FIRESIDE CHATS FOR LOCKDOWN TIMES The frontiers and the challenges - - PowerPoint PPT Presentation

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FIRESIDE CHATS FOR LOCKDOWN TIMES The frontiers and the challenges - - PowerPoint PPT Presentation

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FIRESIDE CHATS FOR LOCKDOWN TIMES The frontiers and the challenges (Part 3) Nicola Marzari, EPFL OUTLINE What is density-functional theory? (Part I) What does it take to perform these calculations? (Part II) Why is it relevant for

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SLIDE 1

FIRESIDE CHATS FOR LOCKDOWN TIMES The frontiers and the challenges (Part 3) Nicola Marzari, EPFL

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SLIDE 2

OUTLINE

  • What is density-functional theory? (Part I)
  • What does it take to perform these

calculations? (Part II)

  • Why is it relevant for science and

technology? (Part III)

  • What can it do? and cannot do? (Part III)

(to keep in touch, info in the Learn section of the Materials Cloud website, and https://bit.ly/3eqighg)

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

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SLIDE 3

WHAT CAN I DO WITH IT?

  • Which properties are “ground state” properties ?
  • How accurate are we?
  • What is the microscopic origin of the observed

behavior ?

  • How can we be realistic? (introduce the effects of

temperature, pressure, composition; study non- periodic systems such as liquids; go from a few atoms to many)

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

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SLIDE 4

EXAMPLES

  • From total energy to thermodynamics

– temperature, pressure, chemical potentials and partial pressures, electrochemical potential, pH

  • From DFT to real electrons

– many-body perturbation theory – quantum Monte Carlo – DMFT, cluster DMFT, DCA

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

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SLIDE 5
  • Length, time, phase and composition sampling

– linear scaling, multiscale, – metadynamics, sketch-map – minima hopping, random-structure searches

  • Complex properties

– phase diagrams – spectroscopies and microscopies: IR, Raman, XPS, XANES, NMR, EPR, ARPES, STM, TEM… – transport: ballistic, Keldysh, Boltzmann

Examples

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

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SLIDE 6

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

Easy: equilibrium volume

Eric B. Isaacs and Chris Wolverton, Phys. Rev. Materials 2, 06380 (2018)

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SLIDE 7

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

Difficult: formation energies

Eric B. Isaacs and Chris Wolverton, Phys. Rev. Materials 2, 06380 (2018)

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SLIDE 8

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

Out-of-bounds: (transport) band gaps

Eric B. Isaacs and Chris Wolverton, Phys. Rev. Materials 2, 06380 (2018)

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SLIDE 9

Hellmann-Feynman Theorem

Think beyond the energy

dE dl

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

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SLIDE 10

Helmann-Feynman theorem

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

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SLIDE 11

Linear-response theory

dE dl

  • S. Baroni et al.,
  • Phys. Rev. Lett.

(’87), Rev. Mod. Phys (‘01)

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

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SLIDE 12

Linear-response theory

  • S. Baroni et al.,
  • Phys. Rev. Lett.

(’87), Rev. Mod. Phys (‘01)

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

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SLIDE 13

Phonons and temperature

  • A harmonic crystal is exactly equivalent to a Bose-

Einstein gas of independent, harmonic oscillators.

  • .

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

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SLIDE 14

Vibrational spectroscopies: IR, Raman

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

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SLIDE 15

Mauri 2001

Magnetic spectroscopies: NMR Chemical Shifts

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

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SLIDE 16

Sampling excitations

Electronic Vibrational Configurational Ψ Ψ

Magnetic (electron spin) Occupation In polymers and bio-molecules, vibrational and configurational can not always be distinguished

Conformational

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SLIDE 17

Statistical mechanics on relevant degrees of freedom

Ensemble

Collection of microscopic states consistent with thermodynamic boundary conditions

P

i =

exp −β Ei

[ ]

Q Q = exp −β Ei

[ ]

i

∑

F = − β ln[Q] S = − kB P

i ln(P i ) i

∑

Probability to be in a given state i Partition Function Free energy (Helmholtz) Entropy

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

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SLIDE 18

For the vibrational free energy, analytically!

