+2 UNIT 1 PAGE-3
ELECTRONIC CONFIGURATIONS
The distribution of electrons into different shells , sub-shells and orbitals of an atom is called electronic configuration.
In order to represent electron population of an orbital, the principal quantum number (n) is written before orbital symbol, while number of electrons in the orbital is written as superscript near the right hand top of the orbital symbol. For example , if we have two electrons in the s-orbital of first energy level then it is written as 1s2. Sometimes electronic configurations are represented in a different way by representing each orbital by a square or a circle and electrons are represented by putting arrows as illustrated below.
STABILITY OF FILLED AND HALF-FILLED ORBITALS
The filled and half-filled orbitals have extra stability due to the following reasons.
(i) Symmetrical distribution of electrons
It is well-known that symmetry leads to stability. The completely filled or half-filled sub-shells have symmetrical distribution of electrons in them and are therefore more stable. Electrons in the same sub-shell (here 3d) have equal energy but different spatial distribution. Consequently, there shielding of one another is relatively small and the electrons are strongly attracted by the nucleus.
(ii) Exchange Energy
Since the electrons in the same sub-shell have equal energies, they can exchange their positions in random in the various orbitals of the same sub-shell. Such exchange of positions results in the release of energy called exchange energy . Half filled arrangement of electrons leads to maximum exchange energy between electrons with parallel spins present in the degenerate orbitals. Maximum exchange energy imparts stability. Consider the following two arrangements of electrons :
Number of exchanges possible in configuration :
d4 = 1 ® 2 ; 1 ® 3 ; 1 ® 4 ; 2 ® 3 ; 2 ® 4 : 3 ® 4 = 6
d5 = 1® 2 ; 1 ® 3; 1® 4 ; 1 ® 5 ; 2 ® 3 ; 2 ® 4 ;
2 ® 5 ; 3 ® 4 ; 3 ® 5 ; 4 ® 5 = 10
Thus d5 configuration possesses higher exchange energy than d4 configuration, i.e., d5 configuration is more stable than d4 configuration.
Exceptional configurations of Chromium and Copper
The electronic configurations of Cr (Z = 24 ) and Cu (Z = 29) do not follow the general trend. The electronic configuration of Cr and Cu are expected to be as follows:
24Cr : 1s2, 2s2, 2p6, 3s2, 3p6, 3d4, 4s2 and
29Cu : 1s2, 2s2, 2p6, 3s2, 3p6, 3d9, 4s2
But actually their configurations are :
24 Cr : 1s2, 2s2, 2p6, 3s2, 3p6, 3d5, 4s1 and
29Cu : 1s2, 2s2, 2p6, 3s2, 3p6, 3d10, 4s1
These anomalies are attributed to the fact that exactly half-filled and completely filled orbitals ( i.e., p3, p6, d5, d10, f7 and f14 ) have lower energy and hence extra stability . The cause of this extra stability has been attributed to the symmetry effects and exchange energy effects. Thus to acquire stability , one of the 4s electrons goes to the nearby 3d-orbitals so that 3d-orbitals get half-filled in Cr and completely filled in copper.
Note : It may be noted that configurations of atoms can also be wreitten in condensed form by taking the configurations of noble gases. The configuration of inert gases representing core are written as [He]2, [Ne]10,[Ar]18, [Kr]36, [Xe]54 and [Rn]86. For example, electronic configuration of Scandium having atomic number 21 may be written as 21Sc : [Ar]3d14s2. The electronic configurations of other elements on this pattern is given in the following page (Page 21).
PROBLEMS
15. Write the electronic configurations of first thirty elements.
16. What atoms are indicated by the following electronic configurations:
i) 1s22s22px22py22pz1 ii) [Ar]4s23d5
iii) 1s22s12px12py12pz1 . Are they in the Ground or excited state ?
