On the performance of ZORA in calculations of NMR, EPR and …static-curis.ku.dk/portal/files/164044186/Sauer.pdf · 2016. 7. 22. · 3) 2 XY]: ZORA/PBE0/QZ4P compared to experiment

On the performance of ZORA in calculations of NMR, EPR and PAC parameters

Stephan P. A. Sauer Department of Chemistry

University of Copenhagen

Department of Chemistry

• Students • Pi A. B. Haase (UCPH) Re, Ir

• Vaida Arcisauskaite (UCPH, Oxford) Hg

• Thorbjørn Morsing (UCPH) RuC

• Marzena Jankowska (Opole) Kr, Xe

• Klaudia Radula-Janik (Opole) Carbazoles

• Postdocs • Stefan Knecht (ETH) Hg

• Evanildo G. Lacerda Jr. (UCPH) Kr, Xe

• Colleagues • Michal Repisky (Tromsø) Re, Ir

• Teobald Kupka (Opole) Kr, Xe, Carbazoles

• Jesper Bendix (UCPH) Re, Ir, Ru

• Lars Hemmingsen (UCPH) Hg

Collaborators


Motivation

• Inhouse collaboration with (bio)inorganic chemists:

• Lasse Hemmingsen:

• Structure of Hg-protein complexes is studied by 199Hg NMR and PAC spectroscopy

• Interpretation of spectra requires calculations of the Hg chemical shifts and field gradients

• Jesper Bendix:

• Re and Ir complexes show interesting molecular magnet properties

• 13C chemical shifts of Ru-terminal carbide complexes exhibits irregular variation with the ligands

• Calculations are asked for

• Relativistic effects have to be accounted for

• Calibration of approximate two-component methods


Relativistic Methods

Solving the Dirac equations:

Four-component fully relativistic linear response theory

Implemented in DIRAC by Saue & Jensen and …

Implemented in ReSpect by Repisky, Komorovsky, Malkin, Malkina, Kaupp, and …

other programs BERTHA, MOLFDIR, BDF, …

Approximating the Dirac equation:

Zeroth Order Regular Approximation (ZORA) by Chang, Pelissier & Durand

Implemented in ADF program by Baerends and co-workers, Ziegler, Autschbach, …

Elimination of the Small Component:

Linear Response Elimination of Small Component (LR-ESC) by Melo, Ruiz de Azua, Aucar

Alternatively: Vaara and co-workers (BPPT), Fukui, …


• NMR absolute shieldings and chemical shifts of

• 199Hg in HgL2 (L = CH3, Cl, Br, I) compounds

• 39Ar, 83Kr and 129Xe in noble gas dimers

• 13C in ruthenium terminal carbide complexes

• 13C in 9-substituted 3,6-diiodo-carbazoles

• EPR hyperfine coupling constants (HFC) of

• Re and Ir in [ReIVF6]2- and [IrIVF6]

2- complexes

• PAC electric field gradients (EFG) of

• 199mHg EFG in HgL2 (L = CH3, Cl, Br, I) compounds

• Summary

Outline


NMR: Absolute shieldings σ and chemical shifts δ

of 199Hg, 39Ar, 83Kr, 129Xe and 13C using DIRAC and ADF


• Basis set effects in 4-component and ZORA calculations

• Comparison of ZORA to 4-component results for 199Hg, 39Ar, 83Kr and 129Xe

• Comparison of ZORA results to experimental values for 13C

NMR: Outline

Hg: Dyall’s cvxz (x = d, t, q) completely uncontracted

Cl: Dunning cc-pCVXZ (X = D, T, Q) completely uncontracted

Unrestricted kinetic balance (UKB) & GIAO for Hg shieldings

Changes < 1% beyond Dyall cvtz/Dunning cc-pCVTZ

Dyall cvtz/Dunning cc-pCVTZ is a good compromise


NMR: GTO Basis Sets for HgCl2 in 4-comp

11800

12000

12200

12400

12600

12800

13000

13200

Dyall.cvdz/ cc-pCVDZ

Dyall.cvtz/ cc-pCVTZ

Dyall.cvqz/ cc-pCVQZ

s(H

g)

/ ppm

s(Hg)

