Prerequisites¶
Before an MCTDH operator file can be generated, the vibronic Hamiltonian must first be parameterized. This requires obtaining the vibrational frequencies, electronic energies, and vibronic coupling constants for every normal mode included in the quantum dynamics calculation.
Most of these quantities are obtained from a series of electronic structure calculations performed with GAMESS. The detailed procedure for performing these calculations is described in the GAMESS documentation, while this section summarizes the information required before constructing an MCTDH operator file.
1. Normal Mode Distortions¶
The first step is to optimize the reference molecular geometry and calculate its harmonic vibrational frequencies.
Each normal mode is then displaced along both the positive and negative directions to generate a series of distorted geometries. Electronic structure calculations are subsequently performed for every distorted geometry to obtain diabatic energies and interstate couplings as functions of the normal coordinate.
The complete procedure for generating distorted geometries and performing the required GAMESS calculations is provided in the GAMESS documentation.
Distortions¶
📘 Distortions along normal modes
2. Nonlinear Curve Fitting¶
The diabatic energies and electronic couplings obtained for every distorted geometry are fitted to analytical functions.
From these fits, the linear and quadratic vibronic coupling constants are extracted. These parameters later appear in the MCTDH operator file as first- and second-order coupling terms.
A typical fitted output file contains
- fitted coefficients,
- fitting errors,
- harmonic frequency,
- Huang–Rhys factor,
- and the reorganization energy (mode strength).
3. Reorganization Energy¶
For every vibrational mode, the coupling strength is estimated using the reorganization energy
where
- \(k\) is the linear vibronic coupling constant,
- \(\omega\) is the harmonic vibrational frequency.
The final column of each fitted output file usually reports this quantity directly.
The reorganization energy provides a simple measure of how strongly a particular vibrational mode interacts with the electronic states.
Modes with larger values contribute more significantly to the vibronic dynamics.
4. Selecting Vibrational Modes¶
In principle, every normal mode may be included in an MCTDH calculation.
However, including all vibrational modes rapidly increases the computational cost.
Instead, the modes are ranked according to their reorganization energies, and only the most strongly coupled modes are retained.
Typical choices include
- 24 modes
- 28 modes
- 32 modes
The exact number is not fixed and depends on the system being studied as well as the available computational resources.
In practice, these numbers often produce a more balanced MCTDH mode-combination tree while retaining the dominant vibronic couplings.
5. Required Files¶
After selecting the active vibrational modes, the following files are required for automatic operator generation.
| File | Purpose |
|---|---|
frequency.dat |
Harmonic frequencies of all normal modes |
Diabatization output (*.log) |
Reference diabatic energies and electronic couplings |
| Mode-dependent fitted coupling files | Linear and quadratic vibronic coupling parameters |
operator-make.sh |
Bash script that generates the complete operator file |
operator.f90 |
Fortran program that formats the coupling terms for MCTDH |
The following tutorial explains how these files are combined automatically to generate a complete MCTDH operator file.
Connection with GAMESS
The normal-mode distortions, diabatic energies, and nonlinear fitting parameters used throughout this tutorial are generated using GAMESS. Those calculations are described in detail in the GAMESS → Vibronic Coupling / Distortion documentation and are not repeated here.