Accuracy of free energies of hydration for organic molecules from 6-31g*-derived partial charges

Absolute free energies of hydration have been computed for 13 diverse organic molecules using partial charges derived from ab initio 6-31G* wave functions. Both Mulliken charges and charges fit to the electrostatic potential surface (EPS) were considered in conjunction with OPLS Lennard–Jones parameters for the organic molecules and the TIP4P model of water. Monte Carlo simulations with statistical perturbation theory yielded relative free energies of hydration. These were converted to absolute quantities through perturbations to reference molecules for which absolute free energies of hydration had been obtained previously in TIP4P water. The average errors in the computed absolute free energies of hydration are 1.1 kcal/mol for the 6-31G* EPS charges and 4.0 kcal/mol for the Mulliken charges. For the EPS charges, the largest individual errors are under 2 kcal/mol except for acetamide, in which case the error is 3.7 kcal/mol. The hydrogen bonding between the organic solutes and water has also been characterized. © John Wiley & Sons, Inc.     

Optimal scaling factors for CM1 and CM3 atomic charges in RM1-based aqueous simulations

Scaling factors for atomic charges derived from the RM1 semiempirical quantum mechanical wavefunction in conjunction with CM1 and CM3 charge models have been optimized by minimizing errors in absolute free energies of hydration, ΔG_hyd, for a set of 40 molecules. Monte Carlo statistical mechanics simulations and free energy perturbation theory were used to annihilate the solutes in gas and in a box of TIP4P water molecules. Lennard–Jones parameters from the optimized potentials for liquid simulations‐all atom (OPLS–AA) force field were utilized for the organic compounds. Optimal charge scaling factors have been determined as 1.11 and 1.14 for the CM1R and CM3R methods, respectively, and the corresponding unsigned average errors in ΔG_hyd relative to experiment were 2.05 and 1.89 kcal/mol. Computed errors in aniline and two derivatives were particularly large for RM1 and their removal from the data set lowered the overall errors to 1.61 and 1.75 kcal/mol for CM1R and CM3R. Comparisons are made to the AM1 method which yielded total errors in ΔG_hyd of 1.50 and 1.64 kcal/mol for CM1A*1.14 and CM3A*1.15, respectively. This work is motivated by the need for a highly efficient yet accurate quantum mechanical (QM) method to study condensed‐phase and enzymatic chemical reactions via mixed QM and molecular mechanical (QM/MM) simulations. As an initial test, the Menshutkin reaction between NH₃ and CH₃Cl in water was computed using a RM1/TIP4P‐Ew/CM3R procedure and the resultant ΔG^?, ΔG_rxn, and geometries were in reasonable accord with other computational methods; however, some potentially serious shortcomings in RM1 are discussed. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Improved interaction potentials for charged residues in proteins

Electrostatic interactions dominate the structure and free energy of biomolecules. To obtain accurate free energies involving charged groups from molecular simulations, OPLS-AA parameters have been reoptimized using Monte Carlo free energy perturbation. New parameters fit a self-consistent, experimental set of hydration free energies for acetate (Asp), propionate (Glu), 4-methylimidazolium (Hip), n-butylammonium (Lys), and n-propylguanidinium (Arg), all resembling charged residue side chains, including beta-carbons. It is shown that OPLS-AA free energies depend critically on the type of water model, TIP4P or TIP3P; i.e., each water model requires specific water-charged molecule interaction potentials. New models (models 1 and 3) are thus described for both water models. Uncertainties in relative free energies of charged residues are approximately 2 kcal/mol with the new parameters, due to variations in system setup (MAEs of ca. 1 kcal/mol) and noise from simulations (ca. 1 kcal/mol). The latter error of approximately 1 kcal/mol contrasts MAEs from standard OPLS-AA of up to 13 kcal/mol for the entire series of charged residues or up to 5 kcal/mol for the cationic series Lys, Arg, and Hip. The new parameters can be used directly in molecular simulations with no modification of neutral residues needed and are envisioned to be particular important in simulations where charged residues change environment.     

