Channel Title: TMP Chem Channel Description: The goal of TMP Chem is to provide free, high-quality physical chemistry study resources to anyone, anywhere. Quantum Chemistry and Spectroscopy (160 videos) and Chemical Thermodynamics and Kinetics (137 videos) are both complete. Theoretical and Computational Chemistry in progress (68 videos). All feedback and suggestions are encouraged in comments or email. Physical chemistry is the use of physics to develop descriptive mathematical models for the behavior of chemical systems. Physical chemistry is typically studied for 2-3 semesters by university chemistry students. Prerequisites includes general chemistry, general physics, algebra, and calculus. <video> Computational Chemistry 4.26 - Orthogonalization Description: 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 diagonalized performing such a unitary transformation. The inverse square root of the overlap matrix is used in symmetric orthogonalization. Symmetric orthogonalization is not always possible due to linear dependencies in the overlap matrix (at least two basis function pairs are nearly identical), making the inverse matrix undefined due to a zero determinant. In such a case canonical orthogonalization may be used which truncates matrix rows whose eigenvalue is sufficiently small, effectively reducing the number of basis functions to K-m. The orthogonalization matrix may then be used to transform the Fock matrix and coefficient matrix as part of the Hartree-Fock procedure. Notes Slide: https://i.imgur.com/fNR1yVF.png --- About TMP Chem --- All TMP Chem content is free for everyone, everywhere, and created independently by Trent Parker. Email: tmpchemistry@gmail.com --- Video Links --- Course Playlist: https://www.youtube.com/playlist?list=PLm8ZSArAXicIWTHEWgHG5mDr8YbrdcN1K Chapter Playlist: https://www.youtube.com/playlist?list=PLm8ZSArAXicIijiVIx0yfk2ZOK-16ycji Other Courses: https://www.youtube.com/playlist?list=PLm8ZSArAXicIXArfap9Tcb8izqRPvE0BK Channel Info: https://www.youtube.com/playlist?list=PLm8ZSArAXicLlGO4Rvpz-D6vX8MFbOn4V --- Social Links --- Facebook: https://www.facebook.com/tmpchem Twitter: https://www.twitter.com/tmpchem LinkedIn: https://www.linkedin.com/in/tmpchem Imgur: https://tmpchem.imgur.com GitHub: https://www.github.com/tmpchem --- Equipment --- Microphone: Blue Yeti USB Microphone Drawing Tablet: Wacom Intuos Pen and Touch Small Drawing Program: Autodesk Sketchbook Express Screen Capture: Corel Visual Studio Pro X8 </video> <video> Computational Chemistry 4.17 - Fock Operator Description: 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 other occupied spin orbitals, respectively. This is a pseudo-eigenvalue equation because the mean-field operator depends on the form of all the other spin orbitals in the molecule. A simplified representation of the Fock operator may be obtained by making use of the permutation operator, which exchanges the indices of electrons 1 and 2 wherever they are encountered when acted upon by the operator. For the current spin orbital, the Coulomb and exchange operators cancel out, thus we can include the current spin orbital as well in the sum over all other occupied orbitals. Notes Slide: https://i.imgur.com/BsVQ3M3.png --- About TMP Chem --- All TMP Chem content is free for everyone, everywhere, and created independently by Trent Parker. Email: tmpchemistry@gmail.com --- Video Links --- Course Playlist: https://www.youtube.com/playlist?list=PLm8ZSArAXicIWTHEWgHG5mDr8YbrdcN1K Chapter Playlist: https://www.youtube.com/playlist?list=PLm8ZSArAXicIijiVIx0yfk2ZOK-16ycji Other Courses: https://www.youtube.com/playlist?list=PLm8ZSArAXicIXArfap9Tcb8izqRPvE0BK Channel Info: https://www.youtube.com/playlist?list=PLm8ZSArAXicLlGO4Rvpz-D6vX8MFbOn4V --- Social Links --- Facebook: https://www.facebook.com/tmpchem Twitter: https://www.twitter.com/tmpchem LinkedIn: https://www.linkedin.com/in/tmpchem Imgur: https://tmpchem.imgur.com GitHub: https://www.github.com/tmpchem --- Equipment --- Microphone: Blue Yeti USB Microphone Drawing Tablet: Wacom Intuos Pen and Touch Small Drawing Program: Autodesk Sketchbook Express Screen Capture: Corel Visual Studio Pro X8 </video> <video> Computational Chemistry 4.21 - Koopman's Theorem Description: 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 other electron in the occupied spin orbitals. The core Hamiltonian energy is the electron's kinetic energy plus its attraction to every nucleus in the molecule. The Coulomb integrals are its classical electrostatic repulsion from every other electron in the molecule. The exchange integrals are a non-classical attraction which arise due to quantum effects necessary to satisfy the antisymmetry principle. The molecular energy is not equal to the orbital energy because the sum of orbital energies double counts electron pair repulsions. Koopman's theorem interprets the orbital energy of occupied spin orbitals as their negative ionization potential, and of virtual orbitals as their electron affinity. Notes Slide: https://i.imgur.com/HI15aQE.png --- About TMP Chem --- All TMP Chem content is free for everyone, everywhere, and created independently by Trent Parker. Email: tmpchemistry@gmail.com --- Video Links --- Course Playlist: https://www.youtube.com/playlist?list=PLm8ZSArAXicIWTHEWgHG5mDr8YbrdcN1K Chapter Playlist: https://www.youtube.com/playlist?list=PLm8ZSArAXicIijiVIx0yfk2ZOK-16ycji Other Courses: https://www.youtube.com/playlist?list=PLm8ZSArAXicIXArfap9Tcb8izqRPvE0BK Channel Info: https://www.youtube.com/playlist?list=PLm8ZSArAXicLlGO4Rvpz-D6vX8MFbOn4V --- Social Links --- Facebook: https://www.facebook.com/tmpchem Twitter: https://www.twitter.com/tmpchem LinkedIn: https://www.linkedin.com/in/tmpchem Imgur: https://tmpchem.imgur.com GitHub: https://www.github.com/tmpchem --- Equipment --- Microphone: Blue Yeti USB Microphone Drawing Tablet: Wacom Intuos Pen and Touch Small Drawing Program: Autodesk Sketchbook Express Screen Capture: Corel Visual Studio Pro X8 </video> <video> Computational Chemistry 4.22 - Restricted Hartree-Fock Description: 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-electron integrals. This doesn't affect our one-electron core Hamiltonian integrals, or our two-electron Coulomb integrals, but it does cut the number of exchange integrals in half. The resulting expression allows us to describe the molecular energy in terms of twice a sum over half the orbitals for one-electron energy, and a full double sum over two-electron energy, where each term is twice a Coulomb integral subtracted by an exchange integral. Orbital energies simplify as well, with the two-electron term reducing to a sum over half as many orbitals of 2J-K. Notes Slide: https://i.imgur.com/W6Al6ar.png --- About TMP Chem --- All TMP Chem content is free for everyone, everywhere, and created independently by Trent Parker. Email: tmpchemistry@gmail.com --- Video Links --- Course Playlist: https://www.youtube.com/playlist?list=PLm8ZSArAXicIWTHEWgHG5mDr8YbrdcN1K Chapter Playlist: https://www.youtube.com/playlist?list=PLm8ZSArAXicIijiVIx0yfk2ZOK-16ycji Other Courses: https://www.youtube.com/playlist?list=PLm8ZSArAXicIXArfap9Tcb8izqRPvE0BK Channel Info: https://www.youtube.com/playlist?list=PLm8ZSArAXicLlGO4Rvpz-D6vX8MFbOn4V --- Social Links --- Facebook: https://www.facebook.com/tmpchem Twitter: https://www.twitter.com/tmpchem LinkedIn: https://www.linkedin.com/in/tmpchem Imgur: https://tmpchem.imgur.com GitHub: https://www.github.com/tmpchem --- Equipment --- Microphone: Blue Yeti USB Microphone Drawing Tablet: Wacom