In the Hartree–Fock method of quantum mechanics, the Fock matrix is a matrix approximating the single-electron energy operator of a given quantum system in a given set of basis vectors.It is most often formed in computational chemistry when attempting to solve the Roothaan equations for an atomic or molecular system. The Fock matrix is actually an approximation to the true Hamiltonian operator of the quantum system. It includes the effects of electron-electron repulsion only in an average way. Because the Fock operator is a one-electron operator, it does not include the electron correlation energy. The Fock matrix is defined by the Fock operator. For the restricted case which assumes closed-shell orbitals and single-determinantal wavefunctions, the Fock operator for the i-th electron is given by: where: is the Fock operator for the i-th electron in the system, is the one-electron Hamiltonian for the i-th electron, is the number of electrons and is the number of occupied orbitals in the closed-shell system, is the Coulomb operator, defining the repulsive force between the j-th and i-th electrons in the system, is the exchange operator, defining the quantum effect produced by exchanging two electrons. The Coulomb operator is multiplied by two since there are two electrons in each occupied orbital. The exchange operator is not multiplied by two since it has a non-zero result only for electrons which have the same spin as the i-th electron. For systems with unpaired electrons there are many choices of Fock matrices. (Wikipedia).
Overview of the F-Test. What it is and how it works with general steps and assumptions.
From playlist F Test
Multivariable Calculus | The gradient and directional derivatives.
We define the gradient of a function and show how it is helpful in finding the directional derivative. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Multivariable Calculus
The Hessian matrix | Multivariable calculus | Khan Academy
The Hessian matrix is a way of organizing all the second partial derivative information of a multivariable function.
From playlist Multivariable calculus
An introduction to how the jacobian matrix represents what a multivariable function looks like locally, as a linear transformation.
From playlist Multivariable calculus
Lecture 04-Jack Simons Electronic Structure Theory- Linear combinations of atomic orbitals
The Hartree-Fock molecular orbitals; LCAO-MO expansion; Hartree-Fock equations in matrix form; one- and two-electron integrals; the iterative SCF process; scaling with basis set size; how virtual orbitals change with basis set; core, valence, polarization, and diffuse basis functions; Slat
From playlist U of Utah: Jack Simons' Electronic Structure Theory course
How to Find the Directional Derivative of f(x, y) = cos(x + y) using the Gradient Vector
Directional Derivative of f(x, y) = cos(x + y) If you enjoyed this video please consider liking, sharing, and subscribing. You can also help support my channel by becoming a member https://www.youtube.com/channel/UCr7lmzIk63PZnBw3bezl-Mg/join Thank you:)
From playlist Calculus 3
Lecture 02-Jack Simons Electronic Structure Theory- Hartree-Fock
Slater-Condon rules; the Hartree-Fock approximation; Coulomb and exchange interactions; Koopmans theorem, the meaning of orbital energies; Brillouin theorem; molecular orbitals are delocalized; reminder on the limitations of single determinant wave functions. (1)Jack Simons Electronic S
From playlist U of Utah: Jack Simons' Electronic Structure Theory course
Lecture 07-Jack Simons Electronic Structure Theory- Configuration interaction theory
Configuration interaction (CI) and multi-configuration self-consistent field (MCSCF) methods; strengths and weaknesses; two-electron integral transformation. (1)Jack Simons Electronic Structure Theory- Session 1- Born-Oppenheimer approximation http://www.youtube.com/watch?v=Z5cq7JpsG8I
From playlist U of Utah: Jack Simons' Electronic Structure Theory course
29. Modern Electronic Structure Theory: Electronic Correlation