Predicting hydration free energies using all-atom molecular dynamics simulations and multiple starting conformations

Molecular dynamics simulations in explicit solvent were applied to predict the hydration free energies for 23 small organic molecules in blind SAMPL2 test. We found good agreement with experimental results, with an RMS error of 2.82 kcal/mol over the whole set and 1.86 kcal/mol over all the molecules except several hydroxyl-rich compounds where we find evidence for a systematic error in the force field. We tested two different solvent models, TIP3P and TIP4P-Ew, and obtained very similar hydration free energies for these two models; the RMS difference was 0.64 kcal/mol. We found that preferred conformation of the carboxylic acids in water differs from that in vacuum. Surprisingly, this conformational change is not adequately sampled on simulation timescales, so we apply an umbrella sampling technique to include free energies associated with the conformational change. Overall, the results of this test reveal that the force field parameters for some groups of molecules (such as hydroxyl-rich compounds) still need to be improved, but for most compounds, accuracy was consistent with that seen in our previous tests.     

Structures,binding energies,temperature effects,infrared spectroscopy of [Mg(NH3)n = 1−10]+ clusters from DFT and MP2 investigations

The possible isomers of [Mg(NH₃)_{n = 1 − 10}]⁺ clusters have been investigated using both M06-2X/6-31++G(d,p) and MP2/6-31++G(d,p) levels of theory. The isomeric distribution for each n size has been studied as a function of temperatures ranging from 25 to 400 K. To the best of our knowledge, for clusters size n > 6, this is the first theoretical study available in the literature. From the calculated values in the considered clusters and using a fitting procedure, we have evaluated the binding energies (−14.0 kcal/mol), clustering energies (−10.1 kcal/mol), clustering free energies (−2.8 kcal/mol), and clustering enthalpies (−10.3 kcal/mol). On the basis of our structural and infrared (IR) spectroscopy outcomes, we find that the first solvation shell can hold up to six ammonia molecules. © 2019 Wiley Periodicals, Inc.     

An Ab initio study on the conformations of protonated,neutral, and deprotonated amidine

Ab initio SCF molecular orbital calculations have been performed to ascertain the conformational preferences of protonated, neutral, and deprotonated amidine [HC(?NH)NH₂], using the 3-21G split valence basis set. The states of eight stable species, eight transition states, and four higher-order saddle points have been determined by complete geometry optimization utilizing analytic energy gradient techniques. Protonation at the amidine ?NH is preferred over the –NH₂ site by 37.1 kcal/mol. Neutral amidine has rotational barriers of 9.6 and 11.7 kcal/mol for the HN?CN cis and trans isomers, respectively, while all the stable HC(NH₂)₂⁺ and HC(NH)₂^? species possess torsional barriers larger than 23 kcal/mol. There is, however, essentially free C—N single-bond rotation in HC(?NH)NH₃⁺, the calculated barriers being 0.7 and 1.8 kcal/mol for the cis and trans HN?CN isomers, respectively.     

The nature of the bonding of Li+ to H2O and NH3; A3 initio studies

Ab initio wavefunctions have been calculated for the complex of Li⁺ with NH₃ and H₂O in order to better characterize the nature of the bonding. Hartree—Fock and generalized valence bond calculations were performed using a double zeta basis plus polarization functions. The binding energies obtained at the GVB level are D_e (Li⁺ — NH₃) = 40.4 kcal/mol and D_e (Li⁺ ? H₂O) = 37.6 kcal/mol, in reasonable agreement with experimental values. Model calculations indicate that the Li⁺ ? base bond is basically electrostatic. Small basis sets were found to lead to D_e as large as 75 kcal/mol for Li⁺ — NH₃, a significant overestimation. Repulsions due to the Li⁺ core are responsible for keeping the Li⁺ too far away for significant relaxation effects.     

Experimentation with different thermodynamic cycles used for pKa calculations on carboxylic acids using complete basis set and Gaussian‐n models combined with CPCM continuum solvation methods

