RealQM — Ab Initio Molecular Dynamics

Atom Simulator — Interactive

RealQM for atoms as shell system in spherical symmetry. Choose electron configuration and run.

Results table (Li–Rn) — click to show

Atom	Z	Shells	Computed	Observed
Li	3	(2)+1	−7.55	−7.48
Be	4	(2)+(2)	−15.14	−14.57
B	5	(2)+(2+1)	−25.3	−24.53
C	6	(2)+(2+2)	−38.2	−37.7
N	7	(2)+(3+2)	−55.3	−54.4
O	8	(2)+(3+3)	−75.5	−74.8
F	9	(2)+(3+4)	−99.9	−99.5
Ne	10	(2)+(4+4)	−132.4	−128.5
Na	11	(2)+(4+4)+(1)	−165	−162
Mg	12	(2)+(4+4)+(2)	−202	−200
Al	13	(2)+(4+4)+(2+1)	−244	−243
Si	14	(2)+(4+4)+(2+2)	−291	−290
P	15	(2)+(4+4)+(3+2)	−340	−340
S	16	(2)+(4+4)+(4+2)	−397	−399
Cl	17	(2)+(4+4)+(3+4)	−457	−461
Ar	18	(2)+(4+4)+(4+4)	−523	−526
Ca	20	(2)+(4+4)+(8)+(2)	−670	−680
Ti	22	(2)+(4+4)+(10)+(2)	−848	−853
Cr	24	(2)+(4+4)+(12)+(2)	−1039	−1050
Fe	26	(2)+(4+4)+(14)+(2)	−1260	−1272
Ni	28	(2)+(4+4)+(16)+(2)	−1516	−1520
Zn	30	(2)+(4+4)+(18)+(2)	−1773	−1795
Ge	32	(2)+(4+4)+(18)+(2+2)	−2089	−2097
Se	34	(2)+(4+4)+(18)+(4+2)	−2416	−2428
Kr	36	(2)+(4+4)+(18)+(4+4)	−2766	−2788
Xe	54	(2)+(4+4)+(18)+(18)+(4+4)	−7355	−7438
Rn	86	(2)+(4+4)+(18)+(32)+(18)+(4+4)	−22800	−23560

Energy in Hartree. Up to 6 shells, Z=2–86.

Molecule Simulator — Interactive

WebGPU simulation with built-in atom placement. Molecules, proteins, dynamics.

Helium — Original p5.js Template

3 lines of code for update of electron densities u, electron potentials P and free boundary level set w:

u += ½d·∇·(w∇u) + dt·(K-2P)·u·w  // ITP eigensolve
P += dt·(ΔP + 2π·u²)              // Poisson solve
w += dt·|c|·Δw + dt·c·|∇w|        // front tracking

He ground state: E = −2.92 Ha (exact −2.904). Two non-overlapping electron densities in half-spaces meeting at a plane through the kernel.

Benchmarks — Atoms, Molecules & Protein Folding

From H&sub2; bond curve vs Kolos-Wolniewicz to 153-residue Myoglobin fold. Full results table.

Protein Folding

RealQM vs AlphaFold2

What AlphaFold2 cannot:
• Predict protein–protein docking from physics (it uses learned patterns, not forces)
• Handle drug–protein binding (no concept of non-protein molecules)
• Model chemical reactions (bond breaking/forming)
• Simulate phase changes (ice melting, water dynamics)
• Account for solvent effects (explicit water molecules in the simulation)
• Work with non-standard chemistry (metals, modified residues, novel molecules)

