A Basis for Joint Interoperability

Hamilton, John A.; Murtagh, Jeanne L.; Deal, John C.

doi:10.21236/ada461922

Cited by 5 publications

(9 citation statements)

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“…The r e SE structures were obtained via a weighted least-squares fit to the semiexperimental moments of inertia. It is difficult to estimate the precision of the moments of inertia; thus, the iterative reweighted least-squares method (IRLS) was used. , Huber’s weighting, whereby the residuals e i are gradually weighted down when they are larger than approximately 2 × MAD, was employed. The MAD (mean absolute deviation) is the median | e i – median( e i )|.…”

Section: Methods Of Structure Determinationmentioning

confidence: 99%

Equilibrium Structures of Heterocyclic Molecules with Large Principal Axis Rotations upon Isotopic Substitution

et al. 2011

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Equilibrium structures, r(e), of the heterocyclic molecules oxirane, furazan, furan, ethylene ozonide, and 1,3,4-oxadiazole have been determined using three different, somewhat complementary techniques: a completely experimental technique (r(m)), a semiexperimental technique (r(e)(SE), whereby equilibrium rotational constants are derived from experimental effective ground-state rotational constants and corrections based principally on an ab initio cubic force field), and an ab initio technique (r(e)(BO), whereby geometry optimizations are usually performed at the coupled cluster level of theory including single and double excitations augmented by a perturbational estimate of the effects of connected triple excitations [CCSD(T)] using quadruple-ζ Gaussian basis sets). All these molecules are asymmetric tops with the moment of inertia I(c) much larger than the other two moments of inertia, I(a) and I(b). Molecules of this shape experience a large rotation of the principal axis system upon certain isotopic substitutions. For such isotopologues it is difficult to obtain a good structural fit to the semiexperimental moments of inertia I(a) and I(b), which may significantly reduce the accuracy of the r(e)(SE) structural parameters. The origin of this difficulty is explained. For the heavy-atom skeleton of these molecules it was possible to determine a rather accurate empirical mass-dependent structure without a priori knowledge of the equilibrium structure.

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Section: Methods Of Structure Determinationmentioning

confidence: 99%

Equilibrium Structures of Heterocyclic Molecules with Large Principal Axis Rotations upon Isotopic Substitution

et al. 2011

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“…At each step, an analysis of the residuals permitted checking the appropriateness of the weights and the compatibility of the rotational constants and the predicate observations. It is possible to automate, at least partly, this procedure by using the Iteratively Reweighted Least Squares (IRLS) method, whereby data with large residuals are weighted down. , Two weighting schemes are used: Huber weighting, where the weight linearly decreases as the residual increases, and biweight weighting, where, in addition, data with large residuals are eliminated.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Equilibrium Structures of Three-, Four-, Five-, Six-, and Seven-Membered Unsaturated N-Containing Heterocycles

2014

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Up to six different techniques are utilized to estimate the equilibrium structures (r(e)) of a series of mostly unsaturated, N-containing heterocycles. Accurate Born-Oppenheimer (r(e)(BO)) and, if allowed, semiexperimental (r(e)(SE)), as well as empirical (r(m)-type) estimates of the equilibrium structures of three-membered (1H- and 2H-azirine, aziridine), four-membered (azete), five-membered (pyrrole, pyrazole, imidazole), six-membered (pyridine, pyrimidine, uracil), and seven-membered (1H-azepine) rings, containing usually one but in some cases two N atoms, are determined. The agreement among the structural results of the different techniques is very satisfactory. It is shown that it is possible to use the CCSD(T) electronic structure method with the relatively small wCVTZ basis set, with all electrons correlated, and the effect of further basis set enlargement, wCVTZ → wCVQZ, computed at the MP2 level, to obtain reliable equilibrium structures for the semirigid molecules investigated. Extension to larger basis sets does not significantly improve the accuracy of the computed results. Although all molecules investigated are oblate, and their principal axis system is subject to large rotations upon isotopic substitution, the semiexperimental method, when applicable, provides accurate results, though in the difficult cases it must be augmented with the mixed regression method. Finally, it is noteworthy that the empirical mass-dependent (r(m)) method also delivers surprisingly accurate structures for this class of compounds.

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“…At each step, an analysis of the residuals permitted checking the appropriateness of the weights and the compatibility of the rotational constants and the predicate observations. It is possible to automate, at least partly, this procedure by using the iteratively reweighted least squares (IRLS) method, whereby data with large residuals are weighted down. , The advantage of the IRLS method is that it is robust, i.e., it mitigates the influence of outliers. Two different weighting schemes are used in this study: Huber weighting, where the weight linearly decreases as the residual increases, and biweight weighting, where, in addition, data with large residuals are eliminated.…”

Section: Computational Detailsmentioning

confidence: 99%

Accurate Determination of the Deformation of the Benzene Ring upon Substitution: Equilibrium Structures of Benzonitrile and Phenylacetylene

2013

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Accurate equilibrium, re, structures of the monosubstituted benzene molecules benzonitrile, C6H5CN, and phenylacetylene, C6H5CCH, have been determined using two different, to some extent complementary techniques. The semiexperimental, r(e)(SE), structural parameters are the result of a least-squares fit to equilibrium rotational constants derived from experimental effective ground-state rotational constants and rovibrational corrections based principally on an ab initio cubic force field. The composite ab initio Born-Oppenheimer, r(e)(BO), structural parameters are obtained from frozen-core and all-electron MP2 and the CCSD(T) geometry optimizations using Gaussian basis sets up to quintuple-zeta quality. The DFT(B3LYP) method, with two different Gaussian basis sets, 6-31G* and 6-311+G(3df,2pd), was used to calculate the cubic force field employed during the r(e)(SE) structure determination. With the 6-31G* basis set, the error of the rovibrational correction is to a large extent random, whereas with the 6-311+G(3df,2pd) basis set it is mainly systematic. As shown here, systematic errors do not have a significant effect on the accuracy of the derived structure; the quality of the structural fit, however, is sensitive to the true accuracy of the ground-state rotational constants. An even more important general conclusion of this study is that the addition of extra rotational constants from multisubstituted species does not seem to improve the accuracy of the r(e)(SE) structures, quite in contrast to the highly desirable availability of data corresponding to all singly substituted species.

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A Basis for Joint Interoperability

Cited by 5 publications

References 0 publications

Equilibrium Structures of Heterocyclic Molecules with Large Principal Axis Rotations upon Isotopic Substitution

Equilibrium Structures of Heterocyclic Molecules with Large Principal Axis Rotations upon Isotopic Substitution

Equilibrium Structures of Three-, Four-, Five-, Six-, and Seven-Membered Unsaturated N-Containing Heterocycles

Accurate Determination of the Deformation of the Benzene Ring upon Substitution: Equilibrium Structures of Benzonitrile and Phenylacetylene

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