Useful Thermochemistry from Gaussian Calculations

Statistical Mechanics is the bridge between microscopic calculations and thermodynamics of a particle ensemble. By means of calculating a partition function divided in electronic, rotational, translational and vibrational functions, one can calculate all thermodynamic functions required to fully characterize a chemical reaction. From these functions, the vibrational contribution, together with the electronic contribution, is the key element to getting thermodynamic functions.

Calculating the Free Energy change of any given reaction is a useful approach to asses their thermodynamic feasibility. A large negative change in Free Energy when going from reagents to products makes up for a quantitative spontaneous (and exothermic) reaction, nevertheless the rate of the reaction is a different story, one that can be calculated as well.

Using the freq option in your route section for a Gaussian calculation is mandatory to ascertain the current wave function corresponds to a minimum on a potential energy hypersurface, but also yields the thermochemistry and thermodynamic values for the current structure. However, thermochemistry calculations are not restricted to minima but it can also be applied to transition states, therefore yielding a full thermodynamic characterization of a reaction mechanism.

A regular freq calculation yields the following output (all values in atomic units):

Zero-point correction=                           0.176113 (Hartree/Particle)
 Thermal correction to Energy=                    0.193290
 Thermal correction to Enthalpy=                  0.194235
 Thermal correction to Gibbs Free Energy=         0.125894
 Sum of electronic and zero-point Energies=           -750.901777
 Sum of electronic and thermal Energies=              -750.884600
 Sum of electronic and thermal Enthalpies=            -750.883656
 Sum of electronic and thermal Free Energies=         -750.951996

For any given reaction say A+B -> C one could take the values from the last row (lets call it G) for all three components of the reaction and perform the arithmetic: DG = GC – [GA + GB], so products minus reagents.

By default, Gaussian calculates these values (from the previously mentioned partition function) using normal conditions, T = 298.15 K and P = 1 atm. For an assessment of the thermochemistry at other conditions you can include in your route section the corresponding keywords Temperature=x.x and Pressure=x.x, in Kelvin and atmospheres, respectively.

(Huge) Disclaimer: Although calculating the thermochemistry of any reaction by means of DFT calculations is a good (and potentially very useful) guide to chemical reactivity, getting quantitative results require of high accuracy methods like G3 or G4 methods, collectively known as Gn mehtods, which are composed of pre-defined stepwise calculations. The sequence of these calculations is carried out automatically; no basis set should be specified. Other high accuracy methods like CBS-QB3 or W1U can also be considered whenever Gn methods are too costly.

About joaquinbarroso

Computational and theoretical chemist in his early forties, in love with life, science, baseball, and literature. Science literacy makes us responsible citizens, it is therefore a scientific duty to talk, write, and engage with the general public; as Feynman said, if you find science boring, your learning from the wrong teacher. "Make like a molecule and react!"

Posted on August 7, 2019, in Computational Chemistry, Gaussian, Reaction Mechanisms, Theoretical Chemistry, Thermodynamics, White papers and tagged , , , , , , , , , . Bookmark the permalink. 1 Comment.

  1. Good evening, Dr. Barroso, please, how does one concretely evaluate the variation of free enthalpy of a given molecule after performing a frequency calculation?

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

%d bloggers like this: