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Worked Examples

See the native execution record and corrections for the checked engine version, input hashes and known engine boundaries.

New to OpenQP? Follow the step-by-step tutorials first. For the scientific basis of each calculation, use the method reference directory.

Each worked example is one small molecule, one complete .oqp input that you can copy and run as it is, and the results that the run produces. The coordinates are written inside the input, so no separate geometry file is needed. Some examples need extra files, downloaded with them into the same folder: the QM/MM examples read their structure and force field from a PDB file and two OpenMM XML files, and the all-electron inputs of the gold hydride example read an uncontracted basis set from a JSON file, the NEB example reads its product structure from an XYZ file, and the alanine QM/MM example reads a PDB file. Run the input, then compare your numbers with the reference values on the page.

openqp water-scf.oqp

Every input on these pages can also be downloaded from the link under its code block. With 2 to 8 CPU threads, most runs take between 2 seconds and 1 minute. These take longer:

Example Run time
HCN IRC, each direction about 3.5 minutes
NH₃ NEB on the 150 × 974 DFT grid about 7 minutes
Ethylene MECI search about 3.5 minutes
NH₃ inversion NEB about 7 minutes
Ethylene S1 minimum-energy path about 4.5 minutes
Methanol ground-state MD about 4.5 minutes
Formaldehyde QM/MM excited-state dynamics about 5 minutes
Alanine-dipeptide QM/MM ground-state MD about 6 minutes
Formaldehyde SOC-NAMD about 2.5 minutes
Ethylene NAMD about 9 minutes
Benzene HF/cc-pVTZ with symmetry(enabled=false) about 1.5 minutes
Alanine-dipeptide QM/MM optimization about 1 minute

Each page states its run time.

Water Water energy and orbitals Total energy, orbital energies, HOMO and LUMO pictures, dipole moment, and atomic charges.

Formaldehyde C=O stretch Geometry and vibrations Optimize formaldehyde, then compute harmonic frequencies, zero-point energy, and thermochemistry.

Formaldehyde pi* orbital UV absorption (TDDFT) Excitation energies and oscillator strengths, and the orbitals behind the n→π* band.

Twisted ethylene Twisted ethylene (MRSF-TDDFT) S0, S1, and S2 along the C=C twist, where S0 becomes a diradical.

Formaldehyde Spin-orbit coupling Singlet-triplet coupling matrix elements in cm⁻¹ and El-Sayed's rule.

Benzene NMR chemical shifts GIAO shieldings of benzene and TMS, converted to ¹H and ¹³C chemical shifts.

HCN transition state Transition state and barrier Locate the HCN → HNC transition state, confirm one imaginary frequency, and compute the barrier.

Water MP2 and CCSD(T) energies Correlation energies of water at the MP2 and CCSD(T) levels.

H2 dissociation H₂ dissociation: six methods RHF, UHF, PBE0, MP2, CASSCF, and CCSD along a breaking bond.

Allyl spin density Allyl radical spin density Open-shell UKS optimization, spin populations, and spin polarization.

Dyson orbital Ionization energies (MRSF-EKT) Ionization energies of water and the Dyson orbital of each ionization.

ACID of benzene Ring current (ACID) Current-density isosurface showing the aromatic ring current of benzene.

Methanol MD Ground-state MD 200 fs of Born–Oppenheimer dynamics and an energy-conservation check.

Conical intersection Conical intersection (MECI) Locate the S0/S1 MECI of ethylene, its g and h vectors, and the cone.

Ethylene NAMD Nonadiabatic dynamics Surface hopping from S1: twisting and return to S0 in 100 fs.

Formaldehyde SOC-NAMD Intersystem crossing (SOC-NAMD) Surface hopping with spin-orbit coupling: formaldehyde hops from S1 to T0 after pyramidalizing (experimental).

SF-TDDFT roots SF-TDDFT and spin contamination SF-TDDFT roots of ethylene identified by ⟨S²⟩, compared with MRSF-TDDFT.

