  Though the effects of metal dopants on the electrostructural transition of
rutile VO$_2$ have been studied for many decades, there is still no consensus
explanation for the observed trends. A major challenge has been to separate the
impact of a dopant's size from other factors such as its electronic
configuration, which stems from the difficulty in directly probing the local
bonding environment around a dopant atom. This work addresses the special case
of larger dopant ions by combining X-ray total scattering experiments on
V$_{0.83}$Mo$_{0.17}$O$_2$ and V$_{0.89}$Nb$_{0.11}$O$_2$ single crystals with
multiple Monte Carlo method models to simulate local size effects in the
high-temperature tetragonal phase (R). We find that sufficiently long apical
metal-oxygen bonds (M$-$O$_{ap}$) induce a strain field in the neighboring
chains that locally resembles the metal-metal dimer formation present in the
low-temperature distorted structure of VO$_2$ (M1). The dimer mode in the M1
structure is antisymmetric along M$-$O$_{ap}$, however, while the
strain-induced pseudodimer motif is symmetric. The implied direct competition
between motifs is verified experimentally. This finding provides a new
mechanistic parameter toward understanding the phase transition. More
generally, the work highlights how local strain fields around dopants can lead
to complex distortions that are ordinarily attributed to electronic origins.
