The HSAB concept can be developed into an universal scheme based on quantum chemistry

Martin-Luther-University of Halle, Institute of Physical Chemistry Geusaerstr., D-06217 MERSEBURG (Germany)

1. Introduction

But very often these structure activity relations (SAR) are based on simple quantities and indices, which were not derived from quantum mechanics. Much of our actual knowledge in chemistry is composed of empirical or semi-empirical rules and concepts. Some of the chemical terms in use have or had no strong definition, but they are very popular and were used to explain a lot of facts in chemistry in qualitative accuracy. This was the case for the well-known HARD and SOFT / ACIDS and BASES concept and related terms, like:

• Electronegativity and Hardness
• Donor- and Acceptor-Numbers
• Electrophilic- and Nucleophilic-Scales
• Polarity- and Polarizability (empirical scales)
• Incremental-Scheme for electronic, magnetic, thermodynamic, and other properties

Tab.1 Some characteristics of the general term ´STRUCTURE´

spatial	electronic	energetic
position of the nuclei	electron distribution	interactions
atomic coordinates	electron densities	force constants
bond length, bond angle	atomic charges	molecular orbitals
molecular volumn CPK- or Ball-Stick-model	molecular electrostatic potential	total energy heat of formation

In the interpretation of intermolecular interactions and chemical reactivity we have to take into account that the reactivity of the molecule as a whole may be divided into regions of different behaviour (regio-selectivity). So we have to replace some global characteristics by local ones. Visualisation of the extent of molecular properties in different areas of the molecule is a helpful and important technique to support structural concepts by computer graphics, to relate the expected or observed physico-chemical properties and the chemical behaviour of molecules to the calculated electronic structure.

2. The concept of Hard and Soft Acids and Bases

• 1963 PEARSON [1] qualitative HSAB-concept with examples of molecules, ligands, and fragments grouping roughly together
• 1968 KLOPMAN [2] quantum mechanical derived concept of Charge and Frontier-Orbital Controlled Chemical Reactions (based on perturbation theoretical treatment) and relating these findings to the terms of hard and soft donors and acceptors.
• 1983 PARR, PEARSON [3] first theoretical definition of electronegativity () and hardness () as global molecular quantities within the quantum mechanical Density Func- tional Theory (DFT). Global softness [4] has been formulated in a similar way.
• 1985 PEARSON [5] empirical scheme of numerical values for "Absolute Hardness" (e.g. [6]) calculated from experimental data of molecular ionisation potentials and electron affinities.
• 1993 NALEWAJSKI [7] "Charge Sensitive Analysis" (CAS) for a new rationalisation of the HSAB principle, in order to get local values of hard- and softness.

This contribution shows, how local atomic quantities of hardness and softness, generated from semi-empirical and ab initio MO-calculations followed by CSA, can be visualized.

In table 2 we summarise some conventional terms of the electronic structure compared with those used in the HSAB concept. Similar to Structure & Dynamics (Tab.2) we have to take into account both of these aspects of an electronic structure (Tab. 3).

Tab. 2 structure and dynamics in relation to the HSAB concept

	STRUCTURE	DYNAMICS
geometrical structure	spatial arrangement of atoms	fexibility
exp. observation	X-ray scattering	NMR relaxation
electronic structure	electron density	electron moveability
exp. observation	polarity, dipole moment (vector)	polarisability (tensor)
HSAB concept	hardness	softness

Tab. 3: Convenient terms to describe the electronic structure

	local	global	HSAB
static	atomic charge	polarity	hardness
dynamic	moveability	polarizability	softness

3. Charge Sensitive Analysis

At the moment we can calculate the following CSA-values [8]:

• molecular and atomic electronegativity:

  

• atomic hardness:

  

• molecular softness:

  

• atomic Fukui-Index: the relation of local to global softness

  

• "rain bow": the calculated values are normalised and coloured linearly to the different colours of the rain bow.
• "intensity": the normalised atomic quantities are used the scale the intensity of the surface colour. The kind of colour is only dependent on the type of the chemical element.

• Ball and Stick model
• CPK volume model
• Connolly surface model

Fig. 1: Aniline atomic hardness coloured with the "rain bow" model	Fig. 2: Aniline atomic hardness coloured with the "intensity" model

It can be seen that the picture 1 gives a better survey about the different elements and their quantities than "intensity" colouring of picture 2. Both pictures are generated from the same set of CSA data.

Figure 1 gives a good impression of the equivalent atomic positions and show the electronic effect in ortho-, meta, and para-position to the amino group in the benzene ring.

The next example (Fig. 3) is the nitrobenzene molecule showing the withdrawing substituent effect of the nitro group.

Fig. 3: Atomic hardness in nitrobenzene

The following three examples wants to show the electronic effect of hetero atoms in aromatic rings.This pictures show the CSA values of the electron distribution of the valence electrons, but there is no possibility for a separate representation of electrons belonging to the - or to the -symmetry (sometimes do they have quite different effects, -I and +M).

Fig. 4: Atomic hardness of pyrrole	Fig. 5: Atomic hardness of furane

Fig. 6 Atomic hardness of pyridine molecule

Further development of the visualisation of the two important properties of an electronic structure, the hard- and softness will be the interpretation of the calculated Fukui function and a distance dependent contribution from neighbouring atoms to the value of an atomic surface area.

4. Summary

We have programmed recently a pictorial representation of hardness and softness on the molecular surface of molecules. The derived numerical values can be visualised with the CSA_VIEW program [9] running with X-Windows on UNIX graphic workstations. The colouring of the atomic spheres is similar to those well-known pictures of the Molecular Electrostatic Potential (MEP) or the Molecular Lipophilic Potential (MLP) which were successfully used in molecular modelling.

We would like at this point cordially thank for the friendly support through the colleagues K. Jug (Hannover), H. Preuss (Stuttgart), and J. Hinze (Bielefeld). Most this work presented here had been supported by a project of the Deutsche Forschungsgemeinschaft (DFG).

5. References

Arbeitsgruppe Computerchemie am Institut für physikalische Chemie der Martin-Luther-Universität Halle-Wittenberg