  The treatment of high-dimensional problems such as the Schr\"odinger equation
can be approached by concepts of tensor product approximation. We present
general techniques that can be used for the treatment of high-dimensional
optimization tasks and time-dependent equations, and connect them to concepts
already used in many-body quantum physics. Based on achievements from the past
decade, entanglement-based methods, -- developed from different perspectives
for different purposes in distinct communities already matured to provide a
variety of tools -- can be combined to attack highly challenging problems in
quantum chemistry. The aim of the present paper is to give a pedagogical
introduction to the theoretical background of this novel field and demonstrate
the underlying benefits through numerical applications on a text book example.
Among the various optimization tasks we will discuss only those which are
connected to a controlled manipulation of the entanglement which is in fact the
key ingredient of the methods considered in the paper. The selected topics will
be covered according to a series of lectures given on the topic "New
wavefunction methods and entanglement optimizations in quantum chemistry" at
the Workshop on Theoretical Chemistry, 18 - 21 February 2014, Mariapfarr,
Austria.
