Complex formation of titanocene dichloride anticancer and Al 12 N 12 nano-cluster: A quantum chemical investigation of solvent,temperature and pressure effects

Abstract

This study investigated the interaction between Al₁₂N₁₂ nano-cluster and titanocene dichloride anticancer drug complex using B3P86 functional in gas and solution phases. Non-covalent interaction (NCI) analysis of this complex was employed for illustration of the Cl⋯Al weak non-covalent interaction. The self-consistent reaction field theory (SCRF) based on the Polarizable Continuum Model (PCM) was applied for testing the solvent effects. The solvent effect on the interaction energy, dipole moment, frontier orbital energy, and global reactivity parameters was examined as well. The changes in the dipole moment, polarizability and electronic spatial extent (ESE) with solvent polarity were analyzed by applying different solvent polarity parameters based on Lippert-Mataga, Bakhshiev and Bilot-Kawski models. In addition, temperature and pressure effects on the thermodynamic parameters of this interaction were illustrated.

Keywords

titanocene dichloride Non-covalent interaction (NCI) analysis solvent effect pressure effect temperature effect

1 Introduction

The discovery of the anticancer activity of titanocene dichloride (namely bis(cyclopentadienly)titanocene dichloride, TiCl₂Cp₂, Cp =η ⁵–(C₅H₅)₂) dates back to 1980s; since then, many experimental studies have been done on it [1 –3]. While the outcomes of phase II clinical trials were not suitable because of the lack of activity against the investigated tumors, the reported significant investigations on titanium compounds, excited the attention in novel titanium compounds with anticancer properties [4 –7].

The action mechanism of the TiCl₂Cp₂ is unknown; initial studies recommended that it might be connected with the purine bases of DNA [8 –10]. Theoretical studies have been conducted on the hydrolysis chemistry of anticancer drug titanocene dichloride [11]. Later, more synthetic attempts have been done for boosting the cytotoxicity of titanocene dichloride derivatives [12 –14]. A novel process starting from titanium dichloride and fulvenes [15, 16] paved the way for directly accessing highly substituted ansa-titanocenes [17 –19].

Nano-structures such as fullerene hollow nano- clusters of elements other than carbon are favored due to their special electronic and optical properties [20 –29]. Group III-nitrides and Group V-nitrides rank among the most favorable nano-clusters [30 –32]. In this family, suitable applications have reported for AlN nano-clusters. These nano-clusters have shown thermodynamic stability, and high thermal conductivity and low electron affinity [33]. The investigation of Aluminum nitride nano-clusters (n = 2-41) showed that (AlN)₁₂ nano-cluster is energetically the most stable one, and can be reflected as an appropriated nano-cluster [34]. Al₁₂N₁₂ nano-cluster was used successfully in gas sensing and hydrogen storage [35]. Many researchers have evaluated the ability of carbon nanotubes (CNT) and nano-clusters for a drug delivery system development [36 –39]. Drug delivery is possible either through filling the inner space of the tubes with metals [40], porphyrins [41] and biomolecules [42] or by attaching proteins and compounds (via a specific adsorption or covalent bond) on their external surface. Other studies focused on loading a phenanthroline-based Platinum(II) complex onto the surface of a carbon nanotube via π–π Stacking [43]. A DFT investigation of the solvent effect, structures, properties, and topologies of the interaction between the C₂₀ Cage and cis-PtCl₂(NH₃)₂ has been reported [37].

Indeed, it is an advantage of preforming such theoretical works to investigate the characteristic features of matters especially those of nano-related complex systems, at the lowest possible molecular and atomic [44, 45].

This theoretical research studied the interaction between Al₁₂N₁₂ nano-cluster and titanocene dichloride in gas and solution phases. Differences in the frontier orbital energies were shown. It was tried to show that this interaction is dependent on the temperature and pressure.

