  We have applied the momentum space version of the Density Matrix
Renormalization Group method ($k$-DMRG) in quantum chemistry in order to study
the accuracy of the algorithm in the new context. We have shown numerically
that it is possible to determine the desired accuracy of the method in advance
of the calculations by dynamically controlling the truncation error and the
number of block states using a novel protocol which we dubbed Dynamical Block
State Selection (DBSS). The relationship between the real error and truncation
error has been studied as a function of the number of orbitals and the fraction
of filled orbitals. We have calculated the ground state of the molecules
CH$_2$, H$_2$O, and F$_2$ as well as the first excited state of CH$_2$. Our
largest calculations were carried out with 57 orbitals, the largest number of
block states was 1500--2000, and the largest dimensions of the Hilbert space of
the superblock configuration was 800.000--1.200.000.
