nonlocal density functional theory for chemical …personal.tcu.edu/bjanesko/pres.pdf1 nonlocal...

1

Nonlocal density functional theory for chemicalreactions

Benjamin G. Janesko

Texas Christian University

2013.02.14

2

Chemistry in Texas

Several large programs: Rice, University of Texas, Texas A&M

Computational chemistry: University of North Texas, TexasTech, Southern Methodist University

Local research support: Welch foundation, collaborations withTexas A&M Qatar

3

Chemistry at TCU

∼ 10, 000undergraduates

11 research-activechemistry faculty

∼ 25 Ph. D. students

Strengths: Organic,bio-inorganic,macromolecularchemistry

Computation isincreasingly important

4

Group research overview

1 Use electronic structure theory, particularly density functionaltheory (DFT), to model molecular structure and reactivity

2 Refine DFT for difficult problems like reactions on catalystsurfaces

3 Develop new DFT approximations for these problems

5

Explanation #1 of density functional theory

E

Freshman chemistry molecular orbital theory, plus approximateelectron-electron interactions

Different DFT methods use different approximations

∼ 2− 6 kcal/mol accuracy for thermochemistry & kinetics ofmedium-sized molecules

Qualitatively correct trends in reactivity

6

Outline

1 DFT for alkyl cross-coupling

2 Other DFT applications

3 New functionals for surface chemistry

4 “Rung 3.5” density functionals

5 Summary

7

Cross-coupling

Noble-metal-catalyzed C-C bond formation

Suzuki, Negishi, Hiyama, Heck, etc.

8

Alkyl Suzuki coupling

Alkyl reactants are challenging

Strong Csp3-X bonds impede initial oxidative additionβ-hydride elimination from coordinatively unsaturated Pd(II)Electron withdrawing substitutent CN is essential

Choice of ligand and reaction conditions is important

SPhos, RuPhos, JohnPhos, etc.

Few “design rules” optimizing ligands for particular reactants

A. He, J. R. Falck, JACS 132, 2524 (2010)

9

Initial oxidative addition

10

Anion accelerates & controls stereoselectivity

B. Pudasaini, B. G. Janesko, Organometallics 31, 4610 (2012)

11

Cyano deactivates β-hydride elimination

B. Pudasaini, B. G. Janesko, Organometallics 31, 4610 (2012)

12

Ligand trans influence and sterics control selectivity

B. Pudasaini, B. G. Janesko, Organometallics 31, 4610 (2012)

13

Ligand trans influence and sterics control selectivity

B. Pudasaini, B. G. Janesko, Organometallics 31, 4610 (2012)

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Ligand protection in another alkyl cross-coupling

Dialkylbiaryl ligand protects coordinatively unsaturated Pd(II )

intermediate from undesirable side reactions.

B. Pudasaini, B. G. Janesko, Organometallics 30, 4564 (2011)

15

Outline

1 DFT for alkyl cross-coupling

2 Other DFT applications

3 New functionals for surface chemistry

4 “Rung 3.5” density functionals

5 Summary

16

Ionic liquid solvents for biofuels

B. G. Janesko, Phys. Chem. Chem. Phys. 13, 11393 (2011)

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Biofuel production in ionic liquids

Solvent Barrier ε

None 20.7 1.0Dichloroethane 23.7 10.1(BMIM)(PF6) 25.7 11.4Water 28.1 78.4

Rate-limiting transition barrier to base-catalyzed lignin hydrolysis

B. G. Janesko, in preparation

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Conducting polymers for organic photovoltaics

P. Sista, B. Xue, M. Wilson, N. Holmes, R. S. Kularatne, H. Nguyen, P. C. Dastoor, W. Belcher, K. Poole, B. G.

Janesko, M C. Biewer, M. C. Stefan; Macromolecules 45, 772 (2012)

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Frustrated Lewis pair nanoribbons

B. G. Janesko, J. Phys. Chem. C 116, 16476 (2012)

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Organocatalysts for organophosphorus production

-10

-5

0

5

10

15

20

25

30

35

40

ΔE

vs.

fre

e r

ea

cta

nts

(k

cal/

mo

l)

Formic acid Thioformic acidDimer

M. Bridle, B. G. Janesko, J.-L. Montchamp, in preparation

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Why bother designing new DFT methods?