Complete basis set and Gaussian‐n methods were combined with Barone and Cossi's implementation of the polarizable conductor model (CPCM) continuum solvation methods to calculate pK_a values for six carboxylic acids. Four different thermodynamic cycles were considered in this work. An experimental value of ?264.61 kcal/mol for the free energy of solvation of H⁺, ΔG_s(H⁺), was combined with a value for G_gas(H⁺) of ?6.28 kcal/mol, to calculate pK_a values with cycle 1. The complete basis set gas‐phase methods used to calculate gas‐phase free energies are very accurate, with mean unsigned errors of 0.3 kcal/mol and standard deviations of 0.4 kcal/mol. The CPCM solvation calculations used to calculate condensed‐phase free energies are slightly less accurate than the gas‐phase models, and the best method has a mean unsigned error and standard deviation of 0.4 and 0.5 kcal/mol, respectively. Thermodynamic cycles that include an explicit water in the cycle are not accurate when the free energy of solvation of a water molecule is used, but appear to become accurate when the experimental free energy of vaporization of water is used. This apparent improvement is an artifact of the standard state used in the calculation. Geometry relaxation in solution does not improve the results when using these later cycles. The use of cycle 1 and the complete basis set models combined with the CPCM solvation methods yielded pK_a values accurate to less than half a pK_a unit. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Solvation free energies calculated using the GB/SA model: Sensitivity of results on charge sets,protocols, and force fields

The sensitivity of aqueous solvation free energies (SFEs), estimated using the GB/SA continuum solvent model, on charge sets, protocols, and force fields, was studied. Simple energy calculations using the GB/SA solvent model were performed on 11 monofunctional organic compounds. Results indicate that calculated SFEs are strongly dependent on the charge sets. Charges derived from electrostatic potential fitting to high level ab initio wave functions using the CHELPG procedure and “class IV” charges from AM1/CM1a or PM3/CM1p calculations yielded better results than the corresponding Mulliken charges. Calculated SFEs were similar to MC/FEP energies obtained in the presence of explicit TIP4P water. Further improvements were obtained by using GVB/6-31G** and MP2/6-31+G** (CHELPG) charge sets that included correlation effects. SFEs calculated using charge sets assigned by the OPLSA* force field gave the best results of all standard force fields (MM2*, MM3*, MMFF, AMBER*, and OPLSA*) implemented in MacroModel. Comparison of relative and absolute SFEs computed using either the GB/SA continuum model or MC/FEP calculations in the presence of explicit TIP4P water showed that, in general, relative SFEs can be estimated with greater accuracy. A second set of 20 mono- and difunctional molecules was also studied and relative SFEs estimated using energy minimization and thermodynamic cycle perturbation (TCP) protocols. SFEs calculated from TCP calculations using the GB/SA model were sensitive to bond lengths of dummy bonds (i.e., bonds involving dummy atoms). In such cases, keeping the bond lengths of dummy bonds close to the corresponding bond lengths of the starting structures improved the agreement of TCP-calculated SFEs with energy minimization results. Overall, these results indicate that GB/SA solvation free energy estimates from simple energy minimization calculations are of similar accuracy and value to those obtained using more elaborate TCP protocols. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 769–780, 1998     

The remarkably invariant interaction energies of lithium first-row compounds with water and with ammonia

Solvation energies of lithium first-row compounds LiX (X ? H, Li, BeH, BH₂, CH₃, NH₂, OH, F) and of the lithium cation with the model solvents, water and ammonia, have been calculated ab inito (MP2/6-31 + G^*//6-31G^* with zero-point vibrational energy corrections at 3-21G//3-21G). The solvation energies are found to be remarkably constant: ?18.0 ± 1.2 and ?21.5 ± 1.3 kcal/mol for the hydrates and ammonia solvates, respectively. This independence on the nature of X is due largely to the ionic character of the LiX compounds (dipole moments 4.7–6.6 debye). The unexpectedly high solvation energies of the lithium molecule (?14.3 and ?17.8 kcal/mol, respectively) are due to the polarizability of Li₂. At the same level, the lithium cation has interaction energies with H₂O and NH₃ of ?34.1 and ?39.7 kcal/mol, respectively. For the hydrates of LiOH and LiF cyclic structures with hydrogen bonds and somewhat increased solvation energies also are described.     

