Normal modes are in Hilbert space: QED !

I want to 'justify' that the normal vibrational mode vectors are in the Hilbert space:

Below imageries compiles some ideas,



thence,

Quod Erat Demonstrandum !

Ammonia and Umbrella

In Holland, the weather is strong enough to invert the umbrella. I (often) 'feel' the celbrated ammonia inversion in a rainy, windy day in Leiden.

Calculations as followed:

Electronic structure: Gamess-US, Restricted Hartree-Fock level with STO/3g

Foundation of pwDFT: PseudoPotential construction

From PWscf forum

On Jan 17, 2008, at 22:20 ,

Paul M. Grant wrote:> I understand PP theory, but their construction, as many point out, is more art than science

Paolo Giannozzi:>I would rather say, "more cooking than science"

...

Paolo Giannozzi - is the main author of the Quantum Espresso
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Acknowledgements

for Computing facilities:

I gratefully acknowledge the support from a PIONIER grant from the Dutch National Research Council (NWO) for G. J. Kroes (my Ph.D. promoter) and a grant for computational resources by the Dutch National Computing Facilities Foundation (NCF). And, SARA people in Amsterdam, since their response is also so quick.