prediction of spectroscopic parameters for bio-organic and ... · prediction of spectroscopic...

Prediction of spectroscopic parameters forbio-organic and bio-inorganic intermediates in

complex systems

Erik Donovan Hedegård

Department of Physics, Chemistry and Pharmacy

University of Southern Denmark

October 11, 2013

Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 1 / 28

Acknowledgements

University of Southern Denmark, Odense, Denmark

Jacob Kongsted and Hans Jørgen Aagaard JensenJógvan Magnus Haugaard OlsenNanna Holmgaard ListMorten Nørby Pedersen

Eidgenössische Technische Hochschule (ETH), Zürich, Switzerland

Stefan Knecht

CNRS, Université de Strasbourg, Strasbourg, France

Emmanuel Fromager

Topics

Part I

Polarizable Embedding with multireference wave functions

Topics

Part I

Part II

Structures and spectroscopy of [Fe]-hydrogenase

Topics

Part I

Polarizable Embedding: General Ideas

Split up the total system

QM region: until now: DFT or CC

Environment: Parameterized

Parameters from first principles

DFT and CC problems

Multireference character

DFT and CC problems

Double Excitations (DFT)

DFT and CC problems

MCSCF problems

DFT and CC problems

MCSCF problems

Lack of dynamical correlation

⇒ Overestimation of excitationenergies

When do we need MCSCF wave functions?

Large mixing of several electronic configurations

Large mixing of several electronic configurationsExample: Carotenoid derivativesKato et al., Nature, (2012), 482, 369. Slamovits et al., Nature Comm., (2011), 2, 183.

Scaling in quantum chemistry

HF scales as N4 with number of basisfunctions

Channel-rhodopsin:≈ 5000 atoms≈ 64000 basis functions (6-31G∗)

Outline (part I)

Embedding with MCSCF wave functions

Incorporation of embedding operators in MCSCF ansatzE. D. Hedegård, N. H. List, H. J. Aa. Jensen and J. Kongsted, JCP, (2013), 139, 044101.

N. H. List, H. J. Aa. Jensen, J Kongsted and E. D. Hedegård, Advances in Quantum Chemistry, (2013), 66, 195.

Outline (part I)

Dynamical correlation with DFT-MCSCF hybrid (MC-srDFT)

Benchmark studies in vacuum. Can this method be used ?E. D. Hedegård, F. Heiden, S. Knecht, E. Fromager, H. J. Aa. Jensen, JCP, (Accepted)

Outline (part I)

Dynamical correlation with DFT-MCSCF hybrid (MC-srDFT)

Benchmark studies in vacuum. Can this method be used ?E. D. Hedegård, F. Heiden, S. Knecht, E. Fromager, H. J. Aa. Jensen, JCP, (Accepted)

MC-srDFT with polarizable embedding

What is the effect from the protein in the retinal chromophore ?E. D. Hedegård, S. Knecht, J. M. H. Olsen, H. J. Aa. Jensen, J. Kongsted, JCP, (in prep.)

Polarizable Embedding energy contributions

Total interaction energy for a polarizable embedded system

Etot = EQM + Epe

Polarizable Embedding energy

Epe = Ees + Eind

Ves =q(rs)

|r − rs|−

1|r − rs|

+ · · ·

Epe = Ees + Eind

Ves =q(rs)

|r − rs|−

1|r − rs|

+ · · ·

Epe = Ees + Eind

Ves =q(rs)

|r − rs|−

1|r − rs|

+ · · ·

Eind = −12〈 F 〉R 〈 F 〉

Polarizable Embedding effective operator

Total interaction energy for a polarizable embedded system

Etot = EQM + Epe

Polarizable Embedding Energy

Epe = Ees + Eind

DefinitionThe polarizable embedding potential

vpe = Ve + R〈0 |F| 0〉Fe

a−111 · · · −T(2)

