QTAIM and ETS-NOCV analyses of intramolecular CH···HC interactions in metal complexes

The topological analysis, based on the quantum theory of atoms in molecules (QTAIM) of Bader and the ETS-NOCV charge and energy decomposition method have been used to characterize coordination bonds, chelating rings, and additional intramolecular interactions in the ZnNTA and ZnNTPA complexes in solvent. The QTAIM and ETS-NOCV studies have conclusively demonstrated that the H-clashes (they are observed only in the ZnNTPA complex and classically are interpreted as steric hindrance destabilizing a complex) are characterized by (i) the electron flow channel between the H-atoms involved, as discovered by the ETS-NOCV analysis (on average, ΔE(orb) = -1.35 kcal mol(-1)) and (ii) QTAIM-defined a bond path that indicates the presence of a preferred quantum-mechanical exchange channel, hence, they should be seen as H-H intramolecular bonding interactions. The main reason for the formation of a weaker ZnNTPA complex was attributed to the strain energy (from both QTAIM and ETS-NOCV techniques) and the larger Pauli repulsion contribution found from the ETS-NOCV analysis. An excellent agreement between physical properties controlling the stability of the two complexes was found from the two techniques, QTAIM and ETS-NOCV.     

Periodic trends and complexation chemistry of tetravalent actinide ions with a potential actinide decorporation agent 5-LIO(Me-3,2-HOPO): A relativistic density functional theory exploration

A relativistic density functional theory (DFT) study is reported which aims to understand the complexation chemistry of An⁴⁺ ions (An = Th, U, Np, and Pu) with a potential decorporation agent, 5-LIO(Me-3,2-HOPO). The calculations show that the periodic change of the metal binding free energy has an excellent correlation with the ionic radii and such change of ionic radii also leads to the structural modulation of actinide–ligand complexes. The calculated structural and binding parameters agree well with the available experimental data. Atomic charges derived from quantum theory of atoms in molecules (QTAIM) and natural bond order (NBO) analysis shows the major role of ligand-to-metal charge transfer in the stability of the complexes. Energy decomposition analysis, QTAIM, and electron localization function (ELF) predict that the actinide–ligand bond is dominantly ionic, but the contribution of orbital interaction is considerable and increases from Th⁴⁺ to Pu⁴⁺. A decomposition of orbital contributions applying the extended transition state-natural orbital chemical valence method points out the significant π-donation from the oxygen donor centers to the electron-poor actinide ion. Molecular orbital analysis suggests an increasing trend of orbital mixing in the context of 5f orbital participation across the tetravalent An series (Th-Pu). However, the corresponding overlap integral is found to be smaller than in the case of 6d orbital participation. An analysis of the results from the aforementioned electronic structure methods indicates that such orbital participation possibly arises due to the energy matching of ligand and metal orbitals and carries the signature of near-degeneracy driven covalency.     

DFT-B3LYP, NPA-, and QTAIM-based study of the physical properties of [M(II)(H2O)2(15-crown-5)] (M = Mn, Fe, Co, Ni, Cu, Zn) complexes

A density functional theory study of the structure of the title compounds with the divalent metal ions in their high-spin ground state, obtained using B3LYP/6-311++G(d,p) in vacuo and in aqueous solution simulated using a polarized continuum medium, is reported for the first time. The modeling reproduces the pseudo pentagonal bipyramidal crystallographic structures very well, including some asymmetry in the equatorial bonds lengths to the crown ether O donors. The very marked asymmetry in the Ni(2+) structure due to a Jahn-Teller distortion of a d(8) system in a D(5h) ligand field is also well reproduced. The gas phase binding energies of the complexes follow the order Mn(2+) < Fe(2+) < Co(2+) < Ni(2+) < Cu(2+) > Zn(2+), in precise agreement with the Irving-William series. Both the NPA and Bader charges show there is ligand-to-metal charge transfer; however, the values obtained from the NPA procedure, unlike those obtained from Bader's quantum theory of molecules approach, do not correlate with the electronegativity of the metal ions, the stabilization energies of the solvated complexes or the ionic radii of the metal ions, and so appear to be less reliable. The nature of the bonding between the ligands and the metal ions has been explored using the topological properties of the electron charge density. The metal-ligand bond distances were found to be exponentially correlated with the electron charge density, its Laplacian, and with its curvature in the direction of the bond path at M-O bond critical points. While the bonding with coordinated H(2)O is predominantly ionic, that to the crown ether donor atoms has some covalent character the extent of which increases across the first transition series. The delocalization indices of M-O bonds in these complexes correlate reasonably well with the electron density and its Laplacian at the bond critical points; this therefore provides a rapid and computationally very efficient way of determining these properties, from which insight into the nature of the bonding can be obtained, obviating the need for time-consuming integration over atomic basins.     

