Royal Institute of Technology
School of Biotechnology

PhD course:

Advanced Course in
Modern Molecular Modeling (ACM3)

YOU DO NOT UNDERSTAND IT
- IF YOU CANNOT MODEL IT !

The information on this page refers to the 2006-2007 version of the course. 2007-2008 is somewhat modified and has a different schedule. Please see course folder (pdf) for more info!

Computational Chemistry is a fast growing and developing field entering many industrial and scientific areas such as drug development, new materials, chemical engineering, climate prediction, environmental protection and biotechnology to mention a few. It is also the theoretical foundation of all modern nano sciences where other rules (basically those of quantum mechanics) apply compared to macroscopic matter. More and more R&D divisions of large companies now invest in modeling, a trend which is growing rapidly. Maybe worth of mentioning is that IDC, a market research firm recently estimated that every $ invested in modeling returns $3-$9 in revenues in nanotechnology and materials sector.

    This course covers virtually all Computational Chemistry there is today. It gives a solid basis for every theoretically oriented scientist to safely enter the field, as well as all those experimentalists realizing the value of modeling as a complementary tool to their measurements. We wish to stress that this course is highly comprehensive as it is given by a group of people both developing and using the most advanced modeling software covering the length and time scales from arbitrary to micro meters/seconds and even beyond. Necessary knowledge will be given even to choose and even build an optimal hardware (pc-clusters) as well as suitable algorithms for parallel computing of large molecular systems and short orientation in programming.

    This course is totally 25 academic credit points, divided to five blocks of 5 credit points. It is possible to enter and exit each block as found most convenient. The two main techniques in the entire course are Quantum Chemistry (QC) and Computer simulations (SIM), QC part consists of three 5 points blocks whereas SIM part is made of two blocks of 5 points of which the first contains the basic physicochemical theory needed in simulations. Short orientation in simulations is given in the first QC block. All blocks contain plenty of practical exercises and the second (more advanced) block of the SIM part ends with a project where both QC and SIM methods are combined.

• Molecular Modeling: Basic Tools (5 credit points) - 3A5711
• Molecular Modeling: Microscopic Concepts (5 credit points) - 3A5712
• Molecular Modeling: Macroscopic Concepts (5 credit points) - 3A5713
• Molecular Modeling: Learning to Fly (5 credit points) - 3A5714
• Molecular Modeling: Grand Applications (5 credit points) - 3A5715

Questions and applications are sent to hammar -at- theochem.kth.se.

Molecular Modeling: Basic tools (part 1)

(3A5711 - 5 credit points)

For schedule, see above.

Lecturer: Pawel Salek, pawsa -at- theochem.kth.se

Lecture 1 - Computers

a. Overview of serial and parallel computer architectures.
b. Memory hierarchies.
c. Overview of national computer use for Computational Chemistry.

Lecture 2 - Algebra

a. 3-dimensional vector algebra.
b. Matrices.
c. Determinants.
d. Operators.
e. Basis sets.
f. The eigenvalue problem.
g. Orthogonal functions and Eigenfunctions.
h. The variation principle.

Lecture 3 - Programming

a. On Fortran, C/C++ and scripting languages.
b. Writing efficient scientific programs.
c. Data locality.
d. Blocked algorithms.
e. Solving linear algebra problems on computers.
f. Matrix transformations.
g. Mathematical libraries.

Lecture 4 - Hartree-Fock theory.

a. The electronic Hamiltonian
b. Coulomb and exchange operators.
c. One- and two electron integrals
d. The total energy of the closed shell.
e. Fock equations.
f. Koopman’s theorem.
g. Roothaan equations.
h. The correlation problem.

Lecture 5 - Basis sets

a. Basis sets: Expansion of real solutions.
b. Gaussian basis sets.
c. Contracted vs primitive. Angular dependence.

Lecture 6 - Density Functional Theory

a. Theoretical background
b. Hohenberg-Kohn theorems
c. Local density approximation
d. Kohn-Sham formulation of DFT
e. Comparison of HF and DFT

Lecture 7 - Exchange-correlation functionals

a. ρ-dependent functionals
b. Gradient corrected and hybrid functionals
c. Asymptotically corrected functional
d. Numerical integration of functionals and its derivatives

Lecture 8 - Calculation of Forces in Quantum Chemistry

a. Analytic gradients and Hessians
b. The Hellman-Feynman theorem
c. The potential surface
d. Geometry optimization
e. Transition state calculations

Lecture 9 - The Monte Carlo method

a Stochastic vs deterministic processes
b Metropolis MC
c Overview of other Monte Carlo schemes
d Applications of MC in Quantum Chemistry

Lecture 10 - The Molecular Dynamics method

a. Newtonian dynamics
b. Time scales of Newtonian MD
c. MD of simple systems
d. Some typical applications of MD

Lecture 11 - Combining Quantum Chemistry and molecular simulations

a Hybrid QM-MM approach
b Ab-initio and Car-Parrinello molecular dynamics

Lecture 12 - Overview of computational chemistry software

Gaussian, GAMESS, GROMACS, NAMD, DL POLY, CPMD, ESPRESSO,
GOpenMol...

