| 1. |
- Aquilante, Francesco, et al.
(författare)
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Accurate ab initio density fitting for multiconfigurational self-consistent field methods
- 2008
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Ingår i: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 129:2, s. 024113-
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Tidskriftsartikel (refereegranskat)abstract
- Using Cholesky decomposition and density fitting to approximate the electron repulsion integrals, an implementation of the complete active space self-consistent field (CASSCF) method suitable for large-scale applications is presented. Sample calculations on benzene, diaquo-tetra-mu-acetato-dicopper(II), and diuraniumendofullerene demonstrate that the Cholesky and density fitting approximations allow larger basis sets and larger systems to be treated at the CASSCF level of theory with controllable accuracy. While strict error control is an inherent property of the Cholesky approximation, errors arising from the density fitting approach are managed by using a recently proposed class of auxiliary basis sets constructed from Cholesky decomposition of the atomic electron repulsion integrals.
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| 2. |
- Aquilante, Francesco, et al.
(författare)
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Analytic derivatives for the Cholesky representation of the two-electron integrals
- 2008
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Ingår i: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 129:3, s. 034106-
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Tidskriftsartikel (refereegranskat)abstract
- We propose a formalism for calculating analytic derivatives of the electronic energy with respect to nuclear coordinates using Cholesky decomposition of the two-electron integrals. The formalism is derived by exploiting the equivalence of Cholesky decomposition and density fitting when a suitable auxiliary basis set is used for expanding atomic orbital product densities in the latter. An implementation of gradients at the nonhybrid density functional theory level is presented, and sample calculations demonstrate that the errors in equilibrium geometries due to the Cholesky representation of the integrals can be controlled by adjusting the decomposition threshold.
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| 3. |
- Aquilante, Francesco, et al.
(författare)
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Atomic Cholesky decompositions: A route to unbiased auxiliary basis sets for density fitting approximation with tunable accuracy and efficiency
- 2009
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Ingår i: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 130:15
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Tidskriftsartikel (refereegranskat)abstract
- Cholesky decomposition of the atomic two-electron integral matrix has recently been proposed as a procedure for automated generation of auxiliary basis sets for the density fitting approximation [F. Aquilante , J. Chem. Phys. 127, 114107 (2007)]. In order to increase computational performance while maintaining accuracy, we propose here to reduce the number of primitive Gaussian functions of the contracted auxiliary basis functions by means of a second Cholesky decomposition. Test calculations show that this procedure is most beneficial in conjunction with highly contracted atomic orbital basis sets such as atomic natural orbitals, and that the error resulting from the second decomposition is negligible. We also demonstrate theoretically as well as computationally that the locality of the fitting coefficients can be controlled by means of the decomposition threshold even with the long-ranged Coulomb metric. Cholesky decomposition-based auxiliary basis sets are thus ideally suited for local density fitting approximations.
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| 4. |
- Aquilante, Francesco, et al.
(författare)
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Cholesky decomposition-based multiconfiguration second-order perturbation theory (CD-CASPT2) : application to the spin-state energetics of Co-III(diiminato)(NPh).
- 2008
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Ingår i: Journal of Chemical Theory and Computation. - : American Chemical Society (ACS). - 1549-9618 .- 1549-9626. ; 4:5, s. 694-702
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Tidskriftsartikel (refereegranskat)abstract
- The electronic structure and low-lying electronic states of a Co-III(diiminato)(NPh) complex have been studied using mulficonfigurational wave function theory (CASSCF/CASPT2) The results have been compared to those obtained with density functional theory. The best agreement with ab initio results is obtained with a modified B3LYP functional containing a reduced amount (15%) of Hartree-Fock exchange. A relativistic basis set with 869 functions has been employed in the most extensive ab initio calculations, where a Cholesky decomposition technique was used to overcome problems arising from the large size of the two-electron integral matrix. It is shown that this approximation reproduces results obtained with the full integral set to a high accuracy, thus opening the possibility to use this approach to perform multiconfigurational wave-function-based quantum chemistry on much larger systems relative to what has been possible until now.
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| 5. |
- Aquilante, Francesco, et al.
(författare)
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Fast noniterative orbital localization for large molecules.
- 2006
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Ingår i: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 125:17
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Tidskriftsartikel (refereegranskat)abstract
- We use Cholesky decomposition of the density matrix in atomic orbital basis to define a new set of occupied molecular orbital coefficients. Analysis of the resulting orbitals (”Cholesky molecular orbitals”) demonstrates their localized character inherited from the sparsity of the density matrix. Comparison with the results of traditional iterative localization schemes shows minor differences with respect to a number of suitable measures of locality, particularly the scaling with system size of orbital pair domains used in local correlation methods. The Cholesky procedure for generating orthonormal localized orbitals is noniterative and may be made linear scaling. Although our present implementation scales cubically, the algorithm is significantly faster than any of the conventional localization schemes. In addition, since this approach does not require starting orbitals, it will be useful in local correlation treatments on top of diagonalization-free Hartree-Fock optimization algorithms.
