  We propose a method using reduced size of Hilbert space to describe an
electron dynamics in molecule and aggregate based on our previous theoretical
scheme [ T. Yonehara and T. Nakajima, J. Chem. Phys. \textbf{147}, 074110
(2017) ]. The real-time time-dependent density functional theory is combined
with newly introduced projected group diabatic Fock matrix. First, this
projection method is applied to a test donor--acceptor dimer, namely, a
naphthalene--tetracyanoethylene with and without initial local excitations and
light fields. Secondly, we calculate an absorption spectrum of
five-unit-polythiophene monomer. The importance of feedback of instantaneous
density to Fock matrix is also clarified. In all cases, half of the orbitals
were safely reduced without loss of accuracy in descriptions of properties. The
present scheme provides one possible way to investigate and analyze a complex
excited electron dynamics in molecular aggregates within a moderate
computational cost.