Computer Excercises 1 - 5

Molecular Modeling: Microscopic Concepts (part 2)

(3A5712 - 5 credit points)

For schedule, see above.

Lecture 1 - Wave-mechanical concepts.

a. Potential well and hydrogen atom
b. Schr¨odinger theory of hydrogen atom
c. Periodic table. SCF AO, Slater AO, Gauss AO
d. Chemical variety as a combination of few notes in music
    - (s, p, d, f
     instead of do, re, mi, fa, ...)

Lecture 2 - Angular momentum and atomic energy levels.

a. Spin of electron.
b. The Antisymmetry rule (Pauli principle). Slater determinant.
c. Spin-orbit coupling (SOC) in atoms
d. The Russell-Saunders scheme
e. Addition of Angular momentum
f. Terms of configurations 2p3p and 2p²
g. Lande interval rule
h. Slater-Condon parameters. Hund’s rule
i. Transition from Russell-Saunders coupling scheme to j - j coupling
j. Mg and Fe in the ground and excited states

Lecture 3 - Born-Oppenheimer approximation.

a. The electronic wave function as a slowly varying function of nuclear displacements
b. Validity of BO approximation in ground and excited states
c. The Jahn-Teller effect

Lecture 4 - Quantum nature of the chemical bond.

a. Ionic bond in NaCl. Covalent bond
b. Heitler-London method for H₂ molecule
c. Orbital and spin wave functions. Overlap integral
d. Exchange integral. The concept of Heisenberg exchange spinhamiltonian
e. The singlet ground state of the H₂ molecule and its chemistry
f. The triplet state of the H₂ molecule and its photochemistry
g. The role of the triplet state in chemistry and catalysis

Lecture 5 - Simple MO Theory of diatomic molecules.

a. Effective single-electron hamiltonian
b. Variation theorem. MO LCAO approximation
c. H₂ molecule
d. Huckel approximations
e. MOs of Homo-nuclear diatomic molecules
f. United atom atom and correlation diagram. Rydberg states
g. Ground and excited states state of the O₂ molecule
h. Hetero-nuclear diatomic molecules. The non-crossing rule

Lecture 6 - Simple polyatomic molecules.

a. H⁺₂ ion. Mass spectrometry
b. The H₂O molecule. The C_2v point group. MO and valence bond description
c. The BeH₂, NH₃ and CH₄ molecules. Hybridization

Lecture 7 - Huckel theory of organic chemistry.

a. Ethylene and butadiene
b. Benzene and nathtalene
c. The use of symmetry in Huckel MO theory
d. Aromaticity and 4n+2 rule
f. Problem of heteroatoms. Formaldehyde dipole moment
g. Atomic charge and electronegativity concept
h. Bond order

Lecture 8 - Molecular Symmetry.

a. Molecular Spectroscopy
b. Vibration-Rotation Spectra
c. Electronic Spectra
d. Symmetry elements
e. Group Theory in quantum mechanics
f. Selection rules in spectra

Lecture 9 - Spectroscopy and molecular orbital concept.

a. Electric dipole transition moment in ethylene and butadiene
b. Polarization of S-S transitions and symmetry selection rules
c. ππ* and nπ transitions. Solvent effects
d. Photoelectron spectra as direct experimental verification of the MO concept
e. EPR spectroscopy for radicals. Anion radicals of hydrocarbons. Hyperfine coupling. Spin polarization

Lecture 10 - Independent Particle Models.

a. The total energy of the closed shell
b. Fock equations
c. Koopman’s theorem
d. Roothaan equations

Lecture 11 - Electron Correlation CI

a. The concept of electronc correltion
b. Configuration Interaction
c. Configuration interaction for single excitations upon the closed shell. Ethylene spectrum
d. Configuration interaction (CI) in ^3,1Σ^-, ^3,1Δ and ^3,1Σ⁺ states of π³π^*1 configuration in diatomics
e. CI for double excitations upon the closed shell
f. Comparison of MO CI and valence bond methods for H2 molecule

Lecture 12 - Perturbation Theory

a. Moller-Plesset Perturbation Theory
b. Ordinary (RS) perturbation theory
c. MP2 energy expresssions in different orders
d. Size-consistency, convergence/divergence of the expansion

Lecture 13 - Relativistic effects in molecules.

a. General role of relativity in molecules
a. Spin-orbit coupling
b. SOC in small molecules
c. SOC in reactions of enzymes

Lecture 14 - Introduction to Second quantization

a. Definition of Fock space
b. Field (creation and annihilation) operators, properties and algebra
c. Quantum mechanical operators in second quantization
d. Spin-orbital vs orbital formulation
e. Unitary transformations
f. Optimization of wave functions

Lecture 15 - Introduction to Response Theory

a. Derivation of response functions
b. Linear and non-linear response functions
c. Residue analysis
d. Singlet versus triplet operators

Computer Excercises 1 - 5

Molecular Modeling: Macroscopic concepts (part 3)

(3A5713 - 5 credit points)

For schedule, see above.