Intuos Pen and Touch Small Drawing Program: Autodesk Sketchbook Express Screen Capture: Corel Visual Studio Pro X8 </video> <video> Computational Chemistry 4.20 - Canonical Hartree-Fock Equations Description: 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 are invariant to the choice of spin orbital set we ultimately make. In the previous video, we saw the Hartree-Fock equations in their non-canonical form, where every orbital contributes the the result of the Fock operator acting on a spin orbital. In canonical form, the set of Lagrange multipliers form a diagonal matrix, and the spin orbitals are pseudo-eigenfunctions of the Fock operator. For a given Hamiltonian, there exists exactly one such set of canonical spin orbitals. Notes Slide: https://i.imgur.com/33W2WxW.png --- About TMP Chem --- All TMP Chem content is free for everyone, everywhere, and created independently by Trent Parker. Email: tmpchemistry@gmail.com --- Video Links --- Course Playlist: https://www.youtube.com/playlist?list=PLm8ZSArAXicIWTHEWgHG5mDr8YbrdcN1K Chapter Playlist: https://www.youtube.com/playlist?list=PLm8ZSArAXicIijiVIx0yfk2ZOK-16ycji Other Courses: https://www.youtube.com/playlist?list=PLm8ZSArAXicIXArfap9Tcb8izqRPvE0BK Channel Info: https://www.youtube.com/playlist?list=PLm8ZSArAXicLlGO4Rvpz-D6vX8MFbOn4V --- Social Links --- Facebook: https://www.facebook.com/tmpchem Twitter: https://www.twitter.com/tmpchem LinkedIn: https://www.linkedin.com/in/tmpchem Imgur: https://tmpchem.imgur.com GitHub: https://www.github.com/tmpchem --- Equipment --- Microphone: Blue Yeti USB Microphone Drawing Tablet: Wacom Intuos Pen and Touch Small Drawing Program: Autodesk Sketchbook Express Screen Capture: Corel Visual Studio Pro X8 </video> <video> Computational Chemistry 4.14 - Hartree-Fock Approximation Description: 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 of all other electrons, rather than an explicit pairwise interaction. This allows the Hamiltonian to be expressed as a sum of one-electron operators and is finally separable. This would result in a straightforward eigenvalue equation, however the form of the mean-field operator depends on all of the other N-1 occupied spin orbitals, thus it is a non-linear pseudo-eigenvalue equation. Notes Slide: https://i.imgur.com/Ky5DTD9.png --- About TMP Chem --- All TMP Chem content is free for everyone, everywhere, and created independently by Trent Parker. Email: tmpchemistry@gmail.com --- Video Links --- Course Playlist: https://www.youtube.com/playlist?list=PLm8ZSArAXicIWTHEWgHG5mDr8YbrdcN1K Chapter Playlist: https://www.youtube.com/playlist?list=PLm8ZSArAXicIijiVIx0yfk2ZOK-16ycji Other Courses: https://www.youtube.com/playlist?list=PLm8ZSArAXicIXArfap9Tcb8izqRPvE0BK Channel Info: https://www.youtube.com/playlist?list=PLm8ZSArAXicLlGO4Rvpz-D6vX8MFbOn4V --- Social Links --- Facebook: https://www.facebook.com/tmpchem Twitter: https://www.twitter.com/tmpchem LinkedIn: https://www.linkedin.com/in/tmpchem Imgur: https://tmpchem.imgur.com GitHub: https://www.github.com/tmpchem --- Equipment --- Microphone: Blue Yeti USB Microphone Drawing Tablet: Wacom Intuos Pen and Touch Small Drawing Program: Autodesk Sketchbook Express Screen Capture: Corel Visual Studio Pro X8 </video> <video> Computational Chemistry 4.19 - Minimum Determinant Energy Description: 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 wavefunction). We then define a Lagrangian which constrains the spin orbitals to remain orthonormal as they are varied. This Hermitian expression expands into many terms as we apply the product rule to both one-electron and two-electron integrals. Refactoring the results ultimately provides a the non-canonical Hartree-Fock equations, where the Fock operator acting on a spin orbital is equal to a sum of a