Perturbation theories development requirements

Btiilding on atomic studies using even-tempered basis sets, universal basis sets and systematic sequences of even-tempered basis sets, recent work has shown that molecular basis sets can be systematically developed until the error associated with basis set truncation is less that some required tolerance. The approach has been applied first to diatomic molecules within the Hartree-Fock formalism[12] [13] [14] [15] [16] [17] where finite difference[18] [19] [20] [21] and finite element[22] [23] [24] [25] calculations provide benchmarks against which the results of finite basis set studies can be measured and then to polyatomic molecules and in calculations which take account of electron correlation effects by means of second order perturbation theory. The basis sets employed in these calculations are even-tempered and distributed, that is they contain functions centred not only on the atomic nuclei but also on the midpoints of the line segments between these nuclei and at other points. Functions centred on the bond centres were found to be very effective in approaching the Hartree-Fock limit but somewhat less effective in recovering correlation effects. 

Spectroscopic methods can yield the required understanding of the complexes. Especially optical spectroscopy provides very detailed information about electronic and vibronic structures, in particular, when highly resolved spectra are available. However, without the development of suitable models, which are usually based on perturbation theory, group theory, and recently also on ab-initio calculations, a thorough understanding of the complexes is very difficult to achieve. In this volume and in a subsequent one some leading researchers will show that such a detailed description of... 

This paper presents an account of the dynamics of electric charges coupled to electromagnetic fields. The main approximation is to use non-relativistic forms for the charge and current density. A quantum theory requires either a Lagrangian or a Hamiltonian formulation of the dynamics in atomic and molecular physics the latter is almost universal so the main thrust of the paper is the development of a general Hamiltonian. It is this Hamiltonian that provides the basis for a recent demonstration that the S-matrix on the energy shell is gauge-invariant to all orders of perturbation theory. 

The accurate calculation of these molecular properties requires the use of ab initio methods, which have increased enormously in accuracy and efficiency in the last three decades. Ab initio methods have developed in two directions first, the level of approximation has become increasingly sophisticated and, hence, accurate. The earliest ab initio calculations used the Hartree-Fock/self-consistent field (HF/SCF) methodology, which is the simplest to implement. Subsequently, such methods as Mpller-Plesset perturbation theory, multi-configuration self-consistent field theory (MCSCF) and coupled-cluster (CC) theory have been developed and implemented. Relatively recently, density functional theory (DFT) has become the method of choice since it yields an accuracy much greater than that of HF/SCF while requiring relatively little additional computational effort. 

Its extension to heavy baryon chiral perturbation theory (HBCHPT) [3] allows to calculate many of the experimentally accessible processes in the meson nucleon sector. The check of the soundness of this approach requires high precision experiments. This resembles the situation in the development of QED during the last 50 years, where the measurement of the Lamb shift contributed much to the development of QED. In a comparable way the measurement of strong interaction shift and width in pionic hydrogen may be a key experiment in strong interaction physics at low energies. 

Direct ab initio methods, in which data are recomputed when required, rather than being stored and retrieved, provide an alternative that seems more useful for parallel development. The simplest level of ad initio treatment (self-consistent field methods) can be readily parallelized when direct approaches are being exploited. Experience demonstrates, however, that data replication methods will not lead to truly scalable implementations, and several distributed-data schemes (described later) have been tried. These general approaches have also been used to develop scalable parallel implementations of density functional theory (DFT) methods and the simplest conventional treatment of electron correlation (second-order perturbation theory, MP2) by several groups. 3-118... 

The incorporation of correlation effects in calculations for periodic solids requires the use of a many-body formalism. Second order many-body perturbation theory, in its MP2 form, should provide the basis of an efficient computational approach to this problem. In particular, the local MP2 methods originally developed for large molecules can be adapted for the treatment of periodic solids. 

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