Novel equations to predict vibrational spectroscopic and electrodynamics properties of molecules

Mathematical relations linking electric and magnetic field-dependent physical properties of molecules have been unveiled. These relations are analogous to Maxwell relations in thermodynamics and are derived from mixed third-order partial derivatives of every alternative Legendre representation of the energy of molecules with respect to the electric or magnetic field and normal coordinates. Some of these novel physical relationships have practical applications in the low computational cost calculation of parameters commonly used in vibrational spectroscopy like the Stark and Zeeman Tuning Rates. Furthermore, other equalities have shown connections and alternative ways of computing physical properties used in electrodynamics as permanent dipolar moments and polarizabilities. (paper)