Subject Chemistry Paper No and Title Paper 7: Inorganic Chemistry-II (Metal-Ligand Bonding, Electronic Spectra and Magnetic Properties of Transition Metal Complexes) Module No and Title 11, Electronic spectra of coordination complexes III Module Tag CHE_P7_M11 CHEMISTRY Paper 7: Inorganic Chemistry-II (Metal-Ligand Bonding, Electronic Spectra and Magnetic Properties of Transition Metal Complexes) Module 11: Electronic spectra of coordination complexes III TABLE OF CONTENTS 1. Learning Outcomes 2. Introduction 3. Spinning of an electron 4. Orbital motion of an electron 4.1 Defining an orbital 4.2 Orbital 5. Spin-Orbit coupling 4.1 What is spin-orbit coupling? 4.2 Free ion terms 6. Summary CHEMISTRY Paper 7: Inorganic Chemistry-II (Metal-Ligand Bonding, Electronic Spectra and Magnetic Properties of Transition Metal Complexes) Module 11: Electronic spectra of coordination complexes III 1. Learning Outcomes After studying this module, you shall be able to Know the difference between spinning and orbital motion of an electron Learn various factors influencing the spin orbit coupling Analyze various free ion terms for different configurations Understand the orbital in an atom along with orbital motion 2. Introduction For multi-electronic atoms and ions, the spin and orbital motion of various electrons are coupled together by spin-orbit coupling or L-S coupling or Russell-Saunders coupling. In this practice the total angular momentum represented by L and total spin angular momentum given by S, combine together to generate a new quantum number given by J. 3. Spinning of an electron A spherical body rotating about a fixed axis that passes through a point at the center of the sphere represents a model that how electron behaves in an atom. This means an electron always spins on its own axis either in a clockwise or anticlockwise direction (figure 1). The concept was first introduced by Uhlenbeck and Goudsmit. The spinning of electron about its own axis gives rise to spin quantum number represented by ms. It is required to fully specify the ambience of an electron in the atom. The spin quantum number can have two values, +1/2 if an electron is spinning clockwise and -1/2 if it is rotating anticlockwise. This spinning of an electron generates an intrinsic angular momentum related to it. The splitting of many spectral lines in the electronic spectra can be analyzed with the presence of spin angular momentum. An electron gyrating about the nucleus experiences the magnetic field produced by the nucleus which is circling about it in its own casing. This magnetic field then operates upon the electron’s own spin magnetic moment to create sub states in terms of energy. Figure 1. The spin of electron on its own axis CHEMISTRY Paper 7: Inorganic Chemistry-II (Metal-Ligand Bonding, Electronic Spectra and Magnetic Properties of Transition Metal Complexes) Module 11: Electronic spectra of coordination complexes III The angular momentum of a spinning particle is mathematically symbolized by a vector (figure 2). For the electronic spin, vector length is given by [s(s + 1)]1/2 where s is the spin quantum number. The vector can acquire only certain values representing specific orientations in space. In case of multi-electronic systems, the spin momentum of various electrons couple together to give a vector sum represented by the symbol S. Associated with S is Ms which represents the magnitude of orientation of the spin. In simple terms S is the quantum number associated with the length of the total spin and Ms is the quantum number associated with the orientation of total spin relative to the z axis. Possible values of Ms = S, (S -1),..., (-S) Figure 2. Angular momentum of the spinning electron represented by the vector in clockwise and anticlockwise direction 4. Orbital motion of an electron 4.1 Defining an orbital An orbital can be suggested as a space around the nucleus where electron can move around. Since due to uncertainty in determining the velocity and angular momentum persists for any electronic movement, an orbital can better be discussed in terms of probability. Hence it is that path surrounding the nucleus where the probability of finding the electron is maximum (figure 3). CHEMISTRY Paper 7: Inorganic Chemistry-II (Metal-Ligand Bonding, Electronic Spectra and Magnetic Properties of Transition Metal Complexes) Module 11: Electronic spectra of coordination complexes III Figure 3. Representing an orbital within the atomic system Since the electron shows dual nature, it behaves as particle and also as a wave, hence the electronic movement can be represented in terms of a wave function and a wave equation. Talking in terms of polar coordinates, the wave function splits into two parts, namely radial part and angular part. The radial part gives an