| 1. |
- Aquilante, Francesco, et al.
(författare)
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Molcas 8 : New capabilities for multiconfigurational quantum chemical calculations across the periodic table
- 2016
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Ingår i: Journal of Computational Chemistry. - : Wiley. - 0192-8651 .- 1096-987X. ; 37:5, s. 506-541
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Tidskriftsartikel (refereegranskat)abstract
- In this report, we summarize and describe the recent unique updates and additions to the Molcas quantum chemistry program suite as contained in release version 8. These updates include natural and spin orbitals for studies of magnetic properties, local and linear scaling methods for the Douglas-Kroll-Hess transformation, the generalized active space concept in MCSCF methods, a combination of multiconfigurational wave functions with density functional theory in the MC-PDFT method, additional methods for computation of magnetic properties, methods for diabatization, analytical gradients of state average complete active space SCF in association with density fitting, methods for constrained fragment optimization, large-scale parallel multireference configuration interaction including analytic gradients via the interface to the Columbus package, and approximations of the CASPT2 method to be used for computations of large systems. In addition, the report includes the description of a computational machinery for nonlinear optical spectroscopy through an interface to the QM/MM package Cobramm. Further, a module to run molecular dynamics simulations is added, two surface hopping algorithms are included to enable nonadiabatic calculations, and the DQ method for diabatization is added. Finally, we report on the subject of improvements with respects to alternative file options and parallelization.
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| 2. |
- Merlot, Patrick, et al.
(författare)
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Attractive electron-electron interactions within robust local fitting approximations
- 2013
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Ingår i: Journal of Computational Chemistry. - : Wiley. - 0192-8651 .- 1096-987X. ; 34:17, s. 1486-1496
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Tidskriftsartikel (refereegranskat)abstract
- An analysis of Dunlap's robust fitting approach reveals that the resulting two-electron integral matrix is not manifestly positive semidefinite when local fitting domains or non-Coulomb fitting metrics are used. We present a highly local approximate method for evaluating four-center two-electron integrals based on the resolution-of-the-identity (RI) approximation and apply it to the construction of the Coulomb and exchange contributions to the Fock matrix. In this pair-atomic resolution-of-the-identity (PARI) approach, atomic-orbital (AO) products are expanded in auxiliary functions centered on the two atoms associated with each product. Numerical tests indicate that in 1% or less of all HartreeFock and KohnSham calculations, the indefinite integral matrix causes nonconvergence in the self-consistent-field iterations. In these cases, the two-electron contribution to the total energy becomes negative, meaning that the electronic interaction is effectively attractive, and the total energy is dramatically lower than that obtained with exact integrals. In the vast majority of our test cases, however, the indefiniteness does not interfere with convergence. The total energy accuracy is comparable to that of the standard Coulomb-metric RI method. The speed-up compared with conventional algorithms is similar to the RI method for Coulomb contributions; exchange contributions are accelerated by a factor of up to eight with a triple-zeta quality basis set. A positive semidefinite integral matrix is recovered within PARI by introducing local auxiliary basis functions spanning the full AO product space, as may be achieved by using Cholesky-decomposition techniques. Local completion, however, slows down the algorithm to a level comparable with or below conventional calculations.
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| 3. |
- Aquilante, Francesco, et al.
(författare)
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Cholesky decomposition techniques in electronic structure theory
- 2011
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Ingår i: Linear-Scaling Techniques in Computational Chemistry and Physics. - Dordrecht : Springer. - 9789048128525 ; , s. 301-304
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- We review recently developed methods to efficiently utilize the Cholesky decomposition technique in electronic structure calculations. The review starts with a brief introduction to the basics of the Cholesky decomposition technique. Subsequently, examples of applications of the technique to ab inito procedures are presented. The technique is demonstrated to be a special type of a resolution-of-identity or density-fitting scheme. This is followed by explicit examples of the Cholesky techniques used in orbital localization, computation of the exchange contributionto the Fock matrix, in MP2, gradient calculations, and so-called method specific Cholesky decomposition. Subsequently, examples of calibration of the method with respect to computed total energies, excitation energies, and auxiliary basis set pruning are presented. In particular, it is demonstrated that the Cholesky method is an unbiased method to derive auxiliary basis sets. Furthermore, details of the implementational considerations are put forward and examples from a parallel Cholesky decomposition scheme is presented. Finally, an outlook and perspectives are presented, followed by a summary and conclusions section. We are of the opinion that the Cholesky decomposition method is a technique that has been overlooked for too long. We have just recently started to understand how to efficiently incorporate the method in existing ab initio programs. The full potential of the Cholesky technique has not yet been fully explored.
