# What are computed energies in DFT and FF methods relative to?

I am not talking about zero-point energy.

I wish to understand how the energy of a system is calculated relative to a zero baseline. This is best explained with an example.

From DFT, the energy could be:

Isolated H = -13.6 eV,
H2 = -31.8 eV


What are these numbers related to? What would be a system at 0 eV? Or what is the zero baseline from which these number are calculated from?

I have also noticed that force-field energies tend to be positive. What is the zero baseline here?

In summary:

• What is the DFT baseline?
• What is the Forcefield baseline?

Start by looking at the Hamiltonian for a molecular system $$$$\label{eq:coulomb_hamiltonian} \hat{H} = - \sum\limits_{α=1}^{ν} \frac{1}{2 m_{α}} \nabla_{α}^{2} - \sum\limits_{i=1}^{n} \frac{1}{2} \nabla_{i}^{2} - \sum\limits_{α=1}^{ν} \sum\limits_{i=1}^{n} \frac{Z_{α}}{r_{αi}} + \sum\limits_{α=1}^{ν} \sum\limits_{β > α} \frac{Z_{α} Z_{β}}{r_{αβ}} + \sum\limits_{i=1}^{n} \sum\limits_{j > i}^{n} \frac{1}{r_{ij}} \, ,$$$$ where $$m_{α}$$ is the rest mass of nucleus $$α$$ and $$Z_{α}$$ is its atomic number, $$r_{αi} = |\vec{r}_{α} - \vec{r}_{i}|$$ is the distance between nucleus $$α$$ and electron $$i$$, $$r_{αβ} = |\vec{r}_{α} - \vec{r}_{β}|$$ is the distance between two nuclei $$α$$ and $$β$$, and $$r_{ij} = |\vec{r}_{i} - \vec{r}_{j}|$$ is the distance between two electrons $$i$$ and $$j$$.