A new betacoronavirus named SARS-CoV-2 has emerged as a new threat to global health and economy. A promising target for both diagnosis and therapeutics treatments of the new disease named COVID-19 is the coronavirus (CoV) spike (S) glycoprotein. By constant-pH Monte Carlo simulations and the PROCEEDpKa method, we have mapped the electrostatic epitopes for four monoclonal antibodies and the angiotensin-converting enzyme 2 (ACE2) on both SARS-CoV-1 and the new SARS-CoV-2 S receptor binding domain (RBD) proteins. We also calculated free energy of interactions and shown that the S RBD proteins from both SARS viruses binds to ACE2 with similar affinities. However, the affinity between the S RBD protein from the new SARS-CoV-2 and ACE2 is higher than for any studied antibody previously found complexed with SARS-CoV-1. Based on physical chemical analysis and free energies estimates, we can shed some light on the involved molecular recognition processes, their clinical aspects, the implications for drug developments, and suggest structural modifications on the CR3022 antibody that would improve its binding affinities for SARS-CoV-2 and contribute to address the ongoing international health crisis.