Computational properties of η6-toluene and η6-trifluorotoluene half-sandwich Ru(II) anticancer complexes

The computational properties of the η6-toluene and η6-trifluorotoluene half-sandwich Ru(II) anticancer complexes and their respective hydrated complexes are computed using DFT method and the quantum theory of atoms in a molecule (QTAIM) analysis. The interatomic properties that are crucial in understanding the noncovalent interactions and the stability of these complexes are considered. We observed that high polarization, charge transfer (CT) and strong networks of intramolecular hydrogen bond (HB) interactions significant influenced the stability of these complexes. The trifluorotoluene and the hydrated models are characterized with higher CT, polarizability, synergistic effect of ligand fragments, stronger and higher HB interactions that support their reported experimental anticancer activities and the mechanism of their activation by hydrolysis. The complexes are predominantly characterized with metal to ligand CT.

The complexes that hydrolyze rapidly have been shown to be active over cancer cells than those that do not aquate easily (Wang et al., 2005) indicating that the significant feature of these cytotoxic metal complexes is hydrolysis (Hanif et al., 2010). The choice of ligands is important because a ligand that bound too strongly could render the drug inactive, while a very labile ligand could be easily replaced . The RAPTA complexes with labile chloride atoms are prone to hydrolysis and would have to be administered in saline to suppress the cleavage of the chloride ligands. The problems that are associated with hydrolyzed complexes are difficulty in their characterization which affect the pharmacokinetics studies and consequently affect the clinical trial . Some of these ruthenium arene complexes are reported to be unstable and have complicated ligand-exchange chemistry (Allardyce et al., 2005). Therefore, noncovalent interactions which have been pointed out as important properties in chemical reactions, molecular recognition, and regulation of biochemical processes (Alkorta, Blanco, & Elguero 2009;Meyer, Castellano, & Diederich, 2003) are computed for the model complexes ( Figure 1) in this work. The deep understanding of these interactions has been pointed out to be of outstanding importance in rationalization of effects that are observed in several fields like biochemistry and materials science (Alkorta et al., 2009). Many quantum calculations have been used to give insight into the chemistry of the Ru-based anticancer complexes and to explain the microscopic properties behind their experimental findings (Chval, Futera, & Burda, 2011;Ciancetta, Genheden, & Ryde, 2011;Deubel & Lau, 2006;Futera, Klenko, Sponer, Sponer, & Burda, 2009;Gossens, Dorcier, Dyson, & Rothlisberger, 2007).
This study therefore, presents the unique features, natures, and magnitudes of the electronic properties with the intramolecular interactions that influence the stability of four Ru-based complexes in relation to their reported anticancer activities. Our interest in this work is to thoroughly study the chemistry of these complexes in order to determine the factors that can influence their stability which will consequentially affect their anticancer properties (Allardyce et al., 2005). For this study, we have selected rapta-T (complex 1) and a model with electron-withdrawing a,a,a-trifluorotoluene ligand [Ru(η 6 -C 6 H 5 CF 3 )(pta)Cl 2 ] (i.e., rapta-CF 3 ) (complex 3) (Egger et al., 2010) to give the feature of the interatomic properties of these complexes, the factors that determine their stability and the properties of their hydrolyzed forms (complexes 2 and 4) respectively ( Figure 1). Researchers have shown that these types of compounds can be characterized with favorable interactions between electron-rich and π-deficient groups (Alkorta et al., 2009). Complex 3 has been found to be most cytotoxic RAPTA compounds especially in A2780 human ovarian cancer cells and also significantly more active than other simple RAPTA compounds (Egger et al., 2010). The biomolecule reaction mixtures of complex 3 has been observed to contain mostly [Ru(pta)]-biomolecule adducts that were not observed in the protein-or DNA-binding studies of [Ru(pta)(arene)] adducts typical of other RAPTA complexes (Egger et al., 2010). Therefore, this facile arene loss is proposed to be responsible for the increased cytotoxicity of complex 3 (Egger et al., 2010).

