Structure and thermodynamics of H3O+(H2O)8 clusters: A combined molecular dynamics and quantum mechanics approach

We have studied the structure and stability of (H3O+)(H2O)8 clusters using a combination of molecular dynamics sampling and high-level ab initio calculations. 20 distinct oxygen frameworks are found within 2 kcal/mol of the electronic or standard Gibbs free energy minimum. The impact of quantum zero-point vibrational corrections on the relative stability of these isomers is quite significant. The box-like isomers are favored in terms of electronic energy, but with the inclusion of zero-point vibrational corrections and entropic effects tree-like isomers are favored at higher temperatures. Under conditions from 0 to 298.15 K, the global minimum is predicted to be a tree-like structure with one dangling singly coordinated water molecule. Above 298.15 K, higher entropy tree-like isomers with two or more singly coordinated water molecules are favored. These assignments are generally consistent with experimental IR spectra of (H3O+)(H2O)8 obtained at 150 K.

The Role of Anharmonicity in Hydrogen-Bonded Systems: The Case of Water Clusters

The nature of vibrational anharmonicity has been examined for the case of small water clusters using second-order vibrational perturbation theory (VPT2) applied on second-order Møller–Plesset perturbation theory (MP2) potential energy surfaces. Using a training set of 16 water clusters (H2O)n=2–6,8,9 with a total of 723 vibrational modes, we determined scaling factors that map the harmonic frequencies onto anharmonic ones. The intermolecular modes were found to be substantially more anharmonic than intramolecular bending and stretching modes. Due to the varying levels of anharmonicity of the intermolecular and intramolecular modes, different frequency scaling factors for each region were necessary to achieve the highest accuracy. Furthermore, new scaling factors for zero-point vibrational energies (ZPVE) and vibrational corrections to the enthalpy (ΔHvib) and the entropy (Svib) have been determined. All the scaling factors reported in this study are different from previous works in that they are intended for hydrogen-bonded systems, while others were built using experimental frequencies of covalently bonded systems. An application of our scaling factors to the vibrational frequencies of water dimer and thermodynamic functions of 11 larger water clusters highlights the importance of anharmonic effects in hydrogen-bonded systems.

Benchmark Structures and Binding Energies of Small Water Clusters with Anharmonicity Corrections

For (H2O)n where n = 1–10, we used a scheme combining molecular dynamics sampling with high level ab initio calculations to locate the global and many low lying local minima for each cluster. For each isomer, we extrapolated the RI-MP2 energies to their complete basis set limit, included a CCSD(T) correction using a smaller basis set and added finite temperature corrections within the rigid-rotor-harmonic-oscillator (RRHO) model using scaled and unscaled harmonic vibrational frequencies. The vibrational scaling factors were determined specifically for water clusters by comparing harmonic frequencies with VPT2 fundamental frequencies. We find the CCSD(T) correction to the RI-MP2 binding energy to be small (<1%) but still important in determining accurate conformational energies. Anharmonic corrections are found to be non-negligble; they do not alter the energetic ordering of isomers, but they do lower the free energies of formation of the water clusters by as much as 4 kcal/mol at 298.15 K.

Accurate Predictions of Water Cluster Formation, (H2O)n=2-10

An efficient mixed molecular dynamics/quantum mechanics model has been applied to the water cluster system. The use of the MP2 method and correlation consistent basis sets, with appropriate correction for BSSE, allows for the accurate calculation of electronic and free energies for the formation of clusters of 2−10 water molecules. This approach reveals new low energy conformers for (H2O)n=7,9,10. The water heptamer conformers comprise five different structural motifs ranging from a three-dimensional prism to a quasi-planar book structure. A prism-like structure is favored energetically at low temperatures, but a chair-like structure is the global Gibbs free energy minimum past 200 K. The water nonamers exhibit less complexity with all the low energy structures shaped like a prism. The decamer has 30 conformers that are within 2 kcal/mol of the Gibbs free energy minimum structure at 298 K. These structures are categorized into four conformer classes, and a pentagonal prism is the most stable structure from 0 to 320 K. Results can be used as benchmark values for empirical water models and density functionals, and the method can be applied to larger water clusters.

