It was Rosenberg, who accidentally found out the biological activity of cisplatin, i.e., cis-[Pt(NH₃)₂Cl₂] in 1965 [1] . Actually it was synthesized by Peyrone in 1844 [2] . The anti-tumor activity of square planar complexes (cis-[Pt(NH₃)₂Cl₂] and [Pt(en)Cl₂]) and octahedral complexes (cis-[Pt(NH₃)₂Cl₄] and [Pt(en)Cl₄]) against sarcoma-180 (in mice) and against murine leukemia (L-1210) cells were also discovered by Rosenberg [3] . Harder and Rosenberg reported selective inhibition of DNA synthesis in vitro by cis-[Pt(NH₃)₂Cl₂] below 5 μM [4] . Cisplatin was launched in 1978 as anticancer drug but it is still used for treatment of testicular [5] , ovarian [6] , bladder [7] and neck cancers [8] in humans. The activity of cis-[Pt(NH₃)₂Cl₂] against tumor is associated with reactions replacing the halides. The effective antitumor compounds have features in common that may aid us in understanding their interaction with biological systems [9] . These agents usually have two exchangeable ligands in cis positions. These complexes are bifunctional reagents that may undergo nucleophilic substitution at two cis positions ( Scheme 1 ), which assumes monomeric species and preservation of the cis configuration thermodynamically [10] . Prediction of atomic, molecular, electronic structure along with spectroscopic characteristic of metal complexes have always been challenging for computational chemists.

$\text{H}-6=1\text{s}=1$

$\text{H}-7=1\text{s}=1$

$\text{H}-8=1\text{s}=1$

$\text{H}-9=1\text{s}=1$

$\text{Cl}-10=3\text{s},3\text{px},3\text{py},3\text{pz}=4$

$\text{Cl}-11=3\text{s},3\text{px},3\text{py},3\text{pz}=4$

$\text{Total}=31$

In total thirty-one atomic orbital (AOs) are involved in the formation of thirty-one molecular orbitals (MOs). But here we discuss only seventeen MOs of one Pt²⁺ (9 MOs) and 2Cl⁻ (2 × 4 MOs), because we have to see the effect of cisplatin (Equation (1) and (2)) formation on these orbitals. The fourteen MOs of ligands 2NH₃ (2 × 7) are kept out of discussion (Equation (2)). The AOs are represented by “χ” and MOs by “f”. Here χ₁ to χ₉ are AOs of Pt and remaining eight AOs of two Cl by χ₂₄ to χ₃₁ viz., χ₁ (6s), χ₂ (6px), χ₃ (6py), χ₄ (6pz), χ₅ (5dx2-y2), χ₆ (5dz2), χ₇ (5dxy), χ₈ (5dxz), χ₉ (5dyz), χ₂₄ (3s), χ₂₅ (3px), χ₂₆ (3py), χ₂₇ (3pz), χ₂₈ (3s), χ₂₉ (3px), χ₃₀ (3py), and χ₃₁ (3pz). The form of the seventeen MOs i.e., the magnitude of contribution of various thirty-one AOs in the formation of seventeen MOs is demonstrated by ${\varphi }_1-{\varphi }_{17}$ as described below.

$\begin{array}{c}{\varphi }_1=-0.0031{\chi }_1+0.0247{\chi }_2-0.0014{\chi }_3+0.0004{\chi }_4+0.0013{\chi }_5+0.0113{\chi }_6\\ -0.0003{\chi }_7+0.0000{\chi }_8+0.0048{\chi }_9-0.0408{\chi }_{24}-0.0023{\chi }_{25}-0.0028{\chi }_{26}\\ +0.0006{\chi }_{27}-0.0386{\chi }_{28}-0.0017{\chi }_{29}+0.0032{\chi }_{30}-0.0006{\chi }_{31}\end{array}$

$\begin{array}{c}{\varphi }_2=+0.0000{\chi }_1+0.0018{\chi }_2+0.0282{\chi }_3-0.0061{\chi }_4-0.0025{\chi }_5+0.0001{\chi }_6\\ -0.0185{\chi }_7+0.0039{\chi }_8-0.0006{\chi }_9-0.0353{\chi }_{24}-0.0086{\chi }_{25}+0.0040{\chi }_{26}\\ -0.0012{\chi }_{27}+0.0339{\chi }_{28}+0.0090{\chi }_{29}+0.0026{\chi }_{30}-0.0010{\chi }_{31}\end{array}$