Actinium coordination chemistry: A density functional theory study with monodentate and bidentate ligands

In the current study, the coordination chemistry of nine-coordinate Ac(III) complexes with 35 monodentate and bidentate ligands was investigated using density functional theory (DFT) in terms of their geometries, charges, reaction energies, and bonding interactions. The energy decomposition analysis with naturals orbitals for chemical valence (EDA-NOCV) and the quantum theory of atoms in molecules (QTAIM) were employed as analysis methods. Trivalent Ac exhibits the highest affinities toward hard acids (such as charged oxophilic donors, fluoride), so its classification as a hard acid is justified. Natural population analysis quantified the involvement of 5f orbitals on Ac to be about 30% of total valence electron natural configuration indicating that Ac is a member of the actinide series. Pearson correlation coefficients were used to study the pairwise correlations among the bond lengths, ΔG reaction energies, charges on Ac and donor atoms, and data from EDA-NOCV and QTAIM. Strong correlations and anticorrelations were found between Voronoi charges on donor atoms with ΔG, EDA-NOCV interaction energies and QTAIM bond critical point densities.     

Density functional theory and topological analysis on the hydrogen bonding interactions in N-protonated adrenaline–DMSO complexes

In this study, complexes formed via hydrogen bond interactions between N-protonated adrenaline (AdH⁺) and DMSO have been studied by density functional theory (DFT). The relevant geometries, energies, and IR characteristics of the hydrogen bonds (H-bonds) have been systematically investigated. The natural bond orbital (NBO) and the quantum theory of atoms in molecule (QTAIM) analysis have also been applied to understand the nature of the hydrogen bonding interactions in complexes. The H-bonds involving amino or hydroxyls as H-donor are dominant H-bonds in complexes and are attributed to strong H-bonds. The weak H-bonds, such as π H-bonds and H-bonds involving methyl (DMSO) or methenyls (C2H6 and C5H7 of AdH⁺) as H-acceptors, were found in complexes as well. The complexes in which the dominant H-bond involves amino of AdH⁺ as H-donor are more stable than those with the dominant H-bond involving hydroxyls as H-donor. Some relationships between various properties of QTAIM, NBO, geometry as well as frequency were also investigated.     

Ab initio investigation of the complexes between bromobenzene and several electron donors: some insights into the magnitude and nature of halogen bonding interactions

Halogen bonding, a specific intermolecular noncovalent interaction, plays crucial roles in fields as diverse as molecular recognition, crystal engineering, and biological systems. This paper presents an ab initio investigation of a series of dimeric complexes formed between bromobenzene and several electron donors. Such small model systems are selected to mimic halogen bonding interactions found within crystal structures as well as within biological molecules. In all cases, the intermolecular distances are shown to be equal to or below sums of van der Waals radii of the atoms involved. Halogen bonding energies, calculated at the MP2/aug-cc-pVDZ level, span over a wide range, from -1.52 to -15.53 kcal/mol. The interactions become comparable to, or even prevail over, classical hydrogen bonding. For charge-assisted halogen bonds, calculations have shown that the strength decreases in the order OH- > F- > HCO2- > Cl- > Br-, while for neutral systems, their relative strengths attenuate in the order H2CS > H2CO > NH3 > H2S > H2O. These results agree with those of the quantum theory of atoms in molecules (QTAIM) since bond critical points (BCPs) are identified for these halogen bonds. The QTAIM analysis also suggests that strong halogen bonds are more covalent in nature, while weak ones are mostly electrostatic interactions. The electron densities at the BCPs are recommended as a good measure of the halogen bond strength. Finally, natural bond orbital (NBO) analysis has been applied to gain more insights into the origin of halogen bonding interactions.     

