physics.chem-ph

arXiv:2501.00001v1 Announce Type: new Abstract: In this paper, a mathematical model is developed to describe the evolution of the concentration of compounds through a gas chromatography column. The model couples mass balances and kinetic equations for all components. Both single and multiple-component cases are considered with constant or variable velocity. Non-dimensionalisation indicates the small effect of diffusion. The system where diffusion is neglected is analysed using Laplace transforms. In the multiple-component case, it is demonstrated that the competition between the compounds is negligible and the equations may be decoupled. This reduces the problem to solving a single integral equation to determine the concentration profile for all components (since they are scaled versions of each other). For a given analyte, we then only two parameters need to be fitted to the data. To verify this approach, the full governing equations are also solved numerically using the finite difference method and a global adaptive quadrature method to integrate the Laplace transformation. Comparison with the Laplace solution verifies the high degree of accuracy of the simpler Laplace form. The Laplace solution is then verified against experimental data from BTEX chromatography. This novel method, which involves solving a single equation and fitting parameters in pairs for individual components, is highly efficient. It is significantly faster and simpler than the full numerical solution and avoids the computationally expensive methods that would normally be used to fit all curves at the same time.

arXiv:2409.19838v2 Announce Type: replace Abstract: Identifying informative low-dimensional features that characterize dynamics in molecular simulations remains a challenge, often requiring extensive manual tuning and system-specific knowledge. Here, we introduce geom2vec, in which pretrained graph neural networks (GNNs) are used as universal geometric featurizers. By pretraining equivariant GNNs on a large dataset of molecular conformations with a self-supervised denoising objective, we obtain transferable structural representations that are useful for learning conformational dynamics without further fine-tuning. We show how the learned GNN representations can capture interpretable relationships between structural units (tokens) by combining them with expressive token mixers. Importantly, decoupling training the GNNs from training for downstream tasks enables analysis of larger molecular graphs (such as small proteins at all-atom resolution) with limited computational resources. In these ways, geom2vec eliminates the need for manual feature selection and increases the robustness of simulation analyses.

arXiv:2412.18263v1 Announce Type: new Abstract: Irreducible Cartesian tensors (ICTs) play a crucial role in the design of equivariant graph neural networks, as well as in theoretical chemistry and chemical physics. Meanwhile, the design space of available linear operations on tensors that preserve symmetry presents a significant challenge. The ICT decomposition and a basis of this equivariant space are difficult to obtain for high-order tensors. After decades of research, we recently achieve an explicit ICT decomposition for $n=5$ \citep{bonvicini2024irreducible} with factorial time/space complexity. This work, for the first time, obtains decomposition matrices for ICTs up to rank $n=9$ with reduced and affordable complexity, by constructing what we call path matrices. The path matrices are obtained via performing chain-like contraction with Clebsch-Gordan matrices following the parentage scheme. We prove and leverage that the concatenation of path matrices is an orthonormal change-of-basis matrix between the Cartesian tensor product space and the spherical direct sum spaces. Furthermore, we identify a complete orthogonal basis for the equivariant space, rather than a spanning set \citep{pearce2023brauer}, through this path matrices technique. We further extend our result to the arbitrary tensor product and direct sum spaces, enabling free design between different spaces while keeping symmetry. The Python code is available in the appendix where the $n=6,\dots,9$ ICT decomposition matrices are obtained in <0.1s, 0.5s, 1s, 3s, 11s, and 4m32s, respectively.

arXiv:2412.18414v1 Announce Type: cross Abstract: Generative model for 2D materials has shown significant promise in accelerating the material discovery process. The stability and performance of these materials are strongly influenced by their underlying symmetry. However, existing generative models for 2D materials often neglect symmetry constraints, which limits both the diversity and quality of the generated structures. Here, we introduce a symmetry-constrained diffusion model (SCDM) that integrates space group symmetry into the generative process. By incorporating Wyckoff positions, the model ensures adherence to symmetry principles, leading to the generation of 2,000 candidate structures. DFT calculations were conducted to evaluate the convex hull energies of these structures after structural relaxation. From the generated samples, 843 materials that met the energy stability criteria (Ehull < 0.6 eV/atom) were identified. Among these, six candidates were selected for further stability analysis, including phonon band structure evaluations and electronic properties investigations, all of which exhibited phonon spectrum stability. To benchmark the performance of SCDM, a symmetry-unconstrained diffusion model was also evaluated via crystal structure prediction model. The results highlight that incorporating symmetry constraints enhances the effectiveness of generated 2D materials, making a contribution to the discovery of 2D materials through generative modeling.

