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

Theoretical Biochemistry

Protein (enzyme)

Mechanisms of life processes

O2

CO2

H2O

Photosynthesis

Photosystem II (enzyme)

6CO2 + 6H2O + hυ --> 6O2 + C6H12O6 (plant tissue)

2H2O --> O2 + 4e- + 4H+

Respiration

Cytochrome oxidase (enzyme)

6O2 + C6H12O6 (food) --> 6CO2+ 6H2O + ATP (energy)

O2 + 4e- + 4H+ --> 2H2O (O2 reduction)

Catalytic cycle of O2 reduction

A

A: Fe(II)-O2 + Cu(I)

O-O bond cleavage:A --> PM

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

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

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

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)

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)

Energy Landscape

Reactants

Products

TS(B)

TS(A)

Exploring the energy landscapeof chemical reactions

Energy surface

Reaction coordinate ->

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

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)

Energy surface

Reaction coordinate ->

A

Mechanisms of chemical reactions

• Find paths in the energy landscape

• Reasonable exothermicity• Barrier heights in agreement with experimental rates

• Agree with other experimental information

Cytochrome oxidase

O2

Cytochrome oxidase -aktive site

X-ray (active site) Model

H+ ?H+

Computed energy surfaces: O-O bond cleavage in cytochrome oxidase

Reaction coordinate ->

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

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

Calculated energy profile: whole catalytic cycle

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

Energetics of proton and electron transfer, one step

Experimental rate data and simple electrostatics -> pump mechanism

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, mb@physto.seAnmälan: Marieanne Holmberg, tfn 553 78 650.Kursbok: F. Jensen: Introduction to Computational Chemistry