The molecular compound K$_6$[V$^{IV}_{15}$As$^{III}_6$O$_{42}$(H$_2$O)] $cdot$ 8H$_2$O, in short V$_{15}$, has shown important quantum effects such as coherent spin oscillations. The details of the spin quantum dynamics depend on the exact form of th
e spin Hamiltonian. In this study, we present a precise analysis of the intramolecular interactions in V$_{15}$. To that purpose, we performed high-field electron spin resonance measurements at 120 GHz and extracted the resonance fields as a function of crystal orientation and temperature. The data are compared against simulations using exact diagonalization to obtain the parameters of the molecular spin Hamiltonian.
