A theoretical study of cyclohexyne addition to carbonyl-Cα bonds: allowed and forbidden electrocyclic and nonpericyclic ring-openings of strained cyclobutenes

The mechanism of cyclohexyne insertion into a C(O)-C(α) bond of cyclic ketones, explored experimentally by the Carreira group, has been investigated using density functional theory. B3LYP and M06-2X calculations were performed in both gas phase and THF (CPCM, UAKS radii). The reaction proceeds through a stepwise [2 + 2] cycloaddition of cyclohexyne to the enolate, followed by three disparate ring-opening possibilities of the cyclobutene alkoxide to give the product: (1) thermally allowed conrotatory electrocyclic ring-opening, (2) thermally forbidden disrotatory electrocyclic ring-opening, or (3) nonpericyclic C-C bond cleavage. Our computational results for the model alkoxide and potassium alkoxide systems show that the thermally allowed electrocyclic ring-opening pathway is favored by less than 1 kcal/mol. In more complex systems containing a potassium alkoxide (e-f), the barrier of the allowed conrotatory ring-opening is disfavored by 4-8 kcal/mol. This suggests that the thermodynamically more stable disrotatory product can be formed directly through a "forbidden" pathway. Analysis of geometrical parameters and atomic charges throughout the ring-opening pathways provides evidence for a nonpericyclic C-C bond cleavage, rather than a thermally forbidden disrotatory ring-opening. A true forbidden disrotatory ring-opening transition structure was computed for the cyclobutene alcohol; however, it was 19 kcal/mol higher in energy than the allowed conrotatory transition structure. An alternate mechanism in which the disrotatory product forms via isomerization of the conrotatory product was also explored for the alkoxide and potassium alkoxide systems.     

Theoretical study on the mechanism of a ring-opening reaction of oxirane by the active-site aspartic dyad of HIV-1 protease

Two possible mechanisms of the irreversible inhibition of HIV-1 protease by epoxide inhibitors are investigated on an enzymatic model using ab initio (MP2) and density functional theory (DFT) methods (B3LYP, MPW1K and M05-2X). The calculations predict the inhibition as a general acid-catalyzed nucleophilic substitution reaction proceeding by a concerted SN2 mechanism with a reaction barrier of ca. 15-21 kcal mol(-1). The irreversible nature of the inhibition is characterized by a large negative reaction energy of ca. -17-(-24) kcal mol(-1). A mechanism with a direct proton transfer from an aspartic acid residue of the active site onto the epoxide ring has been shown to be preferred compared to one with the proton transfer from the acid catalyst facilitated by a bridging catalytic water molecule. Based on the geometry of the transition state, structural data important for the design of irreversible epoxide inhibitors of HIV-1 protease were defined. Here we also briefly discuss differences between the epoxide ring-opening reaction in HIV-1 protease and epoxide hydrolase, and the accuracy of the DFT method used.     

Quantum chemical study of the mechanism of action of vitamin K carboxylase (VKC). IV. Intermediates and transition states

We studied proposed steps for the enzymatic formation of gamma-carboxyglutamic acid by density functional theory (DFT) quantum chemistry. Our results for one potentially feasible mechanism show that a vitamin K alkoxide intermediate can abstract a proton from glutamic acid at the gamma-carbon to form a carbanion and vitamin K epoxide. The hydrated carbanion can then react with CO2 to form gamma-carboxyglutamic acid. Computations at the B3LYP/6-311G** level were used to determine the intermediates and transition states for the overall process. The activation free energy for the gas-phase path is 22 kcal/mol, with the rate-limiting step for the reaction being the attack of the carbanion on CO2. Additional solvation studies, however, indicate that the formation of the carbanion step can be competitive with the CO2 attack step in high-dielectric systems. We relate these computations to the entire vitamin K cycle in the blood coagulation cascade, which is essential for viability of vertebrates.     

