Electronic structure errors associated with

Since the minima of subhamiltonians axe only extremely rough models for real-world electronic structures, it is clear that their use for the modeling of correlation effects is only justified if there is a high degree of cancellation of errors. That is, the errors associated with the use of the subhamiltonian model in the correlated and uncorrelated versions of the problem must be almost equal if the small difference associated with correlation is to be foimd. To see why such cancellation may be expected, we consider schematically the nature of the subhamiltonian and Hartree-Fock approximations. Recall that one could write the exact many-electron atom hamiltonian (for the probability amplitude) as where the four sets... 

The purpose of this chapter is to review the progress which has been made over the past few years on the problem of reducing the error associated with basis set truncation in molecular calculations and in atomic calculations using the algebraic approximation or basis set expansion technique. It is clearly not possible, within the space available, to give a completely comprehensive account of all developments which have recently been made in the field of basis set construction, a field that forms the foundation upon which the vast majority of contemporary atomic and molecular electronic structure studies are based. The review is, therefore, necessarily selective but, nevertheless, should provide an up-to-date account of the most important aspects of current thinking on the basis set expansion method or algebraic approximation. 

To complete the list of errors involved in the solution of the electronic Schrodinger equation, we must also define the error associated with a given calculation, i.e., a given choice of electronic structure method and basis set. The calculational error is given by... 

Figure 1 Definition of the errors associated with electronic structure calculations...

Although orbital wave functions, such as Hartree-Fock, generalized valence bond, or valence-orbital complete active space self-consistent field wave functions, provide a semi-quantitative description of the electronic structure of molecules, accurate predictions of molecular properties cannot be made without explicit inclusion of the effects of dynamical electron correlation. The accuracy of correlated molecular wave functions is determined by two inter-related expansions the many-electron expansion in terms of antisymmetrized products of molecular orbitals that defines the form of the wave function, and the basis set used to expand the one-electron molecular orbitals. The error associated with the first expansion is the electronic structure method error the error associated with the second expansion is the basis set error. Only by eliminating the basis set error, i.e., by approaching the complete basis set (CBS) limit, can the intrinsic accuracy of the electronic structure method be determined. 

Since 1989 there have been over one thousand papers published in the literature that make use of the correlation consistent basis sets. In this Appendix we provide a listing of the papers reporting the development of the correlation consistent basis sets as well as a partial listing of those papers that have explored the basis set convergence errors associated with the use of these sets. Many of these papers also report the intrinsic errors associated with the electronic structure methods. 

Uncertainties of the conventional parameters of H-atoms have been addressed since the early applications of X-ray charge density method. Support from ND measurements appears to be essential, because the neutron scattering power is a nuclear property (it is independent of the electronic structure and the scattering angle). The accuracy of nuclear parameters obtained from ND data thus depends mainly on the extent to which dynamic effects (most markedly thermal diffuse scattering) and extinction are correctable. Problems associated with different experimental conditions and different systematic errors affecting the ND and XRD measurements have to be addressed whenever a joint interpretation of these data is attempted. This has become apparent in studies which aimed either to refine XRD and ND data simultaneously [59] (commonly referred to as the X+N method), or to impose ND-derived parameters directly into the fit of XRD data (X—N method) [16]. In order to avoid these problems, usually only the ND parameters of the H-atoms are used and fixed in the XRD refinement (X-(X+N) method). 

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