Atomic Cholesky decompositions: A route to unbiased auxiliary basis sets for density fitting approximation with tunable accuracy and efficiency

Aquilante, Francesco; Gagliardi, Laura; Pedersen, Thomas Bondo; Lindh, Roland

doi:10.1063/1.3116784

Cited by 225 publications

(281 citation statements)

References 74 publications

Supporting

Mentioning

279

Contrasting

Order By: Relevance

“…[198] To reduce the total number of functions, the atomic compact CD (acCD) procedure performs a second CD on the aCD basis, before the remaining functions are fit to produce an accurate representation of that parent aCD set. [199] For a large iron containing complex, this led to a 70% reduction in the number of ABS primitives, but with no loss of accuracy when compared to aCD. Although it is possible to generate acCD ABSs and store them for later use in a basis set library, in practice this is not carried out as the computational cost for on-the-fly generation is negligible.…”

Section: Auxiliary Basis Setsmentioning

confidence: 99%

Gaussian basis sets for molecular applications

Hill¹

2012

Int J of Quantum Chemistry

188

155

View full text Add to dashboard Cite

The choice of basis set in quantum chemical calculations can have a huge impact on the quality of the results, especially for correlated ab initio methods. This article provides an overview of the development of Gaussian basis sets for molecular calculations, with a focus on four popular families of modern atom-centered, energy-optimized bases: atomic natural orbital, correlation consistent, polarization consistent, and def2. The terminology used for describing basis sets is briefly covered, along with an overview of the auxiliary basis sets used in a number of integral approximation techniques and an outlook on possible future directions of basis set design.

show abstract

Section: Auxiliary Basis Setsmentioning

confidence: 99%

Gaussian basis sets for molecular applications

Hill¹

2012

Int J of Quantum Chemistry

188

155

View full text Add to dashboard Cite

show abstract

“…In the context of PARI, the most interesting aspect of CD-based auxiliary basis sets is their inherent locality. [46,47,58] …”

Section: Control Of Integral Accuracy By Cholesky Decompositionmentioning

confidence: 99%

“…For diagonal AA pairs, atomic CD auxiliary functions span the AO product space with only a limited number of atom-centered functions. [58] We note that the use of atomic CD auxiliary basis sets in conjunction with the PARI approximation is equivalent to the limited-expansionof-diatomic-overlap (LEDO) method of Billingsley and Bloor, [3] with on-site linear dependence removed in advance (by the atomic CD). A simple strategy for spanning AO products locally is to include functions positioned on the line between the two atoms in question.…”

Section: Full Paper Wwwc-chemorgmentioning

confidence: 99%

Attractive electron–electron interactions within robust local fitting approximations

et al. 2013

Self Cite

View full text Add to dashboard Cite

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 resolutionof-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 Hartree-Fock and Kohn-Sham 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.

show abstract

“…III, the results for ethene were performed at the RASPT2(12,2,2;4,6,8)(SD) level, employing the 6s5p4d2f/3s2p1d + 1s1p1d basis set, the default IPEA shift, 45 and Cholesky decomposition 41 to compute the vertical transition energies with the MOLCAS-7 program. [41][42][43] An imaginary level shift of 0.1 a.u. was used throughout.…”

Section: B Excitation Energiesmentioning

confidence: 99%

“…39,40 All multi-state RASPT2 calculations (hereafter MS-RASPT2) were performed with the MOLCAS-7 program. [41][42][43] The large atomic natural orbital ANO-L basis set 44 contracted to [6s5p4d2f] for carbon atoms and [3s2p1d] for hydrogen atoms was employed. In order to describe the Rydberg states, a set of even-tempered 1s1p1d functions was added on carbon atoms.…”

Section: Computation Of Potential Energy Curves For Stretched Etmentioning

confidence: 99%

A distance-dependent parameterization of the extended Hubbard model for conjugated and aromatic hydrocarbons derived from stretched ethene

Schmalz

Serrano‐Andrés

Sauri

et al. 2011

The Journal of Chemical Physics

View full text Add to dashboard Cite

The Hubbard model, which is widely used in physics but is mostly unfamiliar to chemists, provides an attractive yet simple model for chemistry beyond the self consistent field molecular orbital approximation. The Hubbard model adds an effective electron-electron repulsion when two electrons occupy the same atomic orbital to the familiar Hückel Hamiltonian. Thus it breaks the degeneracy between excited singlet and triplet states and allows an explicit treatment of electron correlation. We show how to evaluate the parameters of the model from high-level ab initio calculations on twoatom fragments and then to transfer the parameters to large molecules and polymers where accurate ab initio calculations are difficult or impossible. The recently developed MS-RASPT2 method is used to generate accurate potential energy curves for ethene as a function of carbon-carbon bond length, which are used to parameterize the model for conjugated hydrocarbons. Test applications to several conjugated/aromatic molecules show that even though the model is very simple, it is capable of reasonably accurate predictions for bond lengths, and predicts molecular excitation energies in reasonable agreement with those from the MS-RASPT2 method.

show abstract

Atomic Cholesky decompositions: A route to unbiased auxiliary basis sets for density fitting approximation with tunable accuracy and efficiency

Cited by 225 publications

References 74 publications

Gaussian basis sets for molecular applications

Gaussian basis sets for molecular applications

Attractive electron–electron interactions within robust local fitting approximations

A distance-dependent parameterization of the extended Hubbard model for conjugated and aromatic hydrocarbons derived from stretched ethene

Contact Info

Product

Resources

About