Search results for "basis"
showing 10 items of 760 documents
Assessment of the CTOCD-DZ methodin a hierarchy of coupled cluster methods
2010
Gauge origin independent calculations of nuclear magnetic shielding tensors are carried out inside the formalism of the continuous transformation of the origin of the current density leading to formal annihilation of its diamagnetic contribution (CTOCD-DZ). We employ the unrelaxed linear response approach with a hierarchy of different coupled cluster methods in order to assess the importance of the level of approximation in the coupled cluster expansion. The basis set dependence of the computed nuclear magnetic shielding constants is also analyzed in the series of correlation consistent basis sets, with the aim of designing optimized basis sets of relatively small size.
Algebraic Treatment of a Three-Oscillator System: Applications to Some Molecular Models
1997
Abstract A new algebraic treatment of a three-oscillator system, called 3d formalism, is proposed. First, arbitrary tensor operators, expressed in terms of elementary creation and annihilation boson operators, are built within the standard algebraic chain u (3) ⊃ so (3) ⊃ so (2). Their matrix elements are next derived in a standard basis. Some applications, which require few adaptions or extensions, are proposed. They allow one to recover, for instance, Hecht's and tetrahedral Hamiltonians associated with threefold degenerate modes of spherical molecules and the vibron model Hamiltonian introduced for diatomic molecules.
Baryon Properties with Three-Quark Forces
1987
The Constituent Quark Model (CQM) is very useful for the description of many baryon properties, leading to a fair agreement with the experimental data, especially in the case of the baryon spectrum 1) and of the electromagnetic processes involving baryons2,3). The model is based on a non relativistic QCD-inspired dynamics, which includes a confinement potential and a spin-dependent short-range part, the so called hyperfine interaction4,1). The confinement potential contains as its major part a harmonic oscillator (h.o.) interaction, which has however a too degenerate spectrum with respect to the experimental one and leads to an unreasonable damping of the form factors even at moderate momen…
Next-to-leading order Balitsky-Kovchegov equation beyond large Nc
2020
We calculate finite-Nc corrections to the next-to-leading order (NLO) Balitsky-Kovchegov (BK) equation. We find analytical expressions for the necessary correlators of six Wilson lines in terms of the two-point function using the Gaussian approximation. In a suitable basis, the problem reduces from the diagonalization of a six-by-six matrix to the diagonalization of a three-by-three matrix, which can easily be done analytically. We study numerically the effects of these finite-Nc corrections on the NLO BK equation. In general, we find that the finite-Nc corrections are smaller than the expected 1/Nc2∼10%. The corrections may be large for individual correlators, but have less of an influence…
Spherical symmetric parabolic dust collapse: ${\cal C}^{1}$ matching metric with zero intrinsic energy
2016
The collapse of marginally bound, inhomogeneous, pressureless (dust) matter, in spherical symmetry, is considered. The starting point is not, in this case, the integration of the Einstein equations from some suitable initial conditions. Instead, starting from the corresponding general exact solution of these equations, depending on two arbitrary functions of the radial coordinate, the fulfillment of the Lichnerowicz matching conditions of the interior collapsing metric and the exterior Schwarzschild one is tentatively assumed (the continuity of the metric and its first derivatives on the time-like hypersurface describing the evolution of the spherical 2-surface boundary of the collapsing cl…
Convergence of Nuclear Magnetic Shieldings in the Kohn-Sham Limit for Several Small Molecules.
2015
Convergence patterns and limiting values of isotropic nuclear magnetic shieldings were studied for several small molecules (N2, CO, CO2, NH3, CH4, C2H2, C2H4, C2H6, and C6H6) in the Kohn-Sham limit. Individual results of calculations using dedicated families of Jensen's basis sets (pcS-n and pcJ-n) were fitted toward the complete basis set limit (CBS) using a simple two-parameter formula. Several density functionals were used; calculated vibrational corrections (ZPV) applied; and, for comparison purposes, similar calculations performed using RHF, MP2, SOPPA, SOPPA(CCSD), and CCSD(T) methods and additionally, the aug-cc-pVTZ-J basis set. Finally, the CBS estimated results were critically com…
Parallel Calculation of CCSD and CCSD(T) Analytic First and Second Derivatives.
2007
In this paper we present a parallel adaptation of a highly efficient coupled-cluster algorithm for calculating coupled-cluster singles and doubles (CCSD) and coupled-cluster singles and doubles augmented by a perturbative treatment of triple excitations (CCSD(T)) energies, gradients, and, for the first time, analytic second derivatives. A minimal-effort strategy is outlined that leads to an amplitude-replicated, communication-minimized implementation by parallelizing the time-determining steps for CCSD and CCSD(T). The resulting algorithm is aimed at affordable cluster architectures consisting of compute nodes with sufficient memory and local disk space and that are connected by standard co…
Models of Metal Clusters and Quantum Dots
2007
The electronic structure of simple metal clusters and quantum dots is studied on the basis of the density functional theory and simple models. It is demonstrated that single-particle models explain well the gross features of deformation and magnetism in small clusters, nuclei and quantum dots and that the local density approximation can give valuable information of the internal structure of the manybody state.
Accurate ab initio density fitting for multiconfigurational self-consistent field methods
2008
Using Cholesky decomposition and density fitting to approximate the electron repulsion integrals, an implementation of the complete active space self-consistent field (CASSCF) method suitable for large-scale applications is presented. Sample calculations on benzene, diaquo-tetra- μ -acetato-dicopper(II), and diuraniumendofullerene demonstrate that the Cholesky and density fitting approximations allow larger basis sets and larger systems to be treated at the CASSCF level of theory with controllable accuracy. While strict error control is an inherent property of the Cholesky approximation, errors arising from the density fitting approach are managed by using a recently proposed class of auxi…
Comparison of cartesian and lobe function Gaussian basis sets
1970
The lobe function and cartesian (spherical harmonic) gaussian are compared with reference to calculations for second-row atoms. Single and grouped gaussian basis sets which have been reported for cartesian functions are taken over directly to construct corresponding lobe function bases with identical sets of exponents and with lobe separations chosen by a scaling procedure. Total and orbital energies and SCF coefficients resulting from calculations on the second-row atoms using the two types of functions for both primitive and grouped gaussian basis sets are seen to be in excellent agreement, thereby emphasizing the essential equivalence of lobe functions and cartesian gaussians, at the ver…