Advanced Quantum ESPRESSO school: Hubbard and Koopmans functionals from linear response

28 August – 1 September 2023
University of Pavia (Italy)

Attendees of the school in a courtyard of the University of Pavia

From August 28th to September 1st, 2023, Pavia (Italy) hosted the first in-person edition of the “Advanced Quantum ESPRESSO School: Hubbard and Koopmans functionals from linear response“. Building upon the remarkable success of the virtual edition in 2022, this year’s event welcomed  41 participants from various countries  (carefully selected from a large  pool of 170 applications). They were joined by 20 lecturers and tutors, along with 5 keynote invited speakers who enriched the school program with their seminars related to the topic of each day. This unique blend of a moderate number of students and a high lecturer-to-student ratio set the ideal conditions for learning as the school provided the informal environment and the occasion to stimulate curiosity, strong interactions and vibrant discussions on the treated topics.

With a share of 27% female participants the school showed a degree of diversity not common in physics programmes, which constitutes encouraging data for the field. We are immensely grateful for the generous support from our sponsors: Psi-k, the University of Pavia through its Center for Global Strategic Engagement (GLOBEC), the Swiss National Centre for Competence in Research NCCR MARVEL, the Materials design at the exascale Centre of Excellence MaX, and the Italian Node of CECAM (CECAM-IT-Simul). Their collective commitment made this event possible and a remarkable success. The University of Pavia is also gratefully acknowledged for hosting the event and for providing  rooms, equipment and technical support. 

The core objective of this school was to introduce PhD students, postdocs, and junior scientists to the intricacies of advanced exchange-correlation functionals in density-functional theory (DFT), specifically tailored for modelling complex materials, including extended Hubbard and Koopmans functionals. By eradicating self-interaction errors and restoring piecewise linearity in total energy calculations, these advancements have expanded the horizons of DFT. They enhance the description of ground states for transition-metal and rare-earth compounds and provide precise spectral properties such as fundamental band gaps and band structures. The Hubbard and Koopmans functionals represent a significant milestone in DFT, addressing fundamental challenges within (generalised) Kohn-Sham theory. Their implementation leverages the power of linear-response theory (for example, to compute the effective electronic couplings) through density-functional perturbation theory (DFPT).

This school unfolded in two distinct phases. The first two days provided participants with a comprehensive foundation in DFT, DFPT, and their basic applications, including ground-state calculations and lattice-vibrational properties. The subsequent two days delved deeply into the theoretical underpinnings of Hubbard and Koopmans functionals, the focal point of our event. We also dedicated a half-day to providing our attendees with a primer on automation techniques, centred around the AiiDA platform, for managing computational workflows involving these cutting-edge methods. Additionally, we hosted a vibrant poster session, where 20 students showcased their research and engaged in enriching discussions, and a social dinner that was functional to establish a friendly atmosphere and informal interpersonal relationships.

The chosen computational platform, Quantum ESPRESSO (QE), an open-source electronic-structure software, served as the bedrock for our activities, seamlessly accommodating both extended Hubbard and Koopmans functionals. The immersive program offered a diverse blend of experiences, ranging from enlightening presentations by keynote speakers providing a panoramic view of each day’s topic to theoretical and technical lectures led by the foremost developers of the QE project. Participants also enjoyed hands-on sessions, both introductory and advanced, and practical demonstrations that empowered them with the knowledge and tools to apply these concepts directly in their research and educational endeavours.

This advanced Quantum ESPRESSO school has not only enriched the scientific knowledge and mindset of the participants but has also contributed to strengthen and establish a scientific network and to develop a sense of community in the field  that is being extended to younger generations. The bonds forged during this event (and in similar formative occasions) will undoubtedly be functional to catalyse future collaborations and to stimulate new breakthroughs in the field of condensed-matter physics and materials science.