. . . · · ·

−T(2)1S · · · a−1

J. M. Olsen, K. Aidas and J. Kongsted, JCTC, (2010), 6, 3721.

Polarizable Embedding for proteins

Proteins: Amino acids linked by peptide bonds

The additional PE contributions

vpe = Ve + R〈0 |F| 0〉Fe

E. D. Hedegård, N. H. List, H. J. Aa. Jensen and J. Kongsted, JCP, (2013), 139, 044101.Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 11 / 28

vpe = Ve + R〈0 |F| 0〉Fe

DefinitionThe electronic gradient vector (g) and Hessian (H) matrix

vpe = Ve + R〈0 |F| 0〉Fe

g → gtot = gvac + gpe

vpe = Ve + R〈0 |F| 0〉Fe

g → gtot = gvac + gpe H → Htot = Hvac + Hpe

DefinitionThe response function

〈〈A, V〉〉ω = −A[1](

E[2] − ωS[2])

−1Vω[1]

E. D. Hedegård, N. H. List, H. J. Aa. Jensen and J. Kongsted, JCP, (2013), 139, 044101.

DefinitionThe response function

〈〈A, V〉〉ω = −A[1](

E[2] − ωS[2])

−1Vω[1]

E[2] → E[2]tot = E[2]

vac + E[2]pe E[2]

A BB∗ A∗

E. D. Hedegård, N. H. List, H. J. Aa. Jensen and J. Kongsted, JCP, (2013), 139, 044101.

Proof-of-principle calculation: Uracil

238 water molecules (714 atoms)

120 MD snapshots

Vertical excitation energies (in eV) for uracil.

Environment CAS(10,10) CAM-B3LYP Exp.

π → π∗

Gas phase 6.50 5.39 5.08Water 6.24 5.27 4.77Shift -0.26 -0.12 -0.31

n → π∗

Gas phase 6.14 5.05 4.38Water 6.47 5.65 n.r.Shift 0.32 0.60 -

L. B. Clark, G. G. Peschel, I. Tinoco Jr., JCP, (1965), 69, 3615.M. Daniels, W. Hauswirth, Science, (1971), 171, 675.

M. Fujii, T. Tamura, N. Mikami, M. Ito, CPL, (1986), 126, 583.

MC-srDFT vacuum benchmark: Organic dyes

Dipeptide β-dipeptide Tripeptide

N-phenylpyrrole (PP)

4-(N,N-dimethylamino)benzonitrile (DMABN)

Hydrogen chloride

Split the electronic repulsion in a short-range and a long-range part

Wee = Wsr,µee + W lr,µ

ee W lr,µee =

erf(µr12)

E. D. Hedegård, F. Heiden, S. Knecht, E. Fromager, H. J. Aa. Jensen, JCP, (Accepted)

ee W lr,µee =

erf(µr12)

-3 -2 -1 0 1 2 30,0

Av. Error (eV)

TD-CAM-B3LYP TD-B3LYP TD-MC-srPBE

ee W lr,µee =

erf(µr12)

-3 -2 -1 0 1 2 30,0

Av. Error (eV)

TD-CAM-B3LYP TD-B3LYP TD-MC-srPBE

TD-MC-sr B3LYP CAM-B3LYP

Mean 0.23 -0.76 -0.01

MAD 0.42 0.86 0.25

⇒ Results from total 24 excitations⇒ Comparison with CASPT2

MC-srDFT vacuum benchmark calculations (cont.)

Excitation ∆E (eV) Osc. Str. Exp.

S0 → S1 2.29 1.597 2.03

S0 → S2 3.63 0.522 3.22

Excitation ∆E (eV) Osc. Str. Exp.

S0 → S1 2.29 1.597 2.03

S0 → S2 3.63 0.522 3.22

Config. 3: Double excitation betweenHOMO-LUMO π → π

The retinal chromophore: Influence of the protein

What is the effect of the protein on theexcitation?

Excitation Environment ∆E (eV) Osc. Str.

