Geometry convergence

The experimental geometry for H2O has a bond length of 0.9578 A and an angle of 104.48°. Let us investigate how the calculated geometry change as a function of theoretical sophistication. 

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The geometry converges in 9 steps, resulting in the structure at the left. 

Illustrating the Concepts 264 11.1 Geometry Convergence 264 11.1.1 Ah Initio Methods 264 11.1.2 DFT Methods 267 14.4 Choice of Coordinates 322 14.5 Transition Structure Optimization 327 14.5.1 Methods Based on Interpolation Between Reactant and Product 327 14.5.2 Linear and Quadratic Synchronous Transit 328... 

Geometries converge relatively fast, already at the HF level with a DZP type basis the geometry error is often 1 kcal/mol or less, and a MP2/DZP optimzed geometry is normally sufficient for most applications. The translational and rotational contributions are trivial to calculate, they depend only on the molecular mass and the geometry... 

In earlier studies the gradient thresholds for CAS geometry convergence were often weaker than those used here, and accurate analytic frequencies were unavailable to detect false (transition state) stationary points. The slight effects of B-state torsional deformation (if present at lower CAS levels) may therefore have fallen within the numerical uncertainties. 

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