Electronic Structure Theory¶
Electronic structure theory is the study of how electrons are distributed and how they behave around a fixed set of nuclei — solving (or approximating a solution to) the electronic Schrödinger equation at a given molecular geometry to obtain the wavefunction, the energy, and properties derived from them. This workflow moves through a hierarchy of methods, from a single-reference Hartree–Fock treatment up to multireference perturbation theory, because no single method is adequate for every part of the problem: cheap methods are used first to get oriented (which orbitals matter, which states are close in energy), and progressively more expensive, more accurate methods are layered on top once that picture is known.
Unlike the DFT workflow, which targets a single potential energy surface (ground-state reaction mechanisms), this workflow targets excited states and systems where a single Slater determinant is a poor description of the wavefunction — cases where standard DFT is known to struggle.
What this workflow produces¶
Starting from one chosen molecule, this workflow produces vertical excitation energies (and the character of the corresponding excited states) using the method chain RHF → CIS → CASSCF → XMCQDPT, with each stage feeding information into the next rather than being run in isolation.
Recommended workflow¶
Choose a Molecule
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Optimize Ground-State Geometry (Gaussian)
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Convert Geometry to a GAMESS Input (Open Babel)
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RHF Calculation (GAMESS) ──► converged Molecular Orbitals
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CIS Calculation, GUESS=MOREAD ──► excited states + active-space guess
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Select Active Space
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CASSCF (Multireference)
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XMCQDPT (Multireference Perturbation Theory)
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Report Vertical Excitation Energies
Step 1 — Choose a molecule¶
Pick one specific molecule to carry through the whole pipeline before touching any software. Start small — a system with a handful of heavy atoms and a well-known excited state (a carbonyl, a small aromatic, a simple chromophore) is far easier to sanity-check at every stage than something large or poorly characterized. Everything downstream (basis set cost, active-space size, how many CASSCF states you can realistically converge) scales with this choice, so it is worth making deliberately rather than defaulting to whatever system you already have coordinates for.
Step 2 — Optimize the ground-state geometry (Gaussian)¶
Basic tutorial
Geometry Optimization — Berny algorithm, input/output file structure, and convergence criteria.
Every calculation later in this pipeline is a single-point calculation on one fixed nuclear geometry — RHF, CIS, CASSCF, and XMCQDPT all describe the electrons at a geometry you hand them, they don't move the nuclei. That geometry needs to already be a genuine minimum on the ground-state potential energy surface, obtained the same way as in the DFT workflow: optimize in Gaussian, then confirm with a frequency calculation that there are zero imaginary frequencies. Skipping this step means every excited-state number computed afterward is describing electrons around a geometry the molecule doesn't actually want to be at.
Step 3 — Convert the geometry to a GAMESS input (Open Babel)¶
Gaussian and GAMESS use different input formats, so the optimized geometry needs to be converted rather than retyped by hand. Open Babel reads the optimized geometry directly out of the Gaussian log file:
| Flag | Meaning |
|---|---|
-ig09 |
input format: Gaussian 09 output |
-ogamin |
output format: GAMESS input |
>> |
append the converted geometry block to gamess.inp |
>> appends — it doesn't overwrite
Running this command twice against the same gamess.inp will append the geometry a second time rather than replacing it. Use > instead of >> for a clean file, or double-check gamess.inp before reusing it.
Open Babel only translates the geometry (and a minimal $CONTRL/$BASIS skeleton) — it has no idea whether you're about to run an RHF, CIS, or CASSCF calculation. The GAMESS-specific control blocks ($CONTRL, $BASIS, $GUESS, $DET/$DRT, $MCSCF, etc.) for each stage below still need to be written or edited by hand; the conversion just saves you from retyping Cartesian coordinates.
Step 4 — Restricted Hartree–Fock (RHF) calculation (GAMESS)¶
Basic tutorial
Restricted Hartree–Fock (RHF) — input/output structure, the SCF algorithm, and a worked water-molecule example.
