Skip to content

Optimization, frequencies and thermochemistry

The inputs on this page are educational templates that have not been executed for this course. Use an authorized installation, verify version-specific options and establish your own convergence.

Optimize, then analyze the optimized structure

Save a separate complete water_optfreq.gjf starting from the same approximate geometry:

%Chk=water_optfreq.chk
%Mem=2GB
%NProcShared=2
#p RHF/6-31G(d) Opt=Tight Freq SCF=Tight

Water optimization and harmonic frequencies; 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

Opt changes nuclei while repeatedly solving the electronic problem. Freq requests harmonic analysis after successful optimization in this combined workflow. Optimization thresholds concern forces/displacements; SCF thresholds concern electronic solution. Extra printed digits cannot repair a nonconverged geometry. If splitting jobs, read the verified optimized checkpoint or export the final geometry, not the initial viewer frame.

Four acceptance gates

  1. Optimization completed, rather than hitting a step limit or error.
  2. Force and displacement report meets the criteria; read the full table and summary rather than an energy plateau.
  3. The final structure remains the intended species, without unexplained dissociation, proton transfer or overlap.
  4. Frequency count and mode character fit the intended stationary point.

A nonlinear \(N\)-atom molecule has \(3N-6\) vibrations; a linear one has \(3N-5\). Water has three. An unconstrained minimum has no genuine imaginary mode. Gaussian commonly prints imaginary frequencies as negative numbers. A first-order transition state needs one genuine imaginary mode following the intended reaction coordinate; one negative value alone does not establish connection to desired minima. Constraints change the relevant space: a constrained minimum is not automatically a full-surface minimum.

Tiny imaginary values may reflect residual gradient, numerical settings, integration grid or real soft distortion. Animate the mode, improve justified settings and displace/reoptimize if needed. Do not delete modes or adopt a universal numerical cutoff to certify success.

Extract with context

grep -nE 'Optimization completed|Stationary point found|Frequencies --|Zero-point correction|Thermal correction|Sum of electronic|Normal termination|Error termination' water_optfreq.log

Use this to locate blocks, then read them. Save final atom labels and Å coordinates. Record three water frequencies in cm−1 and assign bending/stretching by animation. IR intensity is distinct from frequency. Separately label electronic energy, zero-point correction, thermal corrections and printed sums. Do not add zero-point energy a second time to an already combined thermal free-energy value. Record actual temperature, pressure and masses.

Thermochemistry has assumptions

The standard molecular treatment uses ideal-gas translation/rotation and harmonic vibration. Flexible low-frequency torsions may make harmonic entropy unreliable; conformers, hindered rotation and anharmonicity can matter. A solvent electronic calculation does not by itself make gas-phase translation a full solution free energy. Declare standard states and consistent corrections for solution reactions.

For a balanced reaction, calculate \(\Delta G=\sum_i\nu_iG_i\), with positive product and negative reactant coefficients. Every term needs compatible temperature, standard state and approximation. A higher-level electronic energy plus lower-level thermal correction is an explicitly documented mixed-level estimate, not an exact output of either job. Avoid one generic frequency scale factor for all methods and properties.

Exercise and sources

Write a validation page containing final geometry, force/displacement evidence, mode count/signs, labeled thermochemical quantities and two model limitations. Official vibrational analysis supports mode interpretation; official thermochemistry paper explains thermal assumptions; Hunt group frequency teaching adds independent practice. Keyword references: Opt and Freq.

Previous：First water single-point calculation · Next：Method, basis and numerical convergence