Computational method
The geometries of the complexes were optimized first using in FIREFLY 7.1.G (Granovsky, 2012) that is partially based on the GAMESS (US) (Schmidt et al., 1993) source code and later in Gaussian 09 (Frisch et al., 2009). The natural bond orbital (NBO) analysis (Foster & Weinhold, 1980) and natural energy decomposition analysis (NEDA) (Glendening & Streitwieser, 1994) were carried out using NBO 5.0G program (Reed, Curtiss, & Weinhold, 1988) as implemented in Firefly QC package. The computations were done using PBE0 hybrid density functional (Adamo & Barone, 1999) with two different external basis sets 6-31G ⁄ for all atoms order than Ru, Cl, and P where SBKJC VDZ (Stevens, Krauss, Basch, & Jasien, 1992) with effective core potential is used (this will be subsequently referred to as PBE0/ECP(Ru, P, Cl)|6-31G ⁄ systems). The basis sets were obtained from EMSL Basis Set Library (Feller, 1996;Schuchardt et al., 2007) and were incorporated into the input file in a format that each FIREFLY and Gaussian programs can read. SBKJC VDZ ECP basis set with PBE0 functional has been shown to be effective in treating complexes with large number of electrons and has been applied in computing properties of many metal clusters (Marchal, Carbonniére, Begue, & Pouchan, 2008;Marchal et al., 2011). On each of the molecules, 28 core electrons were removed from Ru (1s,2s,2p,3s,3p,3d), 10 from P (1s, 2s, 2p) and 10 from Cl (1s, 2s, 2p) atoms and were treated with pseudopotential, while the valence electrons were treated by a double zeta quality functions. All the computed properties including the NBO, NEDA, spin-spin NMR properties and hyperpolarizability were done using hybrid DFT functional B3LYP (Becke, 1993) and different basis sets. The properties are computed first with higher basis set where the Ru atom was treated with DGDZVP basis set, while the remaining atoms treated with 6-21G+(d,p) basis set (it shall subsequently be referred to as B3LYP/DGDZVP(Ru)|6-31 + G(d,p) systems). In the second part, all the atoms in the complexes were treated with minimal basis set 3-21 G (Dobbs & Hehre, 1987) at gas phase of 1 atm and default temperature of 273.15 K. The NBO and NEDA analysis are computed with PBE0/ECP(Ru, P, Cl)|6-31G ⁄ and B3LYP/DGDZVP(Ru)|6-31 + G(d,p) functionals. The electron density topology and interatomic properties were evaluated from the computed wavefunction within quantum theory of atoms in molecules (QTAIM) using AIMAll 12.06.03 (Keith, 2012). The method employed in this work is based on the analysis of electron density distributions (EDDs) which both at experiment and theory levels has shown to be a powerful method for exploration and characterization of chemical bonds (Platts, Overgaard, Jones, Iversen, & Stasch, 2011). Using Bader's QTAIM (Platts et al., 2011), the atomic properties such as electronic population, energies, and (de)localization are evaluated over atomic basins. QTAIM theory through the topological analysis of charge density (ρ(r)) and Laplacian derivative of charge density (r 2 q) (Calhorda & Lopes, 2000) has brought back to light the classical concepts of chemistry such as atoms being separate and transferable chemical entities or chemical bonds connecting atomic nuclei that are somewhat concealed in the wavefunction-based quantum-mechanical description of the molecular electronic structure (Timerghazin, Rizvi, & Peslherbe, 2011).

