Recent Presentations by N. A. W. Holzwarth and collaborators

• Presentation by D. Cory Lynch for Ph. D. Thesis defense on July 29, 2026 "Computational Investigation of Solid Electrolyte Materials Using First Principles and Machine Learning Methodologies"

• Presentation prepared by D. Cory Lynch for March 2026 APS meeting -- Mar. 15-20, 2026 in Denver, Colorado -- "Enabling the Investigation of the Conductivity of Select Lithium (Thio)BoraciteMaterials Using the Allegro Machine Learned Interatomic Potential Package" -- (link to abstract)

• Presentation by Natalie Holzwarth at the 248th meeting of the Electrochemical Society -- October 12-16, 2025 in Chicago, IL -- "Progress and Assessment of Computational Challenges in Simulating Ionic Conductivities of Electrolyte Materials Using Machine-Learned Potentials Trained from First Principles Molecular Dynamics and Statistical Analysis" (with corrections)

• Presentation by N. A. W. Holzwarth at the WFU Condensed Matter Collaborative Seminar on September 12, 2025 in Olin 105 -- "Density functional theory and its role in condensed matter physics"

• Presentation by N. A. W. Holzwarth at the North Carolina Battery Technology Workshop 2025 -- June 5-6, 2025 in Charlotte, NC -- "Computationally Simulating Reproducible Estimates of Ionic Conductivity in Electrolyte Materials"

• Presentation by Natalie Holzwarth during WFU physics colloquium together with Paul Anderson on "Special Colloquium on Perspectives on WFU Physics" on April 3, 2025. "Perspective on WFU Physics Part 2"

• Presentation by N. A. W. Holzwarth at the March 2025 APS meeting -- Mar. 16-21, 2025 in Anaheim, California -- "An assessment of numerical behaviors of the r2SCAN exchange-correlation functional" -- (link to abstract)

• Presentation by D. Cory Lynch (virtual; on demand) at the March 2025 APS meeting -- Mar. 16-21, 2025 in Anaheim, California -- "A Study of Advancements in Ionic Conductivity Methods and Machine Learned Interatomic Potentials to Calculate Ionic Conductivities with a Model Solid Electrolyte (Li₄SiO₄)_x(Li₄PO₄)_1−x" -- (link to abstract)

• Presentation by N. A. W. Holzwarth at the 11th International ABINIT Developer Workshop -- July 1-4, 2024 in Quebec, Canada. "PAW datasets for meta-GGA calculations"

• Presentation by N. A. W. Holzwarth at the North Carolina Battery Technology Workshop 2024 -- June 6-7, 2024 in Charlotte, NC -- "Exploration of Solid-State Electrolytes Based on Lithium (Thio) Boracites through Computer Simulation"

• Poster by D. Cory Lynch intended for the March 2024 APS meeting (Mar. 4-8, 2024). While the official poster had to be withdrawn due to illness, the poster that would have been presented on "Structure and Phonon Investigations of an Extended Family of Lithium (Thio)Boracite Electrolytes for All-Solid-State Batteries" is given here.

• Presentation by N. A. W. Holzwarth at the March 2023 APS meeting -- Mar. 5-10, 2023 in Las Vegas, Nevada -- "Simulations and Analyses of Li 4 and Li 6 (Thio)Boracites As Promising Li Ion Conducting Electrolytes for All-Solid-State Batteries" -- (link to abstract)

• Presentation by Cory Lynch at the 242th ECS Meeting Oct 9-13, 2022 in Atlanta, GA -- "Simulations and Analyses of Li4 and Li6 Boracites and Thioboracites as Promising Li IonConducting Electrolytes" (link to abstract)

• Presentation by N. A. W. Holzwarth at the March 2022 APS meeting -- Mar. 14-18, 2022 in Chicago Illinois. "Development of self-consistent pseudopotentials and PAW datasets for meta-GGA exchange-correlation functionals" -- (link to abstract)

• Presentation by Dr. Yan Li at WFU Physics Colloquium on November 4, 2021 -- "First Principles Investigations of Electrolyte Materials in All-Solid-State Batteries"

• Presentation by Yan Li for Ph. D. Thesis defense on October 21 2021 -- "First Principles Investigations of Electrolyte Materials in All-Solid-State Batteries"