MIT 5.61 Physical Chemistry, Fall 2017 Instructor: Professor Troy Van Voorhis View the complete course: https://ocw.mit.edu/5-61F17 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62RsEHXe48Imi9-87FzQaJg This lecture covers information about modern electronic structure
From playlist MIT 5.61 Physical Chemistry, Fall 2017
Ex: Function Values of a Function of Two Variables Using a Table
This video provides an example of how to evaluate a function of two variables using a table of values. Site: http://mathispower4u.com
From playlist Functions of Several Variables
Lecture 12-Jack Simons Electronic Structure Theory- Gradients and reaction paths
Response theory; molecular deformation gradients and Hessians; reaction paths. (1)Jack Simons Electronic Structure Theory- Session 1- Born-Oppenheimer approximation http://www.youtube.com/watch?v=Z5cq7JpsG8I (2)Jack Simons Electronic Structure Theory- Session 2- Hartree-Fock http://w
From playlist U of Utah: Jack Simons' Electronic Structure Theory course
Directional Derivative of f(x, y) = e^(2y)sin(x)
Directional Derivative of f(x, y) = e^(2y)sin(x) If you enjoyed this video please consider liking, sharing, and subscribing. You can also help support my channel by becoming a member https://www.youtube.com/channel/UCr7lmzIk63PZnBw3bezl-Mg/join Thank you:)
From playlist Calculus 3
Lecture 08 -Jack Simons Electronic Structure Theory- Coupled-cluster theory
Coupled-cluster (CC) theory; analogy to cluster expansion in statistical mechanics; the CC equations are quartic. (1)Jack Simons Electronic Structure Theory- Session 1- Born-Oppenheimer approximation http://www.youtube.com/watch?v=Z5cq7JpsG8I (2)Jack Simons Electronic Structure Theory
From playlist U of Utah: Jack Simons' Electronic Structure Theory course
Transformation: Graph f(|x|), Given f(x)
The video explains how to graph f(|x|) from the graph of f(x). http://mathispower4u.com
From playlist Determining Transformations of Functions
Chem 131A. Lec 20. Quantum Principles: Hartree-Fock Calculations, Spin, and Slater Determinants
UCI Chem 131A Quantum Principles (Winter 2014) Lec 20. Quantum Principles -- Hartree-Fock Calculations, Spin, and Slater Determinants -- View the complete course: http://ocw.uci.edu/courses/chem_131a_quantum_principles.html Instructor: A.J. Shaka, Ph.D License: Creative Commons BY-NC-SA T
From playlist Chem 131A: Week 8
Memories of initial states and density imbalance in dynamics by Rajdeep Sensarma
PROGRAM THERMALIZATION, MANY BODY LOCALIZATION AND HYDRODYNAMICS ORGANIZERS: Dmitry Abanin, Abhishek Dhar, François Huveneers, Takahiro Sagawa, Keiji Saito, Herbert Spohn and Hal Tasaki DATE : 11 November 2019 to 29 November 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore How do is
From playlist Thermalization, Many Body Localization And Hydrodynamics 2019
Lecture 05-Jack Simons Electronic Structure Theory- Basis sets
Basis set notations; complete-basis extrapolation of the Hartree-Fock and correlation energies. (1)Jack Simons Electronic Structure Theory- Session 1- Born-Oppenheimer approximation http://www.youtube.com/watch?v=Z5cq7JpsG8I (2)Jack Simons Electronic Structure Theory- Session 2- Hartr
From playlist U of Utah: Jack Simons' Electronic Structure Theory course
Ex: Find an Inverse Derivative Function Value (Cubic + Rational)
This video explains how to determine an inverse function values and an inverse derivative function value without determining the inverse of a given function.
From playlist Differentiation of Inverse Trigonometric Functions
This clip gives describes a rotation matrix in 2D. The clip is from the book "Immersive Linear Algebra" available at http://www.immersivemath.com.
From playlist Chapter 6 - The Matrix
Lecture 11-Jack Simons Electronic Structure Theory- Density functional theory
Density functional theory fundamentals, strengths and weaknesses. (1)Jack Simons Electronic Structure Theory- Session 1- Born-Oppenheimer approximation http://www.youtube.com/watch?v=Z5cq7JpsG8I (2)Jack Simons Electronic Structure Theory- Session 2- Hartree-Fock http://www.youtube.co
From playlist U of Utah: Jack Simons' Electronic Structure Theory course