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NPTEL – Chemistry and Biochemistry – Coordination Chemistry (Chemistry of transition elements) Coordination Chemistry: Bonding Molecular orbital theory K.Sridharan Dean School of Chemical & Biotechnology SASTRA University Thanjavur – 613 401 Page 1 of 14 Joint Initiative of IITs and IISc – Funded by MHRD NPTEL – Chemistry and Biochemistry – Coordination Chemistry (Chemistry of transition elements) Table of Contents 1 Molecular Orbital Theory ............................................................................................................. 3 1.1 Molecular orbital ............................................................................................................. 3 1.2 How to find the symmetries of the metal 3d, 4s and 4p orbitals? ........................................ 4 1.3 Why t2g orbitals do not overlap? ........................................................................................... 5 1.4 M.O. Diagram for an octahedral complex ............................................................................. 7 1.4.1 Magnetic and spectral properties of complexes based on this MO diagram ................ 7 1.5 M.O. diagram of a tetrahedral complex ................................................................................ 8 1.6 Square planar complex .......................................................................................................... 9 1.6.1 M.O. Diagram for a square planar complex ................................................................. 10 2. Pi bonding & M.O.Theory .......................................................................................................... 10 2.1 Types of π interactions ........................................................................................................ 11 2.2 Metal orbitals used for π‐complex in an octahedral complex ............................................ 11 2.2.1 PR3 ligand is stronger than NH3 .................................................................................. 13 2.2.2 Stabilization .................................................................................................................. 14 3 References .................................................................................................................................. 14 Page 2 of 14 Joint Initiative of IITs and IISc – Funded by MHRD NPTE EL – Chemistrry and Bioche emistry – Coo ordination Che emistry (Chem mistry of transsition eleme ents) 1 Molecula M r Orbita al Theory y 1.1 Molecula M ar orbital Mole ecular orbiitals are formed by y the ove erlap of a atomic orb bitals. The e numb ber of mo olecular orb bitals forme ed will be equal to tthe number of atomicc orbita als overlapping. One of o the mole ecular orbita als formed w will be lowe er in energyy comp pared to the e atomic orrbitals and the t other w will be highe er in energyy. The lower mole ecular orbita al is known as bonding orbital be ecause the electrons p present in it favorr bond form mation and the t other higher orbita al is known as antibon nding orbita al beca ause the ele ectrons pre esent in the ese orbitals will opposse bond formation. For an example, e let us consid der the form mation of h hydrogen m molecule (fo ormed) and d heliu um molecule e (not forme ed): σ* * HA σ HB H2 He e N No He2 He Bond d order = ½[number of electron ns in the b bonding orrbitals – nu umber of electrons in the antib bonding orbitals] Bond d order in hydrogen = ½[2-0] = 1; Bond d order in helium = ½[2-2] ½ =0 In th he case of complexes s, the meta al d-orbitalls and the ligand gro oup orbitalss (LGO Os) will ove erlap to form m the molec cular orbitalls. Exam mple: 3+ [Co(N NH3)6] . The metal atomic a orbitals involve d in formin ng the MOss are 3d, 4ss and 4p. The lig gand orbitals are the sp3 hybridized orbitalls on NH3. They form m ma bonds with w the mettal orbitals. sigm Page 3 of 1 14 Joint Initiative of IIT Ts and IISc – Funded by MHRD M NPTEL – Chemistry and Biochemistry – Coordination Chemistry (Chemistry of transition elements) It is important to note that the metal orbitals and the LGOs should have the same symmetry in order to overlap. 