RHF is the entry point: a single-determinant, mean-field wavefunction that gives a baseline energy and, more importantly for this workflow, a set of canonical molecular orbitals. Nothing downstream needs the RHF energy itself to be accurate — what matters is that the SCF converges cleanly, because those converged orbitals become the starting guess for every calculation that follows.
Step 5 — CIS calculation with GUESS=MOREAD¶
Basic tutorial
Configuration Interaction Singles (CIS) — from RHF to CIS, the CIS Hamiltonian, and the secular equation.
The RHF orbitals from Step 4 are read back in as the starting guess (GUESS=MOREAD) rather than recomputed from scratch, and CIS is run on top of them. CIS is the cheapest genuine excited-state method available here — it won't be quantitatively reliable (see Limitations of CIS), but it is enough to answer the question this workflow actually needs answered next: which orbitals are involved in the transitions of interest? The dominant CI coefficients in the CIS excited-state vectors point directly at which occupied and virtual orbitals matter.
Step 6 — Select the active space¶
Basic tutorial
Active Space — what an active space is and how it's chosen.
Using the orbital character identified from CIS in Step 5, choose which orbitals go into the CASSCF active space: the frontier orbitals involved in the excitation(s) of interest, any orbitals that are near-degenerate with them, and anything with a non-negligible CI coefficient in the relevant CIS state(s). This is the step where the workflow stops being mechanical — the active space choice is a judgment call specific to the molecule, and it is worth revisiting if the CASSCF results in the next step look qualitatively wrong (missing a state you expected, or a state dominated by an orbital you left out).
Step 7 — CASSCF (multireference)¶
Basic tutorial
CASSCF — why RHF fails for these systems, the CASSCF wavefunction, and state-averaged CASSCF.
CASSCF re-optimizes the orbitals while simultaneously allowing a full configuration interaction expansion within the chosen active space, recovering the static (near-degeneracy) correlation that a single-determinant method like RHF or CIS cannot describe. This is what produces a genuinely multireference description of the ground and excited states involved.
Step 8 — XMCQDPT (multireference perturbation theory)¶
Basic tutorial
XMCQDPT — the zeroth-order Hamiltonian, second-order energy corrections, and the complete algorithm.
CASSCF captures static correlation but still misses most of the dynamic correlation (the instantaneous electron-electron correlation that a finite active space can't reach). XMCQDPT adds this back in via second-order multireference perturbation theory on top of the CASSCF reference, and is what turns a qualitatively-correct CASSCF picture into quantitatively meaningful vertical excitation energies.
Step 9 — Report vertical excitation energies¶
The XMCQDPT state energies (relative to the ground state, at the fixed geometry from Step 2) are the vertical excitation energies — typically reported alongside the dominant orbital character of each state (from the CASSCF natural orbitals) and, where relevant, oscillator strengths for the allowed transitions. At this point you have a defensible excited-state picture for one geometry of one molecule: which states exist, roughly where they sit energetically, and what they're made of.
Beyond vertical excitations¶
The pipeline above answers "what are the excited states of this molecule, at this geometry?" It does not by itself describe how the molecule behaves once it's excited. Studying excited-state dynamics — how population moves between states, how the molecule distorts on an excited surface, where conical intersections or spin-crossings sit — builds on top of everything above using additional calculation types:
- Spin-orbit coupling (SOC) — needed for transitions between states of different spin multiplicity (e.g. intersystem crossing).
- Diabatization — converts adiabatic CASSCF/XMCQDPT states into a diabatic basis, useful near state crossings where the adiabatic picture becomes ambiguous.
- Excited-state distortion / relaxation — characterizing how the geometry relaxes on an excited-state surface away from the ground-state minimum used in Step 2.
These aren't covered in this workflow — they belong to a separate, dynamics-focused workflow that doesn't exist on the site yet.
Worked example¶
A complete worked example — one specific molecule taken through every step above with real GAMESS input/output files, the way the Diels-Alder reaction worked example does for the DFT workflow — is planned but not yet available.