On the performance and parameter problems of approximate molecular orbital theory, with comparative calculations on the carbon monoxide molecule

Roby, Keith R.; Ǧlu, Oktay Sinano

doi:10.1002/qua.560030725

Cited by 5 publications

(21 citation statements)

References 17 publications

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“…Specifically, we proposed a strategy to correct for the errors introduced by the NDDO approximation in the two-electron matrices which was inspired by work of Roby and Sinanoǧlu. 34 The two-electron matrix obtained within the NDDO approximation is modified with a correction matrix obtained from a refer-ence HF, KS-DFT, or multi-configurational SCF calculation. These correction matrices are transferable to a certain degree within sequences of related structures.…”

Section: Discussionmentioning

confidence: 99%

“…However, the NDDO approximation has not found acceptance in ab initio calculations due to the significant errors that it introduced in ERIs in the symmetrically orthogonalized basis. [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51] Instead, the NDDO approximation has become popular in SEMO models where it is combined [2][3][4][5][6][7][8][9] with various other approximations made to the ERIs, to the one-electron matrix, and to the nucleus-nucleus repulsion energy which benefit from mutual error compensation. We refer to Ref.…”

Section: Introductionmentioning

confidence: 99%

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Comprehensive Analysis of the Neglect of Diatomic Differential Overlap Approximation

Husch

Reiher

2018

J. Chem. Theory Comput.

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Many modern semiempirical molecular orbital models are built on the neglect of diatomic differential overlap (NDDO) approximation. An in-depth understanding of this approximation is therefore indispensable to rationalize the success of these semiempirical molecular orbital models and to develop further improvements on them. The NDDO approximation provides a recipe to approximate electron-electron repulsion integrals (ERIs) in a symmetrically orthogonalized basis based on a far smaller number of ERIs in a locally orthogonalized basis. We first analyze the NDDO approximation by comparing ERIs in both bases for a selection of molecules and for a selection of basis sets. We find that the errors in Hartree-Fock and second-order Møller-Plesset perturbation theory energies grow roughly linearly with the number of basis functions. We then examine different approaches to correct for the errors caused by the NDDO approximation and propose a strategy to directly correct for them in the two-electron matrices that enter the Fock operator.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Comprehensive Analysis of the Neglect of Diatomic Differential Overlap Approximation

Husch

Reiher

2018

J. Chem. Theory Comput.

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“…The NDDO approximation,

(〈〉|, ϕ_{μ} ϕ_{ν}, ϕ_{λ} ϕ_{σ}) \approx δ_{IJ} δ_{KL} 〈 χ_{normalμ}^{normalI} χ_{normalν}^{normalJ} | χ_{normalλ}^{normalK} χ_{normalσ}^{normalL} 〉,

specifies how ERIs in the ϕ ‐basis may be approximated based on the values of the respective ERIs in the χ ‐basis. It is not immediately obvious why Equation should hold true, especially in view of Equation , but numerical data suggest that there is some merit to the NDDO approximation . We additionally illustrate the NDDO approximation in Figure for three examples.…”

Section: General Considerations For the Formalism Of Nddo‐semo Modelsmentioning

confidence: 99%

“…Contemporary NDDO‐SEMO models have limitations which cannot be addressed by reparameterization and overcoming these limitations requires the adoption of novel parametric functions. Unfortunately, the NDDO approximation causes large and uncontrollable errors in the ERIs in the ϕ ‐basis and these errors propagate to all quantities calculated on the basis of the ERIs . Contemporary NDDO‐SEMO models counteract the errors by introducing parametric expressions to evaluate the one‐electron matrix and the core‐core repulsion energy, that is, they rely on error cancellation.…”

Section: Implicit Description Of Electron Correlation Effects Throughmentioning

confidence: 99%

“…We recently introduced a strategy to directly correct for the error caused by the NDDO approximation in ϕ G which we call the correction inheritance for semiempirics (CISE) approach. We drew inspiration from the work carried out by Roby and Sinanoǧlu who suggested to scale χ G NDDO with a scaling matrix Γ to obtain a better estimate for ϕ G ,

^{ϕ} bold-italicG \approx Γ^{χ} G^{NDDO} .

