kinisot 2.6.0

Kinisot predicts kinetic and equilibrium isotope effects from the frequency calculations you already have. Give it the Gaussian or ORCA output for a reactant and a transition structure (or a product), say which atoms carry the heavy isotope, and it returns the KIE, k(light)/k(heavy), at any temperature. That works for ¹³C, ²H, ¹⁵N, ¹⁷O, ¹⁸O or any other label, at every position, from one frequency job per structure. Kinisot evaluates the Bigeleisen–Mayer equation with Bell's tunnelling correction, the treatment used to test transition structures against natural-abundance KIE measurements. It also handles conformer ensembles, transition structures in series, and parallel pathways. It reads Hessians from xTB and machine-learned potentials too, through ASE.

Kinisot is developed in the Paton group at Colorado State University and is a rewrite of the Fortran Kinisot by Henry Rzepa.

What you need

• A frequency calculation on the reactant and on the transition structure, at the same level of theory. That means a Gaussian freq (or opt freq) output, or an ORCA frequency job with its .hess file. The reactant must be a minimum, with no imaginary frequency. The transition structure must have exactly one, and it must describe the bond changes of the step you are testing.
• Each labelled reactant. For a bimolecular reaction, give each reactant (or a reactant complex). A reactant that carries no label can be left out, because it cancels.
• The atom number of each labelled position, in each file. Kinisot numbers atoms from 1, in the order of the input geometry, for every program; this is the numbering GaussView shows. Take the numbers from your input, not from ORCA's printed tables, which count from 0.
• The temperature of the experiment.

For a competition KIE, the transition structure is the one of the first irreversible step. If no single step is irreversible, for example because an intermediate can return to the reactant, see Several conformers or transition structures.

Quick start

Kinisot needs Python 3.9 or later. The example files come with the source:

pip install kinisot
git clone https://github.com/patonlab/Kinisot && cd Kinisot/tests/data/gaussian
kinisot --rct claisen_gs.out --ts claisen_ts.out --iso 1 -t 393 -s 0.961

This computes the ¹³C KIE at carbon 1 of allyl vinyl ether for its Claisen rearrangement at 393 K, with B3LYP/6-31G(d) frequencies scaled by 0.961:

  KINISOT.py v 2.6.0: 2026-09-28 04:25
  Species: claisen_gs.out isotopologue: 1
  Species: claisen_ts.out isotopologue: 1

                                                     Temp = 393.0K / Vib. scale factor = 0.961
  Labelled atoms: claisen_gs C1 -> 13C; claisen_ts C1 -> 13C
                                                     V-ratio        ZPE        EXC       TRPF        KIE    1D-tunn   corr-KIE

o claisen_gs                                        --------------------------------------------------------------------------
o claisen_ts                                          463.9
o claisen_gs: iso @ 1                                        1.148e+00  1.024e+00  9.246e-01
o claisen_ts: iso @ 1                                 460.3  1.144e+00  1.021e+00  9.269e-01
                                                    --------------------------------------------------------------------------
  KIE @ 393.0 K                                    1.007880   1.003953   1.003421   0.997456   1.012744   1.001970   1.014739
                                                    --------------------------------------------------------------------------

  Vibrational modes (scaled, cm-1): kept in the partition function / discarded as external modes
  claisen_gs (light): 36 kept; discarded: -0.2 -0.0 0.1 5.4 16.5 23.1
  claisen_gs (iso @ 1): 36 kept; discarded: -0.2 -0.0 0.1 5.4 16.3 23.0
  claisen_ts (light): imaginary 463.9i; 35 kept; discarded: -9.7 -0.2 0.1 0.1 13.3 17.0
  claisen_ts (iso @ 1): imaginary 460.3i; 35 kept; discarded: -9.6 -0.2 0.1 0.1 13.2 16.9

The number to report is corr-KIE = 1.015 (the semiclassical KIE of 1.013 times the tunnelling correction). The same block is appended to Kinisot_output.dat. Its first line gives the Kinisot version, which kinisot --version also prints.

Reading the output

The convention. KIE = k(light)/k(heavy): above 1 is a normal isotope effect, below 1 an inverse one. For an equilibrium isotope effect (EIE, labelled EQE in the output) of reactant ⇌ product, the value is K(light)/K(heavy). Above 1, the heavy isotope accumulates in the reactant, the side with the stiffer vibrations.

The number to report is the last column, corr-KIE: the KIE with the tunnelling correction. The other columns show where it comes from.