Modulation of Metallophilic and π–π Interactions in Platinum Cyclometalated Luminophores with Halogen Bonding

Luminescent cyclometalated complexes [M(C^N^N)CN] (M=Pt, Pd; HC^N^N=pyridinyl- (M=Pt 1 , Pd 5 ), benzyltriazolyl- (M=Pt 2 ), indazolyl- (M=Pt 3 , Pd 6 ), pyrazolyl-phenylpyridine (M=Pt 4 )) decorated with cyanide ligand, have been explored as nucleophilic building blocks for the construction of halogen-bonded (XB) adducts using IC₆F₅ as an XB donor. The negative electrostatic potential of the CN group afforded CN⋅⋅⋅I noncovalent interactions for platinum complexes 1 – 3 ; the energies of XB contacts are comparable to those of metallophilic bonding according to QTAIM analysis. Embedding the chromophore units into XB adducts 1 – 3 ⋅⋅⋅IC₆F₅ has little effect on the charge distribution, but strongly affects Pt⋅⋅⋅Pt bonding and π-stacking, which lead to excited states of MMLCT (metal–metal-to-ligand charge transfer) origin. The energies of these states and the photoemissive properties of the crystalline materials are primarily determined by the degree of aggregation of the luminophores via metal–metal interactions. The adduct formation depends on the nature of the metal and the structure of the metalated ligand, the variation of which can yield dynamic XB-supported systems, exemplified by thermally regulated transition 3 ↔ 3 ⋅⋅⋅IC₆F₅.     

A density functional theory and quantum theory of atoms-in-molecules analysis of the stability of Ni(II) complexes of some amino alcohol ligands

The structure of the complexes of the type [Ni(L)(H(2)O)(2)](2+), where L is an amino alcohol ligand, L = N,N'-bis(2-hydroxyethyl)-ethane-1,2-diamine (BHEEN), N,N'-bis(2-hydroxycyclohexyl)-ethane-1,2-diamine (Cy(2)EN), and N,N'-bis(2-hydroxycyclopentyl)-ethane-1,2-diamine, (Cyp(2)EN) were investigated at the X3LYP/6-31+G(d,p) level of theory both in the gas phase and in solvent (CPCM model) to gain insight into factors that control the experimental log K(1) values. We find that (i) analyses based on Bader's quantum theory of atoms in molecules (QTAIM) are useful in providing significant insight into the nature of metal-ligand bonding and in clarifying the nature of weak "nonbonded" interactions in these complexes and (ii) the conventional explanation of complex stability in these sorts of complexes (based on considerations of bond lengths, bite angles and H-clashes) could be inadequate and indeed might be misleading. The strength of metal-ligand bonds follows the order Ni-N > Ni-OH ≥ Ni-OH(2); the bonds are predominantly ionic with some covalent character decreasing in the order Ni-N > Ni-OH > Ni-OH(2), with Ni-OH(2) being close to purely ionic. We predict that the cis complexes are preferred over the trans complexes because of (i) stronger bonding to the alcoholic O-donor atoms and (ii) more favorable intramolecular interactions, which appear to be important in determining the conformation of a metal-ligand complex. We show that (i) the flexibility of the ligand, which controls the Ni-OH bond length, and (ii) the ability of the ligand to donate electron density to the metal are likely to be important factors in determining values of log K(1). We find that the electron density at the ring critical point of the cyclopentyl moieties in Cyp(2)EN is much higher than that in the cyclohexyl moieties of Cy(2)EN and interpret this to mean that Cyp(2)EN is a poorer donor of electron density to a Lewis acid than Cy(2)EN.     

