Mirko Franchini

TCCM Workshop April 19 | Amsterdam

ADFTechnical overview

TCCM workshop | 19 April 2016

The Kohn–Sham equations

TCCM workshop | 19 April 2016

The Kohn–Sham equations

Kinetic energy

TCCM workshop | 19 April 2016

The Kohn–Sham equations

Kinetic energy Electrostaticpotential due to

nuclei

TCCM workshop | 19 April 2016

The Kohn–Sham equations

Kinetic energy Electrostaticpotential due to

nuclei

Electrostatic potential due to electrons

TCCM workshop | 19 April 2016

The Kohn–Sham equations

Kinetic energy Electrostaticpotential due to

nuclei

Electrostatic potential due to electrons

Exchange-correlation Potential(e.g. Xα)

TCCM workshop | 19 April 2016

Self-Consistent Field: SCF

Initial guess

TCCM workshop | 19 April 2016

Self-Consistent Field: SCF

Initial guess

Solve KS equation

TCCM workshop | 19 April 2016

Self-Consistent Field: SCF

yes

SCF Converged

no

New for guess

Initial guess

SCFSolve KS equation

TCCM workshop | 19 April 2016

Basis set expansion and Fock-Matrix

Kohn-Sham Equation(difficult to solve)

TCCM workshop | 19 April 2016

Basis set expansion and Fock-Matrix

orbital basis functionsexpansion coefficients

basis set expansion

Kohn-Sham Equation(difficult to solve)

TCCM workshop | 19 April 2016

Basis set expansion and Fock-Matrix

orbital basis functionsexpansion coefficients

basis set expansion

Fock Matrix Overlap matrix

Kohn-Sham Equation(difficult to solve)

Kohn-Sham Equation In matrix form(easy to solve)

TCCM workshop | 19 April 2016

Basis set expansion and Fock-Matrix

- What basis function do we use in ADF?

- How do we calculate the integrals?

orbital basis functionsexpansion coefficients

Fock matrix

Overlap matrix

TCCM workshop | 19 April 2016

Basis functions: LCAO (linear combination of atomic orbitals)

orbital basis functionsexpansion coefficients

Basis set expansion:

STO (slater type orbital)

GTO (gaussian type orbital)

NAO (numerical atomic orbital)

Solutions of H atom

Numerical solutions for isolated atoms

Mathematically convenient (looks a bit like a STO)

ADF

Band

TCCM workshop | 19 April 2016

Fock-Matrix: how do we calculate these integrals?

Fock Matrix Overlap matrix

Khon-Sham Equation In matrix form

TCCM workshop | 19 April 2016

Fock-Matrix: how do we calculate these integrals?

Fock Matrix Overlap matrix

Khon-Sham Equation In matrix form

Analytical integration?

TCCM workshop | 19 April 2016

Fock-Matrix: how do we calculate these integrals?

Fock Matrix Overlap matrix

Khon-Sham Equation In matrix form

Analytical integration?

Numerical integration

TCCM workshop | 19 April 2016

Numerical Integration

TCCM workshop | 19 April 2016

Numerical Integration

TCCM workshop | 19 April 2016

Numerical Integration

Regular grid Gauss-Legendre grid

Choosing the right integration grid is important!

TCCM workshop | 19 April 2016

Numerical Integration

Becke fuzzy cells integration scheme

Khon-Sham Equation In matrix form

TCCM workshop | 19 April 2016

Wrapping up

- Matrix elements? Numerical integration

- Kohn-Sham Equation: high non-linearity → SCF

- Basis set: integro-differential eq. → eq. in matrix form

TCCM workshop | 19 April 2016

ADF: selected features

Technical:- Relativistic effects (ZORA, spin-orbit coupling)- XC: GGAs, meta-GGAs, Hybrids, RS-hybrids- Efficiently parallelized, linear scaling techniques

Spectroscopy:- IR, Raman, VCD, Franck-Condon factors- UV/Vis spectra (TD-DFT)- Frequency-dependent (hyper-)polarizability - NMR chemical shift and spin-spin coupling- ESR (EPR) g-tensor, hyperfine A-tensor, ZFS- Mössbauer spectroscopy, NRVS

Miscellaneous Features:- Geometry optimization, transition state, IR frequencies - Solvents and environments: COSMO, QM/MM- Analysis: energy decomposition, bond analysis - Electronic transport: NEGF, transfer integrals

TCCM workshop | 19 April 2016

Hands-on session

- ADF-GUI Tutorial 1: Excitation energies and UV/Vis spectrum of ethene- ADF-GUI Tutorial 2: Vibrational frequencies and IR spectrum of ethane- Exercises / AMA (ask me anything)

ADF tutorials: https://www.scm.com/documentation/Tutorials/

TCCM workshop | 19 April 2016

SpectroscopyInteraction between matter and electromagnetic radiation

- Mössbauer spectroscopy, NRVS

- Core excitations

- UV/Vis spectra oscillator strength, (hyper-)polarizability circular dichroism, optical rotation, ...

Electronic Spectroscopy

- IR frequencies VCD, Raman, Frank-Condon, VROA

- EPR g-tensor and hyperfine interaction (A-tensor)

- NMR chemical shift, spin-spin coupling

Gamma-rays

VibrationalSpectroscopy

TCCM workshop | 19 April 2016

Electronic excitations: Time-dependent DFT (TD-DFT)

Kohn-Sham equations(ground state)

Time dependent Kohn-Sham equations(excited states)

Linear response: - excitations energies - oscillator strength

(Line width: gaussian convolution)

TCCM workshop | 19 April 2016

Vibrational spectroscopy

Infra red (IR) spectroscopy: absorption of light to excite molecular vibrations

Harmonic approximation (at the optimized geometry): - parabolic potential wrt nuclear displacements

Molecular vibration Newtonian mechanics

Normal modes 'Q': from Hessian

Absorption intensity: