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61.
Fabio E. Penotti 《International journal of quantum chemistry》2006,106(5):1153-1159
Nonorthogonal single‐configuration and multiconfiguration ab initio calculations are carried out on the BeH2 molecule in its equilibrium (D∞h) geometry, using a highly optimized even‐tempered Slater‐type orbital (STO) basis set. The results are used as a basis for a discussion of the electronic structure of the molecule in modern‐VB terms. A value of Re = 1.329 Å is obtained. Values are also obtained for the symmetric‐stretch harmonic frequency (2053 cm?1), electric quadrupole moment (?5.60 Buckingham), and nuclear quadrupole coupling constants (?3.59 MHz for 9Be and 0.0915 MHz for 2H). © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006 相似文献
62.
Ema I García De La Vega JM Ramírez G López R Fernández Rico J Meissner H Paldus J 《Journal of computational chemistry》2003,24(7):859-868
We present three Slater-type atomic orbital (STO) valence basis (VB) sets for the first and second row atoms, referred to as the VB1, VB2, and VB3 bases. The smallest VB1 basis has the following structure: [3, 1] for the H and He atoms, [5, 1] for Li and Be, and [5, 3, 1] for the B to Ne series. For the VB2 and VB3 bases, both the number of shells and the number of functions per shell are successively increased by one with respect to VB1. With the exception of the H and Li atoms, the exponents for the VB1 bases were obtained by minimizing the sum of the Hartree-Fock (HF) and frozen-core singles and doubles configuration interaction (CISD FC) energies of the respective atoms in their ground state. For H and Li, we minimized the sum of the HF and CISD FC energies of the corresponding diatoms (i.e., of H(2) or Li(2)) plus the ground-state energy of the atom. In the case of the VB2 basis sets, the sum that was minimized also included the energies of the positive and negative ions, and for the VB3 bases, the energies of a few lowest lying excited states of the atom. To account for the core correlations, the VBx (x = 1, 2, and 3) basis sets for the Li to Ne series were enlarged by one function per shell. The exponents of these extended (core-valence, CV) basis sets, referred to, respectively, as the CVBx (x = 1, 2, and 3) bases, were optimized by relying on the same criteria as in the case of the VBx (x = 1, 2, and 3) bases, except that the full CISD rather than CISD FC energies were employed. We show that these polarized STO basis sets provide good HF and CI energies for the ground and excited states of the atoms considered, as well as for the corresponding ions. 相似文献
63.
For real a correspondence is made between the Julia setB
forz(z–)2, in the hyperbolic case, and the set of-chains±(±(±..., with the aid of Cremer's theorem. It is shown how a number of features ofB can be understood in terms of-chains. The structure ofB
is determined by certain equivalence classes of-chains, fixed by orders of visitation of certain real cycles; and the bifurcation history of a given cycle can be conveniently computed via the combinatorics of-chains. The functional equations obeyed by attractive cycles are investigated, and their relation to-chains is given. The first cascade of period-doubling bifurcations is described from the point of view of the associated Julia sets and-chains. Certain Julia sets associated with the Feigenbaum function and some theorems of Lanford are discussed.Supported by NSF grant No. MCS-8104862.Supported by NSF grant No. MCS-8203325. 相似文献
64.
Angelika Baranowska Magdalena Siedlecka Andrzej J. Sadlej 《Theoretical chemistry accounts》2007,118(5-6):959-972
Recent studies of the perturbation-dependent basis sets have indicated the possibility of a significant reduction of the size
of the usual CGTO sets without considerable loss of accuracy in calculations of molecular electric properties. The resulting
(ZPolX) basis sets have been developed for several atoms of the first and second row of the Periodic Table. The same method
of the ZPolX basis set generation is extended for the first-row transition metals and the corresponding contracted ZPolX basis
sets of the size [6s5p3d1f] are determined for both nonrelativistic and scalar relativistic calculations. The performance
of the ZPolX basis sets is verified in calculations on the first-row transition metal oxides at the level of the ROHF, ROHF/CASPT2,
and ROHF/CCSD(T) approximations. Also the study of the dipole polarizability of TiCl4 confirms the excellent features of these very compact basis sets. The ZPolX basis sets for nonrelativistic and relativistic
calculations of molecular electric properties are available on the web page http://www.chem.uni.torun.pl/zchk/basis-sets.html. 相似文献
65.