Mechanistic pathways of the hydroxyl radical reactions of quinoline. 2. Computational analysis of hydroxyl radical attack at C atoms

Density functional theory (DFT) calculations are employed to compare the mechanism of the *OH attacks at all carbon atoms in quinoline. The computational analysis of the energy surface for the reaction of *OH with quinoline reveals that the formation of OH adducts proceeds through exothermic formation of pi-complexes/H-bonded complexes. The gas-phase reactions have activation energies ranging from <1.3 kcal/mol for the attack at positions C3 through C8 to 8.6 kcal/mol for the attack at the C2 position. Solvation, as described by the CPCM cavity model, lowers these activation barriers so that the attack at all carbon atoms except C2 is effectively barrierless. The *OH attack at C2 in solution is significantly different than at all other quinoline positions because it involves the only transition structure with energy higher than that of the starting materials and with an energetic barrier of 5.1 kcal/mol. The specific solvation approach also corroborates this finding because the attack at C2 was shown to have an energy barrier of 2.3 kcal/mol compared to the barrierless attack at C5. These results are in agreement with our recent experimental studies but differ from literature reports on the degradation of quinoline using the photo-Fenton reaction.     

Fundamental reaction pathway and free energy profile for inhibition of proteasome by Epoxomicin

First-principles quantum mechanical/molecular mechanical free energy calculations have been performed to provide the first detailed computational study on the possible mechanisms for reaction of proteasome with a representative peptide inhibitor, Epoxomicin (EPX). The calculated results reveal that the most favorable reaction pathway consists of five steps. The first is a proton transfer process, activating Thr1-O(γ) directly by Thr1-N(z) to form a zwitterionic intermediate. The next step is nucleophilic attack on the carbonyl carbon of EPX by the negatively charged Thr1-O(γ) atom, followed by a proton transfer from Thr1-N(z) to the carbonyl oxygen of EPX (third step). Then, Thr1-N(z) attacks on the carbon of the epoxide group of EPX, accompanied by the epoxide ring-opening (S(N)2 nucleophilic substitution) such that a zwitterionic morpholino ring is formed between residue Thr1 and EPX. Finally, the product of morpholino ring is generated via another proton transfer. Noteworthy, Thr1-O(γ) can be activated directly by Thr1-N(z) to form the zwitterionic intermediate (with a free energy barrier of only 9.9 kcal/mol), and water cannot assist the rate-determining step, which is remarkably different from the previous perception that a water molecule should mediate the activation process. The fourth reaction step has the highest free energy barrier (23.6 kcal/mol) which is reasonably close to the activation free energy (～21-22 kcal/mol) derived from experimental kinetic data. The obtained novel mechanistic insights should be valuable for not only future rational design of more efficient proteasome inhibitors but also understanding the general reaction mechanism of proteasome with a peptide or protein.     

Computational study of the aminolysis of 2-benzoxazolinone

Three possible mechanisms (zwitterionic, neutral stepwise, and neutral concerted) of the ring-opening reaction of 2-benzoxazolinone (BO) upon aminolysis with methylamine were studied at the B3LYP/6-31G* level. In the gas phase, the neutral concerted mechanism is shown to be most favorable, which proceeds via a rate-determining barrier of 28-29 kcal/mol. The transition state, CTS, associated with this barrier is a four-centered one, where 1,2-addition of the N[bond]H of methylamine to the C[bond]O of BO ring occurs. The rate-determining barrier of the neutral stepwise pathway is found to be ca. 42 kcal/mol. The inclusion of solvent effects by a polarizable continuum model (PCM) does not change the conclusions based on the gas-phase study; the barrier at CTS is reduced to 20, 20, and 22 kcal/mol in water, ethanol, and acetonitrile, respectively.     

Accurate pK(a) calculations for 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 CPCM continuum solvation methods to calculate pK(a) values for six carboxylic acids. An experimental value of -264.61 kcal/mol for the free energy of solvation of H(+), DeltaG(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. 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.     