• Labelled atoms names each substituted atom in each file, with its element and the isotope it became (claisen_ts C1 -> 13C). Check it against your structures: an atom number that is off by one but lands on another carbon passes every other check. With --reference, a Reference atoms line does the same for the reference position. (This line is new in 2.6.)

• Species rows show, for the reactant and the transition structure, the imaginary frequency of each isotopologue (cm⁻¹) and three factors as light/heavy ratios:

  • ZPE, the zero-point energy term;
  • EXC, the excitation term (thermally populated vibrational levels);
  • TRPF, the Teller–Redlich product of frequencies (heavy/light), which stands in for the translational and rotational terms.

  Their product is the reduced isotopic partition function ratio (s/s′)f of that species.

• KIE @ T gives, for every column, the reactant's value divided by the transition structure's:

  • V-ratio = ν‡(light)/ν‡(heavy), the ratio of the imaginary frequencies;
  • ZPE, EXC and TRPF as above;
  • KIE = V-ratio × ZPE × EXC × TRPF, the semiclassical KIE;
  • 1D-tunn, Bell's tunnelling correction;
  • corr-KIE = KIE × 1D-tunn.

• Vibrational modes lists how many modes entered each partition function, and the six lowest (five for a linear molecule) that were discarded as overall translations and rotations. On a well-converged geometry the discarded values are within a few tens of cm⁻¹ of zero. A real vibration in that list means the geometry needs tightening.

• For an EIE the line is labelled EQE @ T, V-ratio is empty and 1D-tunn is 1.

The equations behind every column are in docs/theory.md.

Comparing with experiment

• Use the temperature of the experiment (-t). The frequency job does not need to have been run at that temperature.
• Use the same reference. Natural-abundance NMR measurements give KIEs relative to an internal standard assumed to have no isotope effect. --reference ATOMS computes that position as well and prints a relative to line. Compare that line with the measured values.
• Average positions that give one signal. Examples are the two ortho carbons of a phenyl ring, the three hydrogens of a methyl group, and the two oxygens of a nitro group. These are distinct in the transition structure but give one signal, so compute each placement of the label and average them. kinisot.equivalent_positions() in Python does this exactly. When the positions are equivalent in the reactant, the average is the harmonic mean of the separate KIEs, not their arithmetic mean.
• Keep the tunnelling correction. A one-dimensional tunnelling correction brings predicted heavy-atom KIEs to about the experimental uncertainty (Meyer, DelMonte, Singleton, J. Am. Chem. Soc. 1999, 121, 10865). At the two bond-forming carbons of isoprene in its Diels–Alder reaction, Singleton and Thomas measured 1.022(3) and 1.017(2). B3LYP gives 1.018 and 1.014 without tunnelling, and 1.022 and 1.017 with Bell's correction. For primary hydrogen KIEs with a large tunnelling contribution, any one-dimensional correction is only approximate.
• Expect about 0.001 to 0.003 for heavy atoms. At B3LYP/6-31G(d), with scaling and Bell tunnelling, the benchmarks reproduce measured ¹³C and ¹⁷O KIEs with mean absolute deviations of 0.0009 (Claisen rearrangement), 0.0012 (Shi epoxidation) and 0.003 (Diels–Alder, including ²H).
• When prediction and experiment disagree, look at the transition structure first. Bigeleisen–Mayer predictions for heavy atoms are accurate as long as the calculation has the right mechanism and transition-state geometry. Hirschi, Takeya, Hang and Singleton found a theory-independent relation between forming-bond distances and ¹³C KIEs (J. Am. Chem. Soc. 2009, 131, 2397), so calculations that reproduce the measured KIEs share nearly the same transition-state geometry. Then check the mechanism: other conformers, a step that is not rate-limiting alone, or competing pathways. examples/mlip_claisen shows an extreme case: potentials whose saddle point is a different reaction.

Usage

Common cases

Everyday options

More options

The full syntax (python -m kinisot is equivalent to kinisot):

kinisot --rct FILE [FILE ...] [--rct FILE ...] (--ts FILE [FILE ...] | --prd FILE [FILE ...])
        --iso ATOMS [--iso ATOMS ...] [-t K] [-s FACTOR] [--imag-cutoff CM-1] [--tunneling MODEL]
        [--barrier KCAL] [--project] [--reference ATOMS] [--calc SPEC]
        [--weights SCHEME] [--energies TABLE] [--weight-uncertainty KCAL]
        [-o FILE] [--overwrite] [-q] [--json FILE] [--csv FILE]
kinisot --job job.json [-o FILE] [--overwrite] [-q] [--json FILE] [--csv FILE]

Invalid input stops the run with a message and exit code 1: an atom number out of range, a reactant with an imaginary frequency, a file that is not a completed frequency job, and so on.