idea about the probability finding electron at a distance ‘r’ from the nucleus. In case of a radial node, the radial part of a wave function changes sign and when we have an angular node, the angular part of the wave function changes sign. The number of nodes in an orbital is given by: Number of angular nodes = l Number of radial nodes = (n – 1 – l) Total number of nodes = n – 1 Figure 4 shows various atomic orbitals present in the hydrogen atom. The electronic wave functions are deciphered in terms of radial and angular probability plots CHEMISTRY Paper 7: Inorganic Chemistry-II (Metal-Ligand Bonding, Electronic Spectra and Magnetic Properties of Transition Metal Complexes) Module 11: Electronic spectra of coordination complexes III Figure 4. Representing the various atomic orbitals of the hydrogen atom 4.2 Orbital motion Classically, rotational motion refers to the rotation of an object about a fixed point. An electron in an atom moves in a circular path with the fixed radius about the nucleus. This rotational motion of an electron in an orbit, around the nucleus, leads to origin of orbital angular momentum. Orbital angular momentum can be visualized in terms of electron with mass m revolving around the nucleus in an orbit of the radius r and angular velocity v. the expression is given as L= mvr, where L is the angular momentum of the system. The orbital angular momentum can be represented by a vector. Figure 5 shows the vector representation of the electron rotating in the CHEMISTRY Paper 7: Inorganic Chemistry-II (Metal-Ligand Bonding, Electronic Spectra and Magnetic Properties of Transition Metal Complexes) Module 11: Electronic spectra of coordination complexes III Bohr’s orbit. The angular momentum vector is always directed towards the direction where it is perpendicular to the plane in which circular motion of the electron in its orbit is taking place. Angular momentum is represented by the vector length. The features important in the case of classical representation for the angular momentum are: (1) that angular momentum can be represented by a vector whose direction is related to the sense of the direction of rotation; (2) that the representation of the vector can be conveniently placed on the axis of rotation; and (3) that the length of the vector is proportional to the absolute magnitude of the angular momentum. In case of multi-electronic systems, the orbital angular moments of various electrons couple together to give the resultant orbital angular momentum of the system. Thus total angular momentum quantum number represented by L can be given as L = (l1+l2), (l1+l2-1), (l1+l2-2)…………(l1-l2) The quantum number Ml describes the component of L in the direction of the magnetic field for an atomic state. The values of L correspond to the atomic states which can be described in terms of S, P, D, F,……… Ml = 0, ±1, ±2, …….., ±L Figure 5. The vector representation of the electron rotating in the bohr’s orbit. The direction of angular momentum vector is perpendicular to the plane defined by the circular motion of the electron in its orbit. 5. Spin – Orbit coupling 5.1 What is spin-orbit coupling? The electrons in any atom behave in a very similar manner in the sense of having an orbital as well as spin motion. Till this point we have seen that the orbital as well as spin motion of various electrons in a system have to added so as to give resultant total orbital and spin angular moments. Now, we will see that, the spin and angular moments of the electrons also couple together by the process called spin-orbit coupling. This coupling further gives rise to a new quantum number deciphered as J which is called total angular momentum quantum number. The quantum number J can have following values CHEMISTRY Paper 7: Inorganic Chemistry-II (Metal-Ligand Bonding, Electronic Spectra and Magnetic Properties of Transition Metal Complexes) Module 11: Electronic spectra of coordination complexes III J = (L+S), (L+S-1), (L+S-2), ………..,|L-S| 5.2 Free ion terms The atomic states characterized by the values of L, S, J are referred to as free ion terms or Russell-Saunders terms. This is because they actually describe the individual atoms or ions which are ligands free. They are also specified as term symbols. Term symbols are represented in the form where L is designated along with the value of spin multiplicity on the left superscript and value of J on the right subscript. (2S+1) LJ = Term symbol L = Total orbital angular momentum quantum number (2S+1) = Spin multiplicity J = Total angular momentum quantum number 3 For example the term symbol P2 represents the state in which L=1 and the spin multiplicity is 3, whereas also the value of J is 2. Free ions terms are very important in analysis of the absorption spectra of the coordination compounds.