Detailed Program 

DAY 1: Density Functional Theory 

  • Lecture: “Introduction to density-functional theory”, Davide Ceresoli
  • Lecture: “Exchange-correlation functionals of DFT”,  Stefano de Gironcoli
  • Lecture: “Maximally localized Wannier functions: theory and recent developments”, Nicola Marzari
  • Hands-on: “DFT in practice”, Pietro Delugas, Guido Fratesi
  • Hands-on: “Wannier interpolation of band structures”, Antimo Marrazzo 
  • Invited lecture: “Novel correlation energy functionals within the ACFDT formalism”, Maria Hellgren

DAY 2: Density Functional Perturbation Theory

  • Lecture: “Density-functional perturbation theory: Phonons”, Paolo Giannozzi
  • Lecture: “Electron-phonon coupling from first-principles”, Samuel Poncé 
  • Lecture: “Beyond harmonic phonons: Phase diagrams and phase transitions with quantum and thermal effects”, Lorenzo Monacelli
  • Hands-on: “Phonons from DFPT”, Pietro Delugas
  • Hands-on: “Electron-phonon coupling”, Samuel Poncé 
  • Hands-on: “Phonons in the anharmonic approximation”, Lorenzo Monacelli 
  • Invited lecture: “A constrained density functional perturbation theory approach to ultrafast phase transition”, Matteo Calandra

Social dinner

DAY 3: Hubbard Functionals

  • Lecture: “DFT+U and DFT+U+V: Basic concepts and applications”, Matteo Cococcioni 
  • Lecture: “First-principles calculation of Hubbard parameters using linear-response theory”, Iurii Timrov
  • Lecture: “Dynamical extension of DFT+U: U(w)”, Tommaso Chiarotti
  • Invited lecture: “Successes and failures of DFT+U in ferroic materials”,  Silvia Picozzi
  • Hands-on: “DFT+U and DFT+U+V in practice”, Matteo Cococcioni, Iurii Timrov
  • Hands-on: “Calculation of Hubbard parameters using DFPT”, Iurii Timrov, Matteo Cococcioni
  • Lecture: “Phonons and electron-phonon coupling using DFPT+U”, Andrea Floris

Poster session

DAY 4: Koopmans Functionals

  • Lecture: “Koopmans functionals: Basic concepts”, Ismaila Dabo
  • Lecture: “Koopmans compliance: Towards a functional theory of the spectral density”, Andrea Ferretti
  • Lecture: “Koopmans functionals in practice: minimisation, screening coefficients, automation, and more”, Edward Linscott
  • Lecture: “Koopmans spectral functionals: implementation in periodic boundary conditions”, Nicola Colonna 
  • Hands-on: “Spectral properties of finite and extended system with the koopmans package”, Edward Linscott, Marija Stojkovic 
  • Hands-on: “Spectral properties of finite and extended system with the KCW code”, Nicola Colonna, Edward Linscott
  • Invited lecture: “Ab initio many-body perturbation theory”, Davide Sangalli

DAY 5: AiiDA, automation, workflows

  • Lecture: “Introduction to AiiDA”, Christopher Sewell
  • Lecture: “AiiDA-Vibroscopy: all-functional infrared and Raman spectra”, Lorenzo Bastonero
  • Invited lecture: “Computational Workflows for an Accelerated Design of Novel Materials and Interfaces”, Ivano Castelli

Importantly, the recording of the lectures can be found on YouTube and on the Materials Cloud website. Additionally, the hands-on materials are easily accessible on Github.

Lecturers and tutors

Nicola Marzari (EPFL and PSI, Switzerland)

Paolo Giannozzi (University of Udine, Italy)

Davide Ceresoli (University of Milan, Italy)

Stefano de Gironcoli (SISSA, Italy)

Ismaila Dabo (Penn State University, USA)

Samuel Poncé (UCLouvain, Belgium)

Andrea Floris (Lincoln University, UK)

Christopher Sewell (EPFL, Switzerland)

Lorenzo Monacelli (EPFL, Switzerland)

Pietro Delugas (SISSA, Italy)

Guido Fratesi (University of Milan, Italy)

Antimo Marrazzo (University of Trieste, Italy)

Marija Stojkovic (EPFL, Switzerland)

Edward Linscott (EPFL, Switzerland)

Tommaso Chiarotti (EPFL, Switzerland)

Lorenzo Bastonero (University of Bremen, Germany)

Iurii Timrov (EPFL, Switzerland)

