Tutorial: Advanced Usage of EmbASI for QM/QM Embedding

Authors: Gabriel Bramley Date: 2025-11-20

What Does This Tutorial Cover?

Following on from Part 1 (Tutorial: Basic Usage of EmbASI for QM/QM Embedding), the following tutorial provides advanced usage directives for running calculations with post-HF methods and keywords for reducing the cost enabled by basis truncation.

1. Post-HF Methods

Part 1 of the tutorial showed how to perform DFT-in-DFT embedding for a simple test system. However, projection-based embedding can also be used to perform Wavefunction-in-DFT (WF-in-DFT) embedding. The post-HF methods in FHI-aims (including MP2 and RPA) may be used for a high-level of theory by supplying an argument to post_scf for the ProjectionEmbedding object

Projection = ProjectionEmbedding(methanol_dimer,
                                 embed_mask=[2,1,2,2,2,1,2,1,2,2,2,1],
                                 post_scf="RPA",
                                 calc_base_ll=calc_ll,
                                 calc_base_hl=calc_hl,
                                 projection="huzinaga-sc",
                                 localisation="SPADE",
                                 run_dir="dimer",
                                 parallel=True,
                                 gc=True,)

Usage of post-HF methods in EmbASI has the same provisos as a standard FHI-aims calculation (See: GW, BSE, and RPA tutorial). For example, one can change the type of resolution of identity used in the beyond-DFT calculation by adding the RI_method keyword in the high-level calculator object:

calc_hl = Aims(xc='PBE', profile=AimsProfile(command="asi-doesnt-need-command"),
    atomic_solver_xc="PBE",
    override_initial_charge_check=True,
    RI_method="LVL"
  )

As with a standard post-HF calculation with FHI-aims based on the RI framework, special choices for the basis set must be used to obtain well-converged energies with respect to basis size. For these calculations, we recommend using the NAO-VCC-XZ library of basis sets, and applying a basis set extrapolation strategy to approach the complete basis set limit. The two-point extrapolation scheme of Zhang et al. is especially useful in this context:

\[\begin{aligned} E(\infty) = \frac{E(4)(4+d)^{\alpha} - E(5)(5+d)^{\alpha} }{(4 + d)^{\alpha} - (5 + d)^{\alpha}}, \end{aligned}\]

which provides extrapolation to the CBS energy \(E(\infty)\) for the NAO-VCC-4Z and NAO-VCC-5Z basis sets, where \(\alpha=4.51\) and \(d=2.65\).

2. Basis Truncation

In all the examples presented, the high-level calculation is performed with the entire supersystem basis. Although the occupied subspace has been reduced, the basis functions of the environment are still included in the simulation. This means that summations of densities and potentials are still performed over these basis centers, and the corresponding virtual orbitals associated with these basis functions are included in any post-HF calculation. Failing to truncate these basis functions therefore limits the time and memory improvements enabled by QM/QM embedding.

However, basis centers that do not contribute significantly to the high-level subsystem may be excluded by supplying the argument, truncate_basis_thresh to the ProjectionEmbedding object:

Projection = ProjectionEmbedding(methanol_dimer,
                                 embed_mask=[2,1,2,2,2,1,2,1,2,2,2,1],
                                 post_scf="RPA",
                                 calc_base_ll=calc_ll,
                                 calc_base_hl=calc_hl,
                                 projection="huzinaga-sc",
                                 localisation="SPADE",
                                 run_dir="dimer",
                                 truncate_basis_thresh=0.0001,
                                 parallel=True,
                                 gc=True,)

The threshold stated excludes basis centers in the environment subsystem that contribute less than the specified charge to the high-level subsystem. Although basis truncation enables substantial speed-ups for the high-level subsystem calculation, it can also introduce a significant error to the embedding total energy unless properly parameterised. We recommend scanning through a set of truncation tresholds (\(10^{-2}-10^{-6} \|e\|\)) to determine a value that gives the best compromise between accuracy and speed-up. Generally, relative values such as adsorption energies can result in reduced errors from truncation due to cancellation of errors.