Resonance integrals in semi-empirical MO theories

Bruijn, S. de

doi:10.1016/0009-2614(78)85248-8

Cited by 27 publications

(8 citation statements)

References 24 publications

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“…2), as introduced by de Bruijn [11,54]. In this case, the AOs can simply be denoted by the atomic label (e.g.…”

Section: Discussion and Qualitative Interpretationmentioning

confidence: 99%

“…neopentane, too unstable by 15.7 kcal/mol in MNDO). In symmetrical clusters [54] one can no longer dierentiate between``bonded'' and``nonbonded'' interactions, and neglect of the orthogonalization corrections may then lead to an underestimation of the steric strain in clusters and small rings (e.g. cubane, too stable by 49.6 kcal/mol in MNDO).…”

Section: Case 2: Weak or Second-neighbor Interactionsmentioning

confidence: 98%

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Orthogonalization corrections for semiempirical methods

Weber

Thiel

2000

Theoretical Chemistry Accounts: Theory, Computation, and Modeli

392

248

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Based on a general discussion of orthogonalization effects, two new one-electron orthogonalization corrections are derived to improve existing semiempirical models at the neglect of diatomic differential overlap level. The first one accounts for valence-shell orthogonalization effects on the resonance integrals, while the second one includes the dominant repulsive core–valence interactions through an effective core potential. The corrections for the resonance integrals consist of three-center terms which incorporate stereodiscriminating properties into the two-center matrix elements of the core Hamiltonian. They provide a better description of conformational properties, which is rationalized qualitatively and demonstrated through numerical calculations on small model systems. The proposed corrections are part of a new general-purpose semiempirical method which will be described elsewhere

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“…2), as introduced by de Bruijn [11,54]. In this case, the AOs can simply be denoted by the atomic label (e.g.…”

Section: Discussion and Qualitative Interpretationmentioning

confidence: 99%

Section: Case 2: Weak or Second-neighbor Interactionsmentioning

confidence: 98%

Orthogonalization corrections for semiempirical methods

Weber

Thiel

2000

Theoretical Chemistry Accounts: Theory, Computation, and Modeli

392

248

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“…The elements of 'b, given by Ah = S-l/2hS-l/2 7 were investigated by Brown and Roby [8] and, with an emphasis on weak interactions, by the present author [12]; in this section some further conclusions are drawn.…”

Section: B ' H In Terms Of Mmentioning

confidence: 83%

Analysis of the inadequacies of some semi‐empirical MO methods as theories of structure and reactivity

Bruijn

1984

Int J of Quantum Chemistry

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Essential defects of present-day semiempirical methods (CNDO/%, CNDO/S, MIND0/3, MNDO) can be identified on two levels. First, the formalism shared by nearly all these methods treats parametric expressions, supposed to refer to Lowdin orthogonalized orbitals, as transferable. At best, this idea is approximately valid for the B functions for strong bonds. Second, the expressions used for these approximately transferable functions are based on inadequate arguments. As a result, the errors in many terms of the energy expression amount to several electron volts. The mechanism of error compensation through the parametrization is investigated in detail and shown to be surprisingly flexible, at least for some combinations of errors. Some cases of systematic absence of compensation are identified, and for weak interactions, e.g., those responsible for the water dimer, the semiempirical expressions appear to be so irrelevant that a detailed analysis of the causes of their failure is no longer possible. Minimal requirements for a correct semiempirical approach are given in the MORBIT rules. The two-center one-electron integral p is to be replaced by a function introduced by Mulliken; an efficient approximation for this expression is proposed. Defining the ProblemIn the past 20 years several semiempirical methods have been designed which can reproduce chosen experimental results for a wide range of molecules by means of a simple computational scheme. As examples 1 mention M I N D O /~ [l], which is suitable for the calculation of equilibrium geometries and heats of formation, and CNDO/S [2], useful in the study of uv spectra. Whenever such a theory is successful in its chosen domain the term "theory of structure" tends to come up, though its meaning is seldom specified. In the present paper I shall use this term exclusively for those methods which not only give good results for, e.g., bondlengths and energies (although such a method qualifies as a useful algorithm) but also explain why the energy assumes a given minimum value when the R are assigned their equilibrium values {Re}. This means that not only E ( R , ) should be correct, but also that the separate terms in the energy expression must be correct as functions of {R}. What I intend to show is that: (a) several popular semiempirical methods cannot be accepted as theories of structure; (b) any useful algorithm which is not a theory of structure ceases to be useful in specified, frequently occurring, circumstances. Now an analysis of the terms in a semiempirical energy expression is subject to some uncertainty because most of these terms are not clearly defined. This is because semiempirical methods try to condense as much information as possible into the few energy terms which are maintained. The formalism corresponds to

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“…Taking

^{ϕ} H_{μ ν}^{MNDO}

to be proportional to χ S μν has a long history and the initial idea is ascribed to Mulliken . In general, Equation was, however, found to be a poor approximation to the analytical value of ϕ H μν , irrespective of the chosen values for

β_{normall ((), μ)}^{Z_{normalI}}

This can be attributed to the fact that ϕ H μν is not necessarily proportional to χ S μν (for an example, see Figure ). Hence, not even the nodal structure of

^{ϕ} H_{μ ν} =^{ϕ} H_{μ ν} ({\overset{false˜}{R}}_{IJ})

is captured correctly.…”

Section: The Modified Neglect Of Diatomic Overlap Modelmentioning

confidence: 99%

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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Resonance integrals in semi-empirical MO theories

Cited by 27 publications

References 24 publications

Orthogonalization corrections for semiempirical methods

Orthogonalization corrections for semiempirical methods

Analysis of the inadequacies of some semi‐empirical MO methods as theories of structure and reactivity

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

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