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Exercise 2 Consider the three sp? hybridized orbitals, 1 25 + V3 1 2s - V3 2pz +2px 1 43 = V3 1 2Px They are constructed from linear combinations of atomic orbitals s,2px,2py, which themselves are orthonormal. Use this fact to show all three hybridized orbitals are orthonormal. In other words, as opposed to evaluating the triple integral of actual wavefunction for each atomic orbitals So drr² fo* d0sin(0) S™ døymim; (r,0, q)4µ'm{(r,0, p), use the fact the atomic orbitals are orthonormal to compute the overlap integrals symbolically. | drymn = [ dry;vm = [1, if m=n l0, if m # n with ym = 25,2px,2py and t, = 25,2px,2py. Compute the following, (a) ſ drw¡4z (b) S drfj43 (c) ſ dr4543 (d) Sdrøjvı (e) ſ dryz42 (f) S drøj¥3 Exercise 3 Bonus. Using your calculations from Exercise 2, complete the overlap matrix. (2s|2s) S = [ (2px|2s) (2px|2px) (2px|2py) (2py|2s) (2py|2px) (2py|2py)/ (2p:|2s) (2py/2s) The rules for Bra-Ket notation are in Lab 5 and just a symbolic way of abbreviating your calculations in Exercise 2. Note. (m|n) = (n\m)*

Exercise 2 Consider the three sp? hybridized orbitals, 1 25 + V3 1 2s - V3 2pz +2px 1 43 = V3 1 2Px They are constructed from linear combinations of atomic orbitals s,2px,2py, which themselves are orthonormal. Use this fact to show all three hybridized orbitals are orthonormal. In other words, as opposed to evaluating the triple integral of actual wavefunction for each atomic orbitals So drr² fo* d0sin(0) S™ døymim; (r,0, q)4µ'm{(r,0, p), use the fact the atomic orbitals are orthonormal to compute the overlap integrals symbolically. | drymn = [ dry;vm = [1, if m=n l0, if m # n with ym = 25,2px,2py and t, = 25,2px,2py. Compute the following, (a) ſ drw¡4z (b) S drfj43 (c) ſ dr4543 (d) Sdrøjvı (e) ſ dryz42 (f) S drøj¥3 Exercise 3 Bonus. Using your calculations from Exercise 2, complete the overlap matrix. (2s|2s) S = [ (2px|2s) (2px|2px) (2px|2py) (2py|2s) (2py|2px) (2py|2py)/ (2p:|2s) (2py/2s) The rules for Bra-Ket notation are in Lab 5 and just a symbolic way of abbreviating your calculations in Exercise 2. Note. (m|n) = (n\m)*

Chemistry: Principles and Practice
Chemistry: Principles and Practice
3rd Edition
ISBN:9780534420123
Author:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward Mercer
Publisher:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward Mercer
Chapter10: Molecular Structure And Bonding Theories
Section: Chapter Questions
Problem 10.110QE
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-X + -X + -X sp? hybrids 2p, 2p, Hybrids shown together Lemay and Brown, Chemistry: The Central Science, 2020 Exercise 2 Consider the three sp? hybridized orbitals, /2, 2s + 32pz 1 1 1 2 = 2s- 52px V3 V2 1 1 3 = :2s- V3 V2 They are constructed from linear combinations of atomic orbitals s,2pr,2py, which themselves are orthonormal. Use this fact to show all three hybridized orbitals are orthonormal. In other words, as opposed to evaluating the triple integral of actual wavefunction for each atomic orbitals S drr? So" dosin(8) S™ døpnim; (r,0,4)µµ!'m? (r, 0, ¢), use the fact the atomic orbitals are orthonormal to compute the overlap integrals symbolically. [1, if m =n 10, if m + n = = with Pm = 2s,2px,2py and 4, = 25,2px,2py. Compute the following, (a) ſ dtfj42 (b) S dryjv3 (c) ſ dr4š43 (d) ſ dryj4ı (e) ſ dryž42 (f) ſ dryz¥3 Exercise 3 Bonus. Using your calculations from Exercise 2, complete the overlap matrix. (2s|2s) S = | (2px|2s) (2px|2px) (2px|2py) (2py|2s) (2py|2px) (2py|2py)/ (2px|2s) (2py|2s) The rules for Bra-Ket notation are in Lab 5 and just a symbolic way of abbreviating your calculations in Exercise 2. Note. (m|n) = (n|m)*
Transcribed Image Text:-X + -X + -X sp? hybrids 2p, 2p, Hybrids shown together Lemay and Brown, Chemistry: The Central Science, 2020 Exercise 2 Consider the three sp? hybridized orbitals, /2, 2s + 32pz 1 1 1 2 = 2s- 52px V3 V2 1 1 3 = :2s- V3 V2 They are constructed from linear combinations of atomic orbitals s,2pr,2py, which themselves are orthonormal. Use this fact to show all three hybridized orbitals are orthonormal. In other words, as opposed to evaluating the triple integral of actual wavefunction for each atomic orbitals S drr? So" dosin(8) S™ døpnim; (r,0,4)µµ!'m? (r, 0, ¢), use the fact the atomic orbitals are orthonormal to compute the overlap integrals symbolically. [1, if m =n 10, if m + n = = with Pm = 2s,2px,2py and 4, = 25,2px,2py. Compute the following, (a) ſ dtfj42 (b) S dryjv3 (c) ſ dr4š43 (d) ſ dryj4ı (e) ſ dryž42 (f) ſ dryz¥3 Exercise 3 Bonus. Using your calculations from Exercise 2, complete the overlap matrix. (2s|2s) S = | (2px|2s) (2px|2px) (2px|2py) (2py|2s) (2py|2px) (2py|2py)/ (2px|2s) (2py|2s) The rules for Bra-Ket notation are in Lab 5 and just a symbolic way of abbreviating your calculations in Exercise 2. Note. (m|n) = (n|m)*
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