Lecturers:
Aatto - Aatto Laaksonen (aatto -at- physc.su.se) Phone: 162372
Sasha - Alexander Lyubartsev (sasha -at- physc.su.se) Phone: 161193

Project work required passing the course.

Lecture 1 - Thermodynamics

a. States of matter
b. Systems and surrounding
c. Energy and structure
d. Temperature, pressure and intermolecular interactions

Lecture 2 - Thermodynamics

a. State functions and thermodynamical variables
b. Enthalpy, entropy and free energy
c. The laws of thermodynamics
d. The machinery of thermodynamics

Lecture 3 Statistical thermodynamics - Boltzmann distribution

a. Quantum mechanics - statistical thermodynamics - thermodynamics
b. The statistical method
c. Principle of equal probabilities
d. Boltzmann distribution
e. Molecular partition function

Lecture 4 Statistical thermodynamics - Canonical ensemble

a. Canonical ensemble
b. Qauntum and classical canonical partition function
c. Derivation of thermodynamic quantities
d. Statistical interpretation of the 2-nd law of thermodynamics

Lecture 5 Statistical thermodynamics - other ensembles

a. Microcanonical ensemble
b. Grandcanonical ensemble. Chemical potential.
c. Constant-Temperature – Constant-Pressure ensemble
d. Fluctuations

Lecture 6 Statistical thermodynamics - Ideal systems

a. Polyatomic molecules in a gas phase
b. Factorization of the partition function
c. Translation, rotation and vibration
d. Spectroscopy and thermodynamics

Lecture 7 Statistical thermodynamics - non-ideal systems

a. Non-ideal systems
b. Virial expansion
c. Van der Waals equation

Lecture 8 Statistical thermodynamics - Lattice systems

a. Lattice statistics
b. Ising model and spin systems
c. Lattice polymer models. Flory-Huggins theory

Lecture 9 Quantum statistical thermodynamics

a. Quantum statistics, Bosons and fermions.
b. Bose-gas. Bose condensation.
c. Fermi-gas. Electrons in metals

Lecture 10 Kinetics

a. Chemical reactions
b. Chemical kinetics (elementary reactions)
c. Equilibrium
d. Reaction order and molecularity
e. Chemical kinetics (complex reactions)

Lecture 11 Kinetics

a. How reaction rates can be affected
b. Arrhenius law
c. catalysis
d. homogeneous and heterogeneous catalysis
e. transition state theory (part I)

Lecture 12 Kinetics

a. Biological reactions and processes
b. Proteins and enzymes
c. Enzyme catalysis

Lecture 13 Liquid theories

a. Intermolecular interactions
b. Correlation function and Radial distribution function
c. Analytic liquid theories

Lecture 14 Electrolytes and polyelectrolytes

a. Electrochemical models.
b. Coulomb systems and continuum models. Debye-Huckel theory.
c. Strong non-ideality and correlations
d. Poly-electrolytes
e. Poisson-Boltzmann equation

Project work required passing the course.

Molecular Modeling: Learning to Fly (part 4)

(3A5714 - 5 credit points)

For schedule, see above (note! some late changes).

Lecturers:
Aatto - Aatto Laaksonen (aatto -at- physc.su.se) Phone: 162372
Sasha - Alexander Lyubartsev (sasha -at- physc.su.se) Phone: 161193

Project work required passing the course.

Lecture 1 Simulation methods. Molecular Mechanics

a. Force fields (FF) - intro
b. Parameterisation of FFs
c. Molecular mechanics (MM)
d. Energy minimization (EM) techniques
e. Conformational analysis
f. Introduction to some MM software for EM

Lecture 2 Monte Carlo method: background

a. Stochastic processes. Simple Monte Carlo methods.
b. Importance sampling
c. Markovian master equation
d. Phase space sampling
e. Various Monte Carlo techniques
f. Time in MC?

