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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
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 2 / 28
Topics
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 3 / 28
Topics
Part I
Polarizable Embedding with multireference wave functions
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 3 / 28
Topics
Part I
Polarizable Embedding with multireference wave functions
Part II
Structures and spectroscopy of [Fe]-hydrogenase
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 3 / 28
Topics
Part I
Polarizable Embedding with multireference wave functions
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 3 / 28
Polarizable Embedding: General Ideas
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 4 / 28
Polarizable Embedding: General Ideas
Split up the total system
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 4 / 28
Polarizable Embedding: General Ideas
Split up the total system
QM region: until now: DFT or CC
Environment: Parameterized
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 4 / 28
Polarizable Embedding: General Ideas
Split up the total system
QM region: until now: DFT or CC
Environment: Parameterized
Parameters from first principles
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 4 / 28
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
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 4 / 28
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
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 4 / 28
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
Double Excitations (DFT)
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 4 / 28
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
Double Excitations (DFT)
MCSCF problems
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 4 / 28
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
Double Excitations (DFT)
MCSCF problems
Lack of dynamical correlation
⇒ Overestimation of excitationenergies
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 4 / 28
When do we need MCSCF wave functions?
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 5 / 28
When do we need MCSCF wave functions?
Large mixing of several electronic configurations
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 5 / 28
When do we need MCSCF wave functions?
Large mixing of several electronic configurationsExample: Carotenoid derivativesKato et al., Nature, (2012), 482, 369. Slamovits et al., Nature Comm., (2011), 2, 183.
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 5 / 28
When do we need MCSCF wave functions?
Large mixing of several electronic configurationsExample: Carotenoid derivativesKato et al., Nature, (2012), 482, 369. Slamovits et al., Nature Comm., (2011), 2, 183.
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 5 / 28
When do we need MCSCF wave functions?
Large mixing of several electronic configurationsExample: Carotenoid derivativesKato et al., Nature, (2012), 482, 369. Slamovits et al., Nature Comm., (2011), 2, 183.
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 5 / 28
When do we need MCSCF wave functions?
Large mixing of several electronic configurationsExample: Carotenoid derivativesKato et al., Nature, (2012), 482, 369. Slamovits et al., Nature Comm., (2011), 2, 183.
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 5 / 28
When do we need MCSCF wave functions?
Large mixing of several electronic configurationsExample: Carotenoid derivativesKato et al., Nature, (2012), 482, 369. Slamovits et al., Nature Comm., (2011), 2, 183.
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 5 / 28
Scaling in quantum chemistry
HF scales as N4 with number of basisfunctions
Channel-rhodopsin:≈ 5000 atoms≈ 64000 basis functions (6-31G∗)
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 6 / 28
Outline (part I)
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 7 / 28
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.
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 7 / 28
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.
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)
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 7 / 28
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.
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.)
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 7 / 28
Polarizable Embedding energy contributions
Total interaction energy for a polarizable embedded system
Etot = EQM + Epe
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 8 / 28
Polarizable Embedding energy contributions
Polarizable Embedding energy
Epe = Ees + Eind
Ves =q(rs)
|r − rs|−
∑
γ
µγ
(
∇γ
1|r − rs|
)
+ · · ·
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 8 / 28
Polarizable Embedding energy contributions
Polarizable Embedding energy
Epe = Ees + Eind
Ves =q(rs)
|r − rs|−
∑
γ
µγ
(
∇γ
1|r − rs|
)
+ · · ·
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 8 / 28
Polarizable Embedding energy contributions
Polarizable Embedding energy
Epe = Ees + Eind
Ves =q(rs)
|r − rs|−
∑
γ
µγ
(
∇γ
1|r − rs|
)
+ · · ·
Eind = −12〈 F 〉R 〈 F 〉
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 8 / 28
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
R =
a−111 · · · −T(2)
1S...
. . . · · ·
−T(2)1S · · · a−1
SS
J. M. Olsen, K. Aidas and J. Kongsted, JCTC, (2010), 6, 3721.
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 9 / 28
Polarizable Embedding for proteins
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 10 / 28
Polarizable Embedding for proteins
Proteins: Amino acids linked by peptide bonds
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 10 / 28
Polarizable Embedding for proteins
Proteins: Amino acids linked by peptide bonds
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 10 / 28
Polarizable Embedding for proteins
Proteins: Amino acids linked by peptide bonds
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 10 / 28
Polarizable Embedding for proteins
Proteins: Amino acids linked by peptide bonds
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 10 / 28
Polarizable Embedding for proteins
Proteins: Amino acids linked by peptide bonds
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 10 / 28
Polarizable Embedding for proteins
Proteins: Amino acids linked by peptide bonds
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 10 / 28
Polarizable Embedding for proteins
Proteins: Amino acids linked by peptide bonds
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 10 / 28
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
The additional PE contributions
vpe = Ve + R〈0 |F| 0〉Fe
DefinitionThe electronic gradient vector (g) and Hessian (H) matrix
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
The additional PE contributions
vpe = Ve + R〈0 |F| 0〉Fe
DefinitionThe electronic gradient vector (g) and Hessian (H) matrix
g → gtot = gvac + gpe
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
The additional PE contributions
vpe = Ve + R〈0 |F| 0〉Fe
DefinitionThe electronic gradient vector (g) and Hessian (H) matrix
g → gtot = gvac + gpe H → Htot = Hvac + Hpe
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
The additional PE contributions
DefinitionThe electronic gradient vector (g) and Hessian (H) matrix
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.
