The optimized geometry as obtained from molecular mechanics method of platinum(II) chloride is given below ( Figure 1 ).

The MOs of this molecule are formed by linear combination of nineorbitals (five 4d-orbitals, one 5s orbital and three 5p orbitals) from platinum and four orbitals (three 3p orbitals and one 3s orbital) from each chlorine atom as shown below

Pt-1 = 5dx^2_y², 5dz², 5dxy, 5dxz, 5dyz, 6s, 6px, 6py, 6pz = 9AOs

Cl-2 = 3s, 3px, 3py, 3pz = 4AOs

Cl-3 = 3s, 3px, 3py, 3pz = 4AOs

Total = 17AOs

In order to examine the contribution of various AOs in the formation of MOs the LCAO has been made. The 17 AOs on LCAO approximations give 17 MOs. The various AOs are represented by ‘χ’ and MOs by ‘f’. Thus, χ₁ − χ₉ are AOs of platinum (χ₁ = 6s, χ₂ = 6px, χ₃ = 6py, χ₄ = 6pz, χ₅ = 5dx² − y², χ₆ = 5dz², χ₇ = 5dxy, χ₈ = 5dxz, χ₉ = 5dyz) and χ₁₀ − χ₁₇ are AOs of chlorine (χ₁₀ = 3s, χ₁₁ = 3px, χ₁₂ = 3py, χ₁₃ = 3pz for Cl-2 and χ₁₄ = 3s, χ₁₅ = 3px, χ₁₆ = 3py, χ₁₇ = 3pz for Cl-3). The magnitude of contribution of various AOs (χ) in the formation of 17 MOs (f₁ to f₁₇) is demonstrated in Table 1(a) . A close look at this table reflected that seven AOs (χ₂, χ₃, χ₄, χ₈, χ₉, χ₁₃, χ₁₇) have no contribution in the formation of 1^st MO (f₁) as these have zero coefficient values. And the rest ten AOs (χ₁, χ₅, χ₆, χ₇, χ₁₀, χ₁₁, χ₁₂, χ₁₄, χ₁₅, χ χ₁₅) have their contribution in f₁. By adopting same view the contributions AOs in f₂ to f₁₇ MOs can be describe.

The optimized geometry ( Figure 2 ) as obtained from molecular mechanics method of platinum (II) bromide is given below.

The MOs of this molecule as formed by linear combination of nine orbitals (five 4d-orbitals, one 5s orbital and three 5p orbitals) from platinum and four orbitals (three 3p orbitals and one 3s orbital) from each bromine are shown below:

Pt-1 = 5dx² − y², 5dz², 5dxy, 5dxz, 5dyz, 6s, 6px, 6py, 6pz, = 9

Br-2 = 4s, 4px, 4py, 4pz = 4

Br-3 = 4s, 4px, 4py, 4pz = 4

Total = 17

In order to examine the contribution of various atomic orbitals in the formation of molecular orbitals the LCAO has been studied. The 17 AOs on LCAO approximations give 17 MOs. Thus, χ₁–χ₉ are AOs of platinum (χ₁ = 6s, χ₂ = 6px, χ₃ = 6py, χ₄ = 6pz, χ₅ = 5dx² − y², χ₆ = 5dz², χ₇ = 5dxy, χ₈ = 5dxz, χ₉ = 5dyz) and χ₁₀ – χ₁₇ are AOs of chlorine (χ₁₀ = 3s, χ₁₁ = 3px, χ₁₂ = 3py, χ₁₃ = 3pz for Br-2 and χ₁₄ = 3s, χ₁₅ = 3px, χ₁₆ = 3py, χ₁₇ = 3pz for Br-3).The magnitude of contribution of various AOs (χ) in the formation of 17 MOs (f₁ to f₁₇) is demonstrated in Table 1(b) . A close look at this table reflected that six AOs (χ₂, χ₃, χ₄, χ₉, χ₁₃, χ₁₆) have no contribution in the formation of 1^st MO (f₁) as these have zero or near zero coefficient values. And the rest eleven AOs (χ₁, χ₅, χ₆, χ₇, χ₈, χ₁₀, χ₁₁, χ₁₃, χ₁₄, χ₁₅, χ₁₇) have their contribution inf₁. By adopting same view the contributions AOs in f₂ to f₁₇ MOs can be describe.

