Ab Initio Chemistry: StdQM vs RealQM

Discovering the World from a desk.

The ideal mathematical model of some physics is according to Einstein a model without parameters. Newton's Law of Gravitation is the prime example within classical physics/mechanics taking the from

• $\Delta\phi (x)  = \rho (x)$

where $\phi (x)$ is gravitational potential, $\rho$ mass density and $\Delta$ the Laplacian differential operator with respect to a Euclidean coordinate $x$. 

The prime example within modern physics/quantum mechanics is Schrödinger's equation for the hydrogen atom taking the form of an eigenvalue problem with eigenvalue $E$ 

• $-\frac{1}{2}\Delta\psi (x) -\frac{\psi (x)}{\vert x\vert} = E\psi (x)$  

where $\psi (x)$ is a wave-function and $-\frac{1}{\vert x\vert}$ is a kernel potential. No parameter appears if units are properly chosen.

The amazing property of a parameter-free model is to give information about physics without other physics input than a mathematical model without parameters. This allows the theoretical physicist at his desk to make predictions about the world without any input from the world. Such a prediction is said to be ab initio. Amazing! A priori knowledge in the sense of Kant.

In general, however, mathematical models of some physics contain parameters which have to be known from experiment or other models, in order to get anything out of the model. The Standard Model of particle physics contains 19 parameters which cannot be normalised by choice of units. It is very difficult to determine these parameters by experiment. 

Let us now compare StdQM with RealQM as concerns ab initio simulation of chemical bonding. 

For StdQM we turn to chatGPT and get this response stating that this is impossible because the Schrödinger equation of StdQM, which is parameter free, is uncomputable and thus has to be modified or prepared to deliver any result and the preparation builds on massive input of know-how and parameters/experiments.

In contrast the new Schrödinger equation of RealQM is parameter-free and readily computable and thus delivers ab initio simulation capability of e g chemical bonding.  See posts on Real Quantum Chemistry with links to everything about RealQM.

PS Here is what Eric Scerri says about ab initio StdQM in Selected Papers on the Periodic Table:

• Whereas most chemists and educators seem to believe that all is well, I think that there is some benefit in pursuing the question of how much is strictly explained from the theory. 
• It is indeed something of a miracle that quantum mechanics explains the periodic table to the extent that it does at present. 
• But we should not let this fact seduce us into believing that it is a completely ab initio explanation. We have not yet arrived at the super - ab initio phase of quantum chemistry and nor are we even close. 
• If anything, the compromises that have been struck with the acceptance of parametrization as well as the mixing of wavefunction and DFT approaches begin to question the earlier promise of ab initio quantum chemistry.