17. What designations are given to orbitals having :
i) n = 4 ; ℓ = 3 ; iii) n = 2 ; ℓ = 1
ii) n = 2 ; ℓ = 0 iv) n = 4 ; ℓ = 2
iv) n = 4 ; ℓ = 1
18. Give the electronic configurations of :
i) H- ii) Na+ iii) F- iv) Mg2+
19. Write the electronic configurations of Cu2+ and Cr3+
ELECTRONIC CONFIGURATIONS OF ELEMENTS
Atomic number | Element | Electronic configuration | Atomic number | Element | Electronic configuration |
1 | H | 1s1 | 53 | I | [Kr] 4d105s25p5 |
2 | He | 1s2 | 54 | Xe | [Kr] 4d105s25p6 |
3 | Li | [H]e2s1 | 55 | Cs | [Xe] 6s1 |
4 5 6 | Be B C | [He]2s2 [He] 2s22p1 [He] 2s22p2 | 56 57 58 | Ba La Ce | [Xe] 6s2 [Xe] 5d16s2 [Xe]4f26s2 |
7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 | N O F Ne Na Mg Al Si P S Cl Ar K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te | [He] 2s22p3 [He] 2s22p4 [He] 2s22p5 [He] 2s22p6 [Ne] 3s1 [Ne] 3s2 [Ne]3s23p1 [Ne]3s23p2 [Ne]3s23p3 [Ne]3s23p4 [Ne]3s23p5 [Ne]3s23p6 [Ar] 4s1 [Ar] 4s2 [Ar] 3d14s2 [Ar] 3d24s2 [Ar] 3d34s2 [Ar] 3d54s1 [Ar] 3d54s2 [Ar] 3d64s2 [Ar] 3d74s2 [Ar] 3d84s2 [Ar] 3d104s1 [Ar] 3d104s2 [Ar] 3d104s24p1 [Ar] 3d104s24p2 [Ar] 3d104s24p3 [Ar] 3d104s24p4 [Ar] 3d104s24p5 [Ar] 3d104s24p6 [Kr] 5s1 [Kr] 5s2 [Kr] 4d15s2 [Kr] 4d25s2 [Kr] 4d45s1 [Kr] 4d55s1 [Kr] 4d55s2 [Kr] 4d75s1 [Kr] 4d85s1 [Kr] 4d10 [Kr] 4d105s1 [Kr] 4d105s2 [Kr] 4d105s25p1 [Kr] 4d105s25p2 [Kr] 4d105s25p3 [Kr] 4d105s25p4 | 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 | Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi At Rn Fr Ra Ac Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr | [Xe]4f36s2 [Xe]4f46s2 [Xe]4f56s2 [Xe]4f66s2 [Xe]4f76s2 [Xe]4f75d16s2 [Xe]4f96s2 [Xe]4f106s2 [Xe]4f116s2 [Xe]4f126s2 [Xe]4f136s2 [Xe]4f146s2 [Xe]4f145d16s2 [Xe]4f145d26s2 [Xe]4f145d36s2 [Xe]4f145d46s2 [Xe]4f145d56s2 [Xe]4f145d66s2 [Xe]4f145d76s2 [Xe]4f145d96s1 [Xe]4f145d106s1 [Xe]4f145d106s2 [Xe]4f145d106s26p1 [Xe]4f145d106s26p2 [Xe]4f145d106s26p3 [Xe]4f145d106s26p4 [Xe]4f145d106s26p5 [Xe]4f145d106s26p6 [Rn]7s1 [Rn]7s2 [Rn]6d17s2 [Rn]6d27s2 [Rn] 5f26d17s2 [Rn] 5f36d17s2 [Rn] 5f46d17s2 [Rn] 5f67s2 [Rn] 5f77s2 [Rn] 5f76d17s2 [Rn] 5f97s2 [Rn] 5f107s2 [Rn] 5f117s2 [Rn] 5f127s2 [Rn] 5f137s2 [Rn] 5f147s2 [Rn] 5f146d17s2 |
CHEMICAL BONDING
A chemical bond in general may be defined as the force of attraction that binds the constituent particles ( ie., atoms or molecules ) together in various chemical species. Atoms enter into chemical combinations to form molecules because by doing so they attain a state of lowest energy or maximum stability. Based on this idea the formation of a number of different kinds of bonds like ionic, covalent, hydrogen bonds etc. can be discussed.
The concept of covalent bond formation based on sharing of electrons (Lewis concept ) could not explain satisfactorily , the forces of attractive interactions in a molecule. In order to offer a reasonable explanation two theories were proposed. They are :
i) Valence
ii) Molecular Orbital Theory.
