A scaling PNO–MP2 method using a hybrid OSV–PNO approach with an iterative direct generation of OSVs<sup>†</sup>

Schmitz, Gunnar; Helmich, Benjamin; Hättig, Christof

doi:10.1080/00268976.2013.794314

Cited by 61 publications

(61 citation statements)

References 58 publications

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“…Therefore, approximate amplitudes have to be used. Three approximations can be made at this stage: The initial amplitudes are not computed in the full virtual basis, but in pair‐specific domains [ ij ] of PAOs or OSVs . These domains are orthogonalized and made pseudo‐canonical (PC), which means that the orbitals diagonalize the Fock matrix in the subspace of the domain,

f_{ab}^{ij} = ɛ_{a}^{ij} δ_{ab}

for a , b ∈ [ ij ].…”

Section: Theorymentioning

confidence: 99%

“…PNOs are employed to span the domains, which minimizes the domain sizes that are necessary to achieve a certain accuracy relative to the corresponding canonical method. The use of PNOs in local correlation methods has been pioneered by Neese and coworkers, and has also been investigated by Hättig and coworkers . Our method is most similar to the domain‐based local pair natural orbital coupled‐cluster methods [DLPNO‐CCSD(T)] of Riplinger, Neese and coworkers .…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Explicitly correlated local coupled‐cluster methods using pair natural orbitals

Werner

2018

WIREs Comput Mol Sci

183

263

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Recently developed explicitly correlated local coupled-cluster methods [PNO-LCCSD(T)-F12] are reviewed. Extensive benchmarks for reaction energies and intermolecular interaction energies are presented, in which the convergence of the results with respect to all local approximations is studied. The explicit correlation treatment (F12) is shown to be essential to minimize basis set incompleteness errors, as well as errors caused by domain approximations. Generally, the errors of relative energies due to local approximations can be reduced to below 1 kcal/mol. The methods are well parallelized, and using small computer clusters with 100-200 computing cores, calculations for systems with 100-200 atoms using augmented triple-ζ basis sets can be carried out within a few hours of elapsed time. Recommendations are made on how such calculations should be carried out, how the accuracy can be tested, and which computational resources are required. This article is categorized under: Electronic Structure Theory> Ab Initio Electronic Structure Methods Software> Quantum Chemistry K E Y W O R D S explicit correlation, coupled cluster, local correlation, pair natural orbitals 1 | INTRODUCTIONThe coupled-cluster method with single and double excitations and a perturbative treatment of triple excitations [CCSD(T)] is considered the gold standard of quantum chemistry for computing energies and other properties of molecules. Often, the accuracy is comparable or even better than that of experimental data, and chemical accuracy (1 kcal/mol or better for relative energies) can be achieved, provided that the system under consideration is of single-reference character, that is, the Hartree-Fock (HF) Slater determinant dominates the total wave function expansion. However, in its traditional canonical form, the application of the CCSD(T) method is limited to rather small systems (20-30 atoms) due to the steep increase of the computational effort with system size: The central processing unit (CPU) time scales as O N 7 el

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f_{ab}^{ij} = ɛ_{a}^{ij} δ_{ab}

for a , b ∈ [ ij ].…”

Section: Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Explicitly correlated local coupled‐cluster methods using pair natural orbitals

Werner

2018

WIREs Comput Mol Sci

183

263

View full text Add to dashboard Cite

show abstract

“…[55][56][57][58][59][60] These methods have nowadays regained popularity being formulated through a pair natural orbital (PNO), local pair natural orbital (LPNO), and domain-based local pair natural orbital (DLPNO) approximations, 61-66 as well as through explicitly correlated local methods [67][68][69] or by employing the orbital-specific virtual (OSV) approach. [70][71][72] The list is by no means exhaustive as the field has dramatically progressed over the last two decades, being mainly applied to single-reference coupled-cluster and second-and third-order MP ground state methods, even though some recent implementations on CC2 and ADC (2) have been reported, [73][74][75] as well as the first PNO implementation for multireference coupled-cluster to our knowledge. 76 The particular approximation to be employed in the present manuscript, based on the frozen natural orbital (FNO) approach, was introduced in the seventies.…”

