Name: Reduced Density-Matrix Functional Theory: Improving its foundation
Start: 2022-10-03T09:00:00+02:00
End: 2022-10-14T19:00:00+02:00
Location: ECT*

Reduced Density-Matrix Functional Theory: Improving its foundation

from Monday, 3 October 2022 (09:00) to Friday, 14 October 2022 (19:00)

Monday, 3 October 2022

10:00 Registration
Registration
10:00 - 10:30

10:30 Introduction
Introduction
10:30 - 11:00
Room: Sala Leonardi

11:00 Coffee break
Coffee break
11:00 - 11:30
11:30 Welcome - Christian Schilling & Carlos Benavides-Riveros
Welcome
- Christian Schilling & Carlos Benavides-Riveros
11:30 - 13:00
Room: Sala Leonardi
13:00 Lunch
Lunch
13:00 - 14:29
14:29 Symposium 1: Exact results in RDMFT - Carlos Benavides-Riveros (Max-Planck Institute for Complex Systems)
Symposium 1: Exact results in RDMFT
- Carlos Benavides-Riveros (Max-Planck Institute for Complex Systems)
14:29 - 14:30
Room: Sala Leonardi
14:30 DFT, RDMFT, and the challenge of strong correlations - Eberhard Gross
DFT, RDMFT, and the challenge of strong correlations
- Eberhard Gross
14:30 - 15:00
Room: Sala Leonardi
15:00 Density Functional Theory Transformed into a One-electron Reduced Density Matrix Functional Theory for the Capture of Static Correlation - David Mazziotti
Density Functional Theory Transformed into a One-electron Reduced Density Matrix Functional Theory for the Capture of Static Correlation
- David Mazziotti
15:00 - 15:30
Room: Sala Leonardi
15:30 One-body Reduced Density-matrix Functional Theory for the Canonical Ensemble - Sarina Sutter
One-body Reduced Density-matrix Functional Theory for the Canonical Ensemble
- Sarina Sutter
15:30 - 16:00
Room: Sala Leonardi
16:00 Coffee break
Coffee break
16:00 - 16:30
16:30 Convex N-Representability - Federico Castillo
Convex N-Representability
- Federico Castillo
16:30 - 17:00
Room: Sala Leonardi
17:00 Relating the pure and ensemble density matrix functional - Christian Schilling
Relating the pure and ensemble density matrix functional
- Christian Schilling
17:00 - 17:30
Room: Sala Leonardi
17:30 Implications of pinned occupation numbers for natural orbital expansions - Tomasz Maciazek
Implications of pinned occupation numbers for natural orbital expansions
- Tomasz Maciazek
17:30 - 18:00
Room: Sala Leonardi
Tuesday, 4 October 2022