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

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SLIDE 19

Thermomechanics (bulk modulus of diamond)

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

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SLIDE 20

Otherwise, thermodynamical averages

Under hypothesis of ergodicity, we can assume that the temporal average along a trajectory is equal to the ensemble-average over the phase space

ò

=

T

dt t A T A ) ( 1

ò ò

  • =

p d r d E p d r d E A A ! ! ! ! ) exp( ) exp( b b

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

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SLIDE 21

Molecular dynamics

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

m d 2 r dt2 =  F( r) = −  ∇V ( r)

) (t r ! ) (t v !

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SLIDE 22

A drop to drink

Bingqing Cheng, Edgar A. Engel, Jörg Behler, Christoph Dellago, Michele Ceriotti, PNAS 116 1110 (2019)

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

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SLIDE 23

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

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SLIDE 24

We’ll always have Monte Carlo

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

ò ò

  • =

p d r d E p d r d E A A ! ! ! ! ) exp( ) exp( b b

redrawn from the book by D. Frenkel and B. Smith, Understanding Molecular Simulation Academic Press

P

i→ j = 1 when Ej < Ei

P

i→ j = exp(−β(Ej − Ei )) when Ej > Ei

Downhill moves always accepted, uphill moves with some “thermal-like” probability

Metropolis algorithm (by Arianna and Marshall Rosenbluth)

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SLIDE 25

Thermodynamics of substitutional alloys

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

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SLIDE 26

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

Free energy from thermodynamic integration

  • f the dependence of the chemical potential

Nicola Marzari, Stefano de Gironcoli, and Stefano Baroni, Phys. Rev. Lett. 72, 4001

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SLIDE 27

Multi-scale, multi physics: semiclassical transport

1. Vibrational properties from density-functional theory, electrons from many-body perturbation theory 2. Carriers’ scattering rates from density-functional perturbation theory 3. Wannier interpolations for electrons 4. Transport properties from Boltzmann’s equation

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

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SLIDE 28

C.-H. Park et al., Nano Letters (2014)

  • T. Y. Kim, C.-H. Park, and N. Marzari, Nano Letters (2016)

FIRST-PRINCIPLES EXPTS (Efetov and Kim)

Resistivity in doped graphene

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SLIDE 29

Anharmonicity = finite lifetimes

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

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SLIDE 30

Acoustic Optical Transverse modes Acoustic Optical Transverse modes

Thermal conductivity (SMRTA)

K = !2 3N0 ΩkBT 2 cs

2(q)ω2(qs) nqs _ (nqs _ +1)τqs qs

∑

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

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SLIDE 31

Composition dependence in SiGe alloys

  • J. Garg, N. Bonini, B. Kozinsky and N. Marzari, Phys. Rev. Lett. (2011)

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

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SLIDE 32

Generalized Wigner Boltzmann

Peierls + coherences Total K =

Simoncelli, Marzari, Mauri, Nature Physics (2019)

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SLIDE 33

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

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A FUN EXAMPLE

  • G. Prandini, G.M. Rignanese, and N. Marzari,

npj Computational Materials 5, 129 (2019) April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

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SLIDE 35

λH = 3–5 ˚ A E 0 V

permittivity isosurfaces diffuse ion distribution

(b)

Dabo, Bonnet, Li and Marzari, "Ab-initio Electrochemical Properties of Electrode Surfaces", in Fuel Cell Science: Theory, Fundamentals and Bio-Catalysis, A. Wiecowski and J. Norskov (2011).

