255 research outputs found
Optimizing the energy with quantum Monte Carlo: A lower numerical scaling for Jastrow-Slater expansions
We present an improved formalism for quantum Monte Carlo calculations of
energy derivatives and properties (e.g. the interatomic forces), with a
multideterminant Jastrow-Slater function. As a function of the number of
Slater determinants, the numerical scaling of per derivative we have
recently reported is here lowered to for the entire set of
derivatives. As a function of the number of electrons , the scaling to
optimize the wave function and the geometry of a molecular system is lowered to
, the same as computing the energy alone in the sampling
process. The scaling is demonstrated on linear polyenes up to CH
and the efficiency of the method is illustrated with the structural
optimization of butadiene and octatetraene with Jastrow-Slater wave functions
comprising as many as 200000 determinants and 60000 parameters
Optimized Jastrow-Slater wave functions for ground and excited states: Application to the lowest states of ethene
A quantum Monte Carlo method is presented for determining multi-determinantal
Jastrow-Slater wave functions for which the energy is stationary with respect
to the simultaneous optimization of orbitals and configuration interaction
coefficients. The approach is within the framework of the so-called energy
fluctuation potential method which minimizes the energy in an iterative fashion
based on Monte Carlo sampling and a fitting of the local energy fluctuations.
The optimization of the orbitals is combined with the optimization of the
configuration interaction coefficients through the use of additional single
excitations to a set of external orbitals. A new set of orbitals is then
obtained from the natural orbitals of this enlarged configuration interaction
expansion. For excited states, the approach is extended to treat the average of
several states within the same irreducible representation of the pointgroup of
the molecule. The relationship of our optimization method with the stochastic
reconfiguration technique by Sorella et al. is examined. Finally, the
performance of our approach is illustrated with the lowest states of ethene, in
particular with the difficult case of the singlet 1B_1u state.Comment: 12 pages, 2 figure
Simple formalism for efficient derivatives and multi-determinant expansions in quantum Monte Carlo
We present a simple and general formalism to compute efficiently the
derivatives of a multi-determinant Jastrow-Slater wave function, the local
energy, the interatomic forces, and similar quantities needed in quantum Monte
Carlo. Through a straightforward manipulation of matrices evaluated on the
occupied and virtual orbitals, we obtain an efficiency equivalent to
algorithmic differentiation in the computation of the interatomic forces and
the optimization of the orbital paramaters. Furthermore, for a large
multi-determinant expansion, the significant computational gain recently
reported for the calculation of the wave function is here improved and extended
to all local properties in both all-electron and pseudopotential calculations.Comment: 15 pages, 3 figure
Excitation energies from density functional perturbation theory
We consider two perturbative schemes to calculate excitation energies, each
employing the Kohn-Sham Hamiltonian as the unperturbed system. Using accurate
exchange-correlation potentials generated from essentially exact densities and
their exchange components determined by a recently proposed method, we evaluate
energy differences between the ground state and excited states in first-order
perturbation theory for the Helium, ionized Lithium and Beryllium atoms. It was
recently observed that the zeroth-order excitations energies, simply given by
the difference of the Kohn-Sham eigenvalues, almost always lie between the
singlet and triplet experimental excitations energies, corrected for
relativistic and finite nuclear mass effects. The first-order corrections
provide about a factor of two improvement in one of the perturbative schemes
but not in the other. The excitation energies within perturbation theory are
compared to the excitations obtained within SCF and time-dependent
density functional theory. We also calculate the excitation energies in
perturbation theory using approximate functionals such as the local density
approximation and the optimized effective potential method with and without the
Colle-Salvetti correlation contribution
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
Size-consistent variational approaches to non-local pseudopotentials: standard and lattice regularized diffusion Monte Carlo methods revisited
We propose improved versions of the standard diffusion Monte Carlo (DMC) and
the lattice regularized diffusion Monte Carlo (LRDMC) algorithms. For the DMC
method, we refine a scheme recently devised to treat non-local pseudopotential
in a variational way. We show that such scheme --when applied to large enough
systems-- maintains its effectiveness only at correspondingly small enough
time-steps, and we present two simple upgrades of the method which guarantee
the variational property in a size-consistent manner. For the LRDMC method,
which is size-consistent and variational by construction, we enhance the
computational efficiency by introducing (i) an improved definition of the
effective lattice Hamiltonian which remains size-consistent and entails a small
lattice-space error with a known leading term, and (ii) a new randomization
method for the positions of the lattice knots which requires a single
lattice-space.Comment: 10 pages, 4 figures, submitted to the Journal of Chemical Physic
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
Excitations in photoactive molecules from quantum Monte Carlo
Despite significant advances in electronic structure methods for the
treatment of excited states, attaining an accurate description of the
photoinduced processes in photoactive biomolecules is proving very difficult.
For the prototypical photosensitive molecules, formaldimine, formaldehyde and a
minimal protonated Schiff base model of the retinal chromophore, we investigate
the performance of various approaches generally considered promising for the
computation of excited potential energy surfaces. We show that quantum Monte
Carlo can accurately estimate the excitation energies of the studied systems if
one constructs carefully the trial wave function, including in most cases the
reoptimization of its determinantal part within quantum Monte Carlo. While
time-dependent density functional theory and quantum Monte Carlo are generally
in reasonable agreement, they yield a qualitatively different description of
the isomerization of the Schiff base model. Finally, we find that the
restricted open shell Kohn-Sham method is at variance with quantum Monte Carlo
in estimating the lowest-singlet excited state potential energy surface for
low-symmetry molecular structures.Comment: 10 pages, 6 figure
Excited states with selected CI-QMC: chemically accurate excitation energies and geometries
We employ quantum Monte Carlo to obtain chemically accurate vertical and
adiabatic excitation energies, and equilibrium excited-state structures for the
small, yet challenging, formaldehyde and thioformaldehyde molecules. A key
ingredient is a robust protocol to obtain balanced ground- and excited-state
Jastrow-Slater wave functions at a given geometry, and to maintain such a
balanced description as we relax the structure in the excited state. We use
determinantal components generated via a selected configuration interaction
scheme which targets the same second-order perturbation energy correction for
all states of interest at different geometries, and we fully optimize all
variational parameters in the resultant Jastrow-Slater wave functions.
Importantly, the excitation energies as well as the structural parameters in
the ground and excited states are converged with very compact wave functions
comprising few thousand determinants in a minimally augmented double-
basis set. These results are obtained already at the variational Monte Carlo
level, the more accurate diffusion Monte Carlo method yielding only a small
improvement in the adiabatic excitation energies. We find that matching
Jastrow-Slater wave functions with similar variances can yield excitations
compatible with our best estimates; however, the variance-matching procedure
requires somewhat larger determinantal expansions to achieve the same accuracy,
and it is less straightforward to adapt during structural optimization in the
excited state.Comment: 11 pages, 4 figure
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