$\begin{array}{c}{\varphi }_3=-0.0414{\chi }_1+0.0102{\chi }_2-0.0007{\chi }_3+0.0001{\chi }_4+0.0009{\chi }_5+0.0178{\chi }_6\\ -0.0002{\chi }_7+0.0002{\chi }_8+0.0089{\chi }_9-0.6966{\chi }_{24}+0.0047{\chi }_{25}+0.0010{\chi }_{26}\\ -0.0003{\chi }_{27}-0.6987{\chi }_{28}+0.0045{\chi }_{29}-0.0016{\chi }_{30}0.0004{\chi }_{31}\end{array}$

$\begin{array}{c}{\varphi }_4=0.0000{\chi }_1+0.0010{\chi }_2+0.0139{\chi }_3-0.0035{\chi }_4-0.0055{\chi }_5+0.0002{\chi }_6\\ -0.0377{\chi }_7+0.0097{\chi }_8-0.0012{\chi }_9+0.7038{\chi }_{24}-0.0024{\chi }_{25}+0.0084{\chi }_{26}\\ -0.0022{\chi }_{27}-0.7020{\chi }_{28}+0.0035{\chi }_{29}+0.0080{\chi }_{30}-0.0021{\chi }_{31}\end{array}$

$\begin{array}{c}{\varphi }_5=-0.0044{\chi }_1-0.0028{\chi }_2+0.0005{\chi }_3-0.0001{\chi }_4+0.0723{\chi }_5+0.0022{\chi }_6\\ -0.0089{\chi }_7+0.0041{\chi }_8+0.0185{\chi }_9+0.0148{\chi }_{24}-0.0879{\chi }_{25}-0.0144{\chi }_{26}\\ +0.0053{\chi }_{27}+0.0120{\chi }_{28}-0.0732{\chi }_{29}+0.0226{\chi }_{30}-0.0082{\chi }_{31}\end{array}$

$\begin{array}{c}{\varphi }_6=-0.0001{\chi }_1-0.0001{\chi }_2-0.0005{\chi }_3-0.0004{\chi }_4+0.0025{\chi }_5+0.0004{\chi }_6\\ -0.0116{\chi }_7-0.0439{\chi }_8-0.0003{\chi }_9-0.0021{\chi }_{24}+0.0090{\chi }_{25}+0.0000{\chi }_{26}\\ -0.0078{\chi }_{27}+0.0030{\chi }_{28}-0.0146{\chi }_{29}+0.0035{\chi }_{30}-0.0082{\chi }_{31}\end{array}$

$\begin{array}{c}{\varphi }_7=+0.0006{\chi }_1+0.0006{\chi }_2+0.0002{\chi }_3+0.0000{\chi }_4+0.0065{\chi }_5+0.0150{\chi }_6\\ +0.0022{\chi }_7-0.0007{\chi }_8-0.0485{\chi }_9-0.0013{\chi }_{24}+0.0071{\chi }_{25}-0.0001{\chi }_{26}\\ -0.0135{\chi }_{27}-0.0049{\chi }_{28}+0.0246{\chi }_{29}-0.0037{\chi }_{30}+0.0189{\chi }_{31}\end{array}$

$\begin{array}{c}{\varphi }_8=-0.0000{\chi }_1-0.0001{\chi }_2+0.0022{\chi }_3-0.0005{\chi }_4+0.0008{\chi }_5-0.0003{\chi }_6\\ +0.0125{\chi }_7-0.0062{\chi }_8+0.0047{\chi }_9+0.0151{\chi }_{24}-0.0809{\chi }_{25}-0.0037{\chi }_{26}\\ +0.0043{\chi }_{27}-0.0130{\chi }_{28}+0.0700{\chi }_{29}-0.0103{\chi }_{30}+0.0049{\chi }_{31}\end{array}$

$\begin{array}{c}{\varphi }_9=-0.2285{\chi }_{1}0.0095{\chi }_2-0.0007{\chi }_3+0.0001{\chi }_4-0.0129{\chi }_5+0.1983{\chi }_6\\ +0.0002{\chi }_7+0.0004{\chi }_8+0.0830{\chi }_9+0.0582{\chi }_{24}-0.2540{\chi }_{25}+0.4471{\chi }_{26}\\ -0.1179{\chi }_{27}+0.0584{\chi }_{28}-0.3201{\chi }_{29}-0.4053{\chi }_{30}+0.1102{\chi }_{31}\end{array}$