What RealQM has shown:
• Protein folding: 7 proteins from 20 to 153 residues — all-α (Trp-cage, Villin, Myoglobin 153 res), all-β (WW domain), α+β (Crambin, GB1, Ubiquitin). H-bonds converge to 1.5–2.4 Å, disulfides to 5.4–5.6 Å.
• Drug binding: acetaminophen forms H-bond to protein at 2.07 Å (drug binding)
• DNA double helix: 10 bp full B-DNA turn, all Watson-Crick H-bonds stable without water — H-bonds alone hold the helix (helix)
• DNA mismatch detection: G:C correct (2.07 Å) vs G:T wobble (2.62 Å) — QM distinguishes right from wrong base pairing (mismatch)
• Protein–protein docking: coiled-coil and insulin docking, blind, water-mediated (coiled-coil, insulin)
• H-bond physics: formamide H···O=2.04 Å, water dimer O–O=2.95 Å (formamide, water)
• Nucleic acids: RNA hairpin stem G1:C12=1.99 Å (RNA hairpin)
• Phase change: ice O–O=2.73 Å, melting dynamics (ice, melting)
• Proton transfer: HF + H&sub2;O → F&supmin; + H&sub3;O&sup+; (Ht–O=0.99 Å) and HCl + NH&sub3; → Cl&supmin; + NH&sub4;&sup+; (Ht–N=0.97 Å) — acid pushes, base pulls, driven by electron density forces (HF, HCl+NH&sub3;)
• Ion formation: free electron captured by +3 Cl kernel into 4th quadrant — Cl&supmin; forms with 4 electrons in quadrant domains (Cl&supmin; formation)
• Salt dissolution: NaCl + H&sub2;O — water pulls Na&sup+; from Cl&supmin;, ionic bond stretches from 2.36 to 2.84 Å (NaCl)
• Enzyme catalysis: serine protease catalytic triad Asp&supmin;→His→Ser proton relay — electron density forces drive each step (triad)
• Bond breaking: H + H&sub2; → H&sub2; + H exchange (reaction)
• Metallic bonding: Li lattice restores from perturbation (Li metal)

Open challenges: blind folding (without contact biases), full Watson-Crick 3-H-bond alignment from distance, and long-range force accuracy (Poisson convergence).

What drives folding? H-bonds vs water

Polyglycine hairpin (no side chains): folds from 150° → 105° in vacuum via quantum N–H···O=C hydrogen bonds alone. Adding explicit water does not improve folding — both dry and solvated converge to the same angle.
Chignolin GYDPETGTWG (real side chains): unfolds in vacuum — side-chain electron repulsion overwhelms backbone H-bonds. Adding implicit hydrophobic pressure (SASA) fixes this: folds from 135° → 40°.

Conclusion: Our solver captures H-bond driven secondary structure without empirical force fields. But the hydrophobic effect — which is entropic (water loses orientational freedom near hydrophobic surfaces) — cannot emerge from electronic energy alone. For real proteins with side chains, an implicit solvent term (SASA) is needed.

The working recipe: H-bond biases (i→i+4 for helices, interstrand for sheets) handle secondary structure. SASA (one parameter: γ=5.0) handles tertiary packing — replacing all hand-tuned native contacts across every protein below. No explicit water molecules needed.

▶ Side-by-side comparison

Hairpin Folding (dry)

150° → 105° via quantum H-bonds alone. Water does not improve folding.

protein

Chignolin Folding (SASA)

GYDPETGTWG 135° → 40° — quantum H-bonds + implicit hydrophobic pressure.

▶ Run · ▶ Video

protein

Hairpin vs Chignolin

Side chains need hydrophobic pressure to fold — backbone H-bonds alone are not enough.

protein

Trp-cage (20 res)

H-bond biases + SASA packing. Helix forms, Trp6 buries without native contacts.

▶ Run · ▶ Video

protein

Villin HP35 (35 res)

3-helix bundle. H-bond biases + SASA packs 3 helices without native contacts.

▶ Run · ▶ Video

protein

WW Domain 1PIN (34 res)

All-β fold. H-bond biases + SASA. No native hydrophobic contacts.

▶ Run · Initial · Result

protein

Crambin 1CRN (46 res)

α+β fold. H-bond biases + SASA. 3/5 H-bonds form, disulfides approach target.

