IR spectrum and thermochemistry of blocked alanine

This tutorial computes the vibrational normal modes of blocked alanine (bALA) with the semi-empirical AM1 Hamiltonian, plots its infrared (IR) spectrum and computes its ideal-gas thermochemistry. It takes about 5 minutes. The tools are described in Normal modes and IR spectra.

1. Load the molecule and define the QC model

• File > Open examples/tutorials/01_bala/bALA_not_opt.mol (the same structure as the bALA tutorial; 22 atoms).

• Select all atoms, Selection > Set as QC Atoms, and in System > Setup QC Region choose the semi-empirical method AM1, charge 0, multiplicity 1. The whole molecule is now described by AM1.

2. Optimize the geometry

Frequencies are only meaningful at a minimum. Open Simulate > Geometry Optimization, choose the L-BFGS method with an RMS gradient tolerance of 0.05 kJ mol-1 Å-1, and click Run. The optimization converges in a few hundred steps to −374.8 kJ/mol, about 50 kJ/mol below the starting structure. The optimized structure is added as a new object of the system.

3. Compute the normal modes with IR intensities

Open Simulate > Normal Modes (Figure 1). Choose the optimized coordinates, tick Compute IR intensities, keep Save Trajectory (one trajectory per mode is written, used to animate the modes) and click Run. With AM1 the 66 modes of bALA take less than a minute; the IR intensities need about six extra energy-and-dipole evaluations per atom.

4. Inspect the modes

Open Analysis > Normal Modes, choose the system and click Open; select the folder of the job. The table lists the 66 modes (Figure 2): the first six, with frequencies close to zero, are the translations and rotations; the 60 vibrations start at 163 cm-1. bALA has no symmetry (point group C1), so every mode has symmetry "a". Activate a mode and click Play to watch it in the 3D view; Amplitude makes the motion larger or smaller.

5. Plot the IR spectrum

Click Plot IR Spectrum (Figure 3). The strongest bands are at 2027 cm-1 (700 km/mol, the strongest mode) and 1688 cm-1, most likely the C=O stretches of the two amide groups; at 3441 and about 3500 cm-1, in the N–H stretching region; and at 647 cm-1. Animate each mode (below) to check which atoms move.

Harmonic semi-empirical frequencies are too high: the experimental amide I band of peptides is near 1650 cm-1. Use the Scale factor to compare with experiment (scale factors are method dependent; for AM1 the C=O stretch is overestimated much more than other modes, so a single factor is only a rough correction). Click a band to select its mode in the Normal Modes window and animate it. Export Image... and Save Data... save the spectrum.

6. Thermochemistry

Click Thermochemistry (RRHO)... in the Normal Modes window and then Calculate with the defaults: 298.15 K, 1 atm, symmetry number 1 (point group C1, found by pDynamo) and multiplicity 1 (Figure 4). For bALA with AM1:

• Zero-point energy: 514.1 kJ/mol.

• Thermal enthalpy correction H: 539.7 kJ/mol (thermal energy E 537.2 kJ/mol, including the ZPE, plus RT).

• Entropy S: 377.8 J mol-1 K-1 (translational 170.7, rotational 125.6, vibrational 81.4).

• Thermal correction to the Gibbs free energy G = H − TS: 427.1 kJ/mol.

These are corrections relative to the bottom of the well: add the electronic energy of the optimized structure to obtain absolute values, and compare conformers (for example the C7eq and C5 conformers of the bALA tutorial) with the same method. For flexible molecules, tick Quasi-RRHO for low modes: the low-frequency torsions then contribute to the entropy as free rotors, which avoids the overestimated entropy of very soft harmonic modes.

Going further

• Repeat the calculation with another Hamiltonian (PM6, or xTB or DFT through ORCA, see Setting xTB / ORCA / DFTB+) and compare the spectra.

• Run a Transition state search (Baker) and check the result with Normal Modes: a transition state has exactly one imaginary frequency.