relativistic electronic structure calculations for molecules and clusters
kintech lab
 superheavy elements 
 rpp basis sets 
relativistic intermediate hamiltonians
transition property calculations
petersburg nuclear physics institute

Perturbed Transition Density Matrices

The diagonalization of the effective Hamiltonian Heff yields  the model-space parts of the target relativistic wavefunctions (|m>, |n>, ...). Provided that efficient `diagrammatic' algorithms are employed, no explicit approximation for the remainder (outer-space) parts of the wavefunctions is obtained. A convenient way to incorporate the contributions from these parts to transition property values consists in a perturbative calculation of transition density matrices.

The first-order approximation for the m - n transition spin-free density matrix mnR compatible with the use of the present approximation for Heff is given by

mnRrs = <m | Esr | n> +  JJ'  <m | J><J' | m K ( < J |Esr  | K>HKJ'/ D(J',K)
                                                                                      + HJK <K | Esr | J'> / D(J,K))


J and J' are model-space determinant indices and the determinants |K> are out of the model space,
s,r are the spatial orbital indices,
Esr denotes the spin-free one-electron r -> s excitation operator,
the definition of energy denominators  D(I,K) is the same as used for Heff .
Provided that  the spin-orbit interactions outside of the model space are neglected, HJK  = HScJK and the summation over K is similar with that required in non-relativistic or scalar-relativistic calculations.

The  m -> n  transition value of an one-electron property (Anm) is readily obtained as

Anm  = tr (mnR A),

where A is the property matrix in the chosen spatial orbital basis.


  • Nikolayeva O., Klincare I., Auzinsh M., Tamanis M., Ferber R., Pazyuk E.A., Stolyarov A.V., Zaitsevskii A., Cimiraglia R., J Chem Phys 2000, 113, 4896
  • Zaitsevskii A., Ferber R., Teichteil Ch., Phys Rev A  2001, 63, 042511

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