In light of the potential use of single-molecule magnets (SMMs) in emerging quantum information science initiatives, we report first-principles calculations of the magnetic exchange interactions in [$mathrm{Mn}_{3}$]$_{2}$ dimers of $mathrm{Mn}_3$ SMMs, connected by covalently-attached organic linkers, that have been synthesized and studied experimentally by magnetochemistry and EPR spectroscopy. Energy evaluations calibrated to experimental results give the sign and order of magnitude of the exchange coupling constant ($J_{12}$) between the two $mathrm{Mn}_{3}$ units that match with fits of magnetic susceptibility data and EPR spectra. Downfolding into the $mathrm{Mn}$ $d$-orbital basis, Wannier function analysis has shown that magnetic interactions can be channeled by ligand groups that are bonded by van der Waals interaction and/or by the linkers via covalent bonding of specific systems, and effective tight-binding Hamiltonians are obtained. We call this long-range coupling that involves a group of atoms a collective exchange. Orbital projected spin density of states and alternative Wannier transformations support this observation. To assess the sensitivity of $J_{12}$ to external pressure, stress-strain curves have been investigated for both hydrostatic and uniaxial pressure, which have revealed a switch of $J_{12}$ from ferromagnetic to antiferromagnetic with increasing pressure.
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