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 11 / 28
The additional PE contributions
DefinitionThe electronic gradient vector (g) and Hessian (H) matrix
g → gtot = gvac + gpe H → Htot = Hvac + Hpe
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]
vac =
(
A BB∗ A∗
)
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
Proof-of-principle calculation: Uracil
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 12 / 28
Proof-of-principle calculation: Uracil
238 water molecules (714 atoms)
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 12 / 28
Proof-of-principle calculation: Uracil
238 water molecules (714 atoms)
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 12 / 28
Proof-of-principle calculation: Uracil
238 water molecules (714 atoms)
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 12 / 28
Proof-of-principle calculation: Uracil
238 water molecules (714 atoms)
120 MD snapshots
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 12 / 28
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.
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 12 / 28
MC-srDFT vacuum benchmark: Organic dyes
C1N1
O1
C2
N2
H O2
H
C1N1
O1
H
C2N2
O
C1N1
O1
C2
H
N2 C3
O2
N3
O3
H
H
Dipeptide β-dipeptide Tripeptide
N
N-phenylpyrrole (PP)
NNC
4-(N,N-dimethylamino)benzonitrile (DMABN)
HCl
Hydrogen chloride
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 13 / 28
MC-srDFT vacuum benchmark: Organic dyes
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)
r12
E. D. Hedegård, F. Heiden, S. Knecht, E. Fromager, H. J. Aa. Jensen, JCP, (Accepted)
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 13 / 28
MC-srDFT vacuum benchmark: Organic dyes
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)
r12
-3 -2 -1 0 1 2 30,0
0,5
1,0
1,5
2,0
Are
a (n
orm
aliz
ed)
Av. Error (eV)
TD-CAM-B3LYP TD-B3LYP TD-MC-srPBE
E. D. Hedegård, F. Heiden, S. Knecht, E. Fromager, H. J. Aa. Jensen, JCP, (Accepted)
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 13 / 28
MC-srDFT vacuum benchmark: Organic dyes
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)
r12
-3 -2 -1 0 1 2 30,0
0,5
1,0
1,5
2,0
Are
a (n
orm
aliz
ed)
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
E. D. Hedegård, F. Heiden, S. Knecht, E. Fromager, H. J. Aa. Jensen, JCP, (Accepted)
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 13 / 28
MC-srDFT vacuum benchmark calculations (cont.)
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 14 / 28
MC-srDFT vacuum benchmark calculations (cont.)
N
H
Excitation ∆E (eV) Osc. Str. Exp.
S0 → S1 2.29 1.597 2.03
S0 → S2 3.63 0.522 3.22
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 14 / 28
MC-srDFT vacuum benchmark calculations (cont.)
N
H
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
∗
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 14 / 28
The retinal chromophore: Influence of the protein
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 15 / 28
The retinal chromophore: Influence of the protein
What is the effect of the protein on theexcitation?
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 15 / 28
The retinal chromophore: Influence of the protein
What is the effect of the protein on theexcitation?
Excitation Environment ∆E (eV) Osc. Str.
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 15 / 28
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
N
H
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 15 / 28
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
N
H
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 15 / 28
The retinal chromophore: Influence of the protein
What is the effect of the protein on theexcitation?
⇒Environment important to fine-tuneabsorption range
Excitation Environment ∆E (eV) Osc. Str.
S0 → S1 Gas-phase 2.29 1.597
Protein (m2p0) 3.15 1.983
N
H
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 15 / 28
The retinal chromophore: Influence of the protein
What is the effect of the protein on theexcitation?
⇒Environment important to fine-tuneabsorption range
Excitation Environment ∆E (eV) Osc. Str.
S0 → S1 Gas-phase 2.29 1.597
Protein (m2p0) 3.15 1.983
N
H
Experimental value: ≈2.70 eV
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 15 / 28
Conclusions (part I)
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 16 / 28
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.
N. H. List, H. J. Aa. Jensen, J Kongsted and E. D. Hedegård, Advances in Quantum Chemistry, (2013), 66, 195.
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 16 / 28
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.
N. H. List, H. J. Aa. Jensen, J Kongsted and E. D. Hedegård, Advances in Quantum Chemistry, (2013), 66, 195.
Dynamical correlation with MC-srDFT ✓Significant improvement of excitation energiesE. D. Hedegård, F. Heiden, S. Knecht, E. Fromager, H. J. Aa. Jensen, JCP, (Accepted)
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 16 / 28
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.
