There are two main branches of computational chemistry: one is based on
classical mechanics, and the other is based on quantum mechanics. Molecules
are sufficiently small objects that, strictly speaking, the laws of quantum
mechanics must be used to describe them. However, under the right
conditions, it is still sometimes useful (and much faster computationally)
to approximate the molecule using classical mechanics. This approach
is sometimes called the ``molecular mechanics'' (MM) or ``force-field''
method [1]. All molecular mechanics methods are *empirical* in the sense that the parameters in the model are obtained
by fitting to known experimental data.

Quantum mechanical methods can usually be classified either as
*ab initio* or *semi-empirical*. The first label, *ab initio*,
means ``from the beginning'' and implies an approach which contains *no
empirical parameters*. This category includes Hartree-Fock (HF), configuration
interaction (CI), many-body perturbation theory (MBPT), coupled-cluster (CC)
theory, and other approaches [2].
These methods, particularly Hartree-Fock
theory, will be the focus of this lab.
The second category, *semi-empirical*, includes methods which make
serious approximations to the quantum mechanical laws and then
employ a few empirical parameters to (hopefully) patch things up.
These methods include the modified neglect
of differential overlap (MNDO), Austin Model 1 (AM1), and many others.
Density functional theory (DFT) [3]
methods are quantum mechanical approaches
which are hard to categorize as *ab initio* or *semi-empirical*.
Some DFT methods are free from empirical parameters, while others rely
heavily on calibration with experiment. The current trend in DFT research
is to employ increasing numbers of empirical factors, making recent DFT
techniques semi-empirical.

One of the postulates of quantum mechanics is that the wave function
contains all information which is known *or can be known* about a
molecule. Hence, quantum mechanical methods provide all possible
information about a system, in principle at least. In practice, theoretical
chemists have to figure out how to extract the property from the wave
function, and then they have to write computer programs to perform the
analysis. However, it is now fairly routine to compute the following
molecular properties:

- Geometrical structures (rotational spectra)
- Rovibrational energy levels (infrared and Raman spectra)
- Electronic energy levels (UV and visible spectra)
- Quantum Mechanics + Statistical Mechanics
Thermochemistry (,
,
,
*C*_{v},*C*_{p}), primarily gas phase. - Potential energy surfaces (barrier heights, transition states); with a treatment of dynamics, this leads to reaction rates and mechanisms.
- Ionization potentials (photoelectron and X-ray spectra)
- Electron affinities
- Franck-Condon factors (transition probabilities, vibronic intensities)
- IR and Raman intensities
- Dipole moments
- Polarizabilities
- Electron density maps and population analyses
- Magnetic shielding tensors NMR spectra