Quantum Theory of ‘Atoms in Molecules

The theory of atoms in molecules (AIM) of Bader [59, 60] offers criteria enabling the existence and the nature of bonds to be determined from the topological analysis of the electron density. This theory has not only provided new insights into the understanding of intramolecular bonds but has also been successful in the field of intermolecular bonds, such as hydrogen bonds [61], halogen bonds [62], van der Waals bonds [63] and more strongly bound donor/acceptor complexes [64]. 

Electron density function p r) a three-dimensional function defined such that p(r)dT is the probability of finding an electron in the elemental volume dr at point r. This function may be determined experimentally by analysing X-ray diffraction data of solids. Gradient of the electron density Vp(r) a vector that points in the direction of maximum increase in the density. 

Gradient vector field of the electron density obtained by the trajectories traced out by the gradient vectors. 

Critical point special point where Vp(r) vanishes (for instance, a nucleus). 

Nucleus attractor of the gradient vector field of p r) where trajectories starting at infinity terminate. 

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A quantum theory of atoms in molecules insight on the effect of basis set superposition error removal... 

In this paper a method [11], which allows for an a priori BSSE removal at the SCF level, is for the first time applied to interaction densities studies. This computational protocol which has been called SCF-MI (Self-Consistent Field for Molecular Interactions) to highlight its relationship to the standard Roothaan equations and its special usefulness in the evaluation of molecular interactions, has recently been successfully used [11-13] for evaluating Eint in a number of intermolecular complexes. Comparison of standard SCF interaction densities with those obtained from the SCF-MI approach should shed light on the effects of BSSE removal. Such effects may then be compared with those deriving from the introduction of Coulomb correlation corrections. To this aim, we adopt a variational perturbative valence bond (VB) approach that uses orbitals derived from the SCF-MI step and thus maintains a BSSE-free picture. Finally, no bias should be introduced in our study by the particular approach chosen to analyze the observed charge density rearrangements. Therefore, not a model but a theory which is firmly rooted in Quantum Mechanics, applied directly to the electron density p and giving quantitative answers, is to be adopted. Bader s Quantum Theory of Atoms in Molecules (QTAM) [14, 15] meets nicely all these requirements. Such a theory has also been recently applied to molecular crystals as a valid tool to rationalize and quantitatively detect crystal field effects on the molecular densities [16-18]. 

Bader, R. F. W., and T. T. Nguyen-Dang. 1981. Quantum Theory of Atoms in Molecules-Dalton Revisited. Adv. Quant. Chem. 14, 63. 

The atoms defined in the quantum theory of atoms in molecules (QTAIM) satisfy these requirements [1], The atoms of theory are regions of real space bounded by a particular surface defined by the topology of the electron density and they have all the properties essential to their role as building blocks ... 

The quantum theory of atoms in molecules is described in texts and several reviews [1-4]. A qualitative survey of the essential definitions and their application to problems in the field of medicinal chemistry are given here with two purposes ... 

This chapter has provided an introduction to the ideas underlying the quantum theory of atoms in molecules, the theory that gives theoretical expression to chemical concepts and enables one to employ these concepts in a quantitative manner for prediction and for understanding of chemical problems. The theory is particularly well-suited to problems in medicinal chemistry where the important role of building block molecules enables one to make maximum use of the transferability of atoms and groups defined as open quantum systems. 

Recently, quantum calculations and topological analysis using the Quantum Theory of Atoms in Molecules (QTAIM) provide an explanation... 

C. Gatti and A. Famulari Interaction Energies and Densities. A Quantum Theory of Atom in Molecules insight on the Effect of Basis Set Superposition Error Removal , P.G. Mezey and B. Rohertson (Eds.), Understanding Chemical Reactivity Electron, Spin and Momentum Densities and Chemical Reactivity, Vol. 2, Kluwerhook series (1999). In press. 

Malta CF, Boyd RJ (eds) (2007) The quantum theory of atoms in molecules from solid state to DNA and drug design. Wiley-VCH, Weinheim... 

That molecules do have definite bonds, and that these tend to correspond in direction and number to the conventional bonds of simple valence theory, is indicated by the quantum theory of atoms-in-molecules (AIM, or QTAIM) [2], This is based on an analysis of the variation of electron density in molecules. 

