Computational chemistry

Computational chemistry is a branch of chemistry that uses computers to assist in solving chemical problems. It combines the theoretical chemistry and efficient computer programs, to calculate the structures and properties of molecules and solids. Computational chemistry is usually used when a mathematical method is sufficiently well developed that it can be automated for implementation on a computer. Though very few aspects of chemistry can be computed exactly, almost every aspect of chemistry can be described in a qualitative or approximate quantitative computational scheme. Computational studies can be carried out in order to find a starting point for a laboratory synthesis, or to assist in understanding experimental data. Also it can be used to predict the possibility of so far entirely unknown molecules or to explore reaction

mechanisms that are not readily studied by experimental means.

With developed algorithms and computer programs to predict atomic and molecular properties and reaction paths for chemical reactions, computational chemists only need to apply existing computer programs and methodologies to specific chemical questions.

2.2.4.1 Ab initio methods

The programs used in computational chemistry are based on many different quantum-chemical methods that solve the molecular Schrödinger equation associated with the molecular Hamiltonian. Methods that do not include any empirical or semi-empirical parameters in their equations – being derived directly from theoretical principles, with no inclusion of experimental data – are called ab initio methods. This does not imply that the solution is an exact one; they are all approximate quantum mechanical calculations. It means that a particular approximation is rigorously defined on first principles (quantum theory) and then solved within an error margin that is qualitatively known beforehand. If numerical iterative methods have to be employed, the aim is to iterate until full machine accuracy is obtained.

The simplest type of ab initio electronic structure calculation is the Hartree–Fock scheme. This is an extension of molecular orbital theory, in which the correlated electron–electron repulsion is not specifically taken into account but only its average effect included. Many types of calculations (known as post–Hartree–Fock methods) begin with a Hartree–Fock calculation and subsequently correct for electron–electron repulsion. As these methods are pushed to the limit, they approach the exact solution of the non-relativistic Schrödinger equation. However, in order to obtain exact agreement with experiment, it is still necessary to include relativistic and spin orbit terms, both of which are only really important for heavy atoms.

2.2.4.2 Density functional theory (DFT) methods

Density functional theory (DFT) methods are often considered to be ab initio methods for determining the molecular electronic structure, even though many of the most common functionals use parameters derived from empirical data, or from more complex calculations. In DFT, the total energy is expressed in terms of the total one-electron density rather than the wave

expression for the total electron density. DFT methods can be very accurate for little computational cost. Some methods combine the density functional exchange functional with the Hartree–Fock exchange term and are known as hybrid functional methods.

2.2.4.3 Polarizable continuum model (PCM)

The Polarizable Continuum Model (PCM) is one of the most frequently used continuum solvation methods in computation chemistry. The PCM model calculates the molecular free energy in solution as the sum over three terms: Gsol = Ges + Gdr + Gcav. These components

represent the electrostatic (es) and the dispersion-repulsion (dr) contributions to the free energy, and the cavitation energy (cav). All three terms are calculated using a cavity defined through interlocking van der Waals-spheres centered at atomic positions. The reaction field is represented through point charges located on the surface of the molecular cavity.

In the present work, the computation was carried out using a Density functional theory (DFT) method at the B3LYP/6-311+G** level. A polarizable continuum model (PCM) was employed in the single-point energy computations. All computations were performed using the Gaussian03 program package by Prof. M. Bühl from the School of Chemistry in the University of St Andrews.

3 Formation of Self-ordered AAO Nanopore Arrays

Porous anodic aluminium oxide (AAO) was first reported 50 years ago,24and the material has attracted increasing attention from scientists in the fields of materials science, electrochemistry, nanomaterials and nanotechnology in recent years.217-220 However, the driving force for the self-organisation of the pores still remains unclear, although extensive research in the past years has made great achievements in this field.27,40,75,76,89,94,221-224

Figure 3-1 shows the morphologies of AAO samples prepared in 0.3 M oxalic acid under 60 V and 40 V. It can be seen that, the AAO film prepared under 40 V has a better ordered pore array, showing a hexagonal close-packed structure. While from the sectional view SEM images for AAO samples prepared in 2 wt% phosphoric acid under 120 V and 0.3 M oxalic acid under 40 V (Figure 3-2), hemispherical pore bottoms with constant barrier layer thickness can be seen clearly. The pore arrays for AAO film prepared in 0.3 M oxalic acid under 40 V show much better ordering again.

Figure 3-1. Top (a, c) and bottom (b, d) view SEM images for AAO prepared in 0.3 M oxalic acid under 60 V (a, b) and 40 V (c, d), respectively.

Figure 3-2.Sectional view SEM images for AAO prepared in 2 wt% phosphoric acid under 120 V (a), and 0.3 M oxalic acid under 40 V (b), respectively.

During the course of our research on the formation mechanism of AAO and anodic titanium oxide (ATO), an equifield strength model was established to interpret the growth of single pore, self-adjustment of neighboring pores and the ordering of pore arrays.78,225 In the present work, we applied the equifield strength model to explain all the experimental observations during the formation of the porous AAO films, including pore merging, splitting and adjusting. It was also found that the relative dissolution rate of water during the anodisation is very important in the determination of the porosity.78,225We elucidate that the relationship of the relative dissolution rate of water during the anodisation and the porosity can be used not only for the ordered pore arrays, but also for disordered pores in AAO. We also try to establish the relationships between the porosity of AAO films and the applied anodisation conditions.