Periodic Reporting for period 1 - FITMOL (Field-Theory Approach to Molecular Interactions)
Reporting period: 2022-12-01 to 2025-05-31
The quantum-mechanical theory of molecular interactions is firmly established, however its applicability to large molecular complexes is hindered by the rather high computational cost of quantum calculations required to achieve high accuracy. We propose a paradigm shift in the modeling and conceptual understanding of electrostatic and electrodynamic molecular interactions in many-particle systems from the perspective of (quantum) field theory. This development is critical to accurately and efficiently model increasingly intricate and functional molecular ensembles with millions of atoms subject to external excitations (static, thermal, and optical fields; variation in the number of particles; and/or arbitrary macroscopic boundary conditions). This molecular size covers a wide range of functional biological systems, including solvated protein/protein and enzyme/DNA complexes. The theoretical developments in this project will concentrate on two main fronts: fundamental quantum electrodynamics (QED) theory of molecular interactions based on coupled quantum Drude oscillator (cQDO) Hamiltonians, second-quantized field theory (FIT) approach to molecular Hamiltonians for modeling large-scale systems with 104-106 atoms. The applicability of these challenging developments to realistic molecules will be ensured by: implementation of non-local machine learning force fields based on second-quantized matrix Hamiltonians for efficient molecular dynamics simulations of molecular ensembles, implementation of QED/FIT methods in an open-source package FITMOL for increasing the accuracy, improving the efficiency, and enhancing the insight that one obtains from quantum-mechanical calculations of large molecules. It is my vision that revealing fundamental mechanisms of functional (bio)molecules with millions of atoms requires a radically new field-theory approach to molecular interactions. Achieving this goal will be the main breakthrough of the FITMOL project.
We have developed a quantum field theory (FIT) approach and its quantum computing implementation to systems of Drude oscillators interacting with Coulomb potential. This has allowed us to classify all interactions known from the theory of molecular interactions and identify new phenomena, arising from non-trivial coupling between matter and the electromagnetic field. These developments have been published in PRR 5, 043072 (2023) and JCP 160, 094309 (2024) and several additional publications are under preparation.
We also realized that the understanding of excited states of quantum fields and possible transitions between ground and excited states in QFT remains puzzling and needs to be addressed. Hence, we have started to develop a convincing methodology to do this, resulting in two publications: PRD 110, 014503 (2024) and arXiv:2401.17938 (in review). These developments will ultimately allow to study coupled matter and fields in a non-perturbative fashion, which is crucial for a complete understanding of these complex and important systems.
We have developed a novel quantum embedding method that allows us to treat coupled nuclei, electrons, quantum oscillators, and positrons (and any other particles in principle) in a fully quantum mechanical fashion. These developments have been implemented in an in-house quantum Monte Carlo code QMeCha. This code will be made available as an open-source package in 2025. This work has been published in PRL 131, 228001 (2023) and two additional publications are under preparation. In addition, a second quantization approach to the many-body dispersion (MBD) Hamiltonian has been developed and published in Nature Comms 14, 8218 (2023) that allows to define projected many-body states for any composite systems of oscillators and this will form the basis for coupling to quantized fields and for effective machine learning approaches for the MBD Hamiltonian.
To accelerate our computationally intensive simulations, we additionally focused on developing powerful machine-learning approaches that are able to describe long range many-body interactions in a systematic fashion. This has been accomplished by using the newly developed SO3krates neural network architecture and coupling it to unified long-range physical force fields. The resulting method, called SO3LR, is under consideration for publication in PNAS (https://doi.org/10.26434/chemrxiv-2024-bdfr0(opens in new window)). Importantly, the SO3LR model being trained on millions of organic molecules, is a fully fledged force field that can be applied to modelling large biomolecular systems.
We also realized that the understanding of excited states of quantum fields and possible transitions between ground and excited states in QFT remains puzzling and needs to be addressed. Hence, we have started to develop a convincing methodology to do this, resulting in two publications: PRD 110, 014503 (2024) and arXiv:2401.17938 (in review). These developments will ultimately allow to study coupled matter and fields in a non-perturbative fashion, which is crucial for a complete understanding of these complex and important systems.
We have developed a novel quantum embedding method that allows us to treat coupled nuclei, electrons, quantum oscillators, and positrons (and any other particles in principle) in a fully quantum mechanical fashion. These developments have been implemented in an in-house quantum Monte Carlo code QMeCha. This code will be made available as an open-source package in 2025. This work has been published in PRL 131, 228001 (2023) and two additional publications are under preparation. In addition, a second quantization approach to the many-body dispersion (MBD) Hamiltonian has been developed and published in Nature Comms 14, 8218 (2023) that allows to define projected many-body states for any composite systems of oscillators and this will form the basis for coupling to quantized fields and for effective machine learning approaches for the MBD Hamiltonian.
To accelerate our computationally intensive simulations, we additionally focused on developing powerful machine-learning approaches that are able to describe long range many-body interactions in a systematic fashion. This has been accomplished by using the newly developed SO3krates neural network architecture and coupling it to unified long-range physical force fields. The resulting method, called SO3LR, is under consideration for publication in PNAS (https://doi.org/10.26434/chemrxiv-2024-bdfr0(opens in new window)). Importantly, the SO3LR model being trained on millions of organic molecules, is a fully fledged force field that can be applied to modelling large biomolecular systems.
The SO3LR model is a breakthrough in biomolecular simulations. It achieves a new standard of accuracy, efficiency, scalability, and transferability as a molecular force field. This development could have not been foreseen because it came as an integration of many multidisciplinary components coming from the theory of molecular interactions, neural network architectures, accurate quantum data sets, software engineering, and applications to important biomolecular benchmarks. SO3LR was enabled by multiple advancements in all these directions, many but not all of which happened within my group.
The second breakthrough is a culmination of several research directions integrating QFT with the theory of molecular interactions. This started with the breakthrough work reported in PRL 130, 041601 (2023) – a precursor work to the FITMOL project. This work presented a phenomenological model that derives the cosmological constant from self-interaction between fermionic and bosonic quantum fields without any empirical parameters. Within FITMOL we have continued this work to derive the different cosmological observations from first principles of QFT. While this work is in early stages and quite complex, the initial results are very promising, and I am convinced that several breakthroughs are on the way.
The second breakthrough is a culmination of several research directions integrating QFT with the theory of molecular interactions. This started with the breakthrough work reported in PRL 130, 041601 (2023) – a precursor work to the FITMOL project. This work presented a phenomenological model that derives the cosmological constant from self-interaction between fermionic and bosonic quantum fields without any empirical parameters. Within FITMOL we have continued this work to derive the different cosmological observations from first principles of QFT. While this work is in early stages and quite complex, the initial results are very promising, and I am convinced that several breakthroughs are on the way.