The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices
About: This article is published in Journal of Computational Physics.The article was published on 1975-01-01. It has received 2265 citations till now. The article focuses on the topics: Eigenvalue perturbation & Eigenvalues and eigenvectors of the second derivative.
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TL;DR: A detailed description and comparison of algorithms for performing ab-initio quantum-mechanical calculations using pseudopotentials and a plane-wave basis set is presented in this article. But this is not a comparison of our algorithm with the one presented in this paper.
47,666 citations
TL;DR: In this paper, time-dependent density-functional (TDDFT) methods are applied within the adiabatic approximation to a series of molecules including C70, and they provide an efficient approach for treating frequency-dependent response properties and electronic excitation spectra of large molecules.
Abstract: Time-dependent density-functional (TDDFT) methods are applied within the adiabatic approximation to a series of molecules including C70. Our implementation provides an efficient approach for treating frequency-dependent response properties and electronic excitation spectra of large molecules. We also present a new algorithm for the diagonalization of large non-Hermitian matrices which is needed for hybrid functionals and is also faster than the widely used Davidson algorithm when employed for the Hermitian case appearing in excited energy calculations. Results for a few selected molecules using local, gradient-corrected, and hybrid functionals are discussed. We find that for molecules with low lying excited states TDDFT constitutes a considerable improvement over Hartree–Fock based methods (like the random phase approximation) which require comparable computational effort.
4,559 citations
University of Udine1, École Polytechnique Fédérale de Lausanne2, University of Lugano3, Leipzig University4, University of Paris5, University of North Texas6, Princeton University7, National Research Council8, International School for Advanced Studies9, Cornell University10, University of Lincoln11, University of Milan12, École Polytechnique13, International Centre for Theoretical Physics14, University of Paderborn15, University of Oxford16, Jožef Stefan Institute17, University of Padua18, Sapienza University of Rome19, Vietnam Academy of Science and Technology20, University of British Columbia21, Centre national de la recherche scientifique22, University of Lorraine23, École Normale Supérieure24, University of Zurich25, Université Paris-Saclay26, Wake Forest University27, Temple University28
TL;DR: Recent extensions and improvements are described, covering new methodologies and property calculators, improved parallelization, code modularization, and extended interoperability both within the distribution and with external software.
Abstract: Quantum ESPRESSO is an integrated suite of open-source computer codes for quantum simulations of materials using state-of-the-art electronic-structure techniques, based on density-functional theory, density-functional perturbation theory, and many-body perturbation theory, within the plane-wave pseudopotential and projector-augmented-wave approaches Quantum ESPRESSO owes its popularity to the wide variety of properties and processes it allows to simulate, to its performance on an increasingly broad array of hardware architectures, and to a community of researchers that rely on its capabilities as a core open-source development platform to implement their ideas In this paper we describe recent extensions and improvements, covering new methodologies and property calculators, improved parallelization, code modularization, and extended interoperability both within the distribution and with external software
3,638 citations
TL;DR: In this article, a new internally contracted direct multiconfiguration-reference configuration interaction (MRCI) method is described which allows the use of much larger reference spaces than any previous MRCI method.
Abstract: A new internally contracted direct multiconfiguration–reference configuration interaction (MRCI) method is described which allows the use of much larger reference spaces than any previous MRCI method. The configurations with two electrons in the external orbital space are generated by applying pair excitation operators to the reference wave function as a whole, while the singly external and internal configurations are standard uncontracted spin eigenfunctions. A new efficient and simple method for the calculation of the coupling coefficients is used, which is well suited for vector machines, and allows the recalculation of all coupling coefficients each time they are needed. The vector H⋅c is computed partly in a nonorthogonal configuration basis. In order to test the accuracy of the internally contracted wave functions, benchmark calculations have been performed for F−, H2O, NH2, CH2, CH3, OH, NO, N2, and O2 at various geometries. The deviations of the energies obtained with internally contracted and uncontracted MRCI wave functions are mostly smaller than 1 mH and typically 3–5 times smaller than the deviations between the uncontracted MRCI and the full CI. Dipole moments, electric dipole polarizabilities, and electronic dipole transition moments calculated with uncontracted and contracted MRCI wave functions also are found to be in close agreement. The efficiency of the method is demonstrated in large scale calculations for the CN, NH3, CO2, and Cr2 molecules. In these calculations up to 3088 reference configurations and up to 154 orbitals were employed. The biggest calculation is equivalent to an uncontracted MRCI with more than 78 million configurations.
3,375 citations
TL;DR: A fully-vectorial, three-dimensional algorithm to compute the definite-frequency eigenstates of Maxwell's equations in arbitrary periodic dielectric structures, including systems with anisotropy or magnetic materials, using preconditioned block-iterative eigensolvers in a planewave basis is described.
Abstract: We describe a fully-vectorial, three-dimensional algorithm to compute the definite-frequency eigenstates of Maxwell's equations in arbitrary periodic dielectric structures, including systems with anisotropy (birefringence) or magnetic materials, using preconditioned block-iterative eigensolvers in a planewave basis. Favorable scaling with the system size and the number of computed bands is exhibited. We propose a new effective dielectric tensor for anisotropic structures, and demonstrate that O Delta x;2 convergence can be achieved even in systems with sharp material discontinuities. We show how it is possible to solve for interior eigenvalues, such as localized defect modes, without computing the many underlying eigenstates. Preconditioned conjugate-gradient Rayleigh-quotient minimization is compared with the Davidson method for eigensolution, and a number of iteration variants and preconditioners are characterized. Our implementation is freely available on the Web.
2,861 citations
References
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TL;DR: In this article, a systematic method for finding the latent roots and principal axes of a matrix, without reducing the order of the matrix, has been proposed, which is characterized by a wide field of applicability and great accuracy, since the accumulation of rounding errors is avoided, through the process of minimized iterations.
Abstract: The present investigation designs a systematic method for finding the latent roots and the principal axes of a matrix, without reducing the order of the matrix. It is characterized by a wide field of applicability and great accuracy, since the accumulation of rounding errors is avoided, through the process of \"minimized iterations\". Moreover, the method leads to a well convergent successive approximation procedure by which the solution of integral equations of the Fredholm type and the solution of the eigenvalue problem of linear differential and integral operators may be accomplished.
3,947 citations
TL;DR: In this paper, a new method for obtaining the coefficients in a large Cl expansion is proposed, where the expansion coefficients are obtained directly from the list of two-electron integrals by means of an iterative procedure.
468 citations
TL;DR: In this paper, the first-row diatomic hydrides, calculated with accurate configuration-interaction wave functions, were determined at the equilibrium internuclear separation for each molecule and the basis sets used, were capable of reproducing recently published selfconsistent field energies to within 0003 hartrees.
Abstract: Molecular properties of the first-row diatomic hydrides, calculated with accurate configuration-interaction wave functions, are presented Ground-state functions, constructed from approximate natural orbitals, were determined at the equilibrium internuclear separation for each molecule The basis sets used, were capable of reproducing recently published self-consistent-field energies to within 0003 hartrees A minimum of 70% of the correlation energy and an error in the dipole moment of less than 3% were obtained in a systematic study of each molecule To attain this accuracy, large numbers of singly and doubly excited configurations were used in the wave functions
336 citations
TL;DR: The coordinate relaxation method for the iterative calculation of the lowest (or highest) root of a symmetric matrix, based on the minimization (or maximization) of the Rayleigh quotient, has been generalized to make it possible to obtain several of the highest roots in order without explicitly modifying the original matrix.
187 citations
167 citations