Daily Archives: November 17, 2015
In a nutshell, computational chemistry models are about depicting, reproducing and predicting the electronic-based molecular reality. I had this conversation with my students last week and at some point I drew a parallel between them and art in terms of how such reality is approached.
Semi empirical methods
Prehistoric wall paintings depict a coarse aspect of reality without any detail but nevertheless we can draw some conclusions from the images. In the most sophisticated of these images, the cave paintings in Altamira, we can discern a bison, or could it be a bull? but definitely not a giraffe nor a whale, most in the same way Hückel´s method provides an ad hoc picture of π electron density without any regard of the σ portion of the electron density or the conformational possibilities (s-cis and s-trans 1,3-butadiene have the same Hückel description).
More sophisticated semi-empirical Hamiltonians like PM3 or PM6 have better parametrizations and hence yield better results. We are still replacing a lot of information for experimental or adjusted parameters but we still cannot truly adopt it as truthful. Take this pre-medieval painting of one of the first Kings of England, Aelred the Unready. It is, by today standards, a good children´s drawing and not a royal portrait, we now see more detail and can discern many more features yielding a better description of a human figure than those found in Altamira or Egypt.
HF is the simplest of ab initio methods, meaning that no experimental results or adjustable parameters are introduced. Even more so, from the HF equations for a multi-electron system that complies with Pauli’s exclusion principle the exchange operator arises as a new quantum feature of matter with no classical analogue. Still, there are some shortcomings. Correlation energy is disregarded and most results vary according to the basis set employed. Take the impressionist movement, specially in France: In Monet´s Lady with Umbrella we have a more complicated composition, we observe many more features and although we have a better description of color composition some details, like her face, remain obscure. The impressionists are characterized by their broad strokes, the thicker the strokes the harder it is to observe details similar to what happens in HF when we change from a small to a large basis set, respectively.
CI (Configurations Interaction)
Extension of HF to a multi-reference method yields better results. In CI we take the original guess wavefunction -as expressed through a Slater Determinant- and extend it with one or many more wavefunctions; thus a linear combination of Slater Determinants gives rise to a broader description of the ground state because other electronic configurations are involved to include more details like the ionic and covalent pictures (configurations). The more terms we include the more real the results feel. If we take classical figurative paintings we have a similar result; most of these paintings are constituted of many elements and the more realistically each element is captured the more real the whole composition looks even if some are just merely indicated.
CCSD(T) full-CI, CASPT2
In Edwards Much’s the scream, we might think we have lost some information again and went back to impressionism but we know this is actually an expressionist painting; we can now not only observe details of the figurative portion of the image but Munch has captured his subject´s fear in the form of distorsions on the subjective reality. In this way, CCSD(T), full-CI and CASPT2 methods provide a description of the ground as well as the excited states which -in experimental reality- are only accessed through a perturbation of the elecron density by electromagnetic radiation. Something resembling radiation has perturbated the subject in The Scream rendering him frightened and wondering how to return to his ground state or if such thing will be even possible.
Density Functional Methods
At least due to its widespread use, DFT has risen as the preferred method. One of the reasons behind its success is the reduced computing time when compared to previous ab initio methods. So DFT is pretty much like photography, in which reality is captured in full but only apparently after selecting a given lens, an exposition, a filter, shutter speed and the occasional Photoshop for correcting issues such as aliasing. In photography, as in DFT, all details concerning the procedure or method for capturing an uncanny reproduction of reality must be stated in every case for reproduction purposes.
Now, in the end it all comes down to Magritte’s Pipe. Ceci n’est pas une pipe -or, ‘this is not a pipe’- reminds us that painting as with modeling we don’t get reality but rather a depiction of it. In this famous painting we look at an image that in our heads resembles that of a pipe but we cannot grab it, fill it with tobacco and smoke it.
The image above is a digital file, which translated becomes a scaled reproduction of an image painted by Magritte in which we see the 2D projection of the image of an object that reminds us of a pipe. In fact, the real name of this work is The Treachery of Images, definitely quite an epistemology problem on perception and knowledge but before I get too metaphysical I should finish this post.
Can you find where cubism or surrealism should be placed? with MPn methods, perhaps?