3. Result and discussion
In the present investigation, all probable structures of Pt(CN)n complexes (n = 1–6) were modelled using the GaussView 6 software [55]. The cyanide (CN) moiety is an ambient ligand which interacts with Pt atom through two well–known mechanisms. One of them is through the formation of platinum cyanide complex, in which, C atom of CN moiety bonds with Pt producing Pt–C≡N. The other one is through creation of platinum iso–cyanide cluster, where, N atom of CN moiety is directly bonded with Pt atom forming Pt–N≡C. Optimization studies on these isomers indicate that platinum cyanide (PtCN) has lower energy as compared to platinum iso–cyanide complex (PtNC). Hence, the present investigation is primarily focussed towards the study of molecular species containing cyanide (CN) pseudohalogen ligand. The initial geometrical structures of Pt(CN)n neutral complexes (n = 1–6) containing these cyanide (CN) pseudohalogen ligands were optimized using the Gaussian 16W software [54]. The final optimized structures of Pt(CN)n neutral complexes (n= 1–6) are shown in Figure 1. It was observed that these complexes have structures similar to those of PtFn and PtCln (n = 1–6) complexes [42]. Figure 2 displays optimized geometries of their corresponding anionic complexes along with the bond lengths. On comparing Figures 1 and 2, it was observed that the anionic forms of Pt(CN)ncomplexes have geometries similar to neutral complexes with some variations in bond angles and bond lengths. In these complexes, electron configuration of Pt, i.e., [Xe] 4f145d9 6s1 provides a normal valence of 1 which can exceed upto 4 as observed in platinum dioxide (PtO2) also known as Adams’ catalyst [57]. A compound of Pt in higher oxidation state of 6 (PtF6) has also been chemically synthesized [58], however, it is unstable. In view of these facts, present investigation also aims at exploring the stability of higher order Pt(CN)n complexes (4 ≤n ≤ 6) in addition to the lower order complexes (n< 4). In the case of Pt(CN)6, optimization study in the singlet state reveals that after energy minimization, the geometry defaults to a structure similar to n = 4 type of Pt(CN)n complex and NC=CN fragment as provided in the Supporting information sheet (Figure 1S). The complex was then re–optimized in the triplet state providing a stable minimum energy structure. The final obtained geometry of Pt(CN)6 after optimization in triplet state has been included in this work.
It may be observed from Figure 1 that the length of C–N bonds in Pt(CN)n complexes generally lies in the range 1.16 – 1.18 Å. These values are in agreement with the calculated value of C–N bond length in free CN moiety. Hence, it may be inferred that the structure of CN moiety is unaffected when it binds with Pt atom. Pt has oxidation state +1 in Pt(CN) forming a closed shell without any ability to acquire further charge. In the case of Pt(CN)2 complex, a bent structure was found to represent the global minimum on potential energy surface (PES). Optimization of Pt(CN)3 and Pt(CN)3¯ complexes provide structures which are approximately in the shape of letter T. In Pt(CN)3 complex, length of Pt–C bonds, which are part of the horizontal arms of the T–shaped structure were equal to 1.98 Å. The enclosed C–Pt–C bond angle in this arm was 158.6º. However, length of Pt–C bond in vertical arm of T–shaped structure was 1.87 Å. It implies that the bonding between Pt and C is stronger in vertical arm as compared to the horizontal side–arms. Similar observations have been made by Samanta et al. [15] while studying Au(CN)ncomplexes. In the case of anionic structure of Pt(CN)3¯, length of Pt–C bonds in the horizontal arms of T–shaped structure were 2.01 Å, whereas, C–Pt–C bond angle was found to be 172.8° (Figure 2). These differences in structural parameters of Pt(CN)3and Pt(CN)3¯ complexes may be explained by the fact that, in anionic form, the extra electron is delocalized over the entire complex. The Pt(CN)4 complex (Figure 1) exhibits a distorted square geometry in which the C–N bonds are inclined at certain angles with respect to each other. In this structure, one pair of C–N bonds have lengths of 2.01 Å and the enclosing C–Pt–C angle has a value of 172.1°. The other pair of C–N bonds have lengths of 1.92 Å with an associated C–Pt–C angle of 95.6°. Similarly, Pt(CN)5 complex also doesn’t have symmetry and it consists of four CN moieties lying in a horizontal plane, whereas, the fifth CN moiety is attached vertically to this plane. In this complex, bond lengths of Pt–C bonds lying in the horizontal plane varies in the range 2.01–2.04 Å, whereas, Pt–C bond in vertical plane has length of 1.92 Å. In the case of Pt(CN)6, inner d subshell combines with the valence s and p subshells, which, plays an important role in defining the final structure of complex. These hybridized orbitals of Pt have the ability to display an oxidation state of +6 leading to the formation of Pt(CN)6 complex.