Two sufficient criteria for the convergence of the Rayleigh-Ritz Method (RRM) with respect to the eigenvalues (E-convergence) of non-relativistic electronic Hamiltonians of molecules are discussed and compared. Moreover, a necessary and sufficient criterion is given. By example (Sect. 9) it is shown that the L
2-completeness of the basis is not sufficient to guarantee E-convergence. The convergence of the wave functions in different norms (-convergence) is also investigated. In particular, sufficient conditions for the one-particle basis functions (orbitals) are given, such that a CI calculation in this basis is both E- and -convergent. 相似文献
66.
Summary Medium-sized Gaussian basis sets are reoptimized for the ground states of the atoms from hydrogen through argon. The composition of these basis sets is (4s), (5s), and (6s) for H and He, (9s5p) and (12s7p) for the atoms Li to Ne, and (12s8p) and (12s9p) for the atoms Na to Ar. Basis sets for the2
P states of Li and Na, and the3
P states of Be and Mg are also constructed since they are useful in molecular calculations. In all cases, our energies are lower than those obtained previously with Gaussian basis sets of the same size. 相似文献
67.
Hermann Stoll Gerhard Wagenblast Heinzwerner Preuβ 《Theoretical chemistry accounts》1980,57(2):169-178
Two procedures are discussed for the direct variational optimization of localized molecular orbitals which are expanded in local subsets of the molecular basis set. It is shown that a Newton-Raphson approach is more efficient than an iterative diagonalization scheme. The effect of the basis-set truncation on the quality ofab-initio SCF results is investigated for Be, Li2, HF, H2O, NH3, CH4 and C2H6. 相似文献
68.
Summary The first-order polarized basis sets for the use in high-level-correlated investigations of molecular electric properties have been generated for Pb, Bi, Po, and At. The performance of the standard [10.17.14.5/13.11.8.2] and extended [20.17.14.9/13.11.8.4] basis sets has been examined in nonrelativistic and quasirelativistic calculations for atoms and simple closed-shell hydrides. The relativistic contributions to electric dipole properties of those systems have been evaluated by using the recently developed quasirelativistic scheme. The predicted dipole polarizability of At is in good agreement with the results of other relativistic calculations. The calculated quasirelativistic dipole moments of BiH3 (–0.499 a.u.), PoH2 (–0.207 a.u.), and AtH (+0.036 a.u.) involve a significant relativistic contribution which amounts to —0.230 a.u., –0.177 a.u., and –0.097 a.u., respectively. The basis set details append this paper. They are also available as a part of the basis set library of the MOLCAS system. 相似文献
69.
J. B. Lasserre 《Journal of Optimization Theory and Applications》1991,70(3):583-595
We consider two-dimensional discrete-time linear systems with constrained controls. We propose a simple polynomial time procedure to give an exact external representation of theN-step reachable set and controllable set. The bounding hyperplanes are explicitly derived in terms of the data of the problem. By using a result in computational geometry, all the calculations are made in polynomial time in contrast to classical methods. The limit case asN is also investigated. 相似文献
70.
Martin Fuchs 《manuscripta mathematica》1991,72(1):131-140
Given a smooth domain Ω in ℝ
m+1 with compact closure and a smooth integrable functionh: ℝ
m+1→ℝ satisfyingh(x)≥H
∂Ω
(x) on ∂Ω whereH
∂ω denotes the mean curvature of ∂Ω calculated w.r.t. the interior unit normal we show that there is a setA⊂ℝ
m+1 with the properties
andH
∂A=h on ∂A. 相似文献