Analysis
The calculation aligns the two molecular geometries, constructs mass-weighted normal-mode bases, evaluates the Duschinsky rotation matrix and displacement vector, and calculates Huang–Rhys factors in the final-state normal-mode basis.
qf =
Jqi + K
dk =
√ωkKk
Sk =
½dk2
Large-file notice:
This analysis can involve substantial uploads and
numerical processing. A combined input size of
approximately 150 MB or less is recommended
for more reliable use.
The current maximum combined upload size is
200 MB.
Larger calculations may take several minutes and
performance depends on the available server resources.
Gaussian Input Files
Please provide the Hessian / formatted checkpoint (.fchk) and output (.log) files for both the initial and final electronic states.
Initial Electronic State
Frequency and normal-mode information for the initial state.
Gaussian frequency output containing
“Frequencies --” lines.
Formatted checkpoint containing coordinates,
atomic weights and Vib-Modes.
Final Electronic State
Frequency and normal-mode information for the final state.
Gaussian frequency output containing
“Frequencies --” lines.
Formatted checkpoint containing coordinates,
atomic weights and Vib-Modes.
Analysis Settings
cm⁻¹. Default: 100 cm⁻¹.
Modes at or below this value are excluded.
Default: 20. Maximum: 100.
All modes remain available in the ZIP output.
Preparing files...
Huang–Rhys Analysis Results
Final-state Duschinsky-consistent results are highlighted below.
Important Results
Final-state normal-mode basis.
MLJ parameters:
The values highlighted in green,
Seff and
ωeff, are the effective Huang–Rhys
parameters used in Marcus–Levich–Jortner (MLJ)
rate calculations.
Effective Huang–Rhys factor
(Seff)
—
dimensionless
Effective vibrational frequency
(ωeff)
—
cm⁻¹
Effective vibrational energy
(ℏωeff)
—
eV
Intramolecular reorganization energy
(λin)
—
eV
Final-basis HR total
—
dimensionless
Initial-basis HR total
—
comparison value
Aligned RMSD
—
Å
Retained Modes
—
after frequency filtering
Analysis Diagnostics
Number of atoms
—
Frequency cutoff
—
Uploaded data
—
Initial imaginary modes
—
Final imaginary modes
—
Initial near-zero modes
—
Final near-zero modes
—
max |JᵀJ − I|
—
det(J)
—
Initial-basis reconstruction error
—
Final-basis reconstruction error
—
Shift consistency error
—
Detailed Results
Download the complete analysis including CSV tables, Duschinsky matrix J, shift vector K, strongest mode-mixing information, summary data, and plot images. The server stores generated results temporarily, so download the archive after completing the calculation.
Dominant Final-State Huang–Rhys Modes
Ranked by the final-state Huang–Rhys factor Sk.
| Gaussian Mode | Frequency / cm⁻¹ | S | ħω / eV | λin,k / eV |
|---|
Visual Analysis
Duschinsky Rotation Matrix J
Academic Use and References
If this calculator, the underlying methodology, or results generated with this implementation contribute to published work, please cite the relevant methodological literature and associated work below.
Huang, K.; Rhys, A.
Theory of Light Absorption and Non-Radiative
Transitions in F-Centres.
Proceedings of the Royal Society of London.
Series A
1950
,
204 (1078), 406–423.
DOI: 10.1098/rspa.1950.0184
Reimers, J. R.
A Practical Method for the Use of Curvilinear
Coordinates in Calculations of
Normal-Mode-Projected Displacements and
Duschinsky Rotation Matrices for Large Molecules.
The Journal of Chemical Physics
2001
,
115 (20), 9103–9109.
DOI: 10.1063/1.1412875
Kumar, P.; Hele, T. J. H.
Mechanistic Origins of D1
Excited-State Formation in Radical-Based
Organic Light-Emitting Diodes.
ChemRxiv
preprint.
DOI: 10.26434/chemrxiv.15004265/v2
Future development:
Future versions will extend file parsing and
Huang–Rhys/Duschinsky analysis support to additional
quantum-chemistry software packages.
Disclaimer:
This calculator is provided for general academic,
educational, and research purposes only. Users are
responsible for verifying the supplied files,
electronic-state assignments, molecular structures,
atom ordering, frequency calculations, computational
methodology, units, frequency filtering, assumptions,
and calculated results before using them in research
or publications.
The generated values and downloadable files are provided without warranty of any kind. Use of this calculator is entirely at the user's own risk. The author accepts no responsibility for errors, omissions, incorrect interpretation, failed calculations, loss of data, wasted computational resources, financial loss, research outcomes, publication consequences, or any other loss or damage arising from the use of this calculator or its generated results.
The generated values and downloadable files are provided without warranty of any kind. Use of this calculator is entirely at the user's own risk. The author accepts no responsibility for errors, omissions, incorrect interpretation, failed calculations, loss of data, wasted computational resources, financial loss, research outcomes, publication consequences, or any other loss or damage arising from the use of this calculator or its generated results.