2 Computational methods

Optimization and vibrational analysis were done with Gaussian 09 software package [46]. The standard 6-311G(d,p) basis set [47 –50] was considered in the calculations. The B3P86 functional was employed for geometry optimization [51, 52]. B3P86 defines clearly the same functional with the non-local correlation provided by Perdew 86. The identities of the optimized structures as an energy minimum were confirmed by vibrational analysis. Non-covalent interaction (NCI) analysis was performed by evaluating the reduced density gradient and low-gradient isosurfaces [53 –55]. NCI studies were performed on the optimized geometries with the used level of theory for optimization using Multiwfn 3.7 software package [56]. The polarizable continuum model (PCM) was used to include implicit solvation effects [57]. This paper uses the Lippert–Mataga polarity function (called orientation polarizability of the solvent) [58, 59], Bakhshiev polarity function [60] and Bilot and Kawski [61]. These functions have the equations of:

Lippert–Mataga polarity function: $F_{LM} (ɛ, n) = \frac{ɛ - 1}{2 ɛ + 1} - \frac{n^{2} - 1}{2 n^{2} + 1}; equation 2$

ɛ and n are dielectric constants and refractive index of the solvent.

Bakhshiev polarity function: $F_{B} (ɛ, n) = \frac{2 n^{2} + 1}{n^{2} + 2} (\frac{ɛ - 1}{ɛ + 2} - \frac{n^{2} - 1}{n^{2} + 2}); equation 3$

Bilot and Kawski function: $F_{BK} (ɛ, n) = \frac{2 n^{2} + 1}{2 (n^{2} + 2)} (\frac{ɛ - 1}{ɛ + 2} - \frac{n^{2} - 1}{n^{2} + 2}) + \frac{3 (n^{4} - 1)}{2 {(n^{2} + 2)}^{2}}; equation 4$

Also, the studied systems were optimized at the B3LYP-D3/6-311G(d,p) and PBE1PBE1/level of theory for illustration of effect of method in the results. B3LYP-D3 model keeps the advantageousness of B3LYP method in one hand, and on the other hand, it corrects simulates the weak interactions well using Grimme term D3 [62]. PBE1PBE functional uses 25% exchange and 75% correlation weighting [63]. Single point calculations at the B3P86/6-311++G(d,p) [64 –66] level of theory were done on the optimized molecules at the B3P86/6-311G(d,p) level of theory for studying of basis set effect.

3 Results and discussion

3.1 Solvation energies

The structure of Al₁₂N₁₂ nano-cluster (front view), TiCl₂Cp₂ anticancer drug and Al₁₂N₁₂ ⋯ TiCl₂Cp₂ complex are presented in Fig. 1. The total energy values of the Al₁₂N₁₂ ⋯ TiCl₂Cp₂ complex in the gas and solution phases are listed in Table 1. Selected solvents are tetrahydrofuran (THF), dichloromethane (CH₂Cl₂), Cyclohexanone (CH), Propanonitrile (PN), acetonitrile (MeCN) in this study. These values show that stability of the studied complex is greater in solution phase than gas phase. The stabilization energy values by solvents (solvation energy, E_solv) were calculated as: $E_{solvation} = E_{solvent} - E_{gas}$

Fig. 1

(a) Front view of the Al₁₂N₁₂nano-cluster, (b)TiCl₂Cp₂ anticancer dug, and (c) Al₁₂N₁₂ ... TiCl₂Cp₂ complex.

Table 1

Total energy (E, au), solvation energy (E_solv, kcal/mol), and interaction energy (ΔE_int, kcal/mol) values of the Al₁₂N₁₂ ... TiCp₂Cl₂ complex in gas and solution phases. ɛ and n_D are dielectric constants and refractive index of the solvent

	ɛ	n_D	E^a	E_solv^a	E_solv^b	E_solv^c	E_solv^d	ΔE_int^a	ΔE_int^b	ΔE_int^c	ΔE_int^d
Gas	–	–	–5731.5707	–	–	–	–	–25.62	–30.94	–27.08	–19.89
THF	7.43	1.407	–5731.6079	–23.3567	–24.14	–25.24	–23.36	–23.38	–29.33	–24.87	–24.51
CH₂Cl₂	8.93	1.424	–5731.6096	–24.4057	–25.15	–25.47	–24.39	–23.26	–29.07	–24.80	–24.43
CH	15.62	1.451	–5731.6132	–26.6808	–27.69	–25.84	–26.65	–22.87	–28.99	–24.88	–24.03
PN	29.32	1.368	–5731.6158	–28.3131	–29.38	–25.90	–28.27	–22.78	–28.83	–24.81	–23.86
MeCN	35.69	1.344	–5731.6164	–28.6589	–29.74	–26.10	–28.62	–22.76	–28.81	–24.74	–23.83

^aB3P86/6-311G(d,p) level of theory. ^bB3LYP-D3/6-311G(d,p) level of theory. ^cPBE1PBE/6-311G(d,p) level of theory. ^dB3P86/6-311G(d,p) //B3P86/6-311++G(d,p) level of theory.

