Cartesian internal coordinates: translational and rotational invariance |
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| Institution: | 1. School of Mathematics and Physics, Beijing Advanced Innovation Center for Materials Genome Engineering, Beijing Key Laboratory for Magneto-Photoelectrical Composite and Interface Science, Center for Green Innovation, University of Science and Technology Beijing, Beijing 100083, People''s Republic of China;2. Computational Center for Property and Modification on Nanomaterials, College of Science, Liaoning Shihua University, Fushun 113001, People''s Republic of China;1. MOE Key Laboratory of Dynamics and Control of Flight Vehicle, School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China;2. College of Physics, Liaoning University, Shenyang 110036, China |
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| Abstract: | Using translational and rotational invariance conditions for energy derivatives, we show that at a nonstationary point on the molecular potential energy surface the Hessian has at least three zero eigenvalues. Only at a stationary point can there be shown to be six (five for collinear geometries) zero eigenvalues. An infinitesimal transformation is defined such that the six (five for collinear geometries) transformed dependent Cartesian-like coordinates have zero gradients. From the form of this infinitesimal transformation, a translation-rotation free surface walking algorithm is defined. Numerical tests show that this surface walking procedure is practical for both non-collinear and collinear molecules. |
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