Saturday, September 6, 2014

Four Practical Comments Regarding RHF Calculations

1. If the program you use to perform a geometry optimization at the HF level complains of convergence problems, the first step is to determine whether it is the geometry optimization that failed to converge (i.e. the program could not find a geometry with a low gradient given a certain number of steps) or whether it is the SCF-procedure at a particular geometry that failed to converge (i.e. the program could not find a set or orbitals that have stopped changing given a certain number of steps). It is my experience that if the SCF does not converge in the default number of steps, then simply increasing the allowed number of SCF steps does not solve the problem. The problem is usually either in the initial guess orbitals or there is an error in the molecular structure.

2. Most quantum chemistry programs will have RHF as the default method, which implies a singlet wave function. So if you provide the program with a molecule that has an odd number of electrons (e.g. NH4) the program will complain that it cannot do a singlet calculation on a molecule with an odd number of electrons, and asks you to change either the charge or the multiplicity, i.e. to specify whether you want to do an UHF or ROHF calculation on the doublet state of the NH4 radical, or whether you meant to do a singlet RHF calculation on NH4+. You will get very different results depending on your choice, so the object here is not to use trial and error to find a combination of charge and multiplicity that satisfies the program. Rather you have to decide what makes sense chemically, before you do the calculation.

3. Once you have defined the position of the nuclei and the number of electrons (by specifying the overall charge of the molecule) the SCF procedure does the rest. Therefore, you don’t have to specify that the positive charge “is on the NH3 group” in CH3NH3+. Each orbital has access to all the basis functions in the molecule and the electrons generally “go where they want”. Also, changing the CN bond to a double bond in a graphics program does not affect the result (as long as the CN bond length is the same).

4. This should be obvious, but just in case. It makes no sense to compare the total energy (E) of two molecules (or collection of molecules) that have a different number and kinds of atoms. For example, substituting a hydrogen atom in a molecule with a methyl group will lead to a considerable lowering of the RHF energy. Most of this energy lowering will some from the electron-nuclear attraction energy of the electron in the 1s orbital of the C atom, but says nothing about the relative stability of the two molecules. In the Introduction to Molecular Modeling course I used to teach, I used to subtract 20 points (out of a hundred) for such a comparison in a laboratory report
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