-X +-X +-Xsp? hybrids2p,2p,Hybrids showntogetherLemay and Brown, Chemistry: The Central Science, 2020Exercise 2Consider the three sp? hybridized orbitals,/2,2s +32pz1112 =2s-52pxV3V2113 =:2s-V3V2They are constructed from linear combinations of atomic orbitals s,2pr,2py, which themselvesare orthonormal. Use this fact to show all three hybridized orbitals are orthonormal. In otherwords, as opposed to evaluating the triple integral of actual wavefunction for each atomic orbitalsS drr? So" dosin(8) S™ døpnim; (r,0,4)µµ!'m? (r, 0, ¢), use the fact the atomic orbitals are orthonormalto compute the overlap integrals symbolically.[1, if m =n10, 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¥3Exercise 3Bonus. 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 calculationsin Exercise 2. Note. (m|n) = (n|m)*

We have the following wave functions that we will be using during our calculations:…

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

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ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

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Chapter1: Chemical Foundations

Section: Chapter Questions

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This process is an instrumental method in which a sample is changed to fast moving positive ions by electron bombardment. The charged particles vary due to their different mass to charge ratio and are estimated with the help of this difference. It is also called mass spectroscopy.

Question

-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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