epdf.pub_nanotechnology-and-nanoelectronics-materials-devic

6 2 Quantum Mechanical Aspects
the electrons can be calculated as a one-electron solution. The method used for the
calculation is called MOLCAO (molecular orbitals as linear combinations of
atomic orbitals). As can be derived from the acronym, a molecular orbital is assumed
to be a linear combination of orbitals from the atomic component as is
known from the theory of single atoms. The eigenvalues and coefficients are determined
by diagonalization in accordance with the method of linear algebra. Then
the levels, i.e., the calculated eigenenergies will be filled with electrons according
to the Pauli principle. Thereafter the total energy can be calculated by multiplying
the sum of the eigenenergies by the electrons in these levels. A variation calculation
is performed at the end in order to obtain the minimum energy of the system.
The parameter to be varied is the geometry of the atom, i.e., its bonding length and
angle. The simulations are verified by application on several known properties of
molecules (such as methane and silane), carbon-containing clusters (like fullerenes)
and vacancy-containing clusters in silicon. This method is not only capable of
predicting new stable clusters but is also more accurate in terms of delivering their
geometry, energy states, and optical transitions. This is already state-of-the-art [3–
5]. Thus, no examples are given.
Starting from here, a great number of simulations are being performed for industrial
application like hydrogen storage in the economics of energy, the synthesis
of medication in the field of medicine or the development of lubricants for
automobiles. As an example, we will consider the interaction between hydrogen
atoms and fullerenes (Fig. 2.1). An incomplete fullerene (a fullerene with a vacancy)
is selected. If placed in a hydrogen environment (14 in the simulation), the
aforesaid vacancy captures four hydrogen atoms. In conclusion, a vacancy can
take at least four hydrogen atoms. It is simple to produce fullerenes with a higher
number of vacancies so that a fullerene can eventually be expected to be an active
Fig. 2.1 Interaction between a fullerene (which contains a vacancy) and hydrogen. The
dark-gray circles represent carbon, the light-gray ones hydrogen, and the empty circle (arrow)
represents a vacancy with dangling bonds.