Periodic Reporting for period 3 - PTEROSOR (PT-symmetric electronic structure theory)
Berichtszeitraum: 2023-06-01 bis 2024-11-30
The PTEROSOR project is dedicated to advancing the field of excited states in molecular systems. The understanding of these states is crucial for various scientific disciplines, including chemistry, physics, and biology, as it plays a vital role in accurately describing the interaction of light and matter. The project aims to create novel methods for studying and understanding these states, with the ultimate goal of providing a more accurate and comprehensive understanding of their properties and behavior.
In this context, the PTEROSOR project proposes a new approach for obtaining excited-state energies and wave functions by utilizing the properties of non-Hermitian Hamiltonians, such as PT-symmetric Hamiltonians, which are complex extensions of conventional Hermitian Hamiltonians.
Its main idea is to use analytical continuation via the complex plane to connect ground and excited states, and to study both mean-field and correlated methods. Additionally, the project aims to gain new insight into the convergence properties of perturbative methods and how singularities, known as exceptional points, impact the radius of convergence of the perturbative series. The new features developed during the project are continuously implemented in Quantum Package, an open-source, multi-purpose and robust programming environment for quantum chemistry developed by the group and others. This will ensure that the theoretical advances from the project are translated into usable software for the scientific community.
The application of non-Hermitian Hamiltonians in the calculation of excited states is a relatively new and unexplored area of research. The PTEROSOR project aims to delve deeper into this field and uncover the many exciting properties and possibilities that it holds. The project's objective is to make significant strides in our understanding of non-Hermitian quantum mechanics, with a particular focus on determining the properties of excited states. At best, it is expected to provide the scientific community with a groundbreaking new computational tool for the study of excited states. This ambitious project will tackle this area of research with a comprehensive and holistic approach.
In this context, the PTEROSOR project proposes a new approach for obtaining excited-state energies and wave functions by utilizing the properties of non-Hermitian Hamiltonians, such as PT-symmetric Hamiltonians, which are complex extensions of conventional Hermitian Hamiltonians.
Its main idea is to use analytical continuation via the complex plane to connect ground and excited states, and to study both mean-field and correlated methods. Additionally, the project aims to gain new insight into the convergence properties of perturbative methods and how singularities, known as exceptional points, impact the radius of convergence of the perturbative series. The new features developed during the project are continuously implemented in Quantum Package, an open-source, multi-purpose and robust programming environment for quantum chemistry developed by the group and others. This will ensure that the theoretical advances from the project are translated into usable software for the scientific community.
The application of non-Hermitian Hamiltonians in the calculation of excited states is a relatively new and unexplored area of research. The PTEROSOR project aims to delve deeper into this field and uncover the many exciting properties and possibilities that it holds. The project's objective is to make significant strides in our understanding of non-Hermitian quantum mechanics, with a particular focus on determining the properties of excited states. At best, it is expected to provide the scientific community with a groundbreaking new computational tool for the study of excited states. This ambitious project will tackle this area of research with a comprehensive and holistic approach.
The PTEROSOR project, thanks to the support of ERC funding, has made significant progress in developing various methods for targeting molecular excited states. Our research has led to a better understanding of the fundamental concepts of non-Hermitian extensions of quantum chemistry, including the Hartree-Fock approximation and Rayleigh-Schrödinger perturbation theory. We have utilized these new insights to further explore the behavior and positioning of exceptional points and other singularities that arise when perturbation theory is extended into the complex plane.
We have also achieved significant progress in targeting higher-energy solutions of the mean-field and coupled-cluster equations through the development of specialized and robust algorithms. From a theoretical perspective, we have uncovered new similarities between established wave function methods and many-body perturbation theory based on Green's functions, such as exact similarities at the ground and excited state levels between the Bethe-Salpeter formalism and coupled-cluster theory. We have also provided mathematical and physical explanations for the appearance of multiple solutions and discontinuities in various physical quantities computed within Green's function methods. This led us to introduce regularized Green's function methods as a way to address these issues.
In addition, we have developed a protocol for efficiently catching weak and strong correlations through a hybrid scheme that combines seniority and excitation degrees. We are currently working on a new systematically improvable route for excited-state calculations. The research carried out in this project has the potential to provide the scientific community with novel computational tools for the study of excited states, and to deepen our understanding of non-Hermitian quantum mechanics.
We have also achieved significant progress in targeting higher-energy solutions of the mean-field and coupled-cluster equations through the development of specialized and robust algorithms. From a theoretical perspective, we have uncovered new similarities between established wave function methods and many-body perturbation theory based on Green's functions, such as exact similarities at the ground and excited state levels between the Bethe-Salpeter formalism and coupled-cluster theory. We have also provided mathematical and physical explanations for the appearance of multiple solutions and discontinuities in various physical quantities computed within Green's function methods. This led us to introduce regularized Green's function methods as a way to address these issues.
In addition, we have developed a protocol for efficiently catching weak and strong correlations through a hybrid scheme that combines seniority and excitation degrees. We are currently working on a new systematically improvable route for excited-state calculations. The research carried out in this project has the potential to provide the scientific community with novel computational tools for the study of excited states, and to deepen our understanding of non-Hermitian quantum mechanics.
Each of the aforementioned points can be considered a significant achievement that provides a significant advancement to electronic structure theory with a particular focus on excited states in molecular systems.
We are currently exploring new and exciting concepts and methods to further advance our understanding of non-Hermitian quantum mechanics and improve computational tools for studying excited states.
(i) Combining the similarity renormalization group (SRG) from quantum field theory with many-body Green's functions to overcome some limitations of the GW approximation and propose a static self-energy approximation from first principles.
(ii) Extending our recently introduced systematically improvable configuration interaction scheme for excited states to coupled-cluster theory to achieve high accuracy for any family of excited states.
(iii) Developing selected configuration interaction methods for resonant states using the complex absorbing potential to provide benchmark data for this field of research.
(iv) Unifying excited-state methodologies by clearly identifying their similarities and differences.
(v) Automatically generating the working equations for complex wave function ansatze such as single-reference and multireference coupled-cluster theory.
Our goal is to continue to push the boundaries of electronic structure theory, providing new and improved computational tools for the study of excited states and deepening our understanding of non-Hermitian quantum mechanics.
We are currently exploring new and exciting concepts and methods to further advance our understanding of non-Hermitian quantum mechanics and improve computational tools for studying excited states.
(i) Combining the similarity renormalization group (SRG) from quantum field theory with many-body Green's functions to overcome some limitations of the GW approximation and propose a static self-energy approximation from first principles.
(ii) Extending our recently introduced systematically improvable configuration interaction scheme for excited states to coupled-cluster theory to achieve high accuracy for any family of excited states.
(iii) Developing selected configuration interaction methods for resonant states using the complex absorbing potential to provide benchmark data for this field of research.
(iv) Unifying excited-state methodologies by clearly identifying their similarities and differences.
(v) Automatically generating the working equations for complex wave function ansatze such as single-reference and multireference coupled-cluster theory.
Our goal is to continue to push the boundaries of electronic structure theory, providing new and improved computational tools for the study of excited states and deepening our understanding of non-Hermitian quantum mechanics.