State Hund`s Rule of Maximum Multiplicity

It indicates that in the ground state of an atom, the electron first enters the orbital with the lowest energy and later into the orbitals with a higher energy. In quantum chemistry, multiplicity (or spin multiplicity) is defined as the total number of spin orientations and is given by 2S + 1. Here, S is the total spin quantum number, and its value is the sum of all unpaired half-spins. According to the dog`s rule, the lowest energy configuration is reached when the multiplicity, i.e. 2S + 1, is maximum. As a result of Hund`s rule, restrictions are established on how atomic orbitals are filled in the ground state according to the construction principle. Before two electrons occupy an orbital in a subshell, the other orbitals in the same subshell must first contain one electron each. In addition, electrons that fill a subshell have a parallel spin before the shell fills with the opposite spin electrons (after the first orbital has gained a second electron). This ensures the maximum number of unpaired electrons (and thus the maximum total spin state) when filling atomic orbitals. Hund`s rule is called the maximum multiplicity rule because, of the various possible electronic configurations, only the configuration for which the total spin value is maximum is correct.

It is a general rule that when a group of n or fewer electrons occupies a series of n degenerate orbitals, they propagate below the orbitals, resulting in n unpaired spins. This is Hund`s rule or the rule of maximum diversity. This means that electron pairing is an unfavorable process; Energy must be expended to make this possible. The Hund maximum multiplicity rule is a rule based on the observation of atomic spectra used to predict the ground state of an atom or molecule with one or more open electron shells. The rule states that for a given electronic configuration, the lowest energy term is the one with the greatest spin multiplicity value. [1] This implies that if two or more orbitals of equal energy are available, the electrons occupy them individually before filling them in pairs. The rule, discovered by Friedrich Hund in 1925, is of great use in atomic chemistry, spectroscopy, and quantum chemistry, and is often abbreviated as Hund`s rule, ignoring Hund`s other two rules. There are six unpaired electrons in chromium. So, and the multiplicity is 2S + 1 = 7. The Dogs` rule of the maximum multiplicity rule states that for a given electronic configuration, the term with maximum multiplicity is the least energetic.

According to this rule, electron pairing in the p-, d and f orbitals can only occur when each orbital of a given subshell contains an electron or is occupied individually. The Hund maximum multiplicity rule is a rule based on the observation of atomic spectra. This observation is used to predict the electronic configuration of the ground state of an atom or molecule with one or more open electron shells. For example, the electron filling order of 2p orbitals from boron to neon follows the rule of Hund maximum multiplicity. It has many applications in atomic chemistry to predict the electron configuration and spin of an electron, quantum chemistry and spectroscopy, etc. The design principle states that orbitals with the lowest energy are first filled with electrons. Once the orbitals are filled with lower energy, the electrons move to orbitals with higher energy. The problem with this rule is that it does not provide information about the three 2p orbitals and the order in which they are filled. From the total spin quantum number, we can find multiplicity. In 2004, researchers reported the synthesis of 5-dehydro-m-xylylene (DMX), the first organic molecule known to violate the dog rule. [1] 1. For a given electronic configuration, the electron with a maximum spin multiplicity has the lowest energy.

Multiplicity can be represented by (2S+1), where S represents the total spin angular momentum of the electrons. With the principle of construction and the Pauli exclusion principle, the dog is very useful for understanding the electronic configuration of an atom. The design principle is used to predict the electron configuration when the energy difference between orbitals is considerably large, and the Pauli exclusion principle limits the maximum number of electrons in a two-orbital. Dog`s rule is useful for predicting the ground state of atoms or molecules where the same energy orbitals are available. This is especially evident in orbitals of the same subshell, which are the same in energy. For example, in the p-subshell, all its orbitals (px, py and pz) have the same energy. Such orbitals of equal energy are called degenerate orbitals. According to the rule, electrons occupy the same energy orbitally one by one before pairing. This means that electron pairing does not occur until each orbital with the same energy has the occupation of an electron. In addition, all these unpaired electrons must have the same spin, i.e. rise (↑) or decrease (↓).

Although most stable molecules have closed electron shells, a few have unpaired electrons for which the Hund rule applies. The most important example is the oxygen molecule O2, which has two orbitals of degenerate pi-bond molecules (π*) occupied by only two electrons. According to Hund`s rule, the ground state is triplet oxygen with two unpaired electrons in individually occupied orbitals. The singlet state of oxygen with a double π occupied and a vacuum * is an excited state with different chemical properties and greater reactivity than the ground state. Chromium, an element of the d-block, has atomic number 24. Its electronic configuration is [Ar] 3d54s1. The last two orbitals are 3D and 4s. The difference between the energies of these two orbitals is very small. As we can see in the diagram below, both orbitals are half filled and all electrons have the same spin as usual.