Search results for "Linear Algebra"

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…

Classification of basis states for (p-f)-nuclei (41 <= A <= 80) with minimal configuration energy

2003

Submitted by Guilherme Lemeszenski (guilherme@nead.unesp.br) on 2013-08-22T19:01:21Z No. of bitstreams: 1 S0103-97332003000100007.pdf: 99978 bytes, checksum: b0d369bc8873710f3a3ef14fda91bff6 (MD5) Made available in DSpace on 2013-08-22T19:01:21Z (GMT). No. of bitstreams: 1 S0103-97332003000100007.pdf: 99978 bytes, checksum: b0d369bc8873710f3a3ef14fda91bff6 (MD5) Previous issue date: 2003-03-01 Made available in DSpace on 2013-09-30T19:03:17Z (GMT). No. of bitstreams: 2 S0103-97332003000100007.pdf: 99978 bytes, checksum: b0d369bc8873710f3a3ef14fda91bff6 (MD5) S0103-97332003000100007.pdf.txt: 16691 bytes, checksum: c968691a68ca956179c54787a66be7d5 (MD5) Previous issue date: 2003-03-01 Submitt…

Towards a novel energy density functional for beyond-mean-field calculations with pairing and deformation

2018

We take an additional step towards the optimization of the novel finite-range pseudopotential at constrained Hartree-Fock-Bogolyubov level and implement an optimization procedure within an axial code using harmonic oscillator basis. We perform the optimization using three different numbers of the harmonic oscillator shells. We apply the new parameterizations in the O-Kr part of the nuclear chart and isotopic chain of Sn, and we compare the results with experimental values and those given by a parameterization obtained using a spherical code.

Phonon-to-spin mapping in a system of a trapped ion via optimal control

2015

We propose a protocol for measurement of the phonon number distribution of a harmonic oscillator based on selective mapping to a discrete spin-1/2 degree of freedom. We consider a system of a harmonically trapped ion, where a transition between two long-lived states can be driven with resolved motional sidebands. The required unitary transforms are generated by amplitude-modulated polychromatic radiation fields, where the time-domain ramps are obtained from numerical optimization by application of the chopped random basis algorithm (CRAB). We provide a detailed analysis of the scaling behavior of the attainable fidelities and required times for the mapping transform with respect to the size…

Diffuse solar radiation statistics for Italy

1981

Abstract In this paper diffuse radiation is correlated with usually measured or more easy computable quantities in order to have a larger number of data available for the various applications of solar energy. Here are used two types of correlation: (a) diffuse radiation as a function of global and extraterrestrial radiation; (b) diffuse radiation as a function of ralative sunshine and extraterrestrial radiation. On the basis of the above correlations, empirical equations have been proposed and their coefficients have been calculated by fitting the experimental data of three Italian stations. The degree of accuracy of the fit has been estimated by a coefficient introduced and called by us “r…

Ground and Excited State First-Order Properties in Many-Body Expanded Full Configuration Interaction Theory

2020

The recently proposed many-body expanded full configuration interaction (MBE-FCI) method is extended to excited states and static first-order properties different from total, ground state correlation energies. Results are presented for excitation energies and (transition) dipole moments of two prototypical, heteronuclear diatomics---LiH and MgO---in augmented correlation consistent basis sets of up to quadruple-$\zeta$ quality. Given that MBE-FCI properties are evaluated without recourse to a sampled wave function and the storage of corresponding reduced density matrices, the memory overhead associated with the calculation of general first-order properties only scales with the dimension of …

2021

Electronic circular dichroism (ECD) is a powerful spectroscopy method for investigating chiral properties at the molecular level. ECD calculations with the commonly used linear-response time-dependent density functional theory (LR-TDDFT) framework can be prohibitively costly for large systems. To alleviate this problem, we present here an ECD implementation within the projector augmented-wave method in a real-time-propagation TDDFT framework in the open-source GPAW code. Our implementation supports both local atomic basis sets and real-space finite-difference representations of wave functions. We benchmark our implementation against an existing LR-TDDFT implementation in GPAW for small chir…

Some aspects of the orientation of galaxies in clusters

2013

The analysis of Tully's groups of galaxies belonging to the Local Supercluster (LSC) was performed. In the 1975 Hawley and Peebles presented the method for investigations of the galaxies orientation in the large structures. In our previous papers statistical test proposed by Hawley and Peebles for investigation of this problem was analyzed in details and some improvements were suggested. On this base the new method of the analysis of galactic alignment in clusters was proposed. Using this method, God{\l}owski (2012) analyzed the orientation of galaxies inside Tully's group founding no significant deviations from isotropy both in orientation of position angles and $\delta_D$ and $\eta$ angle…

A dynamical systems study of the inhomogeneous Lambda-CDM model

2010

We consider spherically symmetric inhomogeneous dust models with a positive cosmological constant, $\Lambda$, given by the Lemaitre-Tolman-Bondi metric. These configurations provide a simple but useful generalization of the Lambda-CDM model describing cold dark matter (CDM) and a Lambda term, which seems to fit current cosmological observations. The dynamics of these models can be fully described by scalar evolution equations that can be given in the form of a proper dynamical system associated with a 4-dimensional phase space whose critical points and invariant subspaces are examined and classified. The phase space evolution of various configurations is studied in detail by means of two 2-…