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

Analysis of exchange interactions in dimers of Mn3 single-molecule magnets, and their sensitivity to external pressure