We have applied an alignment-free technique to infer functional relatedness among betacoronaviruses. This technique, concurrently being optimized for identifying novel prions, was adapted to gain new insights into coronavirus evolution, specifically in the context of the COVID-19 pandemic caused by novel coronavirus SARS-CoV-2. With COVID-19 already having killed over ∼4.8 million people worldwide as of this writing, novel methods for predicting the capacity for coronaviruses in general to infect human cells are needed. Our proposed method utilizes physicochemical properties of amino acids to develop a fully dynamic waveform representation of proteins that encodes both the amino acid content and the context of amino acids. These waveforms are then subjected to dynamic time warping and distance evaluation to develop a distance metric that is relatively less sensitive to variation in sequence length or primary amino acid composition. Using this method, we show that in contrast to alignment-based maximum likelihood and neighbor-joining phylogenetic analyses, all bat betacoronavirus spike protein receptor binding domains (RBDs) known to bind to the ACE2 receptor are found within a single physicochemical cluster. Further, other RBDs within that cluster are from pangolin coronaviruses, two of which have already been shown to bind to ACE2 while the others are suspected, yet unverified ACE2 binding domains. This finding is important because both SARS-CoV and SARS-CoV-2 use the host ACE2 receptor for cell entry. Surveillance for coronaviruses belonging to this cluster could potentially guide efforts to stifle or curtail potential and/or early zoonotic outbreaks with their associated deaths and financial devastation.