Quantum Mechanical Study of Sulfuric Acid Hydration: Atmospheric Implications

The role of the binary nucleation of sulfuric acid in aerosol formation and its implications for global warming is one of the fundamental unsettled questions in atmospheric chemistry. We have investigated the thermodynamics of sulfuric acid hydration using ab initio quantum mechanical methods. For H2SO4(H2O)n where n = 1–6, we used a scheme combining molecular dynamics configurational sampling with high-level ab initio calculations to locate the global and many low lying local minima for each cluster size. For each isomer, we extrapolated the Møller–Plesset perturbation theory (MP2) energies to their complete basis set (CBS) limit and added finite temperature corrections within the rigid-rotor-harmonic-oscillator (RRHO) model using scaled harmonic vibrational frequencies. We found that ionic pair (HSO4–·H3O+)(H2O)n−1 clusters are competitive with the neutral (H2SO4)(H2O)n clusters for n ≥ 3 and are more stable than neutral clusters for n ≥ 4 depending on the temperature. The Boltzmann averaged Gibbs free energies for the formation of H2SO4(H2O)n clusters are favorable in colder regions of the troposphere (T = 216.65–273.15 K) for n = 1–6, but the formation of clusters with n ≥ 5 is not favorable at higher (T > 273.15 K) temperatures. Our results suggest the critical cluster of a binary H2SO4–H2O system must contain more than one H2SO4 and are in concert with recent findings(1) that the role of binary nucleation is small at ambient conditions, but significant at colder regions of the troposphere. Overall, the results support the idea that binary nucleation of sulfuric acid and water cannot account for nucleation of sulfuric acid in the lower troposphere.

Hydration of the Bisulfate Ion: Atmospheric Implications

Using molecular dynamics configurational sampling combined with ab initio energy calculations, we determined the low energy isomers of the bisulfate hydrates. We calculated the CCSD(T) complete basis set (CBS) binding electronic and Gibbs free energies for 53 low energy isomers of HSO4–(H2O)n=1–6 and derived the thermodynamics of adding waters sequentially to the bisulfate ion and its hydrates. Comparing the HSO4–/H2O system to the neutral H2SO4/H2O cluster, water binds more strongly to the anion than it does to the neutral molecules. The difference in the binding thermodynamics of HSO4–/H2O and H2SO4/H2O systems decreases with increasing number of waters. The thermodynamics for the formation of HSO4–(H2O)n=1–5 is favorable at 298.15 K, and that of HSO4–(H2O)n=1–6 is favorable for T < 273.15 K. The HSO4– ion is almost always hydrated at temperatures and relative humidity values encountered in the troposphere. Because the bisulfate ion binds more strongly to sulfuric acid than it does to water, it is expected to play a role in ion-induced nucleation by forming a strong complex with sulfuric acid and water, thus facilitating the formation of a critical nucleus.

Computational Study of the Hydration of Sulfuric Acid Dimers: Implications for Acid Dissociation and Aerosol Formation

We have investigated the thermodynamics of sulfuric acid dimer hydration using ab initio quantum mechanical methods. For (H2SO4)2(H2O)n where n = 0−6, we employed high-level ab initio calculations to locate the most stable minima for each cluster size. The results presented herein yield a detailed understanding of the first deprotonation of sulfuric acid as a function of temperature for a system consisting of two sulfuric acid molecules and up to six waters. At 0 K, a cluster of two sulfuric acid molecules and one water remains undissociated. Addition of a second water begins the deprotonation of the first sulfuric acid leading to the di-ionic species (the bisulfate anion HSO4−, the hydronium cation H3O+, an undissociated sulfuric acid molecule, and a water). Upon the addition of a third water molecule, the second sulfuric acid molecule begins to dissociate. For the (H2SO4)2(H2O)3 cluster, the di-ionic cluster is a few kcal mol−1 more stable than the neutral cluster, which is just slightly more stable than the tetra-ionic cluster (two bisulfate anions, two hydronium cations, and one water). With four water molecules, the tetra-ionic cluster, (HSO4−)2(H3O+)2(H2O)2, becomes as favorable as the di-ionic cluster H2SO4(HSO4−)(H3O+)(H2O)3 at 0 K. Increasing the temperature favors the undissociated clusters, and at room temperature we predict that the di-ionic species is slightly more favorable than the neutral cluster once three waters have been added to the cluster. The tetra-ionic species competes with the di-ionic species once five waters have been added to the cluster. The thermodynamics of stepwise hydration of sulfuric acid dimer is similar to that of the monomer; it is favorable up to n = 4−5 at 298 K. A much more thermodynamically favorable pathway forming sulfuric acid dimer hydrates is through the combination of sulfuric acid monomer hydrates, but the low concentration of sulfuric acid relative to water vapor at ambient conditions limits that process.