Calculated solvation energy values are shown in Table 1. As shown, the solvation energies depend on the size of the dielectric constant of solvents, and these values decrease with the increase of dielectric constants of solvents. Therefore, the stability of Al₁₂N₁₂ ⋯ TiCl₂Cp₂ complex increases in more polar solvents. This is because a dipole in the molecule will induce a dipole in the medium, and the electric field applied to the solute by the solvent (reaction) dipole will in turn interact with the molecular dipole to result in net stabilization. Hence, the stability of the Al₁₂N₁₂ ⋯ TiCl₂Cp₂ complex is greater in polar solvent than in the gas phase. The calculations at the B3LYP-D3/6-311G(d,p), PBE0/6-311G(d,p) and B3P86/6-311G(d,p)//B3P86/6-311++G(d,p) levels of theory predict a same trend.

Solvation energy values are fitted with quadratic equation with dielectric constants of solvents at the B3P86/6-311G(d,p) level of theory: $E_{solv} = 8.80 \times 10^{- 3} ɛ^{2} - 0.55 ɛ - 20.00; R^{2} = 0.9881$

3.2 Interaction energy

The computed interaction energy values (ΔE_int) for the Al₁₂N₁₂ ⋯TiCp₂Cl₂ complex in gas phase and various solvents are shown in Table 1. The comparison of interaction energy value in gas phase and solution phase show weaker interaction between Al₁₂N₁₂ nano-cluster and TiCp₂Cl₂ anti-cancer drug in solution phase. As expected, the interaction between two fragments decreases in the presence of more polar solvents.

Very strong interactions are unfavorable for drug delivery, for, desorption process will be difficult. Therefore, Al₁₂N₁₂ cluster is a suitable carrier for drug delivery of TiCp₂Cl₂ complex in the presence of more polar solvents. The identical trend is observed in the similar systems [67 –69].

Identical trend is observed at the B3LYP-D3/6-311G(d,p), PBE0/6-311G(d,p) and B3P86/6-311G(d,p)//B3P86/6-311++G(d,p) levels of theory.

3.3 Non-covalent interaction (NCI) analysis

The non-covalent interaction (NCI) method, which is also well-known as reduced density gradient (RDG) method, is a very common technique for illustrating weak interactions. NCI analysis of the Al₁₂N₁₂ ⋯ TiCp₂Cl₂ complex reveals the presence of Cl⋯Al weak non-covalent interaction (Fig. 2). The presence of a green surface accounts for the presence of a non-covalent interaction.

Fig. 2

NCI gradient isosurfaces of Al₁₂N₁₂ ... TiCl₂Cp₂ complex.

3.4 H⋯N and Al⋯Cl distances

H⋯N and Al⋯Cl distances of the Al₁₂N₁₂⋯TiCp₂Cl₂ complex are listed in Table 2 both gas and values show that r2(N⋯H) and r3(Al⋯Cl) distances are shorter in solution phase than gas phase. In contrast, r1(N⋯H) distance is longer in solution phase than gas phase. It can be observed the most variation in the r1(N⋯H), r2(N⋯H) and r3(Al⋯Cl) distances are 0.228, 0.023, 0.024 Å, respectively. Therefore, the most significance variations is occurred for r1(N⋯H). As seen, There is shortest r1(N⋯H) distance in the gas phase. As a result, N ... H hydrogen bonding occurs in the gas phase. This result explains stronger interaction between Al₁₂N₁₂ and TiCp₂Cl₂ in gas phase than solution phase. Increasing attentions have been reported in so-called “weak” CH⋯A (where A = N or O) hydrogen bonds [70 –72]. Their important roles in a wide range of chemistry from catalysis [73] to gelation [74] to polymer structure [75] have been proposed.

