A constant-energy molecular dynamics simulation is used to monitor protein motion at zero-total angular momentum. With a simple protein model, it is shown that overall rotation is possible at zero-total angular momentum as a result of flexibility. Since the rotational motion is negligible on a time scale of 1000 reduced time units, the essentially rotation-free portion of the trajectory provides an unbiased test of the common approximate methods for separating overall rotation from internal motions by optimal superposition. Removing rotation by minimizing the root-mean-square deviation (RMSD) for the entire system is found to be more appropriate than using the RMSD for only the more rigid part of the system. The results verify the existence of positive cross-correlation in the motions of atoms separated by large distances.

The minimum-energy pathway and the energetics of the reaction H + O2 ⇌ HO2 ⇌ O + OH have been computed at four levels of density-functional theory, involving local and nonlocal exchange and correlation terms. The four exchange-correlation potentials produce very similar geometries for the HO2 intermediate, and similar trajectories for the reaction path in the neighborhood of HO2; the pathways begin to differ more significantly at greater distances between reactant or product species, as the surface flattens out toward the asymptotic dissociation energy. The experimental energetics are reproduced most accurately by nonlocal exchange plus local correlation. Addition of a nonlocal correlation term worsens the agreement.

The minimum-energy pathway and the energetics of the reaction H + O-2 reversible arrow HO2 reversible arrow O + OH have been computed at four levels of density-functional theory, involving local and nonlocal exchange and correlation terms. The four exchange-correlation potentials produce very similar geometries for the HO2 intermediate, and similar trajectories for the reaction path in the neighborhood of HO2 the pathways begin to differ more significantly at greater distances between reactant or product species, as the surface flattens out toward the asymptotic dissociation energy. The experimental energetics are reproduced most accurately by nonlocal exchange plus local correlation. Addition of a nonlocal correlation term worsens the agreement. (C) 1998 Elsevier Science B.V. All rights reserved.

We describe the implementation of a new grid-free density-functional technique for exchange-correlation potentials of ρ1/3 form (exchange-only local density-functional theory potentials). The potential is fitted to integrable functional forms by solving a set of nonlinear equations, rather than by fitting on a three-dimensional grid of points. This completely analytical method produces smooth energy surfaces and exact energy gradients. The method is found to be several times faster computationally in single-point calculations than a comparable grid-based method with a moderate number of grid points, and it is more than an order of magnitude faster for geometry optimizations. The analytical method is tested on the torsional energy surfaces of the classic isoelectronic series C2H6, N2H4, and H2O2, using the Hartree–Fock–Slater potential (α=2/3). The locations and relative energies of energy extrema, and the structural variations across the potential surfaces, are in good agreement with experimental data and the results of high-quality ab initio studies.

We have implemented a completely analytical linear combination of atomic orbitals-X alpha local density-functional method with exact energy gradients. The superiority of the analytical method over the corresponding grid-based technique in terms of speed, smooth energy surfaces, and accurate gradients is demonstrated in calculations for the umbrella inversion mode of ammonia. The equilibrium geometry and inversion barrier height are also shown to compare well to experimental data.

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTElectron correlation and density-functional methodsMichael. Cook and Martin. KarplusCite this: J. Phys. Chem. 1987, 91, 1, 31–37Publication Date (Print):January 1, 1987Publication History Published online1 May 2002Published inissue 1 January 1987https://pubs.acs.org/doi/10.1021/j100285a010https://doi.org/10.1021/j100285a010research-articleACS PublicationsRequest reuse permissionsArticle Views218Altmetric-Citations66LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InRedditEmail Other access options Get e-Alerts

AbstractAset of MS‐Xα calculations on the title ion is reported.

Chemischer InformationsdienstVolume 16, Issue 16 Physical Inorganic Chemistry ChemInform Abstract: ELECTRONIC STRUCTURE OF THE MOLYBDENUM-IRON-SULFUR CLUSTER MOFE3S4(SH)63-ION M. COOK, M. COOKSearch for more papers by this authorM. KARPLUS, M. KARPLUSSearch for more papers by this author M. COOK, M. COOKSearch for more papers by this authorM. KARPLUS, M. KARPLUSSearch for more papers by this author First published: April 23, 1985 https://doi.org/10.1002/chin.198516002AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article. Volume16, Issue16April 23, 1985 RelatedInformation

A set of MS-Xα calculations on the MoFe3S4 (SH)3−6 ion is reported. Three levels of theoretical models are considered: spin-restricted, C3v symmetry, which is most easily compared with the traditional ligand-field picture; spin-polarized, C3v symmetry; and spin-polarized, Cs symmetry. An MS=3/2 ground state corresponding closely to the experimental spin-quartet ground state of a single-cube MoFe3S4 cluster is found at the level of the Cs broken-symmetry model. This state has two antiferromagnetically coupled pairs of metal ions: a net majority-spin iron pair and a net minority-spin Mo–Fe pair. The spin densities on the three iron atoms are nearly equal, with 3.06 electrons of spin density on each Fe; Mo carries only a very small net spin, 0.4 electrons. Calculated Mössbauer quadrupole splittings and isomer shifts agree well with experimental results. The model suggests that a quintet ground state should be produced on reduction, consistent with experiment. The present MoFe3S4 cluster calculations are compared extensively with corresponding results for the Fe4S4 cluster.

Xα multiple scattering wave functions and molecular properties are reported for benzene, pyridine, pyrazine, pyrrole, and imidazole. The calculations demonstrate that useful results can be obtained for planar conjugated organic molecules with the Xα method. Values are obtained for ionization potentials and one electron properties, including dipole and quadrupole moments, diamagnetic susceptibilities and nuclear quadrupole coupling constants. In general the results are in better agreement with experiment than minimum basis set Hartree–Fock calculations; this generalization is not true for molecular properties that are dominated by hydrogen atoms, such as deuteron quadrupole coupling constants. The sensitivity of the results to changes in sphere overlap is studied in detail for pyridine and it is found that useful accuracy can be achieved over a fairly broad range of overlap parameters. Calculated ionization potentials agree well with recent assignments of the photoelectron spectra, except for the relative ordering of π and nitrogen lone-pair orbitals. This difference is analysed in terms of correlation effects in lone-pair ionizations. As part of the comparisons, detailed tabulations of one-electron properties and ionization potentials obtained from experiments and other calculations are provided.

A method for calculating two-electron properties from MS Xα wavefunctions is described. Results are presented for Coulomb and exchange integrals of ozone; the Xα integrals are insensitive to the choice of MS Xα parameters, and agree well with Hartiee-Fock values. The use of the method in calculating multiplet splittings is illustrated for ozone.

One-electron properties of LiH are calculated from Xα wave functions for a number of parameter sets by use of the charge-partitioning method. To test the method, the results are compared with the Xα numerical quadrature values of Woodruff and Wolfsberg, with Hartree–Fock and CI results, and with experiment. The charge-partitioning procedure is found to introduce errors on the order of those in the Xα wave function itself and to improve in accuracy with parameter variations that improve the Xα wave function. The variations of one-electron properties as functions of the Xα parameters are studied; it is found that these variations can be interpreted in terms of a simple electronegativity picture. Implications of these results for calculations of one-electron properties of polyatomics are discussed.