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| 6. |
- Aquilante, Francesco, et al.
(författare)
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Low-cost evaluation of the exchange Fock matrix from Cholesky and density fitting representations of the electron repulsion integrals
- 2007
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Ingår i: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 126:19, s. 194106-
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Tidskriftsartikel (refereegranskat)abstract
- The authors propose a new algorithm, “local K” (LK), for fast evaluation of the exchange Fock matrix in case the Cholesky decomposition of the electron repulsion integrals is used. The novelty lies in the fact that rigorous upper bounds to the contribution from each occupied orbital to the exchange Fock matrix are employed. By formulating these inequalities in terms of localized orbitals, the scaling of computing the exchange Fock matrix is reduced from quartic to quadratic with only negligible prescreening overhead and strict error control. Compared to the unscreened Cholesky algorithm, the computational saving is substantial for systems of medium and large sizes. By virtue of its general formulation, the LK algorithm can be used also within the class of methods that employ auxiliary basis set expansions for representing the electron repulsion integrals.
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| 7. |
- Aquilante, Francesco
(författare)
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New Approaches to Large-Scale Electronic Structure Calculations
- 2007
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Recent years have witnessed a growing interest of the scientific community for the use of ab initio and density functional theory methods in theoretical studies of molecules containing many atoms. However, the `scaling wall' of some of the most accurate of such methods is often an obstacle for their applicability to systems of real-life interest, e.g. in biochemistry and nanotechnologies, one bottleneck being the evaluation and storage of the two-electron repulsion integrals. We have explored the possibility to avoid the expensive evaluation of the full integral matrix by designing and implementing approximate approaches based on Cholesky decomposition techniques. The results show the general applicability of this approximation to any quantum chemical model with substantial computational savings compared to conventional implementations -- not uncommonly of 1-2 orders of magnitude. At the same time, the loss of accuracy is minimal and can be systematically reduced at the price of sustainable additional costs. A major theoretical achievement of this study has been the reformulation of the Cholesky approximation in terms of solution to a "density fitting" variational problem. This has lead to an elegant formulation of the analytic derivatives of the Cholesky vectors, a long-standing lack of this technique. Moreover, this observation has paved the way to a new generation of accurate density fitting approximations free from biases and derived fully ab initio.
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| 8. |
- Aquilante, Francesco, et al.
(författare)
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Quartic scaling evaluation of canonical scaled opposite spin second-order Moller-Plesset correlation energy using Cholesky decompositions.
- 2007
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Ingår i: Chemical Physics Letters. - : Elsevier BV. - 0009-2614 .- 1873-4448. ; 449:4-6, s. 354-357
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Tidskriftsartikel (refereegranskat)abstract
- The scaled opposite spin second-order Moller-Plesset (SOS-MP2) energy expression is reformulated using Cholesky decomposition of the amplitude matrix. The resulting algorithm requires an auxiliary basis or Cholesky representation of the two-electron integrals and shows fourth-order scaling with system size. Based on an analysis of operation counts, we estimate that the present approach is computationally advantageous compared to the analogous fourth-order algorithms that employ Laplace transforms.
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| 9. |
- Aquilante, Francesco, et al.
(författare)
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Systematic truncation of the virtual space in multiconfigurational perturbation theory
- 2009
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Ingår i: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 131:3
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Tidskriftsartikel (refereegranskat)abstract
- A method is suggested which allows truncation of the virtual space in Cholesky decomposition-based multiconfigurational perturbation theory (CD-CASPT2) calculations with systematic improvability of the results. The method is based on a modified version of the frozen natural orbital (FNO) approach used in coupled cluster theory. The idea is to exploit the near-linear dependence among the eigenvectors of the virtual-virtual block of the second-order Moller-Plesset density matrix. It is shown that FNO-CASPT2 recovers more than 95% of the full CD-CASPT2 correlation energy while requiring only a fraction of the total virtual space, especially when large atomic orbital basis sets are in use. Tests on various properties commonly investigated with CASPT2 demonstrate the reliability of the approach and the associated reduction in computational cost and storage demand of the calculations.
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| 10. |
- Aquilante, Francesco, et al.
(författare)
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Unbiased auxiliary basis sets for accurate two-electron integral approximations
- 2007
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Ingår i: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 127:11, s. 114107-
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Tidskriftsartikel (refereegranskat)abstract
- We propose Cholesky decomposition (CD) of the atomic two-electron integral matrix as a robust and general technique for generating auxiliary basis sets for the density fitting approximation. The atomic CD (aCD) auxiliary basis set is calculated on the fly and is not biased toward a particular quantum chemical method. Moreover, the accuracy of the aCD basis set can be controlled with a single parameter.
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