The optimized geometry ( Figure 3 ) as obtained from molecular mechanics method of platinum(II) bromide is given below.

The MOs of this molecule as formed by linear combination of nine orbitals (five 4d-orbitals, one 5s orbital and three 5p orbitals) from platinum and four orbitals (three 3p orbitals and one 3s orbital) from each bromine are shown below

Pt-1 = 5dx^2_y², 5dz², 5dxy, 5dxz, 5dyz, 6s, 6px, 6py, 6pz, = 9

I-2 = 4s, 4px, 4py, 4pz = 4

I-3 = 4s, 4px, 4py, 4pz = 4

Total= 17

In order to examine the contribution of various atomic orbitals in the formation of molecular orbitals, the LCAO has been studied. The 17 AOs on LCAO approximations give 17 MOs. Thus, χ₁–χ₉ are AOs of platinum (χ₁ = 6s, χ₂ = 6px, χ₃ = 6py, χ₄ = 6pz, χ₅ =5dx² − y², χ₆ = 5dz², χ₇ = 5dxy, χ₈ = 5dxz, χ₉ = 5dyz) and χ₁₀ – χ₁₇ are AOs of chlorine (χ₁₀ = 3s, χ₁₁ = 3px, χ₁₂ = 3py, χ₁₃ = 3pz for I-2 and χ₁₄ = 3s, χ₁₅ = 3px, χ₁₆ = 3py, χ₁₇ = 3pz for I-3). The magnitude of contribution of various AOs (χ) in the formation of 17 MOs (f₁ to f₁₇) is demonstrated in Table 1(c) . A close look at this table reflected that seven AOs (χ₂, χ₃, χ₄, χ₉, χ₁₂, χ₁₃, χ₁₆) have no contribution in the formation of 1^st MO (f₁) as these have zero or near zero coefficient values. And the rest ten AOs (χ₁, χ₅, χ₆, χ₇, χ₈, χ₁₀, χ₁₁, χ₁₄, χ₁₅, χ₁₇) have their contribution in f₁. By adopting same view the contributions AOs in f₂ to f₁₇ MOs can be describe.

The optimized geometry ( Figure 4 ) as obtained from molecular mechanics method of platinum(II) fluoride is given below.

The MOs of this molecule as formed by linear combination of nine orbitals (five 4d-orbitals, one 5s orbital and three 5p orbitals) from platinum and four orbitals (three 2p orbitals and one 2s orbital) from each bromine are shown below

Pt-1 = 5dx² − y², 5dz², 5dxy, 5dxz, 5dyz, 6s, 6px, 6py, 6pz, = 9

F-2 = 2s, 2px, 2py, 2pz = 4

F-3 = 2s, 2px, 2py, 2pz = 4

Total = 17

In order to examine the contribution of various atomic orbitals in the formation of molecular orbitals the LCAO has been studied. The 17 AOs on LCAO approximations give 17 MOs. Thus, χ₁–χ₉ are AOs of platinum (χ₁ = 6s, χ₂ = 6px, χ₃ = 6py, χ₄ = 6pz, χ₅ = 5dx² − y², χ₆ = 5dz², χ₇ = 5dxy, χ₈ = 5dxz, χ₉ = 5dyz) and χ₁₀ − χ₁₇ are AOs of chlorine (χ₁₀ = 3s, χ₁₁ = 3px, χ₁₂ = 3py, χ₁₃ = 3pz for F-2 and χ₁₄ = 3s, χ₁₅ = 3px, χ₁₆ = 3py, χ₁₇ = 3pz for F-3). The magnitude of contribution of various AOs (χ) in the formation of 17 MOs (f₁ to f₁₇) is demonstrated in Table 1(d) . A close look at this Table 1(d) reflected that nine AOs (χ₂, χ₃, χ₄, χ₇, χ₉, χ₁₂, χ₁₃, χ₁₆, χ₁₇) have no contribution in the formation of 1^st MO (f₁) as these have zero or near zero coefficient values. And the rest eight AOs (χ₁, χ₅, χ₆, χ₈, χ₁₀, χ₁₁, χ₁₄, χ₁₅) have their contribution in f₁. By adopting same view the contributions AOs in f₂ to f₁₇ MOs can be describe.

