149 research outputs found
IRPF90: a programming environment for high performance computing
IRPF90 is a Fortran programming environment which helps the development of
large Fortran codes. In Fortran programs, the programmer has to focus on the
order of the instructions: before using a variable, the programmer has to be
sure that it has already been computed in all possible situations. For large
codes, it is common source of error. In IRPF90 most of the order of
instructions is handled by the pre-processor, and an automatic mechanism
guarantees that every entity is built before being used. This mechanism relies
on the {needs/needed by} relations between the entities, which are built
automatically. Codes written with IRPF90 execute often faster than Fortran
programs, are faster to write and easier to maintain.Comment: 18 pages, 14 figure
An efficient implementation of Slater-Condon rules
Slater-Condon rules are at the heart of any quantum chemistry method as they
allow to simplify -dimensional integrals as sums of 3- or 6-dimensional
integrals. In this paper, we propose an efficient implementation of those rules
in order to identify very rapidly which integrals are involved in a matrix
element expressed in the determinant basis set. This implementation takes
advantage of the bit manipulation instructions on x86 architectures that were
introduced in 2008 with the SSE4.2 instruction set. Finding which spin-orbitals
are involved in the calculation of a matrix element doesn't depend on the
number of electrons of the system.Comment: 8 pages, 5 figure
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 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
-dependent number of determinants is introduced. Numerical results show that
improved FN-DMC energy curves for the F 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
A Sparse SCF algorithm and its parallel implementation: Application to DFTB
We present an algorithm and its parallel implementation for solving a self
consistent problem as encountered in Hartree Fock or Density Functional Theory.
The algorithm takes advantage of the sparsity of matrices through the use of
local molecular orbitals. The implementation allows to exploit efficiently
modern symmetric multiprocessing (SMP) computer architectures. As a first
application, the algorithm is used within the density functional based tight
binding method, for which most of the computational time is spent in the linear
algebra routines (diagonalization of the Fock/Kohn-Sham matrix). We show that
with this algorithm (i) single point calculations on very large systems
(millions of atoms) can be performed on large SMP machines (ii) calculations
involving intermediate size systems (1~000--100~000 atoms) are also strongly
accelerated and can run efficiently on standard servers (iii) the error on the
total energy due to the use of a cut-off in the molecular orbital coefficients
can be controlled such that it remains smaller than the SCF convergence
criterion.Comment: 13 pages, 11 figure
IRPF90
IRPF90 is a Fortran code generator. Schematically, the programmer only writes computation kernels, and IRPF90 generates the "glue code" that will link all these kernels together to produce the expected result
Efficient Monte Carlo Calculations of the One-Body Density
An alternative Monte Carlo estimator for the one-body density rho(r) is
presented. This estimator has a simple form and can be readily used in any type
of Monte Carlo simulation. Comparisons with the usual regularization of the
delta-function on a grid show that the statistical errors are greatly reduced.
Furthermore, our expression allows accurate calculations of the density at any
point in space, even in the regions never visited during the Monte Carlo
simulation. The method is illustrated with the computation of accurate
Variational Monte Carlo electronic densities for the Helium atom (1D curve) and
for the water dimer (3D grid containing up to 51x51x51=132651 points).Comment: 12 pages with 3 postscript figure
A simple and efficient approach to the optimization of correlated wave functions
We present a simple and efficient method to optimize within energy
minimization the determinantal component of the many-body wave functions
commonly used in quantum Monte Carlo calculations. The approach obtains the
optimal wave function as an approximate perturbative solution of an effective
Hamiltonian iteratively constructed via Monte Carlo sampling. The effectiveness
of the method as well as its ability to substantially improve the accuracy of
quantum Monte Carlo calculations is demonstrated by optimizing a large number
of parameters for the ground state of acetone and the difficult case of the
state of hexatriene.Comment: 5 pages, 1 figur
Perturbatively selected configuration-interaction wave functions for efficient geometry optimization in quantum Monte Carlo
We investigate the performance of a class of compact and systematically
improvable Jastrow-Slater wave functions for the efficient and accurate
computation of structural properties, where the determinantal component is
expanded with a perturbatively selected configuration interaction scheme
(CIPSI). We concurrently optimize the molecular ground-state geometry and full
wave function -- Jastrow factor, orbitals, and configuration interaction
coefficients-- in variational Monte Carlo (VMC) for the prototypical case of
1,3-trans-butadiene, a small yet theoretically challenging -conjugated
system. We find that the CIPSI selection outperforms the conventional scheme of
correlating orbitals within active spaces chosen by chemical intuition: it
gives significantly better variational and diffusion Monte Carlo energies for
all but the smallest expansions, and much smoother convergence of the geometry
with the number of determinants. In particular, the optimal bond lengths and
bond-length alternation of butadiene are converged to better than one m\AA\
with just a few thousand determinants, to values very close to the
corresponding CCSD(T) results. The combination of CIPSI expansion and VMC
optimization represents an affordable tool for the determination of accurate
ground-state geometries in quantum Monte Carlo
Quantum Monte Carlo with very large multideterminant wavefunctions
An algorithm to compute efficiently the first two derivatives of (very) large
multideterminant wavefunctions for quantum Monte Carlo calculations is
presented. The calculation of determinants and their derivatives is performed
using the Sherman-Morrison formula for updating the inverse Slater matrix. An
improved implementation based on the reduction of the number of column
substitutions and on a very efficient implementation of the calculation of the
scalar products involved is presented. It is emphasized that multideterminant
expansions contain in general a large number of identical spin-specific
determinants: for typical configuration interaction-type wavefunctions the
number of unique spin-specific determinants
() with a non-negligible weight in the expansion is
of order . We show that a careful implementation
of the calculation of the -dependent contributions can make this
step negligible enough so that in practice the algorithm scales as the total
number of unique spin-specific determinants, , over a wide range of total number of determinants (here,
up to about one million), thus greatly reducing the total
computational cost. Finally, a new truncation scheme for the multideterminant
expansion is proposed so that larger expansions can be considered without
increasing the computational time. The algorithm is illustrated with
all-electron Fixed-Node Diffusion Monte Carlo calculations of the total energy
of the chlorine atom. Calculations using a trial wavefunction including about
750 000 determinants with a computational increase of 400 compared to a
single-determinant calculation are shown to be feasible.Comment: 9 pages, 3 figure
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
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