Kinetic Isotope Effect

Compute a harmonic Kinetic Isotope Effect (KIE) from pre-computed vibrational analyses using the Bigeleisen–Mayer equation with a Bell infinite-parabola tunneling correction.

The KIE is the ratio of rate constants for the light and heavy isotopologues: KIE = k(light) / k(heavy). A value greater than 1 means the light isotopologue reacts faster, which is commonly observed for primary hydrogen KIEs.

Quick Start

The KIE job requires vibrational analyses (hessians and frequencies) for both the reactant and transition state. Run those first, then feed the results into a KineticIsotopeEffect job:

import atomiverse
from atomiverse import (
    Atoms,
    KineticIsotopeEffect,
    Vibrations,
)
from atomiverse.levels import GFN2_XTB

atomiverse.configure(api_key="your-api-key")

# 1. Optimize geometries (not shown) and run vibrational analyses
reactant = Atoms.from_smiles("CC")
ts = Atoms.from_smiles("[CH2]C")  # simplified TS for illustration

rct_vib = Vibrations(atoms=reactant, level_of_theory=GFN2_XTB)
ts_vib = Vibrations(atoms=ts, level_of_theory=GFN2_XTB)

rct_vib.submit(wait=True)
ts_vib.submit(wait=True)

rct_res = rct_vib.require_result()
ts_res = ts_vib.require_result()

# 2. Compute the KIE for H → D on atom index 0
kie_job = KineticIsotopeEffect(
    reactant_atoms=reactant,
    reactant_hessian=rct_res.hessian,
    reactant_frequencies=rct_res.frequencies,
    ts_atoms=ts,
    ts_hessian=ts_res.hessian,
    ts_frequencies=ts_res.frequencies,
    isotopes=[0],          # substitute atom 0 with its heavy isotope
    temperature=298.15,    # K
    freq_scale_factor=1.0,
)

kie_job.submit(wait=True)
result = kie_job.require_result()

print(f"KIE (with tunneling)  : {result.kie:.4f}")
print(f"KIE (no tunneling)    : {result.kie_no_tunnel:.4f}")
print(f"TS imag freq (light)  : {result.ts_imag_freq_light:.2f}i cm⁻¹")

Inputs

Parameter	Type	Description
reactant_atoms	Atoms	Optimized reactant geometry
reactant_hessian	list[list[float]]	Cartesian Hessian in Hartree/Ų from reactant vibrational analysis
reactant_frequencies	list[float]	Harmonic frequencies in cm⁻¹ from reactant vibrational analysis
ts_atoms	Atoms	Optimized transition-state geometry
ts_hessian	list[list[float]]	Cartesian Hessian in Hartree/Ų from TS vibrational analysis
ts_frequencies	list[float]	Harmonic frequencies in cm⁻¹ from TS vibrational analysis (must contain at least one imaginary mode)
isotopes	list[int] or dict[int, float]	List: atom indices to substitute with common heavy isotopes (¹H→²D, ¹²C→¹³C, ¹⁶O→¹⁷O, etc.). Dict: {atom_index: heavy_mass} for explicit masses in amu
temperature	float	Temperature in Kelvin (default 298.15)
freq_scale_factor	float	Harmonic frequency scaling factor (default 1.0)

Result

job.require_result() returns a KineticIsotopeEffectResult:

Field	Type	Description
kie	float	Final KIE including the Bell tunneling correction
kie_no_tunnel	float	KIE without tunneling
freq_factor	float	Ratio of TS imaginary frequencies ν‡_L / ν‡_H
zpe_contrib	float	Zero-point-energy contribution
exc_contrib	float	Vibrational excitation (temperature-dependent) contribution
trpf_contrib	float	Teller–Redlich product-factor contribution
tunnel_corr	float	Bell infinite-parabola tunneling correction factor
ts_imag_freq_light	float	Imaginary frequency (cm⁻¹) of the light TS isotopologue
ts_imag_freq_heavy	float	Imaginary frequency (cm⁻¹) of the heavy TS isotopologue

Theory

The Bigeleisen–Mayer equation decomposes the KIE into four multiplicative factors:

Term	Meaning
ν‡_L / ν‡_H	Ratio of imaginary frequencies at the transition state
ZPE	Zero-point energy contribution
EXC	Vibrational excitation (temperature-dependent)
TRPF	Teller–Redlich product factor

The Bell correction accounts for quantum tunneling through a parabolic barrier. It is only valid when h c ν‡ / 2 k_B T < π. At very low temperatures or for large imaginary frequencies the correction can become unreliable — a warning is logged in such cases.

Isotope Specification

List mode (auto-detection)

Pass a list of atom indices. The current mass of each atom is inspected and the common heavy isotope is selected automatically:

kie_job = KineticIsotopeEffect(
    ...,
    isotopes=[0, 3, 5],  # auto-detect: ¹H→²H(D), ¹²C→¹³C, etc.
)

Supported auto-detections:

Light isotope	Heavy isotope
¹H (1.008)	²H / D (2.014)
¹²C (12.000)	¹³C (13.003)
¹⁴N (14.003)	¹⁵N (15.000)
¹⁶O (15.995)	¹⁷O (16.999)
³²S (31.972)	³⁴S (33.968)
³⁵Cl (34.969)	³⁷Cl (36.966)
⁷⁹Br (78.918)	⁸¹Br (80.916)

Dict mode (explicit masses)

For uncommon isotopes or precise control, specify masses directly:

kie_job = KineticIsotopeEffect(
    ...,
    isotopes={0: 2.01410178, 5: 18.000},  # H→D, O→¹⁸O
)

Compute Resources

KIE calculations are lightweight — they only diagonalize a few matrices and compute statistical-mechanical partition sums. Typical runtime is under one minute regardless of system size.