  • O. Andreussi, I. Dabo and N. Marzari, “Revised self-consistent continuum solvation in electronic

structure calculations”, J. Chem. Phys. 136, 064102 (2012). www.quantum-environment.org

Multi-scale/physics: electrochemistry

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SLIDE 36

Wulff construction, nanoparticle shape

  • N. Bonnet and N. Marzari, Phys. Rev. Lett. 110, 086104 (2013)

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

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SLIDE 37

COMPUTATIONAL EXFOLIATION OF ALL KNOWN INORGANIC MATERIALS

COMPUTATIONAL EXFOLIATION OF ALL KNOWN INORGANIC MATERIALS

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

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SLIDE 38

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

HIGH-THROUGHPUT COMPUTATIONAL EXFOLIATION

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SLIDE 39

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

Band structures Phonon dispersions

ALL AUTOMATED WITH AiiDA (http://aiida.net)

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SLIDE 40

THE DISCOVERY OF JACUTINGAITE

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SLIDE 41

THE DISCOVERY OF JACUTINGAITE

Bulk: topologically-protected 001-surface states, exp vs DFT

  • C. Cucchi et al., Phys. Rev. Lett. 124, 106402 (2020)
  • A. Marrazzo et al., Phys. Rev. Research 2, 012063(R) (2020)

Monolayer: room-temperature Kane-Mele quantum spin Hall insulator – G0Wo with S.O.C.

  • A. Marrazzo et al., Phys. Rev. Lett. 120, 117701 (2018)

H = t X

hijiα

c†

iαcjα

| {z }

1stNN

+ it2 X

hhijiiαβ

vijsz

αβc† iαcjβ

| {z }

KM SOC

+

β

} + t0

2

X

hhijiiα

c†

iαcjα

| {z }

2ndNN

+ it00

2

X

hhijiiαβ

uij(s × d0

ij)z αβc† iαcjβ

| {z }

in-plane SOC

, (1)

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SLIDE 42

What’s wrong with DFT ?

  • In its practice, it is approximate
  • It is a static theory (of the charge

density)

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

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SLIDE 43

LDA

Notable failures I: Photoemission spectra (at least IP from HOMO – should be exact)

EXPT

  • I. Dabo et al. Phys. Rev. B 82 115121 (2010)
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SLIDE 44

Notable failures II: Charge transfer

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

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SLIDE 45

Notable failures II: Charge transfer

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

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SLIDE 46

Neepa Maitra JCTC 2009, Helbig and Rubio JCP 2009

Notable failures III: beautiful, but perverse

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SLIDE 47

Notable failures IV: Delocalization of electrons/holes

  • D. A. Scherlis and N. Marzari, JPCB (2004), JACS (2005)
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SLIDE 48

+

Notable failures V: H2+ dissociation limit

R R R

Schrödinger Kohn-Sham

+ + + + + +

1- 1- ½- ½-

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

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SLIDE 49

So, it doesn’t work even for one electron

HF B3LYP LDA

A.J. Cohen, P. Mori-Sanchez, W. Yang, Science (2008)

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

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SLIDE 50

So, it doesn’t work even for one electron

HF B3LYP LDA

A.J. Cohen, P. Mori-Sanchez, W. Yang, Science (2008)

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

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SLIDE 51

DFT DFT+U correction

A DFT + Hubbard U approach

  • The energy functional has

an unphysical curvature

  • the exact solution is

piecewise linear

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

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SLIDE 52
  • The energy functional has

an unphysical curvature

  • the exact solution is

piecewise linear

  • a +U correction reproduces

the exact solution

U and rotationally-invariant U: V.I. Anisimov and coworkers PRB (1991), PRB (1995); Dudarev, Sutton and coworkers PRB (1995) LRT U: M. Cococcioni (PhD 2002), and M. Cococcioni and S. de

  • Gironcoli. PRB (2005)

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

A DFT + Hubbard U approach

DFT DFT+U correction

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SLIDE 53

U and rotationally-invariant U: V.I. Anisimov and coworkers PRB (1991), PRB (1995); Dudarev, Sutton and coworkers PRB (1995) LRT U: M. Cococcioni (PhD 2002), and M. Cococcioni and S. de

  • Gironcoli. PRB (2005)

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

A DFT + Hubbard U approach

DFT DFT+U correction

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SLIDE 54

DFT + U has nothing to do with correlation !