1. THE VALENCE
This approach was put forward by Heitler and London
i) According to this theory atoms maintain their individuality even in the molecule and the bond formed by interaction of half-filled orbitals belonging to the valence shells of the participating atoms.
ii) The overlapping atomic orbitals must contain the electrons with opposite spins.
iii) The strength of the bond depends upon the extent of overlapping. The greater the overlap the stronger is the bond.
iv) As a result of overlapping and therefore pairing of electrons , energy is released and hence the system acquires a state of lower energy.
v) The stability of the molecule is further explained in terms of exchange of electrons between the atoms participating in the bond formation.
vi) The valence of an element is equal to the number of half-filled orbitals in the valence shell of its atoms.
This theory successfully explained the formation of hydrogen molecule. Besides this, the application of these ideas was also extended to molecules like F2, NH3, H2O, CH4 , C2H2 etc. Though this theory could quite reasonably explain the shapes and bondings of many molecules, yet it failed to explain the magnetic properties of some of the molecules. For example, it could not explain why oxygen is paramagnetic in behaviour. Besides this, the theory fails to explain the bonding in electron deficient compounds as well as metals and inter-metallic compounds.
MOLECULAR ORBITAL THEORY
Molecular orbital theory was put forward by Hund, R.S. Mullikan, Leonard Jones and Charles Coulson (1932) . The theory is modern and rational. It assumes that in molecules atomic orbitals loose their identity and the electrons in molecules are present in new orbitals called molecular orbitals which are not associated with a particular atom but belong to the molecule as a whole.
The salient features of this theory are given below :
i) In molecules , electrons are present in new orbitals called molecular orbitals . Molecular orbitals like atomic orbitals are characterised by a set of quantum numbers.
ii) Molecular orbitals are formed by combination of atomic orbitals of nearly same energies.
iii) Molecular orbitals are not associated with a particular atom but belong to nuclei of all the atoms constituting the molecule. Nuclei of different atoms in the molecule behave as polycentric nucleus.
iv) The number of molecular orbitals formed is equal to the number of atomic orbitals undergoing combination. Among new molecular orbitals formed, half are of lower energy than combining atomic orbitals (bonding molecular orbitals ) and the other half are of energy greater than combining atomic orbitals ( anti-bonding molecular orbitals ).
v) The shapes of molecular orbitals depend upon the shapes of combining atomic orbitals.
vi) The molecular orbitals are filled in the increasing order of energies , starting with orbital of least energy (Aufbau principle ).
vii) A molecular orbital like atomic orbitals can accommodate only two electrons and these electrons must have opposite spins (Pauli’s exclusion principle)
viii) While filling molecular orbitals of equal energy pairing of electrons does not take place until all such orbitals are singly occupied (Hund's Rule).
LINEAR COMBINATION OF ATOMIC ORBITALS (LCAO METHOD)
Molecular orbitals are formed by the combination of atomic orbitals of bonded atoms. In wave mechanics atomic orbitals are expressed by wave functions (Y). The wave functions are obtained as the solutions of Schrodinger wave equation. Just like atomic orbitals, Schrodinger wave equation can be written to describe the behaviour of the electron in molecules also. However, because of the complex nature of the Schrodinger wave equation, it may not be easy to solve it for molecules. Thus, in view of it, for the sake of convenience an approximate technique to obtain the wave functions for molecular orbitals was applied. This approximate method is known as Linear Combination of Atomic Orbitals Method ( LCAO ).
Let us apply this theory to homonuclear diatomic molecules such as hydrogen molecule. Let us consider two atoms of hydrogen in the molecule as A and B. Each hydrogen has one electron in 1s-orbital in the ground state . These atomic orbitals may be represented by wave functions YA and YB. Then according to LCAO method , the molecular orbitals in H2 molecule are given by linear combination ( addition or subtraction of wave functions of individual atoms ) of YA and YB as shown below :
YMO = YA ± YB
Yb = YA + YB
Ya = YA - YB
The molecular orbital Yb formed by the addition overlap ( constructive interference of waves ) of atomic orbitals is called bonding molecular orbitals and the molecular orbital Ya formed by subtraction overlap (destructive interference of waves) of atomic orbitals is called anti-bonding molecular orbital .
The formation of Bonding and Anti-bonding orbitals can be interpreted in terms of sign of wave functions of the orbitals which interact. Such a wave possesses a crest and a trough , therefore the positive and negative signs are arbitrarily assigned to the crest and trough respectively.