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| 4. |
- Aquilante, Francesco, et al.
(författare)
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Inner projection techniques for the low-cost handling of two-electron integrals in quantum chemistry
- 2017
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Ingår i: Molecular Physics. - : Informa UK Limited. - 0026-8976 .- 1362-3028. ; 115:17-18, s. 2052-2064
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Tidskriftsartikel (refereegranskat)abstract
- The density-fitting technique for approximating electron-repulsion integrals relies on the quality of auxiliary basis sets. These are commonly obtained through data fitting, an approach that presents some shortcomings. On the other hand, it is possible to derive auxiliary basis sets by removing elements from the product space of both contracted and primitive orbitals by means of a particular form of inner projection technique that has come to be known as Cholesky decomposition (CD). This procedure allows for on-the-fly construction of auxiliary basis sets that may be used in conjunction with any quantum chemical method, i.e. unbiased auxiliary basis sets. One key feature of these sets is that they represent the electron-repulsion integral matrix in atomic orbital basis with an accuracy that can be systematically improved. Another key feature is represented by the fact that locality of fitting coefficients is obtained even with the long-ranged Coulomb metric, as result of integral accuracy. Here we report on recent advances in the development of the CD-based density fitting technology. In particular, the implementation of analytical gradients algorithms is reviewed and the present status of local formulations - potentially linear scaling - is analysed in detail.
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| 5. |
- Aquilante, Francesco, et al.
(författare)
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MOLCAS-a software for multiconfigurational quantum chemistry calculations
- 2013
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Ingår i: Wiley Interdisciplinary Reviews. Computational Molecular Science. - : Wiley. - 1759-0884 .- 1759-0876. ; 3:2, s. 143-149
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Tidskriftsartikel (refereegranskat)abstract
- At variance, with most of the quantum chemistry software presently available, MOLCAS is a package that is specialized in multiconfigurational wave function theory (MC-WFT) rather than density functional theory (DFT). Given the much higher algorithmic complexity of MC-WFT versus DFT, an extraordinary effort needs to be made from the programming point of view to achieve state-of-the-art performance for large-scale calculations. In particular, a robust and efficient implementation of the Cholesky decomposition techniques for handling two-electron integrals has been developed which is unique to MOLCAS. Together with this 'Cholesky infrastructure', a powerful and multilayer graphical and scripting user interface is available, which is an essential ingredient for the setup of MC-WFT calculations. These two aspects of the MOLCAS software constitute the focus of the present report. (C) 2012 John Wiley & Sons, Ltd.
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| 6. |
- Aurbakken, Einar, et al.
(författare)
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Transient spectroscopy from time-dependent electronic-structure theory without multipole expansions
- 2024
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Ingår i: Physical Review A: covering atomic, molecular, and optical physics and quantum information. - : American Physical Society. - 2469-9926 .- 2469-9934. ; 109:1
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Tidskriftsartikel (refereegranskat)abstract
- Based on the work done by an electromagnetic field on an atomic or molecular electronic system, a general gauge-invariant formulation of transient absorption spectroscopy is presented within the semiclassical approximation. Avoiding multipole expansions, a computationally viable expression for the spectral response function is derived from the minimal-coupling Hamiltonian of an electronic system interacting with one or more laser pulses described by a source-free, enveloped electromagnetic vector potential. With a fixed-basis expansion of the electronic wave function, the computational cost of simulations of laser-driven electron dynamics beyond the dipole approximation is the same as simulations adopting the dipole approximation. We illustrate the theory by time-dependent configuration interaction and coupled-cluster simulations of core-level absorption and circular dichroism spectra.
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| 7. |
- Boström, Jonas, et al.
(författare)
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Ab Initio Density Fitting : Accuracy Assessment of Auxiliary Basis Sets from Cholesky Decompositions
- 2009
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Ingår i: Journal of Chemical Theory and Computation. - : American Chemical Society (ACS). - 1549-9618 .- 1549-9626. ; 5:6, s. 1545-1553
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Tidskriftsartikel (refereegranskat)abstract
- The accuracy of auxiliary basis sets derived by Cholesky decompositions of the electron repulsion integrals is assessed in a series of benchmarks on total ground state energies and dipole moments of a large test set of molecules. The test set includes molecules composed of atoms from the first three rows of the periodic table as well as transition metals. The accuracy of the auxiliary basis sets are tested for the 6-31 G**, correlation consistent, and atomic natural orbital basis sets at the Hartree-Fock, density functional theory, and second-order Moller-Plesset levels of theory. By decreasing the decomposition threshold, a hierarchy of auxiliary basis sets is obtained with accuracies ranging from that of standard auxiliary basis sets to that of conventional integral treatments.
