Periodic Reporting for period 4 - BeStMo (Beyond Static Molecules: Modeling Quantum Fluctuations in Complex Molecular Environments) Reporting period: 2021-09-01 to 2022-08-31 Summary of the context and overall objectives of the project We propose focused theory developments and applications, which aim to substantially advance our ability to model and understand the behavior of molecules in complex environments. From a large repertoire of possible environments, we have chosen to concentrate on experimentally-relevant situations, including molecular fluctuations in electric and optical fields, disordered molecular crystals, solvated (bio)molecules, and molecular interactions at/through low-dimensional nanostructures. A challenging aspect of modeling such realistic environments is that both molecular electronic and nuclear fluctuations have to be treated efficiently at a robust quantum-mechanical level of theory for systems with 1000s of atoms. In contrast, the current state of the art in the modeling of complex molecular systems typically consists of Newtonian molecular dynamics employing classical force fields. We will develop radically new approaches for electronic and nuclear fluctuations that unify concepts and merge techniques from quantum-mechanical many-body Hamiltonians, statistical mechanics, density-functional theory, and machine learning. Our developments will be benchmarked using experimental measurements with terahertz (THz) spectroscopy, atomic-force and scanning tunneling microscopy (AFM/STM), time-of-flight (TOF) measurements, and molecular interferometry.Our final goal is to bridge the accuracy of quantum mechanics with the efficiency of force fields, enabling large-scale predictive quantum molecular dynamics simulations for complex systems containing 1000s of atoms, and leading to novel conceptual insights into quantum-mechanical fluctuations in large molecular systems. The project goes well beyond the presently possible applications and once successful will pave the road towards having a suite of first-principles-based modeling tools for a wide range of realistic materials, such as biomolecules, nanostructures, disordered solids, and organic/inorganic interfaces.Within BeStMo, we have developed a robust hierarchy of methods to study molecules and materials with 1000s of atoms by combining quantum mechanics, approximate many-body methods, and machine learning. These methods have been implemented in open source software codes, and these methods/codes benefit thousands of academic and industrial users. For example, our libMBD software is used by essentially all leading pharmaceutical companies in their drug formulation pipelines for predicting energies of polymorphic molecular crystals. Many of our publications developed within BeStMo have been cited thousands of times, demonstrating further recognition of our research and the wide impact it has had on the field of molecular simulations in physical chemistry and chemical physics. Hence, BeStMo have had substantial impact on both academic research and industrial development, and as a proxy to society at large. Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far The BeStMo project had significant advances in all workpackages WP1, WP2, WP3, and WP4, in most cases exceeding the original expectations.In WP1, we have developed an optimized parameterization of the Quantum Drude Oscillator (QDO) model for arbitrary atoms and molecules. This is a long-standing problem and our results exceed the expectations laid in the ERC proposal. We have published our results in Nat. Comms. (2 publications), Phys. Rev. Lett. (2 publications), and Phys. Rev. Research. We have also developed a method to solve coupled QDOs subject to arbitrary electric fields, allowing us to obtain exact numerical solutions for any number of QDOs under arbitrary fields. This work has been published in J. Phys. Chem. Lett. and Phys. Rev. Research. In WP2, we have developed and applied the dipole-coupled MBD method for general systems (Phys. Rev. Lett.), implemented this in open source libMBD software (publication in preparation; to be submitted to J. Chem. Phys.), demonstrated the wide applicability of MBD to solvated proteins (publication in Science Adv.) and other macroscale systems (publications in Science Adv., Nat. Comms., Phys. Rev. Lett., etc). As an unforeseen consequence of our developments, we have established a strong collaboration with the computational engineering group of Prof. Stéphane Bordas (former ERC fellow) at the University of Luxembourg. Jointly, we have now published three high-impact papers with more publications in the pipeline. Our ideas and methods are starting to be used in the engineering community, which is a breakthrough in my opinion. In WP3, we have pushed the applicability of our machine learning (ML) methods to realistic large molecules and extended solids. We have published several original manuscripts presenting the extension of our GMDL and SchNet models to large systems (published in JPCL and Nat. Comms.). We have also published three comprehensive reviews on the quickly developing field of computational chemistry driven by ML (one in Nature Review Chemistry and two in Chemical Reviews – the prime review journal of the American Chemical Society). In WP4, we have further developed (publication in JCTC) and applied our developed path integral methods to study nuclear quantum effects (NQE) for a wide range of molecules. We arrived at a surprising conclusion that NQEs often stabilize global minima of molecules, instead of the expected destabilization (paper published in Nat. Comms.). Overall, the progress in BeStMo lead to several breakthroughs that I summarize below:(1) We have developed a robust characterization of interatomic interactions through the Coulomb-coupled QDO Hamiltonian. This has led to a plethora of novel effects beyond textbook understanding (f.ex. repulsive van-der-Waals interactions under nano-confinement; macrometer-long van-der-Waals/Casimir interactions for mesoscale materials; reinterpretation of field-induced effects in nanostructures).(2) We have developed robust physically-informed machine learning architectures for molecular systems (such as sGDML and SchNet). These are used by 1000s of researchers and companies worldwide.(3) The MBD method has become a de facto standard for evaluating stabilities of polymorphic molecular crystals as demonstrated by two blind tests of crystal structure predictions carried out by the Cambridge Crystallographic Data Centre (in 2015-2017 and 2020-2022). Our MBD method is now used extensively in drug formulation pipelines by essentially all major pharmaceutical companies. (4) We have discovered new quantum-mechanical long-distance interaction mechanisms in engineered materials. A software code is in preparation to enable anyone in the world to carry out large-scale quantum calculations for realistic materials. Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far) The main goal of the BeStMo project is to develop pioneering methods that include both electronic and nuclear quantum-mechanical many-particle fluctuations in the modeling of dynamics of complex molecular systems with 1000s of atoms. By now, we have essentially accomplished this goal for large biomolecular systems and mesoscale materials by combining machine learning models for short-range interactions with electronic models based on quantum Drude oscillators (QDOs).