The electrochemical hydrogen evolution reaction (HER) is growing in significance as society begins to rely more on renewable energy sources such as wind and solar power. Thus, research on designing new, inexpensive, and abundant HER catalysts is important. Here, we describe how a simple experiment combined with results from density functional theory (DFT) can be used to introduce the Sabatier principle and its importance when designing new catalysts for the HER. We also describe the difference between reactivity and catalytic activity of solid surfaces and explain how DFT is used to predict new catalysts based on this. Suited for upper-level high school and first-year university students, this exercise involves using a basic two-cell electrochemical setup to test multiple electrode materials as catalysts at one applied potential, and then constructing a volcano curve with the resulting currents. The curve visually shows students that the best HER catalysts are characterized by an optimal hydrogen binding energy (reactivity), as stated by the Sabatier principle. In addition, students may use this volcano curve to predict the activity of an untested catalyst solely from the catalyst reactivity. This exercise circumvents the complexity of traditional experiments while it still demonstrates the trends of the HER volcano known from literature.

We derive an expression for the electron to nucleon mass ratio from a reinterpreted lattice gauge theory Hamiltonian to describe interior baryon dynamics. We use the classical electron radius as our fundamental length scale. Based on expansions on trigonometric Slater determinants for a neutral state a specific numerical result is found to be less than three percent off the experimental value for the neutron. Via the exterior derivative on the Lie group configuration space u(3) we derive approximate parameter free parton distribution functions that compare rather well with those for the u and d valence quarks of the proton.

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The Higgs mass value is derived from a Hamiltonian on the Lie group U (3) where we relate strong and electroweak energy scales. The baryon states of nucleon and delta resonances originate in specific Bloch wave degrees of freedom coupled to a Higgs mechanism which also gives rise to the usual gauge boson masses. The derived Higgs mass is around 125 GeV. From the same Hamiltonian, we derive the relative neutron to proton mass ratio and the N and Delta mass spectra. All compare rather well with the experimental values. We predict scarce neutral flavor baryon singlets that should be visible in scattering cross-sections for negative pions on protons, in photoproduction on neutrons, in neutron diffraction dissociation experiments and in invariant mass spectra of protons and negative pions in B-decays. The fundamental predictions are based on just one length scale and the fine structure constant. More particular predictions rely also on the weak mixing angle and the up-down quark flavor mixing matrix element. With differential forms on the measure-scaled wave function, we could generate approximate parton distribution functions for the u and d valence quarks of the proton that compare well with established experimental analysis.

We present a hamiltonian structure on the Lie group u(3) to describe the baryon spectrum. The ground state is identified with the proton. From this single fit we calculate approximately the relative neutron to proton mass shift to within half a percentage of the experimental value. From the same fit we calculate the nucleon and delta resonance spectrum with correct grouping and no missing resonances. For specific spin eigenfunctions we calculate the delta to nucleon mass ratio to within one percent. Finally we derive parton distribution functions that compare well with those for the proton valence quarks. The distributions are generated by projecting the proton state to space via the exterior derivative on u(3). We predict scarce neutral flavour singlets which should be visible in neutron diffraction dissociation experiments or in invariant mass spectra of protons and negative pions in B-decays and in photoproduction on neutrons. The presence of such singlet states distinguishes experimentally the present model from the standard model as does the prediction of the neutron to proton mass splitting. Conceptually the Hamiltonian may describe an effective phenomenology or more radically describe interior dynamics implying quarks and gluons as projections from u(3) which we then call allospace.

Baryons are described by a Hamiltonian on an intrinsic U(3) Lie group configuration space with electroweak degrees of freedom originating in specific Bloch wave factors. By opening the Bloch degrees of freedom pairwise via a U(2) Higgs mechanism, the strong and electroweak energy scales become related to yield the Higgs mass 125.085+/-0.017 GeV and the usual gauge boson masses. From the same Hamiltonian we derive both the relative neutron to proton mass ratio and the N and Delta mass spectra. All compare rather well with the experimental values. We predict neutral flavour baryon singlets to be sought for in negative pions scattering on protons or in photoproduction on neutrons and in invariant mass like Σ + c (2455)D − from various decays above the open charm threshold, e.g. at 4499, 4652 and 4723 MeV. The fundamental predictions are based on just one length scale and the fine structure coupling. The interpretation is to consider baryons as entire entities kinematically excited from laboratory space by three impact momentum generators, three rotation generators and three Runge-Lenz generators to internalize as nine degrees of freedom covering colour, spin and flavour. Quark and gluon fields come about when the intrinsic structure is projected back into laboratory space depending on which exterior derivative one is taking. With such derivatives on the measurescaled wavefunction, we derived approximate parton distribution functions for the u and d valence quarks of the proton that compare well with established experimental analysis.

We find an expression for the Cabibbo angle from quark flavour generators of the first two generations. The flavour generators operate on the toroidal components in an intrinsic dynamics for colour degrees of freedom. The generators have led to parton distributions for u and d valence quarks of the proton that compare well with those derived from experiment. The present result 0.974996 . . . for the cosine of the Cabibbo angle compares rather well with the experimentally established value for the up-down quark mixing element 0.97420+/−0.00021 of the Cabibbo-Kobayashi-Maskawa matrix.

We create quarks from baryons in stead of constituting baryons from quarks. The quantum fields of QCD are generated via the exterior derivative (momentum form) of baryon wave functions on an intrinsic configuration space, the Lie group U(3). Local gauge transformations correspond to coordinate translations in the intrinsic space. A proton spin structure function and a proton magnetic moment are derived. We show how the spectrum of unflavoured baryons, the N and Delta resonances, can be understood from a mass Hamiltonian on the intrinsic space and note how our model resolves the problem of colour confinement. We calculate an approximate value for the relative neutron-to-proton mass shift and give an exact value for the neutron mass. We predict neutral charge singlets that may be interpreted as neutral pentaquarks at LHCb.