2014/08/31 by Maria Cameron, Maria K. Cameron · 13 citations
Chemistry · Computer Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Chemistry #Cluster (spacecraft) #Computer science #Eigenvalues and eigenvectors #Energy landscape #Funnel #Geometry #Icosahedral symmetry #Mathematics #Metastability #Nonlinear Dynamics and Pattern Formation #Path (computing) #Physics #Quantum mechanics #Spectroscopy and Quantum Chemical Studies #Statistical physics #Theoretical physics #Thermodynamics #math.SP #msc:60J28
paper · pdf · doi:10.1063/1.4901131
published in The Journal of Chemical Physics 141(18), 184113 (American Institute of Physics) · 24 pages, 10 figures
openalex publication_date 2014/11/13 · arxiv created 2015/01/15 · arxiv updated 2015/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We develop computational tools for spectral analysis of stochastic networks representing energy landscapes of atomic and molecular clusters. Physical meaning and some properties of eigenvalues, left and right eigenvectors, and eigencurrents are discussed. We propose an approach to compute a collection of eigenpairs and corresponding eigencurrents describing the most important relaxation processes taking place in the system on its way to the equilibrium. It is suitable for large and complex stochastic networks where pairwise transition rates, given by the Arrhenius law, vary by orders of magnitude. The proposed methodology is applied to the network representing the Lennard-Jones-38 cluster created by Wales's group. Its energy landscape has a double funnel structure with a deep and narrow face-centered cubic funnel and a shallower and wider icosahedral funnel. However, the complete spectrum of the generator matrix of the Lennard-Jones-38 network has no appreciable spectral gap separating the eigenvalue corresponding to the escape from the icosahedral funnel. We provide a detailed description of the escape process from the icosahedral funnel using the eigencurrent and demonstrate a superexponential growth of the corresponding eigenvalue. The proposed spectral approach is compared to the methodology of the Transition Path Theory. Finally, we discuss whether the Lennard-Jones-38 cluster is metastable from the points of view of a mathematician and a chemical physicist, and make a connection with experimental works.