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# lecnotes08 - MIT OpenCourseWare http/ocw.mit.edu 5.111...

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MIT OpenCourseWare http://ocw.mit.edu 5.111 Principles of Chemical Science Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .

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________________________________________________________________________________ 5.111 Lecture Summary #8 Readings for today: Section 1.12 (1.11 in 3 rd ed ) – Orbital Energies (of many-electron atoms), Section 1.13 (1.12 in 3 rd ed ) – The Building-Up Principle. Read for Lecture #9: Section 1.14 (1.13 in 3 rd ed ) – Electronic Structure and the Periodic Table, Section 1.15, 1.16, 1.17, 1.18, and 1.20 (1.14, 1.15, 1.16, 1.17, and 1.19 in 3 rd ed) - The Periodicity of Atomic Properties. Assignment: Problem set #3 (due Session #10). Topics: Multi-electron atoms I. Wavefunctions for multi-electron atoms II. Binding energies III. Electron configurations (Aufbau principle) I. WAVEFUNCTIONS FOR MULTIELECTRON ATOMS (Describing atoms with Z=2 or higher) The Schrödinger equation correctly describes the electronic structure for all atoms, not just 1-e atoms. Hydrogen: H ˆ ! (r "# ) = E ! (r "# ) Helium (2 e - s): H ˆ ! (r 1 " 1 # 1 r 2 " 2 # 2 ) = E ! (r 1 " 1 # 1 r 2 " 2 # 2 ) Lithium (3 e - s): H ˆ ! (r 1 " 1 # 1 r 2 " 2 # 2 r 3 " 3 # 3 ) = E ! (r 1 " 1 # 1 r 2 " 2 # 2 r 3 " 3 # 3 ) The equations becomes much more complicated. Approximations are needed! Hartree orbitals: Assume we can write a multi-electron Ψ as the product of 1-electron Ψ s: Helium: Ψ (r 1 θ 1 φ 1 r 2 θ 2 φ 2 ) = Ψ (r 1 θ 1 φ 1 ) Ψ (r 2 θ 2 φ 2 ) Ψ for ______ Ψ for _______ Ψ 100+1/2 Ψ 100 1/2 1s(1) 1s(2) Lithium: Ψ (r 1 θ 1 φ 1 r 2 θ 2 φ 2 r 3 θ 3 φ 3 ) = Ψ (r 1 θ 1 φ 1 ) Ψ (r 2 θ 2 φ 2 ) Ψ (r 3 θ 3 φ 3 ) 1s(1) _____ _____ Electron configuration
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lecnotes08 - MIT OpenCourseWare http/ocw.mit.edu 5.111...

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