Dynamical Role of the Fictitious Orbital Mass in Car-Parrinello Molecular Dynamics

We investigate ion-orbital interaction in Car-Parinnello molecular dynamics (CPMD) analytically and numerically in order to probe the role of the fictitious orbital mass. We show analytically that this interaction can be described by linearly coupled oscillators when the system is sufficiently close to the ground state. This leads to ionic vibrational modes with frequency ωM that depends upon the ionic mass M and the orbital mass μ as \( {{{\omega }}_{\text{M}}}{ = }{{{\omega }}_{\text{0M}}}{{[1 - {\text C}(\mu /M)]}} \) in the limit of zero μ/M; ω0M is the Born-Oppenheimer ionic frequency and C depends upon the ion-orbital coupling force constants. This analysis provides new insight on the orbital mass dependence of the dynamics, and suggests a rigorous method of obtaining accurate ionic vibrational frequency using CPMD. We verify our analytical results with numerical simulations for N2, and discuss in detail the dynamical interaction between the ionic and the fictitious orbital modes in CPMD. Our results demonstrate that displacement from the ground state significantly affects ionic frequencies. In the linear regime this results in the linear dependence of ionic vibrational frequency upon μ/M. In the non-linear regime, even the ionic geometry deviates from the correct ground-state structure, highlighting the importance of staying close to the ground state in CPMD calculations.