Showing papers on "Basis function published in 1978"
TL;DR: In this article, the SCC-DV-Xα molecular orbital method was applied to metal clusters and the numerical basis functions were utilized in the present calculations, and it was proved that the self-consistent charge (SCC) approximation to the SCF method gives accurate orbital energies.
Abstract: Applications of the discrete variational (DV) Xα molecular orbital method based on the self-consistent Hartree-Fock-Slater model to metal clusters are presented. Numerical basis functions are utilized in the present calculations. Variations of orbital energies and populations with exchange scaling parameter α are investigated. It is proved that the self-consistent-charge (SCC) approximation to the SCF method gives accurate orbital energies. The numerical basis SCC-DV-Xα method is shown to be very efficient for studies of rather large metal clusters such as Ni 13 .
877 citations
TL;DR: A computational procedure is outlined for efficient evaluation of four-center coulomb repulsion integrals using contracted Gaussian basis functions and has been incorporated into the GAUSSIAN-70 molecular orbital program.
171 citations
TL;DR: The functional forms of the wave functions for the bound states of hydrogenic systems and for free particles as described by the complex-coordinate method are presented in this article, where the authors present an argument suggesting that when the rotation angle in the complex coordinate method is greater than $|\mathrm{arg}({k}_{r})|$ for the electron resonance, this method is identical to calculations based on a Siegert resonance.
Abstract: The functional forms of the wave functions for the bound states of hydrogenic systems and for free particles as described by the complex-coordinate method are presented. Writing the wave function for an electron resonance as the sum of a "boundlike" or "$Q$-space" part and a "scatteringlike" or "$P$-space" part, we suggest functional forms or bases for these two parts based on the solutions of the hydrogenic and freeparticle systems. We present an argument suggesting that when the rotation angle in the complex-coordinate method is greater than $|\mathrm{arg}({k}_{r})|$ for the electron resonance, this method is identical to calculations based on a Siegert resonance. This assumed structure of the wave function should yield a rate of convergence similar to other methods. The advantages of this method are that the basis functions are all square integrable, a single calculation yields both the position and width, only a solution of a straightforward eigenvalue problem is required, arbitrarily accurate target states are easily incorporated, and polarization terms can be explicitly included. Variational calculations for the position and width of the lowest $^{2}S$ resonance in the negative helium ion are reported using trial wave functions containing 39, 43, 55, 59, and 67 configurations. These wave functions contain 8, 8, 20, 24, and 32 "$P$-space" configurations, respectively. Values of 19.387 eV and 12.1 meV are obtained for the position and width, respectively, of the resonance. One also finds that inclusion of free-particle-like basis functions improves the representation of the scattering states.
35 citations
TL;DR: In this paper, a new technique has been developed to calculate the scattering characteristics of a three-dimensional arbitrarily-shaped conducting body, which employs a moment method which divides the surface of the scatterer into trilateral surface cells and uses the physical-optics type of current on each cell to form the set of basis functions.
Abstract: A new technique has been developed to calculate the scattering characteristics of a three-dimensional arbitrarily-shaped conducting body. The analysis employs a moment method which divides the surface of the scatterer into trilateral surface cells. The physical-optics type of current on each cell has been utilized to form the set of basis functions. A generalized computer program has been written and has been tested on the case of a sphere to demonstrate the numerical advantages of the present technique as compared with other existing surface-type integral approaches and wire-grid modelling techniques.
33 citations
TL;DR: In this article, the atom-density basis functions are split into inner and outer parts, and the atomic charges reflect polarity of the molecule reasonably well and are relatively independent of the orbital bases used in spanning the molecular wave function.
Abstract: Electron population analyses of several molecular one-electron density functions have been studied by least-squares projection methods into several atomic-density basis functions. All studies have been restricted to spherically symmetrical functions, which have been fitted to the atomic-density functions for the ground-state atoms hydrogen through neon. It is found that when the atom-density basis functions are split into inner (K shell) and outer (L shell) parts, then the atomic charges reflect polarity of the molecule reasonably well and, moreover, are relatively independent of the orbital bases used in spanning the molecular wave function. The standard density basis sets given here can be used for a similar electron population analysis of accurate X-ray diffraction data.
