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Computational Chemistry 4.28 - Population Analysis
Short lecture on population analysis to obtain atomic partial charges in Hartree-Fock theory.
Population analysis in Hartree-Fock theory allows us to use the resulting coefficient matrix (C) from the self-consistent field (SCF) procedure to assign partial charges to each nuclear center in the molecule. Using the density matrix, the expectation value of any molecular property can be obtained if the form of the one-electron operator for the property is known. An example is given using the dipole moment operator. Mulliken charges for each nuclear center are obtained by subtracting a trace of the product of the density (P) and overlap (S) matrices from the charge of the nucleus. We can also perform an orbital transformation to any desired degree to compute these partial charges. One such choice is to transform the density matrix using the square root of the overlap matrix, resulting in the expression for Lowdin partial atomic charges.
Notes Slide: i.imgur.com/hQrFNGs.png
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Переглядів: 13 560

Відео

Computational Chemistry 4.27 - Self-Consistent Field
Переглядів 17 тис.6 років тому
Short lecture on the self-consistent field procedure in Hartree-Fock theory. The self-consistent field procedure produces solutions to the Hartree-Fock-Roothaan equations for the best possible approximate molecular orbitals for a molecule within the Born-Oppenhiemer approximation and Hartree-Fock approximation for a particular choice of atomic orbital basis set and nuclear coordinate configurat...
Computational Chemistry 4.26 - Orthogonalization
Переглядів 7 тис.6 років тому
Short lecture on diagonalizing the overlap matrix in Hartree-Fock theory. The overlap matrix (S) in Hartree-Fock theory is a K x K matrix with elements of the overlap integrals of all K atomic orbital basis functions. We may take any linear combination of these basis functions as we like, and transform any representation into another by using a transformation matrix. The overlap matrix may be d...
Computational Chemistry 4.25 - Fock Matrix
Переглядів 10 тис.6 років тому
Short lecture on the Fock matrix in Hartree-Fock theory. The Fock operator is the core Hamiltonian operator (electron kinetic energy plus its attraction to all nuclei) plus a sum over all spatial orbitals of twice the Coulomb operator subtracted by the exchange operator. The Fock matrix is a K by K matrix composed of elements which are the expectation value of the Fock operator acting on an ato...
Computational Chemistry 4.24 - Density Matrix
Переглядів 11 тис.6 років тому
Short lecture on the density matrix in Hartree-Fock theory. The spatial probability density function of a quantum mechanical particle is its wavefunction multiplied by its complex conjugate. For an electron, this wavefunction is a spatial orbital. For a molecule with N electrons, we add the electron density from all electrons to get the total electronic density function. When using a finite ato...
Computational Chemistry 4.23 - Hartree-Fock-Roothaan Equations
Переглядів 10 тис.6 років тому
Short lecture on the Hartree-Fock-Roothaan equations for orbitals and energies of molecular systems. Once we have applied the Born-Oppenheimer approximation (stationary nuclei) to simplify nuclear energy terms and we have applied the Hartree-Fock approximation (mean field) to simplify the electron repulsion many-body problem, there still remains one issue to resolve in order to solve for the Ha...
Computational Chemistry 4.22 - Restricted Hartree-Fock
Переглядів 8 тис.6 років тому
Short lecture on spin-restricted Hartree-Fock operators and energies. Restricted Hartree-Fock (RHF) makes use of restricted Slater determinants to simplify the Hartree-Fock equations. The pairing of opposite-spin electrons in the same spatial orbital allows us to cut the number of necessary orbitals to consider in half. Additionally, we can integrate out the spin in our one-electron and two-ele...
Computational Chemistry 4.21 - Koopman's Theorem
Переглядів 12 тис.6 років тому
Short lecture on Koopman's theorem for interpreting Hartree-Fock orbital energies. The canonical form of the Hartree-Fock equations demonstrates that the Fock operator acting on a spin orbital results in the orbital energy times the same spin orbital. The orbital energy consists of the core Hamiltonian energy plus a sum of the Coulomb and exchange energy of the electron interacting with every o...
Computational Chemistry 4.20 - Canonical Hartree-Fock Equations
Переглядів 8 тис.6 років тому
Short lecture on the canonical Hartree-Fock equations for molecular systems. For a given molecular Hamiltonian, there are an infinite number of sets of spin orbitals which are equally valid solutions to the Schrodinger equation. We can transform any set of orbitals into any other with the appropriate unitary matrix, through a procedure called a unitary transformation. All molecular properties a...