column vector of Lagrange multipliers multiplied by all occupied spin orbitals. We shall see in the next video how this can be transformed into canonical, pseudo-eigenvalue form. Notes Slide: https://i.imgur.com/X1jy9nf.png --- About TMP Chem --- All TMP Chem content is free for everyone, everywhere, and created independently by Trent Parker. Email: tmpchemistry@gmail.com --- Video Links --- Course Playlist: https://www.youtube.com/playlist?list=PLm8ZSArAXicIWTHEWgHG5mDr8YbrdcN1K Chapter Playlist: https://www.youtube.com/playlist?list=PLm8ZSArAXicIijiVIx0yfk2ZOK-16ycji Other Courses: https://www.youtube.com/playlist?list=PLm8ZSArAXicIXArfap9Tcb8izqRPvE0BK Channel Info: https://www.youtube.com/playlist?list=PLm8ZSArAXicLlGO4Rvpz-D6vX8MFbOn4V --- Social Links --- Facebook: https://www.facebook.com/tmpchem Twitter: https://www.twitter.com/tmpchem LinkedIn: https://www.linkedin.com/in/tmpchem Imgur: https://tmpchem.imgur.com GitHub: https://www.github.com/tmpchem --- Equipment --- Microphone: Blue Yeti USB Microphone Drawing Tablet: Wacom Intuos Pen and Touch Small Drawing Program: Autodesk Sketchbook Express Screen Capture: Corel Visual Studio Pro X8 </video> <video> Computational Chemistry 4.18 - Functional Variation Description: 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, including an additional term to enforce an orthonormal spin orbitals as the variations occur. This results in an expression where the Hamiltonian matrix acting on the basis function coefficient eigenvector equals the molecular energy times the overlap matrix acting on the same vector. Notes Slide: https://i.imgur.com/7SjbYhg.png --- About TMP Chem --- All TMP Chem content is free for everyone, everywhere, and created independently by Trent Parker. Email: tmpchemistry@gmail.com --- Video Links --- Course Playlist: https://www.youtube.com/playlist?list=PLm8ZSArAXicIWTHEWgHG5mDr8YbrdcN1K Chapter Playlist: https://www.youtube.com/playlist?list=PLm8ZSArAXicIijiVIx0yfk2ZOK-16ycji Other Courses: https://www.youtube.com/playlist?list=PLm8ZSArAXicIXArfap9Tcb8izqRPvE0BK Channel Info: https://www.youtube.com/playlist?list=PLm8ZSArAXicLlGO4Rvpz-D6vX8MFbOn4V --- Social Links --- Facebook: https://www.facebook.com/tmpchem Twitter: https://www.twitter.com/tmpchem LinkedIn: https://www.linkedin.com/in/tmpchem Imgur: https://tmpchem.imgur.com GitHub: https://www.github.com/tmpchem --- Equipment --- Microphone: Blue Yeti USB Microphone Drawing Tablet: Wacom Intuos Pen and Touch Small Drawing Program: Autodesk Sketchbook Express Screen Capture: Corel Visual Studio Pro X8 </video> <video> Computational Chemistry 4.24 - Density Matrix Description: 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 atomic orbital basis set to represent the spin orbitals, we expand the density in terms of the linear combinations which represent each orbital. This expression can be factored to be the double sum of all basis functions multiplied by all complex conjugates multiplied by a matrix element. This matrix is the density matrix, which for a given basis set completely specifies the charge density, and it is invariant to the choice of orbitals. We find density matrix elements by multiplying the Hermitian adjoint of the coefficient matrix by itself. This allows us to express the Fock operator in terms of the density matrix, making it independent of the choice of orbitals. Notes Slide: https://i.imgur.com/sh0zZPe.png --- About TMP Chem --- All TMP Chem content is free for everyone, everywhere, and created independently by Trent Parker. Email: tmpchemistry@gmail.com --- Video Links --- Course Playlist: https://www.youtube.com/playlist?list=PLm8ZSArAXicIWTHEWgHG5mDr8YbrdcN1K Chapter Playlist: https://www.youtube.com/playlist?list=PLm8ZSArAXicIijiVIx0yfk2ZOK-16ycji Other Courses: https://www.youtube.com/playlist?list=PLm8ZSArAXicIXArfap9Tcb8izqRPvE0BK Channel Info: https://www.youtube.com/playlist?list=PLm8ZSArAXicLlGO4Rvpz-D6vX8MFbOn4V --- Social Links --- Facebook: https://www.facebook.com/tmpchem Twitter: https://www.twitter.com/tmpchem LinkedIn: https://www.linkedin.com/in/tmpchem Imgur: https://tmpchem.imgur.com GitHub: https://www.github.com/tmpchem --- Equipment --- Microphone: Blue Yeti USB Microphone Drawing Tablet: Wacom Intuos Pen and Touch Small Drawing Program: Autodesk Sketchbook Express Screen Capture: Corel Visual Studio Pro X8 </video> <video> Computational Chemistry 4.25 - Fock Matrix Description: 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 atomic orbital basis function and a different basis function complex conjugate. This is equivalently the core Hamiltonian matrix added to a sum of two-electron integrals. The core Hamiltonian matrix (H) is a sum of the kinetic energy (T) and nuclear potential (V) matrices. The two-electron part of the Fock operator can be refactored to be orbital invariant with the G matrix, which is a double sum over all basis functions of the a density matrix (P) element and the difference of two two-electron integrals. Using the Hartree-Fock-Roothaan equations, we can find the orbital coefficient matrix (C) by diagonalizing the Fock matrix to find these eigenvectors. Notes Slide: https://i.imgur.com/JNx53eh.png --- About TMP Chem --- All TMP Chem content is free for everyone, everywhere, and created independently by Trent Parker. Email: tmpchemistry@gmail.com --- Video Links --- Course Playlist: https://www.youtube.com/playlist?list=PLm8ZSArAXicIWTHEWgHG5mDr8YbrdcN1K Chapter Playlist: https://www.youtube.com/playlist?list=PLm8ZSArAXicIijiVIx0yfk2ZOK-16ycji Other Courses: https://www.youtube.com/playlist?list=PLm8ZSArAXicIXArfap9Tcb8izqRPvE0BK Channel Info: https://www.youtube.com/playlist?list=PLm8ZSArAXicLlGO4Rvpz-D6vX8MFbOn4V --- Social Links --- Facebook: https://www.facebook.com/tmpchem Twitter: https://www.twitter.com/tmpchem LinkedIn: https://www.linkedin.com/in/tmpchem Imgur: https://tmpchem.imgur.com GitHub: https://www.github.com/tmpchem --- Equipment --- Microphone: Blue Yeti USB Microphone Drawing Tablet: Wacom Intuos Pen and Touch Small Drawing Program: Autodesk Sketchbook Express Screen Capture: Corel Visual Studio Pro X8 </video> <video> Computational Chemistry 4.28 - Population Analysis Description: 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: https://i.imgur.com/hQrFNGs.png --- About TMP Chem --- All TMP Chem content is free for everyone, everywhere, and created independently by Trent Parker. Email: tmpchemistry@gmail.com --- Video Links --- Course Playlist: https://www.youtube.com/playlist?list=PLm8ZSArAXicIWTHEWgHG5mDr8YbrdcN1K Chapter Playlist: https://www.youtube.com/playlist?list=PLm8ZSArAXicIijiVIx0yfk2ZOK-16ycji Other Courses: https://www.youtube.com/playlist?list=PLm8ZSArAXicIXArfap9Tcb8izqRPvE0BK Channel Info: https://www.youtube.com/playlist?list=PLm8ZSArAXicLlGO4Rvpz-D6vX8MFbOn4V --- Social Links --- Facebook: https://www.facebook.com/tmpchem Twitter: https://www.twitter.com/tmpchem LinkedIn: https://www.linkedin.com/in/tmpchem Imgur: https://tmpchem.imgur.com GitHub: https://www.github.com/tmpchem --- Equipment --- Microphone: Blue Yeti USB Microphone Drawing Tablet: Wacom Intuos Pen and Touch Small Drawing Program: Autodesk Sketchbook Express Screen Capture: Corel Visual Studio Pro X8 </video> <video> Computational Chemistry 4.23 - Hartree-Fock-Roothaan Equations Description: 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 Hartree-Fock orbitals and energies of an arbitrary molecule. We introduce a finite atomic orbital basis set to express the Hartree-Fock equations as a set of matrix equations (Hartree-Fock-Roothaan