• Presentation by Yan Li at the 240th ECS Meeting Oct 10-14, 2021 -- "Computational Investigation of Li Boracite Li₄B₇O₁₂Cl and Related Materials as Solid Electrolytes " (link to abstract)

• Presentation by N. A. W. Holzwarth at the 240th ECS Meeting Oct 10-14, 2021 -- "First Principles Simulations to Understand the Structural and Electrolyte Properties of Idealized Li_7.5B₁₀S₁₈X_1.5 (X = Cl, Br, I) -- Li Superionic Conductors Recently Identified in the Experimental Literature " (link to abstract)

• Presentation by N. A. W. Holzwarth at the Electronic Structure Discussion Group at Cambridge University invited by WFU alum Angela Harper -- June 9, 2021 -- First principles simulations of electrolyte materials with a view toward all solid-state battery technology -- Li₄P₂S₆, Na₄P₂S₆, and possible alloys

• Presentation by N. A. W. Holzwarth at the 10^th ABINIT International Developer Workshop May 31-June 4, 2021 -- Progress on self-consistent meta-gga PAW datasets from ATOMPAW   (PP slides)

• Presentation by Yan Li at the March 2021 APS meeting -- "Li₃BO₃ and Li₃BN₂: Computational study of structural and electrolyte properties of pure and doped crystals" (link to abstract)

• Annotated slides that would have been presented by Yan Li at the cancelled March 2020 APS meeting -- "Prediction and analysis of a sodium ion electrolyte: Li₂Na₂P₂S₆"

• Annotated slides that would have been presented by N. A. W. Holzwarth at the cancelled March 2020 APS meeting -- "Continuity of Phonon Dispersion Curves of Anisotropic Ionic Materials"

• Presentation by N. A. W. Holzwarth at Wake's CFM (Center for Functional Materials) Seminar Series -- "First principles simulations of idealized known And unknown crystalline materials" Dec. 4, 2019.

• Presentation by N. A. W. Holzwarth at Duke University's MEMS Seminar Series, invited by Olivier Delaire -- "Computational Investigation of the Structural and Electrolyte Properties of Li₄P₂S₆, Na₄P₂S₆, and Li₂Na₂P₂S₆" Nov. 6, 2019.

• Presentation by Yan Li at the 236th Meeting of the Electrochemical Society in Atlanta, Ga Oct. 13-17, 2019. Computational (Re)investigation of the Structural and Electrolyte Properties of Li₄P₂S₆, Na₄P₂S₆, and Li₂Na₂P₂S₆

• Poster by Yan Li at the 2019 Workshop on Recent Developments in Electronic Structure at the University of Illinois in Champaign-Urbana, Illinois May 20-22, 2019 Computational Reinvestigation of the Structural and Electrolyte Properties of Li₄P₂S₆ and Na₄P₂S₆

• Presentation by N. A. W. Holzwarth at the Workshop on Precision Quantification in DFT May 23-24, 2019 in Louvain la Neuve, Belgium Assessment of Accuracy and Efficiency of PAW Datasets in Materials Simulations

• Contributed talk presented by Yan Li at the March 2019 Meeting of the American Physical Society, March 4-8, 2019 in Boston, MA Computational and experimental investigation of Na₄P₂S₆ as a promising solid electrolyte material for sodium metal batteries

• Presentation by N. A. W. Holzwarth at the HybriD³ Theory Training Workshop Sept. 28-29, 2018 at Duke University, organized by Volker Blum (Duke) and Yosuke Kanai (UNC). "Practical Density Functional Theory with Plane Waves"

• Invited talk present by N. A. W. Holzwarth at the 2018 Electronic Structure Workshop, June 10-14, 2018 at the University of Pennsylvania, Philadelphia PA. "Perspectives on the Projector Augmented Wave Method (PAW)"

• Contributed talk presented by Jason Howard at the March 2018 Meeting of the American Physical Society, March 6-9, 2018 in Los Angeles, CA Understanding the phase properties of Li₂OHCl, Li₂(OH)_1-xF_xCl, and Li₂OHBr with first principles simulations.

