vibe-qc/Documentation

Slab solvation and electronic hosts

Design investigation. Treat the surface atoms, adsorbate and any explicit first-layer solvent molecules as one electronic system. Repeat the cell in two directions, leave the surface normal open, and let a dielectric polarize outside the solvent-accessible boundary. Electrons can redistribute between the adsorbate and substrate. The same boundary problem should accept either an ab initio or a semiempirical description of that combined solute.

Existing pieces and missing capabilities

Electronic host	What exists	Next development
Conventional slab	True dim=2 Parry electrostatics and a closed-shell slab GDF route. The direct slab route can run semilocal RKS. The third lattice vector is bookkeeping.	Use a neutral, closed-shell PBE slab as the first electronic host and as the ab initio control for later routes. Add SCF reaction-field coupling.
PBC-BIPOLE	The public driver requires three periodic directions. Its exact Ewald-J split and lattice/self conventions assume bulk periodicity.	Qualify a dry two-dimensional BIPOLE Hamiltonian first. Reuse the slab nuclear, electron-nuclear and Hartree operators where compatible. Derive and test the near/far split, multipoles, self terms and cutoff convergence in that convention. Start with semilocal RKS; HF and hybrids also require a qualified slab exchange treatment at the requested k mesh.
AICCM (experimental)	All four public variants require dim=3. There is a scalar slab Green function and a low-dimensional wire SCF. The slab four-centre construction is still a separate problem.	Choose one construction first, for example neutral real-Gamma with two cyclic directions. Build the open-normal Hamiltonian and its AO-pair contractions; verify per-cell normalization and convergence with the in-plane torus. Keep the chi and weighted four-centre variants separately qualified.
MSINDO CCM2D (experimental)	An existing water/MgO adsorption example, a dry two-vector cyclic Hamiltonian, and a molecular COSMO provider with distributed multipoles and two-centre penetration.	Periodize that potential map and its transpose in the CCM density and Wigner-Seitz weighting convention. Couple the field inside the SCF. Use a parameterized ionic oxide. MSINDO is outside its documented domain for metallic bonding.

See the slab route guide, AICCM variant matrix, low-dimensional kernel derivation, section 9, and MSINDO surface example. Other semiempirical methods need adapters for their own energy variables. For example, an SCC-DFTB adapter would differentiate the reaction energy through its population and overlap convention. A monopole substitution would change the existing MSINDO model.

Shared boundary and electronic coupling

1. Define the physical interface. Start at fixed electron number with a neutral, finite-thickness slab. Derive the normal from the two lattice vectors and specify which face contacts liquid. For a top-only interface use vacuum below the slab; for an immersed film expose both faces. Record the far-field conditions on each side. Define the cavity from the union of slab, adsorbate and explicit waters including lateral neighbours. Assign each surface element once per cell. Identify liquid accessible from the designated reservoir across periodic seams. Exclude buried voids and slab interiors; retain a pore connected to that reservoir when it is physically accessible. A cut on atom height alone cannot distinguish an overhang, a wetted sidewall and a sealed pocket.

2. Build the periodic surface operator. Extend the geometric iSwiG cavity and the single-layer operator first. Keep point and Gaussian kernels, self terms, radii and switching conventions explicit. The molecular native MOIST builder uses distances between sites of a finite molecule; repeating those sites a few times does not define a periodic Coulomb solve. Use in-plane lattice sums with an open normal for the surface-surface, core-surface and electron-surface interactions. For a cell of area A, a nonzero in-plane Fourier mode of the bare kernel is proportional to exp(-|G| |z-z’|)/|G|. The zero mode is -(2 pi/A)|z-z’| up to a gauge constant. Convolve consistently for Gaussian sites. Preserve the physical potential step of a neutral polar slab. Define net induced charge and potential references from the chosen boundary problem, including the connectivity of the two liquid regions. In particular, derive the liquid/vacuum asymmetry for a wet top and dry back before reusing a closed molecular conductor constraint. Test conductor and finite-dielectric limits separately.

3. Connect potential and energy. At a given density, supply the total core-plus-electron potential at the surface and return the complete derivative of the environment energy in the host representation. For ab initio k-point SCF this is a Hermitian AO operator at each k, from the spin-summed density with k weights. Verify the adjoint with arbitrary Hermitian density variations, including complex off-diagonal entries. For cyclic hosts, do the same check with their image multiplicities and energy per cell. Add the field during SCF and converge it with the density. If the host energy already includes the applied one-electron operator in full, subtract its actual applied density contraction once and add the environment functional. Keep the dry Hamiltonian and its Coulomb energy intact. Derive forces from that same total, starting with fully reconverged central differences.