Isotopes. A bare atom number gives the usual heavy label: ¹H → ²H, ¹²C → ¹³C, ¹⁴N → ¹⁵N, ¹⁶O → ¹⁸O, ³²S → ³⁴S, ³⁵Cl → ³⁷Cl, ⁷⁹Br → ⁸¹Br, ²⁸Si → ²⁹Si. Any other isotope can be asked for explicitly: --iso 3:17O, --iso 7:D (or 7:T), --iso 5:14C, or an explicit mass --iso 5:13.5. Masses are AME 2020 values for every naturally occurring isotope of 83 elements plus the common radioactive labels. The light isotopologue is built from the most abundant isotopes, as Gaussian does, so Gaussian, ORCA and other programs give the same numbers for the same Hessian. Kinisot 2.3 and earlier used ¹⁷O for a bare oxygen number; 2.4 and later use ¹⁸O and print a note once.

Several conformers or transition structures

One reactant and one transition structure are often enough. When they are not, Kinisot combines several structures, weighting each by its free energy (for the light isotopologue, which is exact).

• Conformers. Give several files after one flag, all with the same atom numbering: kinisot --rct gs_*.out --ts ts_chair.out ts_boat.out --iso 5. The result is not the Boltzmann average of the pairwise KIEs, but a ratio of population-weighted averages. The output lists each conformer's population and its own KIE. It also gives the KIE of the lowest conformers alone, and how much the result moves if each free energy moves by 0.5 kcal/mol. --weights chooses quasi-harmonic free energies (default), harmonic ones, your own (--energies), the lowest conformer, or equal weights. examples/conformers works through allyl vinyl ether, where a secondary ²H KIE moves by 0.010 between the lowest conformer and the ensemble.
• Transition structures in series. When an intermediate can go on or return, no single step commits the substrate, and the KIE is a weighted mean of the steps' KIEs. It depends on the partitioning of the intermediate (the commitment factor), which can come from free energies or from trajectories.
• Parallel pathways. When the substrate is consumed by several routes (for example two enantiomers through diastereomeric transition structures), each with its own labels, their KIEs combine according to each route's share, which can be a measured selectivity.

Series and pathways are set up in a JSON job file (docs/job_files.md). The equations, with worked cases from the Wittig reaction and a Rh-catalysed dynamic kinetic asymmetric arylation, are in docs/theory.md, section 7.

Input files

Atom numbers count from 1 in the order of the input geometry, whatever the program. Details and pitfalls: docs/file_formats.md.

Why the Bigeleisen–Mayer equation rather than free energies

A KIE can also be taken from the free energies a quantum chemistry program prints for each isotopologue, as exp(ΔΔG‡/RT). With exact harmonic frequencies the two routes give the same number, and in practice they often agree to a few 10⁻⁴. Rzepa's Baeyer–Villiger KIEs came out 1.023 (free energies) against 1.0226 (Bigeleisen–Mayer) for ¹³C, and 0.928 against 0.92831 for ²H (Henry Rzepa's blog, 2015). Against natural-abundance measurements, differences of 10⁻³ matter, and there the Bigeleisen–Mayer route (used by QUIVER, PyQuiver and Kinisot) is the more reliable one.

• Soft vibrations cannot spoil it. It uses only ratios of the two isotopologues' frequencies, and a low-frequency mode contributes a factor close to 1 however poorly it is computed. Through free energies the same mode's isotope shift enters in full. A 0.1 cm⁻¹ error in the isotope shift of one torsion of the Claisen reactant moves the ¹³C KIEs by up to 1.5 × 10⁻³ through free energies, and by less than 10⁻⁵ through Bigeleisen–Mayer.
• Printed free energies are too coarse. Gaussian prints six decimals of a hartree. At 393 K, an error of 10⁻⁶ hartree in one of the four free energies changes a KIE by 8 × 10⁻⁴.
• Quasi-harmonic free energies distort it. Raising soft modes to 100 cm⁻¹, as quasi-harmonic thermochemistry does, moves the Claisen ¹⁸O KIE from 1.037 to 1.018 through free energies. The Bigeleisen–Mayer value moves by 10⁻⁴.
• There are no translational terms to get wrong. Leaving them out of a free-energy or enthalpy–entropy treatment costs 1.3% for Cl⁻ + CH₃Br.
• It is less work. One frequency calculation per structure gives every label at every temperature in seconds.

docs/theory.md (section 6) has the derivation and the full comparison, and scripts/compare_free_energy_route.py reproduces it.

