Configuration expansions

Tycho, D. H., Thomas, L. H., and King, K.M., Phys. Rev. 109,369, Numerical calculation of the wave functions and energies of the PS and 23S states of He." Configurational expansion determined by numerical method angular terms up to l— 14 included. 

More recently, Kleinekathofer, Patil, Tang, and Toennies (KPTT) [10] proposed a far more compact wavefunction for He-like systems, based on the use of a functional form that is essentially completely determined by requiring proper behavior of the wavefunction at small and large-r limits. The KPTT wavefunction is more complicated to use than the functions entering the large-scale accurate computations and from the perspective of the present authors is comparable in utility to a moderate-length configuration expansion. Its virtue is its lack of arbitrary parameters. 

In Tables -A, we report oscillator strengths for some fine structure transitions in neutral fluorine, chlorine, bromine and iodine, respectively. Two sets of RQDO/-values are shown, those computed with the standard dipole length operator g(r) = r, and those where core-valence correlation has been explicitly introduced, Eq. (10). As comparative data, we have included in the tables /-values taken from critical compilations [15,18], results of length and velocity /-values by Ojha and Hibbert [17], who used large configuration expansions in the atomic structure code CIVS, and absolute transition probabilities measured through a gas-driven shock tube by Bengtson et al. converted... 

P.E.M. Siegbahn, The Direct Configuration Interaction Method with a Contracted Configuration Expansion, Chem. Phys. 25, 197 (1977). 

The multireference results of Table 5.12 were all based on full valence CASSCF calculations with eleven electrons in twelve active orbitals. This produces a large configuration expansion (about 85 000 CSFs) so it is not possible to perform MRCI(CAS) calculations. Reference configuration lists were selected at the cyclic and linear geometries (taken from MP2 optimized structures) and then merged. The core electrons were not correlated in any of the calculations. One complication in the CASSCF calculations should be pointed out. Since the cyclic state arises as the 2B component, in C3v symmetry, of a 2E state in the D3h symmetry (equilateral triangular) structure, it would be desirable to obtain MOs with D3h symmetry and equivalence restrictions... 

We have in the present paper investigated two fundamentally different, yet complementary, routes to computational studies of radical hyperfine structures. On the one hand, we have the highly accurate MRCI - based approaches, which are able to predict hyperfine structures of small systems to very high accuracy. The role and importance of higher than double excitations in the configuration expansions has been elucidated by means of detailed case studies on a number of first row atoms, as well some selected molecular systems. We have also demonstrated how a newly developed method, the MRD-CI/Bk method, by means of a perturbative method is able to incorporate the effects... 

Most of the present discussion has been concerned with applications of REPs within the framework of otherwise essentially orbital-based calculations. On the other hand, a recent application 110) involved a quantum Monte Carlo (QMC) procedure. [A useful overview of Monte Carlo electronic structure work has been given by Ceperly and Alder 111). ] Currently, QMC offers little, if any, competition for conventional calculations in that the computer time required to reduce statistical errors to acceptable limits increases rapidly as a function of atomic number and is excessive for all but the smallest systems. Recent fluorine calculations required nearly 100 hours of supercomputer time 112). Although, on the surface, it would appear totally impractical, the appeal of this approach in the context of heavy-element work is its avoidance of extensive basis sets and enormous configuration expansions that plague present studies. 

For large configuration expansions the linear transformation Eq. (86) is the time-consuming step in the iterative scheme. For convenience we write the linear transformation as... 

W. Meyer, Configuration Expansion by Means of Pseudonatural Orbitals, Modern Theoretical... 

P.J. Knowles, H.J. Werner, An efficient 2nd-order MC SCF method for long configuration expansions, Chem. Phys. Lett. 115 (3) (1985) 259-267. 

An overview of quantum Monte Carlo electronic structure studies in the context of recent effective potential implementations is given. New results for three electron systems are presented. As long as care is taken in the selection of trial wavefunctions, and appropriate frozen core corrections are included, agreement with experiment is excellent (errors less than 0.1 eV). This approach offers promise as a means of avoiding the excessive configuration expansions that have plagued more conventional transition metal studies. 

Configuring expansion cards for use in ISA buses is a little less complex than configuring 8-bit buses, mainly because there are more choices available for interrupts and DMA channels. Tables 5.3 and 5.4 list the interrupts and DMA channels that are available in an ISA system. 

Once we covered the theory of PC resources, we moved on to the physical act of configuring expansion boards. No book can cover every technique, but we covered the most common methods used to configure components—jumpers, DIP switches, software, and Plug-and-Play technology. 

W. Meyer, Configuration expansion by means of pseudonatural orbitals, in Methods of Electronic Structure Theory, edited by H. F. Schaefer, pages 413-446. Plenum Press, New York, 1977. 

In complete active space self-consistent field (CASSCF) calculations with long configuration expansions the most expensive part is often the optimization of the Cl coefficients. It is, therefore, particularly important to minimize the number of Cl iterations. In conventional direct second-order MCSCF procedures , the Cl coefficients are updated together with the orbital parameters in each micro-iteration. Since the optimization requires typically 100-150 micro-iterations, such calculations with many configurations can be rather expensive. A possible remedy to this problem is to decouple the orbital and Cl optimizations , but this causes the loss of quadratic convergence. The following method allows one to update the Cl coefficients much fewer times than the orbital parameters. This saves considerable time without loss of the quadratic convergence behaviour. 

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