  A new explicitly correlated functional form for expanding the wave function
of an N-particle system with arbitrary angular momentum and parity is
presented. We develop the projection-based approach, numerically exploited in
our previous work [J. Chem. Phys. 149, 184105 (2018)], to explicitly correlated
Gausssians with one-axis shifted centers and derive the matrix elements for the
Hamiltonian and the angular momentum operators by analytically solving the
integral projection operator. Variational few-body calculations without
assuming the Born-Oppenheimer approximation are presented for several
rotationally excited states of three- and four-particle systems. We show how
the new formalism can be used as a unified framework for high-accuracy
calculations of properties of small atoms and molecules.