Methylene transfer or carbometalation? A theoretical study to determine the mechanism of lithium carbenoid-promoted cyclopropanation reactions in aggregation and solvation States

Density functional theory calculations for the lithium carbenoid-promoted cyclopropanations in aggregation and solvation states are presented in order to investigate the controversy of the mechanistic dichotomy, that is, the methylene-transfer mechanism and the carbometalation mechanism. The methylene-transfer mechanism represents the reaction reality, whereas the carbometalation pathway does not appear to compete significantly with the methylene-transfer pathway and should be ruled out as a major factor. A simple model calculation for monomeric lithium carbenoid-promoted cyclopropanations with ethylene in the gas phase is not sufficient to reflect the reaction conditions accurately or to determine the reaction mechanism since its result is inconsistent with the experimental facts. The aggregated lithium carbenoids are the most probable reactive species in the reaction system. The calculated reaction barriers of the methylene-transfer pathways are 10.1 and 8.0 kcal/mol for the dimeric (LiCH2F)2 and tetrameric (LiCH2F)4 species, respectively, compared with the reaction barrier of 16.0 kcal/mol for the monomeric LiCH2F species. In contrast, the reaction barriers of the carbometalation pathways are 26.8 kcal/mol for the dimeric (LiCH2F)2 and 33.9 kcal/mol for the tetrameric (LiCH2F)4 species, compared with the reaction barrier of 12.5 kcal/mol for the monomeric LiCH2F species. The effects of solvation were investigated by explicit coordination of the solvent molecules to the lithium centers. This solvation effect is found to enhance the methylene-transfer pathway, while it is found to impede the carbometalation pathway instead. The combined effects of the aggregation and solvation lead to barriers to reaction in the range of 7.2-9.0 kcal/mol for lithium carbenoid-promoted cyclopropanation reactions along the methylene-transfer pathway. Our computational results are in good agreement with the experimental observations.     

Structures and reaction mechanisms of propene oxide isomerization on H-ZSM-5: an ONIOM study

The isomerization mechanisms of propene oxide over H-ZSM-5 zeolite have been investigated via the utilization of 5T and 46T cluster models calculated by the B3LYP/6-31G(d,p) and the ONIOM(B3LYP/6-31G(d,p):UFF) methods, respectively. The reactions are considered to proceed through a stepwise mechanism: (1) the epoxide ring protonation, and concurrently the ring-opening, and (2) the 1,2-hydride shift forming the adsorbed carbonyl compound. Because of the asymmetric structure of propene oxide, two different C-O bonds (more or less substituted carbon atom sides) can be broken leading to two different types of products, propanal and propanone. The ring-opening step of these mechanisms is found to be the rate-determining step with an activation barrier of 38.5 kcal/mol for the propanal and of 42.4 kcal/mol for the propanone. Therefore, the propanal is predicted to be the main product for this reaction.     

Mechanism of SN2 disulfide bond cleavage by phosphorus nucleophiles. Implications for biochemical disulfide reducing agents

The B3LYP variant of DFT has been used to study the mechanism of S-S bond scission in dimethyl disulfide by a phosphorus nucleophile, trimethylphospine (TMP). The reaction is highly endothermic in the gas phase and requires significant external stabilization of the charged products. DFT calculations (B3LYP) were performed with explicit (water molecules added) and implicit solvent corrections (COSMO model). The transition structures for this SN2 displacement reaction in a number of model systems have been located and fully characterized. The reaction barriers calculated with different approaches for different systems are quite close (around 11 kcal/mol). Remarkably, the calculations suggest that the reaction is almost barrierless with respect to the preorganized reaction complex and that most of the activation energy is required to rearrange the disulfide and TMP to its most effective orientation for the SMe group transfer way. Different reactivities of different phosphorus nucleophiles were suggested to be the result of steric effects, as manifested largely by varying amounts of hindrance to solvation of the initial product phosphonium ion. These data indicate that the gas-phase addition of a phosphine to the disulfide moiety will most likely form a phosphonium cation-thiolate anion salt, in the presence of four or more water molecules, that provide sufficient H-bonding stabilization to allow displacement of the thiolate anion, a normal uncomplicated SN2 transition state is to be expected.     

Study of the Alkaline Hydrolysis of the Azetidin-2-one Ring by ab initio Methods: Influence of the solvent

A comprehensive study of the alkaline hydrolysis of the β-lactam ring of azetidin-2-one was carried out using ab initio molecular-orbital calculations at the RHF/6-31 + G* level. The influence of the solvent on this reaction was investigated by using the reaction field method (SCRF); the solvent was found to suppress the interference of some gas-phase reactions and allow the presence of a transition state to be detected as the nucleophile approaches the β-lactam ring. The transition state corresponds to a structure where the OH^? group lies at a distance of 1.927 Å from the C?O group of the β-lactam ring and exhibits a potential barrier of 13.6 kcal/mol.     

