  We present a formulation of Laplace-transformed atomic orbital-based
second-order M{\o}ller-Plesset perturbation theory (MP2) energies for
two-component Hamiltonians in the Kramers-restricted formalism. This low-order
scaling technique can be used to enable correlated relativistic calculations
for large molecular systems. We show that the working equations to compute the
relativistic MP2 energy differ by merely a change of algebra (quaternion
instead of real) from their non-relativistic counterparts. With a
proof-of-principle implementation we study the effect of the nuclear charge on
the magnitude of half-transformed integrals and show that for light elements
spin-free and spin-orbit MP2 energies are almost identical. Furthermore, we
investigate the effect of separation of charge distributions on the Coulomb and
exchange energy con- tributions, which show the same long-range decay with the
inter-electronic / atomic distance as for non-relativistic MP2. A linearly
scaling implementation is possible if the proper distance behavior is
introduced to the quaternion Schwarz-type estimates as for non-relativistic
MP2.