22

Outline

1 DFT for alkyl cross-coupling

2 Other DFT applications

3 New functionals for surface chemistry

4 “Rung 3.5” density functionals

5 Summary

23

Explanation #2 of density functional theory

Many-body problems are hard

Two moons interacting with a planet and each otherTwo electrons interacting with a nucleus and each other

Analytic solutions generally unavailable

Numerical solutions scale as eN or N! for N particles

Molecular orbital theory ignores electron-electron interactions

DFT does something clever

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Explanation #2 of density functional theory

N noninteracting Fermions in orbitals {φi (~r)}, with electronprobability density

ρ(~r) =N∑i=1

|φi (~r)|2

can exactly model the ground state of N interactingelectrons (Hohenberg & Kohn)

Electron interactions treated by self-Coulomb repulsion

1

2

∫d3~r1

∫d3~r2

ρ(~r1)ρ(~r2)

|~r1 −~r2|

and an “exchange-correlation” density functional (function ofa function) EXC [ρ(~r)]

25

Approximate exchange-correlation functionals

Exact EXC [ρ] requires solving the many-body problem

Not possible in real systems

Real calculations use an alphabet soup of approximate XCfunctionals

While “DFT” is exact, approximate XC functionals are not

Each approximation has costs and benefits

26

Costs and benefits of approximate functionals

Semilocal DFT

EXC [ρ] =

∫d3~r eXC (ρ(~r),∇ρ(~r), . . .)

Inexpensive enough for solids

Over-delocalize electrons (overbinding)

Nonlocal Hybrid

E exX = −1

2

N∑i ,j=1

∫d3~r

∫d3~r ′

φ∗i (~r)φj(~r′)φ∗j (~r)φi (~r

′)

|~r −~r ′|

Empirical admixture of E exX fixes overbinding

All molecular calculations from Part 1 used hybrid DFT

Long range of integrand expensive in metals

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DFT for heterogeneous catalysis

Semilocal DFT used for ∼ 20 years

Successes:

Computational design of catalytic alloys

Limitations:

Science 2005: Two semilocal DFT methods give largediscrepancy in N2 bond breaking on metal surface0.6 eV barrier height discrepancy10 order of magnitude reaction rate discrepancy!

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A solution from DFT for molecules

Screen out long-range exact exchange

ESRX = −1

2

∑ij

∫d3~r

∫d3~r ′

φ∗i (~r)φj(~r′)φ∗j (~r)φi (~r

′)

|~r −~r ′|

× erfc(ω|~r −~r ′|

)HSE06 and HISS screened hybrids are readily applied tometals and surfaces

Can they improve semilocal DFT’s reaction barriers?

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Tests on a model Si cluster

+

-1.60

-1.20

-0.80

-0.40

0.00

0.40

0.80

1.20

Re

lati

ve E

ne

rgy

(eV

)

Adsorbed NH3

Product

TS

Reactants

HISS

PBE revPBE HSE06 CCSD(T)/CBS

NH3 dissociation on Si9H12 cluster

Screened hybrids better reproduce accurateCCSD(T)/CBS-extrapolated benchmarks

R. Sniatynsky, B. G. Janesko, F. El-Mellouhi, E. N. Brothers, J. Phys. Chem. C 116, 26396 (2012)

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Tests on a realistic Si surface

HISSHSE06

PBE

On-DimerPathway

Inter-DimerPathway

+

NH3 Adsorbed

Inter-DimerTransition State

On-DimerTransition State

On-DimerProduct

Inter-DimerProduct

Accurate benchmarks are computationally infeasible

Screened hybrids increase barrier, improve selectivity

R. Sniatynsky, B. G. Janesko, F. El-Mellouhi, E. N. Brothers, J. Phys. Chem. C 116, 26396 (2012)

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Outline

1 DFT for alkyl cross-coupling

2 Other DFT applications

3 New functionals for surface chemistry

4 “Rung 3.5” density functionals

5 Summary

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Rationalizing DFT’s alphabet soup

