Claes Johnson
KTH Royal Institute of Technology, Stockholm, Sweden
claesjohnson@gmail.com

To Dr. Felix Plasser, Handling Editor
International Journal of Quantum Chemistry

Dear Dr. Plasser,

Thank you for your letter and for the invitation to resubmit the manuscript
"A 3D Multiphase Continuum Computational Model for Atoms." I am grateful for
your openness to new ways of viewing quantum mechanics, and I have revised the
manuscript to comply with the author guidelines. Please assign this
resubmission to you as handling editor, as you kindly offered.

REVISIONS IN RESPONSE TO YOUR LETTER

- Abstract. Rewritten and shortened from ~460 to 148 words, within the
  recommended length. It now contains no bold-face elements and no numerical
  literature references, and is fully self-contained.

- Introduction and context (your question). Following your suggestion, I have
  added a paragraph placing the work in the context of the standard
  atomic-structure literature -- correlated non-relativistic wave-function
  methods for the light atoms, relativistic Dirac-Fock for the heavy ones, and
  density-functional and real-space approaches for large-scale work, alongside
  tabulated experimental values -- with the corresponding citations added to
  the bibliography (Hohenberg-Kohn; Kohn-Sham; Szabo-Ostlund; Clementi-Roetti;
  Desclaux; Chakravorty et al.; Beck; NIST ASD). The paragraph states plainly
  what the present uniform, parameter-free test can and cannot establish
  relative to those specialized, higher-accuracy treatments: not competitive
  accuracy on any one atom, but structural correctness across the whole table
  from a single scheme.

- Guidelines. The manuscript has been checked against the IJQC author
  guidelines for structure, formatting, and references.

THE WORK

RealQM is a general, in-principle parameter-free, low-cost real-space method
for quantum mechanics, formulated as 3D continuum mechanics: the N-electron
state is a sum of one-electron components, each carrying unit charge on a
non-overlapping domain of physical 3D space separated by free (Bernoulli)
boundaries, with the ground state the minimizer of the standard Coulomb energy
over both the components and the domain partition. Spatial exclusion replaces
wave-function antisymmetry, so cost scales with the number of mesh points
rather than with the dimension of an N-body configuration space, and the
energy functional contains no fitted constants.

The paper applies the method to a stringent, uniform test: one code computes
the total energies and first ionization energies of all the atoms of the
periodic table, in spherical symmetry, covering the whole table in about a
minute on a laptop. Total energies come within about 1-2% across the table;
first ionization energies within 10-20% for the s-block and heavier p-block;
the closed octet is realized geometrically as 4+4 (two tetrahedra), never a
single eight-shell; and the ionization ordering is correct throughout,
including 4s before 3d across the transition series. The organizing finding is
one of symmetry: inner shells and most valence shells are spherically
symmetric and captured exactly, and only two valence geometries -- the closed
octet and the interpenetrating 4s/3d valence -- break spherical symmetry and
require the full 3D solve. The limits of the spherically reduced model are
stated plainly, so the method is presented as a falsifiable, reproducible
scheme rather than a finished theory. All source code, the validation, and an
interactive gallery are public at the URLs in the manuscript; referees are
encouraged to re-run the periodic table for themselves.

SUGGESTED REFEREES

The scientific content spans real-space electronic-structure methods, atomic
structure and ionization energies, and the applied mathematics of variational
free-boundary problems. Suitable referees would have expertise in one or more
of:
  - real-space / finite-difference or finite-element electronic-structure
    methods;
  - atomic structure and ionization energies (Hartree-Fock, DFT, or correlated
    methods);
  - variational and free-boundary / PDE methods in applied mathematics.

DECLARATIONS

The manuscript is original, has not been published previously, and is not
under consideration elsewhere. The author has no conflicts of interest. In the
interest of transparency, the numerical implementation was developed with the
assistance of an AI coding assistant (Claude, Anthropic); the mathematical
formulation and all scientific claims are the author's own.

Thank you for considering this resubmission.

Sincerely,
Claes Johnson
KTH Royal Institute of Technology, Stockholm, Sweden