Analytical gradient for the domain-based local pair natural orbital second order Møller-Plesset perturbation theory method (DLPNO-MP2)

Pinski, Peter; Neese, Frank

doi:10.1063/1.5086544

Cited by 46 publications

(64 citation statements)

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“…Apparently, the conclusion drawn here for OSVs is applicable to that for the relaxation of PNOs. The block-diagonality condition assumed in previous PNO analytical gradients 69,70 implies only a weakly constrained relaxation of PNOs or OSVs. Summing up, the sufficient and necessary conditions by which the relaxation pair ij, arising from the residual contribution R (ij,ij) in the second term of Eq.…”

Section: Osv Relaxation As Perturbed Non-degenerate Singular Value Prmentioning

confidence: 99%

“…We have chosen DTFS and RESVAN molecules out of LB12 set for which the DLPNO-MP2 optimized Si-N and S-S bond distances report quite large errors in Ref. 70 All electrons are correlated in OSV-MP2 calculations, and both OSV-MP2 geometries are well converged for three OSV-MP2 thresholds. It is observed that l osv = 10 −4.5 is necessary in order to reduce the errors below 1.0 pm.…”

Section: Bond Lengthsmentioning

confidence: 99%

“…b DLPNO-MP2 results with frozen core approximation from Ref. 70 c Our results without frozen core approximation.…”

Section: Bond Lengthsmentioning

confidence: 99%

“…66 The PNO-MP2 and PNO-CCSD analytical energy gradients were developed by Hättig 67 and Neese, 68 respectively, without accounting for the relaxation of PNOs. Most recently, the PNO relaxation problem was circumvented for the domain-based local PNO-MP2 (DLPNO-MP2) by enforcing a block-diagonal semi-canonical external pair density matrix which assumes zero off-blocks between the retained and discarded PNO orbitals, 69,70 making the PNO-MP2 energy invariant to the rotation among the kept PNO orbitals. Despite of the preliminary success of DLPNO-MP2 gradient method, several challenges can be also seen.…”

Section: Introductionmentioning

confidence: 99%

“…Here, we implement the exact OSV relaxation as a perturbed eigenvalue problem by using both orthonormality and eigenvalue conditions for perturbed OSVs. The degenerate eigenvalue issue that was concerned 69,70 does not occur to the OSV relaxation vectors for reasons that will be described in our formalism and implementation.…”

Section: Introductionmentioning

confidence: 99%

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Complete OSV-MP2 Analytical Gradient Theory for Molecular Structure and Dynamics Simulations

Zhou

Liang

Yang

2019

J. Chem. Theory Comput.

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We propose an exact algorithm for computing the analytical gradient within the framework of the orbital-specific-virtual (OSV) second-order Møller-Plesset (MP2) theory in resolution-of-identity (RI) approximation. We implement the exact relaxation of perturbed OSVs through sufficient and necessary constraints of the perturbed orthonormality, the perturbed diagonality and the perturbed singular value condition.We explicitly show that the rotation of OSVs within the retained OSV subspace makes no contribution to gradients, as long as the iterative solution of the unperturbed Hylleraas residual equation is well converged. The OSV relaxation is solved as the perturbed non-degenerate singular value problem between the retained and discarded OSV subspaces. The detailed derivation and preliminary implementations for gradient working equations are discussed. The coupled-perturbed localization method is implemented for meta-Löwdin localization function. The numerical accuracy of computed OSV-MP2 gradients is demonstrated for the geometries of selected molecules that are often discussed in other theories. From OSV-MP2 with the normal OSV selection, the † Equal contributions 1 arXiv:1908.03674v1 [physics.chem-ph] 10 Aug 2019 canonical RI-MP2/def2-TZVP gradients can be reproduced within 10 −4 a.u. The OSV-MP2/def2-TZVPP covalent bond lengths, angles and dihedral angles are in good agreement with canonical RI-MP2 structures by 0.017 pm, 0.03 • and 0.2 • , respectively. No particular accuracy gains have been observed for molecular geometries compared to the recent local pair-natural-orbital MP2 by using the predefined orbital domains. Moreover, the OSV-MP2 analytical gradients can generate atomic forces that are utilized to drive the Born-Oppenheimer molecular dynamics (BOMD) simulation for studying structural and vibrational properties with respect to OSV selections. By performing the OSV-MP2 N V E BOMD calculation using the normal OSV selection, the structural and vibrational details of protonated water cations are well reproduced. The 200 picoseconds N V T well-tempered metadynamics at 300 K has been simulated to compute the OSV-MP2 rotational free energy surface of coupled hydroxyl and methyl rotors for ethanol molecule.

