  This paper delves into the unexplored frequency-dependent characteristics of
beyond diagonal reconfigurable intelligent surfaces (BD-RISs). A generalized
practical frequency-dependent reflection model is proposed as a fundamental
framework for configuring fully-connected and group-connected RISs in a
multi-band multi-base station (BS) multiple-input multiple-output (MIMO)
network. Leveraging this practical model, multi-objective optimization
strategies are formulated to maximize the received power at multiple users
connected to different BSs, each operating under a distinct carrier frequency.
By relying on matrix theory and exploiting the symmetric structure of the
reflection matrices inherent to BD-RISs, relaxed tractable versions of the
challenging problems are achieved for scenarios with obstructed and
unobstructed direct channel links. The relaxed solutions are then combined with
codebook-based approaches to configure the practical capacitance values for the
BD-RISs. Simulation results reveal the frequency-dependent behaviors of
different RIS architectures and demonstrate the effectiveness of the proposed
schemes. Notably, BD-RISs exhibit high reflection performance across the
intended frequency range, remarkably outperforming conventional
single-connected RISs. Moreover, the proposed optimization approaches prove
effective in enabling the targeted operation of BD-RISs across one or more
carrier frequencies. The results also shed light on the potential for harmful
interference in the absence of synchronization between RISs and adjacent BSs.