equations). Using these K basis functions gives use 3 K by K matrices: F the Fock matrix, S the overlap matrix, and C the coefficient matrix. These gives us the equation FC = SCE, where E is a matrix which when diagonalized provides the orbital energies for the molecule. The coefficient matrix elements tell us the coefficient for each basis function (row) in each molecular orbital (column). The primary difficulty in solving this equation is that the form of F depends on the form of C, thus the equations are non-linear and must be solved iteratively. Notes Slide: https://i.imgur.com/WOYfjcL.png --- About TMP Chem --- All TMP Chem content is free for everyone, everywhere, and created independently by Trent Parker. Email: tmpchemistry@gmail.com --- Video Links --- Course Playlist: https://www.youtube.com/playlist?list=PLm8ZSArAXicIWTHEWgHG5mDr8YbrdcN1K Chapter Playlist: https://www.youtube.com/playlist?list=PLm8ZSArAXicIijiVIx0yfk2ZOK-16ycji Other Courses: https://www.youtube.com/playlist?list=PLm8ZSArAXicIXArfap9Tcb8izqRPvE0BK Channel Info: https://www.youtube.com/playlist?list=PLm8ZSArAXicLlGO4Rvpz-D6vX8MFbOn4V --- Social Links --- Facebook: https://www.facebook.com/tmpchem Twitter: https://www.twitter.com/tmpchem LinkedIn: https://www.linkedin.com/in/tmpchem Imgur: https://tmpchem.imgur.com GitHub: https://www.github.com/tmpchem --- Equipment --- Microphone: Blue Yeti USB Microphone Drawing Tablet: Wacom Intuos Pen and Touch Small Drawing Program: Autodesk Sketchbook Express Screen Capture: Corel Visual Studio Pro X8 </video> <video> Computational Chemistry 4.15 - Hartree-Fock Energy Description: 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 repulsion terms consist of a Coulomb integral between all pairs of electrons, and an exchange integral between all same-spin pairs of electrons. The example given for the Boron atom shows how the Hartree-Fock energy expression may be obtained using the pseudo classical interpretation, where we give core Hamiltonian energy to all electrons, and assign Coulomb and exchange terms to all pairs and all same-spin pairs, respectively. Notes Slide: https://i.imgur.com/tu5PROO.png --- About TMP Chem --- All TMP Chem content is free for everyone, everywhere, and created independently by Trent Parker. Email: tmpchemistry@gmail.com --- Video Links --- Course Playlist: https://www.youtube.com/playlist?list=PLm8ZSArAXicIWTHEWgHG5mDr8YbrdcN1K Chapter Playlist: https://www.youtube.com/playlist?list=PLm8ZSArAXicIijiVIx0yfk2ZOK-16ycji Other Courses: https://www.youtube.com/playlist?list=PLm8ZSArAXicIXArfap9Tcb8izqRPvE0BK Channel Info: https://www.youtube.com/playlist?list=PLm8ZSArAXicLlGO4Rvpz-D6vX8MFbOn4V --- Social Links --- Facebook: https://www.facebook.com/tmpchem Twitter: https://www.twitter.com/tmpchem LinkedIn: https://www.linkedin.com/in/tmpchem Imgur: https://tmpchem.imgur.com GitHub: https://www.github.com/tmpchem --- Equipment --- Microphone: Blue Yeti USB Microphone Drawing Tablet: Wacom Intuos Pen and Touch Small Drawing Program: Autodesk Sketchbook Express Screen Capture: Corel Visual Studio Pro X8 </video> <video> Computational Chemistry 4.16 - Coulomb and Exchange Operators Description: 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 field operator consists of the Coulomb and exchange potential operators. Each of these operators is a sum of the Coulomb and exchange operator of all other occupied spin orbitals acting on the spin orbital, respectively. The Coulomb operator of a spin orbital represents the repulsion an electron at a point in space would experience due to the charge density of an electron in that spin orbital integrated over all space. The exchange operator does not have a similarly straightforward classical interpretation, and arises only due to quantum