• Contributed talk presented by N. A. W. Holzwarth on behalf of Ahmad Al-Qawasmeh at the March 2018 Meeting of the American Physical Society, March 6-9, 2018 in Los Angeles, CA Computational Study of the Solid Electrolyte Li₄PS₄I and Related Materials

• Eight minute talk presented by Natalie Holzwarth at the New Ideas Series from the Dean of the College of Wake Forest University, February 22, 2018 in the WFU Library Auditorium -- "Simulations of materials -- focusing on electrolytes for all solid state batteries"

• Poster contributed by Jason Howard and Zachary Hood at the 232nd Meeting of the Electrochemical Society Oct. 1-5, 2017 in National Harbor, MD -- Structural and Electrolyte Properties of Li₂OHCl

• Poster contributed by Jason Howard at the 29th Annual Workshop on Recent Developments in Electronic Structure Methods June 25-28, 2017 at Princeton University -- First Principles Simulations of Li₂(OH)Cl

• Poster contributed by Ahmad Al-Qawasmeh at the 29th Annual Workshop on Recent Developments in Electronic Structure Methods June 25-28, 2017 at Princeton University -- Li₁₄P₂O₃N₆: Computational study of a possible new electrolyte for Li ion batteries

• Invited talk presented by N. A. W. Holzwarth at the SSI: 21st International Conference on Solid State Ionics, Padua, Italy, June 18-23,2017 -- "Simulations of Idealized Solid Electrolytes"
• Invited talk presented by N. A. W. Holzwarth at the EMCMRE-4: 4th Euro-Mediterranean Conference on Materials and Renewable Energies, Marrakech, Morocco May 8-11, 2017. "Simulations of Idealized Solid Electrolytes"
• Talk presented by Jason Howard at the March 2017 Meeting of the American Physical Society, March 13-17, 2017 in New Orleans, LA DFT simulations of Li-ion conductor Li₂(OH)Cl

• Talk presented by Ahmad N. Al-Qawasmeh at the March 2017 Meeting of the American Physical Society, March 13-17, 2017 in New Orleans, LA Li₁₄(PON₃)₂O: Computational study of a possible new electrolyte for Li ion batteries.

• Talk presented by Larry Rush, Jr. at the March 2017 Meeting of the American Physical Society, March 13-17, 2017 in New Orleans, LA Computational Study of Ideal Electrolyte/Anode Interface for Na₃SbS₄/Na.

• Invited talk presented by N. A. W. Holzwarth at the International Material Research Congress, August 15-19, 2016 Cancun, Mexico. "Simulations of Idealized Solid Electrolytes"
• Poster presented by N. A. W. Holzwarth at the 18th International Meeting on Lithium Batteries, June 19-24, 2016 in Chicago, IL. Li₄SnS₄: Simulations of Its Structure and Electrolyte Properties

• Talk presented by Larry Rush, Jr. at the March 2016 Meeting of the American Physical Society, March 14-18, 2016 in Baltimore, MD. First principles investigation of the structural and electrochemical properties of Na₄P₂S₆ and Li₄P₂S₆

• Talk presented by Jason Howard at the March 2016 Meeting of the American Physical Society, March 14-18, 2016 in Baltimore, MD. Computational study of Li_2+xSnO₃ and Li_2+xSnS₃

• Talk presented by Ahmad Al-Qawasmeh at the March 2016 Meeting of the American Physical Society, March 14-18, 2016 in Baltimore, MD. Computational study of Li ion electrolytes composed of Li₃AsS₄ alloyed with Li₄GeS₄

• Talk presented by N. A. W. Holzwarth (based on work of Nicholas Lepley) at the March 2016 Meeting of the American Physical Society, March 14-18, 2016 in Baltimore, MD. A formalism for modeling solid electrolyte/electrode interfaces using first principles methods

• Ph. D. Thesis by Nicholas Lepley, in partial fulfillment of the Wake Forest University requirements for the Doctor of Philosophy in Physics (December 2015) -- "First Principles Investigations of Solid-Solid Interfaces in Lithium Battery Materials".

• Talk presented by Jason Howard at the 228th ECS Meeting , October 11-15, 2015 in Phoenix, AZ. Computational Study of Li₂SnO₃ and Li₂SnS₃".
• Talk presented by N. A. W. Holzwarth at the 228th ECS Meeting , October 11-15, 2015 in Phoenix, AZ. Electrolyte properties of Li₄P₂S₆ -- Simulations and comparison with experiment; Constrast with simulations of Na analog", in collaboration with Z. D. Hood, M. J. Kirkham, and L. E. Rush, Jr..
• Talk presented by N. A. W. Holzwarth at Sandia National Laboratory in Albuquerque, NM at the invitation of Kevin Leung -- June 3, 2015 "Simulations of Idealized Solid Electrolytes for Solid State Battery Designs"
• Undergraduate honors thesis by Hannah Zhang, in partial fulfillment of the Wake Forest University requirements for graduation with Honors in Physics (May 2015) -- "Computational Modeling of Li Diffusion Using Molecular Dynamics" .

