Atoms in a molecule

In essence, a BE-matrix li.sts all the valence clcctron.s of the atoms in a molecule, both the ones involved in bonds and those associated as free electrons with an atom. A BE-matrix has a scries of interesting mathematical properties that directly... 

Section 7.1) have been developed to assign quantitative values to the partial charges of the atoms in a molecule [1, 2. This opens the door to defining chemical reactivity on a more quantitative basis. 

Many phenomena ask for local, site-specific properties of a molecule such as the partial charge on a specific atom in a molecule or the hydrogen bond donor ability of a certain OH group. It would be highly desirable to have methods as simple as an additivity model to estimate such site-specific molecular properties. 

Molecules are usually represented as 2D formulas or 3D molecular models. WhOe the 3D coordinates of atoms in a molecule are sufficient to describe the spatial arrangement of atoms, they exhibit two major disadvantages as molecular descriptors they depend on the size of a molecule and they do not describe additional properties (e.g., atomic properties). The first feature is most important for computational analysis of data. Even a simple statistical function, e.g., a correlation, requires the information to be represented in equally sized vectors of a fixed dimension. The solution to this problem is a mathematical transformation of the Cartesian coordinates of a molecule into a vector of fixed length. The second point can... 

The HOSE code can be determined to various degrees of resolution, depending on how many spheres of neighbor atoms are considered. Figure 10.2-1 shows the first, second, and third spheres of neighbors for the carbon atom being considered, for C NMR spectra a HOSE code for each carbon atom in a molecule has to be determined. 

A descriptor for the 3D arrangement of atoms in a molceulc can be derived in a similar manner. The Cartesian coordinates of the atoms in a molecule can be calculated by semi-empirical quantum mechanical or molecular mechanics (force field) methods, For larger data sets, fast 3D structure generators are available that combine data- and rule-driven methods to calculate Cartesian coordinates from the connection table of a molecule (e.g., CORINA [10]). 

Since IR spectroscopy monitors the vibrations of atoms in a molecule in 3D space, information on the 3D arrangement of the atoms should somehow be contained in an IR spectrum. However, the relationships between the 3D structure and the IR spectrum are rather complex, so no general attempt has yet been successfiil in deriving the 3D structure of a molecule directly from the IR spectrum. 

The quaniity, (R). the sum of the electronic energy computed 111 a wave funciion calculation and the nuclear-nuclear coulomb interaciion .(R.R), constitutes a potential energy surface having 15X independent variables (the coordinates R j. The independent variables are the coordinates of the nuclei but having made the Born-Oppenheimer approximation, we can think of them as the coordinates of the atoms in a molecule. 

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... 

Functional group (Section 4 1) An atom or a group of atoms in a molecule responsible for its reactivity under a given set of conditions... 

Polarizability (Section 4 6) A measure of the ease of distortion of the electric field associated with an atom or a group A fluonne atom in a molecule for example holds its electrons tightly and is very nonpolanzable Iodine is very polanz able... 

Stereochemistry (Chapter 7) Chemistry in three dimensions the relationship of physical and chemical properties to the spatial arrangement of the atoms in a molecule Stereoelectron ic effect (Section 5 16) An electronic effect that depends on the spatial arrangement between the or bitals of the electron donor and acceptor Stereoisomers (Section 3 11) Isomers with the same constitu tion but that differ in respect to the arrangement of their atoms in space Stereoisomers may be either enantiomers or diastereomers... 

The chemical environment for an atom in a molecule is probably unique to that molecule. Chemistry tries to find unifying concepts and the atom type is one of those unifying concepts. For example, the AMBER force field defines five atom types for oxygens ... 

An estimate of the hybridization state of an atom in a molecule can be obtained from the group of the periodic table that the atom resides in (which describes the number of valence electrons) and the connectivity (coordination of the atom). The HyperChem default scheme uses this estimate to assign a hybridization state to all atoms from the set (null, s, sp, sp, sp -, and sp ). The special... 

The number of neighbors is given by the molecular graph and the following rules determine a hybridization state for each atom in a molecule. 

Structural Formula and Prefixes. In the structural formula the sequence and spatial arrangement of the atoms in a molecule are indicated. 

On the assumption that the pairs of electrons in the valency shell of a bonded atom in a molecule are arranged in a definite way which depends on the number of electron pairs (coordination number), the geometrical arrangement or shape of molecules may be predicted. A multiple bond is regarded as equivalent to a single bond as far as molecular shape is concerned. 

Carbon has two common isotopes, and with relative isotopic abundances of, respectively, 98.89% and 1.11%. (a) What are the mean and standard deviation for the number of atoms in a molecule of cholesterol (b) What is the probability of finding a molecule of cholesterol (C27H44O) containing no atoms of... 

The probability of finding an atom of in cholesterol follows a binomial distribution, where X is the sought for frequency of occurrence of atoms, N is the number of C atoms in a molecule of cholesterol, and p is the probability of finding an atom of... 

Portion of the binomial distribution for the number of naturally occurring atoms in a molecule of cholesterol. 

Normal Distribution The binomial distribution describes a population whose members have only certain, discrete values. This is the case with the number of atoms in a molecule, which must be an integer number no greater then the number of carbon atoms in the molecule. A molecule, for example, cannot have 2.5 atoms of Other populations are considered continuous, in that members of the population may take on any value. 

The presence of asymmetric C atoms in a molecule may, of course, be indicated by diastereotopic shifts and absolute configurations may, as already shown, be determined empirically by comparison of diastereotopic shifts However, enantiomers are not differentiated in the NMR spectrum. The spectrum gives no indication as to whether a chiral compound exists in a racemic form or as a pure enantiomer. 

For a molecule as simple as Fl2, it is hard to see much difference between the valence bond and molecular orbital methods. The most important differences appear- in molecules with more than two atoms. In those cases, the valence bond method continues to view a molecule as a collection of bonds between connected atoms. The molecular- orbital method, however, leads to a picture in which the sane electron can be associated with many, or even all, of the atoms in a molecule. We ll have more to say about the similarities and differences in valence bond and molecular- orbital theory as we continue to develop their principles, beginning with the simplest alkanes methane, ethane, and propane. 

Section 2.4 In molecular orbital theory, the molecular orbitals (MOs) are approximated by combining the atomic orbitals (AOs) of all of the atoms in a molecule. The number of MOs must equal the number of AOs that ar e combined. 

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