Result and discussion
3.1. The geometries of the complexes The geometries of the complexes were optimized to their lowest ground state energy characterized with zero imaginary frequencies. The obtained bond distances and angles are within the experimental ranges (Renfrew et al., 2009). The computed Ru-arene bond distances of complex 3 ranges from 2.197 to 2.257 Å which is very closed to the reported experimental range of 2.151-2.169 Å. Comparing the computed geometries of the complexes to the experimental reports (in bracket), the range of bond distances (in Å) for Ru-P is 2.419-2.443 (2.279-2.297), Ru-Cl is 2.481-2.496 (2.410-2.434), while the bond angles (in degree) ranges for Cl-Ru-Cl is 89. 73-90.75 (87.25-87.88) and Cl-Ru-P is 79. 96-82.75 (82.61-87.86). All the bond distances of the ruthenium-ligand (Ru-L) with their respective bond orders are show in Table 1 (for the systems treated with B3LYP/DGDZVP(Ru)|6-31 + G(d,p)). The bond order of the two chloride atoms in each of complex 1 and 3 are relatively the same. This indicates that any one of the two chloride atoms can be a leaving group in their hydrolysis to complexes 2 and 4 respectively (Table 1). After the hydrolysis, the possibility of the last chloride atom becoming a leaving group is rare (Chval et al., 2011) as the bond order of chloride atom increases from the unhydrolyzed complexes (1 and 3) to the hydrolyzed ones (2 and 4) while that of the Ru-P decreases. Therefore, for any possible covalent interactions of the central metal atom with biological residue as proposed experimentally (Casini et al., 2009;Ciancetta et al., 2011;Hanif et al., 2010), the water molecule has to be a leaving group and possibly the pta ligand. The bond order analysis recognized the existence of the hydrogen bond (HB) that exists within each of the complex. The fluorination in complexes 3 and 4, respectively, seems to have very little effect on the bond order of the complexes with a little improvement in the Ru-P and Ru-Cl bond order.
In all the complexes, the natural bond order (NBO) and NEDA properties computed with ECP (PBE0/ECP (Ru, P, Cl)|6-31G ⁄ ) (Supplementary Table S1)) and the QTAIM properties computed with minimal basis set 3-21G (Table S3, S5, and S6) are in a close range with those computed with higher basis sets where Ru atom is treated with DGDZVP basis set and other atoms treated with 6-31 + G(d,p) basis set (Tables 1-8) (referred to as B3LYP/DGDZVP(Ru)|6-31 + G(d,p) systems). This is an indication that the properties computed with minimal basis set 3-21G for these type complexes is reliable enough and can be helpful to treat large system.

NBO analysis
The 4d 7 orbitals are used in bond interactions preferentially to 5s orbitals in all the four models ( Figure 1). The Lewis carries the highest percentage (ranges from 97.68% to 98.11%) which is an indication that the structure is stable. The effect of the non-Lewis orbitals is relatively significant (ranges from 1.71% to 2.16%) as a measure of the back bonding interactions in the complexes. The polarization (c A ) of the bonding atoms and the percentage of the NBO (c A -squared) on each hybrid (Table 2) is in favor of the coordinated ligand atoms as they are associated with higher values. This suggests the possibility of metal to ligand charge transfer (MLCT) transitions. The better feature of the charge transfers is observed when second perturbation energies (E (2) ) of the delocalized orbitals were computed as shown in Table 3. The higher value of E (2) is an indication of higher stability ascribed to contribution due to delocalization. Only the electron communications that have E (2) equal or greater than 10.00 kcalmol À1 and interactions with metal atom are presented. Using the NPA analysis to predict the magnitude of electron transfer (Zeng & Klobukowski, 2008), the feature of electron delocalization acceptor orbitals (Table 3) indicate a predominant MLCT through a high charge transfer from the lone pair of Ru metal to the Lewis orbital lone pair of the arene carbon atoms and the non-Lewis orbital of other Ru-L bonds. A critical observation of the common charge transfer (CT) from the Ru atom to the arene C=C double bonds shows that the stabilization energy (E (2) ) of this CT decreases upon the hydrolysis of the complexes and fluorination of the complexes (Table 3). However, the values of the E (2) do not directly measure the magnitude of CT from the Ru atom to the arene carbon atoms because higher CT observed between these atoms (Table 4) in the hydrolyzed complexes (complexes 2 and 4) and fluorinated complexes (complexes 3 and 4). It is interesting to point out that both hydrolysis and fluorination significantly Note: Polarization coefficient cA is the values with superscript " ⁄ " and its percentage NBO is "cA-squared" on each hybrid orbitals.  Note: E 2 in kcal/mol is the second perturbation energy or stability energy, "n" is lone pair and "σ" is sigma bond.
