Molecular Dynamics as Real Physics

This is a clarification of the previous post and this post.

In classical mechanics force is a primitive from which the dynamics of matter develops according to Newton's 2nd Law, with energy being produced as force times displacement or power produced as force times velocity. Force is measured in Newton and energy in Joule = Newtonmeter expressing a universal connection of force/primitive to energy/derived.   

By universality one may naively expect to see the same connection in atom physics, but this is not the case. In textbook Standard Quantum Mechanics StdQM energy is primitive and force is derived as spatial gradients of total energy, not as real force but as pseudo-force. 

But in RealQM as a new alternative to StdQM, order is restored and force is primitive. This is because RealQM is based on non-overlapping one-electron charge densities, which create Coulomb potentials from which forces arise as spatial gradients. 

Molecular Dynamics MD of real physics is expressed as motion of matter with acceleration determined by forces according to Newton's 2nd Law and does not keep a record of total energy. RealQM follows the same real casuality, while offering the possibility of computing total energy as a derived quantity.

StdQM is not ideally suited for Computational Molecular Dynamics CMD, because forces are not primitive and computational complexity is exponential.

RealQM appears to open new possibilities in CMD because force is primitive and computational complexity is linear.  

Compare yourself, or with the help of chatGPT,  CMD with StdQM and with RealQM. Result?

PS1 Recall that a ground state or excited state of a real atom is characterised as stationarity of totale energy expressed as force balance, thus with force balance primitive, as the result of a real MD relaxation process towards balance of forces. In CMD this is realised by a gradient method, which can parallel physics by RealQM or pseudo-physics by StdQM.

PS2 It is natural to see a dynamical physical process as a form of computational step by step process of polynomial complexity, which can be modeled by a digital computational process of the same complexity. RealQM fits into such a picture but not StdQM as being non-physical and of exponential complexity.