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| 8. |
- Boström, Jonas, et al.
(författare)
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Analytical gradients of Hartree-Fock exchange with density fitting approximations
- 2013
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Ingår i: Journal of Chemical Theory and Computation. - : American Chemical Society (ACS). - 1549-9618 .- 1549-9626. ; 9:1, s. 204-212
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Tidskriftsartikel (refereegranskat)abstract
- We extend the local exchange (LK) algorithm [Aquilante, F.; Pedersen, T. B.; Lindh, R. J. Chem. Phys.2007, 126, 194106] to the calculation of analytical gradients with density fitting. We discuss the features of the screening procedure and demonstrate the possible advantages of using this formulation, which is easily interfaced to a standard integral-direct gradient code. With auxiliary basis sets obtained from Cholesky decomposition of atomic or molecular integral blocks with a decomposition threshold of 10-4Eh, typical errors due to the density fitting in bond lengths, bond angles, and dihedral angles are 0.1 pm, 0.1°, and 0.5°, respectively. The overall speedup of geometry optimizations is about 1 order of magnitude for atomic natural-orbital-type basis sets but much less pronounced for correlation-consistent basis sets.
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| 9. |
- Boström, Jonas, et al.
(författare)
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Analytical gradients of the second-order Møller–Plesset energy using Cholesky decompositions
- 2014
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Ingår i: International Journal of Quantum Chemistry. - : Wiley. - 0020-7608 .- 1097-461X. ; 114:5, s. 321-327
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Tidskriftsartikel (refereegranskat)abstract
- An algorithm for computing analytical gradients of the second-order Møller–Plesset (MP2) energy using density fitting (DF) is presented. The algorithm assumes that the underlying canonical Hartree–Fock reference is obtained with the same auxiliary basis set, which we obtain by Cholesky decomposition (CD) of atomic electron repulsion integrals. CD is also used for the negative semidefinite MP2 amplitude matrix. Test calculations on the weakly interacting dimers of the S22 test set (Jurečka et al., Phys. Chem. Chem. Phys. 2006, 8, 1985) show that the geometry errors due to the auxiliary basis set are negligible. With double-zeta basis sets, the error due to the DF approximation in intermolecular bond lengths is better than 0.1 pm. The computational time is typically reduced by a factor of 6–7.
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| 10. |
- Boström, Jonas, et al.
(författare)
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Coupled Cluster and Moller-Plesset Perturbation Theory Calculations of Noncovalent Intermolecular Interactions using Density Fitting with Auxiliary Basis Sets from Cholesky Decompositions
- 2012
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Ingår i: Journal of Chemical Theory and Computation. - : American Chemical Society (ACS). - 1549-9618 .- 1549-9626. ; 8:6, s. 1921-1928
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Tidskriftsartikel (refereegranskat)abstract
- We compute noncovalent intermolecular interaction energies for the S22 test set [Phys. Chem. Chem. Phys. 2006, 8, 1985-1993] of molecules at the Moller-Plesset and coupled cluster levels of supermolecular theory using density fitting (DF) to approximate all two-electron integrals. The error due to the DF approximation is analyzed for a range of auxiliary basis sets derived from Cholesky decomposition (CD) in conjunction with correlation consistent and atomic natural orbital valence basis sets. A Cholesky decomposition threshold of 10(-4)E(h) for full molecular CD and its one-center approximation (1C-CD) generally yields errors below 0.03 kcal/mol, whereas 10(-3)E(h) is sufficient to obtain the same level of accuracy or better with the atomic CD (aCD) and atomic compact CD (acCD) auxiliary basis sets. Comparing to commonly used predefined auxiliary basis sets, we find that while the aCD and acCD sets are larger by a factor of 2-4 with triple-zeta AO basis sets, they provide results 1-2 orders of magnitude more accurate.
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| 11. |
- Delcey, Mickaël G., 1988-, et al.
