|
A potential energy surface (PES) describes the energy of a system, especially a collection of atoms, in terms of certain parameters, normally the positions of the atoms. The surface might define the energy as a function of one or more coordinates; if there is only one coordinate, the surface is called a ''potential energy curve'' or energy profile. An example is the Morse potential. It is helpful to use the analogy of a landscape: for a system with two degrees of freedom (e.g. two bond lengths), the value of the energy (analogy: the height of the land) is a function of two bond lengths (analogy: the coordinates of the position on the ground).〔(Potential-energy (reaction) surface in Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). )] Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997)〕 The PES concept finds application in fields such as chemistry and physics, especially in the theoretical sub-branches of these subjects. It can be used to theoretically explore properties of structures composed of atoms, for example, finding the minimum energy shape of a molecule or computing the rates of a chemical reaction. == Mathematical definition and computation == The geometry of a set of atoms can be described by a vector, , whose elements represent the atom positions. The vector could be the set of the Cartesian coordinates of the atoms, or could also be a set of inter-atomic distances and angles. Given , the energy as a function of the positions, , is the value of for all of interest. Using the landscape analogy from the introduction, ''E'' gives the height on the "energy landscape" so that the concept of a potential energy ''surface'' arises. To study a chemical reaction using the PES as a function of atomic positions, it is necessary to calculate the energy for every atomic arrangement of interest. Methods of calculating the energy of a particular atomic arrangement of atoms are well described in the computational chemistry article, and the emphasis here will be on finding approximations of to yield fine-grained energy-position information. For very simple chemical systems or when simplifying approximations are made about inter-atomic interactions, it is sometimes possible to use an analytically derived expression for the energy as a function of the atomic positions. An example is the London-Eyring-Polanyi-Sato potential〔Keith J. Laidler, ''Chemical Kinetics'' (3rd ed., Harper & Row 1987) p.68-70 ISBN 0-06-043862-2〕〔Steinfeld J.I., Francisco J.S. and Hase W.L. ''Chemical Kinetics and Dynamics'' (2nd ed., Prentice-Hall 1998) p.201-2 ISBN 0-13-737123-3〕 for the system H + H2 as a function of the three H-H distances. For more complicated systems, calculation of the energy of a particular arrangement of atoms is often too computationally expensive for large scale representations of the surface to be feasible. For these systems a possible approach is to calculate only a reduced set of points on the PES and then use a computationally cheaper interpolation method, for example Shepard interpolation, to fill in the gaps.〔Moving least-squares enhanced Shepard interpolation for the fast marching and string methods, Burger SK1, Liu Y, Sarkar U, Ayers PW, J Chem Phys. 2009 130(2) 024103. doi: 10.1063/1.2996579.〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「potential energy surface」の詳細全文を読む スポンサード リンク
|