Nicola Colonna (PSI, Switzerland)

Andrea Ferretti (CNR Modena, Italy)

Matteo Cococcioni (University of Pavia, Italy)

Keynote speakers

Maria Hellgren (Sorbonne Université, France)

Matteo Calandra (University of Trento, Italy)

Silvia Picozzi (CNR-SPIN, Italy)

Davide Sangalli (Istituto di Struttura della materia (ISM -CNR), Italy)

Ivano Castelli (DTU, Denmark)


Matteo Cococcioni (University of Pavia, Italy)

Iurii Timrov (EPFL, Switzerland)

Nicola Colonna (PSI, Switzerland)

Andrea Ferretti (CNR Modena, Italy)

General remarks

The atmosphere of the school was very exciting, and the participants’ enthusiasm and dedication never wavered, right up to the very end. It was encouraging and motivating to see how many researchers share a deep interest in DFT, DFPT, and advanced functionals. The attendees were highly motivated and eager to learn. This experience was truly rewarding for everyone involved, from the participants (able to lively interact and learn at all levels) to the lecturers (who were also able to discuss and further deepen some of the presented topics). We are confident that this event has made an impact on all of the attendees and it has been an incredible educational adventure for everyone.

Feedback from participants

As the school drew to a close, the attendees were invited to share their thoughts through a feedback questionnaire, and the response was remarkable. More than half of the participants took the time to provide their insights, and their feedback is on the one side extremely useful to the organisers to improve on future editions and, on the other side, a clear statement of the success of this school. A remarkable 91% of respondents expressed a high level of satisfaction with the school. There were several aspects that stood out. First, the opportunity to pose numerous questions was highly valued, fostering an engaging and interactive learning environment. The rich pool of lecturers and experts in the field left a lasting impression, ensuring that participants received diverse perspectives and insights. Participants also expressed their gratitude for the chance to explore new methods and codes, expanding their toolkit for scientific exploration. The productive and informative discussions that took place throughout the school left a clear mark, proving that learning does not only happen in classrooms but thrives through shared conversations. 

Moreover, the participants were delighted by the comprehensive overview of the current state of the art in DFT and beyond. It is evident that they relished the broader context within which they could place their newfound knowledge. And as for aspects to be improved, their valuable input was highly considered. Some participants expressed a desire for longer hands-on sessions, craving for more practical experience to reinforce their learning. Others wished for an extended school duration, suggesting a full 5-day format to delve even deeper into the subject matter. Interestingly, there was a call for a bit less emphasis on equations and a greater focus on painting a broader picture of the topics, enabling a better grasp of the overarching concepts. Lastly, participants requested more time for questions and a prioritisation of questions from fellow students, emphasising the value they place on peer engagement. In summary, the participants gave us precious feedback that will be used to continually enhance and evolve this school, ensuring that it remains a vibrant hub of learning, discussion, and exploration for years to come.

Some examples of the feedback from the participants:

I personally find this school as a great experience, both from a professional and a personal point of view.

Overall, the school was very enjoyable and I am very happy to have attended it. I particularly enjoyed talks where I could understand the big picture and context of the talk (e.g. by Prof. Dabo). I would like to encourage you to organize it the upcoming years as well!

Conclusions and prospects

The school turned out to be very satisfactory on a number of fronts. The number of applicants was deliberately kept manageable to ensure rich, one-on-one interactions with the dedicated lecturers. These educators and the supportive tutors delivered well-prepared lectures and tutorials. The participants injected incredible energy and enthusiasm into the school, creating a vibrant and dynamic learning environment. Their active engagement and positive spirit fueled the collective success of the school. The feedback that was received from the participants has been overwhelmingly positive, with some proposals of improvement and suggestions that will be very valuable for shaping future editions of the school. In the spirit of knowledge-sharing, we have made the lectures accessible to a wider audience. One can find them on YouTube and the Materials Cloud website, ensuring that the wealth of information is readily available. Additionally, the hands-on materials are easily accessible on Github, promoting practical learning for all. The resounding praise from both participants and lecturers underscores the school’s success. New and further improved editions of this school are envisioned for the next years.

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