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- 1. Born–Oppenheimer Approximation Dr. Anjali Devi J S Assistant Professor (Contract Faculty), Mahatma Gandhi University, Kerala 1
- 2. Max Born • German-British physicist. • Born in Breslau (now Wroclaw, Poland), 1882. • Died in Göttingen, West Germany 1970. • Professor Berlin, Cambridge, Edinburgh. • Nobel Prize, 1954. • One of the founders of quantum mechanics. • Originator of the probability interpretation of the (square of the) wave function. Max Born (1882-1970) Nobel Prize for Physics (for his fundamental research in quantum mechanics) 2
- 3. J. Robert Oppenheimer • American physicist. • Born in New York, 1904. • Died in Princeton 1967. • Professor California Institute of Technology. • Fermi award for nuclear research, 1963. • Important contributions to nuclear physics. • Director of the Manhattan Project 1943–1945. Victimized as a security risk by senator Joseph McCarthy’s Un-American Activities Committee in 1954. • Central figure of the eponymous PBS TV series (Oppenheimer: Sam Waterston). J. Robert Oppenheimer 1904-1967 The Father of the atomic bomb 3
- 4. Born–Oppenheimer Approximation • Born and Oppenheimer showed in 1927 that the nuclei in a molecule are stationary with respect to the electrons. The approximation states that the Schrödinger equation for a molecule may be separated into an electronic and a nuclear interaction. 1 pm Nucleus Electron 4
- 5. Consequences To calculate energy of the molecule, -Solve electronic Schrödinger equation -Then add electronic energy to the inter-nuclear repulsion to get the total internal energy. Molecule has a shape. Electron 1 pm 1 pm Electron 5
- 6. Molecule has a shape. The nuclei in a molecule see a time-averaged electron cloud. The nuclei vibrate about equilibrium points which define the molecular geometry; this geometry can be expressed simply as the nuclear Cartesian coordinates, or alternatively as bond lengths and angles r and a here) and dihedrals, i.e. as internal coordinates. As far as size goes, the experimentally determined van der Waals surface encloses about 98% of the electron density of a molecule 6
- 7. A molecule has a definite shape because unlike the electrons, the nuclei are (relatively) stationary (since they are much more massive). If the masses of the nuclei and the electrons could be made equal, the distinction in lethargy would be lost, and the molecular geometry would dissolve. 7 Molecule has a shape…..
- 8. In detail: • Because of the rapid motion of the electrons compared to the nuclei the “permanent” geometric parameters of the molecule are the nuclear coordinates. • The energy (and the other properties) of a molecule is a function of the electron coordinates (E =Ψ(x, y, z of each electron); 8
- 9. Geometry Optimisation • A geometry optimization is the process of changing the system’s geometry ( the nuclear coordinates and potentially the lattice vectors) to minimize the total energy of the systems. 9