leads to the lower energy values of the antibonding orbitals of the complexes which enhances both the MLCT and LMCT properties of the complexes. This should also be responsible for the higher electrical energy (EC) contribution and CT of the hydrolyzed and fluorinated complexes from the NEDA analysis of the complexes (Table 5). There is also back bonding of electrons either from the Ru-L bonds or ligand atoms into the non-Lewis lone pair orbital of Ru atom indicating a little feature of ligand to metal charge transfer (LMCT). The predominant features of MLCT from Ru to both the Lewis and non-Lewis arene carbon atoms lone pair orbitals is due to the lower energy level of these ligand orbitals (Table 4). In hydrated complexes 2 and 4, there is significant values of charge transferred from the oxygen lone pair into the non-Lewis lone pair of Ru atom. The lower feature of LMCT compare with MLCT is as a result of higher energy level of non-Lewis lone pair of Ru atom. There are many interbonding electron communication from the bonding orbitals to the Acceptor orbital σ e-gain Energy (Hatree) Note: "n" is lone pair and "σ" is sigma bond. antibonding orbitals of bonded atoms which enhances the stability of the complexes and responsible for the high contribution of the non-Lewis antibonding orbitals. These observations are typical of π-bonded ligand metal complexes which are systems with intense intramolecular charge transfer (CT) between metal and ligand (MLCT or LMCT) and are usually associated with π back-donation resulting in a very large value of hyperpolarizability (deSilva et al., 2005, Mendesa, Ramalho, Candeias, Robalod, & Garcia, 2005. Many metal complexes are known to possess intense, low-energy MLCT, LMCT, or intraligand charge transfer (ILCT) excitations (Liyanage, de Silva, & de Silva, 2003). Also from NEDA analysis, we observed the total charges transferred from the Ru lone pairs to the ligand lone pairs or Ru-L bonds (after all the transferred from the ligand atoms have been subtracted) to be .494, .472, .533 and .409 e for complexes 1, 2, 3, and 4, respectively, which is an indication that hydrolysis decrease the MLCT while fluorination increases it. The nature of the HOMO and the LUMO of the complexes (Figure 2) further confirmed mixed features of the MLCT and LMCT in the complexes. HOMO is predominantly the Ru, Cl, and PTA atoms, while the arene ligand atoms including also the Cl and Ru atoms dominate the LUMO. The hydrolysis of the complexes results to lower HOMO contribution of Ru atom in the complexes 2 and 4 which is the effect of the significant back bonding of electron from the oxygen atom of the water molecule to the antibonding orbital of the Ru atom ( Table 4). Fluorination of the arene reduces the HOMO contribution of the chloride atoms in the complexes which result to HOMO being predominantly characterized with only the Ru and the PTA atoms (complexes 3 and 4) which further confirm the features obtained from NEDA analysis. The mixed features of HOMO and LUMO contribution of the Ru atoms in the complexes further gives insight into the observed predominant nature of MLCT from the Lewis bonding of the metal atoms to the ligand atoms (both Lewis and non-Lewis orbitals) and lower features of LMCT from the ligand orbitals into the non-Lewis lone pair orbital of Ru atom.