Hydration of methylamine and methylammonium ion: structural and thermodynamic properties from the data of the integral equation method in the RISM approximation

The structural and thermodynamic properties of hydration of methylamine and methyl-ammonium ion were investigated by the integral equations method in the RISM approximation. According to calculations, the average number of water molecules in the first hydration shell of CH₃ group is 14.4 for aqueous methylamine and 12.7 for aqueous methylammonium solution. The first hydration shells of the NH₂ group of methylamine and the NH₃ ⁺ group of methylammonium ion contain 6.9 and 5.6 water molecules, respectively. The average number of H-bonds formed by the NH₂ group is 2.4 and that formed by the NH₃ ⁺ group is 3. The results obtained show no H-bonding between the nitrogen atom of NH^{3 +} group of methylammonium and water molecules. The hydrogen atom of water participating in the hydrogen bonding with the nitrogen atom of methylamine now is a constituent of the NH₃ ⁺ group of methylammonium ion. The hydration free energies and the ionization constant calculated within the framework of the RISM theory are in good agreement with experimental data.     

Solvation free energies of amino acid side chain analogs for common molecular mechanics water models

Quantitative free energy computation involves both using a model that is sufficiently faithful to the experimental system under study (accuracy) and establishing statistically meaningful measures of the uncertainties resulting from finite sampling (precision). In order to examine the accuracy of a range of common water models used for protein simulation for their solute/solvent properties, we calculate the free energy of hydration of 15 amino acid side chain analogs derived from the OPLS-AA parameter set with the TIP3P, TIP4P, SPC, SPC/E, TIP3P-MOD, and TIP4P-Ew water models. We achieve a high degree of statistical precision in our simulations, obtaining uncertainties for the free energy of hydration of 0.02-0.06 kcal/mol, equivalent to that obtained in experimental hydration free energy measurements of the same molecules. We find that TIP3P-MOD, a model designed to give improved free energy of hydration for methane, gives uniformly the closest match to experiment; we also find that the ability to accurately model pure water properties does not necessarily predict ability to predict solute/solvent behavior. We also evaluate the free energies of a number of novel modifications of TIP3P designed as a proof of concept that it is possible to obtain much better solute/solvent free energetic behavior without substantially negatively affecting pure water properties. We decrease the average error to zero while reducing the root mean square error below that of any of the published water models, with measured liquid water properties remaining almost constant with respect to our perturbations. This demonstrates there is still both room for improvement within current fixed-charge biomolecular force fields and significant parameter flexibility to make these improvements. Recent research in computational efficiency of free energy methods allows us to perform simulations on a local cluster that previously required large scale distributed computing, performing four times as much computational work in approximately a tenth of the computer time as a similar study a year ago.     

Reaction mechanism of platinum dimer cation with ammonia based on the relativistic density functional study

The gas‐phase reactions between Pt and NH₃ have been investigated using the relativistic density functional approach (ZORA‐PW91/TZ2P). The quartet and doublet potential energy surfaces of Pt + NH₃ have been explored. The minimum energy reaction path proceeds through the following steps: Pt(⁴Σ_u) + NH₃ → q‐1 → d‐2 → d‐3 → d‐4 → d‐Pt₂NH⁺ + H₂. In the whole reaction pathway, the step of d‐2 → d‐3 is the rate‐determining step with a energy barrier of 36.1 kcal/mol, and exoergicity of the whole reaction is 12.0 kcal/mol. When Pt₂NH⁺ reacts with NH₃ again, there are two rival reaction paths in the doublet state. One is degradation of NH and another is loss of H₂. In the case of degradation of NH, the activation energy is only 3.4 kcal/mol, and the overall reaction is exothermic by 8.9 kcal/mol. Thus, this reaction is favored both thermodynamically and kinetically. However, in the case of loss of H₂, the rate‐determining step's energy barrier is 64.3 kcal/mol and the overall reaction is endothermic by 8.5 kcal/mol, so it is difficult to take place. Predicted relative energies and barriers along the suggested reaction paths are in reasonable agreement with experimental observations. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Solvent effect on K to Na ion mutation: a Monte Carlo simulation study

