Theory of atoms in molecules

Partitioning Electron Density The Theory of Atoms in Molecules... 

R F W Bader s theory of atoms in molecules [Bader 1985] provides an alternative way to partition the electrons between the atoms in a molecule. Bader s theory has been applied to many different problems, but for the purposes of our present discussion we will concentrate on its use in partitioning electron density. The Bader approach is based upon the concept of a gradient vector path, which is a cuiwe around the molecule such that it is always perpendicular to the electron density contours. A set of gradient paths is drawn in Figure 2.14 for formamide. As can be seen, some of the gradient paths terminate at the atomic nuclei. Other gradient paths are attracted to points (called critical points) that are... 

The theory of atoms in molecules of R. F. W. Bader and coworkers provides another, more sophisticated approach to atomic charges and related properties. Jerzy CiosJowski has drawn on and extended this theory, and he is responsible for the AIM faciJityin Gaussian. 

The theory of atoms in molecules defines chemical properties such as bonds between atoms and atomic charges on the basis of the topology of the electron density p, characterized in terms of p itself, its gradient Vp, and the Laplacian of the electron density V p. The theory defines an atom as the region of space enclosed by a zero-/lMx surface the surface such that Vp n=0, indicating that there is no component of the gradient of the electron density perpendicular to the surface (n is a normal vector). The nucleus within the atom is a local maximum of the electron density. 

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]. 

In this chapter we give a brief review of some of the basic concepts of quantum mechanics with emphasis on salient points of this theory relevant to the central theme of the book. We focus particularly on the electron density because it is the basis of the theory of atoms in molecules (AIM), which is discussed in Chapter 6. The Pauli exclusion principle is also given special attention in view of its role in the VSEPR and LCP models (Chapters 4 and 5). We first revisit the perhaps most characteristic feature of quantum mechanics, which differentiates it from classical mechanics its probabilistic character. For that purpose we go back to the origins of quantum mechanics, a theory that has its roots in attempts to explain the nature of light and its interactions with atoms and molecules. References to more complete and more advanced treatments of quantum mechanics are given at the end of the chapter. 

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

The final part is devoted to a survey of molecular properties of special interest to the medicinal chemist. The Theory of Atoms in Molecules by R. F.W. Bader et al., presented in Chapter 7, enables the quantitative use of chemical concepts, for example those of the functional group in organic chemistry or molecular similarity in medicinal chemistry, for prediction and understanding of chemical processes. This contribution also discusses possible applications of the theory to QSAR. Another important property that can be derived by use of QC calculations is the molecular electrostatic potential. J.S. Murray and P. Politzer describe the use of this property for description of noncovalent interactions between ligand and receptor, and the design of new compounds with specific features (Chapter 8). In Chapter 9, H.D. and M. Holtje describe the use of QC methods to parameterize force-field parameters, and applications to a pharmacophore search of enzyme inhibitors. The authors also show the use of QC methods for investigation of charge-transfer complexes. 

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 ... 

The atomic properties satisfy the necessary physical requirement of paralleling the transferability of their charge distributions - atoms that look the same in two molecules contribute identical amounts to all properties in both molecules, including field-induced properties. Thus the atoms of theory recover the experimentally measurable contributions to the volume, heats of formation, electric polarizability, and magnetic susceptibility in those cases where the group contributions are found to be transferable, as well as additive additive [4], The additivity of the atomic properties coupled with the observation that their transferability parallels the transferability of the atom s physical form are unique to QTAIM and are essential for a theory of atoms in molecules that purports to explain the observations of experimental chemistry. 

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... 

In the early 1970s, Dr. Bader invented the theory of "Atoms in Molecules," otherwise known as AIM theory. This theory links the mathematics of quantum mechanics to the atoms and bonds in a molecule. AIM theory adopts electron density, which is related to the Schrodinger description of the atom, as a starting point to mapping molecules. 

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. 

A modem description of a conventional hydrogen bond as well as its older, more accurate definition are based on Bader s theory of atoms in molecules (AIM theory) [4]. Bader considers matter a distribution of charge in real space of point-like nuclei embedded in the diffuse density of electron charge, p(r). All the properties of matter are manifested in the charge distribution and the topology... 

The topological theory of atoms in molecules <2003MI190> has been employed to calculate the conformational preference of monosubstituted 1,3-oxathianes. The preferred conformer results from an energy balance between the ring and the substituent. This method has proven to be general and is a new technique for conformational analysis. 

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

In another paper by C.N. Ramachandran, D. Roy, and N. Sathyamurthy (Chem. Phys. Fetters, 461, 87 (2008)),which was issued after our paper was submitted, the host-guest interaction between C60 fullerene and inserted H+, H-, Pie, and Li ions and atoms, and the Fp molecule was also examined within the MP2 approximation and using Bader s theory of atoms-in-molecules. 

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. 

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