Atomic orbitals and

By expanding the spatial orbitals into atomic orbitals and manipulating them properly, we have... 

The technique for this calcu latioii in volves two steps. Th e first step computes the Hamiltonian or energy matrix. The elem en ts of this matrix are integrals involving the atomic orbitals and terms obtained from the Schrddiiiger equation. The m ost importan t con -... 

Electrons repel each other electrostatically, and the repulsion between an electron in one atomic orbital and an electron m... 

Butadiene The ti molecular orbitals of 1 3 butadiene are shown m Figure 10 10 The four sp hybridized carbons contribute four 2p atomic orbitals and their overlap... 

The atomic absorption spectrum for Na is shown in Figure 10.19 and is typical of that found for most atoms. The most obvious feature of this spectrum is that it consists of a few, discrete absorption lines corresponding to transitions between the ground state (the 3s atomic orbital) and the 3p and 4p atomic orbitals. Absorption from excited states, such as that from the 3p atomic orbital to the 4s or 3d atomic orbital, which are included in the energy level diagram in Figure 10.18, are too weak to detect. Since the... 

Fig. A. Molecular-orbital representation of the 1-centrc F-Xe-F bond, (a) The possible combinations of colinear p, atomic orbitals, and (b) the energies of the resulting MOs (schematic).

A convenient orbital method for describing eleetron motion in moleeules is the method of molecular orbitals. Molecular orbitals are defined and calculated in the same way as atomic orbitals and they display similar wave-like properties. The main difference between molecular and atomic orbitals is that molecular orbitals are not confined to a single atom. The crests and troughs in an atomic orbital are confined to a region close to the atomic nucleus (typieally within 1-2 A). The electrons in a molecule, on the other hand, do not stick to a single atom, and are free to move all around the molecule. Consequendy, the crests and troughs in a molecular orbital are usually spread over several atoms. 

Molecular Orbital. A function made of contributions of Atomic Orbitals and delocalized throughout the entire molecular skeleton. 

The x s can individually be Is, 2s, 2p,. .. atomic orbitals. The lowest-energy solution will be when the x s correspond to Is orbitals on each of the two hydrogen atoms, the next-highest-energy solution will be when one of the ( s is a Is, the other a 2s atomic orbital, and so on. Possible solutions of the electronic problem, with the two H atoms at infinity, are shown in Table 4.1. 

Natural Atomic Orbital and Natural Bond Orbital Analysis... 

NATURAL ATOMIC ORBITAL AND NATURAL BOND ORBITAL ANALYSIS... 

In case the general reader might be wondering about the connection between atomic orbitals and the periodic table, let me address this issue briefly. As mentioned above, in the case of the first paper, the modern explanation for the periodic table is based entirely on the orbital model. It is only by ignoring the approximate nature of the model that the explanation for the periodic system might appear to be full and complete. 

The problems which the orbital approximation raises in chemical education have been discussed elsewhere by the author (Scerri [1989], [1991]). Briefly, chemistry textbooks often fail to stress the approximate nature of atomic orbitals and imply that the solution to all difficult chemical problems ultimately lies in quantum mechanics. There has been an increassing tendency for chemical education to be biased towards theories, particularly quantum mechanics. Textbooks show a growing tendency to begin with the establishment of theoretical concepts such as atomic orbitals. Only recently has a reaction begun to take place, with a call for more qualitatively based courses and texts (Zuckermann [1986]). A careful consideration of the orbital model would therefore have consequences for chemical education and would clarify the status of various approximate theories purporting to be based on quantum mechanics. 

What Do We Need to Know Already This chapter uses atomic orbitals and electron configurations (Chapter 1). It also extends the concept of Lewis structures introduced in Chapter 2. The discussion of polar molecules develops the material on polar bonds described in Section 2.12. 

In Fig. 1 there is indicated the division of the nine outer orbitals into these two classes. It is assumed that electrons occupying orbitals of the first class (weak interatomic interactions) in an atom tend to remain unpaired (Hund s rule of maximum multiplicity), and that electrons occupying orbitals of the second class pair with similar electrons of adjacent atoms. Let us call these orbitals atomic orbitals and bond orbitals, respectively. In copper all of the atomic orbitals are occupied by pairs. In nickel, with ou = 0.61, there are 0.61 unpaired electrons in atomic orbitals, and in cobalt 1.71. (The deviation from unity of the difference between the values for cobalt and nickel may be the result of experimental error in the cobalt value, which is uncertain because of the magnetic hardness of this element.) This indicates that the energy diagram of Fig. 1 does not change very much from metal to metal. Substantiation of this is provided by the values of cra for copper-nickel alloys,12 which decrease linearly with mole fraction of copper from mole fraction 0.6 of copper, and by the related values for zinc-nickel and other alloys.13 The value a a = 2.61 would accordingly be expected for iron, if there were 2.61 or more d orbitals in the atomic orbital class. We conclude from the observed value [Pg.347]

The energy, the phase, and the amphtude characterize sahent features of orbitals. This can be seen in atomic orbitals and bond orbitals (Sect. 1). 

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. 

Before estabiishing the connection between atomic orbitals and the periodic table, we must first describe two additionai features of atomic structure the Pauli exclusion principle and the aufbau principle. 

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