1.2 How to find the symmetries of the metal 3d, 4s and 4p orbitals? The symmetries of the metal atom orbitals can be found out from the Oh character Table 1.2.1. Oh A1g A2g Eg E 8C3 6C2 6C4 3C2 (=C42) 1 1 1 1 1 1 1 -1 -1 1 2 -1 0 0 2 T1g T2g A1u A2u Eu T1u T2u 3 1 1 2 3 6S4 8S6 3σh 6σd i 1 1 2 1 -1 0 1 1 -1 1 1 2 1 -1 0 0 -1 1 -1 3 1 0 -1 -1 0 1 1 -1 0 0 1 1 -1 0 -1 1 -1 1 -1 0 1 -1 -1 1 1 2 -1 -1 3 -1 -1 -2 -3 -3 -1 -1 1 0 -1 1 0 -1 -1 1 0 0 -1 -1 -1 -2 1 1 1 -1 1 0 1 -1 x2+y2+z2 (Rx,Ry, Rz) (2z2-x2y2, x2-y2) (xz,yz,xy) (x,y,z) The ‘s’ orbital is represented by x2+y2+z2 in the last column of the character table and its symmetry is A1g as shown by the first column of the character table. Hence, we say that the ‘s’ orbital transforms as a1g in an octahedral field. Similarly, the ‘p’ orbitals are represented by (x,y,z) in the last but one column of the Oh character table and their symmetry is T1u. Thus, we say that the ‘p’ orbitals transform as t1u in the octahedral field. Similarly, it can be seen that the dx2-y2 and dz2 orbitals transform as eg orbitals and dxy, dyz, and dzx orbitals transform as t2g orbitals. These can be summarized as follows: Page 4 of 14 Joint Initiative of IITs and IISc – Funded by MHRD NPTE EL – Chemistrry and Bioche emistry – Coo ordination Che emistry (Chem mistry of transsition eleme ents) Meta al atom orbiitals symm metry in an octahedrall field s a1g p t1u dxy, dyz, dzx t2g dx2-y y2, dz2 eg 1.3 Why t2g orbitals o do d not ove erlap? The LGOs will point alo ong the ax xes. Since the a1g orbital is sphericallyy symm metrical, it can overlap with LGO Os on all th he axes. Th he t1u and eg orbitalss have e their lobes s pointed on o the axes s and hence e can overlap with LG GOs leading g to bo ond formation. However, the t2g orbitals willl have their lobes in b between the e axes s and hence e cannot ov verlap with the t LGOs a as shown in n Figure 1.3 3.1: dx2-y2 dxy Fig F 1.3.1 eg and t2g 2 orbitals overla p with LGOs The LGOs and the symme etry matched metal ato om orbitals are shown in Figure 1.3.2 2.: Page 5 of 1 14 Joint Initiative of IIT Ts and IISc – Funded by MHRD M NPTEL – Chemistry and Biochemistry – Coordination Chemistry (Chemistry of transition elements) Fig 1.3.2 Metal atom orbitals and matching LGOs Page 6 of 14 Joint Initiative of IITs and IISc – Funded by MHRD NPTEL – Chemistry and Biochemistry – Coordination Chemistry (Chemistry of transition elements) 1.4 M.O. Diagram for an octahedral complex The M.O. diagram for an octahedral complex is shown in Figure 1.4.1. Fig 1.4.1 M.O. Diagram of σ-only octahedral complex M ML6 6LGOs 1.4.1 Magnetic and spectral properties of complexes based on this MO diagram [Co(NH3)6]3+ is diamagnetic and is explained as follows: Total number of electrons = 18; 6 electrons from Co3+ (3d6) and 12 electrons from the six NH3. These electrons are distributed to the MOs in the increasing order of energy of the orbitals. The arrangement is: (a1g)2 (t1u)6 (eg)4 (t2g)6. Here all the electrons are paired and hence the complex will be Page 7 of 14 Joint Initiative of IITs and IISc – Funded by MHRD NPTEL – Chemistry and Biochemistry – Coordination Chemistry (Chemistry of transition elements) diamagnetic. In this case, ∆o > pairing energy. Hence, pairing takes place readily and a diamagnetic complex results. [CoF6]3- is paramagnetic and is explained as follows: Totally 18 electrons; six from Co3+ (d6) and 12 electrons from six F-. The electrons are arranged as follows: (a1g)2 (t1u)6 (eg)4 (t2g)4 (eg*)2 (one electron in each of the two eg* orbitals). Here, ∆o < pairing energy. Hence, the electrons remain unpaired. Thus, MOT is able to explain the magnetic and spectral property of complexes. 1.5 M.O. diagram of a tetrahedral complex The symmetries of the metal atom orbitals are obtained from the Td character table. The ‘s’ orbital (x2+y2+z2) transforms as a1; dx2-y2 and dz2 transform as e; p orbitals (x,y,z) transform as t2 and dxy, dyz and dzx also transform as t2. The LGOs constructed from four ligands will consist of a t2 set and one orbital of a1 symmetry. The MO diagram is shown in Figure 1.5.1. Fig 1.5.1 M.O. diagram of a tetrahedral complex Page 8 of 14 Joint Initiative of IITs and IISc – Funded by MHRD NPTEL – Chemistry and Biochemistry – Coordination Chemistry (Chemistry of transition elements) 2- Example: [CoCl4] 7 Cobalt is in the +2 state and provides 7 electrons (d system) and four Cl- will provide 8 electrons. In total, there will be 15 electrons. They will be accommodated two electrons per orbital starting from the lowest orbital. The arrangement of electrons will be t26a12e4t2*3. 1.6 Square planar complex This has got D4h symmetry and the symmetry of the metal atom orbitals are derived from the D4h character table. Thus, the ‘s’ orbital (x2+y2) will transform as a1g; px and py orbital will transform as eu, pz orbital will transform as a2u, dz as b2g, dxz and dyz will transform as eg. Orbital s px and py pz symmetry a1g eu dz a2u a1g dxy b2g 2 dxz and dyz eg Page 9 of 14 Joint Initiative of IITs and IISc – Funded by MHRD NPTEL – Chemistry and Biochemistry – Coordination Chemistry (Chemistry of transition elements) 1.6.1 M.O. Diagram for a square planar complex M.O. diagram for a square planar complex is given in Figure 1.6.1.1 Fig 1.6.1.1 M.O.Diagram of square planar complex 2. Pi bonding & M.O.Theory Metal atom and ligand orbitals should have the proper symmetry for π