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Courses in computational chemistry are increasingly common at the undergraduate level. Excellent user-friendly programs, which make the execution of ab initio calculations quite simple, are available. However, there is a danger that the underlying SCF procedure (usually coupled with contracted Gaussian atomic orbital basis sets) can become a ‘black box’ for the student. We have attempted to rectify this situation by creating a Microsoft Excel spreadsheet that contains all the essential elements of far more complicated ab initio calculations, but on the simplest possible molecular system. This submission performs Restricted Hartree–Fock (RHF) self-consistent field (SCF) calculations on a two-body, two-electron system. In addition, the spreadsheet makes use of standard minimal Gaussian basis sets for hydrogen and helium. Therefore, one can perform the following ab initio single-point energy calculations for H2, HeH+, or He22+: - RHF/STO-1G
- RHF/STO-2G
- RHF/STO-3G
To fulfill the above pedagogical objectives, all the calculations are carried out using standard Excel cell formulas to make the entire procedure more transparent to the student. Specifically, the spreadsheet contains: - contracted Gaussian atomic orbital basis sets
- calculation of one- and two-electron integrals
- the construction of a Hamiltonian core initial molecular orbital (MO) guess, or the option for the student to provide their own initial MO guess
- calculation of the orthogonalized Fock matrix
- diagonalization of the Fock matrix to generate new MOs, the density matrix, and the total energy of the system
use the new MOs to recalculate the Fock matrix, generate new MOs, and calculate the new energy.
 The potential energy surface of HeH+ at the RHF/STO-3G level of theory. Energies are relative to the minimum, and are calculated at intervals of 0.1 Bohr (a.u.).
This process is then repeated until self-consistency in the energy is achieved. The student is able to step through the SCF procedure one iteration at a time, or step through each part of one iteration; in the latter case, built-in macros walk the student through each step of the SCF cycle and highlight the relevant parts of the spreadsheet to show where a particular calculation is carried out. The spreadsheet makes use of these features: - The student can plot the highest occupied molecular orbital (ψ1), lowest unoccupied molecular orbital (ψ2), |ψ1|2, | ψ2|2, or any combination of the four during the SCF cycle. This allows the student to easily see how the wave function is being improved.
- The contraction coefficients and Gaussian exponents can be changed to demonstrate the variational principle.
- The electronic energy convergence threshold can be changed.
The spreadsheet described here is accompanied by a manuscript that summarizes the RHF SCF method and presents the full form of all the working equations used in the spreadsheet.
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