(författare)
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Analytical gradients of complete active space self-consistent field energies using Cholesky decomposition : Geometry optimization and spin-state energetics of a ruthenium nitrosyl complex
- 2014
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Ingår i: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 140:17, s. 174103-
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Tidskriftsartikel (refereegranskat)abstract
- We present a formulation of analytical energy gradients at the complete active space self-consistent field (CASSCF) level of theory employing density fitting (DF) techniques to enable efficient geometry optimizations of large systems. As an example, the ground and lowest triplet state geometries of a ruthenium nitrosyl complex are computed at the DF-CASSCF level of theory and compared with structures obtained from density functional theory (DFT) using the B3LYP, BP86, and M06L functionals. The average deviation of all bond lengths compared to the crystal structure is 0.042 angstrom at the DF-CASSCF level of theory, which is slightly larger but still comparable with the deviations obtained by the tested DFT functionals, e. g., 0.032 angstrom with M06L. Specifically, the root-mean-square deviation between the DF-CASSCF and best DFT coordinates, delivered by BP86, is only 0.08 angstrom for S-0 and 0.11 angstrom for T-1, indicating that the geometries are very similar. While keeping the mean energy gradient errors below 0.25%, the DF technique results in a 13-fold speedup compared to the conventional CASSCF geometry optimization algorithm. Additionally, we assess the singlet-triplet energy vertical and adiabatic differences with multiconfigurational second-order perturbation theory (CASPT2) using the DF-CASSCF and DFT optimized geometries. It is found that the vertical CASPT2 energies are relatively similar regardless of the geometry employed whereas the adiabatic singlet-triplet gaps are more sensitive to the chosen triplet geometry. (C) 2014 AIP Publishing LLC.
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| 12. |
- Delcey, Mickaël G., 1988-, et al.
(författare)
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Analytical gradients of the state-average complete active space self-consistent field method with density fitting
- 2015
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Ingår i: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 143:4
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Tidskriftsartikel (refereegranskat)abstract
- An efficient implementation of the state-averaged complete active space self-consistent field (SA-CASSCF) gradients employing density fitting (DF) is presented. The DF allows a reduction both in scaling and prefactors of the different steps involved. The performance of the algorithm is demonstrated on a set of molecules ranging up to an iron-Heme b complex which with its 79 atoms and 811 basis functions is to our knowledge the largest SA-CASSCF gradient computed. For smaller systems where the conventional code could still be used as a reference, both the linear response calculation and the gradient formation showed a clear timing reduction and the overall cost of a geometry optimization is typically reduced by more than one order of magnitude while the accuracy loss is negligible.
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| 13. |
- Fernández Galván, Ignacio, et al.
(författare)
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Analytical State-Average Complete-Active-Space Self-Consistent Field Nonadiabatic Coupling Vectors : Implementation with Density-Fitted Two-Electron Integrals and Application to Conical Intersections
- 2016
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Ingår i: Journal of Chemical Theory and Computation. - : American Chemical Society (ACS). - 1549-9618 .- 1549-9626. ; 12:8, s. 3636-3653
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Tidskriftsartikel (refereegranskat)abstract
- Analytical state-average complete-active-space self-consistent field derivative (nonadiabatic) coupling vectors are implemented. Existing formulations are modified such that the implementation is compatible with Cholesky-based density fitting of two-electron integrals, which results in efficient calculations especially with large basis sets. Using analytical nonadiabatic coupling vectors, the optimization of conical intersections is implemented within the projected constrained optimization method. The standard description and characterization of conical intersections is reviewed and clarified, and a practical and unambiguous system for their classification and interpretation is put forward. These new tools are subsequently tested and benchmarked for 19 different conical intersections. The accuracy of the derivative coupling vectors is validated, and the information that can be drawn from the proposed characterization is discussed, demonstrating its usefulness.
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| 14. |
- Freitag, Leon, et al.
