2.3 Molecular geometry and vibrations in vacuum

These are unexecuted teaching inputs and starting settings to test. Original figures are schematics, not computed results. Use licensed VASP and PAW data, replace every placeholder, record the executable version and validate convergence.

2.3.1 Model, units and provenance

Use eV for energy, Å for length and eV/Å for force; 1 kbar = 0.1 GPa. State normalization per atom, molecule, primitive cell or simulation cell. Record PAW identifiers, release, ZVAL, ENMAX and permitted hashes; never redistribute POTCAR. SCF convergence addresses the chosen electronic problem; convergence of the target property requires separate tests.

Molecular geometry and vibrations in vacuum — original conceptual schematic

Original schematic. Curves explain concepts; blank data areas await verified learner results. No calculation is claimed.

\[ N_{\mathrm{internal}}=3N-6\quad\text{(nonlinear molecule)} \]

2.3.2 Worked case: procedure, interpretation and checks

Goal and intuition

A geometry optimizer finds a stationary point by following forces. Vibrations ask a more demanding question: how do the forces change when atoms move slightly? A force nearly zero at one geometry does not establish that all nearby distortions raise the energy. Water provides three familiar internal vibrations and a clear distinction between internal motion, translation and rotation.

Prerequisites: 1.1 Four input files, one physical question, 2.1 A spin-polarized isolated atom, 2.2 H₂ binding: an energy difference needs a reference, a licensed consistent O/H potential set, and basic vector geometry. Use neutral gas-phase H₂O, not liquid water. The target is the isolated-molecule harmonic approximation at the chosen electronic-structure level. It is not a prediction of a room-temperature liquid IR spectrum.

Workflow

Build a visibly bent, non-overlapping initial geometry near the cell center. Confirm O/H species order and use the same order in POTCAR.

Unexecuted templates

This lesson uses IBRION=6, following current documentation's preference for symmetry-assisted finite differences. Older tutorials often use IBRION=5; current documentation marks that route deprecated. Verify behavior for the installed version. A displacement parameter in a vibration calculation is not a molecular-dynamics timestep. Keep all nine Cartesian coordinates free for the full isolated-water normal-mode problem; selective dynamics changes the degrees of freedom being analyzed.

Output interpretation

A nonlinear isolated N-atom molecule has 3N−6 internal vibrational modes. For water, expect three physical internal modes, plus translations/rotations that should be near zero in the ideal isolated, numerically exact limit. Small residual nonzero external-mode frequencies can reveal finite-cell interactions, incomplete relaxation or force noise. A large imaginary internal mode requires investigation of the geometry, electronic convergence and displacement dependence. VASP may print imaginary modes with an f/i label; do not turn them positive by taking an absolute value.

A frequency is a curvature property, so report displacement amplitude, electronic tolerance, geometry force threshold and treatment of external modes alongside it. Frequency alone does not provide IR intensity; that requires the relevant response of the dipole or polarization to displacement. A broadened stick plot without computed intensities is only a mode-location visualization.

Experiment, pitfalls and exercise

Compare displacements 0.01, 0.015 and 0.02 Å at the same relaxed geometry. A displacement too small amplifies force noise; too large samples anharmonic behavior. Recheck one value with tighter EDIFF and a larger box. Do not assume that a visually clean animation is a converged frequency. Exercise: deliver three mode diagrams with directional arrows, a frequency-convergence table, and a paragraph separating harmonic frequency, experimental fundamental and finite-temperature spectral broadening.

2.3.3 Unexecuted inputs and analysis scaffolds

These are unexecuted teaching inputs and starting settings to test. Original figures are schematics, not computed results. Use licensed VASP and PAW data, replace every placeholder, record the executable version and validate convergence.

2.3.3.1 Input block 1

Water starter, not optimized
1.0
18.0 0.0 0.0
0.0 18.0 0.0
0.0 0.0 18.0
O H
1 2
Cartesian
9.000 9.000 9.000
9.760 9.000 9.590
8.240 9.000 9.590

2.3.3.2 Input block 2

# Geometry stage: add to common small-molecule electronic settings
ISPIN = 1
ISMEAR = 0
SIGMA = 0.02
IBRION = 2
NSW = 100
ISIF = 2
EDIFF = 1E-7
EDIFFG = -0.005
# EDIFFG negative: force threshold magnitude in eV/Angstrom
# Fixed cell; Gamma-only sampling; explicit converged ENCUT

2.3.3.3 Input block 3

# Separate harmonic finite-difference stage, starting from relaxed geometry
IBRION = 6
NSW = 1
ISIF = 2
NFREE = 2
POTIM = 0.015
EDIFF = 1E-8
# POTIM is the displacement amplitude in Angstrom for this task
# Remove relaxation-only stopping assumptions; inspect all displacements