Normal modes and IR spectra

EasyHybrid computes vibrational normal modes for any system with an energy model: QC, MM or hybrid QC/MM. It can also compute infrared (IR) intensities, label each mode by its symmetry, plot the IR spectrum and compute ideal-gas thermochemistry (RRHO) from the frequencies.

1. Run the normal-mode calculation

• Optimize the geometry first. Frequencies are only meaningful at a stationary point: imaginary frequencies at a minimum mean that the structure is not fully optimized.

• Open Simulate > Normal Modes (Figure 1).

• Coordinates: the structure used in the calculation.

• Cycles, Frames Per Cycle and Temperature: control the trajectories written to animate each mode (number of oscillations, frames per oscillation and the temperature that sets the amplitude).

• Compute IR intensities: off by default because it is expensive. The dipole moment is differentiated numerically, which needs about six extra energy-and-dipole evaluations per free atom.

• Save Trajectory / Working Folder: the name and folder of the job. One trajectory (modeN.ptGeo) is written for each mode.

Click Run.

2. Inspect the modes

Open Analysis > Normal Modes (or Analysis > IR Spectrum), choose the system and click Open to import the job folder (Figure 2). The table lists, for each mode:

• the frequency (cm-1);

• the Symmetry: the irreducible representation of the molecule's point group (a molecule without symmetry, C1, has only "a" modes);

• the IR Intensity (km/mol). It shows "?" when the job did not compute intensities.

Activate a mode in the table and click Play to animate it in the 3D view. FPS sets the speed and Amplitude (Å) the size of the displacements. The first six modes (five for linear molecules) are translations and rotations and have frequencies close to zero.

3. Plot the IR spectrum

Click Plot IR Spectrum. The IR Spectrum window (Figure 3) shows each mode as a grey line, as high as its intensity, and a broadened spectrum. Imaginary modes and modes below 50 cm-1 (residual translations and rotations) are left out. Options on the left:

• Bands – Scale factor: factor applied to every frequency. Harmonic frequencies are too high: about 0.96 for B3LYP and 0.90 for HF; semi-empirical methods vary.

• Bands – Shape / Width: Lorentzian (default) or Gaussian bands, with the full width at half maximum in cm-1 (default: 20).

• Wavenumber axis: the range (default: 4000 to 400 cm-1), decreasing from left to right as in experimental spectra. Fit to Modes adjusts the range to the computed modes.

• Intensity axis: intensity (km/mol), normalized absorbance, or transmittance (%, peaks pointing down).

• Display: show the modes as grey lines, label the strongest peaks with their wavenumber, and choose the color of the curve.

Clicking a band selects the corresponding mode in the Normal Modes window, so it can be animated with Play. Export Image... saves the plot and Save Data... writes the spectrum as text.

4. Thermochemistry (RRHO)

The Thermochemistry (RRHO)... button of the Normal Modes window computes ideal-gas thermochemistry from the imported frequencies (rigid rotor, harmonic oscillator), at any Temperature and Pressure (Figure 4). The Symmetry number is suggested from the point group found by pDynamo, and the Spin multiplicity enters the electronic entropy. The Quasi-RRHO option (Grimme, 2012, ω0 = 100 cm-1) treats low-frequency modes as free rotors in the entropy, which avoids their overestimated contribution.

Click Calculate. The report lists the translational, rotational and vibrational contributions to the energy, entropy and heat capacity, the zero-point energy, and the thermal corrections to the energy, enthalpy and Gibbs free energy. These are corrections relative to the bottom of the well: add the electronic energy to obtain absolute values.

Notes and limits

• Hybrid QC/MM: pDynamo's dipole moment only includes the QC region, so the intensities describe the QC region only (a warning is written to the log). If there are fixed atoms, the Hessian is partial and only vibrations are reported.

• MM models need charges. A force field without electrostatics gives zero intensities; for DYFF or UFF, assign charges first (for example CM5).

• QC engines: the semi-empirical methods of pDynamo (MNDO family) and ORCA work with pDynamo3 as distributed. xTB needs the updated xTB interface that EasyHybrid's install.py installs into pDynamo3.

• Symmetry labels come from pDynamo's point-group perception. A slightly distorted geometry can lower the detected symmetry.