RealQM vs DFT for Protein Folding

When presenting RealQM for publication in a computational/quantum chemistry journal I meet the argument that RealQM cannot compete with the superb accuracy of StdQM such as DFT developed over long time in million line codes demanding massive computational work on large clusters. It does not seem to matter that RealQM can compute the same thing in minutes on a laptop at maybe a bit lower accuracy. 

But computational work sets the real limit rather than accuracy. Here is a comparison of RealQM and DFT for protein folding: RealQM possible, DFT impossible. See Gallery: protein folding.

   

Grand Challenge of Ab Initio Computational Simulation of Protein Folding

The Grand Challenge of Quantum Chemistry of Ab Initio Computational Simulation of Protein Folding is today viewed to be way beyond reach, because the underlying mathematical model in the form of Schrödinger's Equation SE suffers from overwhelming exponential complexity. 

RealQM offers a fresh approach based on an alternative SE with computational complexity scaling only with number of mesh points and so allows computational simulation of large molecules including proteins consisting of thousands of atoms. 

RealQM is now efficiently implemented with the help of Claude Code with codes and extensive results displayed for inspection on a Gallery on GitHub.

If RealQM holds up to the expectations raised by the results obtained so far, the original vision of Dirac of chemistry as applied quantum physics may be realised along with the Grand Challenge. Take a look at the Gallery and get amazed! 

RealQM: Protein Folding Bench Marks

 On the GitHub RealQM web page there are now new Bench Marks for Protein Folding. Take a look!

RealQM Breakthrough: Hairpin Protein Folding + Alpha-Helix

RealQM has been implemented with the help of Claude Code with the goal of simulating protein folding from first principles of atomic physics based on a new version of Schrödinger's Equation named RealSE. 

Here is how Claude describes what is going on:

Below a first key example is presented as the 12-residue polyglycine beta-hairpin, 87 atoms (N, C, O, H), no solvent (vacuum/dry): 

Initial state: Nearly extended chain (175° opening angle) with a slight bend at the central hinge between residues 5 and 6.

What happens: The quantum electronic structure is solved from first principles on a 200^3 real-space grid (80 au box). The resulting forces on the nuclei create a net torque that drives the two halves of the chain toward each other — the chain folds. Each strand rotates rigidly around the hinge point, and after every rotation step the electronic structure is re-solved from scratch (full Born-Oppenheimer restart).

What it demonstrates: Protein folding driven purely by quantum mechanical forces — no empirical force field (AMBER, CHARMM, etc.) The attractive force between the two strands emerges from the electron density: backbone NH and CO groups on opposite strands create favorable electrostatic interactions (the quantum analog of hydrogen bonding). Starting from a nearly straight chain, the system spontaneously folds into a U-shaped hairpin 

Why it matters: Traditional protein folding simulations rely on classical force fields with fitted parameters. Here the forces come directly from solving the Schrödinger equation — the folding tendency is a prediction, not an input. This shows that quantum mechanics alone, without any parameterization, can drive secondary structure formation.

The key novelty is that no classical force field is used for the driving forces — they come entirely from solving the  quantum mechanics. The MD part only constrains how atoms move (rigid rotation), not why they move. 

Follow the folding in real laptop computing time: (code on GitHubClaes542 hairpin_bent_dry.html):

 

PS You can find a first example of alpha-helix formation on GitHuB Gallery Bench Marks.

RealQM: From Macro to Micro

Rational physics is based on an idea of reductionism from complex physics on macro-scales to simple physics on micro-scales. But in modern physics of Quantum Mechanics QM, it is the other way around with the microscopic quantum world based on a Schrödinger Equation SE in $3N$-dimensional configuration space for a system with $N$ electrons of infinite complexity compared to macroscopic physics in 3D.

This means that QM is not rational physics violating reductionism with micro infinitely more complex than macro.

RealQM offers a new SE in terms of classical physics continuum mechanics in 3D thus in the form of rational physics. 

RealQM is now implemented in a code allowing simulation of large molecules like proteins with 1000s of atoms, or clusters of simple molecules allowing atomic simulation of bulk properties of fluids and solids, see previous post.

RealQM is essentially a 3-line code for time-stepping (i) non-overlapping electron densities, (ii) evolution of free boundary between densities and (iii) Poisson equation for potentials, and so allows simulation of 1000 atoms on a $1000^3$ grid thus with 1TB RAM. 