▶ Run

protein

GB1 (56 res)

α+β fold. H-bond biases + SASA. No native hydrophobic contacts.

▶ Run · Result

protein

Ubiquitin (76 res)

76 residues. H-bond biases + SASA. No native hydrophobic contacts.

▶ Run · ▶ Video

protein

Myoglobin 1MBN (153 res)

Largest: 153 residues, 8 helices. H-bond biases + SASA. No native contacts.

▶ Run · Initial · Result

protein

Drug Binding (Acetaminophen)

Drug-OH···protein C=O H-bond at 2.07 Å. Protein stays folded (H-bonds 2.4–2.6).

▶ Run · Result

drug

Coiled-Coil Docking

Blind helix-helix docking, water-mediated

proteindocking

Insulin A+B Docking

21+30 res, blind chain docking

proteindocking

DNA Double Helix (10 bp)

Full B-DNA turn. All H-bonds stable (min 2.35 Å) — without water. H-bonds alone hold the helix.

▶ Run · Result · G:C pair

DNA

DNA Mismatch Detection

G:C correct (2.07 Å) vs G:T mismatch (2.62 Å) — QM distinguishes right from wrong base pairing.

▶ Run · Result

DNA

Atoms

Single atoms, ions, and excited states. Energy convergence tests compared against published Hartree-Fock and exact reference values.

H atom

1 electron · 200³ grid

Single hydrogen. Exact: −0.500 Ha

atom

He atom

2 electrons · 200³ / 5 au

1s². HF: −2.862 Ha, exact: −2.904 Ha

atom

Li+ ion

Z=3, 2 electrons · 200³ / 10 au

He-like 1s². HF: −7.236 Ha, exact: −7.280 Ha

atom

Li atom

Z=3, 3 electrons · 200³ / 10 au

1s² 2s¹ shell init. HF: −7.433 Ha, exact: −7.478 Ha

atom

Helium Excitation: Ground State to Orthohelium

Three-phase simulation of He excitation from ground state (E=−2.90 Ha) to orthohelium (E=−2.2 Ha):

Phase 1 (steps 0–5000): Two electrons in half-space split share a +2 kernel. Boundary frozen — electrons converge to He ground state with E≈−2.90 Ha.
Phase 2 (steps 5000–10000): Boundary unfreezes, charge asymmetry Z=[1.01, 0.99] perturbs the system. One electron contracts inward, the other expands outward — the half-space split transitions toward a 2-shell (1s+2s) structure.
Phase 3 (steps 10000+): Charges restored to Z=[1,1]. The orthohelium shell structure persists at E≈−2.2 Ha — the metastable excited state is self-sustaining.

Key insight: A tiny perturbation (1% charge asymmetry) is enough to break half-space symmetry and drive the transition to a qualitatively different electronic state. The shell structure, once formed, is stable without the perturbation.

▶ Run · ▶ Orthohelium (direct) · ▶ Orthohelium (atom.js)

atomexcitation

Molecules

Static electron density calculations and nuclear dynamics on 200³ grids.

X2 homonuclear — Binding vs r_c

One-valence-electron model (Z=1, varying pseudopotential r_c). E_bind = E(R_min) - E(R=6).

r_c	RealQM D_e (Ha)	RealQM (eV)	Real atom	Exp D_e (Ha)	Exp (eV)
0.0	−0.1543	−4.20	H2	−0.1745	−4.75
0.3	−0.0609	−1.66	—	—	—
0.4	−0.0561	−1.53	—	—	—
0.5	−0.0561	−1.53	Li2	−0.039	−1.05
0.6	−0.0490	−1.33	—	—	—
0.65	−0.0201	−0.55	—	—	—
0.7	−0.0163	−0.44	—	—	—
0.8	−0.0100	−0.27	Na2	−0.027	−0.73

200³ grid, 10 au screen, sweep R=2–6 au. Binding weakens with r_c, consistent with alkali trend (H2 → Li2 → Na2).

