25,906 research outputs found
Correlated-Gaussian calculations of the ground and low-lying excited states of the boron atom
Benchmark variational calculations of the four lowest 2P and 2S states of the boron atom (including the ground state) have been performed. The wave functions of the states have been expanded in terms of all-particle explicitly correlated Gaussian basis functions and the finite mass of the nucleus has been explicitly accounted for.Variational
upper bounds for the nonrelativistic finite- and infinite-nuclear-mass energies of all considered states have been obtained with the relative convergence of the order of 10−7–10−8. Expectation values of the powers of the inter-particle distances and Dirac δ functions depending on those distances have also been computed. These calculations provide reference values that can be used to test other high-level quantum chemistry method
Correlated-Gaussian calculations of the ground and low-lying excited states of the boron atom
Benchmark variational calculations of the four lowest 2P and 2S states of the boron atom (including the ground state) have been performed. The wave functions of the states have been expanded in terms of all-particle explicitly correlated Gaussian basis functions and the finite mass of the nucleus has been explicitly accounted for.Variational
upper bounds for the nonrelativistic finite- and infinite-nuclear-mass energies of all considered states have been obtained with the relative convergence of the order of 10−7–10−8. Expectation values of the powers of the inter-particle distances and Dirac δ functions depending on those distances have also been computed. These calculations provide reference values that can be used to test other high-level quantum chemistry method
Explicitly correlated plane waves: Accelerating convergence in periodic wavefunction expansions
We present an investigation into the use of an explicitly correlated plane
wave basis for periodic wavefunction expansions at the level of second-order
M{\o}ller-Plesset perturbation theory (MP2). The convergence of the electronic
correlation energy with respect to the one-electron basis set is investigated
and compared to conventional MP2 theory in a finite homogeneous electron gas
model. In addition to the widely used Slater-type geminal correlation factor,
we also derive and investigate a novel correlation factor that we term
Yukawa-Coulomb. The Yukawa-Coulomb correlation factor is motivated by analytic
results for two electrons in a box and allows for a further improved
convergence of the correlation energies with respect to the employed basis set.
We find the combination of the infinitely delocalized plane waves and local
short-ranged geminals provides a complementary, and rapidly convergent basis
for the description of periodic wavefunctions. We hope that this approach will
expand the scope of discrete wavefunction expansions in periodic systems.Comment: 15 pages, 13 figure
Tensor-optimized antisymmetrized molecular dynamics as a successive variational method in nuclear many-body system
We study the tensor-optimized antisymmetrized molecular dynamics (TOAMD) as a
successive variational method in many-body systems with strong interaction for
nuclei. In TOAMD, the correlation functions for the tensor force and the
short-range repulsion and their multiples are operated to the AMD state as the
variational wave function. The total wave function is expressed as the sum of
all the components and the variational space can be increased successively with
the multiple correlation functions to achieve convergence. All the necessary
matrix elements of many-body operators, consisting of the multiple correlation
functions and the Hamiltonian, are expressed analytically using the Gaussian
integral formula. In this paper we show the results of TOAMD with up to the
double products of the correlation functions for the s-shell nuclei, 3H and
4He, using the nucleon-nucleon interaction AV8'. It is found that the energies
and Hamiltonian components of two nuclei converge rapidly with respect to the
multiple of correlation functions. This result indicates the efficiency of
TOAMD for the power series expansion in terms of the tensor and short-range
correlation functions.Comment: 7 pages, 5 figures, added references, corrected typo
Ground state of Li and Be using explicitly correlated functions
We compare the explicitly correlated Hylleraas and exponential basis sets in
the evaluations of ground state of Li and Be. Calculations with Hylleraas
functions are numerically stable and can be performed with the large number of
basis functions. Our results for ground state energies , of Li and Be correspondingly, are the
most accurate to date. When small basis set is considered, explicitly
correlated exponential functions are much more effective. With only 128
functions we obtained about relative accuracy, but the severe
numerical instabilities make this basis costly in the evaluation.Comment: 15 page
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
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