LSDA GGA

Chemical accuracyheaven

Hartree world

Meta-GGA

Hybrid

Fifth-rung Small and medium-sized molecules

Rung 3.5 functionals

Large molecules

Solids and surfaces

“Jacob’s Ladder” ofapproximate XCfunctionals

First 3 rungs often aren’taccurate enough forchemistry

4th rung often expensivefor solids & surfaces

We seek a compromise

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Two problems with standard hybrid DFT

Metal surface, 5-10% screened nonlocal exchange

A

B

C

DCovalent bonds,~25% nonlocal exchange

Transition states,~50% nonlocal exchange

Long-range exact exchange is expensive

Fixed by screened hybrids

Optimum fraction of exact exchange varies for differentsystems & properties

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A closer look at exchange

Exact exchange comes from the noninteracting system’snonlocal density matrix

E exX = −1

2

∫d3~r

∫d3~r ′|γ(~r ,~r ′)|2

|~r −~r ′|

γ(~r ,~r ′) =N∑i=1

φi (~r)φ∗i (~r ′)

Semilocal functionals use a semilocal model constructedfrom information about ~r

ESLX = −1

2

∫d3~r

∫d3~r ′|γSL(ρ(~r),∇ρ(~r), . . . ,~r −~r ′)|2

|~r −~r ′|

Hybrid exchange aE exX + (1− a)ESL

X models nondynamicalcorrelation (chemical bonding)

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The “Rung 3.5” compromise

eX (~r) = −1

2

∫d3~r ′

|γ(~r ,~r ′)|2

|~r −~r ′|

eSLX (~r) = −1

2

∫d3~r ′

|γSL(ρ(~r),~r ′ −~r)|2

|~r −~r ′|

eΠX (~r) = −1

2

∫d3~r ′

γ(~r ,~r ′)γSL(ρ(~r),~r ′ −~r)

|~r −~r ′|

More delocalized than semilocal DFT

Less delocalized than |γ(~r ,~r ′)|2 (hybrids)

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Benefit #1: γSL screens large |~r −~r ′|

eΠX (~r) = −1

2

∫d3~r ′

γ(~r ,~r ′)γSL(ρ(~r),~r ′ −~r)

|~r −~r ′|

-9

-8

-7

-6

-5

-4

-3

-2

10 12 14 16 18

Log1

0 a

bso

lute

en

erg

y e

rro

r (H

artr

ee

)

Range of nonlocal interactions (Angstrom)

PBE

HSE06

Pi-LDA

HSE-2X

B3LYP

B. G. Janesko, in preparation

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Benefit #2: γ includes useful nonlocal information

G3/99 Reaction ReactionMethod ∆Ho

f Energies Barriers

PBE 17.9 3.5 8.9Π1PBE 9.5 2.2 7.6PBE0 5.0 2.2 3.9

6-311++G(2d,2p) MAE (kcal/mol) in G399 and NHTBH38/04data sets

A. Aguero, B. G. Janesko, J. Chem. Phys. 136, 024111 (2012)

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Band gaps

LPPyB PA PITN PEDOT MEH-PPV PTh PCDTBT CN-PPV PFu PPV PPy0

0.5

1

1.5

2

2.5

Bandgap (

eV) Ref

B3LYP

HSE06

Π-LSDA

PBE+Π(s)

M06-L

TPSS

PBE

B. G. Janesko, J. Chem. Phys. 134, 184105 (2011)

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Excitation energies & polarizabilities

2.6

2.7

2.8

2.9

3

3.1

3.2

3.3

3.4

3.5

LDA PBE PiLDA HSE PBE0

Fir

st e

xci

tati

on

en

erg

y (

eV

)

270

275

280

285

290

295

300

305

310

315

LDA PBE PiLDA HSE PBE0

Po

lari

zab

ilit

y (

au

)

G. Scalmani, M. J. Frisch, B. G. Janesko, in preparation

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Potential for surface chemistry

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

E (e

V)

Reference

PBE

Π1-PBE

PBE+Π(s)

+

41

Nonempirical, nonlocal DFT

Lieb-Oxford bound: E exXC ≥ λELDA

X

Variational bound: E exXC ≤ E ex

X

Cauchy-Schwarz: eexX (~r) ≤ (eΠX (~r))2

eSLX (~r)

