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Car-Parrinello molecular dynamics (CPMD) are widely used to investigate the dynamical properties of molecular systems. An important issue in such applications is the dependence of dynamical quantities such as molecular vibrational frequencies upon the fictitious orbital mass μ. Although it is known that the correct Born-Oppenheimer dynamics are recovered at zero μ, it is not clear how these dynamical quantities are to be rigorously extracted from CPMD calculations. Our work addresses this issue for vibrational frequencies. We show that when the system is sufficiently close to the ground state the calculated ionic vibrational frequencies are ω(M) = ω(0M)[1 -C(μ/M)] for small μ/M, where ω(0M) is the Born-Oppenheimer ionic frequency, M the ionic mass, and C a constant that depends upon the ion-orbital coupling force constants. Our analysis also provides a quantitative understanding of the orbital oscillation amplitudes, leading to a relationship between the adiabaticity of a system and the ion-orbital coupling constants. In particular, we show that there is a significant systematic dependence of calculated vibrational frequencies upon how close the CPMD trajectory is to the Born-Oppenheimer surface. We verify our analytical results with numerical simulations for N(2), Sn(2), and H/Si(100)-(2×1).

The physical and chemical properties of transition metal nanoclusters have been extensively investigated. In particular, we study the energetics of the mixed clusters Pt4−n Ni n , focusing on the binding energy of the clusters E bind to a graphene support, and the hydrogenation energy E ads in both the gas-phase and the graphene-supported clusters. For each cluster composition, the cluster can bind to graphene in either a face-on or an edge-on configuration, and in each of these orientations, binding can occur through different atoms; we explore these binding configurations comprehensively. We discuss the variation of E bind and E ads with respect to the composition of the cluster and the binding configuration of the cluster to the graphene support. Our results show that hydrogen is generally chemisorbed at a Pt site and physisorbed at a Ni site, with a dependence of the adsorption energy upon the composition and the adsorption configuration. Compared with the gas-phase cluster, the chemisorption energies are generally reduced, whereas the physisorption energies are generally increased when the cluster is supported on graphene. We show that the reduction in chemisorption energies can be understood in terms of the reduction in the intracluster bond strength and the binding energy to graphene, whereas the increase in physisorption energies can be understood in terms of an increase in the charge transferred to the adsorbed hydrogen. We also show that the binding energy to graphene depends upon composition, both through the elemental identity of the atoms binding to graphene and also through the strength of the intracluster bonding. In general, E bind is reduced upon hydrogen adsorption on the cluster. In some cases, this changes the relative binding energies of different binding configurations, thus leading to a change in the most stable cluster orientation when hydrogen adsorption occurs. Our results show that E ads varies through a significant range with cluster composition and that this variation can be effectively understood through a consideration of the changes in localized charges on the hydrogen, the cluster atoms, and the graphene upon hydrogen adsorption. This dependence should be of broader relevance to other mixed transition metal clusters.

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