LiFePO4

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

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SLIDE 55

H.J. Kulik, M. Cococcioni, D.A. Scherlis, and N. Marzari, Phys. Rev. Lett. (2006) H.J. Kulik and N. Marzari, JCP 129 134314 (2008)

Methane on FeO+: GGA vs MRCI

MRCI GGA

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SLIDE 56

Methane on FeO+: GGA+U vs MRCI

H.J. Kulik, M. Cococcioni, D.A. Scherlis, and N. Marzari, Phys. Rev. Lett. (2006) H.J. Kulik and N. Marzari, JCP 129 134314 (2008)

MRCI GGA+U

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SLIDE 57

2+ 2+ 2+ 2+ LiMPO4 3+ 2+ 3+ 2+ 3+ 3+ 3+ 3+ MPO4 Li0.5MPO4

Mixed-valence olivines for battery cathodes

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

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SLIDE 58

LixFePO,4:,from%PBE%to%scf%DFT+U+V

LiFePO LiFePO4 Li0.5FePO FePO4 FePO ePO4

Method 2+ 3+ 2+ 3+ 2+ 3+

PBE 6.22 6.11 6.08 5.93

PBE+U

6.19 6.19 5.68 5.65

PBE+Uscf

6.21 5.74 6.19 5.70

PBE+Uscf+Vscf

6.22 6.22 5.77 5.76

Method

  • F. E. (meV/FU)

Voltage (V)

Exp > 0 ~ 3.5 PBE

  • 126

2.73 PBE+U 159 4.06 PBE+Uscf 189 3.83

PBE+Uscf+Vscf

128 3.48

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

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SLIDE 59

That That was as good

  • od,

, Ad Adam. . Can you

  • u make

it it mo more gene neral?

April 2020 - Fireside chats for lockdown times: The frontiers and the challenges (Part 3 of 3) - Nicola Marzari (EPFL)

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SLIDE 60

OBJECTIVE: SPECTRAL FUNCTIONALS

  • Spectral properties with a functional theory
  • It’s actually not very difficult, but cannot be done with DFT: a

functional of the local, static density gives you only the energy

  • A functional of the local spectral density 𝜍(r,ω)) provides also

the correct energy levels

  • In a quasi-particle approximation, this spectral functional depends

discretely on the orbital densities 𝜍(r,i)

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SLIDE 61

For every orbital the expectation value does not depend on the occupation of the orbital KOOPMANS’ COMPLIANT SPECTRAL FUNCTIONALS

  • I. Dabo, M. Cococcioni, and N. Marzari, arXiv:0910.2637 (2009)
  • I. Dabo et al., Phys. Rev. B 82, 115121 (2010)
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SLIDE 62

LINEARIZATION (FIRST, AT FROZEN ORBITALS)

remove ~quadratic Slater add linear Koopmans

  • I. Dabo et al., Phys. Rev. B 82, 115121 (2010)
  • G. Borghi et al., Phys. Rev. B 90, 075135 (2014)
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SLIDE 63

SCREENING TO ACCOUNT FOR ORBITAL RELAXATIONS

  • rbital-dependent

screening coefficient 𝞫i

  • I. Dabo et al., Phys. Rev. B 82, 115121 (2010)
  • N. Colonna et al., JCTC in press (2018), and arXiv
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SLIDE 64

Explicitly, the KI Koopmans’ functional adds to the base functional

ρi orbital density at filling fi niorbital density at integer filling

KIPZ adds a screened PZ self-interaction term

NK hamilton funcian

  • G. Borghi et al., Phys. Rev. B 90, 075135 (2014); Phys. Rev. B 91, 155112 (2015)

