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 LUMO –ε 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].