Quantum Mechanical Study of Sulfuric Acid Hydration: Atmospheric Implications

The role of the binary nucleation of sulfuric acid in aerosol formation and its implications for global warming is one of the fundamental unsettled questions in atmospheric chemistry. We have investigated the thermodynamics of sulfuric acid hydration using ab initio quantum mechanical methods. For H2SO4(H2O)n where n = 1–6, we used a scheme combining molecular dynamics configurational sampling with high-level ab initio calculations to locate the global and many low lying local minima for each cluster size. For each isomer, we extrapolated the Møller–Plesset perturbation theory (MP2) energies to their complete basis set (CBS) limit and added finite temperature corrections within the rigid-rotor-harmonic-oscillator (RRHO) model using scaled harmonic vibrational frequencies. We found that ionic pair (HSO4–·H3O+)(H2O)n−1clusters are competitive with the neutral (H2SO4)(H2O)n clusters for n ≥ 3 and are more stable than neutral clusters for n ≥ 4 depending on the temperature. The Boltzmann averaged Gibbs free energies for the formation of H2SO4(H2O)n clusters are favorable in colder regions of the troposphere (T = 216.65–273.15 K) for n = 1–6, but the formation of clusters with n ≥ 5 is not favorable at higher (T > 273.15 K) temperatures. Our results suggest the critical cluster of a binary H2SO4–H2O system must contain more than one H2SO4 and are in concert with recent findings(1) that the role of binary nucleation is small at ambient conditions, but significant at colder regions of the troposphere. Overall, the results support the idea that binary nucleation of sulfuric acid and water cannot account for nucleation of sulfuric acid in the lower troposphere.

Hydration of the Sulfuric Acid−Methylamine Complex and Implications for Aerosol Formation

The binary H2SO4−H2O nucleation is one of the most important pathways by which aerosols form in the atmosphere, and the presence of ternary species like amines increases aerosol formation rates. In this study, we focus on the hydration of a ternary system of sulfuric acid (H2SO4), methylamine (NH2CH3), and up to six waters to evaluate its implications for aerosol formation. By combining molecular dynamics (MD) sampling with high-level ab initio calculations, we determine the thermodynamics of forming H2SO4(NH2CH3)(H2O)n, where n = 0−6. Because it is a strong acid−base system, H2SO4−NH2CH3 quickly forms a tightly bound HSO4−−NH3CH3+ complex that condenses water more readily than H2SO4 alone. The electronic binding energy of H2SO4−NH2CH3 is −21.8 kcal mol−1 compared with −16.8 kcal mol−1 for H2SO4−NH3 and −12.8 kcal mol−1 for H2SO4−H2O. Adding one to two water molecules to the H2SO4−NH2CH3 complex is more favorable than adding to H2SO4 alone, yet there is no systematic difference for n ≥ 3. However, the average number of water molecules around H2SO4−NH2CH3 is consistently higher than that of H2SO4, and it is fairly independent of temperature and relative humidity.

Hydration of the Sulfuric Acid-Methylamine Complex and Implications for Aerosol Formation

The binary H2SO4-H2O nucleation is one of the most important pathways by which aerosols form in the atmosphere, and the presence of ternary species like amines increases aerosol formation rates. In this study, we focus on the hydration of a ternary system of sulfuric acid (H2SO4), methylamine (NH2CH3), and up to six waters to evaluate its implications for aerosol formation. By combining molecular dynamics (MD) sampling with high-level ab initio calculations, we determine the thermodynamics of forming H2SO4(NH2CH3)(H2O)n, where n = 0-6. Because it is a strong acid-base system, H2SO4-NH2CH3 quickly forms a tightly bound HSO4(-)-NH3CH3(+) complex that condenses water more readily than H2SO4 alone. The electronic binding energy of H2SO4-NH2CH3 is -21.8 kcal mol(-1) compared with -16.8 kcal mol(-1) for H2SO4-NH3 and -12.8 kcal mol(-1) for H2SO4-H2O. Adding one to two water molecules to the H2SO4-NH2CH3 complex is more favorable than adding to H2SO4 alone, yet there is no systematic difference for n ≥ 3. However, the average number of water molecules around H2SO4-NH2CH3 is consistently higher than that of H2SO4, and it is fairly independent of temperature and relative humidity.

Comparison of Experimental and Theoretical Structures of a Transition State Analogue Used for the Induction of Anti-Cocaine Catalytic Antibodies

Comparison of the crystal structure of a transition state analogue that was used to raise catalytic antibodies for the benzoyl ester hydrolysis of cocaine with structures calculated by ab initio, semiempirical, and solvation semiempirical methods reveals that modeling of solvation is crucial for replicating the crystal structure geometry. Both SM3 and SM2 calculations, starting from the crystal structure TSA I, converged on structures similar to the crystal structure. The 3-21G(*)/HF, 6-31G*/HF, PM3, and AM1 calculations converged on structures similar to each other, but these gas-phase structures were significantly extended relative to the condensed phase structures. Two transition states for the hydrolysis of the benzoyl ester of cocaine were located with the SM3 method. The gas phase calculations failed to locate reasonable transition state structures for this reaction. These results imply that accurate modeling of the potential energy surfaces for the hydrolysis of cocaine requires solvation methods.