Monte Carlo simulation studies of statistical perturbation theory (SPT) have been carried out to investigate the solvent effects on the relative free energies of solvation and the difference in partition coefficients (log P) for K⁺ to Na⁺ ion mutation in the several solvents. We compared the relative free energies for interconversion of K⁺ to Na⁺, in H₂O (TIP4P) in this study with those published works, that in H₂O (TIP4P) is −16.55 kcal/mol in this study, those of the published works are −17.6, −17.3 and −17.31 kcal/mol and that of the experiment is −17.6 kcal/mol, respectively. Comparing the relative free energies for interconversion of K⁺ to Na⁺, in CH₃OH in this study with those published works, that in CH₃OH is −18.08±0.28 kcal/mol in this study, that of molecular dynamic simulation is −19.6±0.4 kcal/mol and that of the experimental work is −17.3 kcal/mol, respectively. There is good agreement among the several studies if we consider both methods of obtaining the solvation (or hydration) free energies and the standard deviations. For the present K⁺ and Na⁺ ions, the relative free energies of solvation vs Born's function of solvents are decreased with increasing Born's function of solvent except for CH₃OH, THF and MEOME. There is also good agreement between the calculated structural properties in this study and the computer simulation, ab initio and experimental works.     

Gas-phase acidities of cysteine-polyglycine peptides: The effect of the cysteine position

The sequence and conformational effects on the gas-phase acidities of peptides have been studied by using two pairs of isomeric cysteine-polyglycine peptides, CysGly_3,4NH₂ and Gly_3,4CysNH₂. The extended Cooks kinetic method was employed to determine the gas-phase acidities using a triple quadrupole mass spectrometer with an electrospray ionization source. The ion activation was achieved via collision-induced dissociation experiments. The deprotonation enthalpies (Δ_acid H) were determined to be 323.9 ± 2.5 kcal/mol (CysGly₃NH₂), 319.2 ± 2.3 kcal/mol (CysGly₄NH₂), 333.8 ± 2.1 kcal/mol (Gly₃CysNH₂), and 321.9 ± 2.8 kcal/mol (Gly₄CysNH₂), respectively. The corresponding deprotonation entropies (Δ_acid S) of the peptides were estimated. The gas-phase acidities (Δ_acid G) were derived to be 318.4 ± 2.5 kcal/mol (CysGly₃NH₂), 314.9 ± 2.3 kcal/mol (CysGly₄NH₂), 327.5 ± 2.1 kcal/mol (Gly₃CysNH₂), and 317.4 ± 2.8 kcal/mol (Gly₄CysNH₂), respectively. Conformations and energetic information of the neutral and anionic peptides were calculated through simulated annealing (Tripos), geometry optimization (AM1), and single point energy calculations (B3LYP/6-31+G(d)), respectively. Both neutral and deprotonated peptides adopt many possible conformations of similar energies. All neutral peptides are mainly random coils. The two C-cysteine anionic peptides, Gly_3,4(Cys-H)⁻NH₂, are also random coils. The two N-cysteine anionic peptides, (Cys-H)⁻Gly_3,4NH₂, may exist in both random coils and stretched helices. The two N-cysteine peptides, CysGly₃NH₂ and CysGly₄NH₂, are significantly more acidic than the corresponding C-terminal cysteine ones, Gly₃CysNH₂ and Gly₄CysNH₂. The stronger acidities of the former may come from the greater stability of the thiolate anion resulting from the interaction with the helix-macrodipole, in addition to the hydrogen bonding interactions.     

Theoretical Study of Sticking Processes on Molecular Models of Silica Surfaces

The adsorption of small charged and neutral molecules on silica supports was modelled using perturbative post-Hartree–Fock quantum chemical methods (MP2 and MP4). The simplest spherosiloxane compound (H₄Si₄O₆) was used to mimic the surface while several molecules (namely CH₄, NH ₄ ⁺ , NH₃, OH ₃ ⁺ H ₃ ⁺ ) were considered as adsorbed species. Direct sticking of the molecules on one of the (Si–O)₃ ring leads to very different binding energies for cations (more than 11 kcal/mol) and neutral molecules (a few kcal/mol). These results indicate a dominant strong ion–multipole interaction for the first ones and a weak dispersion-type interaction for the latter. If the spherosiloxane cluster is screened by a mantle of accreted dust as it is the case in interstellar environment, the value of the binding energies, computed using the continuum dielectric theory, are predicted to be significantly reduced.     

