  We propose a new form of the frustrated Heisenberg antiferromagnetic
Hamiltonian with spatially anisotropic exchange parameters Jc, Ja, and Jac
extended along the c, a, and a +/- c lattice directions and apply it to
describe fascinating physics of copper carbodiimide CuNCN in the assumption of
resonating valence bond (RVB) type of its phases. These are invoked to explain
the intriguing absence of magnetic order in CuNCN down to 4 K. We show that the
quasiparticle spectrum of the RVB model of the proposed Hamiltonian has three
principal regimes: (i) one with two pairs of lines of nodes, (ii) one with a
pair of lines of nodes (termed as 1D- and Q1D-RVB states), (iii) and one with
two pseudogaps and four nodal points (2D-RVB). We present a complete
parameters-temperature phase diagram of the model constructed with use of the
high-temperature expansion of the free energy. The phase diagram thus obtained
contains eight different phases whose magnetic behavior includes Curie and
Pauli paramagnetism (respectively, in disordered and 1D- or Q1D-RVB phases),
and gapped (quasi-Arrhenius) paramagnetism (2D-RVB phases). Adding
magnetostriction and elastic terms to the free energy we derive possible
structural manifestations of transitions between RVB phases. Assuming a
sequence of transitions between RVB phases to occur in CuNCN while temperature
decreases explains the features observed in the temperature runs of the
magnetic susceptibility and lattice constants. Confronting these with the
magnetic susceptibility and structure data measured as functions of temperature
in the range between ca. 20 and 200 K we show a remarkably good agreement
between our theoretical predictions and the experiment as reached by ascribing
the model parameters values which are intuitively acceptable both in terms of
their absolute and relative magnitudes and of the character of their geometry
dependence.
