From Random Determinants to the Ground State

Hao Zhang and Matthew Otten (2025)
Highlighted by Jan Jensen


The paper introduces a method they call TrimCI that very efficiently finds a relatively small set of determinants that accurately describes strongly correlated systems. (Well, it actually works for any system, but the main advantage is for strongly correlated systems). 

Unlike most new correlation methods, this one is actually simple enough to describe in a few sentences. TrimCI starts by constructing a set of orthogonal (non-optimised!) MOs (e.g. by diagonalising the AO overlap matrix). From these MOs you construct a small number of random determinants (e.g.100), construct the wavefunction (i.e. construct the Hamiltonian matrix and diagonalise, as per usual). Then you compute all the Hamiltonian elements between this wavefunction ($H_{ij}$) and the remaining determinants and add determinants with sufficiently large |$H_{ij}$| to the wavefunction. Finally, there is the trimming step "which removes negligible basis states by first diagonalising randomised blocks of the core and then performing a global diagonalising step on the surviving set." And repeat.

The authors find that this approach converges much quicker than other similar methods, using many fewer determinants. Another big advantage is that the method does not require a single-determinant ground state as a starting point and is thus not sensitive to how much such a single-determinant deviates from the actual wavefunction.

So, what's the catch here? In order to be practically useful, we need to compute energy differences with mHa accuracy, and I did not see any TrimCI results for chemical systems where the energy had converged to that kind of accuracy. It's possible that error cancellation can help here, but that needs to be investigated. The authors do look at extrapolation, which looks promising, but needs to be systematically investigated. Yet another option is to use the (compact) TrimCI wavefunction as an ansatz for dynamic-correlation methods.

It's also not clear what AO basis set it used for some of these calculations (including the one shown above). I suspect small basis sets are used and even FCI energies with very small basis sets are of limited practical use. Are the TrimCI calculations on large systems still practical with more realistic basis sets?

Nevertheless, this seems like a very promising step in the right direction.


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