Blog Entry (c) Friday, October 18, 2024, by James Pate Williams, Jr. Ab Initio Quantum Chemical Calculation

On Wednesday, October 16, 2024, I bought an Amazon Kindle book named “Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory” by Attila Szabo and Neil S. Ostlund. It cost me $10.69 which is a real bargain. In Appendix B there is a listing for a FORTRAN program to perform an ab initio Hartree-Fock Self Consistent Field calculation for a two-electron heteronuclear molecule namely the helium-hydrogen cation. I successfully translated the program from FORTRAN to C++. I had to remember that FORTRAN stores matrices in column major order and C/C++ stores matrices in row major order. I took the transposes of two FORTRAN COMMON matrices to get the correct C++ storage. The authors of the book did an extensive treatment of the test calculation. The application is only 823 lines of monolithic C++ source code. I used FORTRAN like array indexing starting at 1 instead of the C initial beginning index of 0. I think I will try to get in touch with the authors to get permission to post the source code and results on my blog. 

P. S. I got permission from Dover Books to publish my source code and results. I think I will reconsider posting the C++ source code. The actual ground state energy of the cation is -2.97867. My calculation and the book’s computation are in percentage errors of about 4%. The book’s value is a little closer to the exact value than my result. The book calculation was done in FORTRAN double precision on a Digital Equipment Corporation PDP-10 minicomputer. My recreation of the book’s endeavor was executed on an Intel Itanium Core 7 and Windows 10 Professional machine using Win32 C++. The C++ compiler was from Microsoft Visual Studio 2019 Community Version.

Note I added a calculation for a homonuclear molecule, namely, the hydrogen diatomic molecule.

Blog Entry (c) Tuesday, October 15, 2024, by James Pate Williams, Jr. Nonlinear Least Squares Curve Fitting Example from Quantum Chemistry

Blog Entry (c) Monday, October 14, 2024, by James Pate Williams, Jr. Three Hydrogen Molecule Ion Integrals and Energy Values

References: https://web.stanford.edu/~oas/SI/QM/Atkins05.pdf See Example 8.1 The evaluation of overlap and Coulomb integral for the hydrogen molecule ion pages 255 – 256 https://www.physics.udel.edu/~jim/PHYS425_20S/Class%20Notes/Notes_8.pdf https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Introductory_Quantum_Mechanics_(Fitzpatrick)/13%3A_Variational_Methods/13.03%3A_Hydrogen_Molecule_Ion#fh2pa

Blog Entry © Monday, October 7, 2024, by James Pate Williams, Jr. Recent Voyages into the World of Quantum Chemistry

Blog Entry © Saturday, October 5, 2024, by James Pate Williams, Jr. Multidimensional Integrals

Recent Email that I Wrote on May 23, 2024

Does the following thought experiment make sense?

Suppose we have a positively charged quantum mechanical particle in a finite potential energy well. Also suppose there is a free negatively charged quantum mechanical particle outside the potential energy well. There is a measurable probability that the positively charged particle will tunnel through the potential energy well and perhaps be attracted to the negatively charged particle. Likewise, the negatively charged particle has a finite probability of penetrating the potential energy well and hooking up with the positively charged particle should it still be trapped in the well. There is no “spooky action at a distance” to use Albert Einstein’s 1930s definition of quantum entanglement in this example since this electromagnetic attraction is a local phenomenon (?). The positively charged particle cannot exert an attractive force until it tunnels through the energy barrier or otherwise the negatively charged particle winds up breaking into the well. I don’t know exactly how quantum electrodynamics would explain this example. Perhaps the positively charged particle is a positron (antimatter lepton) and the negatively charged particle is a plain vanilla electron. We know that the local result of the interaction of our two matter-antimatter particles is an annihilation event whereby two energetic photons are created, or other products are generated.
https://en.wikipedia.org/wiki/Annihilation#/media/File:Electron_Positron_Annihilation.png

Quantum Mechanical Angular Momentum Ladder Operators by James Pate Williams, Jr. Copyright Thursday, May 23, 2024, All Applicable Rights Reserved