X2 sweep

X2 (+2 kernel) — Split-electron model vs r_c

Each X = +2 kernel with 2 valence electrons in separate halfspaces outside inner shell radius r_c. E_bind = E(R=3) − E(R=6).

r_c	E(R=3)	E(R=6)	E_bind (Ha)	E_bind (eV)	Real molecule	Exp (eV)
0.0	—	—	—	—	He2	−0.0009
0.3	−10.12	−10.05	−0.07	−1.9	—	—
0.5	−8.09	−7.90	−0.19	−5.2	O2	−5.2
0.8	−6.40	−6.15	−0.25	−6.8	—	—

Comparison: split vs non-split electron model

Model	r_c	E_bind (Ha)	E_bind (eV)	Exp (eV)
Split (4 domains)	0.5	−0.19	−5.2	−5.2
Split (4 domains)	0.8	−0.25	−6.8	−5.2
Non-split (2 domains)	0.5	−0.43	−11.7	−5.2
Non-split (2 domains)	0.8	−0.47	−12.8	−5.2

150³ grid, 15 au screen, 5000 steps, free boundary. Split model with r_c=0.5 matches O2 exactly. Non-split overbinds by ~2.5x. r_c=0 corresponds to He2 (essentially unbound).

X2 split

H2 bond sweep

R = 1.0–6.0 au. Live comparison vs Kolos-Wolniewicz.

small molecule

H2O

Single water molecule

small moleculewater

CO2

Carbon dioxide

small molecule

NH3

Ammonia (3D geometry)

small molecule

H2CO

Formaldehyde

small molecule

HNO

Nitroxyl

small molecule

LiH

Lithium hydride

small molecule

Ethanol

CH3CH2OH

small molecule

Caffeine

C8H10N4O2 + water shell

small molecule

Camphor

C10H16O bicyclic terpenoid

small molecule

Materials

Water clusters, ice, metallic bonding, and phase transitions.

Formamide Dimer

H···O=2.04 Å. The peptide H-bond.

foundation

Water Dimer

H···O=1.87, O-O=2.95 Å

water

Ice Ic Crystal

216 molecules, O-O=2.73 Å

ice

Ice Melting — Temperature Sweep

Slider 0–2000 K. O-O = 2.75 Å at 0 K (exp 2.76). Melting at ~300 K (exp 273). Liquid H-bonds form/break dynamically at 500 K (O-O 2.74–3.26 Å).

dynamicsphase transition

Li Metal (100 atoms)

Lattice restores from perturbation

dynamics

Chemical Reactions

Proton transfer, ion formation, salt dissolution, enzyme catalysis, and bond breaking — driven by electron density forces.

Proton Transfer: Acid Pushes, Base Pulls

Four reactions that reveal the difference between StdQM (energy bookkeeping) and RealQM (forces):

Test 1: HF + H&sub2;O → F&supmin; + H&sub3;O&sup+;
StdQM: Compare pKa(HF)=3.2 vs pKa(H&sub2;O)=15.7. ΔG<0, so equilibrium favors products. Proton tunnels through an activation barrier. Transition state theory gives the rate. The reaction happens because the free energy is lower on the product side.
RealQM: Ionic decomposition: F&supmin; (+3 kernel, 4 electrons split into 2 half-spaces, r_c=1.0) repels the bare proton H&sup+; (0 electrons), while O’s lone pair (Z=2, r_c=0.8) pulls it in. Result: Ht–O=0.99 Å (covalent), F–Ht=1.91 Å (released) at 2.4 Å contact.

Test 2: HCl + NH&sub3; → Cl&supmin; + NH&sub4;&sup+;
StdQM: pKa(HCl)=−7 (strong acid), pK_b(NH&sub3;)=4.75 (strong base). Compute the potential energy surface, find the minimum energy path. Proton transfer is nearly barrierless in gas phase. The outcome is predicted by comparing energy states.
RealQM: Ionic decomposition: Cl&supmin; (+1 kernel, 2 electrons split into half-spaces, r_c=1.0) repels the bare proton H&sup+; (0 electrons), while N’s lone pair (Z=3, r_c=0.5) pulls it in. Forces drive the motion. Result: Ht–N=0.97 Å (covalent), Cl–Ht=1.53 Å (released) at 2.1 Å contact.