09:30

09:30 - 11:00
Room: Sala Leonardi

11:00 Coffee break
Coffee break
11:00 - 11:30

11:30

11:30 - 13:00
Room: Sala Leonardi

13:00 Lunch
Lunch
13:00 - 14:30

14:30

14:30 - 16:00
Room: Sala Leonardi

16:00 Coffee break
Coffee break
16:00 - 16:30

16:30

16:30 - 18:00
Room: Sala Leonardi
Wednesday, 5 October 2022
09:29 Symposium 2: RDMFT for quantum chemistry: Computational and theoretical state-of-the-art and open challenges - Christian Schilling (LMU Munich)
Symposium 2: RDMFT for quantum chemistry: Computational and theoretical state-of-the-art and open challenges
- Christian Schilling (LMU Munich)
09:29 - 09:30
Room: Sala Leonardi
09:30 Obstacles on the road to practical implementation of RDMFT - Jerzy Cioslowski
Obstacles on the road to practical implementation of RDMFT
- Jerzy Cioslowski
09:30 - 10:00
Room: Sala Leonardi
10:00 Global Natural Orbital Functional - Mario Piris
Global Natural Orbital Functional
- Mario Piris
10:00 - 10:30
Room: Sala Leonardi Appropriate representations of the electronic structure of atoms, molecules, and solids without explicit recourse to the N-particle density matrix can alternatively be obtained by the one-particle reduced density matrix (1RDM) functional theory [1]. Regrettably, computational schemes based on the exact constrained search formulation are too expensive; so the 1RDM functional requires a practical approach. For a Hamiltonian involving no more than two-body interactions, the ground-state energy can be cast as an exact functional of the two-particle reduced density matrix (2RDM). In practical applications, we employ this exact energy functional but using an approximate 2RDM that is built from the 1RDM. Approximating the energy functional has an important consequence: the functional N-representability problem arises. In this presentation, the role of the N-representability in approximate functionals [2] will be analyzed. The 1RDM functional is called Natural Orbital Functional (NOF) when it is based upon the spectral expansion of the 1RDM. So far, several approximate functionals have been proposed [3], but solely PNOFs [4,5] are based on the reconstruction of the 2RDM subject to necessary N-representability conditions. For the latter, an open source software is available [6] for quantum chemistry calculations. These functionals are capable of producing a correct description of systems with a multiconfigurational nature, however, they also suffer from an important lack of dynamic correlation. To recover this correlation, second-order perturbative corrections have been implemented with significant results [5,7]. Nevertheless, our goal is to recover the missing dynamic correlation only within the NOF theory framework. The 1RDM functional is called Natural Orbital Functional (NOF) when it is based upon the spectral expansion of the 1RDM. So far, several approximate functionals have been proposed [3], but solely PNOFs [4,5] are based on the reconstruction of the 2RDM subject to necessary N-representability conditions. For the latter, an open source software is available [6] for quantum chemistry calculations. These functionals are capable of producing a correct description of systems with a multiconfigurational nature, however, they also suffer from an important lack of dynamic correlation. To recover this correlation, second-order perturbative corrections have been implemented with significant results [5,7]. Nevertheless, our goal is to recover the missing dynamic correlation only within the NOF theory framework. In this talk, a new accurate NOF will be presented for all electronic structure problems, that is, a global NOF [8,9]. Note that the adjective "global" is used instead of "universal" to differentiate our approximate multipurpose NOF from the exact functional. The concept of the dynamic part of the occupation numbers will be introduced. The emergent functional describes the complete intrapair electron correlation and the correlation between orbitals that make up both the pairs and the individual electrons. The interorbital correlation is composed of static and dynamic terms. Different examples will be analyzed where the weak and strong electron correlations are revealed. Our results will be compared with those obtained by established accurate theoretical methods and experimental data. 1. T. L. Gilbert, Phys. Rev. B 12, 2111 (1975); M. Levy, Proc. Natl. Acad. Sci. USA 76, 6062 (1979); S. M. Valone, J. Chem. Phys. 73, 1344 (1980). 2. M. Piris, in Many-body approaches at different scales: a tribute to N. H. March on the occasion of his 90th birthday, Chap. 22, pp. 231-247. New York: Springer (2018). 3. K. Pernal and K. J. H. Giesbertz, Top Curr Chem 368, 125-184 (2016); I. Mitxelena, M. Piris, J. M. Ugalde, Adv. Quantum Chem. 79, 155-177 (2019). 4. M. Piris, J. M. Ugalde, Int. J. Quantum Chem. 114, 1169-1175 (2014). 5. M. Piris, Phys. Rev. Lett. 119, 063002 (2017); Phys. Rev. A 98, 022504 (2018); Phys. Rev. A 100, 032508 (2019). 6. M. Piris, I. Mitxelena, Comp. Phys. Comm. 259, 107651 (2021). 7. M. Piris, X. Lopez, M. Piris, Theor. Chem. Acc. 138, 89 (2019). 8. M. Piris, “Global Natural Orbital Functional: Towards the Complete Description of the Electron Correlation”, Phys. Rev. Lett. 127, 233001 (2021). 9. I. Mitxelena, M. Piris, “Benchmarking GNOF against FCI in challenging systems in one, two and three dimensions”, J. Chem. Phys. 156, 214102 (2022). Keywords: Electron Correlation, Reduced Density Matrix Functional Theory (RDMFT), Natural Orbital Functional Theory (NOFT)
10:30 Functional-Based Description of Electronic Dynamic and Strong Correlation - Neil Qiang Su
Functional-Based Description of Electronic Dynamic and Strong Correlation
- Neil Qiang Su
10:30 - 11:00
Room: Sala Leonardi The slow progress in systematically eliminating intrinsic errors in commonly used approximate functionals limits the applicability of functional-based descriptions to strongly correlated systems. Kohn-Sham density functional theory (KS-DFT) and reduced density matrix functional theory (RDMFT) represent two formally exact theoretical frameworks for the many-electron problem. Commonly, approximate functionals in KS-DFT and RDMFT have advantages in dealing with dynamic correlation and strong correlation, respectively. Hence, establishing a connection between both theories and developing an effective approach to combine functional approximations in both theories can create new possibilities for improving the predictive power of functional-based methods. This talk is about some effort in this direction in our group.
11:00 Coffee break
Coffee break
11:00 - 11:30
11:30 Towards an in-principle-exact density matrix functional embedding theory - Emmanuel Fromager
Towards an in-principle-exact density matrix functional embedding theory
- Emmanuel Fromager
11:30 - 12:00
Room: Sala Leonardi
12:00 Self-consistent-field method for correlated many-electron systems with an entropic cumulant energy - Jian Wang
Self-consistent-field method for correlated many-electron systems with an entropic cumulant energy
- Jian Wang
12:00 - 12:30
Room: Sala Leonardi Using an entropic functional for the correlation energy, an SCF method is found within the density-matrix functional theory. The method is efficient as the SCF method in Hartree-Fock or DFT theory.
12:30 Critical reassessment of recent developments in functional theory: From Hartree-Fock to i-DMFT - Lexin Ding
Critical reassessment of recent developments in functional theory: From Hartree-Fock to i-DMFT
- Lexin Ding
12:30 - 13:00
Room: Sala Leonardi
13:00 Lunch
Lunch
13:00 - 14:30

