Multi-configuration-based approximation

Werner and co-workers [2, 21, 34] used internally-contracted multi-reference configuration-interaction (IC-MRCI) calculations, based on state-averaged (three-state) multi-configuration, self-consistent-field (MCSCF) calculations with large atomic orbital basis sets, to determine the three electronically adiabatic C1(F)+H2 PESs in the reactant arrangement L4, 2A, and lA. These all correlate with X( P) + H2. These three adiabatic electronic states are the IC-MRCI approximations to the three lowest eigenfunctions of Hgi, namely... 

As indicated above, neither the SCF nor the DFT method is able to treat the Van der Waals interaction. This is well established for the SCF approximation [14, 15]. The Van der Waals interaction is a typical correlation effect therefore, its description requires the use of a correlated method . In wave function based ab initio methods correlation effects are described by adding singly, doubly and higher excited configurations to the SCF or to a multi-configuration SCF (MC-SCF or complete active space SCF, CASSCF) wave function. This can be done by means of perturbation theory (PT),by configuration interaction (Cl)... 

The EBO concept rehes on a multi-configurational wavefunction and takes into account the effect of electron correlation involving the antibonding orbitals. There are various ways of quantifying bond orders [12-14]. The Natural Bond Orbital (NBO) valence and bonding concepts are also extensively used in the analysis of multiple bonds. NBO, like EBO, is based on a quantum mechanical wavefunction. The NBO description of a bond can be derived by variational, perturbative, or density functional theory (DFT) approximations of arbitrary form and accuracy [15]. 

When considering the femtosecond photoionization dynamics of complex systems, a completely exact evaluation of the time and energy resolved photoelectron spectrum is often not really necessary. Approximative schemes which require significantly lower computational effort are valuable in such cases. Within the nonperturbative formalism, Meier et al. have proposed an efficient computational scheme which incorporates the multi-configuration time-dependent Hartree method.An approximate method which is based on a classical-trajectory description of the nuclear dynamics has been elaborated by Hartmann, Heidenreich, Bonacic-Koutecky and coworkers and applied, among other systems,to the time-resolved photoionization spectroscopy of conical intersections in sodium fluoride clusters. 

However, if this is not the case, the perturbations are large and perturbation theory is no longer appropriate. In other words, perturbation methods based on single-determinant wavefunctions cannot be used to recover non-dynamic correlation effects in cases where more than one configuration is needed to obtain a reasonable approximation to the true many-electron wavefunction. This represents a serious impediment to the calculation of well-correlated wavefunctions for excited states which is only possible by means of cumbersome and computationally expensive multi-reference Cl methods. 

Apparently, a large number of successful relativistic configuration-interaction (RCI) and multi-reference Dirac-Hartree-Fock (MRDHF) calculations [27] reported over the last two decades are supposedly based on the DBC Hamiltonian. This apparent success seems to contradict the earlier claims of the CD. As shown by Sucher [18,28], in fact the RCI and MRDHF calculations are not based on the DBC Hamiltonian, but on an approximation to a more fundamental Hamiltonian based on QED which does not suffer from the CD. At this point, let us defer further discussion until we review the many-fermion Hamiltonians derived from QED. 

Here we extend the simple three-level EIT system to mote complicated and versatile configurations in a multi-level atomic system coupled by multiple laser fields. We show that with multiple excitation paths provided by different laser fields, phase-dependent quantum interference is induced either constractive or destractive interfereiKe can be realized by varying the relative phases among the laser fields. Two specific examples are discussed. One is a three-level system coupled by bichromatic coupling and probe fields, in which the phase dependent interference between the resonant two-photon Raman transitions can be initiated and controlled. Another is a four-level system coupled by two coupling fields and two probe fields, in which a double-EIT confignration is created by the phase-dependent interference between three-photon and one-photon excitation processes. We analyze the coherently coupled multi-level atomic system and discuss the control parameters for the onset of constructive or destructive quantum interference. We describe two experiments performed with cold Rb atoms that can be approximately treated as the coherently coupled three-level and four-level atomic systems respectively. The experimental results show the phase-dependent quantum coherence and interference in the multi-level Rb atomic system, and agree with the theoretical calculations based on the coherently coupled three-level or four-level model system. 

A brief introduction to the method of configuration interaction has been given in Chapter 3, Section 3.3.1. Approximations based on ci expansions include ci d, ci SD, etc. and their multi-reference variants mr-ci d, mr-ci sd, etc. 

Several attempts have been made to remove the pervasive failing of the perturbative CC approximations at large internuclear separations. The representative examples include the externally-corrected SRCC methods (6,10,63-74), the active-space SRCC approaches (14,19, 75-86), the orbital-optimized SRCC methods (39,87,88), and the perturbative CC approaches based on the partitioning of the similarity-transformed Hamiltonian (89,90) (see ref 91 for the original idea). Of all these approaches, the reduced MRCCSD (RMRCCSD) method (68-74), which uses the multi-reference configuration interaction (MRCI) wave Unctions to extract information about triply and quadruply excited clusters, and the active-space CCSDt and CCSDtq methods (19,85,86) and their earlier state-selective (SS) CCSD(T) and CCSD(TQ) analogs (14, 75-84) are particularly promising. The RMRCCSD approach can be used to success-... 

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