Introduction

Molecular mechanics optimization: UFF

Quantum mechanics optimization: B3LYP/6-31G(d)

Determination of vibrational frequencies: IR spectra

Displaying molecular orbitals and electron density

This section is dedicated to computational chemistry and it describes how some quantum mechanical models can be applied to alliin molecula to optimize its geometry and analysing its vibrational frequencies. The software used to do these quantum mechanical calculations is Gaussian 03. It is the latest in the Gaussian series of electronic structure programs. Gaussian 03 is used by chemists, chemical engineers, biochemists, physicists and others for research in established and emerging areas of chemical interest.
Starting from the basic laws of quantum mechanics, Gaussian predicts the energies, molecular structures, and vibrational frequencies of molecular systems, along with numerous molecular properties derived from these basic computation types.
It can be used to study molecules and reactions under a wide range of conditions, including both stable species and compounds which are difficult or impossible to observe experimentally such as short-lived intermediates and transition structures. |

The term molecular mechanics refers to the use of Newtonian mechanics to model molecular systems. The potential energy of all systems in molecular mechanics is calculated using force fields. A force field refers to the functional form and parameter sets used to describe the potential energy of a system of particles. Force field functions and parameter sets are derived from both experimental work and ab-initio quantum mechanical calculations. "All-atom" force fields provide parameters for every atom in a system, while "united-atom" force fields treat two or more atoms (a fragment of the system) as a single interaction center. "Coarse-grained" force fields, which are frequently used in long-time simulations of proteins, provide even more abstracted representations for increased computational efficiency. In this calculation, UFF method (Universal Force Field) where (1) stands for The result of the optimization is described in this output file: alliin-UFF-opt.out Figure 1. Optimized alliin structure by UFF method |

B3LYP is a DFT hybrid method and it uses Becke's exchange functional, weighted on 3 parameters and Lee-Yang-Parr correlation functional. The basis set choosen for this calculation is 6-31G(d); it is a split-valence basis set, thought up by John Pople (Nobel Prize in Chemistry in 1998). This basis set uses 6 Gaussian primitives to expand the 1s core of second period elements and two sets of functions to describe valence shells: the first set is made of 3 Gaussian primitives, while the second is made of 1 Gaussian primitive. The (d) letter means that a polarization function "d" is added to the heavy atoms p orbitals (second and third line of periodic table). Here there is the input file structure: alliin-B3LYP/6-31G(d)-opt.gjf The result of the optimization is described in this output file: alliin-B3LYP/6-31G(d)-opt.out Figure 2. Optimized alliin structure by B3LYP/6-31G(d) method |

Gaussian 03 can compute a very wide range of spectra and spectroscopic properties, including Infrared spectra.
The keyword "freq" computes force constants and the resulting vibrational frequencies. Intensities are also computed. In the B3LYP method, force constants are determined analytically by default.
Vibrational frequencies are computed by determining the second derivatives of the energy with respect to the Cartesian nuclear coordinates and then transforming to mass-weighted coordinates.
This transformation is only valid at a stationary point. Thus, it is meaningless to compute frequencies at any geometry other than a stationary point for the method used for frequency determination. The result of calculation is described in this output file: alliin-B3LYP-6-31G(d)-freq.out Here there are the two IR spectra to compare: Figure 3. IR spectrum of alliin obtained by us from quantum mechanical calculationFigure 4. IR spectrum of alliin in KBr disc, obtained from experimental analysis ^{4}Note that frequencies computed with methods must be scaled to eliminate known systematic errors in calculated frequencies. The optimal scaling factors vary by basis set; for B3LYP the scale factor is 0.9614. |

Gaussview, the interface of Gaussian, allows to gain interesting information from the output of a calculation. In particular, they can be visualized molecular orbitals, electron density and electrostatic potentials. The electron density of frontier molecular orbitals, HOMO (Highest Occupied Molecular Orbital) and LUMO (Lowest Unoccupied Molecular Orbital), are here shown. Figure 5. HOMO and LUMO of alliin, obtained from B3LYP calculationIn Figure 6. Electron total density surfaceAnother dialog allows to create a surface in which the coloring is determined by the values of a second property. For example, the figure below shows the electron density surface painted according to the value of the electrostatic potential (ESP). Figure 7. Electron total density surface coloured by ESP |