Understanding the GAMESS RHF Output¶
Once the input file is submitted, GAMESS prints a detailed output containing information about the molecular system, the basis set, the SCF procedure, and the final results.
In this section, we will go through the most important parts of the output produced for the RHF calculation of the water molecule.
1. Molecular Geometry¶
THE POINT GROUP OF THE MOLECULE IS C1
THE ORDER OF THE PRINCIPAL AXIS IS 0
ATOM ATOMIC COORDINATES (BOHR)
CHARGE X Y Z
O 8.0 0.0000000000 0.0000000000 0.1129663669
H 1.0 0.0000000000 1.4837712716 -0.8964288797
H 1.0 0.0000000000 -1.4837712716 -0.8964288797
What does this mean?¶
The first section confirms that GAMESS has correctly read the molecular geometry from the input file.
Notice that
- the molecule belongs to the C₁ point group,
- the coordinates are printed in Bohr, even though they were supplied in Ångström.
GAMESS automatically converts the input coordinates into atomic units before beginning the calculation.
2. Interatomic Distances¶
INTERNUCLEAR DISTANCES (ANGS.)
1 O 2 H 3 H
1 O 0.0000000 0.9496419 0.9496419
2 H 0.9496419 0.0000000 1.5703560
3 H 0.9496419 1.5703560 0.0000000
What does this mean?¶
GAMESS calculates all bond lengths from the Cartesian coordinates.
For the water molecule,
- O–H bond length = 0.9496 Å
- H–H distance = 1.5704 Å
This section is useful for verifying that the molecular geometry has been entered correctly.
3. Basis Set Information¶
TOTAL NUMBER OF BASIS SET SHELLS = 4
NUMBER OF CARTESIAN GAUSSIAN BASIS FUNCTIONS = 7
NUMBER OF ELECTRONS = 10
SPIN MULTIPLICITY = 1
NUMBER OF OCCUPIED ORBITALS (ALPHA) = 5
NUMBER OF OCCUPIED ORBITALS (BETA ) = 5
What does this mean?¶
This section summarizes the electronic system.
For this calculation,
- Water contains 10 electrons.
- Since RHF is used, there are 5 occupied α orbitals and 5 occupied β orbitals.
- The STO-3G basis generates 7 basis functions for the entire molecule.
- The spin multiplicity is 1, confirming that water is a closed-shell system.
4. Nuclear Repulsion Energy¶
What does this mean?¶
This is the electrostatic repulsion between the atomic nuclei.
Since nuclei are positively charged, they repel each other, contributing a positive energy to the total molecular energy.
This quantity depends only on the molecular geometry and does not change during the SCF iterations.
5. Initial Guess Orbitals¶
What does this mean?¶
Before solving the Hartree–Fock equations, GAMESS generates an initial approximation to the molecular orbitals using the Hückel method.
These orbitals serve as the starting point for the SCF iterations.
6. RHF SCF Iterations¶
ITER EX DEM TOTAL ENERGY E CHANGE DENSITY CHANGE
1 -74.7995505090
2 -74.9442494628
3 -74.9560149502
4 -74.9573846051
...
13 -74.9576302882
What does this mean?¶
This is the heart of the Hartree–Fock calculation.
During each iteration,
- the Fock matrix is constructed,
- new molecular orbitals are calculated,
- the electron density is updated,
- the total energy is recalculated.
Notice that the energy becomes progressively lower:
| Iteration | Energy (Hartree) |
|---|---|
| 1 | -74.7995505090 |
| 5 | -74.9575876719 |
| 10 | -74.9576302862 |
| 13 | -74.9576302882 |
As the iterations proceed,
- the energy changes become smaller,
- the density changes decrease,
- eventually the calculation reaches self-consistency.
7. SCF Convergence¶
What does this mean?¶
This is the most important message in the entire output.
It confirms that
- the SCF procedure has converged,
- the molecular orbitals are self-consistent,
- the final Hartree–Fock energy is
The calculation required 13 SCF iterations to reach convergence.
8. Molecular Orbital Energies¶
What does this mean?¶
These are the molecular orbital energies (in Hartree).
Since water has 10 electrons, the first five molecular orbitals are occupied.
Therefore,
- HOMO = Orbital 5 = −0.3858 Hartree
- LUMO = Orbital 6 = 0.5988 Hartree
The HOMO–LUMO energy gap is approximately
A larger HOMO–LUMO gap generally indicates greater electronic stability.
9. Energy Components¶
ONE ELECTRON ENERGY = -122.5249813908
TWO ELECTRON ENERGY = 38.3145517546
NUCLEAR REPULSION ENERGY = 9.2527993481
TOTAL ENERGY = -74.9576302882
What does this mean?¶
The total Hartree–Fock energy is obtained by combining
- kinetic energy,
- electron–nucleus attraction,
- electron–electron repulsion,
- nuclear–nuclear repulsion.
For the water molecule,
| Contribution | Energy (Hartree) |
|---|---|
| One-electron | -122.5249813908 |
| Two-electron | 38.3145517546 |
| Nuclear repulsion | 9.2527993481 |
| Total RHF Energy | -74.9576302882 |
10. Mulliken Population Analysis¶
TOTAL MULLIKEN AND LOWDIN ATOMIC POPULATIONS
ATOM MULL.POP. CHARGE
O 8.386339 -0.386339
H 0.806830 0.193170
H 0.806830 0.193170
What does this mean?¶
The Mulliken population analysis estimates how electrons are distributed among the atoms.
For water,
- Oxygen carries a partial negative charge of −0.386.
- Each hydrogen carries a partial positive charge of +0.193.
This agrees with the expected polarity of water, where oxygen is more electronegative than hydrogen.
11. Bond Order Analysis¶
What does this mean?¶
The calculated bond order for each O–H bond is approximately 0.945, which is close to the expected value of 1 for a single covalent bond.
12. Dipole Moment¶
What does this mean?¶
The calculated molecular dipole moment is
1.686 Debye
The dipole moment measures the separation of positive and negative charge within the molecule.
Water is a highly polar molecule because the oxygen atom attracts electron density more strongly than the hydrogen atoms.
13. Normal Termination¶
What does this mean?¶
This is the final confirmation that the calculation completed successfully.
Always verify that this message appears before using any results from the output file.