Search results for "basis"
showing 10 items of 760 documents
Sequential Learning with LS-SVM for Large-Scale Data Sets
2006
We present a subspace-based variant of LS-SVMs (i.e. regularization networks) that sequentially processes the data and is hence especially suited for online learning tasks. The algorithm works by selecting from the data set a small subset of basis functions that is subsequently used to approximate the full kernel on arbitrary points. This subset is identified online from the data stream. We improve upon existing approaches (esp. the kernel recursive least squares algorithm) by proposing a new, supervised criterion for the selection of the relevant basis functions that takes into account the approximation error incurred from approximating the kernel as well as the reduction of the cost in th…
NMR chemical shift calculations within local correlation methods: the GIAO-LMP2 approach
2000
A scheme for the calculation of NMR chemical shifts using local second-order Moller–Plesset (LMP2) perturbation theory together with gauge-including atomic orbitals (GIAOs) is presented. Test calculations on the basis of a preliminary implementation within a conventional GIAO-MP2 code show that the deviations between GIAO-LMP2 and GIAO-MP2 are small, e.g., for 13C typically less than 1 ppm, and that the GIAO-LMP2 approach holds great promise for application to larger molecules.
Fast noniterative orbital localization for large molecules
2006
We use Cholesky decomposition of the density matrix in atomic orbital basis to define a new set of occupied molecular orbital coefficients. Analysis of the resulting orbitals ("Cholesky molecular orbitals") demonstrates their localized character inherited from the sparsity of the density matrix. Comparison with the results of traditional iterative localization schemes shows minor differences with respect to a number of suitable measures of locality, particularly the scaling with system size of orbital pair domains used in local correlation methods. The Cholesky procedure for generating orthonormal localized orbitals is noniterative and may be made linear scaling. Although our present implem…
Fast evaluation of a linear number of local exchange matrices
2002
A fast method is described for evaluating multiple exchange matrices in a Gaussian atomic orbital basis. For insulators, it is asymptotically linear scaling, and is a generalization of the linear scaling exchange (LinK) method, which was formulated for a single exchange matrix [J. Chem. Phys. 109 (1998) 1663]. It is employed to evaluate exchange-type contractions of all derivative density matrices with two-electron integrals for a series of linear alkanes, linear polyacenes, and water clusters using STO-3G, 3-21G, and 6-31G* basis sets. Significant computational savings are obtained for molecules with as few as 10 non-hydrogen atoms.
Axiomatic Foundations Of Fixed-Basis Fuzzy Topology
1999
This paper gives the first comprehensive account on various systems of axioms of fixed-basis, L-fuzzy topological spaces and their corresponding convergence theory. In general we do not pursue the historical development, but it is our primary aim to present the state of the art of this field. We focus on the following problems:
An Analysis of Earthquakes Clustering Based on a Second-Order Diagnostic Approach
2009
A diagnostic method for space–time point process is here introduced and applied to seismic data of a fixed area of Japan. Nonparametric methods are used to estimate the intensity function of a particular space–time point process and on the basis of the proposed diagnostic method, second-order features of data are analyzed: this approach seems to be useful to interpret space–time variations of the observed seismic activity and to focus on its clustering features.
Analytic gradients for the coupled-cluster singles, doubles, and triples (CCSDT) model
2002
The first implementation of analytic gradients for the coupled-cluster singles, doubles, triples (CCSDT) model is described. The relevant theoretical expressions are given in a diagrammatic form together with the corresponding algebraic formulas. The computational requirements of CCSDT gradient calculations are discussed and their applicability demonstrated by performing benchmark calculations for molecular geometries with large correlation-consistent basis sets. A statistical analysis of the data reveals that CCSDT and CCSD(T) in most cases perform equally well. The CCSDT calculations thus provide further evidence for the high accuracy of the CCSD(T) approach.
Theoretical study on hydration of two particular diazanaphthalenes
2005
Abstract Cinnoline (1) and Phthalazine (2), diazanaphthalenes involved in certain biological reactions, have been studied computational with the purpose of comparing their protonation and covalent hydration mechanisms. Geometry optimizations of neutral, mono- and di-protonated cations and hydrated products were performed at HF, DFT/B3LYP levels of theory using 6-311G* basis set and single points energies were calculated at the MP2 level of theory using the same basis set. In agreement with experimental results, calculations predict a two-step mechanism resulting in a hydrated cation in which the OH of the water is located depending on the position of both nitrogen in the diazanaphthalene mo…
About the reliability of the Maximum Entropy Method in reconstructing electron density: the case of MgO
2006
Abstract The reliability of the Maximum Entropy Method (MEM) to reconstruct finite temperature electron density (ED) is here discussed, investigating the case of periclase (MgO). A theoretical electron density has been generated by quantum mechanic calculations and folded with a function simulating atomic thermal motion, in order to produce a reference errorless ED [ρ(r)REF]. The Fourier coefficients of ρ(r)REF have been calculated, and used as “observed” diffraction intensities to reconstruct via MEM the original ED. The electron density attained by MEM [ρ(r)MEM] and ρ(r)REF have been compared with each other (pixel-by-pixel and critical points) to assess the ability of MEM to retrieve EDs…
Structural, vibrational and electrical study of compressed BiTeBr
2016
Compresed BiTeBr has been studied from a joint experimental and theoretical perspective. Room-temperature x-ray diffraction, Raman scattering, and transport measurements at high pressures have been performed in this layered semiconductor and interpreted with the help of ab initio calculations. A reversible first-order phase transition has been observed above 6–7 GPa, but changes in structural, vibrational, and electrical properties have also been noted near 2 GPa. Structural and vibrational changes are likely due to the hardening of interlayer forces rather than to a second-order isostructural phase transition while electrical changes are mainly attributed to changes in the electron mobilit…