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1.16.1
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votca 2026-dev
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Identifies traps (single sites or clusters) of a charge transport network from the slow modes of the master equation, after Chen, van der Hoorn and Baumeier (spectral clustering of molecular charge transport networks). More...
#include <trapfinder.h>
Classes | |
| struct | Settings |
| struct | Trap |
| struct | Result |
Static Public Member Functions | |
| static Result | Find (const ToFGraph &graph, const Settings &settings) |
| static Result | Find (const ToFGraph &graph) |
Identifies traps (single sites or clusters) of a charge transport network from the slow modes of the master equation, after Chen, van der Hoorn and Baumeier (spectral clustering of molecular charge transport networks).
The generator -Q = D - W (D: escape rates) of the hopping graph is diagonalized (dense, all sites with hops). Its eigenvalues 0 = l_0 <= l_1 <= ... are relaxation rates. A trap shows up as a slow mode separated by a gap from the faster ones: the number of slow modes is the index i (1..modes-2) with the largest ratio l_{i+1}/l_i. The density modes (left eigenvectors) of the slow modes are localized on the traps: the sites with |v_k|/max|v_k| > threshold form the trap candidates of mode k; their connected components (in the hopping graph) are traps if they are localized (at most max_size sites carrying at least the fraction mass of the weight of their side of the mode), and components contained in others are dropped. A trap must hold the carrier: its release rate (see below) times gap must not exceed the first fast relaxation rate l_{i+1}. The eigenvalue ratio alone does not separate traps from Gaussian disorder in small networks: when a trap holds most of the equilibrium weight, the slow mode is its capture, which is fast in a small box; the release rate is the discriminating quantity. Unlike the paper, which uses the eigenvectors of the jump chain I - D^-1 W and a subsequent K-means step, the supports of the density modes of the continuous-time generator are used directly: they are localized on the traps also when the trap holds most of the equilibrium weight. A density mode moves weight between the trap and the rest of the network (it sums to zero); the trap is taken on the side with fewer sites.
For every trap the equilibrium weight pi(C) (stationary distribution of the network, also without detailed balance), the relaxation rate of its mode, split into release and capture rates in a two-state picture, and the hop rate sum_{i in C, j not in C} pi_i w_ij / pi(C) are given.
Definition at line 70 of file trapfinder.h.
Definition at line 109 of file trapfinder.h.
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Definition at line 48 of file trapfinder.cc.
1.16.1