Symmetries of nonlinear vibrations in tetrahedral molecular configurations (Q2316409)

The authors study nonlinear vibrations of tetrahedral molecules. The equations of motion are Newton's equation \[\ddot{u} (t) = - \nabla\; V (u (t)), \] where \(V\) is a potential that takes into account the interaction among atoms due to bond stretching, van der Waals forces and electrostatic forces. The authors use the method of equivariant degrees to study the existence of periodic solutions around an equilibrium state that admits \( S_4 \) symmetry. The analysis of the isotypic expansion of the eigenvalues of the Hessian is carried out. The global existence of families of periodic solutions around the tetrahedral equilibrium is proved. Further, space-time symmetries of various families of periodic solutions with a finite Weyl group are described.