Odashima & Capelle 2009

EXC ' βE exX + (1− β)λELDA

X

42

More flexible approximations

Odashima, Capelle, Haunschild, Perdew, Scuseria 2012

EXC =

∫d3~r eXC (~r)

eXC (~r) ' β(~r)eexX (~r) + (1− β(~r))λeLDAX (~r)

Our Rung 3.5 version

eXC (~r) ' β(~r)(eΠ

X (~r))2

eSLX (~r)+ (1− β(~r))λeLDAX (~r)

43

Nomempirical Rung 3.5 functionals

Method Params ∆Hof Barriers Bonds

Semilocal PBE 0 17.9 8.9 2.83Π-PBE 1 19.5 9.5 2.42ΠOC 0 14.3 7.4 2.62PBE0 hybrid 1 4.2 3.9 1.37

One of the most accurate nonempirical DFT methods

B. G. Janesko, J. Chem. Phys. 137, 224110 (2012)

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Outline

1 DFT for alkyl cross-coupling

2 Other DFT applications

3 New functionals for surface chemistry

4 “Rung 3.5” density functionals

5 Summary

45

Summary

DFT calculations can quantify and extend chemical intuition,helping design new catalysts and new materials

Screened hybrids fix some of standard DFT’s limitations forsurface chemistry

“Rung 3.5” DFT functionals provide potential for furtherimprovements

46

Acknowledgements

Group: Bimal Pudasaini, John Determan, Mark Bridle

Undergraduates: Austin Aguero, Jessie Girgis, Katelyn Poole

Collaborators: Ed Brothers (Texas A&M Qatar), Jean-LucMontchamp (TCU), Juan Peralta (Central MichiganUniversity), Mihaela Stefan (UT Dallas), Gaussian, Inc.

TCU startup and undergraduate research funds

Qatar National Research Foundation, NSF REU

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Extra slides

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Oxidative addition, no Lewis base

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β-elimination from OA product

50

Transmetalation

51

β-elimination from TM product

52

γSL models

γLDA1(ρ(~r), |~r −~r ′|) = ρ(~r) exp(−by2

)γGGA(ρ,∇ρ,u) = γLDA2(ρ, u) +

1

2u · ∇ρ exp

(f (s)y2

)∫

d3~rFPBEX (s)

(w(~r)eΠLDA1

X [ρ](~r) + (1− w(r))eLDAX (ρ(~r)))

53

Exchange decay in hydrogen chain

-6

-4

-2

0

2

4

6

12 16 20 24 28 32

Tota

l en

erg

y e

rro

r (1

0^(

-7)

Har

tre

e)

Range of nonlocal interactions (Angstrom)

54

Models for γSL

Simple:

γLDA(ρ(~r), |~r −~r ′|) = ρ(~r)e−by2

y = ρ(~r)1/3|~r −~r ′|

More complicated:

γGGA(ρ,∇ρ,~r −~r ′) = γLDA(ρ, |~r −~r ′|)

+1

2∇ρ · (~r ′ −~r ′)e−f (s)y2

s =|∇ρ|ρ4/3

55

Practical Rung 3.5 implementation

Practical DFT calculations expand the orbitals and densitymatrix in a finite basis set fixed throughout the calculation

φi (~r) =M∑µ=1

ciµχµ(~r)

γ(~r ,~r ′) =∑µν

Pµνχµ(~r)χν(~r ′)

56

Practical Rung 3.5 implementation

Rung 3.5 calculations are more practical if we expand themodel density matrix in a different finite basis

γSL(ρ(~r),~r ′ −~r) =M′∑η=1

cη(ρ(~r)) exp(−αη|~r ′ −~r |2

)eΠX (~r) =

∫d3~r ′

γ(~r ,~r ′)γSL(ρ(~r),~r −~r ′)|~r −~r ′|

=∑µνη

Pµνcη(ρ(~r))χµ(~r)Aνη(~r)

Aνη(~r) =

∫d3~r ′

χν(~r ′) exp(−αη|~r ′ −~r |2

)|~r ′ −~r |

G. Scalmani, M. J. Frisch, B. G. Janesko, in preparation