Theoretical investigation of lone pair inversions, ring openings, and hydride shifts in O-methylated epoxides

Mechanisms associated with the isomerization of the O-methylethylene oxonium ion and its tetramethyl-substituted analogue have been explored using correlated electronic structure calculations. The minima and transition states associated with inversion at the oxygen atom, as well as those associated with opening of the epoxide ring, have been characterized. The calculated barrier to inversion at the oxygen atom for the O-methylethylene oxonium ion, 15.7 kcal/mol, agrees well with the experimentally determined value, 10+/-2 kcal/mol. Our calculations indicate that a significantly higher barrier exists for the ring-opening mechanism that leads to more thermodynamically stable structures. This work includes the first known calculations on the O-methyl-2,3-dimethyl-2-butene oxonium ion along with transition states and intermediates associated with ring opening and inversion at the oxygen atom. Results show that there is a significantly lower barrier to ring opening as compared to the O-methylethylene oxonium ion species, leading to a lower probability of isolating this species. The effects of basis sets and correlation techniques on these ions were also analyzed in this work. Our results indicate that the B3LYP/6-31G* level is reliable for obtaining molecular geometries for both minima and transition states on the C3H7O+ and C7H15O+ potential energy surfaces.     

Mechanism of epoxide hydrolysis in microsolvated nucleotide bases adenine, guanine and cytosine: a DFT study

Six water molecules have been used for microsolvation to outline a hydrogen bonded network around complexes of ethylene epoxide with nucleotide bases adenine (EAw), guanine (EGw) and cytosine (ECw). These models have been developed with the MPWB1K-PCM/6-311++G(3df,2p)//MPWB1K/6-31+G(d,p) level of DFT method and calculated S(N)2 type ring opening of the epoxide due to amino group of the nucleotide bases, viz. the N6 position of adenine, N2 position of guanine and N4 position of cytosine. Activation energy (E(act)) for the ring opening was found to be 28.06, 28.64, and 28.37 kcal mol(-1) respectively for EAw, EGw and ECw. If water molecules were not used, the reactions occurred at considerably high value of E(act), viz. 53.51 kcal mol(-1) for EA, 55.76 kcal mol(-1) for EG and 56.93 kcal mol(-1) for EC. The ring opening led to accumulation of negative charge on the developing alkoxide moiety and the water molecules around the charge localized regions showed strong hydrogen bond interactions to provide stability to the intermediate systems EAw-1, EGw-1 and ECw-1. This led to an easy migration of a proton from an activated water molecule to the alkoxide moiety to generate a hydroxide. Almost simultaneously, a proton transfer chain reaction occurred through the hydrogen bonded network of water molecules and resulted in the rupture of one of the N-H bonds of the quaternized amino group. The highest value of E(act) for the proton transfer step of the reaction was 2.17 kcal mol(-1) for EAw, 2.93 kcal mol(-1) for EGw and 0.02 kcal mol(-1) for ECw. Further, the overall reaction was exothermic by 17.99, 22.49 and 13.18 kcal mol(-1) for EAw, EGw and ECw, respectively, suggesting that the reaction is irreversible. Based on geometric features of the epoxide-nucleotide base complexes and the energetics, the highest reactivity is assigned for adenine followed by cytosine and guanine. Epoxide-mediated damage of DNA is reported in the literature and the present results suggest that hydrated DNA bases become highly S(N)2 active on epoxide systems and the occurrence of such reactions can inflict permanent damage to the DNA.     

Theoretical Calculations of β-Lactam Antibiotics. Part VII. Influence of the solvent on the basic hydrolysis of the β-lactam ring

We used semi-empirical and ab initio calculations to investigate the nucleophilic attack of the OH^? ion on the β-lactam carbonyl group. Both allowed us to detect reaction intermediates pertaining to proton-transfer reactions rather than the studied reaction. We also used the PM3 semi-empirical method to investigate the influence of the solvent on the process. The AMSOL method predicts the occurrence of a potential barrier of 20.7 kcal/mol due to the desolvation of the OH^? ion in approaching the β-lactam carbonyl group. Using the supermolecular approach and a H₂O solvation sphere of 20 molecules around the solute, the potential barrier is lowered to 17.5 kcal/mol, which is very close to the experimental value (16.7 kcal/mol).     