LiH dissociation CASSCF and CASPT2 vs FCI LiH dissociation with RHF, UHF, CASSCF, CASPT2, CCSD(T), and exact FCI.

Formaldehyde with water QM/MM solvent shift n→π* shift of formaldehyde from two water molecules, QM/MM vs full QM.

AuH curves Relativity in gold hydride Non-relativistic vs DKH2 vs relativistic ECP: the Au–H bond shrinks by 0.2 Å.

HI sigma orbital Effective core potentials HI with the def2-SVP ECP: optimization, frequency, dipole, valence orbitals.

MECP Singlet–triplet crossing (MECP) S0/T0 minimum-energy crossing point of ethylene and the spin-orbit coupling there.

QM/MM NAMD QM/MM excited-state dynamics Formaldehyde on S1 with two MM waters: pyramidalization and H-bond breaking.

NH3 NEB Reaction path by NEB Ammonia umbrella inversion with a 9-image nudged elastic band, checked against the planar transition state.

Absorption and emission Excited-state optimization S0 and S1 minima of formaldehyde: absorption, emission, and the 0–0 energy.

NTO Python API and state analysis A Python script: MRSF run, natural transition orbitals, attachment/detachment cubes.

XAS X-ray absorption Carbon and oxygen K-edges of formaldehyde with MRSF-TDDFT ixcore.

UMRSF UMRSF-TDDFT MRSF-TDDFT with an unrestricted (UHF) triplet reference, compared with ROHF.

NACME Coupling between geometries (NACME) State overlaps and derivative coupling between two frames near the S1→S0 hop.

CASSCF CASSCF and XMCQDPT2 CASSCF(2,2) optimizations, the rotation barrier, and XMCQDPT2 states of ethylene.

Alanine dipeptide QM/MM across a covalent bond Link-atom QM/MM optimization and dynamics of the alanine dipeptide.

Symmetry Molecular symmetry Point-group detection, orbital labels, and a 3.4× faster SCF for benzene.

How the reference values were produced

All reference values on these pages come from running exactly the inputs shown, with OpenQP 1.3.1 (GitHub main, commit f5361a2, 20 October 2026) on macOS x86_64 with 2 to 8 OpenMP threads. The one exception is the SOC-NAMD example: it needs the fix in openqp#535 and was run with GitHub main commit 958495f plus that fix (commit 20272ac5b). The NEB example was rerun with commit 958495f plus the frequency-projection fix in openqp#538 (commit be1c9d2); no value on that page depends on that fix. The absolute IR intensities on the frequency page come from GitHub main commit 0b75a06, which includes the IR unit fix openqp#533, as do the frequency tables of the HCN and NH₃ transition states. Molecule and orbital pictures are snapshots of the OQP Studio 3D viewer, made from the output files of the same runs.

On another computer, SCF energies normally agree with the reference values to about 10⁻⁶ hartree. Small differences in the last digits come from DFT integration grids, thread counts, and convergence thresholds. They are not errors.

Where an independent code was available, the reference values were also checked against PySCF 2.13 at the same geometry and basis set. Each page states which values were checked.

Reading an OpenQP run

Every run writes these files beside the input:

File Contents
<name>.log The full text output, including SCF iterations, orbital energies, and all requested properties. Each page quotes the relevant part.
<name>_scf_*.molden Molecular orbitals in Molden format. Open it in OQP Studio Analysis, OpenqpView, Molden, or Avogadro to display orbitals.
<name>.hess.json, <name>.freq.molden Written by Hessian runs: frequencies, normal modes, and thermochemistry data. Open the .freq.molden file to animate the vibrations.
opt.xyz, opt_status.txt Written by geometry optimizations and transition-state searches: the final geometry and a table of the optimization steps.

The end of every log has an ENERGIES AND STATES block, which is the quickest place to read the final energies:

   PyOQP LOG | ENERGIES AND STATES
   PyOQP: Final Energy
   ========================================================================
   PyOQP Energy unit:                 Hartree
   PyOQP electronic energies
   PyOQP state 0                            -76.3256993935

For the full input syntax, see .oqp Input. For larger template decks, see the repository examples.