Properties Predicted by Electronic Structure Theory

According to one of the postulates of quantum mechanics (see below), if we know the wavefunction $\Psi({\bf r}, t)$ for a given system, then we can determine any property of that system, at least in principle. Obviously if we use approximations in determining the wavefunction, then the properties obtained from that wavefunction will also be approximate.

Since we almost always invoke the Born-Oppenheimer approximation, we only have the electronic wavefunction, not the full wavefunction for electrons and nuclei. Therefore, some properties involving nuclear motion are not necessarily available in the context of electronic structure theory. To fully understand the details of a chemical reaction, we need to use the electronic structure results to carry out subsequent dynamics computations. Fortunately, however, quite a few properties are within the reach of just the electronic problem. For example, since the electronic energy is the potential energy felt by the nuclei, minimizing the electronic energy with respect to nuclear coordinates gives an equilibrium configuration of the molecule (which may be the global or just a local minimum).

The electronic wavefunction or its various derivatives are sufficient to determine the following properties:

• 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