| 1. Domain | 1.1 Scope of the Domain | Boundaries | The range of phenomena the science includes and excludes. | Studies atoms, molecules, ions, and electrons using quantum mechanics; excludes classical models unable to represent wavefunctions or quantization. |
| | Scale | The spatial, temporal, or organizational level at which the science operates (e.g., quantum, cellular, social, cosmic). | Operates at atomic and molecular scales: electron densities, orbitals, nuclear geometries, vibrational and electronic transitions. |
| 1.2 Ontological Commitments | Entities | The kinds of things assumed to exist within the domain (particles, organisms, agents, fields, etc.). | Wavefunctions, electrons, nuclei, atomic/molecular orbitals, basis sets, potential energy surfaces, quantized states. |
| | Properties | The fundamental attributes these entities possess (mass, charge, genotype, preference, etc.). | Spin, charge, mass, orbital energies, electron density, symmetry, correlation energy, quantum numbers. |
| | Categories | The basic ontological types used to classify domain elements (substances, processes, relations, structures). | Atoms, ions, molecules, electronic states, eigenstates, excited states, basis functions, PES regions. |
| 1.3 State-Variables | Variables | The measurable or definable properties that describe system conditions. | Electron density, nuclear coordinates, orbital occupations, total energy, spin multiplicity, vibrational quantum numbers. |
| | Parameterization | How variables encode and represent the system’s state. | Wavefunctions, Hamiltonians, density matrices, basis expansions, molecular orbital coefficients. |
| 1.4 Admissible Idealizations | Simplifications | Conceptual reductions used to make the domain tractable (point masses, rational agents, perfect gases). | Born–Oppenheimer approximation, independent-particle orbitals, harmonic modes, symmetry idealizations. |
| | Validity Conditions | The limits and contexts in which idealizations hold or break down. | Break down under strong correlation, non-adiabatic effects, or electron–nuclear coupling. |
| 1.5 Domain Assumptions | Structural Assumptions | Background ontological stances such as determinism, continuity, randomness, discreteness. | Assumes quantized states, wave–particle duality, discrete energy levels, operator-based observables. |
| | Implicit Commitments | Unstated but necessary assumptions that shape the field’s conceptual structure. | Assumes Schrödinger dynamics, convergence of basis sets, meaningful potential surfaces, tractable electron correlation. |
| 1.6 Internal Coherence Requirements | Consistency | The demand that domain concepts do not contradict one another. | Requires compatible Hamiltonians, approximations, and correlation methods. |
| | Compatibility | The requirement that entities, variables, and assumptions fit together into a unified descriptive framework. | Requires alignment between operators, boundary conditions, electron–nuclear partitioning, computational approximations. |
| 2. Evidence Layer | 2.1 Observable Phenomena | Observables | The aspects of the domain that can produce detectable signals accessible to measurement. | Absorption/emission spectra, photoelectron signals, scattering patterns, electron density distributions, reaction energetics, vibrational/rotational transitions. |
| | Detection Limits | The boundaries of what can be resolved or sensed by current instruments or methods. | Resolution limited by photon energy, detector sensitivity, signal-to-noise ratio, thermal noise, and quantum transition probabilities. |
| 2.2 Measurement Systems | Units | Standardized quantifications (meters, seconds, volts, decibels, dollars, etc.) necessary for consistent comparison. | Electronvolts, wavenumbers, hartrees, angstroms, femtoseconds, Debye, atomic units (a.u.). |
| | Instruments | Devices and tools (microscopes, spectrometers, sensors, surveys, detectors) used to produce measurements. | Spectrometers (IR, UV-Vis, Raman), NMR, X-ray diffraction, photoelectron detectors, mass spectrometers, ultrafast lasers, scanning probes. |
| 2.3 Operational Definitions | Definitions | Terms defined by specific measurement procedures, ensuring empirical clarity. | Bond lengths via spectroscopic constants, electron density via computational procedures, orbital energies via eigenvalue solutions. |
| | Procedures | The explicit steps required to perform a measurement in a reproducible way. | Stepwise measurement protocols: calibration, wavelength selection, excitation, signal integration, background subtraction, computational convergence criteria. |
| 2.4 Data Acquisition | Protocols | Formal processes for gathering data under controlled or standardized conditions. | Standardized spectroscopy runs, controlled excitation conditions, temperature-stabilized measurements, reproducible computational workflows. |
| | Sampling | Rules determining which subset of the domain is measured and how representative it is. | Choosing representative molecular conformers, vibrational states, electronic states, or energy regions in spectra. |
| 2.5 Data Character & Format | Data Types | The form raw evidence takes (time series, spectra, images, counts, qualitative records). | Spectra, time series, electron density grids, potential energy surfaces, orbital plots, NMR shifts, peak intensities. |
| | Resolution | The granularity or precision with which data is captured. | Determined by spectral linewidth, integration time, detector precision, computational grid spacing, and basis-set granularity. |
| 2.6 Reliability & Calibration | Calibration | Adjustment procedures ensuring instruments produce accurate results. | Wavelength calibration, intensity scaling, instrument baselining, reference compounds, computational benchmark sets. |
| | Error Characterization | Identification and quantification of noise, uncertainty, bias, and measurement error. | Thermal noise, electronic noise, resolution limits, peak overlap, computation-induced error (basis-set error, convergence error, correlation approximations). |
