Architectural Score Function in the Periodic Table: Definition and Properties
1. Function Definition
The architectural score function is defined as follows:
[F(n, l, m, s) = 2n + 3l + m + 4s]
Here:
- n: Principal quantum number (period)
- l: Angular momentum quantum number (orbital type: s, p, d, f)
- m: Magnetic quantum number (orbital orientation)
- s: Spin quantum number (±1/2)
The function expresses the quantum state of each electron with a single score value.
2. Key Features
a) Linear Combination
A function is a weighted linear combination of quantum numbers. The coefficients (2, 3, 1, 4) determine the impact of each parameter on the architectural role.
b) Period Scaling
- Coefficient n (2n) → with each period increase the score range expands by +2.
- This supports the logic of fractal scaling between periods.
c) Orbital Contribution
- l coefficient (3l) → provides score increase according to orbital type.
- s-orbital (l=0) → low score
- p-orbital (l=1) → middle score
- d-orbital (l=2) → high score
- f-orbital (l=3) → highest score
d) Magnetic Orientation
- m value (−l ≤ m ≤ +l) → fine-tunes the score.
- Orbital orientation produces variations of architectural role.
e) Spin Effect
- The coefficient s (±1/2) → causes the score to change by +2 or −2.
- Spin determines the active/passive state of the module.
3. Relationship to Architectural Roles
Function scores correspond to specific ranges:
| F Score Range | Architectural Role |
| 1–5 | Starting Point |
| 6–10 | Balancer Block |
| 11–20 | Catalytic Bridge |
| 21–25 | Flexible Connector |
| 26–30 | Information Carrier |
| 31–35 | Oxidative Engine |
| 36–40 | Reactive Switch |
| 41+ | Closed Module / Gate |
4. Areas of Use
a) Atomic Architectural Mapping
The architectural diagram of the atom is created by calculating the F score for each electron.
b) Molecule Design
Congruent scores indicate connectable modules, opposite scores indicate reactive interactions.
c) Quantum–Technology Bridge
High score modules (Oxidative Engine, Reactive Switch) play critical roles in quantum information processing and energy transfer.
d) Fractal Systematic
The regular expansion of score ranges across periods enables fractal scaling with motif repetitions.
5. Visual Presentation Opportunities
Function scores in diagrams:
- Node size (score value)
- Color coding (architectural role)
- Connection type (orbital relationship)
Can be used as. This increases the visual and pedagogical clarity of architectural systematics.
6. Summary
The architectural score function is a generative tool that determines the architectural roles of atoms and molecules starting from quantum numbers. It bridges both chemistry, quantum computing and technological architectures. It supports the logic of fractal scaling across periods and clarifies the fit between modules visually, mathematically and functionally.
New Circuit Elements with Chemical Architecture
1. Entrance
This report aims to predict new circuit elements by adapting the chemical architecture derived with the F function to electronic circuit design. Architectural modules derived from quantum parameters have been transformed into circuit elements through hybrid molecules.
2. Architectural Bonding Transistor (MBT)
- Basic Hybrid: Si–Sn
- Architectural Roles: Flexible Linker (Si) + Catalytic Bridge (Sn)
- Function: Controls electron flow with module coherence scores instead of energy barriers.
- Envisaged Use: MOSFET alternative, transistor designs suitable for fractal scaling logic.
3. Catalytic Capacitor
- Basic Hybrid: Ti–N or Cu–S
- Architectural Roles: Catalytic/Oxidative modules ↔ Binding/Information Carrier modules
- Function: Load storage capacity depends on module matching score.
- Intended Use: Fast charge/discharge cycles, energy storage systems.
4. Fractal Diode
- Basic Hybrid: Sn–O
- Architectural Roles: Connector ↔ Initiating Point
- Function: Directs the flow of electrons through fractal motif repetitions.
- Intended Use: Multi-level switching diodes, multi-level diode architecture.
5. Module Switcher (Quantum Switch)
- Basic Hybrid: Cu–S
- Architectural Roles: Reactive Switch ↔ Flexible Connector
- Function: The active/passive status of the module is determined by the spin contribution (±1/2).
- Envisaged Use: Spin-based quantum switches, quantum information processing circuits.
