PAPER No. 7: Inorganic Chemistry - II (Metal-Ligand Bonding, Electronic Spectra and Magnetic Properties of Transition Metal Complexes

Transcription

1 Subject Chemistry Paper No and Title Module No and Title Module Tag 7, Inorganic chemistry II (Metal-Ligand Bonding, Electronic Spectra and Magnetic Properties of Transition Metal Complexes) 10, Electronic spectra of coordination CHE_P7_M10

2 TABLE OF CONTENTS 1. Learning Outcomes 2. Introduction 3. Electronic configurations 3.1 Rules for writing the electronic configurations 4. Quantum numbers 4.1 Need for quantum numbers 5. Summary 4.2 Quantum numbers of multi-electron atoms

3 1. Learning Outcomes After studying this module, you shall be able to Know the rules utilized in writing the electronic configurations Recognize the need and use of various quantum numbers Identify the various possible states and microstates associated with the various multielectronic systems 2. Introduction The chemical properties of the compounds depend on the electronic arrangement of the atoms within. The electronic cloud is sectioned which can be represented by electronic configuration and orbital notations. When we are talking about the multi-electronic systems, the interaction between the various electrons will specify the various electronic states which are feasible for the electronic transitions to take place. In order to find the possible transitions, the various energy levels according to different orientations need to be specified and arranged in order of energy. 3. Electronic configurations 3.1 Rules for writing the electronic configurations There are certain rules to be followed in order to write the electronic configuration and orbital notations for various electrons of an atom. These rules can be specified as, (a) Aufbau principle:- The electrons in orbitals are always filled according to increasing order of energy(figure1). This means that the orbital of lower energy will be filled first and then the orbital of next higher energy. To specify the trend, following chart can be considered. The diagonal rule is followed to find the increasing energy terms. In order to find the energy of orbitals their (n+l) values should be determined. The orbital having lower (n+l) value is of lower energy and if value is same for any two orbitals, the orbital with lower n value will be lower in energy.

4 Figure 1. Increasing energy level in a shell

5 (b) Pauli s exclusion principle: - Any two electrons present inside an atom cannot have all four quantum numbers identical. An orbital can only grasp up to two electrons to the maximum extend and each electron of the orbital should have an opposite spin. If the spin of one electron is parallel then the other electron should be anti-parallel. (c) Hund s rule:- In an orbital the electrons are firstly singly filled and when all are singly filled, the pairing takes place. This happens because the most stable arrangement of the electrons is the one with maximum number of unpaired electrons. This leads to minimum electronic repulsions. For writing the electronic configuration of the atoms the above rules should be followed. The main energy level of an atom contains a total of n sub shells, where n is the main energy level. The sub shells are named as s, p, d, f, g, h and so on. These alphabets are originated from the words sharp, principle, diffusive, fundamental used to describe the spectral lines of the hydrogen atom. Each increasing no of sub shell has odd number of orbitals available. An s sub shell can sustain a maximum of 2 electrons, a p sub shell has 6 electrons, d has 5 and f has 7 electrons in it. 4. Quantum numbers 4.1 Need for quantum numbers In order to completely describe the position of an electron in an atom, four quantum numbers are required. The four quantum numbers are (a) principal quantum number, n (b) azimuthal quantum number, l (c) magnetic quantum number, m l (d) spin quantum number, m s All of the quantum numbers will be described separately (a) Principal quantum number n tells about the basic energy level and distance from the nucleus for the given electron in an atom. It tells about the main shell of the electron. The higher value of n means more amount of energy involved which further suggest that the electron is present farther away from the nucleus. Also, it is noteworthy that the levels of energy get even closer to each other as the distance from the nucleus increases (figure 2).

6 Figure 2. Increasing energy levels of n in the shell (b) Azimuthal quantum number l tells us about the sub-shell or the orbital in which the electron is present. The sub-shell informs us about the shape of the electronic cloud present. It also suggest about the number of nodal planes in the electronic cloud. These orbitals are the volume or space around the atom which electrons occupy 90-95% of the time. Each sub-shell has a number, form, and a letter correlated with it. The outline of the electronic cloud in actual practice presents the prospect of locating an electron in that spatial environment of the atom. In case of an s orbital, the value of l is equal to zero, which represents the shape of a spherical shell. As the value of n increases, the principle energy shell increases and related to it the size of the spheres also become larger and larger but the shape is still the same (figure 3). For a p orbital, l = 1, representing the general form of a dumbbell or peanut. A total of 3 p orbitals are there per principal quantum number n which can be represented as p x, p y and p z as per their lobe orientation along the three axis, but the basic shape of the orbital is same for all the three (figure 4). It has 1 nodal plane, which is a space of zero probability of finding the electron:

7 Figure 3. Shape of the s orbital with increasing value of n Figure 4. Shape of p orbital For a d orbital, l = 2 and there are total of five d orbital per n level. The first d orbital appear in the n = 3 principal shell. Two types of shapes are there for a set of five d orbitals. three are dumbbell shaped or can be said as cloverleaf shaped. They comprise of two nodal planes, bisecting the probability twice, giving the shape of cloverleaf. The fifth one has a peanut shape with a doughnut about it. The orbitals recline straight on the Cartesian axes or can be said as rotated 45 o from the axes. The five d orbitals are named as d xy, d yz, d xz, d x2-y2 and d z2 (figure 5).

8 Figure 5. Shape of d orbitals For an f orbital, l = 3, and the shapes get quite complex. Imagine bisecting each of the cloverleaves above through the middle again: The first f orbitals appear in the n = 4 shell. The f orbitals encompass the most intricate shapes (figure6). There are seven f orbitals per n level. The f orbitals have complex names.