effects. Notes Slide: https://i.imgur.com/N1oqgsg.png --- About TMP Chem --- All TMP Chem content is free for everyone, everywhere, and created independently by Trent Parker. Email: tmpchemistry@gmail.com --- Video Links --- Course Playlist: https://www.youtube.com/playlist?list=PLm8ZSArAXicIWTHEWgHG5mDr8YbrdcN1K Chapter Playlist: https://www.youtube.com/playlist?list=PLm8ZSArAXicIijiVIx0yfk2ZOK-16ycji Other Courses: https://www.youtube.com/playlist?list=PLm8ZSArAXicIXArfap9Tcb8izqRPvE0BK Channel Info: https://www.youtube.com/playlist?list=PLm8ZSArAXicLlGO4Rvpz-D6vX8MFbOn4V --- Social Links --- Facebook: https://www.facebook.com/tmpchem Twitter: https://www.twitter.com/tmpchem LinkedIn: https://www.linkedin.com/in/tmpchem Imgur: https://tmpchem.imgur.com GitHub: https://www.github.com/tmpchem --- Equipment --- Microphone: Blue Yeti USB Microphone Drawing Tablet: Wacom Intuos Pen and Touch Small Drawing Program: Autodesk Sketchbook Express Screen Capture: Corel Visual Studio Pro X8 </video> <video> Computational Chemistry 4.27 - Self-Consistent Field Description: 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 configuration. The high-level algorithmic steps for this procedure are as follows: 1) Specify nuclear charges and positions, number of electrons, and choice of basis set. 2) Calculate all overlap, kinetic energy, nuclear attraction, and two-electron integrals. 3) Diagonalize S and obtain the orthogonalization matrix X. 4) Obtain an initial guess density matrix (P). 5) Calculate the two-electron potential matrix G. 6) Calculate the Fock matrix as the sum of the core Hamiltonian and G matrices. 7) Transform the Fock matrix with the X matrix. 8) Diagonalize the Fock matrix to obtain the coefficient matrix (C) and orbital energy matrix (E). 9) Un-transform the C matrix with the X matrix. 10) Obtain the next density matrix from the last C matrix. 11) Determine if the density matrix is converged. If not, go back to step 5. 12) Use the final C matrix to calculate all desired molecular properties. Notes Slide: https://i.imgur.com/zv22Qm6.png --- About TMP Chem --- All TMP Chem content is free for everyone, everywhere, and created independently by Trent Parker. Email: tmpchemistry@gmail.com --- Video Links --- Course Playlist: https://www.youtube.com/playlist?list=PLm8ZSArAXicIWTHEWgHG5mDr8YbrdcN1K Chapter Playlist: https://www.youtube.com/playlist?list=PLm8ZSArAXicIijiVIx0yfk2ZOK-16ycji Other Courses: https://www.youtube.com/playlist?list=PLm8ZSArAXicIXArfap9Tcb8izqRPvE0BK Channel Info: https://www.youtube.com/playlist?list=PLm8ZSArAXicLlGO4Rvpz-D6vX8MFbOn4V --- Social Links --- Facebook: https://www.facebook.com/tmpchem Twitter: https://www.twitter.com/tmpchem LinkedIn: https://www.linkedin.com/in/tmpchem Imgur: https://tmpchem.imgur.com GitHub: https://www.github.com/tmpchem --- Equipment --- Microphone: Blue Yeti USB Microphone Drawing Tablet: Wacom Intuos Pen and Touch Small Drawing Program: Autodesk Sketchbook Express Screen Capture: Corel Visual Studio Pro X8 </video>

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The goal of TMP Chem is to provide free, high-quality physical chemistry study resources to anyone, anywhere.

Quantum Chemistry and Spectroscopy (160 videos) and Chemical Thermodynamics and Kinetics (137 videos) are both complete. Theoretical and Computational Chemistry in progress (68 videos). All feedback and suggestions are encouraged in comments or email.

Physical chemistry is the use of physics to develop descriptive mathematical models for the behavior of chemical systems. Physical chemistry is typically studied for 2-3 semesters by university chemistry students. Prerequisites includes general chemistry, general physics, algebra, and calculus.

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