The study of van der Waals complexes

The study of van der Waals and hydrogen-bonded complexes is a major area in both experimental and theoretical research, providing direct tests of these intermolecular forces between neutral molecules. The understanding of intermolecular forces in such complexes should lead to the progress in designing highly specific drugs aided by knowledge of the intermolecular forces that control the specific interactions. When the human genome was sequenced [117], it opened up many aspects of fundamental science studies that need to be understood. Eventually, an atomic level understanding of how the genome operates will be expressed in terms of intermolecular forces.

New Models for Intermolecular Repulsion and their Application to van der W aals Helen H.Y. Tsui

3 The Study of van der Waals Complexes and Crystal Structures__________________________ ^

3.2.1 Van der Waals forces

Van der Waals forces are named after the Dutch physicist Johannes van der Waals, who in 1873 first postulated these intermolecular forces in developing a theory to account for the properties of real gases. The van der Waals forces are dispersive forces as described in Chapter 2. The study of gas phase complexes has been particularly important in leading to an understanding of the intermolecular forces. Nowadays, the term 'van der Waals' forces are often used to describe weak intermolecular interactions in general.

3.2.2 Hydrogen bonds

Hydrogen bonds are very important in chemistry and biochemistry. The implications of hydrogen bonds for molecular structure, thermodynamics are far from negligible. According to the account of Lippert [118], evidence of hydrogen bonding dates back to the beginning of the 20“* century, where Werner in 1902 discussed interactions between ammonia and hydrogen chloride [119]. It was not until 1920 that Latimer and Rodebush [120] postulated the existence of a type of bond involving a hydrogen atom and a lone pair: 'The hydrogen nucleus held by two octets constitutes a weak bond".

The hydrogen bond is an attractive donor-acceptor interaction involving a hydrogen atom. It can be represented by A-H ...B, where A is the proton donor, and B is the proton acceptor, and A and B are electronegative atoms such as O, N, F, Cl, etc.

One of the most important instances of hydrogen bonding is in the interactions that determine the shapes of proteins and the genetic code information in DNA and RNA [121]. The DNA molecule is usually double-stranded, with the sugar-phosphate backbone of the polynucleotides on the outside of the helix. In the interior are pairs of nitrogenous bases, holding the two strands together by hydrogen bonds. Hydrogen bonding between the bases is specific. The adenine base can pair only with the thymine base, and the guanine base can only pair with the cytosine base. Hence, the fundamental studies of hydrogen bonds of simple systems may provide information that may be of beneficial to larger system that is difficult to model, and also provide knowledge to aid the studies of the genome [117].

Hydrogen bonds give a shift to lower frequency of the A-H stretching vibration in the infrared spectrum of a complex. The band corresponding to this stretch is intensified and broadened, compared to the free A-H vibration [122]. This gives a large red shift in the infrared absorption. The NMR spectrum also reveals the presence of a hydrogen bond, because the hydrogen bond is deshielded as the electron density o f the A-H bond shifts towards the A atom, thus perturbing the chemical shifts observed during NMR experiments. Typical strength of hydrogen bonds is about 25 kJ/mol, but can vary between 4 and 160 kJ/mol. Hence intermolecular hydrogen bonding is strong enough to affect characteristics of molecule's charge density, implying some rearrangement of charge by the intermolecular forces.

Legon and Millen devised a rule for determining the hydrogen-bonded structures of van der Waals complexes, based on their observations using microwave spectroscopy [123]. The observed gas phase geometry of A-H...B has the axis of the HA molecule coinciding with the supposed axis of a non-bonding pair or as conventionally envisaged. If there are no lone pairs, the axis of the HA New Models for Intermolecular Repulsion and their Application to van d er W aals Helen H.Y. Tsui

