Hidrógeno: más alla de la aproximación clásica

La aproximación clásica para los núcleos es la aproximación más usada en la resolución de problemas en física de materia condesada. Sin embargo, en la naturaleza hay sistemas para los cuales es necesario introducir los grados de libertad nucleares para obtener una correcta descripción de las propiedades. Los sistemas que contienen hidrógeno son un ejemplo de ellos. En este trabajo, hemos estudiado la resolución del problema cuántico nuclear en el caso particular de la molécula de agua. Se ha considerado la aproximación de Hartree, es decir, considerando a los núcleos como partículas distinguibles. Además, hemos propuesto un modelo para resolver el proceso de tunneling, el cual involucra la resolución del problema nuclear para configuraciones del sistema lejos de su posición de equilibrio clásic

Effect of quantization of vibrations on the structural properties of crystals

We study the structural effects produced by the quantization of vibrational degrees of freedom in periodic crystals at zero temperature. To this end we introduce a methodology based on mapping a suitable subspace of the vibrational manifold and solving the Schroedinger equation in it. A number of increasingly accurate approximations ranging from the quasi-harmonic approximation (QHA) to the vibrational self-consistent field (VSCF) method and the exact solution are described. A thorough analysis of the approximations is presented for model monoatomic and hydrogen-bonded chains, and results are presented for a linear HF chain where the potential energy surface is obtained via first-principles electronic structure calculations. We focus on quantum nuclear effects on the lattice constant, and show that the VSCF is an excellent approximation, meaning that correlation between modes is not extremely important. The QHA is excellent for covalently-bonded, mildly anharmonic systems, but it fails for hydrogen-bonded ones. In the latter, the zero-point energy exhibits a non-analytic behavior at the lattice constant where the H-atoms center, which leads to a spurious secondary minimum in the quantum-corrected energy curve. An inexpensive anharmonic appoximation of non-interacting modes appears to produce rather good results for hydrogen-bonded chains, for small system sizes. However, it converges to the incorrect QHA results for increasing size. Isotope effects are studied for the first-principles HF chain. We show how the lattice constant and the HF distance increase with decreasing mass, and how the QHA proves to be insufficient to reproduce this behavior.Comment: 13 pages, 12 figures. To appear in Phys. Rev.