Extrapolation of Hartree–Fock and multiconfiguration self-consistent-field energies to the complete basis set limit

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

doi:10.1007/s00214-016-2016-4

Cited by 36 publications

(45 citation statements)

References 44 publications

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“…A behavior similar to that observed for the correlation energy is encountered for the total energy; all extrapolations are performed with HF‐E( x 1 , x 2 ) and USTE( x 1 , x 2 ) for the HF and correlation energy contributions, respectively. The HF‐E( x 1 , x 2 ) scheme previously developed for V X Z basis sets is then assumed to perform adequately with AV X Z. Table presents the statistics of the total energy, with the reference being approximated by the sum of the HF‐E( h , s )‐ and USTE( p , h )‐extrapolated energies (for the HF and correlation contributions, respectively).…”

Section: Resultsmentioning

confidence: 59%

“…Of course, as neither CCSD(T) nor CCSD(T)‐F12 are variational, it is unclear which is the more accurate solution. Also notable is the fact that both HF‐E and HF‐GE extrapolation schemes yield results for the HF/V X Z‐F12 energy, including CABS, fairly close to each other despite the fact that the hierarchical numbers are here roughly approximated by the V X Z ones.…”

Section: Resultsmentioning

confidence: 86%

“…To test the novel basis sets in open‐shell and ionic molecules, 44 systems used in previous work have been considered. Figure and Tables and show the corresponding absolute deviations both at MP2 and CCSD levels of theory.…”

Section: Resultsmentioning

confidence: 99%

“…Similarly, using the HF‐E( x 1 , x 2 ) scheme to CBS extrapolate the Hartree‐Fock (HF) component of the energy, one obtains:

E_{CBS}^{HF} = E_{x_{2}}^{HF} + \frac{e^{β x_{1}}}{e^{β x_{2}} - e^{β x_{1}}} ((), E_{x_{2}}^{HF} - E_{x_{1}}^{HF}),

where x i = d , t , q , p , and h are the hierarchical numbers at the HF level …”

Section: Methodsmentioning

confidence: 99%

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Optimal diffuse augmented atomic basis sets for extrapolation of the correlation energy

Varandas

Pansini

2019

Int J of Quantum Chemistry

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We seek correlation‐consistent diffuse‐augmented double‐zeta and triple‐zeta basis sets that perform optimally in extrapolating the correlation energy to the one‐electron complete basis set limit, denoted oAVXZ and oAV(X + d)Z. The novel basis sets are method‐dependent in that they are trained to perform optimally for the correlation energy at each specific level of theory. They are shown to yield accurate results in calculating both the energy and tensorial properties such as polarizabilities while not significantly altering the Hartree‐Fock energy. Quantitatively, complete basis set limit (CBS)‐/(oAVdZ,oAVtZ)‐extrapolated correlation energies typically outperform, by 3‐ to 5‐fold, the ones calculated with traditional ansatzes of similar flexibility. Attaining energies of CBS/(AVtZ,AVqZ) type or better accuracy, they frequently outperform expensive raw explicitly correlated ones. Promisingly, a limited test on CBS‐extrapolated energies based on conventional basis sets has shown that they compare well even with extrapolated explicitly correlated ones. Calculated atomization and dissociation energies, molecular geometries, ionization potentials, and electron affinities also tend to outperform the ones obtained with traditional Dunning's ansatzes from which the new basis sets have been determined. The method for basis set generation is simple, and there is no reason of principle why the approach could not be adapted for handling other bases in the literature.

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Section: Resultsmentioning

confidence: 59%

Section: Resultsmentioning

confidence: 86%

Section: Resultsmentioning

confidence: 99%

“…Similarly, using the HF‐E( x 1 , x 2 ) scheme to CBS extrapolate the Hartree‐Fock (HF) component of the energy, one obtains:

E_{CBS}^{HF} = E_{x_{2}}^{HF} + \frac{e^{β x_{1}}}{e^{β x_{2}} - e^{β x_{1}}} ((), E_{x_{2}}^{HF} - E_{x_{1}}^{HF}),

where x i = d , t , q , p , and h are the hierarchical numbers at the HF level …”

Section: Methodsmentioning

confidence: 99%

See 2 more Smart Citations

Optimal diffuse augmented atomic basis sets for extrapolation of the correlation energy

Varandas

Pansini

2019

Int J of Quantum Chemistry

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“…We employ our own HF‐CBS protocol for HF extrapolations from DZ and TZ or TZ and QZ bases, denoted (d,t) and (t,q); X=D, T … are cardinal numbers, whereas x =d, t … are the corresponding hierarchical numbers. These dual‐level extrapolations are of the form A + B exp(− γx ), with the CBS energy obtained from a protocol (see the Supporting Information) believed to yield (d,t) absolute energies converged to a root‐mean‐square error <0.5 kJ mol −1 ; thence satisfactory for the present purposes. The expectations are that convergence gets tighter and tighter with increasing pairs of hierarchical numbers.…”

Section: Introductionmentioning

confidence: 73%

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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Molecules under external electric field: On the changes in the electronic structure and validity limits of the theoretical predictions

2018

Self Cite

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A detailed analysis of the electronic structure of the ground and first excited spin state of three diatomic molecules ( N2, BH and CO) under static applied electric field is performed at CCSD(T), DFT, MRCI and MRCI(Q) levels of theory. Our findings have revealed that by boosting the applied field one induces changes in the occupation numbers of molecular orbitals, giving rise to changes in the equilibrium geometry and in the HOMO-LUMO energy gap. Specifically, singlet to triplet spin transition can be induced by increasing the applied electric field beyond a critical value. Accordingly, affecting the accuracy of the widely used expression of energy expanded in Taylor series with respect to the applied electric field. © 2018 Wiley Periodicals, Inc.

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Extrapolation of Hartree–Fock and multiconfiguration self-consistent-field energies to the complete basis set limit

Cited by 36 publications

References 44 publications

Optimal diffuse augmented atomic basis sets for extrapolation of the correlation energy

Optimal diffuse augmented atomic basis sets for extrapolation of the correlation energy

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

Molecules under external electric field: On the changes in the electronic structure and validity limits of the theoretical predictions

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