Project summary

Accurate electronic-structure calculations face a persistent tradeoff: methods such as coupled-cluster theory can achieve high accuracy but become prohibitively expensive as molecular size grows, while density-functional methods are computationally practical but depend on approximate exchange-correlation functionals.

I have been developing a different approach based on spectral constraints, local quantum structures, and higher-categorical integrability. The underlying hypothesis is that part of the many-electron problem has a reusable compositional structure: accurately solved local electronic environments can be characterized spectrally, transferred between related chemical environments, and assembled into larger systems without globally re-solving the highest-level correlation problem each time.

The foundational theory is presented in my paper “Ab-Initio Density Functional Theory from Higher-Categorical Integrability: Spectral-Law-Constrained Exchange–Correlation without Fitting.” Rather than fitting an exchange-correlation functional to empirical data, this work investigates whether spectral and integrability constraints can determine the missing electronic information from first principles.

I subsequently developed computational realizations based on small local bond or correlation structures—“tiles” or spectral rungs—that can be solved accurately and organized into a reusable catalogue. Initial numerical experiments suggest that this representation may retain high-level electronic-structure information while scaling much more favorably than conventional global correlated calculations.

A particularly concrete application is peptide quantum chemistry. In my paper “Coupled-cluster accuracy at linear cost from a transferable assembly of spectral rungs: dynamical correlation in polypeptides without local pair-natural-orbital re-solution,” local coupled-cluster-level correlation structures are reused across increasingly large peptide systems. The proof of concept suggests that correlation information calculated on small chemical environments can remain transferable enough to predict the correlation energies of larger peptide systems without performing a completely new high-level calculation for every molecule.

The purpose of this project is to determine rigorously how far this principle can be pushed.

What are this project’s goals? How will you achieve them?

The primary goal is to test whether transferable spectral/local electronic structures can form the basis of a genuinely scalable high-accuracy quantum-chemistry method.

I will pursue three connected objectives.

1. Independent accuracy and scaling validation.
I will construct a substantially broader benchmark suite and compare the method with conventional DFT, CCSD(T), DLPNO-CCSD(T), and appropriate multireference reference calculations where feasible. The benchmark will include equilibrium structures, conformational energies, bond distortion, chemically nontrivial systems, and progressively larger molecules.

The important question is not simply whether the method performs well on existing examples, but whether its accuracy persists as molecular complexity increases while its computational scaling remains substantially below conventional correlated methods.

2. Build a transferable quantum-chemical tile catalogue.
I will systematically catalogue accurately solved local bonding and correlation environments together with the spectral information required to transport them into larger systems. The aim is to determine which descriptors are sufficient for transferability, when purely local information fails, and what additional nonlocal corrections are required.

This will turn the present theoretical construction into a testable computational object: a growing library of reusable quantum information rather than a new global electronic-structure calculation for every molecule.

3. Extend the method to chemically heterogeneous peptides.
The existing peptide proof of concept will be expanded beyond simple repeated residues. I will test different amino-acid environments, sequences, conformations, protonation states, and larger peptide systems.

A successful outcome would provide a first-principles quantum-chemical scoring layer that could eventually complement machine-learning peptide generation: AI could generate candidate molecules, while a scalable high-accuracy electronic-structure method could provide physically grounded energetic and electronic validation.

All benchmarks, failure cases, and scaling results will be documented. The project is deliberately falsifiable: a negative result establishing the limits of spectral transferability would itself be scientifically valuable.

How will this funding be used?

Funding will primarily support concentrated research time, computational resources, and software development.

At the minimum funding level, I will prioritize a reproducible benchmark implementation and an expanded accuracy/scaling study sufficient to test the central claim beyond the existing proof-of-concept calculations.

Additional funding will allow me to expand the local spectral catalogue, perform more expensive high-level reference calculations, test more diverse chemical environments, extend the peptide calculations, and develop the current research code into a reusable computational prototype.

The intended outputs are:

• a reproducible benchmark comparing the method with established electronic-structure approaches;

• a first systematic transferable bond/correlation tile catalogue;

• a quantitative map of where transferability succeeds and fails;

• an expanded peptide demonstration;

• research software suitable for subsequent development into a general computational-chemistry platform;

• publication and open scientific dissemination of the validation results, while preserving any genuinely new patentable implementation details until appropriately protected.

Who is on your team? What’s your track record on similar projects?

I am Andrei Tudor Patrascu, a theoretical physicist with a PhD in physics and founder of FAST Foundation for the Acceleration of Scientific Transformation.

My research spans mathematical and high-energy physics, quantum theory, quantum algorithms, quantum chemistry, and nonlinear systems. A recurring theme of my recent work is the use of spectral, geometric, and higher-categorical structures to reformulate difficult computational problems in physics and chemistry.

For this project, I have already developed the underlying theory, implemented initial computational realizations, carried out molecular benchmarks, and demonstrated a first application to transferable electronic correlation in polypeptides.

This means the project is not beginning from an untested idea. The theoretical foundation and initial numerical evidence already exist; the proposed funding is intended to determine whether the method survives significantly broader and more demanding validation.

The project is currently led by me through FAST Foundation. Where useful, I intend to seek external computational and chemical validation rather than rely exclusively on benchmarks designed by the method’s originator.

What are the most likely causes and outcomes if this project fails?

The principal scientific risk is that local spectral information may not transfer with sufficient accuracy once chemical environments become substantially more heterogeneous.

Nonlocal correlation, long-range polarization, strongly multireference electronic structure, unusual bonding environments, or accumulated errors during assembly may require substantially more information than the current local representation contains.

A second possibility is that the method retains good accuracy but the machinery needed to control these corrections grows sufficiently quickly that the anticipated computational advantage over conventional correlated methods is reduced.

A third possibility is that the approach is highly effective only within restricted chemical families—for example peptides or related organic systems—rather than forming a universal electronic-structure method.

These are useful outcomes rather than wasted work. The proposed benchmark is designed to identify precisely these boundaries. Even if the strongest hypothesis of broadly applicable ab-initio accuracy at DFT-like cost fails, the project may still yield useful transferable correlation models for restricted molecular classes, a catalogue of reusable high-level electronic information, and quantitative insight into the locality and composability of electron correlation.

The project therefore has an asymmetric scientific payoff: success could establish a new computational architecture for quantum chemistry, while failure can sharply characterize which aspects of electronic correlation resist transferable local representation.

How much money have you raised in the last 12 months, and from where?

No external funding has yet been raised for this project. The theoretical development, software implementation, and proof-of-concept calculations to date have been carried out independently. I am now seeking relatively modest external support to move from proof-of-concept results to systematic validation.