# Chemistry - Gaussian09 vs home made Hartree-Fock implementation

Diagonalization of the core Hamiltonian provides usually not the best guess for the SCF procedure to say the least, and thus, by default Gaussian uses a more sophisticated guess obtained by diagonalizing the Harris functional (`Guess=Harris`

). With this default guess one get the same energy as OP reported:

```
SCF Done: E(RHF) = -107.495842181 A.U. after 5 cycles
```

Now, `Pop=None`

was a terrible idea, of course. It is always advisable to look at the final orbitals. Everything looks fine for the case of the default guess

```
Alpha occ. eigenvalues -- -15.51806 -15.51612 -1.44283 -0.72249 -0.57311
Alpha occ. eigenvalues -- -0.57311 -0.53949
Alpha virt. eigenvalues -- 0.28131 0.28131 1.12344
```

but results with the core Hamiltonian guess look suspicios

```
Alpha occ. eigenvalues -- -15.44896 -15.44853 -1.34440 -0.64250 -0.60670
Alpha occ. eigenvalues -- -0.52980 -0.16921
Alpha virt. eigenvalues -- -0.07243 0.31047 1.20826
```

The energy of the first virtual orbital is *negative* which is odd. It is difficult to say what went wrong with the core Hamiltonian guess, but some clue can be provided if turning the symmetry back on (this is another very sensible default turning which off was a bad idea, I think).

The default guess yields the electronic state with a particular symmetry ($\sigma_{\mathrm{g}}$)

```
Initial guess orbital symmetries:
Occupied (SGU) (SGG) (SGG) (SGU) (PIU) (PIU) (SGG)
Virtual (PIG) (PIG) (SGU)
The electronic state of the initial guess is 1-SGG.
```

and converges within this symmetry

```
Orbital symmetries:
Occupied (SGG) (SGU) (SGG) (SGU) (PIU) (PIU) (SGG)
Virtual (PIG) (PIG) (SGU)
The electronic state is 1-SGG.
```

But the core Hamiltonian guess yields the electronic state with no symmetry

```
Initial guess orbital symmetries:
Occupied (SGG) (SGU) (SGG) (SGU) (PIU) (PIU) (PIG)
Virtual (PIG) (SGG) (SGU)
```

and converges within this state with no symmetry

```
Orbital symmetries:
Occupied (SGG) (SGU) (SGG) (SGU) (PIU) (PIU) (PIG)
Virtual (SGG) (PIG) (SGU)
Unable to determine electronic state: partially filled degenerate orbitals.
```

which is again suspicious.

So, there is something wrong with the core Hamiltonian guess for this system (I suspect the basis is too small for the core Hamiltonian guess to yield sensible results), thus, SCF spits out some "strange" numbers. Strictly, speaking there is nothing strange with the numbers. Remember that SCF usually converges to a *local* minimum, and which particular depends on which part of the wave function space the initial guess placed the system in. And besides, you're not even guaranteed to have a minimum, SCF might converge to a stationary point of any kind.