• Contributed talk presented by Nicholas Lepley at the March Meeting 2015 of the American Physical Society March 2-6, 2015 in San Antonio, Texas. Modeling Electrolyte-Electrode interfaces with co-author N. A. W. Holzwarth
• Contributed talk presented by N. A. W. Holzwarth at the March Meeting 2015 of the American Physical Society March 2-6, 2015 in San Antonio, Texas. Structure and interface properties of the electrolyte material Li₄P₂S₆ with co-authors Zachary D. Hood (Oak Ridge National Laboratory) and Cameron M. Kates (currently at Duke U.).
• Talk presented by N. A. W. Holzwarth at the Joint School of Nanoscience and Nanoengineering in Greensboro at the invitation of professor Sung-Jin Cho -- January 16, 2015 "Overview of Computer Simulation Methods Used to Study and Design New Materials: Examples from the Study of Solid Electrolytes"
• Contributed poster presented by Nicholas Lepley at 2014 summer school on Transformational Technologies in Molecular Simulations held at University of Wisconsin-Madison, Madison, WI May 19-22, 2014 -- Modeling the Interface of Lithium Metal and Lithium Solid Electrolytes with First Principles calculations.

• Contributed poster presented by Chaochao Dun at The 26th Annual Workshop on Recent Developments in Electronic Structure Methods held at the University of North Texas, May 18-21, 2014 -- First principles simulations of Cu₂ZnSnS_xO_4-x alloys.

• Undergraduate honors thesis by James Drewery, in partial fulfillment of the Wake Forest University requirements for graduation with Honors in Physics (May 2014) -- Modeling Materials: Comparison of Two Projector-Augmented Wave (PAW) Datasets.

• Undergraduate honors thesis by Cameron Kates, in partial fulfillment of the Wake Forest University requirements for graduation with Honors in Physics (May 2014) `-- Computational Modeling of Surface Energy and Structural Behavior of Li₄P₂S₆ Electrolytic Solid Interfacing with Lithium Anodes.

• Contributed talk presented by Chaochao Dun (in collaboration with N. A. W. Holzwarth, Y. Li, W. Huang, and D. Carroll) APS March Meeting 2014, Denver, Colorado Mar. 3 - 7, 2014 -- Cu₂ZnSnS_xO_4-x and Cu₂ZnSnS_xSe_4-x: First principles simulations of optimal alloy configurations and their energies

• Contributed talk presented by N. A. W. Holzwarth (with content from N. D. Lepley, A. Al-Qawasmeh, and C. Kates) at the APS March Meeting 2014, Denver, Colorado Mar. 3 - 7, 2014 -- First principles modeling of lithium (thio) phosphate solid electrolytes and lithium metal anodes

• Invited talk by N. A. W. Holzwarth at the 27th Annual CSP Workshop February 24-28, 2014 in Athens, GA, USA -- First principles modeling of electrolyte materials in all-solid-state batteries"

• Presentation by N. A. W. Holzwarth at the CFCAM meeting "Pseudopotentials and PAW atomic data: beyond a ""black art""?" January 28-29, 2014 at the Ecole National Superieure de Chimie de Paris, Paris, France; organized by F. Jollet, J. J. Mortensen, and G. Rignanese. -- Introduction to generating PAW Atomic Datasets

• Contributed talk presented by N. A. W. Holzwarth (with content from N. D. Lepley and A. Al-Qawasmeh) at the 224^th ECS Meeting, in San Francisco, CA, Oct. 27-Nov. 1, 2013 -- First principles modeling of electrolyte/anode interfaces in an all-solid state battery -- γ-Li₃PS₄/Li

• Contributed poster presented by N. A. W. Holzwarth (with content from N. D. Lepley) at the The 25th Annual Workshop on Recent Developments in Electronic Structure Methods held at the College of William and Mary, June 11-14, 2013 -- First principles modeling of the interface between a solid state lithium thiophosphate electrolyte and a lithium metal anode

