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Welcome to the ab-initio group in the MPI-P!

crystal

The theoretical description and prediction of experimental processes and system properties is an important aspect of scientific work. Theoretical scientists consider the initial conditions and the results of experiments and try to deduce general laws and principles. Based on these laws, predictions for novel systems can be made and subsequently tested against the corresponding experimental results. This procedure can lead to agreement, but equally well to disagreement of the postulated law with reality. Historically, the discovery of new fundamental laws has often been induced by the refutation of principles which had previously been ``accepted knowledge'' for considerable times.

It is a crucial criterion in science to be able to invalidate a statement; also today, such tests are an important part in the process of finding new principles. Since no physical or chemical theory can be verified in the sense of a mathematical proof, the inverse way has to be followed: it has to be shown that other principles - that are contradictory to the new proposed theory - lead to wrong predictions.

The prototype of this process is what happened in the late 19th and early 20th century, when the theory of quantum mechanics was developed. Experimentalists started to measure the energy flux u(T,λ) of a black body as a function of temperature and wavelength with high accuracy and asked for a theoretical explanation. The Rayleigh-Jeans-law for the emitted radiation power of a black body, stating that u(T,λ) ∝ T²/λ, was found to be valid for high temperatures and large wavelengths, while Wien's law, u(T,λ) ∝ λ-3eA/λT, explained the black-body-radiation for low temperatures and small wavelengths. Obviously, both laws could not easily be brought to a mutual agreement. When Planck initially proposed an ``interpolated'' formula, it was mainly because both (only asymptotically correct) laws had been invalidated.

Planck had not yet constructed the full picture of quantum mechanics, but his hypothesis of some kind of oscillators which should change their energies in integer multiples of a fundamental energy unit, was groundbreaking. Planck said about his new idea of energy quanta: ``Experience will prove hypothesis is realised in nature''. It turned out to be the case.

The kind of law that describes an isolated phenomenon like the emitted radiation of a perfect black body can be used for direct comparison between a fundamental theoretical law and the experimental reality. Nowadays, however, many scientific problems and questions have become much less fundamental and cannot be answered by a single new formula proposing a novel basic idea. Instead, a significant part of modern research focuses on the realistic description of systems that actually exist in nature (or at least in the laboratory). The small fragments from which such a real system is composed are governed by fundamental physical laws that are generally assumed to be known, e.g. from quantum mechanics. However, the fact that the fragments are mutually strongly coupled makes the behavior of these fragments and therefore of the total system very complex. As a consequence, the general solution for the evolution of these coupled fragments becomes very difficult or even impossible.

A further step is necessary for the prediction of the properties of more complex systems: the construction of simplified models and realistic approximations, which provide simplifications, but nevertheless describe the system in a realistic way.

This is the aim of the our work. A variety of real-world molecular and supramolecular systems, taken directly from the physical chemistry laboratory, shall be described by a particular computational approach, which is capable of modeling the atomistic structure and dynamics at a high level of accuracy and reliability. For this purpose, the method of choice is electronic structure density functional theory (DFT), combined with density functional perturbation theory for the calculation of spectroscopic parameters, as well as Car-Parrinello molecular dynamics simulations for the efficient incorporation of atomistic motion at a given temperature. Since many chemically relevant systems are actually measured in condensed phases (liquid or solid), the modeling is done under periodic boundary conditions, enabling the simulation of extended systems.

 

We study a variety of phenomena - with a common technique: Electronic structure theory. We compute the electronic orbitals of molecules, crystalline and amorphous solids, liquids, and solutions and derive their properties - from first principles, which means from the electronic orbitals obtained via the Schrödinger equation. We start from the famous ĤΦ=EΦ, and after applying a number of simplifications, we arrive at the Kohn-Sham equations of Density Functional Theory. In this theory, the wavefunctions Φi of the individual electrons are obtained as the lowest-energy solutions of ĤΦiiΦi. These equations are solved numerically, with the help of appropriate computer programs. Once the orbitals Φi are computed successfully, all kinds of properties that depend on them can be obtained successively. Examples are the molecular geometry (bond distances, bond angles etc), crystal packing arrangements, but also spectroscopic properties like IR-, UV-, Raman-, and NMR-spectra.

On the right, a proton conducting crystal (made of hydrogen-bonded Imidazole-PEO-Imidazole molecules) is shown, for which the NMR spectrum was recently computed. From the comparison of the calculated spectrum with experiment, the characteristics of packing effects and hydrogen bonding networks can be investigated.