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In this work we demonstrate that accurate ground state wave functions may be constructed for polarons in a fully ab initio setting across the wide range of couplings associated with both the large and small polaron limits. We present a single general unitary transformation approach which encompasses an ab initio version of the Lee-Low-Pines theory at weak coupling and the coherent state Landau-Pekar framework at strong coupling while interpolating between these limits in general cases. We show that perturbation theory around these limits may be performed in a facile manner to assess the accuracy of the approach, as well as provide an independent route to the ab initio properties of polarons. We test these ideas on the case of LiF, where the electron-polaron is expected to be large and relatively weakly coupled, while the hole-polaron is expected to be a strongly coupled small polaron. 

Alloys of tungsten tetraboride (WB4) with the addition of C and Si were prepared by arc-melting of the constituent elements. The phase purity was established by powder X-ray diffraction (PXRD) and surface morphology by scanning electron microscopy (SEM) analysis. Vickers hardness measurements showed hardness enhancement for alloys with a nominal composition of (W0.98Si0.02):11.6B and (W0.95C0.05):11.6B of 52.2 ± 3.0 and 50.5 ± 2.5 GPa, respectively, compared to 41.2 ± 1.4 GPa for pure WB4. (W0.92Zr0.08):11.6B was determined in previous work to have a hardness of 55.9 ± 2.8 GPa. Bulk moduli were calculated following analysis of high-pressure radial diffraction data and were determined to be 329 ± 4 (K0′ = 2) and 390 ± 9 (K0′ = 0.6) GPa for 8 atom % Zr and 5 atom % C-doping, respectively, compared to 326–339 GPa for pure WB4. Computational analysis was used to determine the dopant positions in the crystal structure, and it was found that Zr primarily substitutes W in the 2c position, Si substitutes for the entire B3 trimers, and C inserts in the Bhex-layer. The hardness enhancement in the case of Zr-doping is attributed primarily to extrinsic hardness effects (nanograin morphology), in the case of C─to intrinsic effects (interlayer bond strengthening), and in the intermediate case of Si─to both intrinsic and extrinsic effects (bond strengthening and fine surface morphology).