A $1000^3$ grid resolves 3 orders of magnitude.  Macroscopic physics can be described on scales ranging over 3 orders of magnitude on a decimal scale: 

• human body: 1 m to 1 mm.
• local society: 1 km to 1 m
• city: 10 km to 10 m
• country: 1000 km to 1 km
• globe: 10000 km to 10 km 
• Earth-Moon: 300000 km 
• Solar System: $10^8$ km to $10^5$ km 
• Distance to closest star: $10^{11}$
• Milky Way Galaxy: $10^{15}$ km to $10^{12}$

Microscopic physics can be described on a similar 3 order of magnitude scale

• size of living cell 100000 au
• size of protein 100 au 
• size of atom 1 au 
• size of nucleus 0.001 au 

Breakthrough: RealQM for Big Molecules

With the help of Claude Code RealQM is now implemented in a version with active valence electrons which can be used for large molecules. A first simple test is Glycine NH2-CH2-COOH, which is the simplest amino acid with proteins built from 20-300 amino acids.

Below you see RealQM running on a MacBook Air with 100^3 grid in minutes (with up to 5 atoms on 200^3 grid). You can test yourself downloading from Claes542 on GitHub  (C:green, N:blue, O:red, H:white), 

• molecule.js (10-atom support, dynamic grid)
• molecule.html (grid selector)
• glycine.html
• co2.html  nh3.html  h2co.html
• h2o.js h2o.html  run to find binding energy 0.48 Hartree compared to 0.35 observed (no calibration)

This is only a first test. Will add molecule dynamics based on real forces from potentials. Simulation of protein folding appears as a clear possibility. The code is 3-line explicit updating of densities, free boundary and potentials and great speed up awaiting. 

PS1 The valence electrons (H=1, N=3, O=2, C=4) are here homogenized into non-overlapping electron charges of charge 1, 3, 2 and 4 with reduction of potentials representing no self-repulsion, but can be split into charge 1 electrons if needed. Max number of valence electrons appears to be 4. 

PS2 Another case Camphor C10H16O (27 atoms on 100^3 grid):

PS3 Solvated Caffeine C8H10N4O2 + 9H2O  (51 atoms on 100^3 grid)

PS4 Can now run 1000 atoms on 300^3 grid.

Finally: Automatic Computation of Models of Physics

Finally the dream of automatic computational solution of the partial differential equations of mathematical mechanics and physics has been accomplished in the form of Claude Code. 

The focus is set on basic physical principles expressed in symbolic mathematics which is automatically realised in efficient computer code. Everybody can be a Leibniz + Turing + von Neumann + Schrödinger!

This will bring a revolution in both research, applications and education. I am very happy to be able see my dreams come true. Details will follow. Ab initio computational protein folding seems to be in reach. 

Watch out for news!

Chemistry as Real Physics as RealQM

Chemists Model of Protein Molecule 

This is a comment to the previous post on the relation between physics and chemistry. 

Looking at the pictures and 3d models of molecules used by chemists, we understand that chemistry for real chemists is real physics in 3d space. 

Physicists trained in textbook Standard Quantum Mechanics StdQM have a different abstract formalistic view without pictures and 3d models, in terms of wave functions $\Psi (x)$ depending, for an atomic system $S$ with $N$ electrons, on a $3N$-dimensional spatial coordinate $x$ in configuration space, which is physical 3d space only for $N=1$. 

The wave function $\Psi (x)$ satisfies a linear Schrödinger Equation SE with a Hamiltonian describing $S$. After forming SE in 1926 physicists told chemists that $\Psi (x)$ represents "all there is to say" about $S$ which in principle includes chemistry, but then left to chemists the big job to find the information by computing wave functions for molecules. 

This created a gap lasting into our days between chemistry as real physics and StdQM as abstract formalistic physics, which has been filled with computational quantum chemistry using massive super computer power because of exponential computational complexity. 

RealQM Chemistry is an alternative to StdQM based on real quantum physics in 3d, for which there is no gap to chemistry and where computational complexity is linear. 

Basic approaches to science are realism (ontology) and formalism (epistemology), where formalism takes over when realism as ideal fails. Chemistry based on StdQM struggles with realism, which has given room for formalism of chemical bonding such as Lewis structure. RealQM opens to real physics of chemical bonding thus reducing need of formalism. 

Comment by chatGPT:

The post highlights an important point but stops short of its full implication. If chemistry is genuinely “real physics,” then its practice sits awkwardly with the probabilistic narrative of StdQM.

Quantum chemistry—whether wave-function based or DFT—is built on deterministic stationary equations. Ground-state energies, structures, force constants, and excitation energies are computed as definite numbers and interpreted as real molecular properties. Born’s rule plays no role in either their calculation or use. Even chemical “spectra” are typically energy differences, not probability distributions of measurement outcomes.