Relativistic density functional theory study of dioxoactinide(VI) and -(V) complexation with alaskaphyrin and related Schiff-base macrocyclic ligands

Formation of complexes of alaskaphyrin 1, bi-pyen 2 and bi-tpmd 3 ligands with actinyl ions AnO2(n+), An = U, Np, Pu and n = 1, 2, was studied using density functional theory (DFT) within the scalar relativistic four-component approximation. The alaskaphyrin complexes of the uranyl are predicted to have a bent conformation, in contrast to the experimentally available X-ray data. This deviation is likely due to crystal packing effects. Apart from these conformational differences, calculated geometry parameters and vibrational frequencies are in agreement with the available experimental data. The character of bonding in the complexes is investigated using bond order analysis and extended transition states (ETS) energy decomposition. Metal-to-ligand bonds can be described as primarily ionic although substantial charge transfer is observed as well. Based on ETS analysis, it is shown that steric and/or fit/misfit requirements of actinyl cations to the ligand cavities, among the studied complexes, are the most favorable for the bi-pyen ligand 2, because its flexibility allows for optimal metal-to-donor-atom distances. Planarity of the equatorial coordination sphere of the actinide atom is found to be less important than the ability of a ligand to provide optimal uranium-to-nitrogen bond lengths. Experimental differences in demetalation rates between similar alaskaphyrin, bi-pyen and bi-tpmd uranyl complexes are explained as a result of easier protonation of the Schiff-base nitrogen of the latter. Reduction potentials calculated for the uranium complexes show a good agreement with the experiment, both in relative and in absolute terms.     

Theoretical investigation on charge‐assisted halogen bonding interactions in the complexes of bromocarbons with some anions

A series of dimeric complexes formed between bromocarbon molecules and two anions (Br^? and CN^?) have been investigated by using MP2 method. The quantum theory of atoms in molecules (QTAIM) and the second‐order perturbation natural bond orbital (NBO) approaches were applied to analyze the electron density distributions of these complexes and to explore the nature of charge‐assisted halogen bonding interactions. As anticipated, these interactions are significantly stronger relative to the corresponding neutral ones. The results derived from ab initio calculations described herein reveal a major contribution from the electrostatic interaction on the stability of the systems considered. Beside the electrostatic interaction, the charge‐transfer force and the second‐order orbital interaction also play an important role in the formation of the complexes, as a NBO analysis suggested. The presence of halogen bonds in the complexes has been identified in terms of the QTAIM methodology, and several linear relationships have been established to provide more insight into charge‐assisted halogen bonding interactions. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Van der Waals complexes of Cu, Ag, and Au with hydrogen sulfide. The bonding character

The electronic and structural features of the Cu...SH2, Ag...SH2, and Au...SH2 complexes are investigated by using the spin-adapted restricted open-shell HF coupled cluster CCSD(T) method combined with the second-order spin-free Douglas-Kroll-Hess (DKH) relativistic approach. M...SH2 complexes are nonplanar with bonding energies -5.99, -1.99, and -9.08 mHartree, respectively. Comparison with analogous M...OH2 and M...NH3 complexes allows us to establish general features of the bonding between coinage metal atoms and ligand molecules with the participation of their lone electron pairs. Consistent interpretation of the interaction effects can be obtained by using the molecular orbital picture of the M...L region. The bonding character is explained by stressing the importance of the charge transfer from the lone pair of the ligand to the metal atom. Relativistic changes of the metal element electron affinity and polarizability facilitate the understanding of major trends in the pattern of interactions between the coinage metal atoms and different lone pair donating ligands.     