Computational Chemistry 4.19 - Minimum Determinant Energy
Переглядів 7 тис.6 років тому
Short lecture on minimization of the Hartree-Fock energy by functional variation of spin orbitals. When we take a Slater determinant of occupied spin orbitals and vary these orbitals to minimize the molecular energy, the resulting expression involves the Fock operator. First we set the molecular energy to the expectation value of the Hamiltonian operator acting on the Slater determinant (the wa...
Computational Chemistry 4.18 - Functional Variation
Переглядів 9 тис.6 років тому
Short lecture on variational minimization of the energy functional in quantum mechanics. Just as the linear variational method can be derived from differentiating coefficients in a basis set expansion, so to do we arrive at this result by minimizing the first variation of an energy functional. This video goes through the derivation where we set the first variation of the energy equal to zero, i...
Computational Chemistry 4.17 - Fock Operator
Переглядів 12 тис.6 років тому
Short lecture on the Fock operator in Hartree-Fock theory. The Fock operator forms a pseudo-eigenvalue equation where the eigenfunction is a spin orbital and the eigenvalue is the orbital energy. The Fock operator consists of the one-electron core Hamiltonian operator plus the Coulomb potential and exchange potential, each of which is a sum of the Coulomb and exchange operators for all the othe...
Computational Chemistry 4.16 - Coulomb and Exchange Operators
Переглядів 14 тис.6 років тому
Short lecture on Coulomb and exchange operators in Hartree-Fock theory. The Fock operator forms a pseudo-eigenvalue equation, where the eigenfunction is a spin orbital and the eigenvalue is the orbital energy. The Fock operator consists of the one-electron core Hamiltonian operator (electron kinetic energy plus electron-nuclear attraction to all nuclei) and the mean-field operator. The mean fie...
Computational Chemistry 4.15 - Hartree-Fock Energy
Переглядів 20 тис.6 років тому
Short lecture on the Hartree-Fock energy on an N-electron Slater determinant. The Hartree-Fock electronic energy of a molecular system consists of two terms: the core-Hamiltonian energy of each electron, and the electron-electron repulsion of all electron pairs. The core Hamiltonian consists of an electron's kinetic energy and it's attraction to every nucleus in the molecule. The two-electron r...
Computational Chemistry 4.14 - Hartree-Fock Approximation
Переглядів 57 тис.6 років тому
Short lecture on the Hartree-Fock approximation for the Hamiltonian operator of molecular systems. Even after applying the Born-Oppenheimer approximation the molecular Schrodinger equation is still an N-body problem for all electrons due to the non-separable two-electron terms. One solution is to use the Hartree-Fock approximation to average the repulsion of electrons over the average position ...
Computational Chemistry 4.13 - Spin Integration
Переглядів 11 тис.6 років тому
Computational Chemistry 4.13 - Spin Integration
Computational Chemistry 4.12 - Two-Electron Integrals
Переглядів 15 тис.6 років тому
Computational Chemistry 4.12 - Two-Electron Integrals
Computational Chemistry 4.11 - One-Electron Integrals
Переглядів 15 тис.6 років тому
Computational Chemistry 4.11 - One-Electron Integrals
Computational Chemistry 4.10 - Restricted Determinants
Переглядів 10 тис.6 років тому
Computational Chemistry 4.10 - Restricted Determinants
Computational Chemistry 4.9 - N-Electron Wavefunctions
Переглядів 12 тис.6 років тому
Computational Chemistry 4.9 - N-Electron Wavefunctions
Computational Chemistry 4.8 - Excited Determinants
Переглядів 13 тис.6 років тому
Computational Chemistry 4.8 - Excited Determinants
Computational Chemistry 4.7 - Slater Determinants
Переглядів 19 тис.6 років тому
Computational Chemistry 4.7 - Slater Determinants
Computational Chemistry 4.6 - Anti-Symmetry Principle
Переглядів 15 тис.6 років тому
Computational Chemistry 4.6 - Anti-Symmetry Principle
Computational Chemistry 4.5 - Hartree Product
Переглядів 19 тис.6 років тому
Computational Chemistry 4.5 - Hartree Product
Computational Chemistry 4.4 - Spin Orbitals
Переглядів 19 тис.6 років тому
Computational Chemistry 4.4 - Spin Orbitals
Computational Chemistry 4.3 - Born-Oppenheimer Approximation
Переглядів 24 тис.6 років тому
Computational Chemistry 4.3 - Born-Oppenheimer Approximation
Computational Chemistry 4.2 - Atomic Units
Переглядів 15 тис.6 років тому
Computational Chemistry 4.2 - Atomic Units
Computational Chemistry 4.1 - Molecular Hamiltonian
Переглядів 43 тис.6 років тому
Computational Chemistry 4.1 - Molecular Hamiltonian
Computational Chemistry 3.13 - Simulated Annealing
Переглядів 6 тис.7 років тому
Computational Chemistry 3.13 - Simulated Annealing
Computational Chemistry 3.12 - MC Program
Переглядів 4,7 тис.7 років тому
Computational Chemistry 3.12 - MC Program