The characteristics of transition metal (TM) elements are due to their d orbitals of (n − 1) shell and s and p orbitals of n shell. When atom of TM elements form compound they adopted either concept of bonded attraction and non-bonded repulsion of VB (Valence Bond) theory, and or positive and negative overlap populations of MO (Molecular Orbital) theory. In the first case they may undergo various type of hybridization that depends upon the oxidation state of TM and number and nature of combing atoms or ions, and in the second case formation of molecular orbital by LCAO approximation. At first we have to examine the extent of involvement of 4d, 5s and 5p AOs of Pt-1 in the formation of MOs in platinum dihalides. For this, values of coefficient ‘χ’ of 5d_z², 5d_xy, 5d_xz, 6s, 6p_x, 6p_y and 6p_z have been separately tabulated for each MO for each platinum halides and are given in Table 2(a)-(d) , respectively. The ‘χ’ of non-bonding orbitals 5d_x2−y2(χ₅) and 5d_yz(χ₉) are excluded. To see the total involvement of seven AOs of Pt-1 in twelve MOs (f₁ − f₁₂), the coefficient value of each orbital has been added. The five vacant MOs (f₁₃ − f₁₇) are exempted here, as there is only 24e⁻ to be filled by Aufbau principle, Hund’s rule and Pauli’s exclusion principle and thus we

considered only twelve MOs among seventeen MOs. The summation values of AOs in these twelve MOs have been placed at the bottom of each table ( Table 2(a)-(d) ), which clearly reflects maximum involvement is of 5d orbital. Next to this is 5s orbital. It is also predicted from the summation values of d orbital. The non-bonding orbitals must have lowest summation values (Σdx² – y² = 0.9656 and Σdyz = 1.0646 in PtCl₂, Σdx² – y² = 1.2117 and Σdyz = 1.1479in PtBr₂, Σdx² – y² = 1.2141 and Σdyz = 1.1467 in PtI₂ and Σdx² – y² = 0.8010 and Σdyz = 1.1210 in PtF₂). The involvement of three p orbitals are negligible as their summation values are very low in comparison to d orbital and considerably low with respect to s orbital.

From Table 2(e) and Figure 5 , it is evident that the involvement of 5p orbital in Pt-X bond is insignificant and the main role is played by ‘ns’ and (n − 1)d orbital. It was Landis, who discovered sdⁿ-hybridization (n = 1 to 5) along with molecular shape and bond angles in his seminal publications. Further, he also explained co-relationship between sdⁿ-hybridization and its bond angle by plotting a graph between energy and bond angle as shown in Figure 6 . This figure reflected that bond angle has two minima one below 90˚ and one above 90˚. This is because the energy curves are function of the bond angles. The bond angles as presented in Figure 1 that also hold up Landis concept sdⁿ hybridization when n = 1. Landis recommended that transition metals in their valency shell can accommodate only 12e⁻ (10e⁻ in five (n − 1)d orbitals and 2e⁻ in one ns-orbital). The 18e⁻ can be in their valency shell (10e⁻ in five (n − 1)d orbitals, 2e⁻ in one ns-orbital and 6e⁻ in three np orbitals). Further, a close look at the Table 2(e) and right side of the curves of Figure 1 clearly demonstrated that the summation values are highest in case of iodide and lowest in chloride. This is due to cloud expending of halides. For a given metal ion, the ability of ligands to induce this cloud expending increases according to nephelauxetic series: F⁻ < H₂O < NH₃ < en < ox < SCN < Cl⁻ < CN⁻ < Br⁻ < I⁻. Thus, iodide produces greater cloud expanding effect than bromide, which inturn produces higher than chloride in platinum diiodide, platinum dibromide and platinum dichloride, respectively. In other words the effective positive charge on Pt(II) is reduced greater by iodide and lesser by chloride. This result is in good agreement with nephelauxetic series of ligands [43] . This effect can further be related with difference in energy level of ns and np orbitals. These two orbitals differ in energy significantly. The energy difference ∆ε in s and p orbitals of chloride, bromide and iodide are not same. The s and p orbitals in iodide are close as compared to s and p orbitals of bromide and chloride, as shown below.

