diff --git a/exercises/ex08_solution/hartree-fock.ipynb b/exercises/ex08_solution/hartree-fock.ipynb index c538bd0183e512b495c89bc4dcb2a7529b0a68fc..6edac4587c9e010ccb0b3c4d05c81f9fcce9056d 100644 --- a/exercises/ex08_solution/hartree-fock.ipynb +++ b/exercises/ex08_solution/hartree-fock.ipynb @@ -352,7 +352,29 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Don't forget to add 1 to the resulting energy: during derivation, the repulsion of the H cores (which is normalised to $1$ Hartree) has been left out." + "Don't forget to add 1 to the resulting energy: during derivation, the repulsion of the H cores ( $\\frac{1}{|R_A-R_B|}=1$ Hartree in the Hamiltonian) has been dropped." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "## Drawbacks" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "* The Born-Oppenheimer approximation neglects nuclei, although this doesn't factor too strongly into the examples we have used.\n", + "\n", + "* The choice of a too small basis and/or one consisting of too simple functions (here GTOs) can be insufficient to describe the system accurately. Bigger sets (STO-6G) and/or more elaborate functions get computationally expensive quickly.\n", + "\n", + "* The wave function is approximated by a single Slater determinant. Each electron sees the average density of all other electrons (compare: mean field theory), which doesn't factor in electron correlation.\n", + "\n", + "The last point is addressed extensively in \"post-Hartree-Fock\" methods (e.g. using a sum of \"excited\" Slater determinants)." ] }, {