The quantum theory of atoms in molecules (QTAIM) [25, 26] is based on analyses of the electron density distribution. The electron density of such systems such as simple molecules or ions, and also complexes, complex molecular and ionic aggregates, as well as crystals may be analyzed using this approach. QTAIM is a powerful tool that allows characterizing of various interactions covalent bonds, ionic bonds, van der Waals interactions and, what is the most important for this review, also HBs. The analysis of critical points of the electron density is very useful. For the critical points (CPs), the gradient of electron density, p(r), vanishes ... 

C. Matta, R.J. Boyd (eds), Quantum Theory of Atoms in Molecules Recent Progress in Theory and Application (Wiley, New York, 2007)... 

C.F. Matta and R.J. Boyd, in The Quantum Theory of Atoms in Molecules, C.F. Matta and R.J. Boyd (editors), WILEY-VCHVerlag GmbH Co. KGaA, Weinheim, Germany, 2007, p. 1. 

The TAE/RECON method, developed by Breneman and co-workers based on Bader s quantum theory of Atoms In Molecules (AIM). The TAB method of molecular electron density reconstruction utilizes a library of integrated atomic basins , as defined by the AIM theory, to rapidly reconstruct representations of molecular electron density distributions and van der Waals electronic surface properties. RECON is capable of rapidly generating 6-31-I-G level electron densities and electronic properties of large molecules, proteins or molecular databases, using TAB reconstruction. A library of atomic charge density fragments has been assembled in a form that allows for the rapid retrieval of the fragments, followed by rapid molecular assembly. Additional details of the method are described elsewhere. ... 

Qm QM RECON Mean absolute atomic charge Quantum mechanics An algorithm for the rapid reconstruction of molecular charge densities and charge density-based electronic properties of molecules, using atomic charge density fragments precomputed from ab initio wave functions. The method is based on Bader s quantum theory of atoms in molecules. 

In the spirit of the opening quote of this chapter, the quantum theory of atoms in molecules (QTAIM) [63] has been extensively applied to classify and understand bonding interactions in terms of a quantum mechanical observable the electron density p(r). In this chapter we will take advantage of this theory to... 

SOME BASIC CONCEPTS OF THE QUANTUM THEORY OF ATOMS IN MOLECULES (QTAIM)... 

Parallel to the exciting reports about new types of hydrogen-hydrogen interactions, a paradigm shift was (and is) taking place in interpretative theoretical chemistry. Since the publication of Bader s classic monograph in 1990 [63], the quantum theory of atoms in molecules (QTAIM) has become a standard tool for the interpretation of theoretical and experimental [65-69] electron density distribution maps. The theory and its applications have been reviewed on a number of occasions by its principal author [63, 70-78] and by others [65-67, 69, 79-84]. A brief reminder of some of the basic concepts of QTAIM will be presented here with the sole purpose of keeping this chapter self-contained, but the interested reader is referred to the previously cited literature for in-depth treatments. 

A resonance energy is a global property of a molecule. Therefore, differences between resonance energies of two isomers or conformers cannot provide any information on regional or atomically resolved relative stabilisation or destabilisation. The quantum theory of atoms in molecules, on the other hand, provides the required atomically resolved partitioning of the total energy, as described in Sect. 4. 

The hydrogen-hydrogen bonding interaction is a phenomenon that occurs in a wide variety of organic and organometallic molecules, intra- and intermolecularly. We have used the quantum theory of atoms in molecules to classify, characterise, and calculate the local changes in the energy associated with this... 

Finally, it is hoped that this presentation has sparked the interest of some readers in the quantum theory of atoms in molecules by showing how the topological properties of an experimental observable, the electron density, can be used to classify and categorise chemical bonding, in the spirit of the opening quote of this chapter. 

C. F. Matta. Applications of the Quantum Theory of Atoms in Molecules to Chemical and Biochemical Problems Ph.D. Thesis (McMaster University, Hamilton, Canada, 2002) (http // chem. utor onto. ca/ cmatta/). 

A. Vila, R. A. Mosquera. Quantum theory of atoms in molecules analysis on the conformation preferences of vinyl alcohol and related ethers. J. Phys. Chem. A 109, 6985-6989 (2005). 

Other quantum-chemical descriptors are TAE descriptors based on the Bader s quantum theory of —> Atoms In Molecules (AIM). 

T.A. Keith, in C.F. Matta, R.J. Boyd (Eds.), Atomic Response Properties, in Quantum Theory of Atoms In Molecules From Solid State to DNA and Drug Design edn., Wiley-VCH, Weinheim, 2007, pp. 61-94 (chapter 3). 

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