Prospects for Three-Electron Donor Boronyl (BO) Ligands and Dioxodiborene (B(2)O(2)) Ligands as Bridging Groups in Binuclear Iron Carbonyl Derivatives

Recent experimental work (2010) on (Cy(3)P)(2)Pt(BO)Br indicates that the oxygen atom of the boronyl (BO) ligand is more basic than that in the ubiquitous CO ligand. This suggests that bridging BO ligands in unsaturated binuclear metal carbonyl derivatives should readily function as three-electron donor bridging ligands involving both the oxygen and the boron atoms. In this connection, density functional theory shows that three of the four lowest energy singlet Fe(2)(BO)(2)(CO)(7) structures have such a bridging η(2)-μ-BO group as well as a formal Fe-Fe single bond. In addition, all four of the lowest energy singlet Fe(2)(BO)(2)(CO)(6) structures have two bridging η(2)-μ-BO groups and formal Fe-Fe single bonds. Other Fe(2)(BO)(2)(CO)(n) (n = 7, 6) structures are found in which the two BO groups have coupled to form a bridging dioxodiborene (B(2)O(2)) ligand with B-B bonding distances of ～1.84 ?. All of these Fe(2)(μ-B(2)O(2))(CO)(n) structures have long Fe···Fe distances indicating a lack of direct iron-iron bonding. One of the singlet Fe(2)(BO)(2)(CO)(7) structures has such a bridging dioxodiborene ligand with cis stereochemistry functioning as a six-electron donor to the pair of iron atoms. In addition, the lowest energy triplet structures for both Fe(2)(BO)(2)(CO)(7) and Fe(2)(BO)(2)(CO)(6) have bridging dioxodiborene ligands with trans stereochemistry functioning as a four-electron donor to the pair of iron atoms.     

Electron density characteristics in bond critical point (QTAIM) versus interaction energy components (SAPT): the case of charge-assisted hydrogen bonding

Charge-assisted hydrogen bonds (CAHBs) of N-H···Cl, N-H···Br, and P-H···Cl type were investigated using advanced computational approach (MP2/aug-cc-pVTZ level of theory). The properties of electron density function defined in the framework of Quantum Theory of Atoms in Molecules (QTAIM) were estimated as a function of distance in H-bridges. Additionally, the interaction energy decomposition was performed for H-bonded complexes with different H-bond lengths using the Symmetry-Adapted Perturbation Theory (SAPT). In this way both QTAIM parameters and SAPT energy components could be expressed as a function of the same variable, that is, the distance in H-bridge. A detailed analysis of the changes in QTAIM and SAPT parameters due to the changes in H···A distance revealed that, over some ranges of H···A distances, electrostatic, inductive and dispersive components of the SAPT interaction energy show a linear correlation with the value of the electron density at H-BCP ρ(BCP). The linear relation between the induction component, E(ind), and ρ(BCP) confirms numerically the intuitive expectation that the ρ(BCP) reflects directly the effects connected with the sharing of electron density between interacting centers. These conclusions are important in view of charge density studies performed for crystals in which the distance between atoms results not only from effects connected with the interaction between atomic centers directly involved in bonding, but also from packing effects which may strongly influence the length of the H-bond.     

Hydrogen-hydrogen bonding: a stabilizing interaction in molecules and crystals

Bond paths linking two bonded hydrogen atoms that bear identical or similar charges are found between the ortho-hydrogen atoms in planar biphenyl, between the hydrogen atoms bonded to the C1-C4 carbon atoms in phenanthrene and other angular polybenzenoids, and between the methyl hydrogen atoms in the cyclobutadiene, tetrahedrane and indacene molecules corseted with tertiary-tetra-butyl groups. It is shown that each such H-H interaction, rather than denoting the presence of "nonbonded steric repulsions", makes a stabilizing contribution of up to 10 kcal mol(-1) to the energy of the molecule in which it occurs. The quantum theory of atoms in molecules-the physics of an open system-demonstrates that while the approach of two bonded hydrogen atoms to a separation less than the sum of their van der Waals radii does result in an increase in the repulsive contributions to their energies, these changes are dominated by an increase in the magnitude of the attractive interaction of the protons with the electron density distribution, and the net result is a stabilizing change in the energy. The surface virial that determines the contribution to the total energy decrease resulting from the formation of the H-H interatomic surface is shown to account for the resulting stability. It is pointed out that H-H interactions must be ubiquitous, their stabilization energies contributing to the sublimation energies of hydrocarbon molecular crystals, as well as solid hydrogen. H-H bonding is shown to be distinct from "dihydrogen bonding", a form of hydrogen bonding with a hydridic hydrogen in the role of the base atom.     

