Accurate relative pKa calculations for carboxylic acids using complete basis set and Gaussian-n models combined with continuum solvation methods

The complete basis set methods CBS-4, CBS-QB3, and CBS-APNO, and the Gaussian methods G2 and G3 were used to calculate the gas phase energy differences between six different carboxylic acids and their respective anions. Two different continuum methods, SM5.42R and CPCM, were used to calculate the free energy differences of solvation for the acids and their anions. Relative pKa values were calculated for each acid using one of the acids as a reference point. The CBS-QB3 and CBS-APNO gas phase calculations, combined with the CPCM/HF/6-31+G(d)//HF/6-31G(d) or CPCM/HF/6-31+G(d)//HF/6-31+G(d) continuum solvation calculations on the lowest energy gas phase conformer, and with the conformationally averaged values, give results accurate to ½ pKa unit. © 2001 American Institute of Physics.

Molecular Dynamics Simulation of a PNA·DNA·PNA Triple Helix in Aqueous Solution

Molecular dynamics simulations have been used to explore the conformational flexibility of a PNA·DNA·PNA triple helix in aqueous solution. Three 1.05 ns trajectories starting from different but reasonable conformations have been generated and analyzed in detail. All three trajectories converge within about 300 ps to produce stable and very similar conformational ensembles, which resemble the crystal structure conformation in many details. However, in contrast to the crystal structure, there is a tendency for the direct hydrogen-bonds observed between the amide hydrogens of the Hoogsteen-binding PNA strand and the phosphate oxygens of the DNA strand to be replaced by water-mediated hydrogen bonds, which also involve pyrimidine O2 atoms. This structural transition does not appear to weaken the triplex structure but alters groove widths and so may relate to the potential for recognition of such structures by other ligands (small molecules or proteins). Energetic analysis leads us to conclude that the reason that the hybrid PNA/DNA triplex has quite different helical characteristics from the all-DNA triplex is not because the additional flexibility imparted by the replacement of sugar−phosphate by PNA backbones allows motions to improve base-stacking but rather that base-stacking interactions are very similar in both types of triplex and the driving force comes from weak but definate conformational preferences of the PNA strands.

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.

Modeling of Magic Water Clusters(H20)2 and (H20)21H+ with the PM3 Quantum-Mechanical Method

The PM3 quantum-mechanical method is able to model the magic water clusters (H20),, and (H20)&+. Results indicate that the H30+ ion is tightly bound within the (H20),, cluster by multiple hydrogen bonds, causing deformation to the symmetric (HzO),, pentagonal dodecahedron structure. The structures, energetics, and hydrogen bond patterns of six local minima (H20)21H+ clusters are presented.

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.

Use of the Supermolecule Approach To Model the Syn and Anti Conformations of Solvated Cyclic 3‘,5‘-Adenosine Monophosphate

The supermolecule approach has been used to model the hydration of cyclic 3‘,5‘-adenosine monophosphate, cAMP. Model building combined with PM3 optimizations predict that the anti conformer of cAMP is capable of hydrogen bonding to an additional solvent water molecule compared to the syn conformer. The addition of one water to the syn superstructure with concurrent rotation of the base about the glycosyl bond to form the anti superstructure leads to an additional enthalpy of stabilization of approximately −6 kcal/mol at the PM3 level. This specific solute−solvent interaction is an example of a large solvent effect, as the method predicts that cAMP has a conformational preference for the anti isomer in solution. This conformational preference results from a change in the number of specific solute−solvent interactions in this system. This prediction could be tested by NMR techniques. The number of waters predicted to be in the first hydration sphere around cAMP is in agreement with the results of hydration studies of nucleotides in DNA. In addition, the detailed picture of solvation about this cyclic nucleotide is in agreement with infrared experimental results.

The ability of the Gaussian-2, Gaussian-3, Complete Basis Set–QB3, and Complete Basis Set–APNO model chemistries to model the geometries of small water clusters

The Gaussian-2, Gaussian-3, Complete Basis Set-QB3, and Complete Basis Set-APNO methods have been used to calculate geometries of neutral clusters of water, (H2O)n, where n = 2–6. The structures are in excellent agreement with those determined from experiment and those predicted from previous high-level calculations. These methods also provide excellent thermochemical predictions for water clusters, and thus can be used with confidence in evaluating the structures and thermochemistry of water clusters.