Effects of ion-pairing and hydration on the SNAr reaction of the F- with p-chlorobenzonitrile in aprotic solvents

Theoretical ab initio calculations including liquid phase optimizations were used to investigate the S(N)Ar reaction of the fluoride ion with p-chlorobenzonitrile in dimethyl sulfoxide solution. The effect of the counter ion and hydration of the fluoride ion with one water molecule was analyzed. The calculations indicate that the gas-phase S(N)Ar reaction is more favorable than the corresponding S(N)2 reactions involving fluoride ion and 2-chlorobutane. However, the substantially higher solvent effect on the S(N)Ar reaction makes the nucleophilic substitution on the aromatic ring less favorable than the aliphatic reaction in the liquid phase. For the anhydrous tetrabutylammonium fluoride system, the theoretical free energy barrier of 22.1 kcal mol(-1) is close to the experimental one of 24.4 kcal mol(-1). The smaller tetramethylammonium cation strongly associates with the fluoride ion and increases the barrier by 5 kcal mol(-1). Similarly, just one water molecule hydrating the fluoride ion has the same effect. An analysis of the reaction involving the ion pair and the free anion in different polarity media predicts an unexpected behavior and indicates there is an ideal solvent polarity for each counter ion.     

A theoretical analysis of the free-energy profile of the different pathways in the alkaline hydrolysis of methyl formate in aqueous solution

The free-energy profile for the different reaction pathways available to the hydroxide ion and methyl formate in aqueous solution is reported for the first time. The theoretical analysis was carried out by using the cluster-continuum method recently proposed by us for calculating the free energy of solvation of ions. Unlike the gas-phase reaction, our results are consistent with the fact that the reaction occurs mainly by nucleophilic attack of the hydroxide on the carbonyl carbon to yield a tetrahedral intermediate (B(AC)2 mechanism). However, an additional pathway, in which the hydroxide ion acts as a general base and a water molecule coordinated to this ion acts as the nucleophile, is also predicted to be important. The relative importance of these pathways is calculated to be 87 % and 13 %, respectively. The tetrahedral intermediate of the hydrolysis reaction has an estimated lifetime of 10 nanoseconds, and its conjugate acid has a pK(a) of 8.8. This tetrahedral intermediate is predicted to proceed to products by two pathways: elimination of methoxide ion (84 %) and by water catalyzed elimination of methanol (16 %). The less common reaction pathway, which involves attack of the hydroxide ion on the formyl hydrogen (decarbonylation mechanism) and leads to water, carbon monoxide, and methanol, is calculated to be only 3 kcal mol(-1) less favorable than the B(AC)2 mechanism. By comparison, direct attack of the hydroxide ion on the methyl group (B(AL)2 or S(N)2 mechanism) leading to an acyl-oxygen bond cleavage has a very high free energy of activation and is not expected to be important. The theoretically observed activation free energy at 298.15 K is calculated to be 15.5 kcal mol(-1), in excellent agreement with the experimentally measured value of 15.3 kcal mol(-1). This present model allows for a clear distinction between contributions due to solvation and those due to intrinsic (gas-phase) effects and proves to yield results in very good agreement with available experimental data.     

The ring-opening reaction of chromenes: a photochemical mode-dependent transformation

The efficiency of the photochemical ring-opening of chromenes (or benzopyrans) depends on the vibronic transition selected by the chosen excitation wavelength. In the present work, ab initio CASPT2//CASSCF calculations are used to determine the excited-state ring-opening reaction coordinate for 2H-chromene (C) and 2,2-diethyl-2H-chromene (DEC) and provide an explanation for such an unusual mode-dependent behavior. It is shown that excited-state relaxation and decay occur via a multimodal and barrierless (or nearly barrierless) reaction coordinate. In particular, the relaxation out of the Franck-Condon involves a combination of in-plane skeletal stretching and out-of-plane modes, while the second part of the reaction coordinate is dominated exclusively by a different out-of-plane mode. Population of this last mode is shown to be preparatory with respect to both C-O bond breaking and decay via an S(1)/S(0) conical intersection. The observed mode-dependent ring-opening efficiency is explained by showing that the vibrational mode corresponding to the most efficient vibronic transition has the largest projection onto the out-of-plane mode of the reaction coordinate. To support the computationally derived mechanism, we provide experimental evidence that the photochemical ring-opening reaction of 2,2-dimethyl-7,8-benzo(2H)chromene, that similarly to DEC exhibits a mode-dependent photoreaction, has a low ( approximately 1 kcal mol(-1)) activation energy barrier.     

