Thursday, July 5, 2012

Overselling ab initio computational chemistry

The great appeal of computational quantum chemistry is that it aims to be ab initio. One simply calculates the properties of molecules from Schrodinger's equation and Coulomb's law. However, the painful reality is that many methods have to include parameters (or make choices about approximations) that are determined by comparison with experiment. Indeed there is now a whole industry of people who tweak parameters in density functionals in order to get better agreement with experiment. Although I am not enthusiastic about this I can live with it as long as people are transparent about what they are doing.

A recent JACS paper Mechanism for Singlet Fission in Pentacene and Tetracene: From Single Exciton to Two Triplets from Martin Head-Gordon's group is not as transparent as it could be about whether it is ab initio. It states
The originally proposed mechanism for SF [Singlet Fission] is based on model Hamiltonians that couple of monomer states between adjacent molecules. The low coupling in the model between the single-exciton and ME states requires that a CT state be invoked as an intermediate (i.e., an indirect mechanism). This requires the assumption that the CT state is relatively low in energy and thus energetically accessible. Herein, systematic ab initio study of the low-lying excited states in tetracene and pentacene provides an alternative mechanism for the photophysics of these materials. This study provides evidence that CT states need not be directly relevant to SF in acenes.  
Because these ab initio simulations capture the correlation of many electrons, they are distinct from model Hamiltonian studies (for instance ref 22). The current understanding of SF comes from model Hamiltonians, where certain electronic states of two monomers are employed as basis sets. While model Hamiltonian studies can yield deep insights into complex physical processes such as SF [Singlet Fission], these invariably require assumptions about the physics which are embedded as model parameters. By contrast, ab initio calculations in principle allow the essential features to emerge directly from simulations.... 
However, if one looks at the Computational Details section of the paper (which comes after the Conclusion) one finds the statement.
One deficiency of CASSCF and RAS-2SF theories is the overestimation of excitation energies due to the limited degree of dynamic correlation. To overcome this difficulty, we shift the excitation energies of T1 and S1 at the equilibrium geometry to the experimental values for the acene crystals.
Surely, this fitting to experiment [of two key observables] undermines the authors claim to be doing ab initio calculations or to be superior to model calculations. Furthermore, most of the calculations in the paper involve a small number of molecules, which is surely a model for the infinite solid, in which significant screening effects may be present. Arguably, ignoring this is comparable to the significant physical assumptions present in model calculations.


  1. I think this highlights the point that the best use of "ab initio" techniques (which are almost ALWAYS based on a self-consistent field) is to identify relevant observables that can be used to produce reduced models. Scaling CASSCF energies is a common strategy; in this case the point is that the self-consistent field is identifying a compact set of "slow" electronic variables that can be used in a reduced state space. The only difference between this and model building is that in the latter case, one asserts the identity of the slow variables based on other means (i.e. deep thought and physical intuition). The methods can be used in tandem; one can use self-consistent fields to support models if it can be shown that the model states correspond to a self-consistent field solution. This supports the model by showing that the relevant variables correspond to "slow" variables as identified by an objective method. Of course, if this fails then it is not a priori true that the "ab initio" approach is better, because self-consistent fields will embody any errors in the Hamiltonian. In this particular case, the errors in the Hamiltonian would include the fact that there is only a cluster model being used to represent a macroscopic lattice, that the clamped-nucleus approximation is invoked, and that the electron correlation treatment may not be appropriate for the physics of the system.

  2. What do you mean by slow electronic variables? Slow with regards to what?