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5.1 From a Hessian to IR and Raman spectra

These are unexecuted teaching inputs and starting models. Original diagrams are schematics, not calculated results. Validate version-specific syntax, licensed or authorized data, numerical convergence and the scientific model before using this workflow.

5.1.1 Model, units and provenance

Geometry in Å; electronic energy in hartree; vibrational wavenumbers in cm⁻¹. Check each printed field and keep thermal and standard-state terms distinct.

Shared inputs, conventions and evidence

Original schematic: From a Hessian to IR and Raman spectra. No numerical results are claimed.
Original schematic: From a Hessian to IR and Raman spectra. No numerical results are claimed.

5.1.2 Unexecuted inputs and explicit deltas

Use the accompanying instructions to identify the parent calculation and placement of every delta; a snippet is not automatically a standalone input. Preserve all blank-line and file-provenance requirements.

5.1.2.1 Input block 1

%chk=water17.chk
%mem=2GB
%nprocshared=2
#p B3LYP/6-31+G(d,p) Opt=Tight Freq=Raman
   SCF=(Tight,XQC) Int=UltraFine

Water: optimized harmonic IR and Raman teaching example

0 1
O    0.000000    0.000000    0.000000
H    0.758000    0.000000    0.586000
H   -0.758000    0.000000    0.586000

5.1.3 Worked investigation

5.1.3.1 Question, intuition, and prerequisites

How can the same vibration produce different IR and Raman signals? Think of a vibration as a coordinated displacement of all nuclei, not a single moving bond. IR activity measures how the dipole changes along that displacement; Raman activity concerns how the polarizability changes. A large IR band need not be a large Raman band. Water is small enough that every normal mode can be animated and explained: one bend and two stretches. Prerequisites are charge/multiplicity, geometry optimization, the idea of a second derivative, and opening a log/checkpoint in a molecular viewer.

5.1.3.2 Complete input

See input block 1 above.

The same functional, basis, and integration grid are used for optimization and frequencies. Freq=Raman explicitly requests Raman properties as well as the harmonic frequency/IR analysis. The file creates the force constants required by Case 18. This is an isolated gas-phase molecule, not a model of the broad liquid-water spectrum.

5.1.3.3 Numbered workflow

  1. Inspect the three atoms, neutral charge, and singlet multiplicity before submission. Save the input, full log, and water17.chk together.
  2. Confirm optimization convergence and normal termination. Find the final frequency block, not an intermediate geometry or an old appended job. A nonlinear three-atom molecule has \(3N-6=3\) vibrational modes.
  3. For each mode record frequency, reduced mass, IR intensity, Raman activity, and, if present, depolarization data. Animate it and assign bend, symmetric stretch, or asymmetric stretch from the displacement pattern, not from frequency order alone.
  4. Make separate stick plots of IR intensity and Raman activity. Give each its own units. For an optional smooth display, broaden every stick using one stated line shape and width, such as a Lorentzian with FWHM 20 cm⁻¹; this width is a visualization choice.
  5. Save the raw frequencies before applying any literature scaling factor. If scaled, record its source, model chemistry, and purpose. A frequency scale factor is not an IR-intensity multiplier.

5.1.3.4 Read and check

Frequencies -- contains harmonic wavenumbers in cm⁻¹; a negative printed value represents an imaginary frequency. IR Inten -- is commonly reported in km mol⁻¹; Raman Activ -- is activity, commonly Å⁴ amu⁻¹. A simulated Raman scattering intensity additionally depends on excitation wavelength, temperature, and scattering convention. Never relabel an unconverted activity plot as measured Raman intensity. For a minimum, all three vibrational modes should be real. As broad diagnostic windows rather than calculated answers, an isolated-water bend is expected in the roughly 1500–1800 cm⁻¹ region and O–H stretches around 3500–4100 cm⁻¹ at ordinary harmonic electronic-structure levels. A 200 cm⁻¹ “O–H stretch” should trigger an atom/geometry/unit check.

A small imaginary mode is an instruction to inspect, not permission to delete it. Tighten the optimization, inspect the displacement, and consider grid sensitivity. Experimental fundamentals also include anharmonicity, temperature, environment, and instrumental broadening. Agreement after arbitrary shifting does not validate the method.

5.1.3.5 Exercise

EN exercise: Which mode has the highest ratio of Raman activity to IR intensity? Explain why this ratio has units and is not a universal measure of detectability. Repeat only the visualization at FWHM 10 and 40 cm⁻¹; explain which molecular conclusions remain unchanged.

5.1.5 Sources and further reading