relativistic electronic structure calculations for molecules and clusters 

The diagonalization of the effective Hamiltonian H^{eff} yields the modelspace parts of the target relativistic wavefunctions (m>, n>, ...). Provided that efficient `diagrammatic' algorithms are employed, no explicit approximation for the remainder (outerspace) 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 firstorder approximation for the m  n transition spinfree density matrix ^{mn}R compatible with the use of the present approximation for H^{eff} is given by ^{mn}R_{rs
}= <m  E_{sr
}
n> + _{
JJ' } <m

J><J'

m> _{
K
}( < J E_{sr }
 K>H_{KJ'}/ D(J',K)
where J and J' are modelspace determinant indices and the determinants K> are out of the model space,Provided that the spinorbit interactions outside of the model space are neglected, H_{JK} = H^{Sc}_{JK} and the summation over K is similar with that required in nonrelativistic or scalarrelativistic calculations. The m > n transition value of an oneelectron property (A_{nm)} is readily obtained as A_{nm} = tr (^{mn}R A), where A is the property matrix in the chosen spatial orbital basis. References
