Computational experience with quadratically convergent minimisation methods

Murtagh, Bruce A.; Sargent, R. W. H.

doi:10.1093/comjnl/13.2.185

Cited by 332 publications

(61 citation statements)

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“…ever, lead to a greater stability of 15c vs. 15b (Table V) Experimental results for the preferred tautomers of 2-and 4-hydroxyquinoline (16,17) are contradictory: while calorimetric measurements of methyltropic isomers gave a slightly greater stability (0.3 kcal mol-') for 16a than for its lactam form,13b results of both mass22 as well as photoelectron s p e c t r o s c~p i c a l~~~ investigations were interpreted by the sole existence of the lactam tautomers 16b and 17b for both compounds in the gas phase. However, in a recent mass spectroscopical investigation based on the kinetic energy release associated with metastable ion fragmentation it was concluded that 2-hydroxyquinoline is the only isomer of hydroxyquinolines for which significant amounts of the quinolone form are present in the gas phase.31 Results of mass spectroscopical investigations on 2,kdihydroxyquinoline (18) were interpreted in terms of the presence of both lactam as well as lactim tautomers with a slight preference for the latter ones.32 However, application of mass spectroscopical fragmentation patterns to the study of tautomeric equilibria relies on the assumption of the same order of stabilities for neutral as well as ionized tautomeric species.32 In the case of hydroxypyridines the possibility of a shift of the tautomeric equilibria in their cation radicals has been discussed. 33 Given these experimental uncertainties the results of AM1 as well as MNDO-PM3 calculations for compounds 16-18 are quite acceptable.…”

Section: Am1mentioning

confidence: 99%

Tautomeric equilibria of heterocyclic molecules. A test of the semiempirical AM1 and MNDO‐PM3 methods

Fabian

1991

J Comput Chem

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Tautomeric equilibria (mainly of the lactam-lactim type) for a rather large number of six-membered heterocyclic molecules are calculated by the semiempirical AM1, MNDO-PM3, and MNDO methods. Except for compounds with adjacent pyridine-like lone pairs both AM1 as well as MNDO-PM3 give rather reliable predictions for relative stabilities of the various tautomeric species-comparable to quite high level ab initio calculations. The known errors associated with MNDO in the treatment of heterocyclic tautomerism are thus largely corrected in AM1 as well as MNDO-PM3. For 2-hydroxypyridine-pyrid-2(lH)-one the effect of self-association is less satisfactorily described by MNDO-PM3 than by AM1. MNDO-PM3 calculated relative stabilities of methylated derivatives are, however, in considerably closer agreement with experimental values than those obtained by AM1. Ionization potentials, especially those for lone-pair orbitals, are overestimated by all three semiempirical methods. MNDO-PM3 results for nitrogen lone-pair orbital energies are slightly better than those obtained by the AM1 or MNDO method.

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Section: Am1mentioning

confidence: 99%

Tautomeric equilibria of heterocyclic molecules. A test of the semiempirical AM1 and MNDO‐PM3 methods

Fabian

1991

J Comput Chem

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“…In the present paper the keto-enol tautomerism for the parent cyclopropanone and its enol counterpart together with stepwise fluorination, have been reinvestigated by the MINDO-Forces method [17], whereby the molecular energy of the compounds obtained from the semiempirical MINDO/3 MO [18] was completely minimized by the Murtagh-Sargent technique [19]. The derivative of the energy was calculated according to Pulay's Force method [20].…”

Section: Introductionmentioning

confidence: 99%

A Theoretical Study of Substituted Stepwise Fluorinated Cyclopropanone Keto-Enol System

El‐Alali¹,

Marashdeh²,

Khalil

2003

Zeitschrift Für Naturforschung A

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MINDO-Forces calculations have been performed with complete optimization of the geometries on stepwise fluorinated cyclopropanones and their enols. Increase in the number of fluorine atoms causes destabilization of cyclopropanone. Perfluorinated enol was found to be present in substantial concentration, as was mentioned in previous work. This is supported by calculations of Gibbs free energies and isodesmic reactions. Geometrical parameters, heats of formation, electron densities, dipole moments and orbital energies (HOMO-LUMO) are reported.

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“…A competitive update which converges to the true Hessian on a quadratic surface without an exact linesearch is the symmetric rank-one update by Murtagh and Sargent [116]. This update is given by…”

Section: Quasi-newton Methodsmentioning

confidence: 99%

Numerical Methods for Electronic Structure Calculations of Materials

Saad¹,

Chelikowsky²,

Shontz³

2010

SIAM Rev.

273

166

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The goal of this article is to give an overview of numerical problems encountered when determining the electronic structure of materials and the rich variety of techniques used to solve these problems. The paper is intended for a diverse scienti£c computing audience. For this reason, we assume the reader does not have an extensive background in the related physics. Our overview focuses on the nature of the numerical problems to be solved, their origin, and on the methods used to solve the resulting linear algebra or nonlinear optimization problems. It is common knowledge that the behavior of matter at the nanoscale is, in principle, entirely determined by the Schrödinger equation. In practice, this equation in its original form is not tractable. Successful, but approximate, versions of this equation, which allow one to study nontrivial systems, took about £ve or six decades to develop. In particular, the last two decades saw a ¤urry of activity in developing effective software. One of the main practical variants of the Schrödinger equation is based on what is referred to as Density Functional Theory (DFT). The combination of DFT with pseudopotentials allows one to obtain in an ef£cient way the ground state con£guration for many materials. This article will emphasize pseudopotentialdensity functional theory, but other techniques will be discussed as well.

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Computational experience with quadratically convergent minimisation methods

Cited by 332 publications

References 0 publications

Tautomeric equilibria of heterocyclic molecules. A test of the semiempirical AM1 and MNDO‐PM3 methods

Tautomeric equilibria of heterocyclic molecules. A test of the semiempirical AM1 and MNDO‐PM3 methods

A Theoretical Study of Substituted Stepwise Fluorinated Cyclopropanone Keto-Enol System

Numerical Methods for Electronic Structure Calculations of Materials

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