$\begin{array}{c}{\varphi }_{10}=-0.0002{\chi }_1+0.0004{\chi }_2+0.0072{\chi }_3-0.0032{\chi }_4-0.0667{\chi }_5+0.0035{\chi }_6\\ -0.4884{\chi }_7+0.1179{\chi }_8-0.0154{\chi }_9-0.0315{\chi }_{24}+0.3166{\chi }_{25}-0.3364{\chi }_{26}\\ +0.0861{\chi }_{27}+0.0314{\chi }_{28}-0.3733{\chi }_{29}-0.2774{\chi }_{30}+0.0751{\chi }_{31}\end{array}$

$\begin{array}{c}{\varphi }_{11}=-0.0499{\chi }_1-0.0503{\chi }_2+0.0045{\chi }_3-0.0008{\chi }_4+0.2047{\chi }_5+0.0568{\chi }_6\\ -0.0235{\chi }_7+0.0039{\chi }_8+0.0673{\chi }_9-0.0049{\chi }_{24}-0.4321{\chi }_{25}-0.4140{\chi }_{26}\\ +0.0943{\chi }_{27}-0.0050{\chi }_{28}-0.3716{\chi }_{29}+0.4838{\chi }_{30}-0.1036{\chi }_{31}\end{array}$

$\begin{array}{c}{\varphi }_{12}=+0.0003{\chi }_1+0.0003{\chi }_2+0.0088{\chi }_3+0.0337{\chi }_4-0.0047{\chi }_5-0.0057{\chi }_6\\ -0.0475{\chi }_7-0.1928{\chi }_8+0.0136{\chi }_9+0.0001{\chi }_{24}+0.0042{\chi }_{25}+0.1744{\chi }_{26}\\ +0.6619{\chi }_{27}-0.0001{\chi }_{28}+0.0047{\chi }_{29}+0.1704{\chi }_{30}+0.6587{\chi }_{31}\end{array}$

$\begin{array}{c}{\varphi }_{13}=+0.0007{\chi }_1+0.0091{\chi }_2+0.1143{\chi }_3-0.0264{\chi }_4+0.0127{\chi }_5-0.0007{\chi }_6\\ +0.1100{\chi }_7-0.0106{\chi }_8+0.0007{\chi }_9-0.0092{\chi }_{24}+0.4776{\chi }_{25}-0.0380{\chi }_{26}\\ +0.0059{\chi }_{27}+0.0096{\chi }_{28}-0.4750{\chi }_{29}+0.0234{\chi }_{30}+0.0038{\chi }_{31}\end{array}$

$\begin{array}{c}{\varphi }_{14}=+0.0023{\chi }_1-0.0026{\chi }_2-0.0006{\chi }_3+0.0002{\chi }_4+0.0460{\chi }_5+0.0929{\chi }_6\\ -0.0040{\chi }_7-0.0164{\chi }_8-0.1961{\chi }_9-0.0003{\chi }_{24}+0.0225{\chi }_{25}-0.1648{\chi }_{26}\\ -0.6613{\chi }_{27}-0.0004{\chi }_{28}+0.0327{\chi }_{29}+0.1642{\chi }_{30}+0.6653{\chi }_{31}\end{array}$

$\begin{array}{c}{\varphi }_{15}=+0.0389{\chi }_1+0.1216{\chi }_2-0.0097{\chi }_3+0.0023{\chi }_4+0.0880{\chi }_5-0.1168{\chi }_6\\ -0.0104{\chi }_7+0.0042{\chi }_8-0.0156{\chi }_9+0.0022{\chi }_{24}-0.4134{\chi }_{25}+0.1078{\chi }_{26}\\ -0.0565{\chi }_{27}+0.0022{\chi }_{28}-0.4273{\chi }_{29}-0.0288{\chi }_{30}+0.0401{\chi }_{31}\end{array}$

$\begin{array}{c}{\varphi }_{16}=0.0001{\chi }_1+0.0062{\chi }_2+0.0621{\chi }_3-0.0141{\chi }_4+0.0019{\chi }_5-0.0013{\chi }_6\\ +0.0199{\chi }_7+0.0055{\chi }_8+0.0005{\chi }_9+0.0024{\chi }_{24}-0.3509{\chi }_{25}-0.5485{\chi }_{26}\\ +0.1439{\chi }_{27}-0.0025{\chi }_{28}+0.2486{\chi }_{29}-0.5891{\chi }_{30}+0.1558{\chi }_{31}\end{array}$

