Calculation of matrix elements in relativistic quantum mechanics

Employing a relativistic version of a hypervirial result, recurrence relations for arbitrary nondiagonal radial hydrogenic matrix elements have recently been obtained in Dirac relativistic quantum mechanics. In this contribution honoring Professor Löwdin, we report on a new relation we have recently discovered between the matrix elements 〈2∣ r λ ∣1〉 and 〈2∣β r λ ∣1〉—where β is a Dirac matrix and the numbers distiguish between different radial eigenstates—that allow for a simplification and hence for a more convenient way of expressing the recurrence relations. We additionally derive another relation that can be employed for simplifying two‐center matrix element calculations in relativistic atomic or molecular calculations. © 2002 John Wiley & Sons, Inc. Int J Quantum Chem, 2002