Atomic orbitals spatial orientations

In addition to the 2s orbital, the second shell also contains three 2p atomic orbitals, one oriented in each of the three spatial directions. These orbitals are called the 2px, the 2py, and the 2pz, according to their direction along the x, y, or z axis. The 2p orbitals... 

Figure 2.14. The molecular orbitals of gas phase carbon monoxide, (a) Energy diagram indicating how the molecular orbitals arise from the combination of atomic orbitals of carbon (C) and oxygen (O). Conventional arrows are used to indicate the spin orientations of electrons in the occupied orbitals. Asterisks denote antibonding molecular orbitals, (b) Spatial distributions of key orbitals involved in the chemisorption of carbon monoxide. Barring indicates empty orbitals.5 (c) Electronic configurations of CO and NO in vacuum as compared to the density of states of a Pt(lll) cluster.11 Reprinted from ref. 11 with permission from Elsevier Science.

The dependence of the j3-deuterium effect on the spatial orientation of the isotopic bond with respect to the developing -orbital, on the a-carbon atom was elegantly demonstrated by Shiner and Humphrey (1963). This work will not be discussed in detail here suffice it to say the suggestion is made that j8-deuterium effects are better correlated by the postulate of hyperconjugation and its angular dependence than by the simple steric model (Shiner and Humphrey, 1963). 

The relative size of atomic orbitals, which is found to increase as their energy level rises, is defined by the principal quantum number, n, their shape and spatial orientation (with respect to the nucleus and each other) by the subsidiary quantum numbers, Z and m, respectively. Electrons in orbitals also have a further designation in terms of the spin quantum number, which can have the values +j or — j. One limitation that theory imposes on such orbitals is that each may accommodate not more than two electrons, these electrons being distinguished from each other by having opposed (paired) spins, t This follows from the Pauli exclusion principle, which states that no two electrons in any atom may have exactly the same set of quantum numbers. 

As you learned from the previous section, three quantum numbers—n, 1, and mi—describe the energy, size, shape, and spatial orientation of an orbital. A fourth quantum number describes a property of the electron that results from its particle-like nature. Experimental evidence suggests that electrons spin about their axes as they move throughout the volume of their atoms. Like a tiny top, an electron can spin in one of two directions, each direction generating a magnetic field. The spin quantum number (mj specifies the direction in which the electron is spinning. This quantum number has only two possible values or —... 

The spatial orientations of the atomic orbitals of the hydrogen atom are very important in the consideration of the interaction of orbitals of different atoms in the production of chemical bonds. 

The complex [(VO)2(dana)2] (dana = l,5-bis(p-methoxyphenyl)-l,3,5-pentanetrionato) was prepared and temperature dependent Xm measurements show antiferromagnetic behaviour with J = —80 cm 1.902 The / value is much lower than with [M2(dana)2(py)2] (M = Co, Cu) and this probably results from a different spatial orientation of the exchanging electrons if the unpaired electron is considered to be initially in a dxy orbital, a direct metal-metal interaction may be possible as the V—V distance is large (ca. 3.0-3.2 A V atoms are probably 0.5-0.6 A out of the plane and possibly one above and one below the ligand plane902), one would expect a weak exchange for the direct V—V interaction. 

The three quantum numbers n, l, and wi/ discussed in Section 5.7 define the energy, shape, and spatial orientation of orbitals, but they don t quite tell the whole story. When the line spectra of many multielectron atoms are studied in detail, it turns out that some lines actually occur as very closely spaced pairs. (You can see this pairing if you look closely at the visible spectrum of sodium in Figure 5.6.) Thus, there are more energy levels than simple quantum mechanics predicts, and a fourth quantum number is required. Denoted ms, this fourth quantum number is related to a property called electron spin. 

The quantum mechanical model proposed in 1926 by Erwin Schrodinger describes an atom by a mathematical equation similar to that used to describe wave motion. The behavior of each electron in an atom is characterized by a wave function, or orbital, the square of which defines the probability of finding the electron in a given volume of space. Each wave function has a set of three variables, called quantum numbers. The principal quantum number n defines the size of the orbital the angular-momentum quantum number l defines the shape of the orbital and the magnetic quantum number mj defines the spatial orientation of the orbital. In a hydrogen atom, which contains only one electron, the... 

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

The quantum content of current theories of chemical cohesion is, in reality, close to nil. The conceptual model of covalent bonding still amounts to one or more pairs of electrons, situated between two atomic nuclei, with paired spins, and confined to the region in which hybrid orbitals of the two atoms overlap. The bond strength depends on the degree of overlap. This model is simply a paraphrase of the 19th century concept of atomic valencies, with the incorporation of the electron-pair conjectures of Lewis and Langmuir. Hybrid orbitals came to be introduced to substitute for spatially oriented elliptic orbits, but in fact, these one-electron orbits are spin-free. The orbitals are next interpreted as if they were atomic wave functions with non-radial nodes at the nuclear position. Both assumptions are misleading. 

Similar treatments may be applied to the other wave functions the i// v wave functions are always real, as also are those members of the d, /, etc., sets which have m = 0. These real wave functions may now be plotted in the form of polar diagrams, as shown in figure 6.2. When we refer to the shape or spatial orientation of an atomic orbital, we are actually referring to a specific member of the set shown in figure 6.2. We could, of course, continue the process to include / orbitals, and higher. 

Bohr applied a quantum condition to the energy states of the hydrogen atom only certain energy states were allowed. Sommerfeld applied a quantum condition to the orientation of electron orbits only certain spatial orientations relative to an applied magnetic field were allowed. The experiment of Stem and Ger-lach was designed to test Sommerfeld s explanation of the Zeeman effect, namely, the idea of space quantization. 

To use the Bohr theory of energy levels in atoms to explain light emission and absorption by gaseous atoms 4.6 To understand the spatial orientation of the most common orbitals and the uncertain nature of locating the electron... 

Particular geometries (spatial orientations of atoms in a molecule) can be related to particular bonding patterns in molecules. These bonding patterns led to the concept of hybridization, which was derived from a mathematical model of bonding. In that model, mathematical functions (wave functions) for the s and p orbitals in the outermost electron shell are combined in various ways (hybridized) to produce geometries close to those deduced from experiment. 

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