Computational Chemistry

The term ``computational chemistry'' is used to mean many different things. It could mean, for example, the use of computers to analyze data obtained in complicated experiments. However, more frequently this term means the use of computers to make chemical predictions. Sometimes computational chemistry is used to predict new molecules or new reactions which are later investigated experimentally. Other times, computational chemistry is used to supplement experimental studies by providing data which are hard to probe experimentally (for example, transition state structures and energies). Since its modest beginnings in the 1950's and 1960's, advances in theoretical techniques and in computer power have dramatically increased the usefulness and importance of computational chemistry.

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:

Properties Obtainable From Quantum Mechanical Methods

• Geometrical structures (rotational spectra)
• Rovibrational energy levels (infrared and Raman spectra)
• Electronic energy levels (UV and visible spectra)
• Quantum Mechanics + Statistical Mechanics $\rightarrow$ Thermochemistry ($\Delta H$, $\Delta S$, $\Delta G$, 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 $\rightarrow$ NMR spectra