КОМЕНТАРІ

  • @beerkan2300
    @beerkan2300 5 днів тому

    Appreciate your work!

  • @blocktube1449
    @blocktube1449 6 днів тому

    But why do I get the wrong answer for hydrogen when I use the Rydberg constant directly?

  • @masoudzankana4023
    @masoudzankana4023 7 днів тому

    Thanks so much for your videos. I am a university lecturer. Honestly I use your videos to prepare some of my lectures. But if you guide me which book resources to use for both physical chemistry and quantum chemistry in order to study the subjects in detail, I will be thankful...

  • @nobody-fq9hc
    @nobody-fq9hc 9 днів тому

    Thank you sir

  • @SomithanKamal-nv1yc
    @SomithanKamal-nv1yc 10 днів тому

    I am in Sri Lankan sir we are so blessed because of your vedio you and your family have a wonderful life always

  • @OwenChen-e4r
    @OwenChen-e4r 14 днів тому

    there is something missing at the last expression it should be ai = <phi*|f> instead of phi

  • @giriff8398
    @giriff8398 14 днів тому

    Very nice intro❤❤❤

  • @rishabghosh7685
    @rishabghosh7685 15 днів тому

    Thank you very much for these videos. You are a life saver.

  • @nghiaphan3318
    @nghiaphan3318 16 днів тому

    pls help me how to add frame.file into this molecule, now I just have 1 frame for this molecule, so I cannot make my molecule vibrated

  • @lzk9933
    @lzk9933 17 днів тому

    very clear explanation, thank you!

  • @manfredbogner9799
    @manfredbogner9799 19 днів тому

    Sehr gut

  • @MissionSilo
    @MissionSilo Місяць тому

    Thanks. Not sure how this would help a wanna be hobbist but thanks

  • @MinooRezaie-fv8se
    @MinooRezaie-fv8se Місяць тому

    I can't download the slides from the link , I think it has a problem

  • @zafhalasdfn3324
    @zafhalasdfn3324 Місяць тому

    Thanks guy. Much appreciated.