Natural energy decomposition energy analysis
The results obtained from the NEDA analysis of the complexes are shown in Table 5 and Table S1. The high values of CT further shows its significance contribution to the stability of the complexes. The values of the charge transfer in the complexes are highly negative which eventually help in overcoming the high core electron repulsion energy (XC + DEF-SE) of the complexes. The hydrolysis of the complexes from 1 and 3 to 2 and 4, respectively, results in more stable complexes as suggested by more highly negative values of interaction energy E. This is due to the enhanced features of the CT, POL and ES after hydrolysis. CT is the most significant factor that determines the stabilization of the un-hydrolyzed complexes, while POL is the most important factor in the hydrolyzed complexes (Table 5). Therefore, total HB stability energy (E) of the complexes is predominantly determined by the CT and the POL which together with ES made up the electrical energy (ES + POL + SE) contribution of the complexes. Using PBE0/ECP(Ru, Cl, P)|6-31G ⁄ , no NEDA information was obtained for complex 2 since no decomposition takes place as the complex was recognized as a single unit (Table S1). A significant increase in the value of hydrogen energy (E) from un-hydrolyzed complexes to the hydrolyzed complexes is an evidence of improved stability which may be responsible for the reported activation of these complexes by hydrolysis (Gasser et al., 2011;Wang et al., 2005). The presence of trifluorotoluene in complexes 3 and 4 lead to increase in the CT and Electrical properties of the complexes but lower overall hydrogen interaction energy (E).
The synergistic effect of fragments in complexes on each other through the decomposition analysis of the complexes can be seen from Table 6 which shows the dipole moment, the energy from both the perturbed (def) wavefunctions of each fragment in isolation and the optimized (cp) wavefunctions for each fragment in the presence of other fragments. The difference between the perturbed and the optimized is the induce value which shows the level of the synergistic effects of the fragments on each others. Each of the unhydrolyzed complexes 1 and 3 are fragmented into two units of which the arene atoms are recognized as a unit (acceptor) while the hydrolyzed complexes 2 and 4 are fragmented into three units where water molecule made up the additional unit. There are significantly high values of induced dipole in the complexes especially from the donor unit which implies that there is no strict orthogonality of wavefunctions required in the first and second fragments but are both characterized by significant polarization. This therefore better exposed the acceptor and donor to nucleophilic and electrophilic attack, respectively. This effect becomes more pronounced in complex 4 as the induce dipole of the acceptor unit significantly increased to 34.83 Debye. We observed that the induced dipole values of complexes 2 and 4 are significantly higher than that of 1 and 3 which can be the reason, while hydrolyzed complexes are often experimentally reported as the active anticancer complex possibly because of better expose surface to macromolecular attack. In a little measure, the induce dipole of complex 3 is also higher than that of complex 1 due to fluorination which can be responsible also for the reported higher anticancer effect of the fluorinated complex than the original complex (Egger et al., 2010). Also, the induce wavefunction values which is a difference between the energy of localized ψA(def) and optimized ψA (cp) wavefunctions of complexes are relatively high which is an indication of the strong synergistic effect of each unit on the others. This effect favors the stability of the arene unit which is associated with higher negative induce values than the donor unit except for the hydrolyzed complex 4. Both the synergistic properties of the induced energy and dipole increases as a result of presence of the trifluorotoluene in complexes 3 and 4 which could be responsible for the reported better anticancer activities of these complexes than complexes 1 and 2 (Egger et al., 2010). The overall strong synergistic effects of ligand units that are coordinated to metal centre in all the complexes can lead to highly cytotoxic species as it was experimentally suggested (Stepanenko et al., 2011).

The QTAIM analysis of bonds
Further analysis of the electron density wavefunction through the quantum theory of atoms in a molecule (QTAIM) as implemented in AIMAll package give a better features of the interatomic interaction in the complexes. The topology from the QTAIM analysis can best be explain in terms of the critical points density (rq) which gives information about the existence of bonds, while the sign of Laplacian of the density (r 2 q) at that point reflects the kind of interaction which if it is negative is a critical point for covalent interactions (between open shells), and if it is positive is a closed shell interactions, such as HBs (Calhorda & Lopes, 2000) or ionic or van der Waals bond (Tiana, 2010). The QTAIM properties obtained from combination of higher basis sets DGDZVP(Ru)|6-31 + G(d,f) (Tables 7 and 8) is very similar to the properties computed using minimal basis set 3-21G (Table S3 and S5). There are similarity between the topological features of complexes 1 and 3 and their respective hydrated complexes 2 and 4. The topological features that are peculiar to the four complexes are six RCPs of the Ru-arene, four RCPs in pta and one CCP at PTA (Figure 3). There are additional two RCP and three RCP that characterized the ring formation by the two HB in the complex 1 and three HB in 2, while extra four RCP exist in complexes 3 and 4 which define the ring formed by the four HB that exist in these complexes.
