linear method” of Umrigar and coworkers, with an arbitrary mix of variance and energy in the objective function.

Blocked, low memory adaptive shift optimizer of Zhao and Neuscamman.

Gaussian, Slater, plane-wave, and real-space spline basis sets for orbitals.

Interface and conversion utilities for plane-wave wavefunctions from Quantum ESPRESSO (Plane-Wave Self-Consistent Field package [PWSCF]).

Interface and conversion utilities for Gaussian-basis wavefunctions from GAMESS, PySCF, and QP2. Many more are supported via the molden format and molden2qmc.

Easy extension and interfacing to other electronic structure codes via standardized XML and HDF5 inputs.

MPI parallelism, with scaling to millions of cores.

Fully threaded using OpenMP.

Highly efficient vectorized CPU code tailored for modern architectures. [MLC+17]

GPU (NVIDIA CUDA) implementation (limited functionality - see Supported GPU features for real space QMC).

Analysis tools for minimal environments (Perl only) through to Python-based environments with graphs produced via matplotlib (included with Nexus).

## Auxiliary-Field Quantum Monte Carlo¶

The orbital-space Auxiliary-Field Quantum Monte Carlo (AFQMC) method is now also available in QMCPACK. The main input data are the matrix elements of the Hamiltonian in a given single particle basis set, which must be produced from mean-field calculations such as Hartree-Fock or density functional theory. A partial list of the current capabilities of the code follows. For a detailed description of the available features, see Auxiliary-Field Quantum Monte Carlo.

Phaseless AFQMC algorithm of Zhang et al. [ZK03].

Very efficient GPU implementation for most features.

“Hybrid” and “local energy” propagation schemes.

Hamiltonian matrix elements from (1) Molpro’s FCIDUMP format (which can be produced by Molpro, PySCF, and VASP) and (2) internal HDF5 format produced by PySCF (see AFQMC section below).

AFQMC calculations with RHF (closed-shell doubly occupied), ROHF (open-shell doubly occupied), and UHF (spin polarized broken symmetry) symmetry.

Single and multideterminant trial wavefunctions. Multideterminant expansions with either orthogonal or nonorthogonal determinants.

Fast update scheme for orthogonal multideterminant expansions.

Distributed propagation algorithms for large systems. Enables calculations where data structures do not fit on a single node.

Complex implementation for PBC calculations with complex integrals.

Sparse representation of large matrices for reduced memory usage.

Mixed and back-propagated estimators.

Specialized implementation for solids with k-point symmetry (e.g. primitive unit cells with k-points).

## Supported GPU features for real space QMC¶

The “legacy” GPU implementation for real space QMC uses NVIDIA CUDA and achieves very good speedup on NVIDIA GPUs. However, only a very limited subset of features is available. As detailed in QMCPACK Roadmap, a new full-featured GPU implementation is currently being made that is both high performing and portable to other GPU architectures. The existing implementation supports multiple GPUs per node, with MPI tasks assigned in a round-robin order to the GPUs. Currently, for large runs, 1 MPI task should be used per GPU per node. For smaller calculations, use of multiple MPI tasks per GPU might yield improved performance.

Supported GPU features:

VMC, wavefunction optimization, DMC.

Periodic and open boundary conditions. Mixed boundary conditions are not supported.

Wavefunctions:

Single Slater determinants with 3D B-spline orbitals. Twist-averaged boundary conditions and complex wavefunctions are fully supported. Gaussian type orbitals are not supported.

Hybrid mixed basis representation in which orbitals are represented as 1D splines times spherical harmonics in spherical regions (muffin tins) around atoms and 3D B-splines in the interstitial region.

One-body and two-body Jastrow functions represented as 1D B-splines. Three-body Jastrow functions are not supported.

Semilocal (nonlocal and local) pseudopotentials, Coulomb interaction (electron-electron, electron-ion), and model periodic Coulomb (MPC) interaction.

## Sharing of spline data across multiple GPUs¶

Sharing of GPU spline data enables distribution of the data across multiple GPUs on a given computational node. For example, on a two-GPU-per-node system, each GPU would have half of the orbitals. This allows use of larger overall spline tables than would fit in the memory of individual GPUs and potentially up to the total GPU memory on a node. To obtain high performance, large electron counts or a high-performing CPU-GPU interconnect is required.

To use this feature, the following needs to be done:

The CUDA Multi-Process Service (MPS) needs to be used (e.g., on OLCF Summit/SummitDev use “-alloc_flags gpumps” for bsub). If MPI is not detected, sharing will be disabled.

CUDA_VISIBLE_DEVICES needs to be properly set to control each rank’s visible CUDA devices (e.g., on OLCF Summit/SummitDev create a resource set containing all GPUs with the respective number of ranks with “jsrun –task-per-rs Ngpus -g Ngpus”).

In the determinant set definition of the <wavefunction> section, the “gpusharing” parameter needs to be set (i.e., <determinantset gpusharing=“yes”>). See Spline basis sets.

- MLC+17
Amrita Mathuriya, Ye Luo, Raymond C. Clay, III, Anouar Benali, Luke Shulenburger, and Jeongnim Kim. Embracing a new era of highly efficient and productive quantum monte carlo simulations. In

*Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis*, SC '17, 38:1–38:12. New York, NY, USA, 2017. ACM. URL: http://doi.acm.org/10.1145/3126908.3126952, doi:10.1145/3126908.3126952.- ZK03
Shiwei Zhang and Henry Krakauer. Quantum Monte Carlo Method using Phase-Free Random Walks with Slater Determinants.

*Physical Review Letters*, 90(13):136401, April 2003. doi:10.1103/PhysRevLett.90.136401.