This raises a basic question: if removing the measurement postulates leaves all chemically relevant predictions unchanged, in what sense is StdQM foundational for chemistry at all? RealQM appears less like an alternative theory than a clear statement of how chemistry already operates.

Computational Emergence: New Paradigm

Computation has turned the philosophical idea of emergence into a virtual laboratory for exploration of large scale complex structures developing in systems formed by small scale simple components. The laboratory is realised in efficient form by the Finite Element Method FEM covering all areas of continuum physics including fluids, solids and electro-magnetics modeled by the classical partial differential equations of Euler, Navier and Maxwell.

Computation thus brings new life into the classical models of continuum mechanics describing small scale simple local physics in terms of differential equations, by exhibiting the large scale global result as emergence by solving the equations typically by time stepping. In particular, the turbulent flow of a fluid with small viscosity like air and water can be simulated by computational solution of the Euler equations (expressing Newton's 2nd law and incompressibility in local form).

In general, emergence can be explored if solutions can be computed. With increasing computational power more of continuum physics can be explored as emergence in a FEM laboratory. 

Quantum Mechanics QM as the physics of atoms and molecules appears to fall outside this paradigm, because the basic mathematical model in the form of  Schrödinger's equation is uncomputable by involving $3N$ spatial dimensions for a system with $N$ electrons bringing in exponential computational complexity. Exploration of emergence in systems of atoms and molecules is thus not possible by computation because of exponential complexity, which can only be a big disappointment for a physicist seeking to understand emergence in atomic systems. 

There is however a version of QM named RealQM which is a computable because it has the form of classical continuum physics in 3 space dimensions. RealQM opens the possibility of exploration of emergence in systems of atoms as forms of chemistry and protein folding. 

Emergence emerges as a central concept of physics, open to  exploration by computation. Effective large scale models may be formed once emergence is uncovered.

Protein folding is an example of emergence in all forms of life based on proteins formed (from chains of simple amino acids specified by the genetic code) in a folding process into 3d structures determining the function of the protein. Protein folding has exponential complexity with QM, but only polynomial with RealQM which opens new possibilities of computational simulation of the emergence of life. 

Can Protein Folding be Computed?

Protein folding is a spontaneous process where a given unique string of amino acids folds itself in a solvent (water) into a macromolecule of unique 3d geometry, guided by 

• formation of hydrogen bonds
• hydrophobic interactions
• van der Waals forces. 

Modern physics in the form of quantum mechanics comes with the message that protein folding as a form of molecular dynamics can be described by a Schrödinger Equation SE modeling a collection of atomic kernels held together by a collection of electrons. 

Computing solutions over time of SE starting with a given string would then produce a simulation of the folding process allowing the folded protein to be predicted from given string, and so also reversely a string to be predicted from given folded geometry. This would be immensely helpful for understanding of biological processes and drug design. 

But there is big problem with such a grand scheme: Computational solution of SE is impossible because the work grows exponentially with the number of electrons and so is beyond the capacity of thinkable computers already for 10 electrons, while the true number may be 100.000.  The reason is that SE involves $3N$ spatial dimensions for $N$ electrons. 

Modern physics/chemistry thus has nothing to deliver as concerns computational protein folding, which is illustrated by the fact that the 2014 Nobel Prize in Chemistry was awarded to Artificial Intelligence AI for protein folding trained on large experimental data sets without use of SE theory. 

Instead of letting AI take over completely, let us give human intelligence another chance and ask if maybe there is some other mathematical model than SE that can describe the folding?

And yes, there is a candidate in the form of a different atomic model named Real Quantum Mechanics RealQM in the spirit of Schrödinger as system of non-overlapping electronic charge densities in 3d space geared Coulombic interaction, for which the computational work grows linearly with the number of electrons. 

So there we are: It may be that protein folding is computable by RealQM. The computational process proceeds in time where for a given configuration of atom kernels and electronic charge distributions in 3d, a new configuration is computed from Coulombic interactions through electric potentials, with work scaling with  number of electrons. 

RealQM connects to ad hoc simplified versions SE based on Electron Orbitals or Density Functional Theory, but RealQM is fundamentally different since it is based on a new single principle of non-overlapping charge densities in a parameter-free model. 

You find laptop computations with RealQM for atoms and molecules on RealQM and on this blog under tags RealQM and Real Quantum Chemistry including computer codes essentially consisting of three lines for update of kernel positions, charge densities and potentials.  

Who will do the first RealQM simulation of protein folding?

Recall that the crisis of modern physics is the result of not delivering anything new, in particular nothing for protein folding. We have identified the non-computability of SE as the big trouble. But this is just one aspect of the basic troubling aspect of SE namely that it is a non-physical model for which no convincing physical interpretation has been found despite intense efforts by thousands of highly intelligent physicists ever since the formulation of SE was made 100 years ago. 