N. H. List, H. J. Aa. Jensen, J Kongsted and E. D. Hedegård, Advances in Quantum Chemistry, (2013), 66, 195.
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.)
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 16 / 28
Topics
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 17 / 28
Topics
Part II
Structures and spectroscopy of [Fe]-hydrogenase
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 17 / 28
Hydrogenase Enzymes (Collaboration with Ulf Ryde)
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 18 / 28
Hydrogenase Enzymes (Collaboration with Ulf Ryde)
H2 −−⇀↽−− H++ H –
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 18 / 28
Hydrogenase Enzymes (Collaboration with Ulf Ryde)
H2 −−⇀↽−− H++ H –
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 18 / 28
Hydrogenase Enzymes (Collaboration with Ulf Ryde)
H2 −−⇀↽−− H++ H –
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 18 / 28
Hydrogenase Enzymes (Collaboration with Ulf Ryde)
H2 −−⇀↽−− H++ H –
What is the binding site (and/or binding mode) of H2
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 18 / 28
The [Fe]-hydrogenase enzyme: The substrate
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 19 / 28
The [Fe]-hydrogenase enzyme: The substrate
[Fe]-hydrogenase is the only hydrogenase which has an(additional) substrate
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 19 / 28
The [Fe]-hydrogenase enzyme: The substrate
[Fe]-hydrogenase is the only hydrogenase which has an(additional) substrate
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 19 / 28
The [Fe]-hydrogenase enzyme: The substrate
[Fe]-hydrogenase is the only hydrogenase which has an(additional) substrate
The enzyme is inactive without this substrate
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 19 / 28
The [Fe]-hydrogenase enzyme: Mechanism
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 20 / 28
The [Fe]-hydrogenase enzyme: Mechanism
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 20 / 28
The [Fe]-hydrogenase enzyme: Mechanism
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 20 / 28
The [Fe]-hydrogenase enzyme: Mechanism
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 20 / 28
The [Fe]-hydrogenase enzyme: Mechanism
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 20 / 28
Structures from X-ray
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 21 / 28
Structures from X-ray
Open form structure with active site has been obtained
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 21 / 28
Structures from X-ray
Open form structure with active site has been obtained
Closed form structure has also been obtained but without theactive site
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 21 / 28
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)
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 21 / 28
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
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 21 / 28
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
Solvate (total system size ≈ 83000 atoms)
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 21 / 28
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
Solvate (total system size ≈ 83000 atoms)
Modify active site with H2 and perform QM/MM optimizations onopen form (a) and closed form + substrate (b)
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 21 / 28
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
Solvate (total system size ≈ 83000 atoms)
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)
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 21 / 28
The [Fe]-hydrogenase enzyme: The intermediates
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 22 / 28
The [Fe]-hydrogenase enzyme: The intermediates
a b c
Configuration Open Closed Closed
Substrate No Yes Yes
MD No No Yes
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 22 / 28
The [Fe]-hydrogenase enzyme: The intermediates
a b c
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
The [Fe]-hydrogenase enzyme: The intermediates
a b c
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 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 - -
Using B97-D/SV(P)-def2Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 23 / 28
The [Fe]-hydrogenase enzyme: The intermediates
a b c
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 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 - -
Using B97-D/SV(P)-def2Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 24 / 28
The [Fe]-hydrogenase enzyme: The intermediates
a b c
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 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 - -
Using B97-D/SV(P)-def2Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 24 / 28
The [Fe]-hydrogenase enzyme: The intermediates
a b c
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 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 - -
Using B97-D/SV(P)-def2Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 24 / 28
Vacuum calculations for the active site
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 25 / 28
Vacuum calculations for the active site
Optimize 2a structure in vacuum
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 25 / 28
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.
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 25 / 28
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.
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 25 / 28
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.
⇒ With B97-D the H2 ligand floats away
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 25 / 28
The [Fe]-hydrogenase enzyme: The intermediates
a b c
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.
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 26 / 28
The [Fe]-hydrogenase enzyme: The intermediates
a b c
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.
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 26 / 28
The [Fe]-hydrogenase enzyme: The intermediates
a b c
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 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
The [Fe]-hydrogenase enzyme: The intermediates
a b c
Configuration Open Closed ClosedSubstrate No Yes YesMD 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 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 - -
Using TPSSh/SV(P)-def2Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 27 / 28
The [Fe]-hydrogenase enzyme: The intermediates
a b c
Configuration Open Closed ClosedSubstrate No Yes YesMD 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 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 - -
Using TPSSh/SV(P)-def2Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 27 / 28
The [Fe]-hydrogenase enzyme: The intermediates
a b c
Configuration Open Closed ClosedSubstrate No Yes YesMD 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 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 - -
Using TPSSh/SV(P)-def2Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 27 / 28
Conclusions (part II)
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 28 / 28
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)
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 28 / 28
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)
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 28 / 28
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)
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)
Erik Donovan Hedegård (SDU) Fall Meeting Chemsoc (theory) October 11, 2013 28 / 28