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Biomolecular simulation: Algorithms for trajectory analysis top of page 
A simulation of FABP in
water. The protein carries a large waterfilled cavity in the
interior. How can we extract this internal water?

Essentially, we represent the protein barrel by its C_{α} skeleton, triangulate it, and determine all water molecules inside the polyhedron. 
Some details on the algorithm. The triangulation exploits locality and can thus be performed in linear time. 
Biomolecular simulation: FABP top of page 
Using the above algorithm, we may
analyze the entire trajectory
and identify the distribution of 3 (apo) and 4 (holo)
water molecules which in NMR experiments have been found to be
particularly immobile,

or analyze the entire interior water density 
or even timeresolved interaction potentials with other water, with protein residues, and with the ligand to improve our understanding of the internal water dynamics. 
Biomolecular simulation: Carbopeptoids top of page 
Carbopeptoids are homooligomers of sugarcontaining peptides,
and they serve as rigidified peptide models with potential
applications as drugs that block proteinprotein interactions
and inhibit enzyme catalysis.

MD simulations reproduce experimentally (NOE) derived distance constraints. Cluster analyses of MD trajectories demonstrates, however, that the experimentally postulated helical structure is only one of several dominating structural motifs comprising the entire ensemble, and that the unfolded state is in fact not structureless. Such insight is hard if not impossible to obtain from experiment alone. 
Cluster analysis combining the ensembles of the tetrapeptide and equally long blocks of the hexapeptide demonstrates the repetition of structural motifs in longer peptide chains, a result, that was postulated in experimental studies. Note the "overlapping" (blue/red) clusters in the graph. 
MD simulation software: Pair list algorithms top of page 
MD simulations often apply a distancecutoff for pair potentials,
and the scan of the atom pair matrix is one of the very
timecritical parts of such an MD simulation. While linearscaling
gridcell techniques become efficient for very large system sizes,
improved doubleloop algorithms are beneficial for intermediate
sizes often considered in currentday simulations.

Here we take advantage of the fast processor cache found in modern CPUs and replace the rowwise atom pair scan (unshaded) by a window scan (shaded) which can process a number of pairs that scales quadratically, rather than linearly, with the number of atoms loaded into cache memory. The triangular atompair matrix may be reordered to become rectangular, in which case all rhombic windows become quadratic. 
Giant fullerenes top of page 
Fullerenes were discovered in the mid80's and have attracted
a lot of attention as new allotropes of carbon. The prototype
buckminsterfullerene, C_{60}, is spherical due to its
high symmetry.

Despite earlier claims, however, our semiempirical calculations have shown that larger fullerenes of icosahedral symmetry prefer facetted over spherical shapes. These results were confirmed by more rigorous density functional calculations . The picture above shows the facetted form of C_{960} from two different perspectives and a hypothetical spherical alternative. 
Ab initio thermochemistry: CBS extrapolation top of page 
The development of accurate
extrapolation formulas for electron correlation energies is
an important field in ab initio thermochemistry. Electron correlation
energies are known to converge slowly to the complete basis set
limit, and finite basis set calculations will thus carry substantial
error. On the other hand, computational restraints usually force one
to resort to small basisset calculations. The graph compares
residual errors for our newly developed and theoretically
wellmotivated extrapolation formula (2nd and 4th panel) to those of
the best alternative formulations (1st and 3rd panels). The large
improvement is expected to have a significant impact on producing
reliable ab initio reference data for the calibration of empirical
and semiempirical potentials.

Ab initio thermochemistry: ATOMIC protocol top of page 
The ATOMIC approach
was developed with the needs in mind that are posed by the
calibration of modern approximate models of quantum
chemistry, such as semiempirical methods. It is a robust
and computationally efficient approach to otherwise dauntingly
expensive calculations of atomization energies. The graph shows
how the use of bond separation reactions (BSRs) helps to reduce
errors in each of the components contributing to the CCSD(T)(full)
atomization energy at the completebasis set limit. Each single
chart shows RMS errors for a particular component as function of
the basisset cardinal number, without (top) or with (bottom)
extrapolation. In practice only small basisset calculations
are feasible for larger systems.

Corrections to atomization energies beyond the CCSD(T) level of theory are estimated from thermoneutral BSRs. This simplification renders the calculation of these corrections a trivial task of summing up bond increments. Such an approach is astonishingly accurate for scalar relativistic corrections and works reasonably well even for CCSDTQCCSD(T) corrections. 