9.2: Introduction to Electronic Structure Calculations

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Calculation of the electronic structure of a molecule (i.e. the molecular orbitals) can be accomplished by the following steps:

Preparation of the input data: Within the Born-Oppenheimer approximation, nuclei are held fixed while solving for the electronic motion. Before you begin your calculations, you must first define the fixed nuclear positions at which the electronic structure calculation will be performed -- i.e. you must define a molecular geometry. In Spartan^®, this is done graphically in much the same way in which you built molecules when you took organic chemistry courses.

Many of the calculations you undertake here will use a variational approach in which the molecular wavefunction is written as a single Slater determinant of molecular orbitals (MO), where each MO, in turn, is written as a Linear Combination of Atomic Orbitals (LCAOMO). To begin this variational approach, you must obtain a starting "trial wavefunction." In the LCAOMO method, this requires definition of the atomic functions that will be used to construct the MO's. Recall the variational approach to the electronic structure of H₂ -- to begin we used a trial LCAOMO wavefunction \( \Psi \) written as a linear combination of a 1s atomic orbital on HA (\( \Phi \)1sA) and a 1s atomic orbital on HB ((\( \Phi \)1sB); i.e., we defined the atomic functions that were used to construct the MO's. In Spartan^® you will find a reasonable collection of such sets of atomic functions built into the software, and consequently, selection of an appropriate set of atomic functions is usually achieved by simply choosing from a selection of available methods and basis sets.
Running the calculation: After building the molecule of interest and selecting the type of calculation to be run, and other relevant parameters, one submits this job for calculation.
Analysis of the results: This may involve such tasks as viewing electron densities, exploring the bonding or antibonding character of molecular orbitals, animating vibrational modes associated with nuclear motion, viewing energy-minimized structures and determining bond lengths and bond angles, or calculating molecular properties. Most of this analysis is done using the graphical interface available in Spartan^® thereby minimizing the need to examine multiple pages of numerical data! Again, Spartan^® simplifies the analysis by providing numerous visualizations and menu-driven data displays.

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