Ground state electron orbitals

All m oleciilar orbitals are com biiiations of the same set of atom ic orbitals they differ only by their LCAO expansion coefficients. HyperC hem computes these coefficients, C p. and the molecular orbital energies by requiring that the ground-state electronic energy beat a minimum. That is, any change in the computed coefficients can only increase the energy. 

Here, the bonding between carbon atoms is briefly reviewed fuller accounts can be found in many standard chemistry textbooks, e.g., [1]. The carbon atom [ground state electronic configuration (ls )(2s 2px2py)] can form sp sp and sp hybrid bonds as a result of promotion and hybridisation. There are four equivalent 2sp hybrid orbitals that are tetrahedrally oriented about the carbon atom and can form four equivalent tetrahedral a bonds by overlap with orbitals of other atoms. An example is the molecule ethane, CjH, where a Csp -Csp (or C-C) a bond is formed between two C atoms by overlap of sp orbitals, and three Csp -Hls a bonds are formed on each C atom. Fig. 1, Al. 

We would normally write the electronic ground state electron configuration of a carbon atom as ls-2s 2p-. Despite the intellectual activity that has gone into defining mythical valence states for carbon atoms in different bonding situations, no one would include a d-orbital in the description of ground state carbon. 

The lowest-energy arrangement, or ground-state electron configuration, of an atom is a listing of the orbitals occupied by its electrons. We can predict this arrangement by following three rules. 

An atom consists of a positively charged nucleus surrounded by one or more negatively charged electrons. The electronic structure of an atom can be described by a quantum mechanical wave equation, in which electrons are considered to occupy orbitals around the nucleus. Different orbitals have different energy levels and different shapes. For example, s orbitals are spherical and p orbitals are dumbbell-shaped. The ground-state electron configuration of an... 

This procedure gives the ground-state electron configuration of an atom. Any other arrangement corresponds to an excited state of the atom. Note that we can use the structure of the periodic table to predict the electron configurations of most elements once we realize which orbitals are being filled in each block of the periodic table (see Fig. 1.44). 

When N valence atomic orbitals overlap, they form N molecular orbitals. The ground-state electron configuration of a molecule is deduced by using the building-up principle to accommodate all the valence electrons in the available molecular orbitals. The bond order is the net number of bonds that hold the molecule together. 

The ground-state electron configurations of diatomic molecules are deduced by forming molecular orbitals from all the valence-sbell atomic orbitals of the two atoms and adding the valence electrons to the molecular orbitals in order of increasing energy, in accord ivith the building-up principle. 

A neutral helium atom has two electrons. To write the ground-state electron configuration of He, we apply the aufbau principle. One unique set of quantum numbers is assigned to each electron, moving from the most stable orbital upward until all electrons have been assigned. The most stable orbital is always ly( = l,/ = 0, JW/ = 0 ). 

A lithium atom has three electrons. The first two electrons fill lithium s lowest possible energy level, the 1. S orbital, and the third electron occupies the 2 5 orbital. The three representations for the ground-state electron configuration... 

Two of the 7i molecular orbitals of 1,3-butadiene are bonding molecular orbitals, i) In the ground state these orbitals hold the four tz electrons with two spin-paired... 

This mode of hyperfine interaction will become important only when the impaired electron is able to partially occupy a low-lying excited state (AE small), and the ground state has orbital angular momentum (L 0). The adsorbed nitric oxide molecule and the superoxide ion with 170 are typical examples where hyperfine coupling via spin-orbit interaction may be observed. 

The ground-state electron configuration of B suggests an ability to form one B—F bond, rather than three., JB JB -Jil I I Again, excitation, or promotion of an electron to a higher energy orbital, followed by hybridization is required to form three equivalent half-filled B orbitals. 

It is possible to divide electron correlation as dynamic and nondynamic correlations. Dynamic correlation is associated with instant correlation between electrons occupying the same spatial orbitals and the nondynamic correlation is associated with the electrons avoiding each other by occupying different spatial orbitals. Thus, the ground state electronic wave function cannot be described with a single Slater determinant (Figure 3.3) and multiconfiguration self-consistent field (MCSCF) procedures are necessary to include dynamic electron correlation. 

In Equation 9.21, T yields n and is orthogonal to the first i — 1 state of the Hamiltonian for which n0 is the ground-state density. Here, this Hamiltonian is the // in Equation 9.19. Note that instead of the ground-state electron density n0, we could use the external potential v or any ground-state Kohn-Sham orbital, etc. Thus we could use Ft[n, v]. The extension to degenerate states is studied in Section 9.4. 

Let s look at the ground state electron configuration and orbital diagram of the beryllium atom (4Be) which is the first element in group 2A. 

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