Hückel cyclobutadiene energies

[@lseinjr1]

(For mobile users) 00:08 Structure 01:08 Hückel determinant 02:53 Divide through by β, set x = α - E / β 04:31 Expand 4 × 4 determinant by minors 07:19 Expand 3 × 3 determinants by minors 11:47 Expand 2 × 2 determinants by definition 13:52 Simplify polynomial 14:22 Factor polynomial 14:40 Find roots 15:31 Backsubstitute to find E 16:00 Energy level diagram

[@nurlatifahmohdnor8939]

What is Aufbau principle?

[@lseinjr1]

@@nurlatifahmohdnor8939 "Aufbau" comes from the German verb "aufbauen", meaning "to build up." "Aufbau" is a noun, and German nouns are always capitalized. The Aufbau principle means that, to find the ground state of an atom or molecule, we start putting electrons in the lowest energy level, and then, as each level becomes filled, we start filling the next highest energy level. We try to adapt as many of the principles used for atoms to molecules, so just as we use the Aufbau principle to find the ground state electron configuration for atoms (starting at 1s, then 2s, then 2p, and so on), we do the same for molecules, starting at the lowest energy molecular orbital, and then moving to the next highest energy one once the previous one becomes full. Just as we can only put two (2) electrons into an atomic orbital because of the Pauli Exclusion Principle, we can only put two (2) electrons into a molecular orbital. Dos that help?

[@angelamarineau5279]

Wow, that was incredibly well explained! Thank you so much, keep up the great work!

[@lseinjr1]

You're very welcome!

[@hamstrung22]

Thank you so much. Great explanation.

[@Shubhi694]

thanku so much sir ,,, very helpful

[@LindseyNjanja]

Thank you so much for this!

[@lseinjr1]

Glad it was helpful!

[@allofgiack9434]

broo, thank you so much 😊

[@aatishsuryawanshi4039]

very nice explaination

[@lseinjr1]

Thanks!

[@Supriyalahane]

Thankyou for this video

[@trantrung8544]

Thank you so much sir!

[@aprilsfools]

Can you please explain to me again why you didn’t do the second coefficient of the third matrix ( 10:44 ) ?

[@lseinjr1]

Yes. When we expand by minors, we can use either the first column or the first row. To make life easier, we pick the one that has the most zeroes. Notice that the first row is 1 0 1. Therefore, the coefficients will be 1, then 0, then 1. Since 0 times anything is still zero, I simply omitted that term. Does this help?

[@weekendsfun4766]

@@lseinjr1 waw i've been wondering for quite a while sir, now i got it, thank you so much sir

[@adelekeolamilekan2015]

Why in the third bracket with orange did you change the method of solving the 3by 3

[@lseinjr1]

The method is not "different", since we are still expanding by minors. However, we can work along the first column for the coefficients (as we have been mostly doing), OR along the first row. We always want to solve the problem as efficiently as possible. Notice that the first row has elements: 1, 0, 1. Zeroes (0) are great, because anything times zero equals zero. Ones (1) are almost as good, since one is the identity element for multiplication. The first column, however, has three non-zero elements, one of which is the variable "x". Using the first row means less work. Does that make sense?

[@Pankajydv0807]

After this......... how we calculate coefficient ???

[@hamstrung22]

kzbin.info/www/bejne/o5iUYYuhh6x8itU

[@chenzhongmin7509]

Could you please also explain how do we calculate values of alpha and beta, therefore the delocalisation energy??

[@lseinjr1]

Great question! Neither α nor β is calculated. Within the theory, α is the energy of an electron in a carbon 2p orbital, and β is the energy of a pi bond between two (2) carbon atoms. As such, these values can be estimated from experimental data. Note that Hückel theory does not take atomic distances into account, though the energy of a pi bond between two (2) carbon atoms certainly depends on distance. The delocalization energy of "ordinary" compounds (ones usually found in the lab, or available for purchase) can be easily found by calorimetry. One could also use this method to make estimates of α and β. Does that make sense?

[@chenzhongmin7509]

@@lseinjr1 Yes! And your videos are very much appreciated.

[@zootfitzgerald]

Thank you!

[@riccardobianco2659]

With the substitution proposed, shouldn't α-E become xβ and β become (α-E)/x?

[@lseinjr1]

No. The first step is to use a property of the determinant, that if we divide each element by c(≠0), the value of the determinant as a whole is divided by c. THEN we apply the substitution that x = (α-E)/β.

[@upsclearningmotivation9454]

How to Calculate wave function of cyclobutadiene

[@lseinjr1]

Here: kzbin.info/www/bejne/gYevlqJoerOSnMU