• Invited talk presented by N. A. W. Holzwarth at the 6th International ABINIT Developer Workshop in Dinard, France April 15-18, 2013 -- Comments on Generating and Testing PAW Datasets

• Contributed talk presented by N. A. W. Holzwarth (in collaboration with K. Senevirathne, C. Day, A. Lachgar, and M. Gross) at the APS March Meeting 2013 in Baltimore, MD, Mar. 18 - Mar. 22, 2013 -- Design and synthesis of a crystalline LiPON electrolyte

• Contributed talk presented by Nicholas Lepley (in collaboration with N. A. W. Holzwarth) at the APS March Meeting 2013 in Baltimore, MD, Mar. 18 - Mar. 22, 2013 -- Surface Structure and Stability in Li₃PS₄ and Li₃PO₄ Electrolytes from First Principles

• Talk presented by N. A. W. Holzwarth at Oak Ridge National Laboratory at the invitation of Dr. Paul Kent -- March 11, 2013 "Design and Synthesis of a Crystalline LiPON Electrolyte"
• Talk presented by N. A. W. Holzwarth at the Duquesne University at the invitation of Professor Jennifer Aitken, Department of Chemistry and Biochemistry -- October 19, 2012 "Solid electrolytes for battery applications -- a theoretical perspective"
• Poster presented by N. Lepley at the ES12: 24th Annual Meeting of the Electronic Structure Workshop -- June 5-8, 2012 -- Computer Modeling of Crystalline Electrolytes - Lithium Thiophosphates and Phosphates.

• Poster presented by N. Holzwarth at the ES12: 24th Annual Meeting of the Electronic Structure Workshop -- June 5-8, 2012 -- First Principles Computer Simulations of Li₁₀GeP₂S₁₂ and Related Lithium Superionic Conductors.

• Talk presented by N. A. W. Holzwarth at the University of Louisville at the invitation of Professor Yongsheng Lian, Mechanical Engineering Department and the Conn Center for Renewable Energy Research -- April 6, 2012 -- "Solid electrolytes for battery applications -- a theoretical perspective"
• Contributed talk presented by N. A. W. Holzwarth at the APS March Meeting 2012 in Boston, MA, Feb. 27 - Mar. 2, 2012 -- First principles computer simulations of Li₁₀GeP₂S₁₂ and related lithium superionic conductors

• Contributed talk presented by Nicholas Lepley at the APS March Meeting 2012 in Boston, MA, Feb. 27 - Mar. 2, 2012 -- First principles investigation of the superionic electrolyte Li₇P₃S₁₁

• Contributed talk presented by Xiao Xu at the APS March Meeting 2012 in Boston, MA, Feb. 27 - Mar. 2, 2012 -- Projector Augmented Wave formulation of orbital-dependent exchange-correlation functionals

• Talk presented by N. A. W. Holzwarth for WFU's Center for Energy, Environment, and Sustainability -- Renewable Energy Research (CEES-RER) Sept. 30, 2011 -- Solid electrolytes for battery applications -- a theoretical perspective

• Contributed talk presented by N. A. W. Holzwarth at the 219th ECS Meeting, in Montreal, Canada, May 1-6, 2011 -- "Computer Modeling of crystalline electrolytes -- Lithium Thiophosphates and Phophosphates"

• Invited talk presented by N. A. W. Holzwarth at the 5th International Abinit Developer Workshop in Han-sur-Lesse, Belgium April 11-15, 2011 -- The ATOMPAW Generator

• Contributed talk presented by N. Lepley at the APS March 2011 meeting in Dallas, Texas March 21-25, 2011 -- Computer Modeling of crystalline electrolytes: Lithium thiophosphates and phosphates

• Contributed talk present by X. Xu at the APS March 2011 meeting in Dallas, Texas March 21-25, 2011 -- A Projector Augmented Wave Formulation of the Hartree-Fock and KLI Approximations

• Poster presented by N. A. W. Holzwarth and N. Lepley at The 15th International Meeting on Lithium Batteries in Montreal, Canada June 27 - July 2, 2010 -- Computer Modeling of Lithium Phosphate and Thiophosphate Electrolyte Materials