Now if the crest of one wave overlaps with the crest of the other , the two waves interact in a constructive interference and therefore the new resulting wave is reinforced i.e., add up or there is in-phase overlap , hence bonding orbitals result by overlap of atomic orbitals with the same sign. On the contrary, if crest of one overlaps with the trough of the other two waves interact in a destructive manner or out of phase overlap or subtraction overlap and thus the resulting wave gets weakened. Thus the anti-bonding orbitals result form atomic orbitals with opposite sign.
The combination of 1s orbitals of hydrogen atoms to form molecular orbitals has been shown in Fig 20.
Fig 20 Molecular orbitals formed by combination of
two 1s-orbitals
As is clear from the figure, in the bonding molecular orbital the electron density is mainly concentrated in between the nuclei , so the electrons feel greater force of attraction in the orbital. Hence bonding molecular orbital is of lower energy as compared to atomic orbitals. On the other hand , in anti-bonding molecular orbital the electron density is mainly concentrated away from the nuclei ; in between the nuclei there is a node. So the electrons feel less force of attraction in this orbital and hence anti-bonding molecular orbital is of higher energy as compared to atomic orbitals. Relative energies of atomic orbitals and molecular orbitals are shown in Fig 21.
Fig 21 Relative energies of bonding and
anti-bonding molecular orbitals.
It may be noted that bonding molecular orbital is stabilised almost to the same extent as the anti-bonding molecular orbital is destabilised relative to atomic orbitals.
Differences between bonding and anti-bonding
molecular orbitals.
Bonding Molecular Orbital | Anti-bondingMolecular Orbital |
1. Bonding molecular orbital is formed by the addition overlap of atomic orbitals. | 1. Anti-bonding molecular orbital is formed by the subtraction overlap of atomic orbitals. |
2. It may or may not have a node | 2. It always has a node in between the nuclei of bonded atoms. |
3. It has lower energy than the AOs from which it is formed. | 3. It has higher energy than the AOs from which it is formed. |
1. The electron charge density in between the nuclei is high and hence the repulsion between the nuclei is very low. This results in stabilisation of BMO , in other words, the electrons in the BMO favour stable bond formation. | 4. The electron charge density in between the nuclei is less and hence the repulsion between the nuclei is high. This results in de-stabilisation of anti-bonding MO. In other words, the electron in the ABMO oppose bond formation. |
CONDITIONS FOR COMBINATION OF ATOMIC ORBITALS
For atomic orbitals to combine, resulting in the formation of molecular orbitals , the main conditions are :
i) The combining atomic orbitals should have almost the same energies. For example, in the case of diatomic molecules, 1s-orbital of one atom can combine with 1s - orbital of the other atom, but 1s-orbital of one atom cannot combine with 2s-orbital of the other atom.
ii) The extent of overlap between the atomic orbitals of the two atoms should be large.
iii) The combining atomic orbitals should have the same symmetry about the molecular axis. For example, 2Px orbital of one atom can combine with 2Px orbital of the other atom but not with 2Pz orbital .
Note : It may be noted that Z-axis is taken as the inter-nuclear axis according to modern conventions.
Designations of Molecular Orbitals
Just as atomic orbitals are designated as s, p, d, f etc molecular orbitals of diatoimic molecules are named as s (sigma) , p (pi ) , d (delta ) etc.
MOLECULAR ORBITALS
The molecular orbitals which are cylindrically symmetrical around inter-nuclear axis are called s - molecular orbitals. The molecular orbital formed by the addition of 1s orbitals is designated as s 1s and the molecular orbital formed by subtraction of 1s orbitals is designated as s*1s (Fig 20) . Similarly combination of 2s orbital results in the formation of two s - molecular orbitals designated as s2s and s*2s as illustrated in Fig 22.