$\begin{array}{c}{\varphi }_{17}=+0.0011{\chi }_1-0.0007{\chi }_2-0.0022{\chi }_3+0.0152{\chi }_4+0.0128{\chi }_5+0.0317{\chi }_6\\ +0.2237{\chi }_7+0.9513{\chi }_8-0.0622{\chi }_9-0.0009{\chi }_{24}-0.0044{\chi }_{25}+0.0487{\chi }_{26}\\ +0.1590{\chi }_{27}+0.0011{\chi }_{28}+0.0071{\chi }_{29}+0.0501{\chi }_{30}+0.1586{\chi }_{31}\end{array}$

Here, the coefficient of χ is the eigenvector (taken from Table 1 ). The remaining fourteen MOs, f₁₈-f₃₁, were kept out of discussion as these remaining MOs have been formed by fourteen AOs of two NH₃ molecules as neutral ligands following Equation (1) and Equation (2), respectively. Equation (1) represents formation of molecular compound PtCl₂, which in Equation (2) complexes with 2NH₃ ligands and thus cisplain is formed. Hence, only seventeen MOs have been considered here.

${\text{Pt}}^{2+}+2{\text{Cl}}^{-}\to {\text{PtCl}}_2$ (1)

${\text{PtCl}}_2+2{\text{NH}}_3\to \text{cis-}\left[\text{Pt}{\left({\text{NH}}_{\text{3}}\right)}_{\text{2}}{\text{Cl}}_{\text{2}}\right]$ (2)

When platinum forms compound it adopts 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 [13] . In the first case platinum may undergo various types of hybridization that depend upon its oxidation state, and number and nature of combing atoms or ions [11] , and in the second case platinum forms molecular orbital by LCAO approximation [20] . In cisplatin, platinum acquires + 2 oxidation state that may neutralized by two chloride ion (2Cl⁻), while two neutral ammine ligands (2NH₃) complex through coordinate bonds by donating two pairs of its lone pair of electrons. At first, we have to examine the extent of involvement of 5d, 6s and 6p AOs of Pt-1 in the formation of MOs in cis-[Pt(NH₃)₂Cl₂]. For this, values of coefficient “χ” of 5d, 6s and 6p of platinum metal have been tabulated in Table 2 . To see the total involvement of seven AOs of Pt-1 in fourteen MOs (f₁-f₁₄), the coefficient value of each orbital has been added. The rest vacant MOs are exempted here, as there is only 28e⁻ to be filled by Aufbau principle, Hund’s rule and Pauli’s exclusion principle as described in our previous publication [14] and thus we considered only these MOs among seventeen MOs. The summation values of AOs in these fourteen MOs have been placed same table, which clearly reflects maximum involvement of 5d orbital. Next to this is 6s orbital. It is also predicted from the summation values of d orbital. The non-bonding orbital i.e., 5dxz must have the lowest summation value which is 0.0251. The involvement of three p orbitals is negligible as their summation values are very low in comparison to d orbital and considerably low with respect to s orbital (0.3315). From Table 2 and Figure 1 , it is evident that the involvement of 6p orbital in Pt—L bond in cis-[Pt(NH₃)₂Cl₂] is insignificant and the main role is played by “ns” and (n-1)d orbital. It was Landis, who discovered sdⁿ-hybridization (here n = 3) along with molecular shape and bond angles in his seminal publications [21] .

The shape of each MO (f₁-f₁₇) has been determined by the relative magnitudes and signs of the different coefficients. For this cis-[Pt(NH₃)₂Cl₂] 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 ruthenium (Pt-1) and halogens (X-2 and X-2) in each MO will be 88. After that overlap populations have been calculated by solving equation: $n_{r-s,i}=n_i\left(2c_{ri}{c}_{si}{S}_{rs}\right)$. To calculate overlap populations for 88 overlaps (overlap of 2NH₃ ligands have been excluded) in MOs of cis-[Pt(NH₃)₂Cl₂], 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 cis-[Pt(NH₃)₂Cl₂] have been taken from Table 1 and Table 3 , respectively. The number of electrons is taken as two for f₁ to f₁₄ and zero for f₁₅ to f₁₇. In order to get a precise description, the sums of overlap population for the fourteen MOs of cis-[Pt(NH₃)₂Cl₂] have also been worked out and results are presented in Table 4 . As can be seen from this table that among the fourteen molecular orbital, twelve are bonding, one is nonbonding and one is antibonding. The bonding molecular orbitals are f₁, f₃-f₅, f₇-f₁₄. The nonbonding molecular orbital is f₆, which is purely dxz atomic orbital of platinum. The antibonding molecular orbital is f₂.