Relative stabilities of Pt(CN)n complexes can be determined by calculating their dissociation energies for fragmentation into Pt(CN)n –1 + CN, and Pt(CN)n –2 + (CN)2, which are termed as CN and (CN)2 decay channels respectively. Dissociation energies for neutral and anionic complexes are denoted by the terms ΔEn and ΔEn ¯ respectively. Table 1 presents the values of ΔEnand ΔEn ¯ calculated by utilizing the following expressions:
ΔEn = – {E[Pt(CN)n ] – E[Pt(CN)n–m ] – E[(CN)m ]}, m = 1,2 (1)
ΔEn ¯ = – {E[Pt(CN)n ¯] – E[Pt(CN)n–m ¯] – E[(CN)m ]}, m = 1,2 (2)
Analysis of Table 1 indicates that neutral and anionic Pt(CN)n complexes are in general stable towards dissociation in CN pathway. ΔEn values (CN channel) exhibit a general trend of successive decrease for neutral complexes with increasing values of n , except for the case ofn = 4. Relative stability of these complexes has also been studied by using the principle of maximum hardness [59]. According to this principle, absolute hardness (η ) is defined by the expression [42]
η = (ε LUMOε HOMO)/2. (3)
In above equation, η represents a measure for determining stability of chemical complexes. The complex having the highest value ofη is expected to be most stable. ε HOMO andε LUMO represent the energies of highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) respectively. Using Figure 3 the variation of η with respect ton can be ascertained for neutral Pt(CN)ncomplexes. Analyzing the figure, it may be observed that, Pt(CN)6 complex is most stable as per theprinciple of maximum hardness [59]. The HOMO and LUMO plots of Pt(CN)6 complex are shown in Figure 4. The GaussSum 2.2 [56] program has been used to determine the percentage (%) contribution of Pt, C and N atoms towards the LUMO and HOMO of the complexes. The calculated % atomic contribution values for the different complexes are shown in Table 2. The corresponding partial density of states spectra (PDOS) of Pt(CN)n neutral complexes (n = 1–6) denoting the % contribution of different atoms in the molecular orbitals are depicted in Figures 2S(A) – (F) of Supporting information sheet.
Electron affinity (EA) of a compound represents its capability to accept an electron leading to the formation of an anion. In the current investigation, variation of EA values of Pt(CN)ncomplexes versus the number of CN moieties has been plotted in Figure 5. The CN moieties have high EA, which enables them to withdraw electrons from Pt in the Pt(CN)n complexes, providing it with a positive charge. Hence, Pt(CN)n complexes (n ≥ 2) show EA values greater than EA value of chlorine (Figure 5). It may also be observed from Figure 5 that, EA values of Pt(CN)n complexes with n ≥ 5, are higher than even twice the EA value of Cl atom. This observation allows the authors to safely assign Pt(CN)n complexes withn ≥ 2 to the category of superhalogens. Their EA values are also found to be comparable with the EA values of PtFncomplexes [42]. The highest EA value of 7.922 eV was obtained for Pt(CN)6. Figure 5 shows an increasing trend of EA values as the number of cyanide moieties increases in Pt(CN)n complexes, except for the case of Pt(CN)4, where, the EA value shows an abrupt lowering. Deviation in EA value from the general trend in case of Pt(CN)4 maybe understood from the fact that platinum has general tendency to exist in oxidation states +2 and +4. The oxidation state +3 for Pt is rare and considered to be unstable. In this state platinum compounds have higher capability of accepting an electron due to unstable nature. Hence, Pt(CN)3 displays an EA value higher than the general trend and thus, EA value of Pt(CN)4 in comparison appears to be lowered.
Single halogen atoms can combine to form diatomic molecules such as Cl2, F2, etc. Since, superhalogens mimic the chemical behavior of halogens, they must also be able to form dimers. In order to probe this aspect of Pt(CN)nsuperhalogens, the authors have considered the test case of Pt(CN)4. Investigation on dimer of Pt(CN)4 superhalogens was conducted by choosing two initial geometries. In the first configuration, both complexes were positioned parallel to each other in such a manner that the Pt atom of one complex was closer to CN moieties of the other complex and vice versa. In the second configuration, planes of both complexes were set perpendicular to each other under the constraint that Pt and CN were adjacent to each other. After geometry optimization, it was observed that the first configuration had higher stability. Optimized geometrical structure of this stable configuration of dimer and corresponding HOMO and LUMO plots are shown in Figures 6 and 7 respectively. Stability of dimer was determined by analyzing normal mode frequencies, binding energies and HOMO–LUMO gaps. Frequencies corresponding to all the normal modes have real values. The binding energy of [Pt(CN)4]2 is 2.37 eV, which is greater than the binding energy of F2 molecule (1.21 eV) and also the binding energy of (PtF4)2i.e., 1.72 eV [42]. An interesting point to be noted from the HOMO and LUMO orbitals (Figure 7) is that they are distributed over the entire dimer.