A Semiempirical Transition State Structure for the First Step in the Alkaline Hydrolysis of Cocaine. Comparison between the Transition State Structure, the Phosphonate Monoester Transition State Analog, and a Newly Designed Thiophosphonate Transition State Analog

Semiempirical molecular orbital calculations have been performed for the first step in the alkaline hydrolysis of the neutral benzoylester of cocaine. Successes, failures, and limitations of these calculations are reviewed. A PM3 calculated transition state structure is compared with the PM3 calculated structure for the hapten used to induce catalytic antibodies for the hydrolysis of cocaine. Implications of these calculations for the computer–aided design of transition state analogs for the induction of catalytic antibodies are discussed.

Using the Franck-Hertz Experiment To Illustrate Quantization Energy States of the Neon Atom by Electron Impact

na provide students with motivation for the study of quantum mechanics. That microscopic matter exists in quantized states can be demonstrated with modem versions of historic experiments: atomic line spectra (I), resonance potentials, and blackbody radiation. The resonance potentials of mercury were discovered by Franck and Hertz in 1914 (2). Their experiment consisted of bombarding atoms by electrons, and detecting the kinetic energy loss of the scattered electrons (3). Prior to the Franck-Hertz experiment, spectroscopic work bv Balmer and Rvdbere revealed that atoms emitted radiatibn at discrete ekergiis. The Franck-Hertz experiment showed directly that auantized enerm levels in an atom are real, not jist optiEal artifacts. atom can be raised to excited states by inelastic collisions with electrons as well as lowered from excited states by emission of photons. The classic Franck-Hertz experiment is carried out with mercury (4-7). Here we present an experiment for the study of resonance potentials using neon.

AM1 and PM3 Calculations of the Potential Energy Surfaces for CH2OH Reactions with NO and NO2

The AM1 and PM3 molecular orbital methods have been utilized to investigate the reactions of CH20H with NO and NO2 PM3 and AM1 calculated heats of formation differ from experimental values by 8.6 and 18.8 kcal mol-', respectively. The dominant reaction of CH20H with NO is predicted to produce the adduct HOCH2N0, supporting the hypothesis of Pagsberg, Munk, Anastasi, and Simpson. Calculated activation energies for the NO2 system predict the formation of the adducts HOCH2N02 and HOCH20N0. In addition, the PM3 calculations predict that the abstraction reaction producing CH20 and HN02 is more likely than one producing CH20 and HONO from reactions of CH20H with NO2.

Molecular Dynamics Simulations of the d(TAT) Triple Helix

Molecular dynamics (MD) simulations have been used to study the dynamical and time-averaged characteristics of the DNA triple helix d(T)10âd(A)10âd(T)10. The structures sampled during the trajectory resemble closely the B-type model for the DNA triplex proposed on the basis of NMR data, although there are some subtle differences. Alternative P- and A-type conformations for the triplex, suggested from X-ray experiments, are not predicted to contribute significantly to the structure of the DNA triplex in solution. Comparison with the best available experimental data supports the correctnes of the MD-generated structures. The analysis of the collected data gives a detailed picture of the characteristics of triple-helix DNA. A new and interesting pattern of hydration, specific for triplex DNA, is an important observation. The results suggest that molecular dynamics can be useful for the study of novel nucleic acid structures.

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.

Experiment in Quantization: Atomic Line Spectra

Laboratory exercises that confront students with decisive ouantum ohenomena nrovide valuable motivation for the kudy of quantum m&hanics. The idea that microscopic matter exists in quantized states can be demonstrated with modern versions of historic experiments: atomic line snectra. blackbodv radiation. and resonance potentials. In this experiment, we present a strikingly simple and visual method for determining the wavelength of spectral lines. This experiment not only shows the inadequacy of classical physics, but also indicates the power of optical measurements.

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.