Table 2
H ... N and Cl ... Al distances (in Å) of the Al₁₂N₁₂ ... TiCp₂Cl₂ complex in gas and solution phases

r1 r2 r3

Gas 2.266 2.515 2.359

THF 2.484 2.408 2.338

CH₂Cl₂ 2.490 2.410 2.338

CH 2.562 2.442 2.337

PN 2.490 2.539 2.335

MeCN 2.494 2.538 2.335

	r1	r2	r3
Gas	2.266	2.515	2.359
THF	2.484	2.408	2.338
CH₂Cl₂	2.490	2.410	2.338
CH	2.562	2.442	2.337
PN	2.490	2.539	2.335
MeCN	2.494	2.538	2.335

3.5 Dipole moment

Dipole moment values of the Al₁₂N₁₂⋯TiCp₂Cl₂ complex are determined in gas and several solvents (Table 3). These values indicate that dipole moment values of the complex increase in solution phase in comparison with the gas phase. These values increase in the presence of more polar solvents. Increased dipole moment values can be ascribed to long range interactions solvent with the solute molecules. Linear correlation between dipole moment values and dielectric constant of solvent show the following equations: $μ = 0.0379 ɛ + 13.289; R^{2} = 0.8911$

Table 3
Dipole moment (μ, Debye), Electronic spatial extent (ESE, in au), isotropic and anisotropic polarizability (α _iso, α _aniso, in Bohr³) of the Al₁₂N₁₂ ... TiCp₂Cl₂ complex in gas and solution phases

μ ESE α _iso α _aniso

Gas 10.01 24783.52 458.91 137.59

THF 13.42 24956.54 620.91 98.20

CH₂Cl₂ 13.58 24957.27 629.63 94.04

CH 14.14 24884.89 649.72 83.86

PN 14.47 24856.85 664.01 75.47

MeCN 14.52 24853.39 667.08 73.73

	μ	ESE	α _iso	α _aniso
Gas	10.01	24783.52	458.91	137.59
THF	13.42	24956.54	620.91	98.20
CH₂Cl₂	13.58	24957.27	629.63	94.04
CH	14.14	24884.89	649.72	83.86
PN	14.47	24856.85	664.01	75.47
MeCN	14.52	24853.39	667.08	73.73

As shown, these parameters are not linearly correlated.

It was tried to study the linear correlations between the dipole moment of this complex and solvent polarity function frequently covering both the refractive index [76] and the dielectric constant of the liquid medium.

The linear correlations between μ and these solvent polarity functions are: $\begin{matrix} μ = 11.151 F_{LM} (ɛ, n) + 11.21; R^{2} = 0.9232 \\ μ = 3.768 F_{B} (ɛ, n) + 11.139; R^{2} = 0.9968 \\ μ = 8.5732 F_{BK} (ɛ, n) + 9.455; R^{2} = 0.9635 \end{matrix}$

As shown, a better correlation is observed between the dipole moment and Bakhshiev function in the investigated complex. Therefore, this model reveals a better linear correlation between dipole moment values and solvent polarity functions by considering the dielectric constant and refractive index.

3.6 Polarizability

Isotropic and anisotropic polarizability values of the Al₁₂N₁₂⋯TiCp₂Cl₂ complex are calculated in gas and several solvents (Table 3).

3.6.1 Isotropic polarizability

These values indicated that isotropic polarizability values of the complex increase in solution phase in comparison with gas phase. These values increase in the presence of more polar solvents. Linear correlation between isotropic polarizability values and dielectric constant of solvent show the following equations: $α_{iso} = 1.5529 ɛ + 616.15; R^{2} = 0.9056$

The linear correlations between α _iso and these solvent polarity functions are: $\begin{matrix} α_{iso} = 456.34 F_{LM} (ɛ, n) + 531.09; R^{2} = 0.9364 \\ α_{iso} = 153.3 F_{B} (ɛ, n) + 528.86; R^{2} = 0.9995 \\ α_{iso} = 346.97 F_{BK} (ɛ, n) + 461.32; R^{2} = 0.9559 \end{matrix}$

As shown, a better correlation is observed between the isotropic polarizabiliy and Bakhshiev function in the investigated complex. Therefore, this model shows a better linear correlation between isotropic polarizability values and solvent polarity functions by considering the dielectric constant and refractive index.