MOs is molecular orbitals, BMO is bonding molecular orbital, ABMO is antibonding molecular orbital and NBO is nonbonding molecular orbitals.

Metallic complexes generally have two selective absorption bands [22] . The first lies in the visible region. First band is attributed to electron transitions in the unsaturated transition shell of the central ion. The complexes which co-ordinate only one kind of ligand should naturally have narrower, symmetrical first bands than those that have ligands of different kinds, and among the latter, those that have ligands situated far apart in the spectrochemical series should have broader and less symmetrical first bands and sometimes these bands may analyzed into two or more component. The second lies in the near ultra-violet region. The second band may be attributed to the co-ordination electrons, and is, therefore, the most general characteristic which a co-ordination compound should possess. Some complexes however, give the third band in the region of shorter wave-length. All the co-ordination compounds that have or seem to have at least a pair of negative ligands in tans-position showed the third bands ( Table 5 ), but none of those were deficient in the condition. Some of the co-ordinated compounds lack the first bands and most of them the third, they never fail to give the second bands. Cisplatin shows one absorption band ( Figure 2 ) as opted by Gaussian-03 [17] . The PBE1PBE functional is a hybrid density functional theory (DFT) method, and SDD (Stuttgart-Dresden) pseudopotentials are a type of pseudopotential used in DFT calculations to represent the interaction between the core and valence electrons. Using PBE1PBE functional with SDD pseudopotentials can be a computationally efficient and accurate way to model the electronic structure and properties of materials [23] . By RTD-pbe1pbe-FC method with sdd basis set was used to calculate the UV-Vis spectrum of cisplatin. Figure 2 reflects excitation energies and oscillator strengths. The band of absorption was recorded at 3.9845 eV with peak corresponded to 311.16 nm and shows oscillator strength 0.0014, as shown in Table 6 .

By default, the pbe1pbe functional and sdd pseudo-potentials were used to calculate IR-spectrum by Gaussian-03 ( Figure 3 ). The number of the normal vibrations of a single cisplatin molecule is 27, distributed in 9A₁ + 5A₂ + 8B₁ + 5B₂, as shown in Table 7 . The notations for modes used are ʋ-stretching, δ-bending, ρ-rocking, π-out of plane bending and τ-torsion; the “s” and “as” stands for symmetric and asymmetric, respectively, and the index “op” denotes out-of-plane, and TED for total energy distribution.

Following points have been reflected from the above study: 1) AOs analysis shows sd³-hybridization and thus supports Landis concept of sdⁿ-hybridization, where n = 3. The result showed involvement of three p orbitals is negligible as their summation values are very low in comparison to d orbital and considerably low with respect to s orbital. 2) In total thirty-one AOs are involved in the formation of thirty one MOs of cisplatin. As, there are only 28e⁻ to be filled, hence, we considered only fourteen MOs (f₁-f₁₄) and rest vacant MOs (f₁₅-f₃₁) have been exempted. Among fourteen MOs, twelve are bonding, one is antibonding (f₂) and one is non-bonding (f₆). 3) Cisplatin showed one absorption band at 3.9845 eV with peak corresponded to 311.16 nm of low oscillator strength (0.0014). 4) Cisplatin molecule showed 27 normal vibrations, which distributed in 9A₁ + 5A₂ + 8B₁ + 5B₂.

I am very thankful to Principal and Head of Department of Chemistry, Shia P. G. College, Sitapur Road, Lucknow-226020 (U.P.) for laboratory facilities and also to Department of Higher Education, Prayagraj, Uttar Pradesh for financial assistance (Letter No./Reginal Office Lucknow/5496-99/2021-22; Dated: 15-03-2022 and G.O. No.-107/2021/2584/70-4-2021-4(28)/2021; Dated: 28-12-2021).