72 research outputs found
Tensor Numerical Methods in Quantum Chemistry: from Hartree-Fock Energy to Excited States
We resume the recent successes of the grid-based tensor numerical methods and
discuss their prospects in real-space electronic structure calculations. These
methods, based on the low-rank representation of the multidimensional functions
and integral operators, led to entirely grid-based tensor-structured 3D
Hartree-Fock eigenvalue solver. It benefits from tensor calculation of the core
Hamiltonian and two-electron integrals (TEI) in complexity using
the rank-structured approximation of basis functions, electron densities and
convolution integral operators all represented on 3D
Cartesian grids. The algorithm for calculating TEI tensor in a form of the
Cholesky decomposition is based on multiple factorizations using algebraic 1D
``density fitting`` scheme. The basis functions are not restricted to separable
Gaussians, since the analytical integration is substituted by high-precision
tensor-structured numerical quadratures. The tensor approaches to
post-Hartree-Fock calculations for the MP2 energy correction and for the
Bethe-Salpeter excited states, based on using low-rank factorizations and the
reduced basis method, were recently introduced. Another direction is related to
the recent attempts to develop a tensor-based Hartree-Fock numerical scheme for
finite lattice-structured systems, where one of the numerical challenges is the
summation of electrostatic potentials of a large number of nuclei. The 3D
grid-based tensor method for calculation of a potential sum on a lattice manifests the linear in computational work, ,
instead of the usual scaling by the Ewald-type approaches
Open-shell Tensor Hypercontraction
The extension of least-squares tensor hypercontracted second- and third-order
M{\o}ller-Plessett perturbation theory (LS-THC-MP2 and LS-THC-MP3) to
open-shell systems is an important development due to the scaling reduction
afforded by THC and the ubiquity of molecular ions, radicals, and other
open-shell reactive species. The complexity of wavefunction-based quantum
chemical methods such as M{\o}ller-Plessett and coupled cluster theory is
reflected in the steep scaling of the computational costs with the molecular
size. The least-squares tensor hypercontraction (LS-THC) method is an
efficient, single-step factorization for the two-electron integral tensor, but
can also be used to factorize the double excitation amplitudes, leading to
significant scaling reduction. Here, we extend this promising method to
open-shell variants of LS-THC-MP2 and -MP3 using diagrammatic techniques and
explicit spin-summation. The accuracy of the resulting methods for open-shell
species is benchmarked on standard tests systems such as regular alkanes, as
well as realistic systems involving bond breaking, radical stabilization, and
other effects. We find that open-shell LS-THC-MP methods exhibit errors
highly comparable to those produced by closed-shell LS-THC-MP, and are
highly insensitive to particular chemical interactions, geometries, or even to
moderate spin contamination
ADVANCING COUPLED CLUSTER METHODS: TENSOR FACTORIZATION AND ANALYTIC GRADIENT IMPLEMENTATION
With the rapid advancement of computing capabilities, computational chemistry has become increasingly indispensable in both experiment design and the interpretation of experimental outcomes. Wave-function-based quantum mechanistic methods are highly sought after for their ability to provide high-accuracy data and their potential for systematic improvement. However, to extend their applicability to larger molecules, it is essential to employ rank-reducing approximations to these methods. This dissertation dedicates Chapters Three and Four to the development of rank-reduced methodologies. Additionally, beyond single-point energies, molecular geometries and properties of molecule-excited states hold paramount importance across diverse fields of chemistry. Hence, Chapter Five presents the work on the implementation of the analytic gradient for the EOM-CCSD* method. Moreover, molecular mechanisms play an indispensable role, particularly in their scalability to biocomplexes. Chapter Six exemplifies this by demonstrating the advantageous application of molecular dynamics in exploring the protein allostery mechanism
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
Threading a path to exascale with chemical scissors and integral compressors in a singular manner
Research presented in this dissertation aims at enabling (correlated) fragmentation methods to explore biochemistry and catalysis effects of macrosystems at high levels of accuracy using exascale computing resources. The target is the second-order MollerPlesset perturbation theory (MP2), and MP2 in the FMO framework (FMO/MP2). First, the 2-electron integral bottleneck is addressed by using the resolution-of-the-identity (RI) approximation to reduce the memory storage and the computational cost of the integral transformation from the atomic orbital (AO) to the molecular orbital (MO) basis. The RI approximation is also combined with the singular value decomposition (SVD) to introduce a flexible compression factor that fully controls the accuracy of the integral compression. The RIMP2 energy and analytic energy gradient are implemented in the GAMESS electronic structure program and are parallelized with an efficient hybrid distributed/shared memory model with the support of the MPI and OpenMP APIs. Both the RI-MP2 energy and gradient are interfaced to the FMO framework for large system calculations
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