(författare)
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Orbital entanglement and CASSCF analysis of the Ru-NO bond in a Ruthenium nitrosyl complex
- 2015
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Ingår i: Physical Chemistry, Chemical Physics - PCCP. - : Royal Society of Chemistry (RSC). - 1463-9076 .- 1463-9084. ; 17:22, s. 14383-14392
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Tidskriftsartikel (refereegranskat)abstract
- Complete active space self-consistent field (CASSCF) wavefunctions and an orbital entanglement analysis obtained from a density-matrix renormalisation group (DMRG) calculation are used to understand the electronic structure, and, in particular, the Ru-NO bond of a Ru nitrosyl complex. Based on the configurations and orbital occupation numbers obtained for the CASSCF wavefunction and on the orbital entropy measurements evaluated for the DMRG wavefunction, we unravel electron correlation effects in the Ru coordination sphere of the complex. It is shown that Ru-NO pi bonds show static and dynamic correlation, while other Ru-ligand bonds feature predominantly dynamic correlation. The presence of static correlation requires the use of multiconfigurational methods to describe the Ru-NO bond. Subsequently, the CASSCF wavefunction is analysed in terms of configuration state functions based on localised orbitals. The analysis of the wavefunctions in the electronic singlet ground state and the first triplet state provides a picture of the Ru-NO moiety beyond the standard representation based on formal oxidation states. A distinct description of the Ru and NO fragments is advocated. The electron configuration of Ru is an equally weighted superposition of Ru-II and Ru-III configurations, with the Ru-III configuration originating from charge donation mostly from Cl ligands. However, and contrary to what is typically assumed, the electronic configuration of the NO ligand is best described as electroneutral.
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| 15. |
- Olsen, Jogvan Magnus Haugaard, et al.
(författare)
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Dalton Project : A Python platform for molecular- and electronic-structure simulations of complex systems
- 2020
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Ingår i: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 152:21
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Tidskriftsartikel (refereegranskat)abstract
- The Dalton Project provides a uniform platform access to the underlying full-fledged quantum chemistry codes Dalton and LSDalton as well as the PyFraME package for automatized fragmentation and parameterization of complex molecular environments. The platform is written in Python and defines a means for library communication and interaction. Intermediate data such as integrals are exposed to the platform and made accessible to the user in the form of NumPy arrays, and the resulting data are extracted, analyzed, and visualized. Complex computational protocols that may, for instance, arise due to a need for environment fragmentation and configuration-space sampling of biochemical systems are readily assisted by the platform. The platform is designed to host additional software libraries and will serve as a hub for future modular software development efforts in the distributed Dalton community.
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| 16. |
- Pedersen, Thomas Bondo, et al.
(författare)
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Density fitting with auxiliary basis sets from Cholesky decompositions
- 2009
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Ingår i: Theoretical Chemistry accounts. - : Springer Science and Business Media LLC. - 1432-881X .- 1432-2234. ; 124:1-2, s. 1-10
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Tidskriftsartikel (refereegranskat)abstract
- Recent progress in the use of Cholesky decomposition techniques within the density fitting approximation of two-electron integrals is reviewed with emphasis on the theoretical background. Special attention is paid to the fact that errors due to the density fitting approximation can be controlled by constructing auxiliary basis sets by means of Cholesky decomposition of either the entire or certain subblocks of the molecular two-electron integral matrix. Finally, the prospects of trivial linear-scaling calculation of fitting coefficients in the Cholesky decomposition-based density fitting scheme are outlined.
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| 17. |
- Pedersen, Thomas Bondo, et al.
(författare)
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The versatility of the Cholesky decomposition in electronic structure theory
- 2024
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Ingår i: Wiley Interdisciplinary Reviews. Computational Molecular Science. - : John Wiley & Sons. - 1759-0876 .- 1759-0884. ; 14:1
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Tidskriftsartikel (refereegranskat)abstract
- The resolution-of-the-identity (RI) or density fitting (DF) approximation for the electron repulsion integrals (ERIs) has become a standard component of accelerated and reduced-scaling implementations of first-principles Gaussian-type orbital electronic-structure methods. The Cholesky decomposition (CD) of the ERIs has also become increasingly deployed across quantum chemistry packages in the last decade, even though its early applications were mostly limited to high-accuracy methods such as coupled-cluster theory and multiconfigurational approaches. Starting with a summary of the basic theory underpinning both the CD and RI/DF approximations, thus underlining the extremely close relation of the CD and RI/DF techniques, we provide a brief and largely chronological review of the evolution of the CD approach from its birth in 1977 to its current state. In addition to being a purely numerical procedure for handling ERIs, thus providing robust and computationally efficient approximations to the exact ERIs that have been found increasingly useful on modern computer platforms, CD also offers highly accurate approaches for generating auxiliary basis sets for the RI/DF approximation on the fly due to the deep mathematical connection between the two approaches. In this review, we aim to provide a concise reference of the main techniques employed in various CD approaches in electronic structure theory, to exemplify the connection between the CD and RI/DF approaches, and to clarify the state of the art to guide new implementations of CD approaches across electronic structure programs.
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