3.6.2 Anisotropic polarizability

These values show that anisotropic polarizability values of the complex decrease in solution phase in comparison with the gas phase. These values decrease in the presence of more polar solvents. Linear correlation between anisotropic polarizability values and dielectric constant of solvent show the following equations: $α_{aniso} = - 0.8344 ɛ + 101.25; R^{2} = 0.9246$

The linear correlations between α _aniso and these solvent polarity functions are: $\begin{matrix} α_{aniso} = - 244.77 F_{LM} (ɛ, n) + 146.84; R^{2} = 0.9527 \\ α_{aniso} = - 81.538 F_{B} (ɛ, n) + 147.5; R^{2} = 0.9998 \\ α_{aniso} = - 182.98 F_{BK} (ɛ, n) + 182.6; R^{2} = 0.9401 \end{matrix}$

As shown, a better correlation is observed between the anisotropic polarizability and Bakhshiev function in the investigated complex. Therefore, this model shows a better linear correlation between isotropic polarizability values and solvent polarity functions by considering the dielectric constant and refractive index.

3.7 Electronic spatial extent

The electronic spatial extent (ESE) for each molecule is defined as the surface area covering a volume around the molecule and describes the gross receptivity of the molecule from an external electric field.

ESE values of the studied complex are reported in the gas and solution phases (Table 3). These values show that ESE values of the complex increase in solution phase in comparison with gas phase. These values decrease in the presence of more polar solvents. Linear correlation between ESE values and dielectric constant of solvent show the following equations: $ESE = - 3.8142 ɛ + 24976; R^{2} = 0.856$

As shown, these parameters are not linearly correlated.

The linear correlations between ESE values and these solvent polarity functions are: $\begin{matrix} ESE = - 1120.4 F_{LM} (ɛ, n) + 25185; R^{2} = 0.8844 \\ ESE = - 381.07 F_{B} (ɛ, n) + 25194; R^{2} = 0.9676 \\ ESE = - 871.5 F_{BK} (ɛ, n) + 25366; R^{2} = 0.9449 \end{matrix}$

As shown, a better correlation is observed between the ESE values and Bakhshiev function in the investigated complex. Therefore, this model reveals a better linear correlation between ESE values and solvent polarity functions by considering the dielectric constant and refractive index.

3.8 Molecular orbital analysis

Frontier orbital energy values of the studied complex are calculated in gas and various solvents (Table 4). As shown, the stability of the HOMO increases in solution phase; however, stability of LUMO decreases. The solvent, especially polar solvents, could really influence the geometry through solvent-solute interactions, thus stabilizing HOMO. In contrast, weak solvent-solute interactions destabilize LUMO.

Table 4
Frontier orbital energy, HOMO-LUMO gap, hardness (η), chemical potential (μ), electrophilicity (ω) values (in eV) and electrophilicity-based charge transfer (ECT) of the Al₁₂N₁₂ ... TiCp₂Cl₂ complex in gas and solution phases

E(HOMO) E(LUMO) Gap η μ ω ECT

Gas –6.54 –4.09 2.45 1.22 –5.31 23.07 –0.327

THF –6.85 –3.96 2.88 1.44 –5.40 20.26 –0.491

CH₂Cl₂ –6.86 –3.96 2.90 1.45 –5.41 20.19 –0.498

CH –6.89 –3.96 2.93 1.47 –5.43 20.10 –0.514

PN –6.92 –3.96 2.95 1.48 –5.44 20.05 –0.526

MeCN –6.92 –3.97 2.96 1.48 –5.44 20.05 –0.528

	E(HOMO)	E(LUMO)	Gap	η	μ	ω	ECT
Gas	–6.54	–4.09	2.45	1.22	–5.31	23.07	–0.327
THF	–6.85	–3.96	2.88	1.44	–5.40	20.26	–0.491
CH₂Cl₂	–6.86	–3.96	2.90	1.45	–5.41	20.19	–0.498
CH	–6.89	–3.96	2.93	1.47	–5.43	20.10	–0.514
PN	–6.92	–3.96	2.95	1.48	–5.44	20.05	–0.526
MeCN	–6.92	–3.97	2.96	1.48	–5.44	20.05	–0.528

3.8.1 HOMO-LUMO energy gap

The HOMO-LUMO energy gap characterizes the kinetic stability and chemical reactivity of the molecule. The low energy gap between the donor and acceptor shows the suitable transfer of energy between them. As shown, the HOMO-LUMO gap values of the complex increase in solution phase in comparison with the gas phase (Table 4). These values increase in the presence of more polar solvents. It is observed that in the polar solvents, the HOMO of the molecules is stabilized more than the LUMO via solvent-solute interactions thereby giving rise to a wider HOMO-LUMO gap as against the lower HOMO-LUMO gap in non-polar solvents.

