Fano-ADC Theory of Electronic Decay Widths

It can be shown [16,17] that the bound-like state 4 , once prepared, will decay approximately exponentially in time, 

Consider the Hartree-Fock (HF) ground state of the N-electron neutral cluster, One can form a complete orthonormal set of the (N — l)-electron basis functions, fI/v 11, applying the so-called physical excitation operators, 

The ADC method overcomes these drawbacks by using a more complicated basis for the expansion of the (N — l)-electron wavefunctions. The idea is to apply the physical excitation operators, Q, to the perturbation-theoretically corrected, or correlated , ground state of the neutral system, 

The expansion coefficients, YJr are obtained by the diagonalization of the Hamiltonian matrix constructed in the basis of the intermediate states. It is a crucial feature of the ADC approach that the Hamiltonian matrix elements of the type ( Tj H T / can be expressed analytically via the orbital energies and the electron repulsion integrals if one performs the orthonormalization 

Consequently, in order to obtain the ADC(n) approximation for t , one can limit the physical excitation operators used in the construction of the CESs to those which satisfy the appropriate energy criterion  

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