It is highly desirable for a numerical approximation of a stationary point for a potential energy landscape to lie in the quadratic convergence basin of that stationary point. However, it is possible that an approximation may lie only in the linear convergence basin, or even in a chaotic region, and hence not converge to the actual stationary point when further optimization is attempted. Proving that a numerical approximation will quadratically converge to the associated stationary point is termed certifying the numerical approximation. We employ Smale's α-theory to stationary points, providing a certification that serves as a mathematical proof that the numerical approximation does indeed correspond to an actual stationary point, independent of the precision employed. As a practical example, employing recently developed certification algorithms, we show how the α-theory can be used to certify all the known minima and transition states of Lennard-Jones LJ$_{N}$ atomic clusters for N = 7, ...,14.
Global perspectives on the energy landscapes of liquids, supercooled liquids, and glassy systems: Geodesic pathways through the potential energy landscape
Potential energy landscape picture of zero-temperature avalanche criticality governing dynamics in supercooled liquids
Toyota Central R&D Labs., Inc.（丰田中央研究所）；D3 Center, The University of Osaka（大阪大学D3中心）；Department of Physics, The University of Osaka（大阪大学物理系）；Department of Physics, Nagoya University（名古屋大学物理系）；Division of Chemical Engineering, Graduate School of Engineering Science, The University of Osaka（大阪大学工学研究科化学工程专攻）
势能景观盆地的深度、数量和形状是Stillinger和Weber引入的固有结构热力学形式主义的关键成分[F. H. Stillinger和T. A. Weber，Phys.Rev.A25，978（1982）]。在这种形式主义，状态方程的基础上，只有这些景观属性的体积依赖性。振动和组态的压力的贡献，整理出一个透明的方式。预测成功地与数据进行了比较，从广泛的分子动力学模拟的一个简单的模型为脆弱的液体邻三联苯。
Exploring the energy landscape of the logarithmic potential: local minima and stationary states
Facultad de Ciencias, CUICBAS, Universidad de Colima（科利马大学理学院）；Facultad de Ciencias, Universidad de Colima（科利马大学理学院）；Quantum Universe Center, Korea Institute for Advanced Study（韩国高等研究院量子宇宙中心）
Design of a Protein Potential Energy Landscape by Parameter Optimization
我们提出了一个自动化的协议，通过优化其参数来设计蛋白质能量函数的能量景观。参数进行优化，使不仅全球最低能量构象成为天然的，但也不同于天然结构的构象具有更高的能量比那些接近天然的。我们成功地应用我们的协议的UNRES势能的参数优化，使用betanova，1fsd，36个残基的子结构域的鸡绒毛蛋白头（PDB ID 1vii），和10-55个残基的片段的葡萄球菌蛋白A（PDB ID 1bdd）的训练集。新的协议的参数优化表现出更好的性能比以前的方法，其中只有最低能量的天然的和非天然的构象之间的差异进行了调整，而不考虑各种程度的天然相似的构象。我们还对未包含在训练集中的其他蛋白质进行了折刀测试，并获得了有希望的结果。结果表明，我们使用的四种蛋白质的训练集获得的参数在一定程度上可以转移到其他蛋白质。