What Kinisot assumes

• Harmonic vibrations and rigid rotors. There is no anharmonic correction. One scaling factor multiplies every frequency, the imaginary one included. Kinisot checks that it reproduces the frequencies the program printed and warns if not.
• Transition-state theory. Each transition structure has one imaginary frequency; a second one triggers a warning. Recrossing and dynamic effects are outside the model, except through a commitment factor you supply for steps in series.
• One-dimensional tunnelling. Bell's model is the default; Wigner and Skodje–Truhlar corrections are options. Bell's correction is not defined below the crossover temperature hc|ν‡|/2πk (229 K for a 1000i cm⁻¹ mode), and Kinisot refuses it there. Multidimensional tunnelling, which primary hydrogen KIEs can need, is outside Kinisot.
• Solvent enters only through the frequency calculation. An implicit-solvent frequency job is used as it is.
• Overall translations and rotations are removed by discarding the six lowest modes (five for a linear molecule), or by projecting them out with --project. For converged Gaussian geometries the two differ by less than 4 × 10⁻⁷ in the KIE. Projection matters for the noisier Hessians of finite-difference calculations.
• Symmetry numbers are left out. The reduced partition function ratio excludes them. If a substitution changes a symmetry number (CH₃ → CH₂D, for example), multiply by the ratio yourself.
• Several structures. Conformers given together are in fast equilibrium (Curtin–Hammett). Transition structures in series are combined at steady state, and parallel pathways at low conversion.

Python API

For scripting and notebooks; everything above is also available from Python.

from kinisot import compute_kie, parse_gaussian

r = compute_kie(rct="claisen_gs.out", ts="claisen_ts.out", iso="1", temperature=393.0, scale=0.961)
r.kie_tunnel                          # 1.014739 (the corr-KIE column)
r.kie, r.zpe, r.exc, r.trpf, r.imag_ratio, r.tunnel_corr
r.other.light.imaginary               # 463.9  (light TS reaction coordinate, cm-1)
r.reactant.rpfr, r.other.rpfr         # reduced partition function ratios (s/s')f
r.to_dict(); r.to_json()              # everything, JSON-serializable
r.summary_row()                       # one flat row, as written by --csv

gs, ts = parse_gaussian("claisen_gs.out"), parse_gaussian("claisen_ts.out")   # parse once,
[compute_kie(rct=gs, ts=ts, iso=a, temperature=393.0, scale=0.961).kie_tunnel  # scan positions
 for a in ("1", "2", "3", "4", "5", "6")]

compute_kie(rct, ts=None, prd=None, iso=None, temperature=298.15, scale=1.0, imag_cutoff=50.0, tunneling="bell", scale_type="zpe", project=None, barrier=None, reference=None, calculator=None) takes Gaussian or ORCA file paths or HessianInput objects (one or a list per side), scale=None for automatic Truhlar lookup, and tunneling in "bell", "wigner", "none". It returns a frozen IsotopeEffect whose reactant and other (transition structure or product) sides hold the light and heavy isotopologues with their kept, discarded and imaginary frequencies, masses and substitutions. Problems raise kinisot.KinisotInputError / KinisotParseError (both ValueError subclasses); non-fatal ones are KinisotWarnings and are listed in r.warnings. See examples/api_example.py and examples/examples.ipynb. The 2.x function compute_isotope_effect() still works but is deprecated.

Conformer ensembles. A species given as a list of files, or as Conformers(files, free_energies=None, degeneracy=None), is an ensemble of conformers with the same atom numbering:

from kinisot import Conformers, compute_kie

r = compute_kie(rct="gs.out", ts=[["ts_chair.out", "ts_boat.out"]], iso="5", temperature=393.0)
r.kie_tunnel                          # sum_i x_i rho_i / sum_j y_j rho'_j
r.conformers                          # per conformer: free energy, population, its own KIE
r.kie_tunnel_lowest, r.n_effective, r.kie_tunnel_range
compute_kie(rct="gs.out", ts=Conformers(["a.out", "b.out"], free_energies=[0.0, 1.2]), iso="5", weights="user")

It returns an EnsembleIsotopeEffect with the same kie, kie_tunnel, kie_relative, to_dict() and summary_row(), but no ZPE/EXC/TRPF breakdown, which exists per conformer only. One conformer per species gives the ordinary IsotopeEffect. kinisot.equivalent_positions(results) gives the exact isotope effect for positions made equivalent by fast motion (the hydrogens of a rotating methyl group) from one result per placement of the label. docs/theory.md, section 7 has the equations.