  • @user-to3fx2do4d
    @user-to3fx2do4d Місяць тому

    Unfortunately, in general, neither symmetric nor anti-symmetric wavefunctions can be said to be eigenfunctions of the Hamiltonian. The wave function for an electron in a hydrogen-like atom with atomic number Z in the ground state is RZ(r)=2(Z/a0)^(3/2)*exp(-Zr/a0). RZ(r) is an eigenfunction of HZ=1/(2m)*p^2-Ze^2/(4πε0r). But RZ(r) is not an eigenfunction of HZ'=1/(2m)*p^2-Z'e^2/(4πε0r), Z'≠Z. Let us consider the case where a hydrogen-type atom with atomic number Z and a hydrogen-type atom with atomic number Z' are sufficiently separated from each other. And each electron in each atom is in the ground state. The anti-symmetric wave function Ψ={RZ(r1)RZ'(r2)-RZ(r2)RZ'(r1)}/2^(1/2) is not an eigenfunction of the Hamiltonian H=1/(2m)*p1^2-Ze^2/(4πε0r1)+1/(2m)*p2^2-Z'e^2/(4πε0r2). It should be an ironclad rule of quantum mechanics that the wave function is an eigenfunction of the Hamiltonian.

  • @RAWM13
    @RAWM13 Місяць тому

    Do you like Spartan? My prof uses it but I have never heard of it

  • @strikegamer4832
    @strikegamer4832 Місяць тому

    Thank you so much ❤

  • @walacross
    @walacross Місяць тому

    For some stupid reason I couldn’t figure out what I would do if it wasn’t a cubical box due to the equations in my textbook simply writing L^3, but you writing them separately as lx,ly,and lz made it make way more sense, thank you so much :D. Sometimes these simple concepts can be overlooked.

  • @madhurjyachakravarty7237
    @madhurjyachakravarty7237 2 місяці тому

  • @madhurjyachakravarty7237
    @madhurjyachakravarty7237 2 місяці тому

    🙏

  • @SampleroftheMultiverse
    @SampleroftheMultiverse 2 місяці тому

    This video shows under the right conditions, the quantization of a field is naturally produced. The ground state energy is induced via Euler’s contain column analysis. The containment of the column must come in to play before over buckling occur or the effect will not work. The system response in a quantized manor when force is applied in the perpendicular direction. Bonding at the points of highest probabilities and maximum duration( peeks and troughs) of the fields/sheet produced a stable structure out of three fields People say I am just plucked guitar strings. I said you can not make structures with vibrating guitar strings or harmonic oscillators. ua-cam.com/video/wrBsqiE0vG4/v-deo.htmlsi=waT8lY2iX-wJdjO3 In the model, “U” shape waves are produced as the loading increases and just before the wave-like function shifts to the next higher energy level. Over-lapping all the waves frequencies together using Fournier Transforms, I understand makes a “U” shape or square wave form. If this model has merit, seeing the sawtooth load verse deflection graph produced could give some real insight in what happened during the quantum jumps. You can reproduce my results using a sheet of Mylar* ( the clear plastic found in school folders.

  • @Everson_Computational
    @Everson_Computational 2 місяці тому

    Great video.

  • @Everson_Computational
    @Everson_Computational 2 місяці тому

    Thanks.

  • @mahmoudhammad812
    @mahmoudhammad812 2 місяці тому

    6:43; it should be 5 and not 4

  • @yarenderinel6926
    @yarenderinel6926 2 місяці тому

    what if the max values are present but the another term for -1 is lost ?

  • @the.kemetic.Religion.believers
    @the.kemetic.Religion.believers 2 місяці тому

    great job from egypt

  • @Abcs-o7j
    @Abcs-o7j 3 місяці тому

    Please make some lectures on machine learning in chemistry

  • @sdeb3333
    @sdeb3333 3 місяці тому

    Great job ! We need more tutors like you. ❤

  • @manrajlally
    @manrajlally 3 місяці тому

    Thanks

  • @hayleebridge5156
    @hayleebridge5156 3 місяці тому

    thank you thank you thank you

  • @hewaahmedmustafa8027
    @hewaahmedmustafa8027 3 місяці тому

    these preprint papers claimed reversing entropy by mixing Raoult's law with osmosis principle and extended Gibbs Donnan Equilibrium . What do you think about this novel approach? Title of the papers: Experimental Demonstration of Energy Harvesting by Maxwell's Demon Device DOI: 10.20944/preprints202403.1698.v1 .... An Autonomous Mechanical Maxwell's Demon DOI: 10.14293/S2199-1006.1.SOR-.PP5S6NK.v1

  • @InquilineKea
    @InquilineKea 3 місяці тому

    What is sigma h of water

  • @kekero540
    @kekero540 3 місяці тому

    Time for me to develop another unhealthy hyperfixation for the next few months.

