  Developing a bottom-up (molecular) theory for the electromechanical response
of aperiodic materials is a prerequisite for understanding the piezoelectric
properties of systems such as nanoparticles, (non-crystalline) polymers, or
biomolecule agglomerates. The focus of this publication is to establish a new
language and formalism for describing molecular piezoelectric responses. More
specifically, we define the molecular piezoelectric response tensor d, which
necessarily differs from the known bulk definition due to the anisotropy and
inhomogeneity at the molecular scale, and derive an analytical theory to
calculate this tensor. Based on this new theory, we develop a computational
procedure for practical calculations of piezoelectric matrices for molecular
systems. Our studies demonstrate that the new analytical theory yields results
that are consistent with fully numerical computations. This publication is the
first in a series; this work establishes the theoretical molecular foundation
and follow-up publications will show how to bridge molecular and macroscopic
piezoelectric responses. It is expected that the present work will aid in
developing design strategies for piezoelectric materials by revealing
connections between molecular structure and piezoelectric response. We expect
that the language and formalism developed here may also be useful to describe
mechanochemical phenomena.