29 citations
27 citations
TL;DR: The exact decision-theoretic solution is given for two cases: (1) where the input image is fully known within a specified domain, and (2) where a scanning process gives only partial knowledge of the image.
22 citations
TL;DR: The method of orthogonal collocation on finite elements (OCFE) as discussed by the authors combines the features of OCE with those of the finite element method, and is illustrated for a Poisson equation (heat conduction with source term) in a rectangular domain.
21 citations
TL;DR: In this paper, the authors applied the close coupling method with conventional, l -dominant, and adiabatic basis functions to electron-molecule elastic scattering and rotational excitation.
21 citations
TL;DR: In the paper, the procedure for minimizing the energy is outlined, and the different steps of the calculations are presented in some detail.
18 citations
TL;DR: Using the unitary group approach, the authors showed that the amount of storage needed for the construction of symbolic CI matrix element lists for N-electron basis functions with large numbers of open shells and arbitrary multiplicities may substantially reduce compared to methods currently available in the literature.
Abstract: Using the unitary group approach it is shown that the amount of storage needed for the construction of symbolic CI matrix element lists for N-electron basis functions with large numbers of open shells and arbitrary multiplicities may substantially be reduced compared to methods currently available in the literature
TL;DR: In this article, the weighted residuals (MWR) in the form of a modified Galerkin method with trigonometric basis functions was used to compute the transmission of sound in an axisymmetric duct.
TL;DR: In this paper, Courant's approach to the variational-difference method and the definition of basis functions, as well as the method of construction of coordinate functions are presented.
Abstract: The article begins with a presentation of Courant's approach to the variational-difference method and of the definition of basis functions, as well as the method of construction of coordinate functions. Then the completeness of a system of coordinate functions is studied, and also the degree of approximation of functions of Sobolev classes and of some other (similar) classes, as well as basis functions of more complex structure. Some new problems related to approximate calculation of eigenvalues are also examined, as well as methods of construction of variational-difference equations and, in particular, difference schemes with a boundary layer; the stability of the variational-difference process is studied, as well as the condition number of the corresponding matrix. In the concluding part of the article it is shown that the obtained approximation formulas yield in the one-dimensional case the classical Euler-MacLaurin quadrature formula, and in the multidimensional case the obvious counterparts of this formula.
TL;DR: In this article, the harmonic vibralional response and the resulting acoustic radiation from an arbitrary elastic structure immersed in an infinite inviscid fluid are formulated using a set of computer programs given the acronym FIST, which allows the use of the interior points to solve the set of over-determined system equations in the least-squares sense to obtain the solution at the resonance frequency.
08 Dec 1978
TL;DR: In this article, a coherent optical method capable of performing arbitrary two-dimensional linear transformations has been studied, in which transform coefficients are given by two dimensional inner products of the input image and a set of basis functions.
Abstract: A coherent optical method capable of performing arbitrary two-dimensional linear transformations has recently been studied, in which transform coefficients are given by two-dimensional inner products of the input image and a set of basis functions. Since the inner product of two functions is equal to the value of their correlation when there is zero shift between the functions, it is possible to use an optical correlator to solve for the coefficients of the transform. By using random phase masks in the input and the filter planes of the correlator, we have been able to pack many coefficients close together in the output plane, and thus take better advantage of the space-bandwidth product of the optical system. Both the input random phase mask and the spatial filter are computer-generated holographic elements, created by a computer-controlled laser beam scanner. The system can be "programmed" to perform arbitrary two-dimensional linear transformations. For demonstration, the set of two-dimensional Walsh functions was chosen as a transform basis. When the resolution of the Walsh functions was limited to 128 x 128, up to 256 transform coefficients were obtained in parallel. The signal-to-noise and accuracy of the transform coefficients were compared to the theory.© (1978) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
TL;DR: In this paper, a generalisation of the finite element method is used to construct a series of highly efficient finite-basis set methods for the solution of a one-dimensional Schrodinger equation in the continuum part of the eigenvalue spectrum.
