Atomic orbitals characteristic shapes

Figure 1.7. The symmetry characteristics of (a) s, (b) p, and (c) spn (hybrid) atomic orbitals. The shapes of the electron distributions are similar if one ignores the phases.

There are many different atomic orbitals, and each has a characteristic energy and shape. How the electrons of an atom distribute themselves among the atomic orbitals is the subject of the next two sections. 

So far we have looked at molecular orbitals in a simplified way as electron pairs that try to seek locations of minimum potential energy. Now that double bonds are under consideration, it will pay us to examine in greater detail the characteristics of both atomic and molecular orbitals. You recall that an atomic orbital is a volume element oriented with respect to the nucleus of the atom where there is a high probability of finding (at the most) two electrons that are identical in quantum numbers except for direction of spin. The orbital of each type of electron (5, p, [Pg.134]

It has not proved mathematically feasible to calculate the electron-electron repulsion that causes this change in orbital-energies for many-electron molecules. It is even difficult to rationalize the qualitative changes in sequence on the basis of the shapes of the 11orbitals. Greater success has been achieved by an approximate method which begins with orbitals characteristic of the isolated atoms present in the molecule, and assumes that molecular orbital wave functions can be obtained by taking linear combinations of atomic orbital wave functions (abbreviated L.C.A.O.). For... 

CHARACTERISTIC SHAPES AND SPATIAL ORIENTATIONS OF s, p, AND d ATOMIC ORBITALS THE ORIGIN OF THE COORDINATE AXIS SYSTEM IS THE ATOMIC NUCLEUS... 

Different types of atomic orbitals have characteristic shapes that are designated by different letters. 

In order to begin to understand the behavior of atoms, we must first look at some of the details of the quantum mechanical model of the atom. Schrodinger s equation predicts the presence of certain regions in the atom where electrons are likely to be found. These regions, known as orbitals, are located at various distances from the nucleus, are oriented in certain directions, and have certain characteristic shapes. Let s look at some of the basic components of the atom as predicted by the equation, and at the same time we will review quantum numbers. 

An orbital is also an area of space in which an electron will be found 90% of the time. Orbitals are of different shapes. Each orbital has a characteristic energy state and a characteristic shape. The s orbital is spherical, and located closest to the nucleus. Since each orbital can hold a maximum of two electrons, atomic numbers above 2 must fill the other orbitals. The px, Py, and pz orbitals are dumbbell shaped, along the x, y, and z axes respectively. The major energy levels (also known as shells) into which electrons fit, are (from the nucleus outward) K, L, M, and N. Sometimes these are numbered, with electron configurations being ls 2s 2p etc. This nomenclature tells us the 1st energy level (shell) has 2 electrons in the s orbital, and 2nd energy level has 2 electrons in its s orbital, plus one electron in its p orbital. 

Each sublevel of the H atom consists of a set of orbitals with characteristic shapes. As you ll see in Chapter 8, orbitals for the other atoms have similar shapes. 

What is a covalent bond, and what characteristic gives it strength And how can we explain molecular shapes based on the interactions of atomic orbitals The most useful approach for answering these questions is valence bond (VB) theory. 

VB theory explains that a covalent bond forms when two atomic orbitals overlap and two electrons with paired (opposite) spins occupy the overlapped region. Orbital hybridization allows us to explain how atomic orbitals mix and change their characteristics during bonding. Based on the observed molecular shape (and the related electron-group arrangement), we postulate the type of hybrid orbital needed. 

Atoms have a series of principal energy levels indexed by the letter n. The w = 1 level is closest to the nucleus, and the energies of the levels increase as the value of n (and distance horn the nucleus) increases. Each principal energy level is divided into sublevels (sets of orbitals) of different characteristic shapes designated by the letters s, p, d, and f. Each s subsheU consists of a single s orbital each p subsheU consists of a set of three p orbitals each d subsheU consists of a set of five d orbitals and so on. An orbital can be empty or it can contain one or two electrons, but never more than two electrons (if an orbital contains two electrons, then the electrons must have opposite spins). The shape of an orbital represents a probability map for finding electrons—it does not represent a trajectory or pathway for electron movements. 

For an isolated atom of a given element, the electrons are in atomic orbitals (Figures 3.1, 3.2, and 3.4), but in a molecule, the electrons reside in different orbitals known as molecular orbitals. One way to visualize a molecular orbital is to mix atomic orbitals to indicate the directionality of the new orbital toward the atom to which the bond is formed. Mixing a spherical s-orbital and a dumbbell-shaped p-orbital, for example, leads to a hybrid orbital, 1. This new molecular orbital is more or less a hybrid of the s- and p-orbitals from which it was derived, with characteristics of both. 

Within a shell (defined by the value of n, the principal quantum number), different sublevels or subshells are possible, each with a characteristic shape. The angular momentum quantum number, f, designates a sublevel, or a specific shape of atomic orbital that an electron may occupy. This number, f, may take integral values from 0 up to and including ( - 1) ... 

Atomic orbitals have characteristic shapes, as represented (crudely) in Fig. 6.18. These shapes correspond to the mathematical solutions of the Schrbdinger equation for different quantum numbers. For example, the s orbitals have no angular dependence. The only solid figure that has no angular dependence is a sphere and, therefore, s orbitals are considered to be spherical. The shapes of p, d, and / orbitals have angular dependence. 

Each shell contains subshells known as atomic orbitals. Each atomic orbital has a characteristic shape and energy and occupies a characteristic volume of space. 

The bonding MO in this pair looks something like candy in a wrapper, with increased electron density in the intemuclear region due to constractive interference between the two 2p atomic orbitals. It has the characteristic a shape (it is cylindrically symmetric about the bond axis) and is therefore called the bonding orbital. The antibonding orbital, called a- p, has a node between the two nuclei (due to destructive interference between the two 2p orbitals) and is higher in energy than either of the 2p orbitals. 

The characteristic shapes of atomic and molecular orbitals (Section 1-6), which provide a feeling for the location of the reacting electrons around the nuclei. 

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