On the convergence of the M�ller-Plesset perturbation series

Handy, Nicholas C.; Knowles, Peter J.; Somasundram, K.

doi:10.1007/bf00698753

Cited by 305 publications

(132 citation statements)

References 8 publications

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“…The Pople approximation energy was thus enhanced to approximately 0.001 E h . The result is in agreement with that of Handy, et al [7]; the Pople approximation performs well at the RHF calculation of H 2 O carried out at the equilibrium geometry. Meanwhile, the reported convergence rates at the considered basis sets confirm that they are basis set size independent.…”

Section: Lithium Hydride [2ns ][(N )S ] [2ns ][(N +1)s ] and [2ns ][supporting

confidence: 91%

“…As stated in the introduction, Møller-Plesset perturbation energies, up to as much as the 48th order have been calculated by Handy et al [7], where the higher order terms were calculated on the basis of a developed vectorized full-configuration interaction algorithm [15] for the RHF orbitals with a slight adjustment for the UHF case. Since the systematic sequences of even-tempered basis sets of Gaussian type functions of s-symmetry are restricted Hartree-Fock solution, restricted Møller-Plesset perturbation energies of the nth order, where n = 2-4 are calculated from explicit mathematical expressions implemented in several GAUSSIAN packages.…”

Section: The Convergence Of Møller-plesset Perturbation Seriesmentioning

confidence: 99%

“…Handy et al [7] found that the Pople approximation is as good as the Padé [3,2] approximant, in general terms, and is of course much easier to calculate, because it does not rely on E (5) . In (4) is given in the last column.…”

Section: Lithium Hydride [2ns ][(N )S ] [2ns ][(N +1)s ] and [2ns ][mentioning

confidence: 99%

“…Møller-Plesset perturbation energies, up to as much as 48th order, have been calculated by Handy et al [7]. Investigations into the convergence of the Møller-Plesset perturbation series [8] for the energy of a molecule have also been reported [9].…”

Section: Introductionmentioning

confidence: 99%

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Converged Hartree‐Fock and electron correlation calculations using systematically constructed basis sets of primitive Gaussian type functions of s‐symmetry

Shalabi

1996

Elect J Theoret Chem

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SUMMARYThe convergence of the matrix Hartree-Fock energies of Li + , H − and LiH prototype systems and electron correlation energies of LiH are studied when a systematic procedure for the construction of even-tempered basis sets of primitive Gaussian type functions of s-symmetry is employed. It is shown that an accuracy approaching the sub-µ Hartree level can be achieved for the total energies of Li + , H − and LiH within the Hartree-Fock approximation. While an accuracy approaching the sub-µ Hartree level can be achieved for the total energy of LiH within the Møller-Plesset perturbation level, an accuracy approaching the µ Hartree level can be achieved within the configuration interaction level. The Hartree-Fock energies of LiH approach the saturation faster than do the electron correlation energies. The convergence of Møller-Plesset perturbation series was basis set size dependent, but the convergence rate and the related Pople approximation were basis set size independent.

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Section: Lithium Hydride [2ns ][(N )S ] [2ns ][(N +1)s ] and [2ns ][supporting

confidence: 91%

Section: The Convergence Of Møller-plesset Perturbation Seriesmentioning

confidence: 99%

Section: Lithium Hydride [2ns ][(N )S ] [2ns ][(N +1)s ] and [2ns ][mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Converged Hartree‐Fock and electron correlation calculations using systematically constructed basis sets of primitive Gaussian type functions of s‐symmetry

Shalabi

1996

Elect J Theoret Chem

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“…First, there is no guarantee that a perturbation series will be wellbehaved, [40] and indeed, divergence has been noted. [41] In the latter study of the Ne atom, divergence was due to intruder states and occurred with the addition of diffuse functions to the cc-pVDZ basis set (i.e., aug-cc-pVDZ).…”

Section: Om P Ut At I Ona L M Eth Od Smentioning

confidence: 99%

The effects of higher orders of perturbation theory on the correlation energy of atoms and bonds in molecules

Vincent

Silva

McDonagh

et al. 2017

Int J of Quantum Chemistry

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We examine, for the first time, the effects of higher orders of Møller-Plesset perturbation theory on the individual atoms within a molecule and the bonds between them, via the topological energy partitioning method of interacting quantum atoms. In real terms (i.e., not by absolute value) MP3 decreases the correlation energy of a bond, and MP4SDQ also decreases the energy of the atoms at either end of the bond. In addition, we investigated long-range through-space dispersive effects on a H 2 oligomer. Overall, MP3 is the largest correction to the correlation energy, and most of that energy is allocated to chemical bonds, reducing their values in actual terms. The MP4SDQ bond correlation correction, despite being relatively small, tends to have two effects: (i) for small or negative correlation energies MP4SDQ tends to decrease the bond correlation values even more, and (ii) for large (positive) bond correlation energies MP4SDQ tends to restore the bond correlation energies from the MP3 back toward the MP2 values. Furthermore, each individual part of a molecule or complex (atom or bond) has a specific convergence pattern for the MPn series: throughspace interactions converge at MP2 but bonds converge at MP3 level. The atomic correlation energy appears to head toward convergence at the MP4 level.glycine, interacting quantum atoms, MPn, QTAIM, quantum chemical topology | I N TR ODU C TI ONThe electron correlation problem is a well-studied field of research with many solutions as to how this residual post-Hartree-Fock energy can be obtained. While accurate and computationally efficient solutions serve the cause of making reliable chemical predictions of energy and geometry, they do not offer chemical insight. If one is interested in chemical insight originating from electron correlation energies then their atomic partitioning is a manifest starting point. An option amongst several possible partitioning methods is that of quantum chemical topology (QCT). [1][2][3][4][5] QCT introduces topological atoms, which are space-filling objects defined without parameters, a hallmark of minimality. Central to QCT are so-called separatrices, which are natural sharp boundaries occurring in a vector field. The vectors in this field are typically gradient vectors but not always. [6] These separatrices partition real space into subspaces; if they partition the electron density then the subspaces are the topological atoms.Very recently QCT has been used to partition the correlation energy of a system (i.e., molecule or molecular complex) such that the correlation energy of an atom or a bond was successfully obtained. [7][8][9][10] The approach that makes this partitioning possible, under the umbrella of QCT, is called interacting quantum atoms (IQA). [11] This topological "energy decomposition analysis" (EDA) does not suffer from the conceptual and numerical problems associated with older EDA schemes, [12,13] as recently reviewed. [14] IQA rigorously defines the primary energy contributions from which all chemical phenomena f...

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Density functional study of isomerization of fluoro- and chloroformaldehyde radical cations

Ventura¹,

Kieninger²,

Coitiño³

1996

J. Comput. Chem.

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On the convergence of the M�ller-Plesset perturbation series

Cited by 305 publications

References 8 publications

Converged Hartree‐Fock and electron correlation calculations using systematically constructed basis sets of primitive Gaussian type functions of s‐symmetry

Converged Hartree‐Fock and electron correlation calculations using systematically constructed basis sets of primitive Gaussian type functions of s‐symmetry

The effects of higher orders of perturbation theory on the correlation energy of atoms and bonds in molecules

Density functional study of isomerization of fluoro- and chloroformaldehyde radical cations

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