Test 3: NaCl + H&sub2;O → Na&sup+;(aq) + Cl&supmin;(aq)
StdQM: Lattice energy (786 kJ/mol) vs hydration enthalpy of Na&sup+; (−406 kJ/mol) + Cl&supmin; (−363 kJ/mol). ΔG_solvation<0, so the salt dissolves. Born model computes ion solvation energies. The outcome is predicted by comparing lattice vs solvation energies.
RealQM: Na&sup+; (+1 kernel, 0 electrons) and Cl&supmin; (+1 kernel, 2 electrons split). Water’s O lone pair creates a force pulling Na&sup+; away from Cl&supmin;. No energy bookkeeping. Result: Na–Cl stretches from 2.36 to 2.84 Å, Na–O shrinks to 1.99 Å.

Test 4: Enzyme catalysis — Serine Protease Triad
StdQM: Asp&supmin; stabilizes His via electrostatics, lowering Ser–OH pKa from ~13 to ~7. Proton hops when the free energy landscape permits. Transition state theory gives the rate.
RealQM: Asp&supmin; (O&supmin;, 2 electrons) pushes H1 toward His N (+3 kernel, r_c=0.5). His then pulls H2 from Ser O, creating the O&supmin; nucleophile. Two proton transfers in sequence, driven by local electron density forces. No energy computation needed.

The key difference: StdQM predicts whether a reaction occurs by comparing energy states. RealQM shows how it occurs through forces. Nature doesn’t keep a record of energy or look up pKa tables. Nature acts through forces — local, instantaneous forces between electrons and nuclei. RealQM does what nature does.

▶ HF + H&sub2;O · ▶ HCl + NH&sub3; · ▶ NaCl + H&sub2;O · ▶ Cl&supmin; formation · ▶ Enzyme triad

reaction

H + H&sub2; Bond Breaking

Exchange reaction through H&sub3;

dynamics

Nuclear Physics

RealQM applied to atomic nuclei: protons and electrons as charged density domains interacting via Coulomb forces. The old proton-electron model of the nucleus (4 protons + 2 electrons = He-4, total charge +2) revisited with modern computational methods.

RealQM for the Atomic Nucleus

The atomic nucleus is modeled as a system of oppositely charged density distributions: an inner electron kernel (2 domains, charge −1 each) surrounded by an outer proton shell (4 domains, charge +1 each), interacting through Coulomb attraction/repulsion alone. A happy marriage: electrons confine protons (attractive well) while protons confine electrons (potential box). With only 1 electron (charge −1), the attraction is too weak to bind 4 protons — proving that 2 electrons are essential. The e-p boundary is fixed at radius R, with energy minimized over R. Key features:

• Mutual confinement: electrons attract protons inward, protons attract electrons outward — neither species is confined by an external potential
• Signed Poisson: charge-weighted density gives attractive potential between opposite charges, repulsive within same charge
• Per-domain mass: Laplacian coefficient ∝ 1/mass for different kinetic energy scales
• Energy sweep: automated R scan plots E(R), T(R), V(R) to find the binding minimum

Generalisation to stable nuclei: In the proton-electron model, a neutron = proton + electron. A nucleus with Z protons and N neutrons contains (Z+N) protons and N electrons. Stable nuclei have N ≈ Z, giving about twice as many protons as electrons. For He-4: Z=2, N=2 → 4 protons + 2 electrons, as modeled here. The 2:1 proton-to-electron ratio is key to binding — with only 1 electron (charge −1 vs +4), binding fails.

RealQM for the Atomic Nucleus (PDF) · Blog