Atomic orbitals electron shells

Chemical bonds together with other concepts such as atomic orbitals, electron shells, lone pairs, aromaticity, atomic charges, (hyper-) conjugation, strain, etc. do not correspond to physical observables. Such concepts therefore cannot be unambiguously defined in pure quantum theory, but constitute a rich set of fuzzy , yet invaluably useful concepts [11-14]. They lead to constmctive ideas and developments when appropriately used and defined. 

Let us summarize, in tabular form, some of the information we have developed to this point. The principal quantum number n indicates the main shell. The number of subshells per shell is equal to , the number of atomic orbitals per shell is and the maximum number of electrons per shell is 2 , because each atomic orbital can hold two electrons. 

Ionization Potential (IP) The ionization potentiai of a compound is defined as the energy requited to remove a given electron from the molecule s atomic orbit (outermost shell) and is expressed in electron volts (eV). One electron volt is equivalent to 23,053 cal/mol. 

The principal quantum number n describes the average distance of the orbital from the nucleus — and the energy of the electron in an atom. It s really about the same as Bohr s energy-level numbers. It can have positive integer (whole number) values 1,2,3,4, and so on. The lau-ger the value of n, the higher the energy and the larger the orbital. Chemists sometimes call the orbitals electron shells. 

Table 8.4. NAO (natural atomic orbital) electron occupancies In outer-shell orbitals of C and Ag...

CASPT2 calculation. Spin-orbit interaction, when necessary, can be included a posteriori as a perturbation. This intrinsically one-component formalism allows one to treat molecules of extended size compared to the four-component approach. As an alternative to CASSCF/CASPT2, truncated MRCI calculations can be envisaged. Limitations arise at the horizon when spin-orbit splitting of atomic one-electron shells starts to become large. Then, a spin-averaged orbital picture will no longer be sufficient. It can be expected that this will be the case for the heavy open-shell p-block elements Bi, Po, and At. 

The electron configuration is the orbital description of the locations of the electrons in an unexcited atom. Using principles of physics, chemists can predict how atoms will react based upon the electron configuration. They can predict properties such as stability, boiling point, and conductivity. Typically, only the outermost electron shells matter in chemistry, so we truncate the inner electron shell notation by replacing the long-hand orbital description with the symbol for a noble gas in brackets. This method of notation vastly simplifies the description for large molecules. 

There are several issues to consider when using ECP basis sets. The core potential may represent all but the outermost electrons. In other ECP sets, the outermost electrons and the last filled shell will be in the valence orbital space. Having more electrons in the core will speed the calculation, but results are more accurate if the —1 shell is outside of the core potential. Some ECP sets are designated as shape-consistent sets, which means that the shape of the atomic orbitals in the valence region matches that for all electron basis sets. ECP sets are usually named with an acronym that stands for the authors names or the location where it was developed. Some common core potential basis sets are listed below. The number of primitives given are those describing the valence region. 

Thus for H and He, the basis set consists of one orbital, a Is atomic orbital. For atomsLi to Ne the 2 inner-shell electrons are combined with the nucleus and the basis set consists of 4 orbitals, the 2s, 2p, ... 

Carbon has six electrons around the atomic core as shown in Fig. 2. Among them two electrons are in the K-shell being the closest position from the centre of atom, and the residual four electrons in the L-shell. TTie former is the Is state and the latter are divided into two states, 2s and 2p. The chemical bonding between neighbouring carbon atoms is undertaken by the L-shell electrons. Three types of chemical bonds in carbon are single bond contributed from one 2s electron and three 2p electrons to be cited as sp bonding, double bond as sp and triple bond as sp from the hybridised atomic-orbital model. 

In standard quantum-mechanical molecular structure calculations, we normally work with a set of nuclear-centred atomic orbitals Xi< Xi CTOs are a good choice for the if only because of the ease of integral evaluation. Procedures such as HF-LCAO then express the molecular electronic wavefunction in terms of these basis functions and at first sight the resulting HF-LCAO orbitals are delocalized over regions of molecules. It is often thought desirable to have a simple ab initio method that can correlate with chemical concepts such as bonds, lone pairs and inner shells. A theorem due to Fock (1930) enables one to transform the HF-LCAOs into localized orbitals that often have the desired spatial properties. 

The orbitals in an atom are organized into different layers, or electron shells, of successively larger size and energy. Different shells contain different numbers and kinds of orbitals, and each orbital within a shell can be occupied by two electrons. The first shell contains only a single s orbital, denoted Is, and thus holds only 2 electrons. The second shell contains one 2s orbital and three 2p orbitals and thus holds a total of 8 electrons. The third shell contains a 3s orbital, three 3p orbitals, and five 3d orbitals, for a total capacity of 18 electrons. These orbital groupings and their energy levels are shown in Figure 1.4. 

Figure 1.4 The energy levels of electrons in an atom. The first shell holds a maximum of 2 electrons in one Is orbital the second shell holds a maximum of 8 electrons in one 2s and three 2p orbitals the third shell holds a maximum of 18 electrons in one 3s, three 3p, and five 3dorbitals and so on. The two electrons in each orbital are represented by up and down arrows, 4.

Figure 5. Niels Bohr came up with the idea that the energy of orbiting electrons would be in discrete amounts, or quanta. This enabled him to successfully describe the hydrogen atom, with its single electron, In developing the remainder of his first table of electron configurations, however, Bohr clearly relied on chemical properties, rather than quantum theory, to assign electrons to shells. In this segment of his configuration table, one can see that Bohr adjusted the number of electrons in nitrogen s inner shell in order to make the outer shell, or the reactive shell, reflect the element s known trivalency.

In 1926 Llewellyn Thomas proposed treating the electrons in an atom by analogy to a statistical gas of particles. Electron-shells are not envisaged in this model, which was independently rediscovered by Enrico Fermi two years later. For many years the Thomas-Fermi method was regarded as a mathematical curiosity without much hope of application since the results it yielded were inferior to those obtained by the method based on electron orbitals.17... 

When multi-electron atoms are combined to form a chemical bond they do not utilize all of their electrons. In general, one can separate the electrons of a given atom into inner-shell core electrons and the valence electrons which are available for chemical bonding. For example, the carbon atom has six electrons, two occupy the inner Is orbital, while the remaining four occupy the 2s and three 2p orbitals. These four can participate in the formation of chemical bonds. It is common practice in semi-empirical quantum mechanics to consider only the outer valence electrons and orbitals in the calculations and to replace the inner electrons + nuclear core with a screened nuclear charge. Thus, for carbon, we would only consider the 2s and 2p orbitals and the four electrons that occupy them and the +6 nuclear charge would be replaced with a +4 screened nuclear charge. 

The location of an electron in an atom is described by a wavefunction known as an atomic orbital atomic orbitals are designated by the quantum numbers , l, and mi and fall into shells and subshells as summarized in Fig. 1.30. 

In valence-bond theory, we assume that bonds form when unpaired electrons in valence-shell atomic orbitals pair the atomic orbitals overlap end to end to form cr-bonds or side by side to form ir-bonds. 

In the molecular orbital description of homonuclear diatomic molecules, we first build all possible molecular orbitals from the available valence-shell atomic orbitals. Then we accommodate the valence electrons in molecular orbitals by using the same procedure we used in the building-up principle for atoms (Section 1.13). That is,... 

Step 1 Identify all the atomic orbitals in the valence shells, ignoring how many electrons they contain. 

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