# What does 'forces' mean in the output of Gaussian calculations?

## In the output of a Gaussian calculation of frequencies, I can see a table listing all the 'forces' of all the atoms. It looks like this:

Center Number Atomic Number Forces (Hartrees/Bohr) X Y Z

  1        6          -0.001094502   -0.000768130   -0.006919164
2        6           0.000528733   -0.000637636    0.005949765
3        6           0.000424174   -0.000366750   -0.002904382
4        6          -0.002619381   -0.000001885    0.005496979


...

What are these 'forces'? Are they related to those vibrations? But during vibrations, the force on each atom by other atoms is always changing, so why is only one constant 'force' value assigned to each atom?

• I am not sure, but those might be related to the Hessian matrix, the partial second derivatives, which is diagonalized in a frequency calculation. Note that $F=m\frac{\mathrm{d}^2}{\mathrm{d}x^2}$ in 1D. – Feodoran Jan 21 '18 at 12:43
• Did you optimize the geometry before running the frequency calculation? Frequency calculations don't have any meaning if they aren't taken at a stationary point of the potential energy surface. – Tyberius Jan 21 '18 at 16:59
• @Feodoran But the forces are not calculated from that formula, right? The forces are calculated from the electronic structures of the atoms, regardless of the masses of the atoms, right? – OhLook Jan 21 '18 at 19:36
• I always took them as force constant (spring on my mind) – Alchimista Jan 21 '18 at 20:09
• @Alchimista But they're not. Look at their unit - Hartree/Bohr. Obviously they are just forces. – OhLook Jan 21 '18 at 21:26