(For mobile users) 00:08 Sketch of structure 00:52 Hückel determinant 01:33 Divide by β; let x = α - E / β 02:26 Expand 4 × 4 determinant by minors to 3 × 3 03:58 Expand 3 × 3 determinants by minors to 2 × 2 06:17 Expand 2 × 2 determinants by definition 08:09 Simplify polynomial 08:50 Use substitution y = x² 09:24 Solve polynomial in y by quadratic formula 10:45 Back substitute to find x's 11:18 Back substitute for x to find energies (E)
In short, the Hückel theory is a way to calculate the energies of a pi system. It is required that a certain matrix is equal to 0. This matrix will be a square n x n matrix, where n is the number of carbon atoms in the pi system. The energy of an electron in a carbon 2p orbital is alpha (α). The energy of a pi bond between carbon atoms is defined as beta (β). The energies of the molecular orbitals as the E's. There will be n E's (if we include degeneracies). To make the calculations possible in an age before computers, there are many (often crude) approximations made. First, we assume that the energy of a carbon 2p pi electron is a fixed value (α), which does not change no matter the environment of the carbon atom. All atoms other than carbon are ignored in Simple Hückel theory. Second, we ignore sigma bonding completely. This is a reasonable assumption, since there will generally be no symmetry operation which interconverts sigma and pi bonds. Third, we assume that bonding occurs only between carbon atoms that are neighbors. If the carbons are NOT neighbors, we assume that the bonding energies are exactly zero. Fourth, we set all overlap integrals (of two different atoms) to 0. Does that help?
You can see: th-cam.com/video/Tu5JWvMRgN8/w-d-xo.html and th-cam.com/video/6v9_YTlFJXk/w-d-xo.html Alpha is the energy of a 2p electron in a carbon atom; beta is the bond energy of a pi bond between two (2) neighboring carbon atoms. The bond energy between carbon atoms that are NOT neighbors is set to zero (0) in the Simple Hückel Method.
On my channel, the largest Hückel energies I've derived is for tropylium (7 x 7 determinant): th-cam.com/video/Q5W9YreyK_s/w-d-xo.html I look forward to seeing the simple derivation for naphthalene (10 x 10 determinant) on your channel!
You explained in 12 minutes what my professor failed to explain in 2 hours. Great video, Thanks.
Great to hear!
(For mobile users)
00:08 Sketch of structure
00:52 Hückel determinant
01:33 Divide by β; let x = α - E / β
02:26 Expand 4 × 4 determinant by minors to 3 × 3
03:58 Expand 3 × 3 determinants by minors to 2 × 2
06:17 Expand 2 × 2 determinants by definition
08:09 Simplify polynomial
08:50 Use substitution y = x²
09:24 Solve polynomial in y by quadratic formula
10:45 Back substitute to find x's
11:18 Back substitute for x to find energies (E)
Thanks Man❤️
Thank you so much sir. Well explained, easy to follow, easy to understand.
this is such a well-explained video! thanks!
Thank you very much!! It is so easy after watching this video
You don't deserves a like bro
U deserves a superlike😘
How did you get the 4X4 Huckel determinant in blue?
In short, the Hückel theory is a way to calculate the energies
of a pi system. It is required that a certain matrix is equal to 0.
This matrix will be a square n x n matrix, where n is the number of carbon atoms in the pi system. The energy of an electron in a carbon 2p orbital is alpha (α). The energy of a pi bond between carbon atoms is defined as beta (β).
The energies of the molecular orbitals as the E's. There will
be n E's (if we include degeneracies).
To make the calculations possible in an age before computers, there are many (often crude) approximations made. First, we assume that the energy of a carbon 2p pi electron is a fixed value (α), which does not change no matter the environment of the carbon atom. All atoms other
than carbon are ignored in Simple Hückel theory.
Second, we ignore sigma bonding completely. This is a reasonable assumption, since there will generally be no symmetry operation which interconverts sigma and pi bonds.
Third, we assume that bonding occurs only between carbon atoms that are neighbors. If the carbons are NOT neighbors, we assume that the bonding energies are exactly zero.
Fourth, we set all overlap integrals (of two different atoms) to 0.
Does that help?
@@lseinjr1 Yes, thank you so much for your response.
is there a video i have to watch before this? i dont know what is alpha beta and that determinant
You can see:
th-cam.com/video/Tu5JWvMRgN8/w-d-xo.html
and
th-cam.com/video/6v9_YTlFJXk/w-d-xo.html
Alpha is the energy of a 2p electron in a carbon atom; beta is the bond energy of a pi bond between two (2) neighboring carbon atoms. The bond energy between carbon atoms that are NOT neighbors is set to zero (0) in the Simple Hückel Method.
Awesome and fruitful lecture👌👌👌👌
It Is simple culculate for napthaline
On my channel, the largest Hückel energies I've derived is for tropylium (7 x 7 determinant):
th-cam.com/video/Q5W9YreyK_s/w-d-xo.html
I look forward to seeing the simple derivation for naphthalene (10 x 10 determinant) on your channel!
nice lesson, simple explanation and very clear :) ty
plz sir make a vedio for wave function of butadiene by hmo theory
Yes i want also
Thank you so much!!
Thanks sooo much!!
Glad it helped!
thank you so much i have everything understand
MAAAAAANNN U AMAZIng!!
Excelente.
nice