3.8.2 Global reactivity descriptors

Some global reactivity descriptors such as hardness, chemical potential and electrophilicity index facilitate characterizing the nature and interaction of the molecule.

Hardness: The calculated hardness values of the complex increase in solution phase in comparison with the gas phase. According to Table 4, these values increase in the presence of more polar solvents. The low global hardness value reveals that the molecule is ready for sharing electrons.

Chemical potential: According to the values in Table 4, the chemical potential values of the complex decrease in solution phase in comparison with gas phase. These values decrease in the presence of more polar solvents.

Electrophilicity: According to these values, the electrophilicity values of the complex decrease in solution phase in comparison with the gas phase. According to Table 4, these values decrease in the presence of more polar solvents. According to the low electrophilicity index, the molecule is capable of acting as nucleophile donating electrons while undergoing interaction with the bio-molecule.

3.9 Electrophilicity-based charge transfer (ECT)

Electrophilicity-based charge transfer (ECT) is calculated defined as the difference between ΔN_max values of interacting molecules [77]: $ECT = Δ N_{\max} (c p_{2} TiC l_{2}) - Δ N_{\max} (A l_{12} N_{12})$

In this equation ΔN_max is defined as: ${(Δ N_{max})}_{i} = - \frac{μ_{i}}{η_{i}} = \frac{2 ω_{i}}{χ_{i}}$

ω and χ are electrophilicity and electronegativity of the system. They are defined as global reactivity descriptors [78 –81] and determined on the basis of Koopman’s theorem [82]. These values for Al₁₂N₁₂ ... TiCl₂Cp₂ complex in the gas and solution phase are summarized in Table 4. The negative values of the ECT values reveal that charge transfer from TiCl₂Cp₂ to Al₁₂N₁₂. It can be observed, the variations of the ECT values with the dielectric constant of solvents are obeyed the following quadratic equation: $ECT = 6 \times 1 0^{- 5} ɛ^{2} - 0.00 39 ɛ - 0.467; R^{2} = 0.9886$

3.10 Thermodynamic parameters

Free energy, enthalpy and entropy changes values (ΔG, ΔH and ΔS, respectively) of Al₁₂N₁₂ ⋯TiCp₂Cl₂ complex formation are calculated according to the following reactions: $\begin{matrix} A l_{12} N_{12} + TiC p_{2} C l_{2} \to A l_{12} N_{12} \dots TiC p_{2} C l_{2}; \\ Δ X = X (A l_{12} N_{12} \dots TiC p_{2} C l_{2}) X (A l_{12} N_{12}) - X (TiC p_{2} C l_{2}); X = G, H, S \end{matrix}$

The calculated ΔG, ΔH and ΔS values of this reaction in the 298 K and 1atm pressure are –6.05 kcal/mol, –18.01 kcal/mol and –40.10 cal/mol.K, respectively. The negative ΔG and ΔH values of the Al₁₂N₁₂⋯TiCp₂Cl₂ complex formation shows that this reaction is spontaneous and exothermic, respectively. The negative ΔS values of these reactions seem logical since formation of one molecule after interaction between two molecules decreases the entropy of reaction. Formation constant values (K) of the Al₁₂N₁₂⋯TiCp₂Cl₂ complex is calculated by the following formula: $Δ G = - nRT ln K$

The calculated K value is 2.74×10⁴.