In QTAIM analysis of the complexes, all the interatomic bonds within each of the ligand are characterized with covalent bonds which is an open shell interaction with negative value of r 2 q(r) (Figure 3), higher ρ(r) value, low kinetic energy per electron (K) and higher magnitude of potential to Lagrangian kinetic energy ratio (Platts et al., 2011). A positive r 2 q(r) characterized all the metal-ligand bonds (dotted lines in the contour plots of Figure 3) and the HB (Tables 7 and Table S3) which is an indication of a closed shell interactions typical of HBs (Calhorda & Lopes, 2000) or dative or ionic or van der Waals bond (Tiana, 2010). The very high positive r 2 q(r) is an indication that the metal-ligand bonds in these complexes are dative bond (Tiana, 2010) except Ru-Cl bonds that may be suggested to be ionic bond. Also, all the HB bonds have the same properties of M-L bonds but lower values of ρ(r) and r 2 q(r) (Calhorda & Lopes, 2000) and are weaker than the dative bond that exist within the M-L bonds (Table S3). The values of ρ(r) and r 2 q(r) of all the M-C (carbon atoms are from arene) are higher than that of the Cl and PTA which suggest the reason why arene unit is not the leaving unit in the biological interaction of these complexes. Also, the relatively the same values of ρ(r) and r 2 q(r) of the two chloride atoms in complexes 1 and 3 further confirmed the observation from the bond order that any of these two atoms can be the leaving unit during hydrolysis. The ellipticity (ɛ) value usually ranges from zero to infinity and is widely regarded as a quantitative index of the π-character of the bond (Gopakumar, Ngan, Lievens, & Nguyen, 2008). The ellipticity of some of the arene carbon atoms of the trifluorotoluene complexes significantly increased which is an indication that the aromaticity of the arene unit is improved in the trifluorotoluene complexes. The communication of electron through HB interactions between the arene and PTA units which are remote to each other improved significantly due to fluorination. All the four complexes are associated with intramolecular HB interaction some of which are unusual (Brovarets' et al., 2013;Nikolaienko, Bulavina, & Hovorun, 2012;Yurenko, Zhurakivsky, Samijlenko, & Hovorun, 2011). In complex 1 and 2, there is unusual HB between the C of arene and one H atoms of the PTA which is as a result of the arene unit acting as charge acceptor since it is a π-ligand that is characterized with electron deficiency. In all the complexes, the strongest HB exist in the hydrated complexes between the Cl and the H atoms of water molecule (Figure 3) which were also confirmed by the bond order analysis and higher values of ρ(r) and r 2 q(r) (Tables S3). There is also a common HB in the unhydrated complexes 1 and 3 that exists between one of the Cl and the H atoms of the PTA which is far less in strength to that of the hydrated. Fluorination in complexes 3 and 4 significantly improved their HB network and can be ascribed to the higher charge transfer and electrical properties but lower overall hydrogen interaction Note: ρ(r) is electron density, r 2 q(r) is the Laplancian of Rho, BPL -GBL_I is bond strain, V is virial field (potential energy density), G is Lagrangian form of kinetic energy density, K is hamiltonian form of kinetic energy density, L (i.e. K -G) is lagrangian density which is (À1/4)r 2 q(r) while |V/G| is the ratio of PE to KE and the higher its magnitude the stronger the bond. energy observed for these complexes (Table 5 and  Table S1). This may be responsible for the reported higher anticancer activities of the fluorinated complexes as a result of increasing in number and strength of HB which can lead to increase in the sensitivity of some of the atoms and stability of complexes.