bond formation in addition to energy. π bond has a nodal surface and this includes the bond axis. The π bonding orbital will have lobes of opposite sign on each side of this nodal surface. The important difference between a sigma and π bonding complex is that the metal as well as ligand orbitals will be perpendicular to the internuclear axis. Page 10 of 14 Joint Initiative of IITs and IISc – Funded by MHRD NPTEL – Chemistry and Biochemistry – Coordination Chemistry (Chemistry of transition elements) 2.1 Types of π interactions There are essentially four types, viz., (1) pπ-dπ (2) dπ-dπ (3) dπ- π* and (4) dπσ* (1) pπ-dπ complex Here, electrons are donated from the filled p-orbitals of the ligand to the empty d-orbitals of the metal. Examples for such ligands are: RO-, RS-, O2-, F-, Cl-, Br-, I-, R2N(2) dπ-dπ complex Here, electrons are donated from filled d-orbitals of the metal to the empty d-orbitals of the ligand. Examples: R3P, R3As, R2S (3) dπ- π* complex Here, electrons are donated from filled d-orbitals of the metal to the empty π - antibonding orbitals (π*) of the ligand. Examples: CO, RNC, pyridine, CN-, N2, NO2-, ethylene (4) dπ-σ* complex Here, electrons are donated from filled d-orbitals of the metal to the empty σ - antibonding orbitals (σ*) of the ligand. Examples: H2, R3P, alkanes 2.2 Metal orbitals used for π-complex in an octahedral complex As far as the LGOs are concerned, there will be four groups belonging to four symmetries, viz., t2g, t1u, t2u, and t1g. However, the transition metal will have a1g, t1u, t2g, and eg. Comparing these two, it is clear that the metal atom orbitals with t2g (dxy, dyz and dzx) and t1u (px, py, and pz) symmetries are suitable for πbonding. But the t1u orbitals point towards the ligands and hence form σbonds. Hence, only t2g orbitals are involved in π-bonds. The LGOs having the t2u, and t1g symmetries will remain non-bonding because there is no matching Page 11 of 14 Joint Initiative of IITs and IISc – Funded by MHRD NPTEL – Chemistry and Biochemistry – Coordination Chemistry (Chemistry of transition elements) symmetry in the metal atom orbitals. Example: [CoF6]3LGOs constructed from the fluorine 2p orbitals with t2g symmetry interact with t2g metal orbitals to form π bonding and antibonding MOs. The corresponding M.O.diagram is shown in Figure 2.2.1. Fig 2.2.1 M.O.diagram for a π-complex Fluorine is more electronegative than cobalt and has filled orbitals. Hence the orbitals are lower in energy than the metal d orbitals. Hence, the π-bonding MOs will resemble more closely the ligand orbitals than the metal orbitals. The antibonding π* orbitals resemble the metal orbitals more closely than the ligand orbitals. The electrons from the F- ligands (2p orbitals) will fill the t2g π-orbitals. The electrons from the metal d orbitals (t2g) will be present in the π* orbitals. Page 12 of 14 Joint Initiative of IITs and IISc – Funded by MHRD NPTEL – Chemistry and Biochemistry – Coordination Chemistry (Chemistry of transition elements) These new π* orbitals will be at a higher energy than the original t2g orbitals due to π-bonding. The eg* orbitals are not affected. Because of this new π* orbitals, Δo decreases. That is, the splitting will be less. This is the reason for the halides being the weak ligands in spectrochemical series in spite of their negative charges. 2.2.1 PR3 ligand is stronger than NH3 NH3 ligand can only donate electrons to the metal and cannot accept electrons from the metal because it has no d orbitals, while P in PR3 can accept electrons from metal because it has got empty d orbitals. The LGOs from this ligand will be having higher energy because the orbitals are empty and P is less electronegative than metal. This type of ligand is known is known as acceptor ligand. The MO diagram for this type of ligand is shown in Figure 2.2.1.1: *(t2g*) t2g eg eg*( *) t2g o (t2g) -complex -complex ligand -orbitals Fig 2.2.1.1 π-complex M.O.diagram for PR3 type ligands Page 13 of 14 Joint Initiative of IITs and IISc – Funded by MHRD NPTEL – Chemistry and Biochemistry – Coordination Chemistry (Chemistry of transition elements) The net effect is the increase in the splitting (Δo) and thus PR3 is stronger than NH3. 2.2.2 Stabilization The flow of electrons from metal to ligand stabilizes the complex when the metal is in the low oxidation state because the excess electron density built up around the metal due to σ-donation by ligands is removed. However, this back donation of electrons from metal to ligands does not stabilize the complex when the metal is in a higher oxidation state. 3 References 1. “Inorganic Chemistry: Principles of Structure and Reactivity”, James E.Huheey, Ellen A.Keiter, Richard L.Keiter, Okhil K.Medhi, Pearson Education, Delhi, 2006 Page 14 of 14 Joint Initiative of IITs and IISc – Funded by MHRD