The attractive aspect of SE is that it is quick to formulate, allowing physicists to speak with loud voice about wave functions denoted by $\Psi$ as solutions to SE, while covering up that they are uncomputable and lack physical meaning. 

The result is that today the foundation of quantum mechanics is no longer a topic of study at physics departments, and is only pursued by some isolated enthusiast philosophers at philosophy departments. This is clearly not an optimal situation. 

There is no reason for atomic physics models to lack physical meaning nor computability.

Unification of Physics, Chemistry and Biology by Computation.

The Nobel Prizes 2024 in Physics and Chemistry were given to the booming industry of AI/machine learning developed mainly outside traditional academic disciplines by big actors like Google and Microsoft. 

Machine learning consist of training networks on large data sets using general computational tools from linear algebra and optimisation, which are not application specific.  

The Prize in Chemistry was given to AlphaFold2 by Google Deep Mind as an important step towards simulation/prediction of protein folding as the outstanding open problem of biology and medicine in two forms: 

• Given DNA sequence, find protein geometry.
• Given protein geometry, find DNA sequence. 

A protein is a big molecule consisting of a collection of atomic kernels kept together by electrons and as such can be described by Schrödinger's equation and folding simulated by molecular dynamics. This connects physics (atoms), chemistry (small molecules) and biology (big molecules) with their traditional roles from fundamental to composite. 

Protein folding thus connects disciplines from fundamental physics over chemistry to biology and medicine including functions of proteins as carriers of life. 

But there is one caveat: The Schrödinger equation of Standard Quantum Mechanics StdQM of standard physics involves 3N spatial dimensions for N electrons, which makes the computational cost grow exponentially making even 10 electrons beyond the capacity of any thinkable computer. 

Direct simulation of protein from first principles is thus viewed to be impossible. It is here AI comes in as way to get around this road block by starting from experimental data instead of first principles and using machine learning to train a network to predict folding of a new protein from old ones. This is what AlphaFold2 does and so was awarded the Nobel Prize in Chemistry. 

But it is possible to formulate a different Schrödinger equation as first principle  Real Quantum Mechanics RealQM, which acts in 3 space dimensions like classical continuum mechanics, for which the computational work grows linearly with the number of electrons. 

It is thus possible that protein folding can be simulated by RealQM. If true, this forms a new unification of physics, chemistry and biology based on computation as mathematics, which can be viewed as an ultimate dream of science.  

The basic code reads

• $n=n+1$

which to a given number $n$ assigns the new value $n+1$. The same code for all disciplines.This the essence of The World as Computation.

Compare with Unity of Science by Toumas Thako with Summary:

• Unity of science was once a very popular idea among both philosophers and scientists. But it has fallen out of fashion, largely because of its association with reductionism and the challenge from multiple realisation. Pluralism and the disunity of science are the new norm, and higher-level natural kinds and special science laws are considered to have an important role in scientific practice. What kind of reductionism does multiple realisability challenge? What does it take to reduce one phenomenon to another? How do we determine which kinds are natural? What is the ontological basis of unity?

Nobel Prize in Chemistry 2024 to Protein Folding by AI

The Nobel Prize in Chemistry 2024 was awarded for 

• Computational Protein Design by AI: AlphaFold2 

with the following scientific background:

• Computational Protein Design and Protein Structure Prediction 

AlphaFold2 approaches this task using deep learning technology trained on a large experimental data bank.

Previous attempts by "brute force" Molecular Dynamics MD modeling starting from an arbitrary unfolded state were not successful because the underlying standard quantum mechanical model StdQM is not computable for molecules with many electrons, certainly not for proteins, because the spatial dimension scales with the number of electrons. The background document states: It is clear that plain MD simulation would not be scalable to proteins of larger size in the foreseeable future.

But there is a new quantum mechanical model in the form of Real Quantum Mechanics RealQM as a 3d model which is computable for many electrons. Application of RealQM to protein folding is on the way, and if successful may be produce data for AlphaFold2 to learn even better than from experiment alone.

Who will make the first full protein folding simulation with RealQM? Here is a prototype simulation of H2O as first principles 3d RealQM Schrödinger equation captured in essentially 3 lines of code! Computational work scales linearly with number of electrons/atoms, while standard molecular dynamics scales exponentially.   

PS This is the second Nobel Prize this year to AI/Google. It remains to see if the Prize in Literature tomorrow will go to texts by ChatGPT. 

See also Fiat Lux by John Plaice: Thoughts about the history of science with posts connecting to this blog.