Lecture 3 Monte Carlo method: techniques

a. Optimizing MC runs
b. MC averages
c. Simple MC algorithms
d. Write your own MC code

Lecture 4 Molecular dynamics: background

a. Classical mechanics: Newtonian, Lagrangian and Hamiltonian equations
b. Basic molecular dynamics algorithms
c. Constant-Pressure and Constant-temperature molecular dynamics
d. Molecular dynamics (MD) : rigid molecules
e. Molecular dynamics : flexible molecules
f. MD vs MC

Lecture 5 Molecular dynamics: HowTo

a. Planning a simulation study for MD
b. Start, equilibration and production phases
c. Trajectory: what is it?
d. Averages from trajectories
e. Static and dynamical properties from MD
f. Visualization of simulation results
g. How do I know to trust the results?
h. Write your own MD code from short modules

Lecture 6 Molecular dynamics: techniques

a. Calculating electrostatic forces
b. Time scales and motional modes
c. Extending/restricting the phase space
d. Rare events
e. Parallel computational strategies for MD
f. Examples of large-scale or tricky simulations

Lecture 7 Free energy computations

a. Free energy from simulations
b. Various free energy simulation schemes
c. A closer look: The expanded ensemble method
d. Applications: solubility, protein folding

Lecture 8 Mesoscale Simulation methods 1

a. Non-equilibrium MD
b. Stochastic (Brownian and Langevin) dynamics
c. Dissipative particle dynamics
d. Coarse-graining techniques

Lecture 9 Mesoscale Simulation methods 2

a. Boltzmann eqation
b. Lattice gas models
c. Cellular automata
d. Lattice Boltzmann method

Lecture 10 Mesoscale Simulation methods 3

a. Kinetic Monte Carlo (kMC) method
b. Hydrodynamics
c. Multi-scale modeling (bridging the scales)

Lecture 11 Simulation methods

a. How can QC and simulation studies combined.
b. Simulations and property surfaces
c. MD simulations and spectroscopy

Lecture 12 Simulations and computers

a. Hardware aspects to speed up simulations.
b. Strategies and advices to build and maintain a pc-cluster
c. National HPC resources for various types of simulations

Project work is done during the last week of the course and
the results will be presented and discussed in a special seminar at
the end of the block.

Molecular Modeling: Grand Applications (part 5)

(3A5715 - 5 credit points)

Lecture 1 - Geometry calculations

a. Optimization
b. Practical strategies
c. Zero point and isotope effects

Lecture 2 - Transition state calculations

a. Solvation models and solvation effects
b. Basis set effects.
c. Accuracy of DFT methods.
d. Calculation and interpretation of potential energy surfaces
e. Modeling reaction pathways

Lecture 3 - Calculations of molecular response properties

a. HF - response functions (TDHF, RPA)
b. DFT - response functions (TDDFT)
c. MCSCF and coupled cluster response
d. Excited state properties
e. Brief survey of applications

Lecture 4 - Magnetic Resonance Parameters

a. Effective spin Hamiltonians
b. Hyperfine interaction
c. g-tensors
d. Zero-field splitting

Lecture 5 - Magnetic Resonance Spectroscopy

a. Spin relaxation
b. NMR
c. EPR
d. Related spectroscopies (ODMR, ENDOR)
e. Paramagnetic systems
f. NMR and EPR as tools in biochemistry

Lecture 6 - Vibrational Spectroscopy

a. Force fields and normal modes
b. Calculation of Infrared spectra
c. Calculation of Raman spectra

Lecture 7 - Optical / UV spectra

a. Fundamental optical excitations
b. Oscillator strengths
c. Polarization and Dichroism
d. Vibronic spectra
e. Franck Condon principle
f. Optical/UV spectroscopy as a diagnostic tool

Lecture 8 - X-ray spectroscopy

a. Photoelectron spectra
b. X-ray absorption
c. X-ray emission
d. Auger spectroscopy
e. Resonant X-ray spectroscopies

Lecture 9 - Non-linear phenomena

a. Polarizabilities and hyperpolarizabilities
b. Harmonic generation
c. Many-photon excitation
d. Few-state models
e. Vibrational contributions
f. NLO as application tool

Lecture 10 - Wave packets and ultra-fast phenomena

a. Time-dependent representation
b. The concept of wave packets
c. Comparison with classical trajectories, semiclassical Landau-Zener model
d. Representation (grids, basis functions)
e. Numerical techniques for propagation of wave packets
f. Multidimensional wave packets

Lecture 11 - Applications of wave packets

a. Vibrational spectroscopy
b. Reaction dynamics
c. Photodissociation and photochemistry
d. Pump-probe spectroscopy

Lecture 12 - Electronic and Optical properties of nanoparticles

a. Scale consideration v.s. molecular and solid-state systems
b. Electronic properties of individual nanoparticle
c. Optical properties of individual nanoparticle
d. Nanoparticle assembly/network: electronic and photonic crystals

Lecture 13 - Applications of nanoparticles in bio and medical fields

a. Multiphoton quantum dots for confocal microscopy
b. Medical/biochemical diagnostic using nanoparticles
c. Future nano devices

Computer Excercises 1 - 5

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