BP86: HgCl2

PBE0: HgCl2

BHandHLYP: HgCl2

[Arcisauskaite, Melo, Hemmingsen & Sauer, JCP 135, 044306 (2011)]


NMR: STO Basis Sets for HgCl2 in ZORA

Standard ADF all-electron Slater type orbital basis sets DZ, TZP, TZ2P, QZ4P

Self-constructed basis sets with less polarization functions: TZ, QZ, QZ2P

DFT/BP86

Two opposing trends: Increase of shielding: DZ -> TZ -> QZ Decrease of shielding: TZ -> TZP -> TZ2P or QZ -> QZ2P -> QZ4P

QZ4P necessary for converged results

TZ2P may give errors of ~500 ppm (~4%)

s(Hg) X XP X2P X4P

X = DZ 9 732

X = TZ 10 452 9 606 9 541

X = QZ 10 408 9 957 9 948


Standard ADF all-electron Slater type orbital basis sets DZ, TZ2P, QZ4P

Kr, Kr2, Xe and Xe2 shieldings with SO-ZORA at DFT/B3LYP

Larger changes in σ from TZ2P to QZ4P than from DZP to TZ2P

QZ4P or larger should be used

Chemical shifts δ might be ok with smaller basis sets


NMR: STO Basis Sets for noble gases in ZORA

6370

6390

6410

6430

6450

6470

6490

3350

3370

3390

3410

3430

3450

3470

DZ TZP TZ2P QZ4P

s(X

e)

/ p

pm

s(K

) /

pp

m

Kr

Kr2

Xe

Xe2

[Jankowska, Kupka, Stobiński, Faber, Lacerda Jr & Sauer, JCC 37, 395 (2016)]

• In 4-component and ZORA calculations at BP86 level

•

• Absolute shieldings σ(Hg):

• ZORA underestimates σ(Hg) by ~2100 ppm.

• ZORA reproduces the trend correctly

• Chemical shifts δ(Hg):

• ZORA differs less than 60 ppm from 4-component results.


NMR: Relativistic Effects on σ(Hg) and δ(Hg)

0

2000

4000

6000

8000

10000

12000

14000

16000

Hg(CH3)2 HgCl2 HgBr2 HgI2

s(H

g)

/ p

pm

s(Hg)

NR

ZORA

4-comp.

-5000

-4500

-4000

-3500

-3000

-2500

-2000

-1500

-1000

-500

0

HgCl2 HgBr2 HgI2

d(H

g)

/ p

pm

d(Hg)

NR

ZORA

4-comp.

Exp. in THF



NMR: Spin-Orbit contributions to s(Hg)

In 4-component and ZORA calculations at BP86 level

ZORA defines spin-orbit contributions differently

BUT: 4-component and ZORA calculations agree on trend in spin-orbit contributions

-1500

-500

500

1500

2500

3500

4500

5500

6500


sS

O(H

g) /

pp

m

ZORA

4-comp.



NMR: Finite (Gaussian) Nuclear Coulomb Potential

In 4-component and ZORA calculations at BP86 level

The effect increases with the atomic number of the ligands

Reduces σ(Hg) by ~100–500 ppm (2–3%)

The effect is ~2 times larger in 4-component calculations than in ZORA

Increases δ(Hg) by 1–143 ppm (1-3%).

-450

-400

-350

-300

-250

-200

-150

-100

-50

0


Ds

(Hg

) / p

pm

Changes in s(Hg)

4-component

ZORA

-20

0

20

40

60

80

100

120

140

160

HgCl2 HgBr2 HgI2

Dd

(Hg

) /

pp

m

Changes in d(Hg)

4-component

ZORA


• Difference from 4-component results at HF level

• Absolute shieldings σ:

• ZORA differs from 4-comp by up to 533 ppm (8%).

• ZORA recovers ~60% of the relativistic effects

• Chemical shifts δ:

• To large compared to 4-component

• Differences of 1-2 ppm from 4-component results (5%).


