Martin-Luther-Universität Halle-Wittenberg

Header Theoretische Chemie

Weiteres

Login für Redakteure

Methods

Density Functional Theory & Molecular Dynamics

The complexity of the many-body Schrödinger equation for a  system of interacting electrons makes it impossible to approach its  solution in a straightforward way. A certain set of assumptions,  simplifications and other approximations must be used to obtain a  reasonable description of the electronic structure of a complex system.  Besides the traditional Hartree-Fock pathway, density functional theory  (DFT), founded by P. Hohenberg and W. Kohn, has emerged in the last  decade as the method of choice, since it enables the calculation of  increasingly large systems at a moderate computational cost, together  with a sufficient accuracy.

Density Functional Theory & Molecular Dynamics

Density Functional Theory & Molecular Dynamics

Density Functional Theory & Molecular Dynamics

In DFT, the electronic structure is represented by a set  of independent wavefunctions. They are the solution of a  single-particle  Schrödinger equation, governed by the electrostatic  potential created  by the total electronic density of all these  wavefunctions. The  complicated quantum-mechanical restrictions of the  “true”  electronic wavefunction, such as exchange and correlation  effects, are  taken into account by means of a further potential energy  term, the exchange-correlation potential. It is made such that  physical properties of the total  electronic density are reproduced as  good as possible. Unfortunately,  this exchange-correlation potential is not unique. There is a  whole theory behind it, and many  variants have been proposed for the  exact shape of this potential. So  far, there seems to be no optimal way  of expressing exchange and  correlation effects within DFT. However,  for the most common choices of  this particular element, density  functional theory has shown to yield  very useful predictions of the  properties of matter, and it is becoming  more and more popular.

Molecular Dynamics means the numerical time-integration   of Newton's equations of motion. In particular, this can be done for a   system of atoms, which interact directly and by means of their   electrons. The total force felt by an atom is determined by the   surrounding atoms as well as the electronic structure. The combination   of density functional theory with molecular dynamics techniques, as   pioneered by R. Car and M. Parrinello, enables the direct observation  of  microscopic processes through the calculation of atomistic   trajectories.

Nuclear Magnetic Resonance

Nuclear Magnetic Resonance

Nuclear Magnetic Resonance

Nuclear Magnetic Resonance (NMR) deals with the phenomenon that  in a magnetic field, nuclear spins have discrete, quantized energy  levels. The energy difference between these states depends on the local  magnetic field at the position of the nucleus. Apart from the externally  applied magnetic field (Bext), there is an additional contribution to the local field (Bind), due to the response of the electrons around the atom (jind).  This response is of quantum-mechanical nature, but often it is referred  to as “ring currents”. They are determined by the specific electronic  structure in the neighborhood of the considered nucleus and give  characteristic information of its chemical environment. The additional  field induced by those currents is anisotropic, so that different  orientations of identical molecules result in different local fields for  their atoms.

Nuclear Magnetic Resonance 2

Nuclear Magnetic Resonance 2

Modern experiments measure the precession frequency of the nuclear spin  rather than the energy levels directly. In their ground state, the spins  are aligned along the quantization axis of the magnetic field. Upon  irradiation with suitable radio-frequency pulses, they are “flipped”  into a plane orthogonal to the external field, in which they start  precessing with a characteristic frequency (the Larmor frequency) which  is proportional to the local magnetic field. Subsequently, they fall  back to their all-aligned state during a characteristic relaxation time.  The experimental detection of the Larmor frequency is performed by a  Fourier transformation of the free induction decay of the  electromagnetic field emitted by the precession motion. From the  precession frequency, one can obtain the local magnetic field at the  position of the nucleus. There are numerous excellent textbook about the  elementary interactions between nuclear spins and electrons in magnetic  fields that describe this procedure extensively on the  quantum-mechanical level.

Nuclear Magnetic Resonance 3

Nuclear Magnetic Resonance 3

Nuclear Magnetic Resonance 3

The change in the resonance frequency of a given nuclear spin with  respect to a reference spin of the same type is called NMR chemical  shift δ. It is given by the dimensionless proportionality tensor between  the induced part of the local magnetic field and the homogeneous  external field, and the typical order of magnitude of this quantity is  ppm (parts per million, 10-6). The spectrum of these chemical shifts  represents a fingerprint of all spins of the system and can be used to  obtain valuable insight into microscopic structure. The information that  is nowadays routinely extracted from NMR experiments ranges from the  atomic bonding characteristics (bond lengths and bond angles) over the  characterization of hydrogen bonding networks up to packing effects on  the supramolecular and macromolecular level. On the right, the  dependence of the proton NMR chemical shift on the distance of an  imidazole dimer is illustrated.

CPMD: Car-Parrinello Molecular Dynamics

CPMD means both the general Car-Parrinello Molecular Dynamics method and  a particular computer simulation code that is based on this approach.  The CPMD code is a popular density-functional-theory based code that  relies on the plane-wave basis set and pseudopotentials to screen the  core electrons.

CP2K

CP2K is a newer code that is also developed in the Parrinello-family.  Inside CP2K, there is a classical and a density functional module. The  latter is based on a mixed basis which uses Gaussian basis functions for  the representation of the electronic orbitals, but plane waves for the  description of the electronic density.

Zum Seitenanfang