The correlation table was constructed for all the bond parameters computed during the QTAIM analysis (Table S2) over all the existing bonds in each of the four complexes. This is to understand the relative effect of these parameters on the strength of all atomic bond interactions in the complexes. The values of the density Table 8. Selected atomic properties derived through the quantum theory of atoms in molecules analysis for the four complexes using combined basis sets DGDZVP(Ru)|6-31 + G(d,p) (all the data in atomic units).    (ρ(r)) are shown to be highly inversely proportional to the Laplacian values of the density (r 2 q(r)) which is an indication that a bond with high ρ(r) values will be associated with very high negative values of r 2 q(r) which is typical of strong covalent bonds except the metal-ligand bonds with high positive r 2 q(r). The bonds with high ρ(r) and highly negative r 2 q(r) will be characterized with shorter bond length (GBL_I), lower bond stretch (GPL-GBL_I), averagely higher kinetic energy (K), highly negative potential (V) and high magnitude of the V and Lagrangian kinetic energy G ratio (V/G). The correlation shows that a high bond stretching is averagely a consequence of longer bond distance (GBL_I) and is characterized with averagely lower K and higher V. The Lagrangian density (L which is K -G) is the direct inverse of r 2 q(r) (showing to be À1/4r 2 q(r)), it is inversely proportional to GBL_I and ratio V/G. The value of GBL_I is directly proportional to V/G which is an indication that the shorter bonds are characterized with high magnitude of V/G. The ellipticity on the average is inversely correlated with the ρ(r) which means it must be directly correlated with r 2 q(r) which is an indication that bonds that are strong non-covalent which are usually characterized with high positive values of r 2 q(r) will have high values of ellipticity. It has been shown that a very flat electron density region that is characterized with a very low average values for ρ(r) and r 2 q(r) are usually found to have a relatively high ellipticity (Farrugia & Senn, 2012).

The QTAIM analysis of intra-and inter-atomic properties
The properties of selected atoms of interest which participate in the M-L bond (Table 8), HB and nitrogen atoms of the PTA (Table S5)  numerical integration (Platts et al., 2011). All the atoms (except H atoms) in the complexes are more localized with higher % Loc(A) while H atoms are characterized with higher % Deloc(A,A′) which is an indication that the H atoms of these complexes can easily be perturbed by external influences such as an electric field (Platts et al. 2011). Atoms such as Cl, Ru, and P have the highest Vol(A) in a descending order (Table 8 and Table S5) which consequently resulted in lower ρ(r) and r 2 q(r) bond interactions for the Ru-Cl and Ru-P bonds (Table 7 and Table S3) that involve the interaction of two atoms of large V(A). The changes in the atomic properties of Ru metal give insight into the hypothesis of the activation of these complexes by hydrolysis. The charge distribution on the arene carbon atoms (Table 8 and Table S5) shows that they are charge acceptor centre which further explain the observed MLCT. In order to understand the chemistry of each atom in the complexes, the correlation of all the computed atomic properties is constructed over all the atoms present in each complex (Table S4). The electronic kinetic energy of each atom (K(A)) is significantly affected by the magnitude of the bond dipole moment of each atom (|Mu_Bond(A)|) and the total dipole of each atom (|Mu (A)|). The Mu-Bond(A) is the main determinant factor of the total dipole (|Mu(A)|) and also have high effect on all the computed atomic properties except its poor correlation with the atomic charge (q(A)). Also, the number of total electron (N(A)), localized electron (Li(A)), and percentage localized electrons (%Loc(A)) have very high direct effect on the |Mu-Bond(A)| while percentage delocalized electrons (%Deloc(A,A′)) has reverse effect. Each atomic volume (Vol(A)) constructed using isovalue of .001 is mostly influenced by the Mu_Bond(A) and Mu (A) than the N(A). There is a noticeable inverse relation in between the q(A) and the Vol(A).