Transition structures in series and parallel channels.

from kinisot import Series, channels, compute_kie, series_kie

# (atom numbers illustrative) steps none of which alone commits the substrate: one label per reactant, then per step
r = compute_kie(rct=["aldehyde.out", "ylide.out"], ts=Series(["ts_4.out", "ts_6.out"], commitment=128 / 76),
                iso=["8", "0", "20", "20"], temperature=340.15)
r.kie_tunnel, r.shares, r.commitment, r.commitment_for(1.033)
# parallel routes with their own files and labels; shares from a measured selectivity
r = channels([dict(rct="3.out", ts="ts_S.out", iso=["1", "40"]), dict(rct="3.out", ts="ts_R.out", iso=["3", "38"])],
             shares=[3.3, 1], temperature=313.15)
r.kie_tunnel, r.selectivity_for(1.0244)
series_kie([1.043, 1.015], free_energies=[25.9, 26.0], temperature=340.15)   # 1.0280, from KIEs you have

On the command line these come from a JSON job file, kinisot --job job.json (docs/job_files.md), which also runs several isotopologues at once.

Machine-readable output from the command line: --json run.json (the full result of one run) and --csv runs.csv (one row per run, appended).

Examples and documentation

• examples/: the Claisen rearrangement (¹³C, ¹⁸O/¹⁷O and ²H KIEs, projection, reference isotopologue, tunnelling models, temperature scans), a Diels–Alder reaction with one or two reactant files, the same KIE from ORCA and from ASE inputs (with the machine-learned potential workflow), a conformational EQE, and a conformer ensemble (eight allyl vinyl ether conformers and the chair and boat Claisen transition structures), each with the commands, the expected numbers and the literature background.

• docs/theory.md, docs/file_formats.md, docs/job_files.md, docs/faq.md, docs/comparison.md (PyQuiver, PyQuiverHS, Gaussian's readisotopes, GoodVibes).

• benchmarks/: computed versus experimental KIEs, one directory per reaction, with a runner that regenerates the report. At B3LYP/6-31G(d), Kinisot reproduces the measured KIEs of three reactions:

  • the Claisen rearrangement of allyl vinyl ether (five ¹³C and ¹⁷O KIEs, mean absolute deviation 0.0009);
  • the Diels–Alder reaction of isoprene with maleic anhydride (nine ¹³C and ²H KIEs, mean absolute deviation 0.003);
  • the Shi epoxidation of trans-β-methylstyrene (six ¹³C KIEs at 0 °C, mean absolute deviation 0.0012). Kinisot also matches the authors' own QUIVER predictions for all 18 published transition structures: 102 of 108 values exactly at three decimals, the rest within 0.0008.

  Five more systems come from the SI of the PyQuiverHS paper (Grazioli et al., 2026), with their measured values: conformational KIEs of three biaryl and cyclophane ring flips, a gas-phase SN2 α-secondary KIE, and a CD₃ axial/equatorial EIE.

  • Six of the seven measured values are reproduced within 0.016.
  • The SN2 KIE is 0.08 too high: harmonic transition-state theory at HF/6-31+G(d) misses it, and PyQuiverHS gives the same value.
  • tests/test_pyquiverhs.py checks Kinisot against PyQuiverHS's own output for these files over 10–1000 K.

• CHANGELOG.md and IMPLEMENTATION_PLAN.md for what changed and what is coming.

• A video guide to an older version, and Henry Rzepa's blog post on computing KIE values.

Citing Kinisot

Please cite the Zenodo record, DOI 10.5281/zenodo.19272 (CITATION.cff has the metadata; GitHub's "Cite this repository" button formats it). Vibrational scaling factors come from I. M. Alecu, J. Zheng, Y. Zhao, D. G. Truhlar, J. Chem. Theory Comput. 2010, 6, 2872.

Support and contributing

Questions and bug reports: the issue tracker or patonlab@colostate.edu. See SUPPORT.md for what to include and CONTRIBUTING.md for how to run the tests and add a backend. MIT licensed.