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.
Simulation of Raman Spectroscopy and crystal cell effects – Selenium Carboxylate Eur. J. Inorg. Chem.
Computing spectroscopic features of molecules is always an interesting challenge, specially when intermolecular contacts are into play. Take vibrational spectroscopy for instance, all the non-covalent interactions present in a solid will have an important effect on the the calculated frequencies and their intensities. However calculating the spectroscopical properties of a solid quickly becomes a daunting task.
My colleague and friend Dr. Vojtech Jancik asked me to calculate the Raman frequencies for a new compound: Selenoyl bis-carboxylate, which according to him was very hard to obtain due to the very nature of selenium. So we performed various calculations on the isolated molecule to reproduce the measured Raman spectrum but we soon realized that a calculation on the crystal cell was needed if we wanted to get a more thorough picture of the experiment.
The level of theory used was PBEPBE/LANL2DZ. Optimization of the title structure pointed to a low coordination capacity by carboxylate groups as evidenced by the longer Se -O-C=O distances and reduced Wiberg bond indexes. A blue shift was observed for all bands and so we calculated the Raman frequencies at the crystal structure which gave us a better correspondence between spectra. Finally we computed the Raman spectra for the full unit cell comprised of four molecules with which an excellent agreement was obtained (a scaling factor of 0.8 was used).
Unfortunately we failed to further extend this calculation to a larger system with four unit cells and 32 molecules apparently due to insufficient memory; the calculation just stalled and stopped without error after consuming its time in the queue. I’ll try to take a look into it some day.
You can read the whole story in: Synthesis and Crystal Structure of the First Selenonyl Bis(carboxylate) SeO2(O2CCH3)2
Lukas Richtera · Vojtech Jancik · Joaquín Barroso‐Flores · Petr Nykel · Jiri Touzin · Jan Taraba
Thanks for reading!