3.10.1 Solvent effect

Absolute free energy and enthalpy values of studied Al₁₂N₁₂⋯TiCl₂Cp₂ complex in the gas and various solvents are reported in Table 5. The solvation free energy and enthalpy values are computed via the following equation:

$Δ X_{solvation} = X_{solv} - X_{gas}; X = G, H, S$

Table 5
Solvation free energy (ΔG_solv, kcal/mol), solvation enthalpy (ΔH_solv, kcal/mol), and solvation entropy (ΔS_solv, cal/mol.K), values of the Al₁₂N₁₂ ... TiCp₂Cl₂ complex in various solvents

solvent ΔG_solv ΔH_solv ΔS_solv

THF –23.88 –86.22 0.28

CH₂Cl₂ –24.83 –24.87 –0.11

CH –28.09 –27.32 2.59

PN –29.57 –28.98 1.99

MeCN –30.00 –29.33 2.22

solvent	ΔG_solv	ΔH_solv	ΔS_solv
THF	–23.88	–86.22	0.28
CH₂Cl₂	–24.83	–24.87	–0.11
CH	–28.09	–27.32	2.59
PN	–29.57	–28.98	1.99
MeCN	–30.00	–29.33	2.22

According to Table 5, the amount of ΔG_solv and ΔH_solv of Al₁₂N₁₂⋯TiCl₂Cp₂ complex decreases with increasing the dielectric constant. There is a good relationship between ΔG_solv and ΔH_solv with dielectric constant values: $\begin{matrix} Δ G_{solv} = - 0.2063 ɛ - 23.272; R^{2} = 0.8719 \\ Δ H_{solv} = - 0.1855 ɛ - 23.261; R^{2} = 0.8996 \end{matrix}$

As shown, these parameters are not linearly correlated. These calculated parameters are fitted with quadratic equations: $\begin{matrix} Δ G_{solv} = 0.0 118 ɛ^{2} - 0.7082 ɛ - 19.46; R^{2} = 0.9812 \\ Δ H_{solv} = 0.00 94 ɛ^{2} - 0.5847 ɛ - 20.228; R^{2} = 0.9878 \end{matrix}$

There is a good relationship between ΔG_solv and dipole moment values: $μ = - 0.1816 Δ G_{solv} + 9.072; R^{2} = 0.9981$

Therefore, in more polar solvents, the increase in dipole moment of Al₁₂N₁₂⋯TiCl₂Cp₂ complex affects its interaction with the solvent.

3.10.2 Effect of temperature

The effect of temperature on the thermodynamic properties of the interaction is explored. The temperature dependent behaviors of this interaction is investigated under various conditions (T = 100–1000 K) (Table 6).

Table 6
Changes of the free energy (ΔG, kcal/mol), enthalpy (ΔH, kcal/mol) and entropy (ΔS, cal/mol.K) values of the Al₁₂N₁₂ ... TiCp₂Cl₂ complex in various temperature (in K)

ΔG ΔH ΔS K

100 –13.98 –18.71 –47.25 3.59×10³⁰

200 –9.29 –18.60 –46.54 1.42×10¹⁰

300 –4.67 –18.45 –45.94 2.52×10³

400 –0.10 –18.30 –45.49 1.13

500 4.43 –18.13 –45.13 1.15×10^–2

600 8.93 –17.96 –44.82 5.59×10^–4

700 13.40 –17.79 –44.55 6.56×10^–5

800 17.84 –17.60 –44.30 1.34×10^–5

900 22.26 –17.42 –44.08 3.93×10^–6

1000 26.66 –17.22 –43.88 1.49×10^–6

	ΔG	ΔH	ΔS	K
100	–13.98	–18.71	–47.25	3.59×10³⁰
200	–9.29	–18.60	–46.54	1.42×10¹⁰
300	–4.67	–18.45	–45.94	2.52×10³
400	–0.10	–18.30	–45.49	1.13
500	4.43	–18.13	–45.13	1.15×10^–2
600	8.93	–17.96	–44.82	5.59×10^–4
700	13.40	–17.79	–44.55	6.56×10^–5
800	17.84	–17.60	–44.30	1.34×10^–5
900	22.26	–17.42	–44.08	3.93×10^–6
1000	26.66	–17.22	–43.88	1.49×10^–6

During the interaction process, the enhancement of ΔG, ΔH and ΔS are observed distinctly along with the increasing of the temperature. Therefore, the interaction occurs easily under lower temperature. There are good linear correlations between of ΔG, ΔH and ΔS with temperature: $\begin{matrix} Δ G = 0.0 451 T - 18.256; R^{2} = 0.9999 \\ Δ H = 0.00 17 T - 18.936; R^{2} = 0.996 \\ Δ S = 0.00 36 T - 47.159; R^{2} = 0.9541 \end{matrix}$