Iodide, in which s and p orbitals are much close causes greater nephelauxetic effect and thus increases the covalent bond character in the molecule. Percentage of ionic and covalent bond character of PtCl₂, PtBr₂ and PtI₂ has been calculated by solving equation “% ionic character = 16 × ∆χ + 3.5 × (∆χ)²”, and results are shown below:

The result is in good agreement with experiment results that covalent character increases in the order: PtI₂ > PtBr₂ > PtCl₂ > PtF₂.

The shape of each MO (f₁ − f₁₇) has been determined by the relative magnitudes and signs of the different coefficients [38] . For this the Pt(II)X₂ has been decomposed into three parts: Pt-1, X − 1 and X − 2, and the MO of the complete system has been obtained by allowing the orbitals of Pt − 1 (5d, 6s, 6p), X − 1 (ns and np) and X − 2 (ns and np) to overlap. The possible overlaps between the various AOs of platinum (Pt − 1) and halogens (X − 2 and X − 2) in each MO will be 88, as describes. To solve Equation (3) for these 88 overlapsin MOs of platinum dihalides, we need eigenvector values ( $c_{ri}$ and $c_{si}$), values of overlap matrix ( $S_{rs}$) and number of electrons ( $n_i$) in each MO. The eigenvector and overlap integral values for platinum dihalides have been taken from Table 1(a)-(d) and Table 3(a)-(d) , respectively. The number of electrons is taken as two for f₁ to f₁₂ and zero for f₁₃

Table 3. (a) Overlap matrix or overlap integrals values (S_rs) of various overlaps of atomic orbitals of constituent atoms in PtCl₂; (b) Overlap matrix or overlap integrals values (S_rs) of various overlaps of atomic orbitals of constituent atoms in PtBr₂; (c) Overlap matrix or overlap integrals values (S_rs) of various overlaps of atomic orbitals of constituent atoms in PtI₂; (d) Overlap matrix or overlap integrals values (S_rs) of various overlaps of atomic orbitals of constituent atoms in PtF₂.

to f₁₇. Finally, Equation (3) has been solved for twelve MOs with respect to each halide. In order to get a precise description, the sums of overlap population for the eleven MOs of platinum halides have also been worked out and results are presented in Table 4(a)-(d) . As can be seen from the table that among the twelve molecular orbital, eight are bonding, two are nonbonding and two are antibonding. The bonding molecular orbitals are f₁ − f₈. The nonbonding molecular orbital are f₉ and f₁₀, which are purely two d atomic orbitals of platinum namely dx² − y² and dyz. The antibonding molecular orbital are f₁₁ − f₁₂. A comparative study of Table 4(a)-(d) reflected that in all cases the non-bonding electrons are present in 9^th and 10^th molecular orbitals. Further, similarity in positions of nonbonding molecular orbitals prompted us to examine the eigenvalues of Pt⁺² ion and to compare them with the eigenvalues of the halides. The eigenvalues of the molecular orbitals of all the halides are included in Table 5 , which shows that nonbonding orbitals are degenerate in all the cases.