• Poster presented by Xiao Xu at 22nd Annual Workshop on Electronic Structure Methods at the University of Texas - Austin, June 7-10, 2010 -- Projector augmented wave (PAW) formulation of Hartree-Fock calculations of electronic structure -- HF-PAW

• Poster presented by N. A. W. Holzwarth at 22nd Annual Workshop on Electronic Structure Methods at the University of Texas - Austin, June 7-10, 2010 -- Two implementations of the Projector Augmented Wave (PAW) formalism

• Talk presented by N. A. W. Holzwarth at 2010 APS March Meeting in Portland, OR March 2010 -- "Prediction of a New Material -- Lithium Phosphorus Oxynitride Li₂PO₂N"

• Talk presented by N. A. W. Holzwarth at 216^th Biannual Meeting of the Electrochemical Society Meeting October 4-9, 2009 in Vienna, Austria -- First principles simulations of Li ion migration in materials related to LiPON electrolytes

• Talk presented by N. A. W. Holzwarth at 7th Canadian Computational Chemistry Conference July 20-24, 2009 , Dalhousie University in Halifax, Nova Scotia -- A Projector Augmented Wave Formulation of the Optimized Effective Potential Formalism

• Poster presented by N. A. W. Holzwarth at 21th Annual Workshop on Recent Developments in Electronic Structure Methods at the University of California Davis campus, June 22-25, 2009 -- Simulations of Li-ion migration in LiPON electrolytes

• Talk presented by Yaojun Du at 2009 APS March Meeting in Pittsburgh, PA, March 2009 -- First-principles simulations of extended structures in the lithium phosphorous oxynitride electrolytes

• Talk presented by Xiao Xu at 2009 APS March Meeting in Pittsburgh, PA, March 2009 -- Implementation of the Optimized Effective Potential Method within the Projector Augmented Wave Scheme

• Poster presented by Xiao Xu at 20th Annual Workshop on Recent Developments in Electronic Structure Methods in the University of Illinois at Urbana-Champaign, June 17-20, 2008 -- "Projector Augmented Wave Formulation of Optimized Effect Potential Density Functional Theory -- PAW-OEP"

• Talk presented by Yaojun Du at 213th Biannual Meeting of the Electrochemical Society in Phoenix, AZ May 18-22, 2008 -- "Li ion migration in Li₃PO₄ electrolytes: Effects of O vacancies and N substitutions"

• Talk presented by N. A. W. Holzwarth at "Workshop on Pseudopotentials and the Quantum Theory of Materials" in Austin, TX Apr. 9-11 2008 in honor of J. R. Chelikowsky -- Simulations of Li ion diffusion in the electrolyte material -- Li₃PO₄

• Talk presented by N. A. W. Holzwarth at 2008 APS March Meeting in New Orleans, LA, March 2008 -- Simulation of Li ion diffusion near electrolyte-metal interface -- Li₃PO₄ and Li

• Poster presented by William Hodge at 2008 APS March Meeting in New Orleans, LA, March 2008 -- The One-Hole, One-Dimensional Hubbard Model at U = ∞

• Talk presented by N. A. W. Holzwarth at 74th Annual Meeting of the Southeastern Section of the APS in Nashville, November 2007 -- Simulations of Li ion diffusion in the electrolyte Li₃PO₄

• Poster presented by Xiao Xu at 19th Annual Workshop on Recent Developments in Electronic Structure Methods in Raleigh, NC June 2007 -- Projector Augmented Wave Formulation of Exact Exchange Density Functional Theory -- PAW-EXX

• Poster presented by Yaojun Du at 19th Annual Workshop on Recent Developments in Electronic Structure Methods in Raleigh, NC June 2007 -- Li ion diffusion mechanisms in Li₃PO₄ electrolytes

• Talk presented by Xiao Xu at March 2007 APS meeting in Denver -- Simulated electrolyte-metal interfaces -- Li₃PO₄ and Li

• Talk presented by Dr. Yaojun Du at March 2007 APS meeting in Denver -- Li-ion diffusion mechanisms in crystalline Li₃PO₄ electrolytes

• Poster presented by William Hodge at March 2007 APS meeting in Denver -- Pair State Analysis of the Hubbard Hamiltonian in One-Dimension

• CEACAM workshop -- Lyon, France -- June 12-14, 2006: State of the art, developments and perspectives of electronic structure calculations in the frame of the Projector Augmented-Wave (PAW) method