Jose R. De la Vega

Motion of the proton in an asymmetric double minimum potential

A method different from the semiclassical WKB method was developed for calculating the energy levels of a proton and its penetration through a barrier under an asymmetric double minimum potential. The potential was written as the sum of a parabolic term with minimum at X = 0 and a Gaussian with maximum at X0. The stationary states were found by the variational method using the eigenfunctions of the harmonic oscillator for the parabolic potential. The time dependence of the system was found by expanding the eigenstate of the proton at t = 0 in terms of the stationary states. A Gaussian centered at the minimum of the left well and with an exponent consistent with the ground state of the proton in this well represented the proton at t = 0. The proton is found to oscillate anharmonically between the two wells. The penetration through the barrier is conveniently described in terms of the average frequency of oscillation and in terms of the extreme of the expectation value of the protons position in the second...

Tunneling in the proton transfer between two water molecules

Abstract SCF CNDO calculations were performed for the species H5O+2 at several positions of the intervening proton and at interoxygen distances of 2.65, 2.70 and 2.75 A. The energy profile was fitted to a potential energy function containing a quadratic term plus a gaussian. The eigenvalues and eigenvectors were obtained by using the variational method with the eigenfunctions of the parabolic potential as basis set. The results indicate that at 2.65 A the top of the barrier is below the first energy level and that at 2.75 A the first two energy levels are below the top of the barrier with the splitting of the symmetric-antisymmetric pair of 0.00132 au indicating that tunneling occurs at a frequency of 1014 reciprocal seconds.

Calculations of bond angles in five-membered conjugated ring systems

Abstract We have calculated the bond angles in furan, pyrrole, imidazole and oxazole by minimizing the molecular energies with respect to the angles. The excellent agreement between theory and experiment confirms our assumption that bond distortion does not occur in these molecules.

Proper functional representation of symmetric double minimum potentials

Abstract The suitability of using either a parabola and gaussian or two-Morse potentials as the analytic function for a symmetric double-minimum potential is examined. It is determined that the choice must be made by evaluating a simple expression. An expression for the matrix elements of the secular equation using the two-Morse potential is given.

Calculation of the proton transfer between water molecules

Abstract An ab initio calculation has been made for the reaction 2H 2 O a H 3 + + OH − . The hydrogen transfer pathway of minimal energy occurs with a change of oxygen-oxygen distance from 5.615715 au in the water case to 4.225715 au in the acid-base case.

Simultaneous proton transfer along a linear water polymer

SCF CNDO calculations were performed for species H3O+·(H2O)n·OH− where n was varied from one to three. The position of the intervening protons was changed simultaneously while the oxygens and remaining hydrogens were kept fixed. It was found that only one minimum occurs when n is one or two while an asymmetric double minimum potential is found when n is equal to three. A barrier of 10.4 kcal/mole was found.

Effect of methyl substitution on the intramolecular exchange of hydrogen-bonded protons

Abstract Of the two possible monomethyl naphthazarins only the 2-methyl derivative has been encountered. Efforts to obtain the 7-methyl derivative always lead to the 2-methyl tautomer. Previous studies suggested a near symmetric double minimum potential for the intramolecular proton exchange with a high barrier and 0.9 kcal mol −1 difference between the 2- and 7-tautomers. If there were fast exchange, the two tautomers would have been detected. Now, with a much larger and better basis set and better algorithms for finding stationary points, a new study finds a barrier of 29 kcal mol −1 . Two more (intermediate) minima were found, corresponding to structures in which the protons are on different rings. However, the energy difference between the absolute minima and the intermediates is so large that the latter do not contribute to the exchange process. In monomethylnaphthazarin, the difference between the two lowest minima was found to be 1.09 to 1.79 kcal mol −1 . The rotation of the methyl group changes the energy difference between the minima, but the minimum of the 2-methyl isomer is always below that of the 7-methyl isomer, thus maintaining the asymmetry of the double minimum potential, without accidental degeneracy, in contrast to dimethylnaphthazarins and 6-methyl-9-hydroxyphenalen-1-one, as already reported. The exchange process is described by two quantities: the fraction of the proton emerging into the other well (2.7 × 10 −11 ) and the frequency with which it leaks (6 × 10 12 ). This will make the 7-methyl derivative undetectable by NMR. The product of the two factors suggests that the equivalent of a full proton is exchanging every six milliseconds.