3 The Study of van der Waals Complexes and Crystal Structures__________________________ ^ molecule intersects the internuclear axis of the atoms forming the n bond and is perpendicular to the nodal plane of the n orbital. This directionality of hydrogen bonds is not predicted correctly with simple electrostatic models. An early treatment of hydrogen bond in 1928 due to Pauling [124], who viewed hydrogen bonding as electrostatic in nature, assigning point charges to the atoms involved. This remains the general view and is used widely, but due to the oversimplified electrostatic model, it failed in many cases. Buckingham and Fowler [60] concluded that a new model is needed to give a truly accurate description of the electrostatic interaction, and showed a distributed multipole electrostatic model (Chapter 2), with a crude repulsion term is sufficient to describe the hydrogen bonding. Buckingham and Fowler [71] used the method to study many complexes involving polar molecules. Work such as this demonstrated that electrostatics dominate orientation dependence. The simplicity of the Buckingham-Fowler model that includes a detailed description of the electrostatic interactions with a hard-sphere repulsion for each heavy atom, prevents its use in certain situations where the balance between different contributions is subtle. The exceptions are where hydrogen bonding often requires a complete description of the different contributions of the intermolecular forces in order to provide an accurate representation to describe the behaviour of the interaction. This has been demonstrated in the water dimer potential of Stone and co-workers [48,84], where their potential has been used successfully to describe the gas phase behaviour of water clusters [91,125]. One must note that isotropic atom-atom van der Waals potentials lack such directionality and therefore would be poor for modelling hydrogen-bonded systems.

3.2.3 The modelling of van der Waals complexes

Theoretical modelling of van der Waals complexes has been improved with the advances of computational power, but has often been ahead or done in conjunction with experiments. Experiments are difficult, requiring low temperature molecular beams. Recent reviews [121,126-129] have reported most of the current methods used and progress in the field, ranging from intermolecular potentials using monomer wavefunctions from theory to experimental studies of ultrafast reactions in clusters, studied in real time using new laser spectroscopic methods. Especially with the advances being made in experimental techniques [127,129], it is now possible to validate previous theoretical studies of van der Waals complexes that did not have experimental data at the time of study. Although there have been studies using supermolecule calculations [11,19] performed on the system since 1992, the binding energy was only determined in 1998 [8]. This is shown by the study of phenol-water complex in Chapter 5.

The most common approach to modelling van der Waals complexes is to carry out supermolecule calculations. The size of the system and the accuracy of the calculation are dependent on the choice of basis sets and treatment of electron correlation, and limited only by the amount of computational resources available. Common ab initio calculations that are used to model van der Waals complexes are supermolecule calculations and density functional theory (DFT) calculations. Of course these calculations are relatively easy to implement, but there are problems that are encountered in providing reliable studies. As mentioned in Chapter 2, supermolecule calculations have problems with BSSE [79,82], and DFT cannot provide good description for the dispersion forces [130,131].

New Models for Intermolecular Repulsion and their Application to van d er W aals Helen H.Y. Tsui

3 The Study of van der Waals Complexes and Crystal Structures__________________________ 52 Nevertheless, ab initio methods are still the most common approaches taken in the study of van der Waals complexes, and applied to the phenol-water complex in Chapter 5.

Modelling the van der Waals interaction using pairwise potentials is another approach for complexes of larger molecules. The model potential has to accurately model the interatomic potential surface, using a simple expression that can be easily calculated. This includes the commonly used

Lennard-Jones potential (Equation (2.1)), that can be empirically determined [74]. More realistic expression has been proposed, as demonstrated by the water dimer potential discussed in Chapter 2. These model potentials can be used in program such as ORIENT [132], which uses a site-site potential specified by the user. The energy of the assembly can be calculated at specified configurations, and the geometry can be optimised to find minima and transition states and the paths between them. This would be useful in determining many data that can be compared with experiments. The most important data are the geometry and binding energy of the investigated system. These are the minimal criteria that must be achieved in order to provide a reasonable description of the interactions. An accurate calculation can further be judged by its reproduction of spectroscopic data, such as rotational constants and vibrational frequencies. However, the effect of zero-point motion is neglected, and therefore the minimum energy geometry cannot be compared with experiment directly. One method that could overcome this is to use the quantum diffusion Monte Carlo (DMC) method [6,24,25,29,30]. Recent studies with the DMC method have shown that zero-point effects need not be negligible, especially for weakly bound van der Waals complexes such as water dimer [125], benzene-water complex [133], etc. This is a method that can determine the vibrational averaged structure of a system, and give a binding energy that includes the zero-point motion. The accuracy of DMC is dependent only on the quality of the model potential. The methodology of this method will be explained in detail in Chapter 8. This method will be used to validate our model potential for our own study of the phenol-water complex.