  We study spin 1/2 isoscalar and isovector, even and odd parity candidates for
the $\Theta^+(1540)$ pentaquark particle using large scale lattice QCD
simulations. Previous lattice works led to inconclusive results because so far
it has not been possible to unambiguously identify the known scattering
spectrum and tell whether additionally a genuine pentaquark state also exists.
Here we carry out this analysis using several possible wave functions
(operators). Linear combinations of those have a good chance of spanning both
the scattering and pentaquark states. Our operator basis is the largest in the
literature, and it also includes spatially non-trivial ones with unit orbital
angular momentum. The cross correlator we compute is 14$\times$14 with 60
non-vanishing elements. We can clearly distinguish the lowest scattering
state(s) in both parity channels up to above the expected location of the
pentaquark, but we find no trace of the latter. Based on that we conclude that
there are most probably no pentaquark bound states at our quark masses,
corresponding to $m_\pi$=400--630 MeV. However, we cannot rule out the
existence of a pentaquark state at the physical quark mass corresponding to
$m_\pi$=135 MeV or pentaquarks with a more exotic wave function.
