Toward a unified single-parameter extrapolation scheme for the correlation energy: Systems formed by atoms of hydrogen through neon

Pansini, F.N.N.; Varandas, A. J. C.

doi:10.1016/j.cplett.2015.04.052

Cited by 25 publications

(23 citation statements)

References 37 publications

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“…The extrapolation formula has been shown to be a simple polynomial formula including a term inversely proportional to the third power of X , which has been proposed by Helgaker and coworkers . The extrapolation can normally be performed by the one‐ or two‐parameter schemes to predict the correlation energy at the CBS limit. However, it is known that the energy calculated with the double‐zeta (DZ) basis set is not located in the extrapolation curve.…”

Section: Introductionmentioning

confidence: 99%

Informatics‐Based Energy Fitting Scheme for Correlation Energy at Complete Basis Set Limit

Seino

Nakai

2016

J Comput Chem

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Energy fitting schemes based on informatics techniques using hierarchical basis sets with small cardinal numbers were numerically investigated to estimate correlation energies at the complete basis set limits. Numerical validations confirmed that the conventional two-point extrapolation models can be unified into a simple formula with optimal parameters obtained by the same test sets. The extrapolation model was extended to two-point fitting models by a relaxation of the relationship between the extrapolation coefficients or a change of the fitting formula. Furthermore, n-scheme fitting models were developed by the combinations of results calculated at several theory levels and basis sets to compensate for the deficiencies in the fitting model at one level of theory. Systematic assessments on the Gaussian-3X and Gaussian-2 sets revealed that the fitting models drastically reduced errors with equal or smaller computational effort. © 2016 Wiley Periodicals, Inc.

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Section: Introductionmentioning

confidence: 99%

Informatics‐Based Energy Fitting Scheme for Correlation Energy at Complete Basis Set Limit

Seino

Nakai

2016

J Comput Chem

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“…Other accurate methodologies have been applied to describe the CBS energy, such as the methods referred to as: USPE, USTE, GUSTE, OAN(C), and OAN(P) . The first one requires calculations at a single level of theory, whereas the others use formulas to be adjusted with calculations from two levels.…”

Section: Introductionmentioning

confidence: 99%

“…The first one requires calculations at a single level of theory, whereas the others use formulas to be adjusted with calculations from two levels. The USPE method is based on the formula:

E_{CBS}^{corr} = E_{X}^{corr} + A ((), E_{X}^{italictot}) / x^{3}

, where x represents a hierarchical series based on the cardinality, D, T, Q, 5‐zeta, and 6‐zeta, and

E_{X}^{tot}

is the total energy obtained with the X ‐zeta basis. The USTE method considers the formula:

E_{X}^{corr} = E_{CBS}^{corr} + A_{3} / {(X + α)}^{3} ([], 1 + τ_{53} / {(X + α)}^{2})

, where A 3 and τ 53 are fitted from energies of 23 atoms and molecules at the MP2, CCD, CCSD/VXZ e MRCI(Q)/AVXZ (X = D‐6) levels of theory.…”

Section: Introductionmentioning

confidence: 99%

Assessment of a composite method based on selected density functional theory methods and complete basis set extrapolation formulas

Chinini

Custódio

2019

Int J of Quantum Chemistry

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Extrapolation formulas based on power and exponential formulas, as well as alternatives from a Taylor series, were tested and used with density functional theory (DFT) for the calculation of enthalpies of formation. The following four functionals were analyzed: B3LYP, BMK, M06‐2X, and B2PLYP. Preliminary tests pointed to B2PLYP and B3LYP as the best and worst functionals, respectively. Taylor series expressions were as accurate as the power formulas and presented better performance than the exponential equation. The power formula (Equation (2)) and one of the simplest Taylor expressions (Equation (13)) were selected for the calculations with B3LYP and B2PLYP, with further empirical adjustments based on the higher level correction (HLC) and scaling of the experimental atomization energies used to calculate enthalpies of formation. HLC improved the B3LYP mean absolute error (MAE) from approximately 4.3 to 3.5 kcal mol−1 using both extrapolation alternatives. For B2PLY, the MAEs were improved from 2.7 to 2.6 kcal mol−1. Regarding the G3/05 test set, a significant improvement in the MAEs around 2.5 and 1.5 kcal mol−1 were achieved using B3LYP and B2PLYP, respectively. The accuracy obtained from these empirical corrections was equivalent to other composite methods. The MAEs from B3LYP and B2PLYP may be suggested as ranges for the possible accuracy to be achieved by some DFT methods. The empirical corrections suggested in this work are improvements that may be considered to provide acceptable accuracy for enthalpies of formation and possibly other properties.

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“…The CBS protocol employs the inverse power form,

E_{X}^{cor} = E_{\infty}^{cor} + A_{3} / x^{3}

, in which

E_{normalX}^{cor}

is the correlation energy for cardinal number X, and

E_{\infty}^{cor}

and A are parameters determined from calculations for two affordable hierarchical numbers ( x or X); notably, the hierarchical x values are theory specific . Traditional extrapolation protocols are reliable only when based on X values typically larger than Q, which makes re‐hierarchization crucial for affordability (use of D and T bases or just D or T; the number of basis functions scales as X 3 ). Thus, the protocol utilized herein also assumes a popular form (see the Supporting Information) that has been shown to yield accurate results for a variety of systems and methods …”

Section: Introductionmentioning

confidence: 99%

“…As af airly clear goal to pursue, the question may then arise of why it has only now been posed.A si tw ill becomec learl ater,t he major motivation can be attributed to the relatively good performance of extrapolation techniques to yield CBS results. Although the successo f multilevel techniques, such as CBS, is well recognized, [15] the noveltyi si ni ts demonstrated reliability, [16][17][18] even when using the mostc ost-effective MO-correlated single-reference raw energies;t hus allowing au seful comparison with the experimental values.…”

Section: Introductionmentioning

confidence: 99%

Assessing How Correlated Molecular Orbital Calculations Can Perform versus Kohn–Sham DFT: Barrier Heights/Isomerizations

Varandas

González

Montero‐Cabrera

et al. 2017

Chemistry A European J

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To assess the title issue, 38 hydrogen transfer barrier heights and 38 non-hydrogen transfer barrier heights/isomerizations extracted from extensive databases have been considered, in addition to 4 2 p-isomerization reactions and 6 others for large organic molecules. All Kohn-Sham DFT calculations have employed the popular M06-2X functional, whereas the correlated molecular orbital (MO)-based ones are from single-reference MP2 and CCSD(T) methods. They have all utilized the same basis sets, with raw MO energies subsequently extrapolated to the complete basis set limit without additional cost. MP2 calculations are found to be as cost-effective as DFT ones and often slightly more, while showing a satisfactory accuracy when compared with the reference data. Although the focus is on barrier heights, the results may bear broader implications, in that one may see successes and difficulties of DFT when compared with traditional MO theories for the same data.

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Toward a unified single-parameter extrapolation scheme for the correlation energy: Systems formed by atoms of hydrogen through neon

Cited by 25 publications

References 37 publications

Informatics‐Based Energy Fitting Scheme for Correlation Energy at Complete Basis Set Limit

Informatics‐Based Energy Fitting Scheme for Correlation Energy at Complete Basis Set Limit

Assessment of a composite method based on selected density functional theory methods and complete basis set extrapolation formulas

Assessing How Correlated Molecular Orbital Calculations Can Perform versus Kohn–Sham DFT: Barrier Heights/Isomerizations

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