  • @Kevinfreddo
    @Kevinfreddo 3 місяці тому

    Do the terms [aa|bb] & [ab|ba] represent the exact coulomb and exchange integrals (with double integration over x1 and x2), or do they represent the mean field approximation (with a single integral over solely x2?) I can’t tell if the Fock operator results from the substitution of the approximate mean-field integrals for J and K, or if the Fock operator is a natural result (without any need for substitution in this derivation) of assuming the total electronic wave-function takes the form of a slater determinant of one-electron spin orbitals

  • @wendellespinales1714
    @wendellespinales1714 3 місяці тому

    Great video 👌👌

  • @Unidentifying
    @Unidentifying 3 місяці тому

    I think theres something wrong with your partition function notation Q, when you sum over the states and use index i, the E_i would also change , so you change/sum over the energy level and not the states which you say it will do? Confusing

  • @Everson_Computational
    @Everson_Computational 3 місяці тому

    Thank you so much.

  • @InquilineKea
    @InquilineKea 3 місяці тому

    what are triply/quadruply excited determinants?

  • @alexandrfedorov7297
    @alexandrfedorov7297 3 місяці тому

    You are the best😮

  • @martinsisrael12
    @martinsisrael12 4 місяці тому

    Quem entender esses princípios entenderá o inicial conceito de como funciona o computador quântico e o que é o conceito da superposição. Não é tão fácil quanto as portas lógicas mas com a mente aberta é possível começar a compreender esses conceitos.

  • @ezequielson5677
    @ezequielson5677 4 місяці тому

    So good. I loved the explanation. Thank you!!!

  • @ariadnaborrasbadia1146
    @ariadnaborrasbadia1146 4 місяці тому

    you sound like ryan reynolds

  • @b6kf367
    @b6kf367 4 місяці тому

    in the previous video, J, K were having 2 indices now why it's only one here?

    • @b6kf367
      @b6kf367 4 місяці тому

      okay I got it's due to mean field but J need 2 wave functions on the right to operator right? your green equation on right has only 1 electrons wave fucntion

  • @user-eb3th4hb3d
    @user-eb3th4hb3d 4 місяці тому

    the un(x,t) function serves as the basis of U(x,t) wave. Is un(x,t) quantised here? or components withing un(x,t) are quantised? I feel un(x,t) shouldn't be quantised since we get to choose the coeff. An, so unless An are equal to 0,1,2,3...(integral values) I feel I'm thinking something wrong please correct me and share the correct way to look at this problem(What exactly is quantised here)

  • @jaybae8056
    @jaybae8056 4 місяці тому

    so how do you get the overall N factor? i am new to this. can you do the complete thing for lets say 2s e-? like, all longhand.

  • @TheOwlGilga
    @TheOwlGilga 4 місяці тому

    You're the king of chemistry, doing the job of 10 of my professors as what appears to be from your latest video's comment section, pure altruism. I am constantly at the verge of being expelled from my chemistry major for being so bad at chemistry in my university (in my nation you get banned from your major nationwide if you fail an exam thrice) yet your videos always come in clutch. 🤗

  • @NVANAPALLIVENKATASATYAUMASHANK
    @NVANAPALLIVENKATASATYAUMASHANK 5 місяців тому

    thank you

  • @NVANAPALLIVENKATASATYAUMASHANK
    @NVANAPALLIVENKATASATYAUMASHANK 5 місяців тому

    thank you so much

  • @rebekkakanerva4292
    @rebekkakanerva4292 5 місяців тому

    My material science prof decided not to go over this at all because "surely you've all already familiar with the Schrödinger equation", which we chemistry students, in fact, were not. So this was such a great and clear explanation of this model! Thank you!

  • @GiStormy
    @GiStormy 5 місяців тому

    Thank you so much for this!