The goal of Roby and Sinanoǧlu in 1969 was to speed up single‐point HF calculations for a diverse set of small molecules, and hence, they attempted to define universal rules to assemble Γ which, not surprisingly, turned out to be impossible . It is, however, possible to exactly determine

boldΓ ({{\overset{false˜}{bold-italicR}}_{I}^{n}})

for a given structure

{{\overset{false˜}{bold-italicR}}_{I}^{n}}

from a reference self‐consistent field (ie, HF, KS‐DFT, or general multi‐configurational SCF) calculation (yielding the exact

^{ϕ} bold-italicG ({{\overset{false˜}{bold-italicR}}_{I}^{n}})

\begin{matrix} lefttrue \\ Γ (({}, {\overset{R}{true}}_{normalI}^{normaln})) & =^{ϕ} G (({}, {\overset{R}{true}}_{normalI}^{normaln})) \cdot {((), ^{χ} G^{NDDO} ((), \{{\overset{false˜}{bold-italicR}}_{I}^{n}\}))}^{- 1} . \end{matrix}

Obviously, we will then not achieve a speed‐up with respect to the reference calculation.…”

Section: Implicit Description Of Electron Correlation Effects Throughmentioning

confidence: 99%

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Semiempirical molecular orbital models based on the neglect of diatomic differential overlap approximation

Husch

Vaucher

Reiher

2018

Int J of Quantum Chemistry

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Semiempirical molecular orbital (SEMO) models based on the neglect of diatomic differential overlap (NDDO) approximation efficiently solve the self-consistent field equations by rather drastic approximations. The computational efficiency comes at the cost of an error in the electron-electron repulsion integrals. The error may be compensated by the introduction of parametric expressions to evaluate the electron-electron repulsion integrals, the one-electron integrals, and the core-core repulsion. We review the resulting formalisms of popular NDDO-SEMO models (such as the MNDO(/d), AM1, PMx, and OMx models) in a concise and self-contained manner. We discuss the approaches to implicitly and explicitly describe electron correlation effects within NDDO-SEMO models and we dissect strengths and weaknesses of the different approaches in a detailed analysis. For this purpose, we consider the results of recent benchmark studies. Furthermore, we apply bootstrapping to perform a sensitivity analysis for a selection of parameters in the MNDO model. We also identify systematic limitations of NDDO-SEMO models by drawing on an analogy to Kohn-Sham density functional theory. K E Y W O R D SNDDO approximation, semi-empirical methods | INTRODUCTIONThe driving force for the development of semiempirical molecular orbital (SEMO) models has always been the desire to accelerate quantum chemical calculations. At the outset of the development of SEMO models in the middle of the last century, [1][2][3][4][5][6][7][8][9][10] the goal was to carry out electronic structure calculations for small molecules, which was not routinely possible with ab initio electronic structure methods at that time. Since then, theoretical chemistry has seen a remarkable development not only in terms of computational resources but also in terms of ab initio methodology. [11] One must not forget that most electronic structure methods which we apply routinely today, such as Kohn-Sham density functional theory (KS-DFT) [12] and coupled cluster theory, [13] were developed concurrently with today's SEMO models. As a consequence of algorithmic and methodological developments, [11] accurate ab initio electronic structure methods have long replaced SEMO models in their original areas of application (electronic structure calculations for small molecules). Nevertheless, SEMO models did not become extinct. Instead, they opened up different areas of application which can broadly be divided into three categories (see also Ref. [14] for a recent review): (1) simulations of very large systems such as proteins [15][16][17][18][19][20][21][22] and those with thousands of small molecules, [23,24] (2) calculations for a large number of isolated and unrelated medium-sized molecules, for example, in virtual high-throughput screening schemes for materials discovery [25,26] and docking-and-scoring of potential drug candidates, [27][28][29][30][31][32] and (3) entirely new applications such as real-time quantum chemistry where ultra-fast SEMO models allow the perception of visual and h...

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Extended basis NDDO calculations on diatomic molecules

Gleghorn

McConkey

1982

Theoret. Chim. Acta

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On the performance and parameter problems of approximate molecular orbital theory, with comparative calculations on the carbon monoxide molecule

Cited by 5 publications

References 17 publications

Comprehensive Analysis of the Neglect of Diatomic Differential Overlap Approximation

Comprehensive Analysis of the Neglect of Diatomic Differential Overlap Approximation

Semiempirical molecular orbital models based on the neglect of diatomic differential overlap approximation

Extended basis NDDO calculations on diatomic molecules

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