6. General Evaluation
- The F function defines circuit elements by architectural module conformations rather than energy barriers.
- This approach allows electronic circuits to be designed according to fractal scaling logic.
- A new paradigm for quantum information processing is presented by developing generative circuit elements through hybrid molecules.
7. Conclusion
Circuit elements based on chemical architecture can gain new functions beyond classical semiconductor technology. This report reveals the generative contribution of the F function to electronic circuit design.
Transition from Quantum to Architecture with F Function and Prediction of New Circuit Elements
Key Words: F function, quantum mechanics, chemical architecture, hybrid molecule, fractal scaling, circuit elements
1. Summary
This study reveals that the F function derived from quantum parameters turns the chemical architecture into a generative systematic and that new circuit elements can be predicted through this systematic. Hybrid molecules (Fe–Si, Sn–O, Ti–N, Cu–S) were paired with architectural modules, and these pairings were transformed into electronic circuit elements. The study proposes a new paradigm that works with fractal scaling and module fits beyond classical semiconductor technology.
2. Entrance
In quantum mechanics, the states of electrons (n, l, m, s) are defined by their energy levels and orbital symmetries. In the literature, these parameters are often used for energy calculations; No functional architectural role derivation is made. The F function defined in this study:
𝐹(𝑛, 𝑙, 𝑚, 𝑠) = 2𝑛 + 3𝑙 + 𝑚 + 4𝑠
It determines the functional role of each electron by deriving an architectural score from quantum parameters.
3. Method
3.1 F Function and Architectural Roles
- Score ranges correspond to specific architectural modules: Initiator Point, Stabilizer Block, Catalytic Bridge, Flexible Linker, Information Carrier, Oxidative Engine, Reactive Switch, Closed Module.
3.2 Hybrid Molecule Suggestions
- Fe–Si → Catalytic semiconductor
- Sn–O → Oxidative–binding hybrid
- Ti–N → Hard–reactive hybrid
- Cu–S → Photocatalytic hybrid
3.3 Physical Formation Process
- Synthesis: Hybrid molecules are produced by CVD/MBE methods.
- Crystal Control: Fractal motif continuity is confirmed by XRD and electron microscopy.
- Electronic Measurement: Conductivity, band gap, spin behavior are tested.
- Circuit Integration: Circuit geometry is drawn with lithography and completed with electrodes.
4. Findings
4.1 New Circuit Elements
- Architectural Bonding Transistor (MBT): Si–Sn hybrid, flow control with module compliance scores.
- Catalytic Capacitor: Ti–N or Cu–S hybrid, charge storage capacity depends on module matching.
- Fractal Diode: Sn–O hybrid, multi-level switching diode.
- Module Switcher (Quantum Switch): Cu–S hybrid, spin-based on/off behavior.
4.2 Fractal Scaling
Scaling the F function by +2 across periods allows circuit elements to be designed with fractal motif continuity.
5. Argument
- In the literature, orbital contribution functions are energy-oriented; This study focuses on architectural role.
- Although similar to machine learning-based transition state calculations, the F function provides direct generative module generation.
- This approach builds a new bridge between quantum chemistry and electronic circuit design.
6. Conclusion
The F function turns the chemical architecture into a generative systematic with scores derived from quantum parameters. New circuit elements are predicted through this systematic and a paradigm based on fractal scaling logic beyond classical semiconductor technology is proposed. The work provides a strong foundation for quantum information processing and advanced circuit designs.
7. Source
1. Hoffmann, R. (2015). Chemistry as a generative science. Angewandte Chemie International Edition, 54(1), 2–10.
2. Aspuru-Guzik, A., et al. (2018). The matter of matter: Generative models for molecules. Nature Reviews Chemistry, 2(10), 347–358.
3. Curtarolo, S., et al. (2013). Materials genome approach to accelerated discovery of new materials. Nature Materials, 12(3), 191–201.
4. Zunger, A. (2018). Inverse design in materials science. Nature Reviews Chemistry, 2(4), 0121.
5. Kohn, W., & Sham, L. J. (1965). Self-consistent equations including exchange and correlation effects. Physical Review, 140(4A), A1133.
6. MIT News (2023). Machine learning accelerates transition state calculations in quantum chemistry.