Abstract: A generalisation of the finite-element method is used to construct a series of highly efficient finite-basis-set methods for the solution of a one-dimensional Schrodinger equation in the continuum part of the eigenvalue spectrum. These methods are far more accurate than the standard R-matrix method and effectively eliminate the need for the correction procedures commonly applied to this earlier method. The poor convergence of the R-matrix method is found to be the result of an analogue of the Gibb's phenomenon of Fourier series expansions arising due to the inability of the basis functions to resolve the boundary conditions. It is shown how this problem can be removed by adding a few local basis functions which then allow the boundary conditions to be resolved at any energy.
TL;DR: In this article, the authors derived the equation of the actual curve that results when a curved edge is approximated using an isoparametric cubic finite element, which depends only on the parameters of the nodes associated with the curved side and does not depend on the shape of the element or on the basis functions used.
01 Apr 1978
TL;DR: The 'waveform synthesis' technique is particularly well suited for microprocessor implementation and as shown in the paper two D-A converters in conjunction with a standard microprocessor and associated ROM, RAM and I/O can be used to implement this technique.
Abstract: This paper presents a time domain technique for the generation of speech which offers significant advantages over current formant synthesis and linear predictive coder (LPC) techniques. A set of basis functions in conjunction with a time-compression (and expansion) operation is shown to span the parameter space of the vocal tract model. The relationship between these basis functions and the formant synthesis parameters is derived and graphically illustrated. The 'waveform synthesis' technique is particularly well suited for microprocessor implementation and as shown in the paper two D-A converters in conjunction with a standard microprocessor and associated ROM, RAM and I/O can be used to implement this technique.
TL;DR: In this paper, the authors apply the method of correlated basis functions to inhomogeneous systems such as electrons in a solid, in systems bounded by surfaces, and in systems with impurities.
Abstract: In applying the method of correlated basis functions to inhomogeneous systems such as electrons in a solid, in systems bounded by surfaces, and in systems with impurities, matrix elements of multiple density fluctuation operators are needed. These are the multiple density correlation functions. We evaluate these functions in the convolution approximation and express them in usable forms.
TL;DR: Unlike in previous approaches, the system partial differential equations are satisfied exactly at every stage of the computation without, however, explicitly solving them, which results in both a decreased computational load and an increased solution accuracy.
Abstract: A computational technique is developed for the solution of optimal control problems for distributed-parameter systems. The method involves an expansion of the state variables in terms of multivariate spline basis functions. The optimal control problem is thereby reduced to a finite-dimensional constrained minimization problem that may be solved numerically using standard algorithms. Unlike in previous approaches, the system partial differential equations are satisfied exactly at every stage of the computation without, however, explicitly solving them. This feature results in both a decreased computational load and an increased solution accuracy. A numerical example is presented.
TL;DR: The difficulties arising in the applications of a new basis function to many-electron computations are discussed for STP functions and even tempered restr is discussed.
TL;DR: In this paper, pair energy diagrams are evaluated to infinite order, which include non-diagonal as well as the usual diagonal contributions, and preliminary calculations are performed on the correlation energy of the ground state of the helium atom using a numerical V N-1 basis set.
Abstract: Integral equations are developed diagrammatically for atomic and molecular pair energies. The equations are solved with numerical basis functions by transforming the integral equations into linear algebraic equations with the introduction of a suitable quadrature formula. For the first time, pair energy diagrams are evaluated to infinite order, which include non-diagonal as well as the usual diagonal contributions. Preliminary calculations are performed on the correlation energy of the ground state of the helium atom using a numerical V N-1 basis set. In the case of helium, the diagonal contribution to the total pair result is found to be in error by less than 5 per cent.
TL;DR: In this paper, a practical scheme for obtaining total and local densities of states from non-orthogonal basis functions is described, and results for bulk SrTiO3 are presented by way of an example.
Abstract: A practical scheme for obtaining total and local densities of states from non-orthogonal basis functions is described, and results for bulk SrTiO3 are presented by way of an example.