3. From many-body to single-particle: Quantum modeling of molecules
ฝัง
- เผยแพร่เมื่อ 2 ต.ค. 2024
- MIT 3.021J Introduction to Modeling and Simulation, Spring 2012
View the complete course: ocw.mit.edu/3-0...
Instructor: Michelle Tomasik
This lecture briefly reviews the previous lesson, discusses the many-body problem, Hartree and Hartree-Fock, density functional theory (DFT), and covers computational approaches, modeling software, and PWscf (plane-wave self-consistent field) input.
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
More courses at ocw.mit.edu
Never learn and attend computational chemistry before, and I want to try DFT in my recent research. This lecture really helps me a lot in understanding the basics of DFT. Thank you!
Great Lecture ,thanks
Hello ! Generally, Slaters Determinant (the anti-symmetric wave function) is not the eigenfunction of the system.
Example. Please suppose the system composed of two electrons.
Electron 1 is in a hydrogen atom. Electron 2 is in a helium ion He+.
rA, rB : the position of each nucleus. The two electrons are far enough.
H1=(p1^2/2m)-(e^2/4πε0❘r1-rA❘), H2=(p2^2/2m)-(2e^2/4πε0❘r2-rB❘),
H1φA(r1)=EAφA(r1), H2φB(r2)=EBφB(r2).
Hartree productφA(r1)φB(r2) is the eigenfunction of operator H1+H2,
and lead us the energy of the system EA+EB.
But, another productφA(r2)φB(r1) is not the eigenfunction of operator H1+H2.
(Please calculate it. It's very easy.)
Therefore, the anti-symmetric wave function ψ=φA(r1)φB(r2)-φA(r2)φB(r1) is not the eigenfunction of the system.
Really helpful
Thankyou :) This video helped me a lot! :)
Great lecture, very helpful, thank you very much!
From 6:30 to 8:00, but especially 7:03 to 7:22, is a great example of what an observation in QM is. There is an observable, ml, which can be probed, the magnetic field, and when the system is probed it takes a stand into one of it's eigenstates, spin up or spin down.
modeling software 50:34
1:00:00 properties that can be calculated
Thank you for demystifying the complex Schrodinger equation for many bodies system. At 12:20, is it more correct to include 4* pi* epsilon_0 in the coulombic terms (2nd. 4th, and 5th)?
Thank you (Dr?) Michele! I wondered if you had ever done podcasting, your audio explanation was inspiring!
The contrast between the enthusiasm of the teacher and students is so sad and unfortunately so true in general.
have an interview on a PhD project heavily based on dft so this really helped with the introduction, thank you.
1:13
0:53
I don't feel like these students were trying. idk, Maybe they're shy 'cause there's a camera in the room but still I feel like at least 2 of them knew the answer to some of her questions.
im 16 years and i really love this videos
Good Stuff!
please, do not stop it is a good beginning
My all time favorite instructor
19:59 can the original equation (the equation without all the simplifications) be solved with random search ??? (monte carlo) yeah, it is going to take a while, but random search will solve everything, proven fact! just throw more hardware at the problem and you are done
Hello. To give you an example, in order to evaluate the many electron wavefunction of a single Sulphur atom, with a precision of just 100 points per dimension, would take more points to evaluate than the elemental particles on the observable universe. That is, if we could write each evaluated value over each single particle, we would ran out of particles to write in.
@@Puentezz that's the power of random search , it doesn't need to evaluate all the points, it makes many evaluations at random locations and depending on the result it moves towards the minimum of the function gradually, like gradient descent, but without getting stuck in local minima. So, while the space of all possible evaluations is infinite you don't need to scan all the domain of the function. If we use the logic you propose, then even to find the minimum of a simple equation like a parabola y=x^2 + k we would have to scan all the numbers from -infinity to +infinity and we would also run out of atoms in the universe to compute it. Also, we can improve the process if at the end of random search we switch to coordinate descent algorithm this way we will quickly accelerate towards the minimum.
@@absolute___zero you're right, but maybe wrong at some point. The actual reason the number of points is too big is because of the 3N coordinates, being N the number of electrons, ¡and it's not taking an infinite domain for each, but considering only 100 points per spacial direction! So, 100 is a fairly low number, taking less points would be either consider a low amount of points per dimension, or directly not considering a certain amount of electrons. The problem cannot be taken down evaluating just random points, or evaluating weighted points like a Monte-Carlo type of thing. In advance, this is just for a Sulphur atom, not to mention the complexity for a peptide or a Pd-metallic complex.
감동 그 자체 what a lecture!
Great lecture
may i know any good book in DFT
Density Functional theory- A practical Introduction {David sholl , Janice Steckel}
Thank you
Thank you for the lecture. This video made me want to go to MIT
Which book do you prefer for condense matter physics and material physics
Bransden and Jochain, solid state physisics
In INDIA we learn them when we are 13 😂 if we prepare for JEE
Its a bit too much! Please calm down🤣
speak loudly next time
Turn up your youtube volume bro.