**Abstract**

It is proposed to use a norm of a *n*th order effective
Hamiltonian, for analyzing the convergence property of the
multireference many-body perturbation theory (MR-MBPT). The
utilization of the norm allows us to employ only (1) a *single*
number for the all the states that we are interested in, and (2)
values which decreases from the *positive* side to zero as the
order *n* of the perturbation increases. This characteristic
features are in contrast to thosed in the usually used scheme
where *several* numbers, namely, the eivenvalues of the target
states, should be used and they may *oscillate* around exact
eigenvalues. The present method has been applied to MR-MBPT
calculations of the (H_{2})_{2}, CH_{2}, and
LiH molecules based on the multireference versions of
Rayleigh–Schrödinger PT,
Kirtman–Certain–Hirschfelder PT, and the canonical Van
Vleck PT; and following features are found: (1) the above three
versions of the perturbation theories have essentially the same
convergence property judged from the lowering of the norm; (2) the
lower order truncation of the perturbation series gives reasonable
solutions; (3) the norm decreases irrespective of the perturbation
expansion being convergent for the first several orders (up to about
the sixth order).