S0 → S1 Gas-phase 2.29 1.597

Protein (m2p0) 3.15 1.983

⇒Environment important to fine-tuneabsorption range

S0 → S1 Gas-phase 2.29 1.597

Protein (m2p0) 3.15 1.983

⇒Environment important to fine-tuneabsorption range

S0 → S1 Gas-phase 2.29 1.597

Protein (m2p0) 3.15 1.983

Experimental value: ≈2.70 eV

Conclusions (part I)

Embedding with MCSCF wave functions ✓Embedding operators have been described in an MCSCFframework (implemented in DALTON)E. D. Hedegård, N. H. List, H. J. Aa. Jensen and J. Kongsted, JCP, (2013), 139, 044101.

Dynamical correlation with MC-srDFT ✓Significant improvement of excitation energiesE. D. Hedegård, F. Heiden, S. Knecht, E. Fromager, H. J. Aa. Jensen, JCP, (Accepted)

MC-srDFT with polarizable embedding ✓Protein effects can now be studied for multiconfigurationalsystems and for double excitationsE. D. Hedegård, S. Knecht, J. M. H. Olsen, H. J. Aa. Jensen, J. Kongsted, JCP, (in prep.)

Topics

Part II

Structures and spectroscopy of [Fe]-hydrogenase

Hydrogenase Enzymes (Collaboration with Ulf Ryde)

H2 −−⇀↽−− H++ H –

What is the binding site (and/or binding mode) of H2

The [Fe]-hydrogenase enzyme: The substrate

[Fe]-hydrogenase is the only hydrogenase which has an(additional) substrate

The enzyme is inactive without this substrate

The [Fe]-hydrogenase enzyme: Mechanism

Structures from X-ray

Open form structure with active site has been obtained

Closed form structure has also been obtained but without theactive site

Further problems: A mutant (Cys176 →Ala176) has been used anddithiotheretinol (DTT) has been added (coordinates to iron)

Workflow

Back-mutate Ala176 → Cys176

Workflow

Solvate (total system size ≈ 83000 atoms)

Workflow

Modify active site with H2 and perform QM/MM optimizations onopen form (a) and closed form + substrate (b)

Workflow

Modify active site with H2 and perform QM/MM optimizations onopen form (a) and closed form + substrate (b)

MD (10 ns) on the closed form + substrate (c)

The [Fe]-hydrogenase enzyme: The intermediates

Configuration Open Closed Closed

Substrate No Yes Yes

MD No No Yes

a From Fe(H2)(H)(dppe)2]+ and Fe(H2)(H)2(PEtPh2)2J. Am. Chem. Soc. 111 (1989), 8823.J. Am. Chem. Soc. 112 (1990), 4831.

b From various sourcesCoord. Chem. Rev. 252 (2008), 2381.

Chem. Soc. Rev. 33 (2004), 175.

Bond 2a Exp.

Fe−N 2.093 2.006

Fe−C 1.929 1.914

Fe−S 2.419 2.376

Fe−CO 1.763 1.844

Fe−H 1.958 1.5–1.7a

Fe−H 2.009 1.5–1.7a

H−H 0.785 -

Using B97-D/SV(P)-def2Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 22 / 28

MD No No Yes

Chem. Soc. Rev. 33 (2004), 175.

Bond 3a Exp.

Fe−N 2.085 2.006

Fe−C 1.956 1.914

Fe−S 2.442 2.376

Fe−CO 1.734 1.844

Fe−H 1.557 1.5–1.6b

Fe−H - -

H−H - -

MD No No Yes

Chem. Soc. Rev. 33 (2004), 175.

Bond 2b Exp.

Fe−N 2.068 2.006

Fe−C 1.878 1.914

Fe−S 2.402 2.376

Fe−CO 1.763 1.844

Fe−H 2.641 1.5–1.7a

Fe−H 2.675 1.5–1.7a

H−H - -

MD No No Yes

Chem. Soc. Rev. 33 (2004), 175.

Bond 2b Exp.