9 Figure 6. Shape of f-orbitals (c) Magnetic quantum number, m l basically specifies the different orbitals possible associated with the value of l. The orbitals suggest the orientation of the electronic cloud around a central point called the nucleus in an x, y, z plane. The total number of orientations feasible is based upon the sub-shell or the value of l. The value of m l can vary between +l.. up to -l. Now if the value of l is zero, there is only one value of m l possible and that is zero. It means only one orientation of the electronic cloud is probable around the nucleus. The fact can also be verified since the shape of an s orbital is a sphere and no matter what way we turn it, it will still be a sphere; there is no difference (figure 3). For the value of l = 1 the orbital specified is p orbital which can have three orientation by the rule m l = -1, 0, +1. This means there are three possible orientations of the electronic cloud around the nucleus (figure 4). Similarly for l = 2 which specifies a d orbital, we have a total of five orientations possible for ml= -2, -1, 0, +1, +2(figure 5). for l=3, an f orbital, there are seven orientations namely m l = -3,-2,-1,0,+1,+2,+3 (figure 6). (d) Spin quantum number m s is the last thing we need to fully describe an electron in an atom. This means to know that which way it is spinning on its own axis. The electron is either spinning clockwise or anticlockwise. These are labeled as either +1/2 or 1/2 (figure 7).

10 Figure 7. The spin of electron on its own axis 4.2 Quantum numbers of multi-electron atoms The quantum numbers for the single individual electron can be easily stated but in case we are taking a system of electrons as a whole, the quantum state becomes somewhat difficult to describe since now the electronic interactions play a major part. Because of the electronic repulsions the electrons tend to occupy separate orbitals following Hund s rule of maximum multiplicity and also the interactions lead to parallel spin of electrons in different orbitals which actually enhances the exchange energy. In order to understand the various electronic interactions let us consider a system of carbon atom having two electrons in the last orbital. The electronic configuration of the atom is 1s 2 2s 2 2p 2. For the valence electrons we have the following set of quantum numbers n = 2, l = 1 from the value of l it can be depicted that we can have three values of ml which are +1,0,-1 respectively. m l = +1, 0, -1 the value of spin quantum number can take two values +1/2 and -1/2. m s = +1/2 and -1/2

11 Each of the 2p electrons can have a set of m l and m s values with various combinations. The 2p electrons are not autonomous with respect to each other, since their orbital and spin angular moments interact together by the Russell-Saunders coupling phenomenon which is also called L- S coupling. By the interaction are produced new quantum states for the system which are termed as microstates. A new set of quantum numbers is then used to describe this new quantum state of the system. The new quantum numbers are then designated as Ml and Ms which states the total orbital momentum and total spin angular momentum of the system. M l = Σ m l M s = Σ m s Now we will tabulate the various microstates possible according to their Ml and Ms Values for a p 2 case we can get a total of 15 microstates. The notation 1+ signifies that the electron is having value of m l = 1 with spin, m s = -1/2. On the similar terms the microstate table can be constructed (figure 8). Figure 8. Microstate table for p 2 configuration

12 The quantum numbers Ml and Ms further determines the value L, S and J which are the atomic quantum numbers. The difference between Ml, Ms and L, S is clear. Ml and Ms represent the microstates themselves whereas L and S is the collection of microstates. L and S are the largest possible values of Ml and Ms. According to the values of L the atomic states of the system can be S, P, D, F. The values of S are used to find the value of spin multiplicity represented by 2S+1. The value of Land S are called free ion terms because they describe individual atoms or ions, free of ligands. The free ion terms are very important in the interpretation of the spectra of coordination compounds. These terms also interpret the energy and symmetry of an atom or ion and determine the possible transitions between states of different energies. Now in order to reduce the microstate table to its constituent atomic terms first of all we have to look for the largest Ml values and with it associated largest values of Ms. By this means we get three free ion terms represented in the following microstate table (figure 9). The three terms 3P, 1D and 1S specify three distinct energy states with different electronic interactions. Figure 9. Calculation of free ion terms for the p 2 configuration Out of the three terms the lowest energy term is the one with highest spin multiplicity. In this case 3P is the ground state. If in any case we have two states with same spin multiplicity then the ground state will be one with highest value of L.

13 5. Summary 1) The chemical properties of the compounds depend on the electronic arrangement of the atoms within. 2) In multielectron system, the interaction between the various electrons will specify the various electronic states which are feasible for the electronic transitions to take place. 3) Aufbau principle stares that the electrons in orbitals are always filled according to increasing order of energy. 4) Pauli s exclusion principle states that any two electrons present inside an atom cannot have all four quantum numbers identical. 5) Hund s rule says that pairing of the electrons in an orbital will never take place unless each orbital is individually singly occupied. 6) Principal quantum number n tells about the basic energy level and distance from the nucleus for the given electron in an atom. 7) Azimuthal quantum number l tells us about the subshell in which the electron is present. 8) Magnetic quantum number, ml basically specifies the different orbitals possible associated with the value of l. The orbitals suggest the orientation of the electronic cloud around a central point called the nucleus in an x, y, z plane. The number of orientations feasible is based upon the sub-shell or the value of l. 9) Spin quantum number ms is needed to fully describe an electron in an atom. This means to know that which way it is spinning on its own axis. The electron is either spinning clockwise or anticlockwise. 10) The electrons are not independent of each other in multielectronic systems, since their orbital and spin angular momenta interact together by the Russell-Saunders coupling phenomenon which is also called L-S coupling. 11)By the interaction of electrons are produced new quantum states for the system which are termed as microstates. The new quantum numbers are then designated as Ml and Ms which states the total orbital momentum and total spin angular momentum of the system. M l = Σ m l M s = Σ m s