Category Archives: Reaction Mechanisms
The energy of your calculated transition state (TS) is lower than that of the reagents. That’s gotta be an error right? Well, maybe not.
Typically, in classical transition state theory, we associate the reaction barrier to the energy difference between the reaction complex and the TS, in other words, we associate the reaction barrier to the relative energy of the TS. However, this isn’t always the case, since the TS isn’t always located at the barrier, which simply may not exist or may be a submerged one, i.e. the TS relative energy is negative with respect to the reaction complex. This leads to negative activation energies, but one must bear in mind that the activation energy is not equal to the relative energy of the TS but rather to the slope of the Arrhenius plot, which in turn comes from the Arrhenius equation given below.
k = Aexp(Ea/RT) or in logarithmic form Lnk = LnA + (Ea/RT) The Arrhenius plot is then the plot of Lnk vs T-1, with slope Ea
Caution is advised since the apparent presence of such a barrier may be due to a computational artifact rather than to the real kinetics taking place, that’s why an IRC calculation must follow a TS optimization in order to verify the truthfulness of the TS; keep in mind that in classical transition state theory, we’re ‘slicing‘ a multidimensional map along a carefully chosen reaction coordinate but this choice might not entirely be the right one, or even an existing one for that matter. I also recommend to change the level of theory, reconsider the reaction complex structure (because a hidden intermediate or complex may be lurking between reactants and TS, see figure 1) and fully verifying the thermochemistry of all components involved before asserting that any given reaction under study has one of these atypical barriers.
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.
I found it surprising that the trichloromethyl group could be chemically reduced into a methyl group quite rapidly in the presence of thiophenol, but once again a failed reaction in the lab gave us the opportunity to learn some nuances about the chemical reactivity of organic compounds. Even more surprising was the fact that this reduction occured through a mechanism in which chlorine atoms behave as electrophiles and not as nucleophiles.
We proposed the mechanism shown in figure 1 to be consistent with the 1H-NMR kinetic experiment (Figure 2) which shows the presence of the intermediary sulfides and leads to the observed phenyl-disulfide as the only isolable byproduct. The proposed mechanism invokes the presence of σ-holes on chlorine atoms to justify the attack of thiophenolate towards the chlorine atom leaving a carbanion behind during the first step. The NMR spectra were recorded at 195K which implies that the energy barriers had to be very low; the first step has a ~3kcal/mol energy barrier at this temperature.
To calculate these energy barriers we employed the BMK functional as implemented in Gaussian09. This functional came highly recommended to this purpose and I gotta say it delivered! The optimized geometries of all transition states and intermediaries were then taken to an MP2 single point upon which the maximum electrostatic potential on each atom (Vmax) was calculated with MultiWFN. In figure 3 we can observe the position and Vmax value of σ-holes on chlorine atoms as suggested by the mapping of electrostatic potential on the electron density of various compounds.
We later ran the same MP2 calculations on other CCl3 groups and found that the binding to an electron withdrawing group is necessary for a σ-hole to be present. (This fact was already present in the literature, of course, but reproducing it served us to validate our methodology.)
We are pleased to have this work published in PhysChemChemPhys. Thanks to Dr. Moisés Romero for letting us into his laboratory and to Guillermo Caballero for his hard work both in the lab and behind the computer; Guillermo is now bound to Cambridge to get his PhD, we wish him every success possible in his new job and hope to see him again in a few years, I’m sure he will make a good job at his new laboratory.