Fe−N 2.068 2.006

Fe−C 1.878 1.914

Fe−S 2.402 2.376

Fe−CO 1.763 1.844

Fe−H 2.641 1.5–1.7a

Fe−H 2.675 1.5–1.7a

H−H - -

MD No No Yes

Chem. Soc. Rev. 33 (2004), 175.

Bond 2b Exp.

Fe−N 2.068 2.006

Fe−C 1.878 1.914

Fe−S 2.402 2.376

Fe−CO 1.763 1.844

Fe−H 2.641 1.5–1.7a

Fe−H 2.675 1.5–1.7a

H−H - -

Vacuum calculations for the active site

Optimize 2a structure in vacuum

2a Fe−H Fe−H

B3LYP 1.833 1.886

TPSS 1.839 1.893

TPSSh 1.805 1.850

PBE 1.796 1.843

PBE0 1.748 1.786

B97-D N.A. N.A.

2a Fe−H Fe−H

B3LYP 1.833 1.886

TPSS 1.839 1.893

TPSSh 1.805 1.850

PBE 1.796 1.843

PBE0 1.748 1.786

B97-D N.A. N.A.

2a Fe−H Fe−H

B3LYP 1.833 1.886

TPSS 1.839 1.893

TPSSh 1.805 1.850

PBE 1.796 1.843

PBE0 1.748 1.786

B97-D N.A. N.A.

⇒ With B97-D the H2 ligand floats away

MD No No Yes

Chem. Soc. Rev. 33 (2004), 175.

MD No No Yes

Chem. Soc. Rev. 33 (2004), 175.

MD No No Yes

Chem. Soc. Rev. 33 (2004), 175.

Bond 2b Exp.

Fe−N 2.051 2.006

Fe−C 1.907 1.914

Fe−S 2.362 2.376

Fe−CO 1.769 1.844

Fe−H 1.831 1.5–1.7a

Fe−H 1.875 1.5–1.7a

H−H - -

Using TPSSh/SV(P)-def2Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 26 / 28

Configuration Open Closed ClosedSubstrate No Yes YesMD No No Yes

Chem. Soc. Rev. 33 (2004), 175.

Bond 2c Exp.

Fe−N 2.037 2.006

Fe−C 1.903 1.914

Fe−S 2.378 2.376

Fe−CO 1.771 1.844

Fe−H 1.877 1.5–1.7a

Fe−H 1.873 1.5–1.7a

H−H - -

Chem. Soc. Rev. 33 (2004), 175.

Bond 2c Exp.

Fe−N 2.037 2.006

Fe−C 1.903 1.914

Fe−S 2.378 2.376

Fe−CO 1.771 1.844

Fe−H 1.877 1.5–1.7a

Fe−H 1.873 1.5–1.7a

H−H - -

Chem. Soc. Rev. 33 (2004), 175.

Bond 2c Exp.

Fe−N 2.037 2.006

Fe−C 1.903 1.914

Fe−S 2.378 2.376

Fe−CO 1.771 1.844

Fe−H 1.877 1.5–1.7a

Fe−H 1.873 1.5–1.7a

H−H - -

Conclusions (part II)

Structures of [Fe]-hydrogenase intermediates ✓A series of structures in both open and closed configurations havebeen optimizedE. D. Hedegård, U. Ryde, J. Kongsted, Angew. Chem. Int. Ed., (to be submitted)

Functional dependence of structural parameters ✓The dispertion corrected B97-D functional becomes problematicfor η

2-bonded (side-on) H2E. D. Hedegård, U. Ryde, J. Kongsted, Angew. Chem. Int. Ed., (to be submitted)

Functional dependence of structural parameters ✓The dispertion corrected B97-D functional becomes problematicfor η

2-bonded (side-on) H2E. D. Hedegård, U. Ryde, J. Kongsted, Angew. Chem. Int. Ed., (to be submitted)

Further studies

Spectroscopic parameters (Mössbauer, NMR)Environmental effectsRelativistic effectsE. D. Hedegård, S. Knecht, U. Ryde, J. Kongsted, T. Saue, Phys. Chem. Chem. Phys., (to be submitted)

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