State-specific many-electron method

Introduction of state-specific many-electron methods for the treatment of resonance states... 

The design of the mass spectrometer may influence its use in a particular kind of measurement. The study of electronic state-specific ions and their reactions has mainly been carried out using the GIB method. Metastable ions (ions produced by the ionization process but decomposing on the way to detection) can be observed in many of Type (1) mass spectrometers and metastable ions aid our understanding of the ionization process and stability of ions. Sequential reactions and kinetic studies of ion-molecule reactions are difficult with the simpler mass spectrometers of Type 1 and so more complex hybrid mass spectrometers have to be used. The ions observed in micro- or milliseconds after the ionization process may or may not be the same as ion observed seconds after the ionization process, which is a limitation in the use of Type 1 mass spectrometers. 

C.A. Nicolaides, Theory and State-Specific Methods for the Analysis and Computation of Field-Free and Field-Induced Unstable States in Atoms And Molecules, Adv. Quant. Chem. 60 (2010) 163 C.A. Nicolaides, Time-Dependence, Complex Scaling and the Calculation of Resonances in Many-Electron Systems, Int. J. Quant. Chem. 14 (1978) 457. 

Photodissociation of small polyatomic molecules is an ideal field for investigating molecular dynamics at a high level of precision. The last decade has seen an explosion of many new experimental methods which permit the study of bond fission on the basis of single quantum states. Experiments with three lasers — one to prepare the parent molecule in a particular vibrational-rotational state in the electronic ground state, one to excite the molecule into the continuum, and finally a third laser to probe the products — are quite usual today. State-specific chemistry finally has become reality. The understanding of such highly resolved measurements demands theoretical descriptions which go far beyond simple models. 

States whose zero-order labels are configurations, which are multiply excited (e.g., doubly, triply, or even quadruply excited) with respect to the ground main configuration, for example, see Ref. [10]. They can be created by the absorption of one or more photons. It is important to stress that these states are determined as solutions of their state-specific Schrbdinger equations and do not correspond, except perhaps by occasional accident, to the hierarchy of virtual excitations that appear in the many-electron treatments of electron correlation in ground states by the conventional methods of computational chemistry. 

One of the aims of this chapter, then, is to discuss the problem of calculating a property of a many-electron atom with suflicient precision so that the new physics of radiative corrections can be studied. The challenge to many-body theory is quite specific. As will be discussed below, properties of cesium, the atom in which the most accurate PNC measurement has been made [5] must be calculated to the fraction of a percent level to accurately study PNC and radiative corrections to it can this level in fact be reached by modern many-body methods While great progress has been made, the particular nature of this problem, in which relativity has to be incorporated from the start, and a transition between two open-shell states calculated in the presence of a parity-nonconserving interaction, has not permitted solution of the many-body problem to the desired level. It may well be that a reader of this chapter has developed techniques for some other many-electron problem that are of sufficient power to resolve this issue this chapter is meant to clearly lay out the nature of the calculation so that the reader can apply those techniques to what is, after all, a relatively simple system by the standards of quantum chemistry, an isolated cesium atom. 

So far most of the computations have been performed for few-electron atoms or for medium atoms modeled by one-electron potentials. However, there are methods, like the state specific CESE and MEMPT approach (13), which can be applied to leurger systems. Also combination of complex-rotation technique with the many body perturbation theory (30) or coupled cluster method (31), which are addressed to large systems, seems to be promissing in this context. 

More appropriate than perturbation approaches for improving on the energy are variational approaches (under the specific caveats discussed in chapter 8 with respect to the negative-energy states), because the total electronic energies obtained are much better controlled, an essential property since the exact reference is not known for any interesting many-electron molecule. In particular, we shall address the second-generation MCSCF methods mentioned in chapter 8. For reference to molecular Cl and CC theory, please consult sections 8.5.2 and 8.9, respectively. 

Multiple PESs may be of simultaneous interest based not only on physical reasons, as emphasized in the previous paragraph, but also for mathematical or computational reasons. Consider the basic paradigm of state-selective methods the nondynamical electron correlation for a specific state is calculated within a model space and then the dynamical electron correlation is calculated. The implicit assumption is that the zero-order model space many-electron basis functions (MEBFs) (e.g., MCSCF functions and MCSCF complementary space... 

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