Antibiotic deactivation by a dizinc beta-lactamase: mechanistic insights from QM/MM and DFT studies

Hybrid quantum mechanical/molecular mechanical (QM/MM) methods and density functional theory (DFT) were used to investigate the initial ring-opening step in the hydrolysis of moxalactam catalyzed by the dizinc L1 beta-lactamase from Stenotrophomonas maltophilia. Anchored at the enzyme active site via direct metal binding as suggested by a recent X-ray structure of an enzyme-product complex (Spencer, J.; et al. J. Am. Chem. Soc. 2005, 127, 14439), the substrate is well aligned with the nucleophilic hydroxide that bridges the two zinc ions. Both QM/MM and DFT results indicate that the addition of the hydroxide nucleophile to the carbonyl carbon in the substrate lactam ring leads to a metastable intermediate via a dominant nucleophilic addition barrier. The potential of mean force obtained by SCC-DFTB/MM simulations and corrected by DFT/MM calculations yields a reaction free energy barrier of 23.5 kcal/mol, in reasonable agreement with the experimental value of 18.5 kcal/mol derived from kcat of 0.15 s(-1). It is further shown that zinc-bound Asp120 plays an important role in aligning the nucleophile, but accepts the hydroxide proton only after the nucleophilic addition. The two zinc ions are found to participate intimately in the catalysis, consistent with the proposed mechanism. In particular, the Zn(1) ion is likely to serve as an "oxyanion hole" in stabilizing the carbonyl oxygen, while the Zn(2) ion acts as an electrophilic catalyst to stabilize the anionic nitrogen leaving group.     

Fixation of heterocumulenes. 1. A theoretical study on the irreversible reaction of CO(2) with a 2-lithio-1,3-dithiane

The mechanism of electrophilic addition of CO(2) to 2-lithio-2-phenyl-1, 3-dithiane-tetrahydrofuran-tetramethylethylendiamine, a Corey-Seebach "umpolungs" reagent for nucleophilic acylation, was investigated at the B3YLP/6-311+G//HF/6-31+G level of theory with specific solvation effects being included in the study. The overall reaction is exothermic by 18.8 kcal/mol and proceeds via precomplexation of the CO(2) (necessary for activation). The reaction barrier is calculated to be 11.9 kcal/mol (relative to the precomplex 2a) and represents a lower boundary for the activation energy. The reaction barrier is shown to originate from specific solvent effects. A detailed survey of the electronic effects governing the reaction is given. The ab initio results were then compared with semiempirical PM3 calculations, which were extended to include the heterocumulenes COS and CS(2). As expected, the reduced electrophilicity of these molecules leads to a higher activation barrier by retention of the same reaction mechanism.     

Performance of SM8 on a test to predict small-molecule solvation free energies

The SM8 quantum mechanical aqueous continuum solvation model is applied to a 17-molecule test set proposed by Nicholls et al. (J. Med. Chem. 2008, 51, 769) to predict free energies of solvation. With the M06-2X density functional, the 6-31G(d) basis set, and CM4M charge model, the root-mean-square error (RMSE) of SM8 is 1.08 kcal mol(-1) for aqueous geometries and 1.14 kcal mol(-1) for gas-phase geometries. These errors compare favorably with optimal explicit and continuum models reported by Nicholls et al., having RMSEs of 1.33 and 1.87 kcal mol(-1), respectively. Other models examined by these workers had RMSEs of 1.5-2.6 kcal mol(-1). We also explore the use of other density functionals and charge models with SM8 and the RMSE increases to 1.21 kcal mol(-1) for mPW1/CM4 with gas-phase geometries, to 1.50 kcal mol(-1) for M06-2X/CM4 with gas-phase geometries, and to 1.27-1.64 kcal mol(-1) with three different models at B3LYP gas-phase geometries.