  The phenomenon of self-assembly of constituent elements to form molecules at
low temperatures appears ubiquitously in transition metal compounds with
orbital degrees of freedom. Recent progress in local structure studies using
synchrotron radiation x-rays is shifting the interest in structural studies in
such molecule-forming systems from the low-temperature ordered phase to the
short-range order that appears like a precursor at high temperatures. In this
study, we discuss both experimentally and theoretically the relationship
between the trimer structure that appears in the layered LiV$X_2$ ($X$ = O, S,
Se) system with a two-dimensional triangular lattice of vanadium and the zigzag
chain-like local structure that appears near the phase transition boundary
where molecular formation occurs. The vanadium trimerization that persistently
appears in both low-temperature phases of LiVO$_2$ and LiVS$_2$ disappears in
LiVSe$_2$, and a regular triangular lattice is thought to be realized in
LiVSe$_2$, but this study reveals that the zigzag chain local distortion
appears with a finite correlation length. This zigzag chain state local
distortions are similar to the motif of local distortions in the
high-temperature phase of LiVS$_2$, indicating that the local distortions are
persistent away from the trimer phase transition boundary. On the other hand,
it is concluded that the zigzag chain order appearing in LiVSe$_2$ is more
stable than that in LiVS$_2$ in terms of the temperature variation of atomic
displacement and correlation length. The zigzag chain order is considered to be
competitive with the trimer order appearing in the LiV$X_2$ system. In this
paper, we discuss the similarities and differences between the parameters that
stabilize these electronic phases and the local distortions that appear in
other molecular formation systems.
