[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-124853-en":3,"doc-seo-124853-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},124853,549758252649,"Ivy","https://ap-avatar.wpscdn.com/avatar/8000253669c5317157?_k=1778319167496531819",8,"Research & Report","Machine Learning Many-Body Green’s Functions for Molecular Excitation Spectra","A machine learning framework predicts Green’s functions for molecular systems, enabling photoemission spectra and quasiparticle energies at the quantum many-body level. Kernel ridge regression learns self-energy matrix elements on compact imaginary-frequency grids from static and dynamical mean-field electronic features, then obtains real-frequency Green’s functions via analytic continuation and Dyson’s equation. Symmetry-adapted basis representations enforce rotational invariance. Results show strong transferability and data efficiency across molecular sizes and chemistries, with small mean absolute errors for HOMO/LUMO and successful DOS predictions for larger organic molecules.","arXiv :2310 .09911v2 [physics .chem-ph] 4 Dec 2023  \nMachine Learning Many-Body Green’s Functions for Molecular Excitation Spectra  \nChristian Venturella, Christopher Hillenbrand, Jiachen Li, and Tianyu Zhu∗ Department of Chemistry, Yale University, New Haven, CT, USA 06520  \nWe present a machine learning (ML) framework for predicting Green’s functions of molecular systems, from which photoemission spectra and quasiparticle energies at quantum many-body level can be obtained. Kernel ridge regression is adopted to predict self-energy matrix elements on compact imaginary frequency grids from static and dynamical mean-field electronic features, which gives direct access to real-frequency many-body Green’s functions through analytic continuation and Dyson’s equation. Feature and self-energy matrices are represented in a symmetry-adapted intrinsic atomic orbital plus projected atomic orbital basis to enforce rotational invariance. We demonstrate good transferability and high data efficiency of proposed ML method across molecular sizes and chemical species by showing accurate predictions of density of states (DOS) and quasiparticle energies at the level of many-body perturbation theory (GW) or full configuration interaction. For the ML model trained on 48 out of 1995 molecules randomly sampled from the QM7 and QM9 datasets, we report the mean absolute errors of ML-predicted HOMO and LUMO energies to be 0.13 eV and 0.10 eV compared to GW@PBE0 . We further showcase the capability of this method by applying the same ML model to predict DOS for significantly larger organic molecules with up to 44 heavy atoms.  \nI. INTRODUCTION  \nComputational modeling of molecular excitation spectra plays a crucial role in revealing charge and energy transfer in light-matter interactions, understanding electron correlation in many-electron systems, and designing new optoelectronic materials and catalysts [1–4] . Despite many developments in quantum chemistry and physics, accurate and fast first-principles prediction of photoemission spectra and quasiparticle energies of molecules and materials remains a significant challenge. While density functional theory (DFT) [5] has been the workhorse for this task, molecular orbital energies from Kohn-Sham DFT are not true quasiparticle energies, and its accuracy heavily depends on underlying DFT functional [6–8] . On the other hand, a rigorous and systematic solution to photoemission spectra beyond DFT can be obtained within the many-body Green’s function (MBGF) framework [9] . In recent years, promising ab initio MBGF methods have been developed for molecules and periodic systems, based on many-body perturbation theory (GW) [10–24], second-order perturbation theory (GF2) [25–29], coupledcluster theory (CC) [30–37], algebraic diagrammatic construction (ADC) [38, 39], density matrix renormalization group (DMRG) [40], and quantum Monte Carlo [41] . Moreover, Green’s function embedding methods including dynamical mean-field theory (DMFT) [42–46] and self-energy embedding theory (SEET) [47–49] represent an efficient way to accelerate MBGF calculations of many-electron systems. In spite of these advances, the high computational scaling of MBGF methods prohibits their use in large-scale computational discovery of optoelectronic materials.  \nData-driven machine learning (ML) has recently been employed to predict density of states (DOS) and quasiparticle energies at the DFT level from only atomic configurations [50– 54] . Using thousands of (or more) discretized DOS on real frequency axis as training data, Gaussian process regression  \n∗ [tianyu.zhu@yale.edu](tianyu.zhu@yale.edu)  \nor deep neural network models are trained to predict DOS of organic molecules, bulk crystals, and amorphous materials, although the quality of results often depends on the resolution chosen to smooth the DOS [51] . A different ML approach is based on the SchNet model, where a latent Hamiltonian matrix is first predicted and molecular resonance","cbCainu4DxzsZk8f","https://ap.wps.com/l/cbCainu4DxzsZk8f","pdf",2557979,1,15,"English","en",105,"# Introduction\n## Background and challenge in predicting excitation spectra\n## Many-body Green’s function approaches and embedding methods\n## Prior machine learning efforts and gaps\n# Proposed ML framework (MLGF)\n## Training target: self-energy on imaginary frequency grids\n## Model details: kernel ridge regression and features\n## Symmetry-adapted basis for rotational invariance\n## Transferability, data efficiency, and benchmarks","[{\"question\":\"What does the proposed ML framework predict in molecular systems?\",\"answer\":\"It predicts many-body Green’s functions by learning self-energy matrix elements, which can be used to derive photoemission spectra and quasiparticle energies.\"},{\"question\":\"How are real-frequency Green’s functions obtained from the ML predictions?\",\"answer\":\"Self-energy predictions are made on compact imaginary-frequency grids, then real-frequency Green’s functions are accessed through analytic continuation and Dyson’s equation.\"},{\"question\":\"What is the key modeling strategy used to enforce rotational invariance?\",\"answer\":\"Feature and self-energy matrices are represented in a symmetry-adapted intrinsic atomic orbital plus projected atomic orbital (SAIAO) basis.\"}]","Machine Learning Many-Body Green’s Functions for Molecular Excitation Spectra | 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does the proposed ML framework predict in molecular systems?","Question",{"text":75,"@type":76},"It predicts many-body Green’s functions by learning self-energy matrix elements, which can be used to derive photoemission spectra and quasiparticle energies.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How are real-frequency Green’s functions obtained from the ML predictions?",{"text":80,"@type":76},"Self-energy predictions are made on compact imaginary-frequency grids, then real-frequency Green’s functions are accessed through analytic continuation and Dyson’s equation.",{"name":82,"@type":73,"acceptedAnswer":83},"What is the key modeling strategy used to enforce rotational invariance?",{"text":84,"@type":76},"Feature and self-energy matrices are represented in a symmetry-adapted intrinsic atomic orbital plus projected atomic orbital (SAIAO) 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