Computational Chemistry 4.11 - One-Electron Integrals

Short lecture on one-electron integrals of spin orbital expectation values.

Terms in the total energy of a molecular system are either of the one-electron or two-electron form, depending on the number of electrons in the operator. One-electron terms include electron kinetic energy and electron-nuclear attraction. One-electron terms can be factored to only depend on the coordinates of one-electron at a time, and are thus "separable". Two-electron terms (electron-electron repulsion) are not separable, and thus the primary source of difficulty in obtaining molecular energy expressions. This video performs a derivation to show how the one-electron energy of a molecular energy depends only on the core Hamiltonian operator applied to each occupied spin orbital, multiplied by its complex conjugate, and integrated over all space (i.e. one-electron integrals).

Notes Slide: https://i.imgur.com/Pt7sfcy.png

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