quantum chemistry at fysikum - teori.atom.fysik.su.selindroth/comp08/microsoft powerpoint -...
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Quantum chemistry at Fysikum
Theoretical actinide chemistry:Ulf Wahlgren et al
Surface chemical physics:Lars Pettersson, Michael Odelius et al
Theoretical Biochemistry:Per Siegbahn, Margareta Blomberg et al
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Theoretical Biochemistry
Protein (enzyme)
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Mechanisms of life processes
O2
CO2
H2O
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Photosynthesis
Photosystem II (enzyme)
6CO2 + 6H2O + hυ --> 6O2 + C6H12O6 (plant tissue)
2H2O --> O2 + 4e- + 4H+
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Respiration
Cytochrome oxidase (enzyme)
6O2 + C6H12O6 (food) --> 6CO2+ 6H2O + ATP (energy)
O2 + 4e- + 4H+ --> 2H2O (O2 reduction)
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Catalytic cycle of O2 reduction
A
A: Fe(II)-O2 + Cu(I)
O-O bond cleavage:A --> PM
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How does the O2 bond cleavage occur
in cytochrome oxidase?
Biochemical experiments
• Crystal structure of enzyme• Spectroscopy of intemediates• Life time measurements and isotope effects• Mutation experiments• Etc, etc
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How does the O2 bond cleavage occur
in cytochrome oxidase?
Theory (quantum mechanics)
• Construct a model of the enzyme
• Solve the Schrödinger equation (approximately)
• Computer programs (Jaguar, Gaussian)
• Compare to the experimental information
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Quantum mechanics --> quantum chemistry
• H Ψ = E Ψ (Schrödinger equation)• We mainly need the energy, E• Ψ (x1,y1,z1; x2,y2,z2;……;xn,yn,zn)• Chemistry: nuclei and electrons• Protein: thousands of atoms• Model: ca 150 atoms => ca 700 electrons• Accurate approximate wave-function, Ψ:20-30 atoms
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Density functional theory (DFT)
• H Ψ = E Ψ (Schrödinger equation)• Electron density: ρ(x,y,z) = Ψ(x1,y1,z1,..)2
• E(ρ) (functional) 1962• Only approximate forms of the functional• Better functionals constructed in the 1990’s• 150 atoms can be handled accurately• Biochemical models can be studied• Nobel price in chemistry 1998 (Kohn och Pople)
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Chemical reactions
• H Ψ = E Ψ
• Nuclear mass >> electron mass
• Born-Oppenheimer approximation
• Solve electronic Schrödinger equation for different nuclear arrangements
• Energy surface (energy landscape)
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Energy Landscape
Reactants
Products
TS(B)
TS(A)
Exploring the energy landscapeof chemical reactions
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Energy surface
Reaction coordinate ->
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Solve the Schrödinger equation for a molecule in a single geometry
• INPUT:
• Coordinates and type of atoms
• Total charge (=number of electrons)
• Total spin
• Method to be used (which approximation)
• Basis set (mathematical functions to express wave functions or electron density)
• OUTPUT:
• Energy and electron distribution
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Potential energy surface:find different stationary points
• INPUT:
• Same as singel point
• Type of stationary point (minimum or saddle point)
• Program calculates:
• First and second derivatives of energy with respect to nuclear coordinates
• OUTPUT:
• Optimized geometry and energy
• Frequency analysis (zero point)
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Energy surface
Reaction coordinate ->
A
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Mechanisms of chemical reactions
• Find paths in the energy landscape
• Reasonable exothermicity• Barrier heights in agreement with experimental rates
• Agree with other experimental information
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Cytochrome oxidase
O2
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Cytochrome oxidase -aktive site
X-ray (active site) Model
H+ ?H+
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Computed energy surfaces: O-O bond cleavage in cytochrome oxidase
Reaction coordinate ->
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Cytochrome oxidase - proton pump
N-side
P-side
H+
H+e-
O2
H2O
ATPsynthase
H+
H+
ATP(energy)
membrane (mitochodrial)
H+ H+
heme a
BNC
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Catalytic cycle of O2 reduction
Use experimental data(redox potentials) to calculate the energy ofthe electrons and protons entering the enzyme during the reaction, too difficultto calculate accurately
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Calculated energy profile: whole catalytic cycle
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The gating problem of proton pumping
inside
outside
H+
H+H+
X
The pumped protons must
1. come from the inside
2. must not go too earlyto active site
3. must not return to theinside
O2 chemistry
X
pump site
heme aBNC
X
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Energetics of proton and electron transfer, one step
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Experimental rate data and simple electrostatics -> pump mechanism
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Kvantkemi, 15 hpFysikum, Stockholms universitet
(tidigare kallad Teoretisk kemi)
Tid och plats: Kursen går på halvfart under höstterminen 2008.Tisdagar kl 10:15-12.00 + datorlaborationer. Start: 26 augusti påRoslagstullsbacken 17, AlbaNova Universitetscentrum.Information: Margareta Blomberg, tfn 16 12 64, [email protected]älan: Marieanne Holmberg, tfn 553 78 650.Kursbok: F. Jensen: Introduction to Computational Chemistry