5,810 research outputs found
Accurate ab initio spin densities
We present an approach for the calculation of spin density distributions for
molecules that require very large active spaces for a qualitatively correct
description of their electronic structure. Our approach is based on the
density-matrix renormalization group (DMRG) algorithm to calculate the spin
density matrix elements as basic quantity for the spatially resolved spin
density distribution. The spin density matrix elements are directly determined
from the second-quantized elementary operators optimized by the DMRG algorithm.
As an analytic convergence criterion for the spin density distribution, we
employ our recently developed sampling-reconstruction scheme [J. Chem. Phys.
2011, 134, 224101] to build an accurate complete-active-space
configuration-interaction (CASCI) wave function from the optimized matrix
product states. The spin density matrix elements can then also be determined as
an expectation value employing the reconstructed wave function expansion.
Furthermore, the explicit reconstruction of a CASCI-type wave function provides
insights into chemically interesting features of the molecule under study such
as the distribution of - and -electrons in terms of Slater
determinants, CI coefficients, and natural orbitals. The methodology is applied
to an iron nitrosyl complex which we have identified as a challenging system
for standard approaches [J. Chem. Theory Comput. 2011, 7, 2740].Comment: 37 pages, 13 figure
Self-Consistent Electron-Nucleus Cusp Correction for Molecular Orbitals
We describe a method for imposing the correct electron-nucleus (e-n) cusp in
molecular orbitals expanded as a linear combination of (cuspless) Gaussian
basis functions. Enforcing the e-n cusp in trial wave functions is an important
asset in quantum Monte Carlo calculations as it significantly reduces the
variance of the local energy during the Monte Carlo sampling. In the method
presented here, the Gaussian basis set is augmented with a small number of
Slater basis functions. Note that, unlike other e-n cusp correction schemes,
the presence of the Slater function is not limited to the vicinity of the
nuclei. Both the coefficients of these cuspless Gaussian and cusp-correcting
Slater basis functions may be self-consistently optimized by diagonalization of
an orbital-dependent effective Fock operator. Illustrative examples are
reported for atoms (\ce{H}, \ce{He} and \ce{Ne}) as well as for a small
molecular system (\ce{BeH2}). For the simple case of the \ce{He} atom, we
observe that, with respect to the cuspless version, the variance is reduced by
one order of magnitude by applying our cusp-corrected scheme.Comment: 23 pages, 5 figure
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
Orbital Dependent Exchange-Only Methods for Periodic Systems
Various orbital-dependent exchange-only potentials are studied which exhibit
correct long-range asymptotic behaviour. We present the first application of
these potentials for polymers and by one of these potentials for molecules.
Kohn-Sham type calculations have been carried out for polyethylene in order to
make valuable comparison of these potentials with each other as well as with
Hartree-Fock and exchange-only LDA methods. The Kohn-Sham band gap obtained
with the optimized effective potetial method is corrected with the exchange
contribution to the derivative discontinuity of the exchange-correlation
potential. The corrected band gap obtained with the Slater's exchange potential
is 9.7 eV close to the experiment.Comment: 11 pages, 2 figures. Phys. Rev. B60, 1999, in pres
Excited electronic states from a variational approach based on symmetry-projected Hartree--Fock configurations
Recent work from our research group has demonstrated that symmetry-projected
Hartree--Fock (HF) methods provide a compact representation of molecular ground
state wavefunctions based on a superposition of non-orthogonal Slater
determinants. The symmetry-projected ansatz can account for static correlations
in a computationally efficient way. Here we present a variational extension of
this methodology applicable to excited states of the same symmetry as the
ground state. Benchmark calculations on the C dimer with a modest basis
set, which allows comparison with full configuration interaction results,
indicate that this extension provides a high quality description of the
low-lying spectrum for the entire dissociation profile. We apply the same
methodology to obtain the full low-lying vertical excitation spectrum of
formaldehyde, in good agreement with available theoretical and experimental
data, as well as to a challenging model insertion pathway for BeH.
The variational excited state methodology developed in this work has two
remarkable traits: it is fully black-box and will be applicable to fairly large
systems thanks to its mean-field computational cost
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
Multi-component symmetry-projected approach for molecular ground state correlations
The symmetry-projected Hartree--Fock ansatz for the electronic structure
problem can efficiently account for static correlation in molecules, yet it is
often unable to describe dynamic correlation in a balanced manner. Here, we
consider a multi-component, systematically-improvable approach, that accounts
for all ground state correlations. Our approach is based on linear combinations
of symmetry-projected configurations built out of a set of non-orthogonal,
variationally optimized determinants. The resulting wavefunction preserves the
symmetries of the original Hamiltonian even though it is written as a
superposition of deformed (broken-symmetry) determinants. We show how short
expansions of this kind can provide a very accurate description of the
electronic structure of simple chemical systems such as the nitrogen and the
water molecules, along the entire dissociation profile. In addition, we apply
this multi-component symmetry-projected approach to provide an accurate
interconversion profile among the peroxo and bis(-oxo) forms of
[CuO], comparable to other state-of-the-art quantum chemical
methods
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