quantum chemistry - How to choose proper active space in method such as CASPT2 and CASSCF?

I am confused about other research paper which use CASPT2 method. I am not clear about how to choose active space. What can I refer to? (tutorial reviews, papers, or any other things)

Answer

Choosing the active space in any calculation with a multiconfigurational reference (CASSCF, RASSCF, GASSCF, CASPT2, NEVPT2, MRCI, the list goes on) requires more chemical intuition than more commonly-used "black box" quantum chemistry methods, such as DFT. Here, chemical intuition means preexisting knowledge about 1. the system under investigation, and 2. the properties being calculated. For example, a minimal active space may be sufficient to qualitatively capture static correlation in a system, but the active space might change when targeting excitation energies, and might be different again when calculating spin-orbit coupling constants. More specifically, it is understanding what orbitals are most important in composing your wavefunction and have the largest influence on molecular properties of interest. Unfortunately, this can also involve quite a bit of trial and error.

Some very general recommendations on the workflow for performing multiconfigurational calculations are in the numbered list in this answer (yes, a shameless plug).

Here is a more complete list of references I've found useful in my own research:

• 
  

  [1], [2] are slides from the group that develops GAMESS, one of the premier packages for multiconfigurational calculations. The second set of slides in particular has examples that highlight the chemical motivation for different active spaces depending on the molecule and the property (internal rotation in ethylene, internal rotation in $\ce{H2C=NH}$, dissociation of $\ce{H2C=O} \rightarrow \ce{CH2} + \ce{O}$, isomerization of bicyclobutane to 1,3-butadiene, and others).

  
  


• 
  

  [3] (paywalled) is a more formal overview of the above. Excellent.

  
  


• 
  

  [4] is a set of very detailed and theory-focused slides from the original authors of DALTON. I link to them only for completeness; there aren't many practical examples here.

  
  



• 
  

  [5] (paywalled) is a comprehensive review article from the authors of COLUMBUS, with many examples. Excellent.

  
  


• 
  

  [6] (paywalled) is an article from the authors of COLUMBUS on the application of multiconfigurational methods to geometries of small molecules. It has good explanations on the choice of active space based on electronic configurations.

  
  

In addition, there are many other online resources that are more tutorial oriented: [7], [8], [9], [10]. These may appear to be program-specific, but the chemistry is transferable between different programs; only small technical details in how to set up calculations should be different.

Finally, some programs have nice examples or helpful hints in their documentation. DALTON (PDF), Molcas, and ORCA (PDF) come to mind.

References

• 
  

  [3]: Schmidt, M. W.; Gordon, M. S. The construction and interpretation of MCSCF wavefunctions. Annual Review Of Physical Chemistry 1998, 49, 233-266. DOI: 10.1146/annurev.physchem.49.1.233

  
  


• 
  

  [5]: Szalay, P. G.; Müller, T.; Gidofalvi, G.; Lischka, H.; Shepard, R. Multiconfiguration Self-Consistent Field and Multireference Configuration Interaction Methods and Applications. Chemical Reviews 2012, 112, 108-181. DOI: 10.1021/cr200137a

  
  


• 
  

  [6]: Shepard, R.; Kedziora, G. S.; Lischka, H.; Shavitt, I.; Müller, T.; Szalay, P. G.; Kállay, M.; Seth, M. The accuracy of molecular bond lengths computed by multireference electronic structure methods. Chemical Physics 2008, 349, 37-57. DOI: 10.1016/j.chemphys.2008.03.009