# energy difference vs absolute energy

When dealing with determining the ground state energy of a system, people often say that it is better to know the energy difference rather than the absolute minimum energy. I understand that the absolute minimum energy depend on the model so the more complex your model, the lower or closer the energy you found to the true ground state energy.

But what do people refer to when they say energy difference here? Different between what energies exactly?

• They are referring to the energy difference between electronic or vibrational states or between rotational states. Energy in QM calculations must always be in reference to something. Usually it is specified as the minimum of the PES for the lowest electronic state. As you mentioned, absolute energies will depend on the method and choice of expansion, basis, etc. – Bertram Dec 15 '20 at 6:24
• Absolute energies returned from ab initio software is usually with reference to infinite separation of all particles which is usually hundreds of hartree away from the minimum energy of the PES so that it is a useless reference point. – Bertram Dec 15 '20 at 6:29
• The energy difference can also be from the bottom of the potential well, but being trapped at the bottom of the well is not an accessible state. – Buck Thorn Dec 15 '20 at 8:42
• At the end is due to the fact that nothing has absolute zero energy, just a minimum. As far you are able to get or locate values versus the same reference, than you can compare them. – Alchimista Dec 15 '20 at 11:45
• @Bertram Regard to your first comment: Let's say I use two different methods to calculate the electronic ground state energies. Then is it right for me to say that the energy differences here refer to the differences in energy I get from different geometry configurations? For example, I calculate it the ground state energy at bond distance of 1,2, and 3 Angstrom. I found that I get min energy occurred at 2 Angstrom on both method. Now, I will take the difference between the energies between 1 and 2 Angstrom and 3 and 2 Angstrom on both methods and compare? – user102247 Dec 15 '20 at 15:21