In the spirit of a succint answer (3 paragraphs maximum) to create a useful resource, what are the types of excited state calculation available for solids? Please add to the list:

Quasiparticle excitations

  • DFT: density functional theory
  • $\Delta$SCF [link to answer]
  • Constrained DFT
  • GW: Many-body perturbation theory in the GW approximation
  • VMC: Variational Quantum Monte Carlo
  • DMC: Diffusion Quantum Monte Carlo

Two-particle excitations

  • TDDFT: Time-dependent density functional theory
  • BSE: Bethe-Salpeter equation
  • VMC: Variational Quantum Monte Carlo
  • DMC: Diffusion Quantum Monte Carlo
  • $\begingroup$ +1. Would comment further if it weren't 3am! $\endgroup$ – Nike Dattani Jul 19 at 7:02
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    $\begingroup$ I mentioned some more methods for excited states here: mattermodeling.stackexchange.com/a/489/5 including DMRG, EOM-CC (a.k.a. LR-CC), STEOM-CC, Fock-Space CC, CI and FCIQMC, but I don't know how to put them in the categories of 2-particle excitations or quasiparticle excitations 😂. $\endgroup$ – Nike Dattani Jul 19 at 17:04
  • $\begingroup$ @NikeDattani, thanks for your comment. I don't know these methods you mention, so wouldn't know either where to classify them... :D What I meant by "2-particle" is sometimes called "neutral excitation" do you think updating to that language would help? $\endgroup$ – ProfM Jul 19 at 18:12
  • $\begingroup$ Unfortunately I'm not familiar with "neutral excitation" either, maybe because I come from a different community that uses different terms :D For DMRG, FCIQMC, and SHCI, instead of finding just the lowest (ground) state, we would find maybe the lowest 5 states and orthogonalize them against each other, so we don't need to think about quasiparticles or 2-particle pairs. I'm talking about electronic excited states (not excited vibrational states or excited rotational states or something else). I'll ask Tyberius and others how we can incorporate these excited-state methods into your question. $\endgroup$ – Nike Dattani Jul 19 at 18:28


This method generates excited states by changing the occupancy of a ground state determinant and then carrying out a new SCF with that initial guess, with some restriction throughout to prevent variational collapse back to the ground state [1]. The most common approach to stay out of the ground state is the Maximum Overlap Method (MOM), which fills orbitals based on overlap with the occupied orbitals of the previous step rather than following the Aufbau principle. Another recently developed approach is the Squared Gradient Method (SGM), which is designed to converge to the closest minima [2].

$\Delta$SCF is one of the conceptually simplest ways to generate an excited state and it makes it very easy to target an excited state of a particular symmetry. It has also been shown to be effective for modeling double excitations which is difficult or impossible for standard TDDFT calculations [2]. One drawback is that excited states are often best described with multiple configurations, which $\Delta$SCF can't represent. Another issue, and the flip side of being able to target specific symmetry excited states, is that the method is not particularly blackbox and you have to have some sense of the character of the excited state you are looking for.


  1. Ziegler, T.; Rauk, A.; Baerends, E. J. Theoretica chimica acta 1977, 43, 261−271
  2. Diptarka Hait and Martin Head-Gordon J. Chem. Theory Comput. 2020, 16, 3, 1699–1710
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  • $\begingroup$ +1. RIP Tom Ziegler :'( $\endgroup$ – Nike Dattani Jul 19 at 15:53

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