Quantum Mechnical Investion of Cyclic 3',5'- Adenosine Monophosphate, the Second Hormonal Messenger

Full geometry optimizations using the PM3, AM1, 3-21G∗/HF and 6-31G∗/HF levels of theory were conducted on the syn and anti conformations of cyclic3′,5′-adenosine monophosphate (cAMP). Comparison of the anti crystal structures with the semiempirical and ab initio results revealed that the ab initio results agree well with the experimental results. The results of semiempirical calculations are in qualitative agreement with experimental and ab initio values, with the exception of the glycosyl torsion angle for the anti conformer. Sugar puckering, which is not handled properly by semiempirical methods for unconstrained sugars, nucleosides, nucleotides and nucleotide base pairs, is modeled reasonably well by the semiempirical methods for cAMP. This improvement results from the constraints introduced by the cyclization of AMP to form the phosphodiester.

Investigation of the Potential Energy Surface for the First Step in the Alkaline Hydrolysis of Methyl Acetate

The potential energy surface for the first step of the alkaline hydrolysis of methyl acetate was explored by a variety of methods. The conformational search routine within SPARTAN was used to determine the lowest energy am1 and pm3 structures for the anionic tetrahedral intermediate. Ab initio single point and geometry optimization calculations were performed to determine the lowest energy conformer, and the linear synchronous transition (lst) method was used to provide an initial structure for transition state optimization. Transition states were obtained at the am1, pm3, 3-21G, and 3-21 + G levels of theory. These transition states were compared with the anionic tetrahedral intermediates to examine the assumption that the intermediate is a good model for the transition state. In addition, the Cramer/Truhlar sm3 solvation model was used at the semiempirical level to compare gas phase and aqueous alkaline hydrolysis of methyl acetate.

Hydrogen bonding of nucleotide base pairs: Application of the PM3 method

The ability of the pm3 semiempirical quantum mechanical method to reproduce hydrogen bonding in nucleotide base pairs was assessed. Results of pm3 calculations on the nucleotides 2′-deoxyadenosine 5′-monophosphate (pdA), 2′-deoxyguanosine 5′-monophosphate (pdG), 2′-deoxycytidine 5′-monophosphate (pdC), and 2′-deoxythymidine 5′-monophosphate (pdT) and the base pairs pdA–pdT, pdG–pdC, and pdG(syn)–pdC are presented and discussed. The pm3 method is the first of the parameterized nddo quantum mechanical models with any ability to reproduce hydrogen bonding between nucleotide base pairs. Intermolecular hydrogen bond lengths between nucleotides displaying Watson–Crick base pairing are 0.1–0.2 Å less than experimental results. Nucleotide bond distances, bond angles, and torsion angles about the glycosyl bond (χ), the C4′C5′ bond (γ), and the C5′O5′ bond (β) agree with experimental results. There are many possible conformations of nucleotides. pm3 calculations reveal that many of the most stable conformations are stabilized by intramolecular CHO hydrogen bonds. These interactions disrupt the usual sugar puckering. The stacking interactions of a dT–pdA duplex are examined at different levels of gradient optimization. The intramolecular hydrogen bonds found in the nucleotide base pairs disappear in the duplex, as a result of the additional constraints on the phosphate group when part of a DNA backbone. Sugar puckering is reproduced by the pm3 method for the four bases in the dT–pdA duplex. pm3 underestimates the attractive stacking interactions of base pairs in a B-DNA helical conformation. The performance of the pm3 method implemented in SPARTAN is contrasted with that implemented in MOPAC. At present, accurate ab initio calculations are too timeconsuming to be of practical use, and molecular mechanics methods cannot be used to determine quantum mechanical properties such as reaction-path calculations, transition-state structures, and activation energies. The pm3 method should be used with extreme caution for examination of small DNA systems. Future parameterizations of semiempirical methods should incorporate base stacking interactions into the parameterization data set to enhance the ability of these methods.

Quantum-Mechanical Investigation of Large Water Clusters

The PM3 quantum-mechanical method has been used to study large water clusters ranging from 8 to 42 water molecules. These large clusters are built from smaller building blocks. The building blocks include cyclic tetramers, pentamers, octamers, and a pentagonal dodecahedron cage. The correlations between the strain energy resulting from bending of the hydrogen bonds formed by different cluster motifs and the number of waters involved in the cluster are discussed. The PM3 results are compared with TIP4P potential and ab initio results. The number of net hydrogen bonds per water increases with the cluster size. This places a limit on the size of clusters that would fit the Benson model of liquid water. Many of the 20-mer clusters fit the Benson model well. Calculations of the ion cluster (H20)4o(H30+)2 reveal that the m/e ratio obtainable by mass spectrometry experiments can uniquely indicate the conformation of the 20 water pentagonal dodecahedron cage present in the larger clusters.