Fig 22 Molecular orbitals formed by
addition and subtraction of 2s-orbitals
They differ from s1s and s*1s MOs with regard to their size only,
Combination of p-atomic orbitals
There are three p-atomic orbitals represented as Px, Py, and Pz. As a convention, the Z-axis is taken as the internuclear axis. The X- and Y-axes would then be perpendicular to the nuclear line. The combination of two Pz atomic orbitals belonging to different nuclei would give a sigma bonding molecular orbital, represented as s2Pz and sigma anti-bonding molecular orbital s*2Pz. The combination of two Px atomic orbitals or two Py atomic orbitals on the other hand would give rise to pi-Bonding Molecular orbitals represented as : p2Px and p2Py and pi-antibonding Molecular Orbitals represented as : p*2Px and p*2Py. The region of overlapping of pi MOs is at right angles to the molecular axis ie., Z-axis.
The formation of s2Pz BMO by linear additive combination of two Pz atomic orbitals is represented in the Fig 23. The thick dots represent the nuclei.
Fig 23 Formation of s(2Pz) BMO by the linear additive combination of two Pz atomic orbitals.
In this combination, the positive lobes of two AOs overlap so that the electron charge density between the two nuclei is enhanced. The nuclei are thus well shielded from each other since the repulsion between the nuclei in such case is minimum, the energy of the MO is lower than the energy of any atomic orbitals which have gone into its formation.
The corresponding ABMO is obtained by the linear subtractive combination of two Pz atomic orbitals , as represented in the following figure (Fig 24).
Fig 24 Overlapping of two Pz atomic orbitals by the linear subtractive combination to form an s*(2Pz) ABMO orbital.
COMBINATION OF Px AND Py ORBITALS
Suppose a Px orbital of an atom overlaps with a Px orbital of another atom. The overlap would be positive , but it would be side to side and not end to end as in the case of Pz orbitals. The resulting molecular orbitals will , thus be called pi-molecular orbitals. The formation of the BMO designated as p(2Px) and is shown in Fig 25.
Fig 25 Overlapping of two Px AO’s formed by
linear additive combination to give p2Px BMO
The corresponding ABMO formed by linear subtractive combination of Px AOs designated as p*2Px is shown in Fig.
Fig 26 Overlapping of two Px AO's by linear subtractive combination to give p*2Px ABMO.
The energy of the anti-bonding molecular orbital would be high because the similarly charged nuclei are not effectively screened by the electronic charge and therefore repel each other considerably.
The formation of p2Py BMO and p*2Py ABMOs is similar to the formation of p2Px and p*2Px MOs. The only difference is that the AOs which combine and MOs which are formed now lie perpendicular to the plane of the paper.
ENERGY LEVEL DIAGRAM FOR MOLECULES
The combination of two 1s atomic orbitals of atoms form two new molecular orbitals designated as s1s and s*1s. In the same manner , the 2s and 2p atomic orbitals ie., eight atomic orbitals of two atoms give rise to eight new molecular orbitals viz.,
s2s , s*2s; p2Px, p*2Px ; p2Py , p*2Py ; s2Pz ; s*2Pz.
The increasing order of energies of various molecular orbitals are given below.
s1s , s*1s ; s2s , s*2s; s2Pz ; p2Px = p2Py ; p*2Px =p*2Py ; s*2Pz.
The molecular orbital energy diagram for homonuclear diatomic molecules like H2, H2+, He2, He2+, Li2, Be2, O2 , F2 and Ne2 is given in Fig 27 .
Fig 27 Molecular Energy Level Diagram for
Diatomic Molecules such as O2, F2 etc.
However, the given sequence of energy levels of molecular orbitals is not correct for all molecules. For instance , it has been observed experimentally that in some diatomic molecules such as B2 , C2 , N2 etc, the molecular orbital energy level diagram shown in Fig 28 is followed.
Fig 28 Molecular Orbital Energy Level Diagram for Diatomic Homonuclear molecules such as B2, C2, N2 etc.
Note
The order for writing molecular orbital configurations of B2 , C2 and N2 molecules can be understood in terms of electron-electron or orbital-orbital interactions which come into play during overlap of orbitals. Thus, owing to these interactions the energy level diagram is modified. Due to the close proximity of 2s and 2Pz orbitals , s2s , s*2s and s*2Pz. orbitals undergo mixing interactions in view of which the energy of s2Pz orbitals is raised and it becomes greater than p2Px and p2Py which do not experience these intermixing interactions.
It may be noted that following N2, the next molecules O2 and F2 do not exhibit these interactions. It is presumably because of large difference of energy between their 2s and 2Pz orbitals ,such intermixing is insignificant. The fact is also supported by spectroscopic measurements.