In addition, during the interaction process, the decreasing of K values is observed distinctly along with the increasing of the temperature. Therefore, the interaction occurs easily under lower temperature. There are good linear correlations between of log (K) values with temperature: $Log (K) = 2.3026 T 3 \times 1 0^{- 15}; R^{2} = 1$

3.10.3 Effect of pressure

The effect of pressure on the thermodynamic properties of the interaction is explored. The pressure-dependent behaviors of this reaction is investigated under various conditions (P = 0.1–1000 atm) (Table 7).

Table 7
Changes of the free energy (ΔG, kcal/mol), enthalpy (ΔH, kcal/mol) and entropy (ΔS, cal/mol.K) values of the Al₁₂N₁₂ ... TiCp₂Cl₂ complex in various pressure (in atm)

P ΔG ΔH ΔS

0.1 –3.39 –18.45 –50.53

1 –4.75 –18.45 –45.95

10 –6.12 –18.45 –41.37

100 –7.48 –18.45 –36.80

1000 –8.85 –18.45 –32.22

P	ΔG	ΔH	ΔS
0.1	–3.39	–18.45	–50.53
1	–4.75	–18.45	–45.95
10	–6.12	–18.45	–41.37
100	–7.48	–18.45	–36.80
1000	–8.85	–18.45	–32.22

During the interaction process, the decreasing of ΔG values is observed distinctly along with the increasing of the pressure. Therefore, the interaction occurs easily under higher pressure. There are good linear correlations between of ΔG with logarithm of pressure: $Δ G = - 1 . 3644 \log (P) - 4.7534; R^{2} = 1$

The variation of ΔS during the interaction increases distinctly along with the enhancement of pressure. There are good linear correlations between of ΔS with logarithm of pressure: $Δ S = 4 . 5756 \log (P) - 45.95; R^{2} = 1$

4 Conclusion

Computational investigation of the interaction behavior of TiCp₂–Cl₂– anticancer drug with Al₁₂N₁₂ cluster was explored in the gas and solution phases. The calculated interaction energy values revealed the weaker interactions in the presence solution phase rather than gas phase. NCI analysis of the Al₁₂N₁₂⋯TiCp₂Cl₂ revealed the presence of Cl⋯Al weak non-covalent bond. The changes in the dipole moment, polarizability and electronic spatial extent (ESE) with solvent polarity showed good correlation with Bakhshiev function models. The HOMO-LUMO gap values of the complex increased in solution phase in comparison with gas phase. These values increased in the presence of more polar solvents. Thermodynamics analysis showed easy interaction under lower temperature and higher pressure.

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Complex formation of titanocene dichloride anticancer and Al 12 N 12 nano-cluster: A quantum chemical investigation of solvent,temperature and pressure effects

Abstract

Keywords

1 Introduction

2 Computational methods

3 Results and discussion

3.1 Solvation energies

3.3 Non-covalent interaction (NCI) analysis

Table 2 H ... N and Cl ... Al distances (in Å) of the Al12N12 ... TiCp2Cl2 complex in gas and solution phases r1 r2 r3 Gas 2.266 2.515 2.359 THF 2.484 2.408 2.338 CH2Cl2 2.490 2.410 2.338 CH 2.562 2.442 2.337 PN 2.490 2.539 2.335 MeCN 2.494 2.538 2.335

3.6.1 Isotropic polarizability

3.6.2 Anisotropic polarizability

3.7 Electronic spatial extent

3.8 Molecular orbital analysis

3.8.2 Global reactivity descriptors

3.9 Electrophilicity-based charge transfer (ECT)

3.10 Thermodynamic parameters

3.10.1 Solvent effect

References

Table 2
H ... N and Cl ... Al distances (in Å) of the Al₁₂N₁₂ ... TiCp₂Cl₂ complex in gas and solution phases

r1 r2 r3

Gas 2.266 2.515 2.359

THF 2.484 2.408 2.338

CH₂Cl₂ 2.490 2.410 2.338

CH 2.562 2.442 2.337

PN 2.490 2.539 2.335

MeCN 2.494 2.538 2.335