The sum total of all the intra-and interatomic properties computed over all the atoms in each complex is presented in Supplementary Table S6. The sum over of the total dipole (Mu) and K(A) of the trifluorotoluene complexes 3 and 4 is higher than that of complexes 1 and 2 which may contribute to the reported higher anticancer activities of the fluorinated complexes. Comparing the properties of the hydrolyzed complexes to the unhydrolyzed complexes, there is an decrease in the Li(A), K(A) and dipole properties, while there is a increase in the DI(A,A′)/2.
3.6. QTAIM analysis using PBE0/ECP(Ru, Cl, P)| 6-31G ⁄ The topological features using the mixed basis set where the SBKJC VDZ ECP basis set is applied on Ru, P, and Cl atoms of the complexes as explained in the computational method referred to as PBE0/ECP(Ru, Cl, P)|6-31G ⁄ , shows a common non-nuclear attractor (NNA) critical point (CP) that is, (3, -3) between the Ru-P bond which was never observed when all electron higher basis sets DGDZVP(Ru)|6-31 + G(d,P) and when minimal basis set 3-21G were used. This is an indication that the presence of NNA in these complexes is just a computational artifact of ECP basis set which could not effectively account for all the electrons density around the atoms. The NNA is introduced to compensate for the electrons deficiency which specifically appears to be within the electron density of P atom indicating the possibility of limiting the ECP basis set to metal atom only when computing the properties that demand all electron density. There have been reports on NNA feature which show that it is beyond just an artifact of computational methods but a genuine feature of the EDD of some complexes (Timerghazin et al., 2011) with an instance of the first unambiguous experimental evidence of such a feature in a stable molecule has been reported (Platts et al., 2011). Our observation of NNA where the core electrons are not explicitly accounted for in ECP basis set, agrees well with the reason that the NNA originate from the shape of valence molecular orbitals and that it might occur in bonds of low polarity in which core contributions are negligible and the radial form of the valence orbitals dominates the total density (Edgecombe, Esquivel, Smith, & Muller-Plathe, 2002;Platts et al., 2011).

Conclusions
In this paper, the intramolecular properties of rapta-T, rapta-CF3 and their hydrated models are computed through the NBO, NPA, and QTAIM analysis using Firefly, G09 and AIMAll packages. Several factors that characterized the behavior of each atom in the complexes and their interatomic bond interactions are presented. The natures of the polarization (c A ), second perturbation energies (E (2) ) of the delocalized orbitals, HOMO and LUMO show that the complexes are characterized with MLCT and a little features of LMCT observed especially from the hydrated complexes. The bond order analysis and the Laplacians of the electron density (r 2 q(r)) show that any of the two chloride atoms in unhydrolyzed complexes can be a leaving group in order for the hydrolysis to take place but the possibility of the second chloride leaving after the hydrolysis becomes rare as their bond order and r 2 q(r) appreciably increased. The NEDA analysis shows that the stability of the hydrated complexes are predominantly characterized by the charge transfer while polarization is predominant in the unhydrated complexes. The hydrolyzed complexes are characterized with higher values induced dipole and HB stabilization energy which gives a rational behind the reported activation of the complexes by hydrolysis. The features QTAIM analysis show that the stability of the complexes are significantly enhanced by the strength of the exiting HB and all the Ru-Ligand bonds are shown to be dative covalent bond characterized with high values of density and positive Laplacian of density. The complexes with trifluorotoluene are found to be characterized with stronger and higher number of intramolecular HB interactions which consequently resulted in higher charge transfer, polarizability and synergistic effects (higher induced dipole and induced wavefunction) of the different units of ligands that made up the complexes. This synergistic effects of each coordinated ligand on other ligands through the charge transfer and network of HB can lead to highly cytotoxic species as it was experimentally suggested (Stepanenko et al., 2011). The atomic properties of the Ru atom change from the unhydrolyzed complexes to the hydrolyzed complexes which further highlight the mechanism of activation by hydrolysis. The higher total K(A) and Mu(A) of the trifluorotoluene complexes can possibly contribute to their reported higher anticancer activities. Also, the correlation that exists among the computed properties can help in the development of force field for these complexes.