NMR: Relativistic Effects for σ of noble gas dimers

-1600

-1400

-1200

-1000

-800

-600

-400

-200

0

Ne2 Ar2 Kr2 Xe2

s/

pp

m

Error in

absolute shielding

NR

ZORA

-5

-4

-3

-2

-1

0

1

2

3

4

5

Ne2 Ar2 Kr2 Xe2

Dd

/ p

pm

Error in chemical shiftNR

ZORA

[Jankowska, Kupka, Stobiński, Faber, Lacerda Jr & Sauer, JCC 37, 395 (2016)]

[RuC(PR3)2XY]: ZORA/PBE0/QZ4P compared to experiment

• Errors within ± 7 ppm (1.5%) • Trends mostly reproduced:

CN complexes are the exception


NMR: d(13C) of Ru-carbide complexes

[RuC

(PR3)

2ClI]

[RuC

(PR3)

2ClI]

[RuC

(PR3)

2ClB

r]

[RuC

(PR3)

2Cl2]

[RuC

(PR3)

2ClF

]

[RuC

(PR3)

2Cl(N

CO)]

[RuC

(PR3)

2Cl(C

N)]

[RuC

(PR3)

2Cl(N

CS)]

[RuC

(PR3)

2Cl(N

CCH3)

]+

-8

-6

-4

-2

0

2

4

6

8

D d1

3C

[pp

m]

ZORA

Compound ZORA Experiment

[RuC(PR3)2(CN)2] 467 464.7

[RuC(PR3)2ClI] 463 469.7

[RuC(PR3)2ClBr] 466 471.4

[RuC(PR3)2Cl2] 470 471.7

[RuC(PR3)2ClF] 474 473.4

[RuC(PR3)2Cl(NCO)] 480 474.7

[RuC(PR3)2Cl(CN)] 476 474.9

[RuC(PR3)2Cl(NCS)] 484 477.5

[RuC(PR3)2Cl(NCCH3)]+

493 485.7

[Morsing, Reinholdt, Sauer, & Bendix, Organometallics 35, 100 (2016)]

In 3,6-diiodo-9-benzyl-9H-carbazole: BHandHLYP/DZP compared to experiment

• HALA effect of ~40 ppm – reproduced by ZORA • Errors within 5 ppm (4%); RMS = 3.3 ppm


NMR: HALA effect on d(13C)

C1=

C8

C2=

C7

C3=

C6

C4=

C5

C4A

=C5A

C8A

=C9A C

10C11

C12

=C16

C13

=C15

C14-5

0

5

10

15

20

25

30

35

40

45

50

D d1

3C

[pp

m]

atom numbering

NR

SR ZORA

ZORA

Atom numbering

Theoretical calculations

Experimental data

NR ZORA

C1=C8 112.35 112.48 111.08

C2=C7 137.64 137.94 134.70

C3=C6 123.80 87.83 82.23

C4=C5 131.64 132.34 129.33

C4A=C5A 127.21 127.38 127.74

C8A=C9A 144.32 143.89 139.62

C10 47.89 47.94 46.56

C11 140.74 140.78 136.10

C12=C16 128.40 128.37 124.05

C13=C15 130.43 130.40 128.88

C14 128.81 128.75 126.18 RMS 12.85 3.34

[Radula-Janika, Kupka, Ejsmonta, Daszkiewicza & Sauer, Struct. Chem. 26, 997 (2015)]

In 3,6-diiodo-9-ethyl-9H-carbazole: BHandHLYP/DZP compared to experiment

• HALA effect of ~40 ppm – reproduced by SO ZORA • Errors within 5 ppm (4%); RMS = 0.9 ppm


NMR: HALA effect on d(13C)

C1=

C8

C2=

C7

C3=

C6

C4=

C5

C4A

=C5A

C8A

=C9A C

10C11

-15

-10

-5

0

5

10

15

20

25

30

35

40

45

D d1

3C

[pp

m]

NR

ZORA

Atom numbering

Theoretical calculations

Experimental data

NR ZORA C1=C8 121.41 110.12 110.65 C2=C7 130.88 136.90 134.52 C3=C6 125.97 85.92 81.67 C4=C5 143.04 131.70 129.42 C4A=C5A 109.97 126.18 124.08 C8A=C9A 136.64 142.60 138.98 C10 37.42 37.44 37.74 C11 12.61 12.60 13.68 RMS 6.23 0.87

[Radula-Janika, Kupka, Ejsmonta, Daszkiewicza & Sauer, Struct. Chem. 27, 199 (2016)]


NMR: Conclusions

Absolute shieldings σ:

ZORA does not recover all relativistic corrections

ZORA reproduces the trend of relative relativistic corrections

Large basis sets (QZ4P) are necessary for ZORA calculations.

The TZ2P basis set may give large errors

Chemical shifts δ:

ZORA agrees well with 4-component calculations

ZORA reproduces HALA effects

Smaller basis sets might be ok


EPR: HFCs of Re and Ir

in [ReIVF6]2- and [IrIVF6]

2- complexes using ReSpect and ADF


• Basis set effects

• Variational versus perturbational treatment of SOC in ZORA

• Dependence of DFT functional

EPR: Outline


• Hyperfine couplings in

• d3 (PPh4)2[ReIVF6]·2H2O

• d5 (PPh4)2[IrIVF6]·2H2O

[Haase, Repisky, Bendix & Sauer, to be submitted]

EPR: Relativistic effects for Ir- and Re-complexes

ADF all-electron STO basis sets DZ, TZ2P, QZ4P

Dyall’s vxz (x = d, t, q) completely uncontracted

[ReIVF6]2- and [IrIVF6]

2- with ZORA and 4-comp at DFT/PBE0

No monotonic convergence within STO DZ, TZ2P, QZ4P series

Dyall’s basis set converged at vtz


EPR: Basis Set dependence of HFC

40

60

80

100

120

140

160

180

1220

1240

1260

1280

1300

1320

1340

DZ/vdz TZ2P/vtz QZ4P/vqz

[IrI

VF

6]2

- H

FC

/MH

z

[Re

F6]2

- H

FC

/MH

z

ADF: [ReF6]2- 4-comp: [ReF6]2-

ADF: [IrF6]2- 4-comp: [IrF6]2-



• Comparison of 4-component with ZORA treating spin-orbital coupling variational or with perturbation theory

• PBE0 with Dyall vqz or QZ4P & Xray geometries

• Comparison of 4-component

Complex Contribution ZORA PT SOC

ZORA variational

SOC

4-comp

[ReF6] 2- Total -1324 --- -1303

Non-SOC -1087 --- -1076

SOC -237 --- -227

[IrF6]2- Total

Non-SOC

SOC


EPR: Variational versus perturbational SOC in ZORA






ZORA variational

SOC

4-comp

[ReF6] 2- Total -1324 --- -1303

Non-SOC -1087 --- -1076

SOC -237 --- -227

[IrF6]2- Total 83 98

Non-SOC --- -42

SOC --- 140






• Perturbation theory SOC breaks down for [IrF6]2-



ZORA variational

SOC

4-comp

[ReF6] 2- Total -1324 --- -1303

Non-SOC -1087 --- -1076

SOC -237 --- -227

[IrF6]2- Total 955 83 98

Non-SOC -93 --- -42

SOC 1048 --- 140




• Why does perturbation theory fail for d5 [IrIVF6]2-?

• Electron configuration

• ZORA electronic excitation energies

Complex Transition Energy (eV) Orbitals Weight

[ReIVF6] 2- 1 3.13 b2g α → ligand α 99%

2 3.17 eg α → ligand α 99%

3 3.18 eg α → ligand α 99%

[IrIVF6]2- 1 0.06 eg β → b2g β 99%

2 0.07 eg β → b2g β 99%

3 2.82 eg β → ligand β

eg α → ligand α

51%

37%




• 3 functionals: BP86, B3LYP, PBE0 using vtz or QZ4P

• Variation with functional larger than with basis set

• Hybrid functionals perform better

• Deviation from experiment 6% for [IrF6]2- & 19% for [ReF6]

2-

Complex Functional ZORA PT/var SOC 4-comp

[ReF6] 2- BP86 -971 -940

B3LYP -1240 -1193

PBE0 -1324 -1303

Experiment ±1607

[IrF6]2- BP86 80 ---

B3LYP 83 97

PBE0 83 98

Experiment ±92


EPR: Dependence on the functional


• Varying the amount of HF exchange in 4-component PBE0/vdz calculations:


