A. Hidalgo

Rovibrational energy levels and expectation values for perturbed Kratzer oscillators

A perturbative treatment for perturbed Kratzer potentials is carried out. Recursion expressions for the energy and expectation values of powers of the internuclear separation are derived by using conmutation relations. An application to the Simons, Parr, and Finlan potential is made. Numerical results are compared with those derived by direct numerical integration.

Two‐center matrix elements for Kratzer oscillators

An exact expression for two‐center Kratzer oscillator matrix elements of rβ (r is the internuclear distance) is derived. Using the hypervirial‐like theorem procedure, several recursion relations among these matrix elements are obtained. It is shown that these relations can be used to calculate recursively two‐center Kratzer oscillator matrix elements of rβ and rβd/dr in a very simple way.

Amide-imide tautomerism of acetohydroxamic acid in aqueous solution: quantum calculation and SMD simulations

The kinetics and the thermodynamics of the amide-imide tautomerizations of acetohydroxamic acid in aqueous solution are studied from a theoretical point of view. Quantum electronic structure calculations (QCISD//MP2, MP2 and M06-2X, applying two continuum solvation methods) and steered molecular dynamic (SMD) simulations (with solute–solvent interaction potentials derived from AMBER van der Waals parameters and electrostatic charges in solution) are taken into account. The elementary and complex tautomerizations from the E-Amide and Z-Amide forms are studied with and without the explicit assistance of a water molecule. The Gibbs free energy of activation for the E-Amide ⇆ E-Imide and Z-Amide ⇆ Z-Imide processes are considerably reduced when these processes are assisted by one water molecule. The Gibbs free energy of reaction was also reduced, but to a lesser degree, for each of the processes considered when in the presence of an explicit solvent molecule. The Z-Amide ⇆ Z-Imide tautomerization, which occurs in two elementary steps, seems to be slightly more favoured from a thermodynamic point of view; however, the E-Amide ⇆ E-Imide tautomerization, which is an elementary process, is the most kinetically favoured. The SMD simulations led to results which are consistent with those obtained by the three electronic structure methods applied.

Amino Acid Tautomerization Reactions in Aqueous Solution via Concerted and Assisted Mechanisms Using Free Energy Curves from MD Simulation

A theoretical study is described of chemical reactions in solution by means of molecular dynamics simulations, with solute-solvent interaction potentials derived from AMBER van der Waals parameters and QM/MM electrostatic charges in solution. The solvent is used as the reaction coordinate, and the free energy curves to calculate the properties related to the reaction mechanism. The proposed scheme is applied to the tautomerization process in aqueous solution for some amino acids H(2)NCHR-COOH (with R = H being glycine, R = CH(3) alanine, R = CH(2)OH serine, and R = CH(2)COOH aspartic acid), focusing on the role of the solvent in the reaction (assisted versus unassisted mechanisms) and on the effect of the hydrophilic/hydrophobic character of the radical R on the activation and reaction energies.

Theoretical determination of aqueous acid–base pK values: electronic structure calculations and steered molecular dynamic simulations

The equilibrium constant (K) of several acid–base equilibria involving isomers of acetohydroxamic acid in aqueous solution is studied from a theoretical point of view applying electronic structure methods (at the M06-2X-SMD/6-311++G(d,p) and MP2-PCM/6-311++G(d,p) levels of theory) and steered molecular dynamic (SMD) simulations. The similarity of the results obtained indicates that SMD simulations can be successfully used to evaluate Gibbs energy changes in acid–base reactions in solution and pK values since these properties are in agreement with those found with quantum calculation and thermodynamic cycles. In the process of proton transfer from the imide isomers (the ZI and EI structures) toward the anion Z-amide, the deprotonation of the ZI(COH) molecule is the most favorable process kinetically and thermodynamically. It is observed that pK values are slightly higher for E-isomers and, particularly, for the deprotonation from the oxime group EI(NOH). Finally, we must emphasize the goodness of SMD simulations in solution to calculate this property as an alternative to using continuum solvation methods.

Theoretical study of enzymatically catalyzed tautomerization of carbon acids in aqueous solution: quantum calculations and steered molecular dynamics simulations.

The thermodynamics and kinetics of enzymatically assisted reactions of carbon acids were studied theoretically in this work. Quantum electronic (QE) structure calculations and steered molecular dynamics (SMD) simulations were carried out. Three 3-butenal tautomerization reactions that proceed from the β,γ-unsaturated reactant (R) to the α,β-unsaturated carbon acid product (P) and occur in two elementary steps through an intermediate (I) were studied, ignoring or including the surrounding aqueous medium in the calculations. The Gibbs free energies of activation of the R ⇆ I enolization and I ⇆ P ketonization steps were found to decrease considerably when residues simulating enzymes were introduced into these processes. Although the processes became slightly more favorable thermodynamically when the solution was included in the simulations, they became less favorable kinetically. The results from SMD simulations of these reactions were qualitatively consistent with the values we obtained using QE as well as those found by other authors in similar studies. Our simulations also allowed us to perform a detailed study of these reactions in solution.

Theoretical study of mechanisms for the hydrolytic deamination of cytosine via steered molecular dynamic simulations

Gibbs free energy profiles of the cytosine deamination assisted by a water molecule in a discrete aqueous medium were obtained by the application of Steered Molecular Dynamic (SMD) simulations. Two pathways were considered to explain the mechanism of this process, where the water molecule attacks the C–N bond to give an intermediate (an amino–hydroxy–oxo structure in the A-path, and a hydroxy–oxo in the B-path) as the determinant step of reaction. Stationary structures along both energy profiles were analyzed at molecular dynamics level, obtaining states with higher free energies than those from electronic calculations in the gas phase and in solution described as a continuous medium. From the results obtained, the more complex A-pathway, with five steps, was kinetically the most favorable (with an endergonic reaction energy of 7.41 kcal mol−1, a high barrier of 67.53 kcal mol−1, and a small velocity constant k2 = 1.80 × 10−37 s−1), concluding that the uracil base can participate in a spontaneous genetic mutation since the uracil–ammonia complex has a long lifetime of 6.10 × 1027 s. This process turns out exergonic and faster when carried out in gas phase simulation or electronic calculation with a continuous medium, due to the disappearance of explicit water molecules that can compete with the assistant molecule.