4. Add models in order. Provide slab COSMO and the native MOIST CPCM/iSwiG recipe with their respective dielectric scaling conventions. Share operators wherever the discretizations are identical. The molecular external MOIST interface remains a molecular-limit reference. Running external MOIST on a slab would also require a verified periodic upstream operator/API. Add SvdW-DROP, then isodensity-DROP after implementing periodic projection and the moving-boundary contribution to the Fock matrix. Each further PCM needs its own operators and energy adjoints. LPB adds ionic screening and ion accessibility. PV/GOSTSHYP need a defined per-area or excess volume/work reference at an open interface. For charged electrodes or constant potential, specify physical countercharge, ionic reservoirs, electrode potential reference and the thermodynamic ensemble before enabling the route.

Demonstration and acceptance

An exact numerical target before SCF. In a square 12 by 12 bohr cell place charges +1 and -1 at (0,0,2) and (3,0,2) bohr above an ideal grounded plane at z=0. The induced energy per cell, including the one-half charging factor and excluding the direct energy of the real charges, is G2D((3,0),4) - G2D((0,0),4) = -0.0405866692359 hartree. It follows by reflecting each source across the interface with opposite sign. The scalar kernel gives this value at reciprocal half-widths 32 and 64. A separate square-shell real-space sum of the reflected charges, extrapolating its leading inverse-width tail from half-widths 200 and 400, gives -0.0405866693911 hartree. This is a reference for the future surface solver. For the exact planar dielectric problem multiply the conductor answer by (epsilon-1)/(epsilon+1) when the charges sit in vacuum. Judge an empirical COSMO scaling by its own stated approximation. The neutral lateral pair cancels the sheet mode, so add a separate normal dipole-sheet test with a known potential jump and zero external field.

First chemical case. Reuse the fixed water/MgO(100) coordinates. Run dry and solvated semilocal RKS and experimental MSINDO CCM2D at the same geometry, coverage, wet face and cavity conventions. A symmetric two-face control separates dipole errors from cavity errors; qualify the one-face adsorbate explicitly. Record energies, induced charge per face and the plane-averaged potential through the solid and into the liquid. Reuse the in-tree dry results as regression controls. Compare dry periodic energies with CRYSTAL where the Hamiltonian matches; compare wet electrostatics with a periodic implementation such as BAND COSMO where radii, surface discretization and dielectric convention can be matched. A different cavity is a model comparison. Require invariance to bookkeeping cell height, lateral wrapping and rigid translations. Replicating the entire decorated cell at fixed coverage must preserve the per-adsorbate result. Increasing area while keeping one molecule changes coverage and is a separate physical convergence study. Check slab thickness, k mesh, surface grid and solvent-accessibility convergence.

Suggested initial engineering targets are 1e-6 hartree per cell on the flat conductor fixture after surface refinement, 1e-7 hartree in a normalized directional density derivative on a step-size plateau, and 1e-5 hartree/bohr in a reconverged force component. For an application, set an accuracy budget before the run; a useful starting proposal is 0.01 eV per adsorbate on the solvent shift under numerical refinement at fixed coverage. These are proposed criteria. The point-charge reference above is the only new numerical result in this investigation.

For adsorption from solution, compute the electronic contribution E_wet(slab+X) - E_wet(slab) - E_solution(X) with consistent conventions. Compare it with the dry adsorption cycle using E_gas(X). Divide by the number adsorbed when a symmetric cell contains two adsorbates. Report the fixed-geometry solvent shift separately from relaxation, thermal and standard-state contributions. For water taken from bulk liquid, a physical adsorption free energy requires the liquid chemical potential. For site or orientation preferences a same-stoichiometry difference cancels that reservoir term. Once the neutral oxide tests pass, reproduce a published metal/solution case with a qualified metallic host, k mesh and occupations.

Primary references and comparison tools. Delley, periodic COSMO, methods and surface examples provides a periodic surface discretization precedent. Andreussi and Marzari, periodic electrostatics in solution treat boundary conditions and solvent-dependent periodic corrections. BAND COSMO documents a top-side solvent option. Steinmann, Sautet and Michel compare continuum and explicit-solvent descriptions for adsorbates on Ru(0001), including competing binding modes of levulinic acid.