Search results for "basis"
showing 10 items of 760 documents
Random Walk in a N-cube Without Hamiltonian Cycle to Chaotic Pseudorandom Number Generation: Theoretical and Practical Considerations
2017
Designing a pseudorandom number generator (PRNG) is a difficult and complex task. Many recent works have considered chaotic functions as the basis of built PRNGs: the quality of the output would indeed be an obvious consequence of some chaos properties. However, there is no direct reasoning that goes from chaotic functions to uniform distribution of the output. Moreover, embedding such kind of functions into a PRNG does not necessarily allow to get a chaotic output, which could be required for simulating some chaotic behaviors. In a previous work, some of the authors have proposed the idea of walking into a $\mathsf{N}$-cube where a balanced Hamiltonian cycle has been removed as the basis o…
Molecular equilibrium structures from experimental rotational constants and calculated vibration–rotation interaction constants
2002
A detailed study is carried out of the accuracy of molecular equilibrium geometries obtained from least-squares fits involving experimental rotational constants B(0) and sums of ab initio vibration-rotation interaction constants alpha(r)(B). The vibration-rotation interaction constants have been calculated for 18 single-configuration dominated molecules containing hydrogen and first-row atoms at various standard levels of ab initio theory. Comparisons with the experimental data and tests for the internal consistency of the calculations show that the equilibrium structures generated using Hartree-Fock vibration-rotation interaction constants have an accuracy similar to that obtained by a dir…
A theoretical study of the collinear reaction F+H2→HF+H using multiconfigurational second-order perturbation theory (CASPT2)
1993
Abstract The second-order perturbation method (CASPT2) with a single state multiconfigurational reference function generated in complete active self-consistent field (CASSCF) calculations has been used to compute the collinear barrier height, saddle point geometry, and exothermicity of the reaction F+H 2 →HF+H. Comparison with full configuration (FCI) calculations with small basis sets shows that the CASPT2 method is capable of reproducing accurately the exact benchmark results correlating seven electrons. Large atomic natural orbital basis sets are used at the seven- and nine-electron level of correlation. With the largest ANO basis set used, F[7s6p5d4f2g]/H[6s5p4d2f], the computed nine-el…
Quantifying Structural Subsidy Values for Systemically Important Financial Institutions
2013
Abstract Claimants to Systemically Important Financial Institutions (SIFIs) would receive transfers when governments are forced into bailouts. Ex ante, this bailout expectation lowers SIFIs’ daily funding costs. The funding cost advantage reflects both the structural level of the government support and the time-varying market valuation for such a support. Based on a large worldwide sample of banks, we estimate the value of the structural subsidy, by exploiting expectations of state support embedded in credit ratings and by applying the long-run average value of the rating bonus. The value of the structural subsidy was already sizable, 60 basis points (bp), as of the end-2007, before the cri…
Conservatism and Accounting Earnings
2015
The article refers to accounting conservatism and its relation with accounting earnings. After providing the conceptual background of the prudence concept, which is the basis of accounting conservatism, the paper introduces some more empirically testable concepts, known as conditional and unconditional conservatism. It also explains the economics behind this accounting practice, mainly associated to contracting due to the asymmetric information between managers and external stakeholders, but also linked to litigation risks, taxation, political and regulatory processes. After providing a brief explanation of the empirical measures of conservatism, it gives a summary of the vast empirical res…
Estimation of formamide harmonic and anharmonic modes in the Kohn-Sham limit using the polarization consistent basis sets.
2010
Formamide harmonic and anharmonic frequencies of fundamental vibrations in the gas phase and in several solvents were successfully estimated in the B3LYP Kohn-Sham complete basis set limit (KS CBS). CBS results were obtained by extrapolating a power function (two-parameter formula) to the results calculated with polarization-consistent basis sets. Anharmonic corrections using the second order perturbation treatment (PT2) and hybrid B3LYP functional combined with polarization consistent pc-n (n = 0, 1, 2, 3, 4) and several Pople’s basis sets were analyzed for all fundamental formamide vibrational modes in the gas phase and solution. Solvent effects were modeled within a PCM method. The anhar…
From small to medium and beyond: a pragmatic approach in predicting properties of Ne containing structures
2013
In this study, we outlined a pragmatic approach for structural studies leading to better understanding of polycarbon structures using 21Ne as a nuclear magnetic resonance (NMR) probe. 21Ne NMR parameters of a single neon atom and its dimer were predicted at the CCSD(T) level in combination with large basis sets. At a lower level of theory, an interaction of neon atom with 1,3-cyclopentadiene ring and with five- and six-membered rings in carbazole was studied using the restricted Hartree–Fock (RHF) and density functional theory (DFT) combined with smaller basis sets. The RHF and DFT modelling of neon interaction with nanosized objects were performed on cyclacenes and selected fullerenes.
Efficient Modeling of NMR Parameters in Carbon Nanosystems
2015
Rapid growth of nanoscience and nanotechnology requires new and more powerful modeling tools. Efficient theoretical modeling of large molecular systems at the ab initio and Density Functional Theory (DFT) levels of theory depends critically on the size and completeness of the basis set used. The recently designed variants of STO-3G basis set (STO-3Gel, STO-3Gmag), modified to correctly predict electronic and magnetic properties were tested on simple models of pristine and functionalized carbon nanotube (CNT) systems and fullerenes using the B3LYP and VSXC density functionals. Predicted geometries, vibrational properties, and HOMO/LUMO gaps of the model systems, calculated with typical 6-31G…
3 He NMR: from free gas to its encapsulation in fullerene
2013
The (3)He nuclear magnetic shieldings were calculated for single helium atom, its dimer, simple models of fullerene cages (He@Cn), and single wall carbon nanotubes. The performances of several levels of theory (HF, MP2, DFT-VSXC, CCSD, CCSD(T), and CCSDT) were tested. Two sets of polarization-consistent basis sets were used (pcS-n and aug-pcS-n), and an estimate of (3)He nuclear magnetic shieldings in the complete basis set limit using a two-parameter fit was established. Theoretical (3)He results reproduced accurately previously reported theoretical values for helium gas, dimer, and helium probe inside several fullerene cages. Excellent agreement with experimental values was achieved. (3)H…
Edelstein-Suzuki-type resuls for self-mappings in various abstract spaces with application to functional equations
2016
Abstract The fixed point theory provides a sound basis for studying many problems in pure and applied sciences. In this paper, we use the notions of sequential compactness and completeness to prove Eldeisten-Suzuki-type fixed point results for self-mappings in various abstract spaces. We apply our results to get a bounded solution of a functional equation arising in dynamic programming.