Density Fitting Overview Part 1
We’ve been trying to get high-local electron correlation methods with low-order scaling of computational cost which is a function of molecular size.
Category: Many-body methods
Matrix Multiplication in Coupled Cluster
Electronic structure theory deals in tensor quantities. Matrices are a special type of tensor, and matrix multiplication is a special type of tensor contraction. In the practical implementation of coupled cluster theory, we store amplitudes are stored in matrix form where we use compound row and col indices ij and cd respectively. This storage scheme… Read More Matrix Multiplication in Coupled Cluster
CC, Basis set, Inner/Outer products
Discussion of basis set convergence, CCSD, discussion of cusps, outer and inner products
Coupled Cluster
Consider a system of four electrons moving in an arbitrary electrostatic field generated by the nuclei.
Jacobi – SVD Algorithm
Although I’m not a 100% on how this benefits us by reducing computations, I think I have the algorithm down. The Jacobi transformation works on symmetric positive definite matrices. They say (internet) that SVD uses up too much space because we have to calculate the AT*A (?). The Jacobi transformation requires you to calculate At*A,… Read More Jacobi – SVD Algorithm
Coming to the point
The point of the last two posts was to talk about the theory that I struggled with over the past few months. Today we covered matrix elements of a full basis set and notation. Lots of notation. All N-electrons in the system can be in any of the occupied orbitals as long as antisymmetry is… Read More Coming to the point
Basis Sets, Hartree Fock Approximation
We take the simplest antisymmetric wavefunction of ground state of N-electron system. This is single Slater determinant of the form, Psi0 = | X1, X2…..Xn> By the variational principle, the best wavefuntion is the one that gives the lowest energy. To do this we take the expectation value <Psi0|H|Psi0> = E0. So now we know… Read More Basis Sets, Hartree Fock Approximation
Electronic Problem, Orbitals, Slater Determinants
Szabo Chap 2 : Many Electron Wavefunctions and Operators Born-Oppenheimer Approximation states that we can consider the electrons to be moving in a field of fixed nuclei because nuclei are heavier than electrons and move more slowly. This approximation leads to further approximations in which the kinetic energy portion of the equation is neglected and… Read More Electronic Problem, Orbitals, Slater Determinants
LU Decomposition
Fixed Gaussian elimination code. In formula, base/temp. Inspiring speech by advisor. Note : don’t misapply efforts. LU decomposition. Started writing the code using arrays but that was quicksand. Figured out the formula to be used to calculate upper and lower triangles. Sum function. Swap rows function. Algorithm : Ax = b; (LU)x = b. This… Read More LU Decomposition
MacTex and Gauss Elimination
Install Mactex using brew cask. LaTex bulleted, numbered, to-do (checkboxes) lists. Manipulating indices in matrix so that previous row remains untouched as rows swapped. Lower triangular part of matrix should become zero. Gaussian elimination with partial pivoting To solve a system of linear equations given by Ax=b, get augmented matrix [A|b]. All normalize and swap… Read More MacTex and Gauss Elimination
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