Easily-Built Fragment-Based CASSCF Initial Guess Wavefunction
Jiawei Xu
Released: 2025-03-20 / Updated: 2025-03-20
1. Review of workflows applied to build initial guess
Preparing an initial guess wavefunction is the most important step when performing CASSCF (or similar) calculations. Regarless how subjective it can be, there are a lot of methods, suitable or not, have been applied in different references. Before introducing our fragment-based workflow, we first quickly review some known workflows in references. (P.S. the article is limited to ground state calculation.)
1.1 based on (R/U)HF or (R/U)KS wavefunction
(R/U)HF and (R/U)KS wavefunction have the same form. Most time, we carry out CASSCF calculation based on DFT-optimized structures, therefore, using (R/U)KS wavefunction as initial guess has an obvious advantage, that is, no more additional computation is required. While (R/U)HF wavefunction is also easy to obtain.
There’s no theoretical problem with using RHF wavefunction. However, there are a lot of references, even in recent years, using UHF wavefunction as initial guess for CASSCF, yet this is not correct. The CASSCF calculation should be based on RESTRICTED or RESTRICTED-OPEN wavefunction. This does not mean we can’t perform UCASSCF, but UCASSCF is only used for development reason, not for daily calculations. Basically, almost all CASSCF codes are formulated using spin-restricted orbitals, therefore you can’t feed in symmetry broken orbitals. The main reason for this is that defining an active space would be very difficult, if the spatial parts could be different. Still, broken symmetries are typically just artefacts caused by the lack of proper treatment of electron correlation in the wavefunction. Going from RHF to UHF may give you lower energy, because you’re freeing the opposite-spin electrons to avoid each other. But, if you include opposite-spin correlation, which is missing from Hartree-Fock, in your treatment like in CASSCF, then you probably won’t get spin symmetry breaking anymore.
As to (R/U)KS,
1.2 based on localized orbitals or natural orbitals
Although (R/U)HF wavefunction is easy to obtain, usually we do not prefer to use it. Some possible reasons for this can be: (1) The largest drawback of (R/U)HF wavefunction is, for most systems, MOs are highly delocalized, and therefore brings much difficulty to pick out expected orbitals. (2) For some complicated systems, (R/U)HF cannot correctly describe the electronic structure, or has difficulty to converge to the desired electronic state. (3) Since extended basis is used, high angular momentum component cannot be avoided in unoccupied orbitals, which is a shared drawback for most methods.
For the first problem, a common idea is to perform localization to help canonical MOs correspond to chemical ideas like bonding or anti-bonding orbitals. There are a lot of well-known localization methods, e.g. Edmiston-Ruedenberg method, Boys method, Pipek-Mezey method (all named by developers), .
UNO (J. Chem. Phys. 1988, 88, 4926–4933.)
1.3 based on GVB orbitals
1.4 summary