Mechanism and kinetics of the reaction of the 2-propargyl radical with ammonia

Gas-phase mechanism and kinetics of the reactions of the 2-propargyl radical (H₂CCCH), an important intermediate in combustion processes, with ammonia were investigated using ab initio molecular orbital theory at the coupled-cluster CCSD(T)//B3LYP/6-311++G(3df,2p) method in conjunction with transition state theory (TST), variational transition state theory (VTST), and Rice–Ramsperger–Kassel–Macus (RRKM) calculations for rate constants. The potential energy surface (PES) constructed shows that the C₃H₃ + NH₃ reaction has four main entrances, including two H-abstraction and two addition channels in which the former are energetically more favorable. The H-abstraction channels occur via energy barriers of 24 (T0/P2) and 26 kcal/mol (T0/P3) forming loose van de Waals complexes, COM_1 (12 kcal/mol) and COM_2 (14 kcal/mol), respectively. These complexes can easily be decomposed via barrier-less processes resulting HCCCH₃ + NH₂ (P2, 14 kcal/mol) and HCCCH₃ + NH₂ (P3, 15 kcal/mol), respectively. The additional channels occur initially by formation of two intermediate states, H₂CCCHNH₃ (35 kcal/mol) and H₂CC(NH₃)CH (37 kcal/mol) via energy barriers of 37 and 40 kcal/mol at T0/1 and T0/5, respectively, followed by isomerization and decomposition yielding 21 different products. These processes are fully depicted in an as-complete-as-possible PES. The rate constants and product branching ratios for the low-energy channels calculated show that the C₃H₃ + NH₃ reaction is almost pressure-independent. For the temperature range of 300–2000 K, the HCCCH₃ + NH₂ is the major product, whereas the minor one, HCCCH₃ + NH₂, has more contribution when temperature increases. Theoretical results on the mechanism and kinetics of the reaction considered may be helpful for future experiments as well as for understanding the role of the propargyl radical in combustion chemistry.     

An ab initio molecular orbital study of the deprotonation of amines

The geometries of the amines NH₂X and amido anions NHX^?, where X = H, CH₃, NH₂, OH, F, C₂H, CHO, and CN have been optimized using ab initio molecular orbital calculations with a 4-31G basis set. The profiles to rotation about the N? X bonds in CH₃NH^?, NH₂NH^?, and HONH^? are very similar to those for the isoprotic and isoelectronic neutral compounds CH₃OH, NH₂OH, and HOOH. The amines with unsaturated bonds adjacent to the nitrogen atoms undergo considerable skeletal rearrangement on deprotonation such that most of the negative charge of the anion is on the substituent. The computed order of acidity for the amines NH₂X is X = CN > HCO > F ≈ C₂H > OH > NH₂ > CH₃ > H and for the reaction NHX^? + H⁺ → NH₂X the computed energies vary over the range 373–438 kcal/mol.     

Ab initio MO calculation of hydration energies of ammonium ions and their solvation effect

The hydration energies for the NH⁺₄ and CH₃NH⁺₃ ions were calculated by an ab initio MO method. The aqueous solvation energy difference between these two ions was found to be accounted for by the interactions of the ions with a few solvent molecules.     

Clustering and activation in reactions of CoCp with hydrogen and methane

Gas-phase clustering reactions of CoCp⁺ with H₂ and with CH₄ were investigated using temperature-dependent equilibrium experiments. In both systems, the CoCp⁺ ion was found to form strong interactions with two ligands. The first and second H₂ groups cluster to CoCp⁺ with bond energies of 16.2 and 16.8 kcal/mol, respectively, while the first and second CH₄ groups cluster to CoCp⁺ with bond energies of 24.1 and 12.1 kcal/mol, respectively. These bond energies are in good agreement with those determined by density functional theory (DFT). Molecular geometries for the four clusters determined with DFT are also presented. Weak experimental bond energies of 0.9 kcal/mol for the third H₂ and 2.2 kcal/mol for the third CH₄ clustering to CoCp⁺ suggest these ligands occupy the second solvation shell of the ion. In addition to clustering in the methane system, H₂-elimination from CoCp(CH₄)₂⁺ was observed. The mechanism for this reaction was investigated by collision-induced dissociation experiments and DFT, which suggest the predominate H₂-elimination product is (c-C₅H₆)Co⁺---C₂H₅. Theory indicates that dehydrogenation requires the active participation of the Cp ring in the mechanism. Transfer of H and CH₃ groups to the C₅-ring ligand allows the metal center to avoid the high-energy Co(IV) oxidation state required when it forms two covalent bonds in addition to its interaction with a C₅-ring ligand.