  We analyse the properties of the kaonic nuclear cluster (KNC) anti-KNN with
the structure Nx(anti-KN)_(I = 0), having the quantum numbers I(J^P) =
1/2(0^-), and treated as a quasi-bound hadronic molecule state. We describe the
properties of the hadronic molecule, or the KNC Nx(anti-KN)_(I = 0), in terms
of vibrational degrees of freedom with oscillator wave functions and chiral
dynamics. These wave functions, having the meaning of trial wave functions of
variational calculations, are parameterised by the frequency of oscillations of
the (anti-KN)_(I = 0) pair, which is fixed in terms of the binding energy of
the strange baryon resonance Lambda(1405), treated as a quasi-bound
(anti-KN)_(I = 0) state. The binding energies B_X and widths Gamma_X of the
states X = (anti-KN)_(I = 0) and X = anti-KNN, respectively, are calculated in
the heavy-baryon approximation by using chiral Lagrangians with meson-baryon
derivative couplings invariant under chiral SU(3)xSU(3) symmetry at the
tree-level approximation. The results are B_(anti-KNN) = 40.2 MeV and
Gamma_(anti-KNN) = Gamma^(non-pionic)_(anti-KNN) + Gamma^(pionic)_(anti-KNN) ~
(85 - 106) MeV and, where Gamma^(non-pionic)_(anti-KNN) ~ 21 MeV and
Gamma^(pionic)_(anti-KNN) ~ (64 - 86) MeV are the widths of non-pionic anti-KNN
-> N Lambda^0, N Sigma and pionic anti-KNN -> N Sigma pi decay modes,
calculated for B_(anti-KN) = 29 MeV and Gamma_(anti-KN) = (30 - 40) MeV,
respectively.
