njit-etd2003-111 - New Jersey Institute of Technology

8
2.2 Computational Chemistry
Ab initio molecular orbital theory is concerned with predicting the properties of atomic
and molecular systems. It is based upon the fundamental laws of quantum mechanics and
uses a variety of mathematical transformation and approximation techniques to solve the
fundamental equations, i.e. 5chr6dinger partial differential quation,
Here H is the Hamiltonian, a differential operator representing the total energy. E
is the numerical value of the energy of the state, in terms of kinetic energy of symbolized
by T and potential energy V. IPA is the wavefunction.
Model chemistries are characterized by the combination of a theoretical procedure
and a basis set. 19 A basis set is a mathematical representation of the molecular orbitals
within a molecule. The basis set can be interpreted as restricting each electron to a
particular region of space. Large basis sets impose fewer constraints on electrons and
more accurately approximate exact molecular orbitals. The computation of atomic or
molecular properties with large basis sets requires correspondingly more computational
resources.
Standard basis sets for electronic structure calculation use linear combinations of
Gaussian functions to form the orbitals.19 Basis sets assign a group of basis functions to
each atom within a molecule to approximate its orbitals. These basis functions
themselves are composed of a linear combination of Gaussian functions. The linear
combined basis functions are referred to as contracted functions, and the component
Gaussian functions are referred to as primitives. A basis function consisting of a single