We study the energy landscapes of particles with short-range attractive interactions as the range of the interactions increases. Starting with the set of local minima for $6\le N\le 12$ hard spheres that are "sticky", i.e. they interact only when their surfaces are exactly in contact, we use numerical continuation to evolve the local minima (clusters) as the range of the potential increases, using both the Lennard-Jones and Morse families of interaction potentials. As the range increases, clusters merge, until at long ranges only one or two clusters are left. We compare clusters obtained by continuation with different potentials and find that for short and medium ranges, up to about 30% of particle diameter, the continued clusters are nearly identical, both within and across families of potentials. For longer ranges the clusters vary significantly, with more variation between families of potentials than within a family. We analyze the mechanisms behind the merge events, and find that most rearrangements occur when a pair of non-bonded particles comes within the range of the potential. An exception occurs for nonharmonic clusters, those that have a zero eigenvalue in their Hessian, which undergo a more global rearrangement.

中文翻译：

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从峡谷到山谷：从数值上讲，连续的粘性硬球团簇到势能更平滑的景观

随着相互作用范围的增加，我们研究具有短程吸引相互作用的粒子的能量分布。从一组局部最小值开始$6\le ñ\le 12$“粘性”硬球，即仅当它们的表面完全接触时才相互作用，我们使用数值连续性随着势能范围的增加来演化局部最小值（簇），同时使用Lennard-Jones和Morse族互动潜力。随着范围的增加，群集会合并，直到长距离时只剩下一个或两个群集。我们比较了通过连续获得的具有不同电势的簇，发现对于短距离和中距离范围（最多约30％的粒径），连续的簇在电势家族之内和之间都几乎相同。对于更长的范围，群集的变化很大，电位家族之间的差异比家族内更大。我们分析了合并事件背后的机制，并发现大多数重排发生在一对未键合的粒子进入电势范围内时。对于非谐波群集，在其Hessian中具有零特征值的群集会发生例外，该群集会进行更全局的重排。