# Is enthalpy of activation the same as activation energy? Is there a purely mathematical way to find that value?

I asked about the effect of pressure on a reaction, and since then I learned a lot more. One of the things I learned was the Eyring equation:

$$\kappa = \frac{\kappa_B T}{h} e^\frac{\Delta^\ddagger S°}{R} e^\frac{- \Delta^\ddagger H°}{R}$$

where:

$\begin{multline} \begin{split} \kappa &= \text{reaction rate} \\ \kappa_B &= \text{Boltzmann constant} \\ T &= \text{temperature} \\ h &= \text{Planck's constant} \\ R &= \text{gas constant} \\ \Delta^\ddagger S° &= \text{entropy of activation} \\ \Delta^\ddagger H° &= \text{enthalpy of activation} \\ \end{split} \end{multline}$

My questions:

1. Is the enthalpy of activation the same thing as the activation energy?

2. Is there a purely mathematical way to determine both $\Delta^\ddagger S°$ and $\Delta^\ddagger H°$? (without having a laboratory to use to observe the reaction)

(1) Enthalpy of activation is a component of activation energy. The other component is temperature * entropy of activation. Enthropy controls "heat difference" while entropy controls "measure of disorder difference".

$\Delta$G = $\Delta$H - T*$\Delta$S. This applies to activation energy too.

(2) DFT functionals rely on 4 parameters per atom make predictions. So, if you give 4*5=20 parameters, then you can in theory predict behaviour of any compound, build with only C, H, N, O, S atoms. This covers most of biochemistry, excluding nucleic acids (you would need additional 4 parameters to characterize P).

These 4 parameters are known for most of the atoms (excluding some elements, going after uranium). But those four parameters were experimentally measured by fitting behavior of modeled molecules to real molecules.

Should we count it as "purely theoretically predict?"

Also there are purely ab initio methods like Hartree-Fock with even less input required. You would still need some input. In math you can build many different plausible worlds. For example purely "newtonian" vs "newtonian + quantum mechanics" words. experiment is the only way to tell, which model is correct.

• Wow, I downloaded JDFTx and it is way beyond my understanding. Do you have an idea of something easier to use? – FinnTheHuman Jul 21 '16 at 16:43
• In my PhD QM 30% of work was relevant to QM. I am now working as a coder. JDFTx is above my head. It is a "plugin" (one of the DFT potentials) to work with a very specific case "calculations of electronic systems in contact with liquid environments". It is not a mainstream approach so you might not find tutorials. – sixtytrees Jul 21 '16 at 17:00
• Feasible steps for you would be (1) ACD/ChemSketch to draw molecules -> (2) convert to 3D (in ChemSketch) -> (3) use Gaussian to compute properties. If you try to build Minecraft level from ab initio QM, it will not work. Currently professors in computational chemistry develop methods to model protein-protein interaction. A computational model of a whole cell is a dream in the field. The problem isn't that they can't find solutions to the equations. The problem is that using modern supercomputers you would use a billion years to model a nanosecond of life of a single cell. – sixtytrees Jul 21 '16 at 17:04
• Licensed Gaussian costs money, but it is a de-facto standard. You can check alternatives here reddit.com/r/chemistry/comments/s6m0w/…, but I've never worked with those. – sixtytrees Jul 21 '16 at 17:15
• All that just to predict entropy and enthalpy of activation of a reaction? – FinnTheHuman Jul 21 '16 at 17:25