Tovacian Chemistry: The Quaternion Periodic Chart, Placement on the Clifford Torus, the Golden Construction, and the Configuration Rules

Tovacian Chemistry builds the elements, their bonds and their nuclei from one algebra: A. L. Baker's quaternions, the five-member unit set {0, s, i, j, k} of the author's Quaternion Periodic Chart, and the orthogonal charge bond F = Rc e^2 / 4r^2 set on a Clifford torus. The central result is a placement law with no fitted quantity. If n equal transmutations close a shell, the shell versor is U_n = cos(360°/n) + ε sin(360°/n), and block l of shell n sits on the torus at θ(n, l) = (l - 1) · 360°/n; its reach is floor(|sec θ|) - 1. With this placement and ten configuration rules written only in cos θ, sec θ and unit counts, the ground configurations of all 30 d-block elements, their 30 singly and 30 doubly charged ions, and all 28 f-block elements are reproduced, the anomalous ones included (Cr, Cu, Nb, Mo, Ru, Rh, Pd, Ag, Pt, Au, La, Ce, Gd, Ac, Th, Pa, U, Np, Cm, Lr). The rules were assembled with the data in view and are now frozen; the first test of the frozen set on unseen data (f-block cations) failed by one ion. The secants of the block angles are exactly the lengths of the author's golden construction (Figure 24.4): e^0 for 4f, X = 2/Φ for 5f, 2 for 3d and 6d, and 2Φ for 5d, and their product 2Φ · 2/Φ = 2^2 is the power of a point on that figure. The rational blocks are exactly the shells for which cos(360°/n) is rational (n ∈ {1, 2, 3, 4, 6}, Niven); shell 5 gives the golden blocks. The same algebra passed registered tests elsewhere in chemistry: A zero energy step at the start of each second pass (6/6 ionization series) The residual of that step on electron affinities (3/3) The second-pass dip in every d and f block tested (3d, 4d, 4f, 5d, 5f) The O–H hydrogen bond (17/17 liquids within 6%) The α-helix from a 2.90 Å hydrogen bond The odd–even alternation of nuclear neutron separation energies (57/57)