EPR: Importance of Hartree-Fock exchange


EPR: Conclusions

ZORA

Large basis sets are necessary: QZ4P

Gives similar results as 4-component calculations

Perturbation theory treatment of spin-orbit coupling

breaks down for [IrF6]2-

but works for [ReF6]2-

Variational spin-orbit treatment works for [IrF6]2-

Agreement with experiment not perfect - yet


199mHg PAC electric field gradient (EFG) at Hg

using Dirac and ADF

Hg, Br & I: Dyall’s cvxz (x = d, t, q) completely uncontracted

Cl: Dunning cc-pCVXZ (X = D, T, Q) completely uncontracted

Unrestricted (UKB) and restricted kinetic balance (RKB)

Changes < 1% beyond Dyall cvtz/Dunning cc-pCVTZ with UKB


-10

-9.5

-9

-8.5

-8

-7.5

-7

Dyall.cvdz/ cc-

pCVDZ

Dyall.cvtz/ cc-

pCVTZ

Dyall.cvqz/ cc-

pCVQZ

Vzz

/ a

u

Vzz(Hg): BH&H HgCl2 RKB

HgCl2 UKB

HgBr2 RKB

HgBr2 UKB

HgI2 UKB

EFG: Basis Sets for HgCl2, HgBr2 & HgI2 in DIRAC

[Arcisauskaite, Knecht, Sauer & Hemmingsen, PCCP 14, 2651 (2012); PCCP 14, 16070 (2012)]

In 4-component and ZORA calculations at BH&H level

• NR reproduces the trend correctly

• ZORA results differ only by 2 to 6 % from 4-component results

• ZORA reproduces geometry dependence of 4-component


EFG: Relativistic Effects

-18

-16

-14

-12

-10

-8

-6


Vzz / a

u

NR

ZORA

4-comp.

-13

-12

-11

-10

-9

-8

-7

-6

2.102 2.152 2.202 2.252 2.302 2.352 2.402V

zz / a

u

R / Å

HgCl2

ZORA

4-comp.


Deviation from CCSD-T in 4-component calculations

• Triples corrections are important, but not which version

• Large variation of DFT results

• BH&H shows best performance compared to CCSD-T


EFG: Electron correlation corrections

-5

-4

-3

-2

-1

0

1

2

3

4

5


DV

zz

/ a

u

MP2

CCSD

CCSD+T

CCSD(T)

HF

-5

-4

-3

-2

-1

0

1

2

3

4

5


DV

zz

/ a

u

BP86 BH&HPBE0 B3LYPCAMB3LYP CAMB3LYP*HF


• HF gives twice as large relativistic corrections as CCSD-T

• Non-relativistic correlation effects are too small

• Coupling between electron correlation and relativistic effects is larger than the non-relativistic correlation effects


EFG: Coupling electron correlation and relativity

-8

-6

-4

-2

0

2

4

6


DV

zz

/ a

u

Relativity HFRelativity CCSD-TCorrelation NRCorrelation 4-compCorrelation-Relativity



Conclusions

Electric field gradient

SO-ZORA agrees well with 4-component calculations also on

changing the geometry

BH&H best reproduces 4-component CCSD-T results

Electron correlation – relativity coupling is larger than NR

electron correlation correction


ZORA/QZ4P worked for us – so far …

But which functional should one use ?

Summary


• My collaborators and students

• The authors of Dirac, ADF and ReSpect

• Funding: FNU, DCSC, Carlsberg, Lundbeck

• You for your attention!

Thanks


• Task:

• Correlated relativistic linear response theory

• 4-component or ZORA

• Requirements:

• Experience with programming in DIRAC

or a linear response ZORA program

• Expertise in

• Relativistic quantum chemistry

• Linear response theory

• PhD finished after 30.04.14

• Latest starting date: 30.04.17

• Application deadline from now until filled

1 year Postdoc Position in Copenhagen

Documents

On the performance of ZORA in calculations of NMR, EPR and …static-curis.ku.dk/portal/files/164044186/Sauer.pdf · 2016. 7. 22. · 3) 2 XY]: ZORA/PBE0/QZ4P compared to experiment