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Section: Osv Relaxation As Perturbed Non-degenerate Singular Value Prmentioning

confidence: 99%

Section: Bond Lengthsmentioning

confidence: 99%

“…b DLPNO-MP2 results with frozen core approximation from Ref. 70 c Our results without frozen core approximation.…”

Section: Bond Lengthsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Complete OSV-MP2 Analytical Gradient Theory for Molecular Structure and Dynamics Simulations

Zhou

Liang

Yang

2019

J. Chem. Theory Comput.

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Empirical Double‐Hybrid Density Functional Theory: A ‘Third Way’ in Between WFT and DFT

Martin

Santra

2019

Israel Journal of Chemistry

175

227

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Double hybrid density functional theory arguably sits on the seamline between wavefunction methods and DFT: it represents a special case of Rung 5 on the "Jacob's Ladder" of John P. Perdew. For large and chemically diverse benchmarks such as GMTKN55, empirical double hybrid functionals with dispersion corrections can achieve accuracies approaching wavefunction methods at a cost not greatly dissimilar to hybrid DFT approaches, provided RI-MP2 and/ or another MP2 acceleration techniques are available in the electronic structure code. Only a half-dozen or fewer empirical parameters are required. For vibrational frequencies, accuracies intermediate between CCSD and CCSD(T) can be achieved, and performance for other properties is encouraging as well. Organometallic reactions can likewise be treated well, provided static correlation is not too strong. Further prospects are discussed, including range-separated and RPA-based approaches.These are not the final page numbers! �� quantum Monte Carlo results [18] for uniform electron gases. The LDA XC functional only depends on the electronic density and not on any derivatives nor any other entities.Rung two corresponds to GGAs or generalized gradient approximations, in which the reduced density gradient is introduced in the XC functional. Examples are the popular BP86 [19,20] and PBE [21] functionals.Rung three consists of meta-GGAs (mGGAs), which additionally involve higher density derivatives (or the kinetic energy density, which contains similar information to the density Laplacian). TPSS [22] is a popular meta-GGA, as is the recent SCAN (strongly constrained and appropriate normed [23] ).Rungs two and three are often collectively referred to as semi-local functionals.Orbital-dependent DFT [24] covers rungs four and five: on rung four, only occupied orbital-dependency is introduced, while on rung five the unoccupied orbitals make their appearance. The most important rung four functionals are the hybrids, which can be further subdivided into four subclasses: * global hybrid GGAs, such as the popular B3LYP [25,26] and PBE0 [27] hybrids, as well as B97-1. [28] (We note that Hartree-Fock theory itself is a special case, with 100 % exact exchange and null correlation.) * global hybrid meta-GGAs, such as M06, [29] M06-2X, [29] and BMK [30] * range-separated hybrid GGAs, such as CAM-B3LYP [31] and ωB97X-V [32] * range-separated hybrid meta-GGAs, such as ωB97M-V [33] This leaves rung five, of which we will presently consider one subcase, the double hybrids. More general reviews have been published earlier; [34][35][36] the present review will focus primarily on our own work, as well as the broader context.

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Software update: The ORCA program system—Version 5.0

Neese

2022

WIREs Comput Mol Sci

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Analytical gradient for the domain-based local pair natural orbital second order Møller-Plesset perturbation theory method (DLPNO-MP2)

Cited by 46 publications

References 147 publications

Complete OSV-MP2 Analytical Gradient Theory for Molecular Structure and Dynamics Simulations

Complete OSV-MP2 Analytical Gradient Theory for Molecular Structure and Dynamics Simulations

Empirical Double‐Hybrid Density Functional Theory: A ‘Third Way’ in Between WFT and DFT

Software update: The ORCA program system—Version 5.0

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