arXiv:2405.06659v2 Announce Type: replace-cross Abstract: Due to the vast design space of molecules, generating molecules conditioned on a specific sub-structure relevant to a particular function or therapeutic target is a crucial task in computer-aided drug design. Existing works mainly focus on specific tasks, such as linker design or scaffold hopping, each task requires training a model from scratch, and many well-pretrained De Novo molecule generation model parameters are not effectively utilized. To this end, we propose a two-stage training approach, consisting of condition learning and condition optimization. In the condition learning stage, we adopt the idea of ControlNet and design some meaningful adjustments to make the unconditional generative model learn sub-structure conditioned generation. In the condition optimization stage, by using human preference learning, we further enhance the stability and robustness of sub-structure control. In our experiments, only trained on randomly partitioned sub-structure data, the proposed method outperforms previous techniques by generating more valid and diverse molecules. Our method is easy to implement and can be quickly applied to various pre-trained molecule generation models.

arXiv:2412.16483v1 Announce Type: new Abstract: Molecular representation learning plays a crucial role in various downstream tasks, such as molecular property prediction and drug design. To accurately represent molecules, Graph Neural Networks (GNNs) and Graph Transformers (GTs) have shown potential in the realm of self-supervised pretraining. However, existing approaches often overlook the relationship between molecular structure and electronic information, as well as the internal semantic reasoning within molecules. This omission of fundamental chemical knowledge in graph semantics leads to incomplete molecular representations, missing the integration of structural and electronic data. To address these issues, we introduce MOL-Mamba, a framework that enhances molecular representation by combining structural and electronic insights. MOL-Mamba consists of an Atom & Fragment Mamba-Graph (MG) for hierarchical structural reasoning and a Mamba-Transformer (MT) fuser for integrating molecular structure and electronic correlation learning. Additionally, we propose a Structural Distribution Collaborative Training and E-semantic Fusion Training framework to further enhance molecular representation learning. Extensive experiments demonstrate that MOL-Mamba outperforms state-of-the-art baselines across eleven chemical-biological molecular datasets. Code is available at https://github.com/xian-sh/MOL-Mamba.

arXiv:2411.15722v2 Announce Type: replace Abstract: We investigate the convergence of a backward Euler finite element discretization applied to a multi-domain and multi-scale elliptic-parabolic system, derived from the Doyle-Fuller-Newman model for lithium-ion batteries. We establish optimal-order error estimates for the solution in the norms $l^2(H^1)$ and $l^2(L^2(H^q_r))$, $q=0,1$. To improve computational efficiency, we propose a novel solver that accelerates the solution process and controls memory usage. Numerical experiments with realistic battery parameters validate the theoretical error rates and demonstrate the significantly superior performance of the proposed solver over existing solvers.

arXiv:2403.09549v3 Announce Type: replace Abstract: Understanding the interactions of atoms such as forces in 3D atomistic systems is fundamental to many applications like molecular dynamics and catalyst design. However, simulating these interactions requires compute-intensive ab initio calculations and thus results in limited data for training neural networks. In this paper, we propose to use denoising non-equilibrium structures (DeNS) as an auxiliary task to better leverage training data and improve performance. For training with DeNS, we first corrupt a 3D structure by adding noise to its 3D coordinates and then predict the noise. Different from previous works on denoising, which are limited to equilibrium structures, the proposed method generalizes denoising to a much larger set of non-equilibrium structures. The main difference is that a non-equilibrium structure does not correspond to local energy minima and has non-zero forces, and therefore it can have many possible atomic positions compared to an equilibrium structure. This makes denoising non-equilibrium structures an ill-posed problem since the target of denoising is not uniquely defined. Our key insight is to additionally encode the forces of the original non-equilibrium structure to specify which non-equilibrium structure we are denoising. Concretely, given a corrupted non-equilibrium structure and the forces of the original one, we predict the non-equilibrium structure satisfying the input forces instead of any arbitrary structures. Since DeNS requires encoding forces, DeNS favors equivariant networks, which can easily incorporate forces and other higher-order tensors in node embeddings. We study the effectiveness of training equivariant networks with DeNS on OC20, OC22 and MD17 datasets and demonstrate that DeNS can achieve new state-of-the-art results on OC20 and OC22 and significantly improve training efficiency on MD17.