  The Green's function coupled cluster (GFCC) method is a powerful many-body
tool for computing the electronic structure of molecular and periodic systems,
especially when electrons of the system are strongly correlated. However, for
the GFCC to be routinely used in the electronic structure calculations, robust
numerical techniques and approximations must be employed to reduce its high
computational overhead. In our recent studies, we demonstrated that the GFCC
equations can be solved directly in the frequency domain using iterative linear
solvers, which can be easily distributed in a massively parallel environment.
In the present work, we demonstrate a successful application of
model-order-reduction (MOR) techniques in the GFCC framework. Briefly, for a
frequency regime which requires high resolution spectral function, instead of
solving GFCC linear equation of full dimension for every single frequency
point, an efficiently-solvable linear system model of a reduced dimension may
be built upon projecting the original GFCC linear system onto a subspace. From
this reduced order model is obtained a reasonable approximation to the full
dimensional GFCC linear equations in both interpolative and extrapolative
spectral regions. Here, we show that the subspace can be properly constructed
in an iterative manner from the auxiliary vectors of the GFCC linear equations
at some selected frequencies within the spectral region of interest. During the
iterations, the quality of the subspace and the linear system model can be
systematically improved. The method is tested in terms of the efficiency and
accuracy of computing spectral functions for some typical molecular systems
such as carbon monoxide, 1,3-butadiene, benzene, and adenine. As a byproduct,
the obtained reduced order model may provide a high quality initial guess which
improves the convergence rate for the existing iterative linear solver.
