Finding Accurate and Scalable Theories for Electronic Correlation – FASTcorrelation

The theoretical and methodological developments proposed in this project build on the concept of response function. Indeed, a possible way to introduce a systematic improvement in the description of the ground state electronic correlation energy is the adiabatic connection fluctuation and dissipation theorem (ACFDT). Within this framework, the correlation energy is expressed only in terms of linear response functions (the polarizability for molecules or the dielectric matrix for solids). The polarizability and the dielectric matrix describe the response of the electronic density to an external perturbing potential (e.g. visible light). The response functions are also a necessary ingredient to treat the screening in many-body Green’s function approaches, such as the GW approximation and the Bethe-Salpeter equation (BSE), that are used to theoretically/computationally describe electronic excited states. Even if the ACFDT and Green’s function methods are derived from different theoretical backgrounds, from a practical point of view these two methods can intertwine within the same framework based on response functions. This project exploits this combination and aims to introduce an improvement in the way ground state and excited state properties are computed by investigating several possible paths to improve the description of response functions. While most response function methods are based on simple approximations (i.e. the random phase approximation RPA), the FASTcorrelation project aims to find new theories with improved accuracy. Response functions will be improved by exploring three different research directions based on (1) time-dependent density functional theory (2) Green’s function theory, and (3) analogies with traditional quantum chemical methods.

By investigating several different scenarios and approximations, two new methods were developed within the FASTcorrelation project: An adiabatic connection analog of the second order screened exchange (AC-SOSEX) and a time-dependent Hartree-Fock based on an electron-hole approximation (eh-TDHF). By using the eigenvalue decomposition of the dielectric matrix, these two approaches are particularly suitable for a numerical implementation within a plane wave basis set. Through a systematic study to benchmark these two approaches against established molecular test sets, it was shown that both these methods show significant improvements over the traditional random-phase approximation and, in several cases, an accuracy similar to coupled-cluster single and doubles was reached. Additionally, further algorithm development improved the numerical efficiency of the AC-SOSEX and eh-TDHF approximations and allowed for applications to large systems with up to 100 electrons and 400k plane-waves in the basis set. These results represent a milestone of the project, since it was shown that within a solid state
framework based on the plane-wave basis set a very high level of accuracy can be reached with a good computational efficiency.
This project is not limited to academic applications but also aims to include applications to realistic materials. We considered the computation of accurate adsorption energies of molecules in zeolites. In order to introduce temperature effects, several snapshot were extracted from molecular dynamics calculations and single point calculations were carried out with the new methodologies developed. This part of the work, currently still underway, will be instrumental for demonstrating that our approaches can also be used for realistic systems and contribute to the modeling of important experimental and technological problems.

The FASTcorrelation project is going beyond the state of the art and is significantly contributing to improve the description of the ground-state electronic correlation within a practical framework. Two new accurate approximations were developed that are suitable for an efficient numerical implementation to treat both molecules and solids. Importantly, an effort has been carried out to bridge abstract theory and algorithms with the reality, for example, by addressing applications related to catalytic processes in zeolites. A large amount of work is still underway to further establish the accuracy of the new techniques for realistic systems and to extend them to excited state calculations. Thanks to the methodological development contributed by the FASTcorrelation project more and more problems posed by experimental and technological applications will be addressed with unprecedented accuracy in the future.

So far, the project has lead to 4 publications in international peer reviewed journals (1 J. Chem. Theory Comput., 2 J. Chem. Phys., and 1 J. Chem. Phys. Communications).
Results produced within this project have been presented in 5 invited talks at international conferences (including 2 CECAM workshops), 2 invited seminars at Universities in Turkey and the USA, and 4 contributed talks (including 2 at the American Physical Society March Meeting).

The development of quantum mechanics in the first part of the 20th century has had profound implications for the understanding of matter on the microscopic scale. Starting only from the chemical composition, quantum mechanics, through the solution of the Schrödinger equation, can describe the properties of molecular or extended systems, such as the structure, elasticity, electrical properties, optical absorption, and many more. Together with the invention of computers and the introduction of suitable approximations and algorithms, this concept has led to the development of several general purpose methodologies to compute the properties of materials from first principles. Because of the complexity of the electronic correlation problem, the numerical methods available today solve the Schrödinger equation by approximating the electronic correlation contribution and require a compromise between accuracy and scalability to treat large systems (up to hundreds or thousands of atoms). The goal of the FASTcorrelation project is to develop and apply new powerful theoretical tools to compute the properties of materials from first principles by using quantum mechanics. The need for a breakthrough in this field is particularly urgent to accurately understand and predict the microscopic mechanisms and interactions involved in complex experimental and technological applications. For example, the weak dispersion forces necessary to understand the interactions in molecular crystals or in surface catalysis applications are poorly described by the commonly used ground state density functional methods. Other applications that require better theoretical descriptions involve electronic excitations such as, for example, the optimization of light absorption and electronic transfer in next generation solar cells. This proposal will address these different problems, involving both electronic ground state and excited state processes, within the same framework. The proposed theoretical and methodological development will build on the concept of linear response function (i.e. dielectric matrix or polarizability). Polarizability and dielectric matrix describe the response of electrons to an external perturbing potential and are intimately related to the problem of the electronic correlation, since each electron can be seen as an external perturbation acting on all the other electrons in the system. By systematically seeking better approximations of linear response functions, this proposal will, at the same time, improve the accuracy of the ground state correlation energy through the adiabatic connection fluctuation dissipation theorem and the description of excited states within Green’s function based methods. In combination with the powerful algorithms recently developed by the project coordinator, the proposed research will lead to revolutionary approaches to treat, with unprecedented accuracy, realistic models with hundreds of atoms and address within the same framework molecules, solids and nanostructures. A series of applications will also be explored, including molecular crystals and materials used in catalysis and solar cells. Such applications of high scientific and technological relevance will help test the accuracy of the new methodologies and demonstrate their computational efficiency.
By developing a new general framework for first principles calculations and applying it to systems of significant technological interest, the outcomes of this proposal will have profound implications for science and society.