| 3. Structural Layer | 3.1 Patterns & Regularities | Laws / Relations | Stable, repeatable patterns governing how observables behave across conditions. | Schrödinger equation, quantized energy levels, orbital formation rules, electron correlation patterns, symmetry-based selection rules. |
| | Invariants | Quantities or properties that remain constant under transformations (symmetries, conservation laws). | Total spin, parity, molecular symmetry numbers, conserved quantum numbers, invariance under rotations and particle exchange. |
| 3.2 Causal Architecture | Mechanisms | Underlying processes or structures that produce the observed regularities. | Electron redistribution, orbital hybridization, tunneling, correlation-driven interactions, photonic excitation pathways. |
| | Pathways | Organized sequences of interactions forming a causal chain or network. | Reaction coordinate progression, electron transfer chains, vibrational relaxation sequences, photochemical and photophysical cascades. |
| 3.3 Theoretical Vocabulary | Concepts | Core terms that encode the domain’s structure (force, gene, equilibrium, field). | Wavefunction, orbital, electron density, potential energy surface, correlation, basis set, Hamiltonian, eigenstate, transition dipole. |
| | Classifications | Taxonomies, categories, or typologies that organize entities and relations. | Orbital types (s, p, d, f), term symbols, spin states, molecular point groups, bonding types (σ, π, δ), excitation classes (singlet, triplet). |
| 3.4 Formal Representations | Equations | Mathematical constructs expressing laws, relations, or mechanisms. | Schrödinger equation, Hartree–Fock equations, Kohn–Sham DFT equations, coupled-cluster expansions, transition moment integrals. |
| | Models | Structured representations—mathematical, computational, or conceptual—used to predict and explain phenomena. | Molecular orbital theory, valence bond theory, density functional theory, perturbation theory, configuration interaction, tight-binding models. |
| 3.5 Idealized Structures | Simplified Models | Purposeful abstractions that capture essential dynamics while omitting irrelevant detail. | Born–Oppenheimer separation, harmonic oscillator modes, rigid rotor, particle-in-a-box, single-determinant approximations. |
| | Limit Conditions | Regimes where specific models or approximations hold (classical vs. quantum, linear vs. nonlinear). | Valid in weak coupling, small correlation regimes, near-equilibrium structures; break down for strong correlation, conical intersections, nonadiabatic regions. |
| 3.6 Integrative Frameworks | Unifying Theories | Higher-order structures that connect disparate laws or mechanisms under a coherent whole. | Quantum mechanics as foundational framework integrating spectroscopy, bonding theories, and electron-structure models. |
| | Interdisciplinary Links | Points where the theory connects to adjacent sciences or larger explanatory systems. | Connects to materials science, surface chemistry, photochemistry, quantum information, condensed matter physics. |
| 4. Method Layer | 4.1 Inquiry Design | Experimental Design | Structured plans for manipulating variables to test causal claims. | Manipulating excitation wavelengths, pulse durations, molecular environments, or external fields to probe electronic and vibrational structure. |
| | Observational Design | Systematic approaches for gathering non-manipulated data (surveys, field studies, natural experiments). | Passive acquisition of spectra, emission profiles, scattering data, and computational outputs without direct perturbation of the system. |
| 4.2 Testing & Validation | Hypothesis Testing | Procedures for evaluating whether evidence supports or contradicts specific claims. | Comparing predicted spectra, energies, or structures against empirical or high-level computational benchmarks. |
| | Replication | The requirement that results be independently reproducible under similar conditions. | Reproducing spectral signatures, optimized geometries, transition energies, or reaction pathways across instruments, labs, and computational methods. |
| 4.3 Inference & Evaluation | Statistical Inference | Rules for drawing conclusions from noisy or incomplete data. | Extracting parameters from noisy spectra, fitting potential energy curves, estimating uncertainties in computed energies or densities. |
| | Model Comparison | Criteria (fit, simplicity, predictive accuracy, robustness) used to evaluate competing models. | Evaluating Hartree–Fock vs. DFT vs. coupled-cluster predictions in terms of accuracy, computational cost, correlation treatment, and physical realism. |
| 4.4 Error Management | Error Analysis | Identification and quantification of random and systematic errors. | Quantifying basis-set error, convergence error, electron correlation error, instrumental noise, and line broadening. |
| | Bias Control | Methods for minimizing subjective, instrumental, or procedural biases. | Preventing overfitting in spectral assignments, ensuring unbiased sampling of conformers, avoiding method-driven distortions (e.g., functional bias in DFT). |
| 4.5 Adjudication & Revision | Peer Scrutiny | Collective evaluation of claims through critique, review, and debate. | Independent evaluation of method choices, spectral interpretations, convergence criteria, and model validity. |
| | Theory Revision | Procedures for modifying, replacing, or discarding models based on new evidence. | Updating Hamiltonians, correlation treatments, approximations, or basis sets in response to discrepancies with experimental data or higher-level theory. |
| 4.6 Integrity Conditions | Transparency | Requirements to disclose methods, data, assumptions, and limitations. | Disclosing basis sets, convergence thresholds, functionals, approximations, calibration methods, and data-processing protocols. |
| | Ethical Standards | Norms ensuring responsible conduct in experimentation, data handling, and publication. | Ensuring honest reporting, reproducible workflows, proper citation of methods, and responsible handling of computational and experimental data. |