In order to understand the nature of supersalts of Pt(CN)n superhalogen complexes, interaction between K and Pt(CN)4 was studied. An initial geometry consisting of K atom placed above the Pt atom of Pt(CN)4was provided to Gaussian 16W software for optimization. After geometry optimization, K atom was found to be displaced from its original position to a side position (Figure 8). Normal mode analysis predicted that all frequencies were real, so, the supersalt is expected to be stable. Figure 9 displays HOMO and LUMO of the supersalt K– Pt(CN)4. In this figure, it may be observed that both HOMO and LUMO are spread over the entire supersalt complex, except over the K atom. Similar study for the case of KF reveals that HOMO doesn’t contribute to K site, however, LUMO contribute to K site.
Superacidity properties of hydrogenated Pt(CN)ncomplexes represented as H–Pt(CN)n , have been analyzed for the corresponding energy minimum structures. These optimized structures of H–Pt(CN)n are displayed in Figure 10. In these hydrogenated Pt(CN)ncomplexes, bond length of Pt–CNH bond was found to have increased in comparison with Pt–CN bond. Bond length of H–CN bond in the species H–Pt(CN)n , for n = 2–6, lies in the range 0.99 – 1.0 Å, which is comparable with the bond length of H–CN in free state. These observations lead to the conclusion that HCN moiety weekly interacts with the central Pt atom in H–Pt(CN)n . In the protonated Pt(CN)n species, bond length of C–N bond is almost equal to the bond length of C–N bond in free cyanide molecule.
An important concept which has been widely accepted as a tool for prediction of relative strength of superacids is gas–phase acidity (GPA). GPA for a superacid can be obtained by calculating the changes in Gibbs’ free energies (∆Gdepro) due to deprotonation chemical reactions and is defined as 1/∆Gdepro. Researchers consider a molecular species to be in the category of superacids, if the ∆Gdepro value is less than 300 kcal/mol [27–29]. The calculated values of HOMO–LUMO energy band gap (∆Egap) and ∆Gdepro for H–Pt(CN)n species are listed in Table 3. ∆Gdepro has been calculated by utilizing the below mentioned equation:
ΔGdepro = ΔG [Pt(CN)n ¯] + ΔG [H+] – ΔG [H–Pt(CN)n ], (4)
where, ΔG denotes the change in Gibbs’ free energy which includes thermal enthalpy and entropy terms at 298.15 K. The value of G [H+] = –6.3 kcal/mol has been taken from literature [27,60]. From Table 3, it may be observed that the values of ∆Gdepro for H–Pt(CN)n , whenn = 2–6 are lower as compared to ∆Gdepro value of H2SO4 (302.2 kcal/mol) [26]. It may also be noted that, ∆Gdepro value of the strongest superacid HSbF6 is 255.5 kcal/mol [27]. The ∆Gdepro value of HSbF6 is 7.6492 kcal/mol and 4.6611 kcal/mol greater as compared to the corresponding values of H­–Pt(CN)5 and H–Pt(CN)6respectively. Hence, these two superacids viz. H­–Pt(CN)5 and H–Pt(CN)6 are predicted to be stronger than the strongest superacid HSbF6. ∆Gdepro values of H–Pt(CN)n forn = 2–6 are also found to be lower as compared to the corresponding values of H2SO4 [26], HNO3 [26] and HCl [25,61]. Hence, considering these results, it may be proposed that, superhalogen anions Pt(CN)n¯ with n = 2–6, can be used to develop a new class of superacids. Relative chemical reactivity of molecular species can be predicted through analysis of HOMO–LUMO energy band gap (ΔEgap) values provided in Table 3. It is interesting to note that, ΔEgap values of odd order superacids are greater than previous even order superacids. In Figure 11, the HOMO–LUMO plots for H–Pt(CN)5 are shown. From these plots, it is observed that, HOMO covers almost the entire complex except the HCN portion, however, LUMO is spread over the complete complex. It reinforces the fact that the nature of bonding is electrovalent.
In order to substantiate the current investigation, correlation plot of GPA (calculated as 1/∆Gdepro) of H–Pt(CN)n species versus vertical detachment energy (VDE) of corresponding Pt(CN)n¯ anions has been drawn as shown in Figure 12. VDEs of Pt(CN)n¯ anions have been calculated by using the following equation
VDE = E[Pt(CN)n ]SP – E[Pt(CN)n¯ ]Opt,
where, E[Pt(CN)n¯ ]Optrepresents the total energy of optimized anions and E[Pt(CN)n ]SP denotes the single point energies of neutral compounds whose structural parameters are same as that of corresponding optimized anion geometries [25]. In Figure 12, a linear relationship is found to exist for the best fit line between GPA (1/∆Gdepro) × 10–2(in eV–1) of H–Pt(CN)nspecies and VDE (in eV) of corresponding Pt(CN)n¯anions expressed in the form:
GPA (1/∆Gdepro) × 10–2 = 0.39898 × VDE + 5.96849.
The correlation coefficient r = 0.9834 calculated for the linear relationship suggests a strong positive linear relationship as described by Ratner [62].