ORBITAL-DENSITY DEPENDENT

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SLIDE 65

minimization

GW100 TEST SET

  • 0.9
  • 0.6
  • 0.3

0.3 0.6 0.9 1.2 KIPZ qpGW pKIPZ DDH scGW KI G0W0[HF] ∆SCF[PBE] G0W0[PBE] HF LDA-1/2 PZ-SIC Error [eV] MAE MSE

0.20 0.22 0.24 0.27 0.32 0.35 0.35 0.40 0.44 0.64 0.70 1.00 0.04 0.15

  • 0.16
  • 0.14
  • 0.30

0.21 0.26

  • 0.30
  • 0.42

0.46

  • 0.63

0.96

  • 0.9
  • 0.6
  • 0.3

0.3 0.6 0.9 1.2 KIPZ pKIPZ KI Error [eV]

  • N. Colonna et al., JCTC in press (2018)
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SLIDE 66

UPS (fullerene)

  • L. Nguyen, G. Borghi, A. Ferretti, I. Dabo, N. Marzari, Phys. Rev. Lett. 114, 166405 (2015)

EXP KI[PZ] KI[PBE] PZ[PBE] PBE

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SLIDE 67

SOLID-STATE LIMIT

0.1 0.2 0.3 0.4 0.5 0.6

1/Lz [Å

  • 1]

13 12 11 10 9 8 7

IP [eV]

C100H100, C60H122 C40H82, C30H62 C25H52, C20H42 C16H34, C14H30 C12H26, C11H24 C10H22, C9H20 C8H18, C7H16 C6H14 C5H12 C4H10 C3H8 C2H6

PBE ∆SCF KI KIPZ CCSD(T) Expt.

12 10 8

IP [eV]

PBE KI KIPZ Expt. Alkane Polyethylene

Canonical orbital Variational (minimizing)

  • rbital
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SLIDE 68

BAND GAPS AND IPs (30 SOLIDS)

GW: W. Chen and A. Pasquarello PRB 92 041115 (2015); Koopmans: L. Nguyen, N. Colonna, A. Ferretti, and N. Marzari, PRX (2018)

1 2 3 4 5 6 7 8 Experimental band gap [eV] 1 2 3 4 5 6 7 8 Theoretical band gap [eV]

InSb InAs InN, Ge, GaSb SiInP, CdTe, GaAs AlSb, CdSe BP, AlAs GaP, ZnTe, AlP, CdS, SiC ZnSe GaN, TiO2 ZnO, ZnS AlN MgO BN C

Ar, LiF Ne

PBE KI KIPZ

5 10 15 20 5 10 15 20

MAE (eV) Gap IP PBE 2.54 1.09 G0W0 0.56 0.39 QSGW 0.18 0.49 KI 0.27 0.19 KIPZ 0.22 0.21

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SLIDE 69
  • Linearity as a foundation (orbital energies independent from

their occupation), plus screening, plus localization.

  • Beyond-DFT orbital-density formulation
  • Functional theory of both energies and spectral properties
  • Can we substitute diagrammatic approaches like GW or

DMFT with spectral functionals?

Linearity + screening + localization

Resonance with many ideas, from… 1. Short-range hybrid functionals (Scuseria, many) 2. Range-separated hybrids (Kronik, Baer, Neaton) 3. Self-consistent hybrids (Galli) 4. Many-body self-interaction free (Weitao Yang) KI functional applied to:

  • HOMO/LUMO → ensemble-DFT (Kreisler-Kronik 2013)
  • Maximally-localized Wannier functions → Koopmans-Wannier method (Lin-Wan Wang, 2015)
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SLIDE 70
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SLIDE 71

I. It’s very popular! Everyone does it II. It’s fast and easy, and requires no thinking

  • III. You can swipe functionals left until

you find the one that works for you, for a while

  • N. Marzari, Materials modelling: The frontiers and the

challenges, Nature Materials 15, 381 (2016)

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SLIDE 72

Acknowledgements

The people I learnt from – Mauro Ferrari, Alfonso Baldereschi, Stefano Baroni, Alessandro de Vita, Mike Payne, David Vanderbilt, Roberto Car

http://theossrv1.epfl.ch/Main/People

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SLIDE 73

Ab About your cat, Mr. Sc Schrödinger – I I have good news, and bad news.