1,084 research outputs found
Virtual orbital many-body expansions: A possible route towards the full configuration interaction limit
In the present letter, it is demonstrated how full configuration interaction
(FCI) results in extended basis sets may be obtained to within sub-kJ/mol
accuracy by decomposing the energy in terms of many-body expansions in the
virtual orbitals of the molecular system at hand. This extension of the FCI
application range lends itself to two unique features of the current approach,
namely that the total energy calculation can be performed entirely within
considerably reduced orbital subspaces and may be so by means of embarrassingly
parallel programming. Facilitated by a rigorous and methodical screening
protocol and further aided by expansion points different from the Hartree-Fock
solution, all-electron numerical results are reported for HO in polarized
core-valence basis sets ranging from double- (10 , 28 ) to
quadruple- (10 , 144 ) quality.Comment: 20 pages, 3 figures, 1 table. * With respect to the original arXiv
version (v1), the present version of the letter contains updated results. The
original TZ and QZ values were unfortunately in error due to a subtle PySCF
bug, which has since then been fixe
Development of efficient electronic-structure methods based on the adiabatic-connection fluctuation-dissipation theorem and Møller–Plesset perturbation theory
One of the major goals of quantum chemistry is to develop electronic-structure methods, which are not only highly accurate in the evaluation of electronic ground-state properties, but also computationally tractable and versatile in their application. A theory with great potential in this respect, however, without being free from shortcomings is the random phase approximation (RPA).
In this work, developments are presented, which address the most important of these shortcomings subject to the constraint to obtain low- and linear-scaling electronic-structure methods. A scheme combining an elegant way to introduce local orbitals and multi-node parallelism is put forward, which not only allows to evaluate the RPA correlation energy in a fraction of the time of former theories, but also enables a scalable decrease of the high memory requirements. Furthermore, a quadratic-scaling self-consistent minimization of the total RPA energy with respect to the one-particle density matrix in the atomic-orbital space is introduced, making the RPA energy variationally stable and independent of the quality of the reference calculation. To address the slow convergence with respect to the size of the basis set and the self-correlation inherent in the RPA functional, range-separation of the electron-electron interaction is exploited for atomic-orbital RPA, yielding a linear-scaling range-separated RPA method with consistent performance over a broad range of chemical problems. As a natural extension, the concepts including local orbitals, self-consistency, and range-separation are further combined in a RPA-based generalized Kohn–Sham method, which not only shows a balanced performance in general main group thermochemistry, kinetics, and noncovalent interactions, but also yields accurate ionization potentials and fundamental gaps.
The origin of the self-correlation error within RPA lies in the neglect of exchange-effects in the calculation of the interacting density-density response functions. While range-separation is a reasonable approach to counteract this shortcoming — since self-correlation is pronounced at short interelectronic distances — a more rigorous but computationally sophisticated approach is to introduce the missing exchange-effects, at least to some extent. To make RPA with exchange methods applicable to systems containing hundreds of atoms and hence a suitable choice for practical applications, a framework is developed, which allows to devise highly efficient low- and linear-scaling RPA with exchange methods.
The developments presented in this work, however, are not only limited to RPA and beyond-RPA methods. The connection between RPA and many-body perturbation theory is further used to present a second-order Møller–Plesset perturbation theory method, which combines the tools to obtain low- and linear-scaling RPA and beyond-RPA methods with efficient linear-algebra routines, making it highly efficient and applicable to large molecular systems comprising several thousand of basis functions
On the Cholesky Decomposition for electron propagator methods: General aspects and application on C60
To treat the electronic structure of large molecules by electron propagator
methods we developed a parallel computer program called P-RICD. The
program exploits the sparsity of the two-electron integral matrix by using
Cholesky decomposition techniques. The advantage of these techniques is that
the error introduced is controlled only by one parameter which can be chosen as
small as needed. We verify the tolerance of electron propagator methods to the
Cholesky decomposition threshold and demonstrate the power of the
P-RICD program for a representative example (C60). All decomposition
schemes addressed in the literature are investigated. Even with moderate
thresholds the maximal error encountered in the calculated electron affinities
and ionization potentials amount to a few meV only, and the error becomes
negligible for small thresholds.Comment: 30 pages, 6 figures submitted to J.Chem. Phy
Diagrammatic Coupled Cluster Monte Carlo
We propose a modified coupled cluster Monte Carlo algorithm that
stochastically samples connected terms within the truncated
Baker--Campbell--Hausdorff expansion of the similarity transformed Hamiltonian
by construction of coupled cluster diagrams on the fly. Our new approach --
diagCCMC -- allows propagation to be performed using only the connected
components of the similarity-transformed Hamiltonian, greatly reducing the
memory cost associated with the stochastic solution of the coupled cluster
equations. We show that for perfectly local, noninteracting systems, diagCCMC
is able to represent the coupled cluster wavefunction with a memory cost that
scales linearly with system size. The favorable memory cost is observed with
the only assumption of fixed stochastic granularity and is valid for arbitrary
levels of coupled cluster theory. Significant reduction in memory cost is also
shown to smoothly appear with dissociation of a finite chain of helium atoms.
This approach is also shown not to break down in the presence of strong
correlation through the example of a stretched nitrogen molecule. Our novel
methodology moves the theoretical basis of coupled cluster Monte Carlo closer
to deterministic approaches.Comment: 31 pages, 6 figure
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