Section: Introductionmentioning

confidence: 98%

Multiconfigurational Second-Order Perturbation Theory with Frozen Natural Orbitals Extended to the Treatment of Photochemical Problems

Segarra‐Martí

Garavelli

Aquilante

2015

J. Chem. Theory Comput.

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A new flavor of the frozen natural orbital complete active space second-order perturbation theory method (FNO-CASPT2, Aquilante et al., J. Chem. Phys. 131, 034113) is proposed herein. In this new implementation, the virtual space in Cholesky decomposition-based CASPT2 computations (CD-CASPT2) is truncated by excluding those orbitals that contribute the least toward preserving a predefined value of the trace of an approximate density matrix, as that represents a measure of the amount of dynamic correlation retained in the model. In this way, the amount of correlation included is practically constant at all nuclear arrangements, thus allowing for the computation of smooth electronic states surfaces and energy gradients-essential requirements for theoretical studies in photochemistry. The method has been benchmarked for a series of relevant biochromophores for which large speed-ups have been recorded while retaining the accuracy achieved in the corresponding CD-CASPT2 calculations. Both vertical excitation energies and gradient calculations have been carried out to establish general guidelines as to how much correlation needs to be retained in the calculation for the results to be consistent with the CD-CASPT2 findings. Our results feature errors within a tenth of an eV for the most difficult cases and have been validated to be used for gradient computations where an up to 3-fold speed-up is observed depending on the size of the system and the basis set employed.

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“…While the PAO basis allows for significant reductions in terms of the number of CC amplitudes to consider, the virtual parameter space may be further compressed using pair natural orbitals (PNOs), which are constructed from (an approximation to) the MP2 correlation density matrix for each electron pair. For example, the domain‐based local PNO (DLPNO) CCSD(T) method has been used successfully for many applications within computational chemistry .…”

Section: Local Correlation Methodsmentioning

confidence: 99%

The divide–expand–consolidate coupled cluster scheme

Kjærgaard

Baudin

Bykov

et al. 2017

WIREs Comput Mol Sci

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The Divide‐Expand‐Consolidate (DEC) scheme is a linear‐scaling and massively parallel framework for high accuracy coupled cluster (CC) calculations on large molecular systems. It is designed as a black‐box method, which ensures error control in the correlation energy and molecular properties. DEC is combined with a massively parallel implementation to fully utilize modern manycore architectures providing a fast time to solution. The implementation ensures performance portability and will straightforwardly benefit from new hardware developments. The DEC scheme has been applied to several levels of CC theory and extended the range of application of those methods. WIREs Comput Mol Sci 2017, 7:e1319. doi: 10.1002/wcms.1319 This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods Software > Quantum Chemistry

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A scaling PNO–MP2 method using a hybrid OSV–PNO approach with an iterative direct generation of OSVs^†

Cited by 61 publications

References 58 publications

Explicitly correlated local coupled‐cluster methods using pair natural orbitals

Explicitly correlated local coupled‐cluster methods using pair natural orbitals

Multiconfigurational Second-Order Perturbation Theory with Frozen Natural Orbitals Extended to the Treatment of Photochemical Problems

The divide–expand–consolidate coupled cluster scheme

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A scaling PNO–MP2 method using a hybrid OSV–PNO approach with an iterative direct generation of OSVs†

Cited by 61 publications

References 58 publications

Explicitly correlated local coupled‐cluster methods using pair natural orbitals

Explicitly correlated local coupled‐cluster methods using pair natural orbitals

Multiconfigurational Second-Order Perturbation Theory with Frozen Natural Orbitals Extended to the Treatment of Photochemical Problems

The divide–expand–consolidate coupled cluster scheme

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A scaling PNO–MP2 method using a hybrid OSV–PNO approach with an iterative direct generation of OSVs^†