Exchange Energy

Spin-exchange interaction :Mutual electrostatic repulsion causes the molecules to interact in two ways.

• The first method is known as charge rectification. When two electron particles are separated by r, their Coulombic energy is equal to e²/r, where e = electrostatic charge. As a result, as r grows, two electrons are stable.
• Spin correction is the second interaction, and it is more significant than charge correction. According to the spin correlation of electrons, electrons with the same spin prefer to stay apart, whereas electrons with the opposite spin tend to get closer.

Exchange-correlation energy

Similar-spin electrons form an exchange contact, which stabilises the system. As a result, electrons with identical spin repulsion are reduced by an amount known as exchange energy. As a result, the higher the number of electrons with parallel spins, the higher the exchange energy and the more stable the system. The Hund’s rule of maximal spin multiplicity is based on this hypothesis.

Maximum stability is achieved at the d quantum level when five d electrons with parallel spins are arranged in five d orbitals, each containing one electron. The total exchange energy of the electron is calculated using K = exchange energy per pair of parallel spins and n = number of electrons in parallel spins. As a result, the exchange energy = n. (n-1) K/2

Stability of half-filled shells

Thus, the exchange energy for five unpaired electrons with parallel spins is 10K. We have a      d 4 system with exchange energy = 6K when one electron has withdrawn. When we take d-block elements in the periodic table and add six electrons to the d quantum level, the exchange energy remains at 10K, but there is strong Coulombic repulsion due to two electrons sharing orbitals.

We can see that a half-filled subshell is more stable than a subshell that is less than half-filled or more than half-filled. As a result, chromium with atomic number 24 has an electrical configuration.

Examples

The amount of energy released when electrons with the same spin swap positions in degenerate orbitals is known as exchange energy. As energy is released, the energy level of the degenerate orbital decreases, increasing stability. We know that half and fully filled orbitals are more stable than other orbitals. With the assistance of two instances, we can comprehend it. In chromium and copper, for example, there are two possible arrangements of electrons in the 3d and 4s orbitals: the first is 4 electrons in the 3d orbital and 2 electrons in the 4s subshell as per the Aufbau principle, and the other is 5 electrons in the 3d orbital and 1 electron in the 4s orbital. However, the second type configuration is possible, which does not follow the Aufbau principle but is more stable.We know that the lower the energy of a system, the more stable it is. For example, if we compare the energy of a 3d subshell with four electrons and a 3d subshell with five electrons, we can see that the latter is more stable. In the case of copper, there are two possible electronic arrangements: 9 electrons in the 3d subshell and 2 electrons in the 4s subshell, and 10 electrons in the 3d subshell and 1 electron in the 4s subshell. The first type of electronic arrangement follows the Aufbau principle, while the second type does not.Similarly, we must compare the energy of a 3d subshell with 9 electrons with a 3d subshell with 10 electrons. The lower the energy, the more stable the system.

Conclusion

When electrons are present, exchange energy = calculated orbital energy – actual orbital energy

Because estimated orbital energy is constant, an increase in exchange energy will result in a decrease in real orbital energy. Because the orbital has less real orbital energy, it is closer to the nucleus than it should be. As a result, electrons are more closely bonded, increasing the valence shell electrons’ stability.

Only valence shell orbitals with electron exchange are capable of exhibiting exchange events. The exchange energy is reduced to some extent when electrons are paired.

Exchange energy is a crucial component of many solids’ covalent bonds and is also responsible for ferromagnetic coupling.

When you travel from the top to the bottom of a group, the exchange energy drops because the valence electrons in the nucleus already have a lot of room to move due to their existence in huge orbitals, thus they don’t need the help of exchange energy.