Isatin‐Schiff base copper(II) complexes—A DFT study of the metal‐ligand bonding situation

Herein, we report results of calculations based on density functional theory (BP86/TZVP) of a set of isatin‐Schiff base copper(II) and related complexes, 1‐12, that have shown significant pro‐apoptotic activity toward diverse tumor cells. The interaction of the copper(II) cation with different ligands has been investigated at the same level of theory. The strength and character of the Cu(II)‐L bonding was characterized by metal‐ligand bond lengths, vibrational frequencies, binding energies, ligand deformation energies, and natural population analysis. The metal‐ligand bonding situation was also characterized by using two complementary topological approaches, the quantum theory of atoms‐in‐molecules (QTAIM) and the electron localization function (ELF). The calculated electronic g‐tensor and hyperfine coupling constants present significant agreement with the EPR experimental data. The calculated parameters pointed to complex 10 as the most stable among the isatin‐Schiff base copper(II) species, in good agreement with experimental data that indicate this complex as the most reactive in the series. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Red- and blue-shifted hydrogen bonds: the Bent rule from quantum theory of atoms in molecules perspective

MP2/6-311++G(3pd,3df) calculations were performed on complexes of acetylene and fluoroform acting as the proton donating systems and different Lewis bases being the proton acceptors since these complexes are linked through C-H···Y hydrogen bonds. Quantum Theory of Atoms in Molecules (QTAIM) is applied to explain the nature of these interactions. The characteristics of bond critical points are presented for these complexes. The inter-relations between energetic and geometrical parameters as well as the parameters derived from the Natural Bond Orbital (NBO) theory are analyzed here. Red- and blue-shifted hydrogen bonds are detected for the complexes investigated and the differences between those interactions are analyzed from the QTAIM perspective. It is shown that such differences are in agreement with the Bent rule. The position of the bond critical point of the proton donating bond is connected with the nature of hydrogen bonding, that is, if it is blue- or red-shifted.     

Characterizing Pressure‐Induced Uranium CH Agostic Bonds

The diuranium(III) compound [UN′′₂]₂(μ‐η⁶:η⁶‐C₆H₆) (N′′=N(SiMe₃)₂) has been studied using variable, high‐pressure single‐crystal X‐ray crystallography, and density functional theory . In this compound, the low‐coordinate metal cations are coupled through π‐ and δ‐symmetric arene overlap and show close metal? CH contacts with the flexible methyl CH groups of the sterically encumbered amido ligands. The metal–metal separation decreases with increasing pressure, but the most significant structural changes are to the close contacts between ligand CH bonds and the U centers. Although the interatomic distances are suggestive of agostic‐type interactions between the U and ligand peripheral CH groups, QTAIM (quantum theory of atoms‐in‐molecules) computational analysis suggests that there is no such interaction at ambient pressure. However, QTAIM and NBO analyses indicate that the interaction becomes agostic at 3.2 GPa.     

Halogen bond versus hydrogen bond: The many‐body interactions approach

The analysis of interrelation between halogen bond and hydrogen bond in the (RX)(HNC)(HCN) complexes (R = CH₃, CF₃ and X = Cl, Br, I) was performed on the basis of DFT calculations. Both two‐body additive contributions and three‐body nonadditive contributions to the total interaction energy were discussed. QTAIM was used for topological analysis of electron density. Additionally, QTAIM analysis of electron density was performed for both two‐ and three‐body complexes. The electron charge transfer in trimers showed the dual character of the fragment with halogen atom involved into the investigated interactions—it acts as Lewis acid and Lewis base, depending on the type of interaction considered. The effect of cooperativity of X‐ and H‐bonding was assessed on the basis of many‐body interaction energy and electron density analysis. Additionally, an alternative two‐body model with the same situation (in the context of intermolecular interactions) is investigated. The anti‐cooperative effect was found also for this model.