14:30

14:30 - 16:00
Room: Sala Leonardi

16:00 Coffee break
Coffee break
16:00 - 16:30

16:30

16:30 - 18:00
Room: Sala Leonardi

19:30 Dinner (Ristorante Ca dei Gobj)
Dinner (Ristorante Ca dei Gobj)
19:30 - 21:30
Room: Sala Leonardi
Thursday, 6 October 2022

09:30

09:30 - 11:00
Room: Sala Leonardi

11:00 Coffee break
Coffee break
11:00 - 11:30

11:30

11:30 - 13:00
Room: Sala Leonardi

13:00 Lunch
Lunch
13:00 - 14:30

14:30

14:30 - 16:00
Room: Sala Leonardi

16:00 Coffee break
Coffee break
16:00 - 16:30

16:30

16:30 - 18:00
Room: Sala Leonardi
Friday, 7 October 2022
09:29 Symposium 3: Extending the scope of RDMFT (Bosons, ultracold gases, and superconductors) - Derk Kooi
Symposium 3: Extending the scope of RDMFT (Bosons, ultracold gases, and superconductors)
- Derk Kooi
09:29 - 09:30
Room: Sala Leonardi
09:30 Oportunities for RDMFT: Lee-Huang-Yang Fluids: from liquid droplets to supersolidity - Alessio Recati
Oportunities for RDMFT: Lee-Huang-Yang Fluids: from liquid droplets to supersolidity
- Alessio Recati
09:30 - 10:00
Room: Sala Leonardi
10:00 Reduced density matrix functional theory for bosons - Christian Schilling
Reduced density matrix functional theory for bosons
- Christian Schilling
10:00 - 10:30
Room: Sala Leonardi
10:30 Functional theory for Bose-Einstein condensates - Julia Liebert
Functional theory for Bose-Einstein condensates
- Julia Liebert
10:30 - 11:00
Room: Sala Leonardi
11:00 Coffee break
Coffee break
11:00 - 11:30
11:30 Repulsively diverging gradient of the density functional in the Reduced Density Matrix Functional Theory - Tomasz Maciazek
Repulsively diverging gradient of the density functional in the Reduced Density Matrix Functional Theory
- Tomasz Maciazek
11:30 - 12:00
Room: Sala Leonardi
12:00 Density functional theory of the superconducting state - Eberhard Gross
Density functional theory of the superconducting state
- Eberhard Gross
12:00 - 12:30
Room: Sala Leonardi
12:30 Reduced density matrix functional theory for superconductors - Carlos Benavides-Riveros
Reduced density matrix functional theory for superconductors
- Carlos Benavides-Riveros
12:30 - 13:00
Room: Sala Leonardi
13:00 Lunch
Lunch
13:00 - 14:30

14:30

14:30 - 16:00
Room: Sala Leonardi

16:00 Coffee break
Coffee break
16:00 - 16:30
Saturday, 8 October 2022
Sunday, 9 October 2022