Spectral Structures Of The Hydrogen Molecule And The Hydrogen Molecular Ion In Strong Magnetic Fields

The subject of atomic and molecular systems in magnetic fields is a very interesting branch in the physics. The corresponding investigation plays an important role on the development of physics. Since the discovery of the strong magnetic field on while dwarfs and neutron stars and the diamagnetism (quadratic Zeeman Effect) in strong magnetic field, the electronic structure and properties of atomic and molecular systems in strong magnetic fields have been paid much attention by the physical community.This dissertation focuses on the electronic structure and properties of hydrogen molecule H2in a parallel strong magnetic field from zero up to2.35×107T within the Born-Oppenheimer approximation. With the Hylleraas-Gaussian basis set the overlap matrix is obtained analytically. The kinetic, Zeeman and diamagnetic terms of the Hamiltonian can be reduced to the overlap matrix. Based on the Singer transform, the nucleus-electron and electron-electron integrals are expressed in the form of hypergeometric functions with the Taylor expansion.The accuracies of the total energies of the lowest singlet states1∑g/u and1∏u have an improvement of the order of magnitude of10-4by the Hylleraas-Gaussian basis compared with that by Gaussian basis. The improvement is of the order of magnitude of10-5for the lowest triple states3∑g and3∏u. The dissociation energies of the states1∑g/u and3∏u increase monotonically with increasing the field strength, while the dissociation energies of the states3∑g and1∏u first decrease and then increase. With the wave functions at the equilibrium distances the electronic density distributions in the z1-z2and ρ1-ρ2subspace are calculated for the five states at some specific field strengths. The relationship between the dissociation energies and the electronic density distribution is illuminated. Pauli principle plays an important role on the change of the dissociation energy of the state3∑g. For the lowest1∏u state the change of the dissociation energy is synchronous with the change of the position of the largest probability in z1-z2subspace with increasing the field strength. On the Born-Oppenheimer approximation we investigated the equilibrium configuration of H2+in non-parallel magnetic field, the direction of which is changed while the molecular axis is fixed. The Zeeman term can still reduce to the overlap matrix. However, the nucleus-electron integral can’t be expressed in the form of hypergeometric functions, as shown in the corresponding performance of H2. Finally, it is numerically obtained by the algorithm CHEBQU, in which the Chebyshev polynomial is used to approach the integral.For the field strength γ=0.1a.u.(1a.u. corresponds to2.35×105T) the equilibrium configuration is the vertical configuration, i.e.,θ=90°(0is the angle of the magnetic field relative to the molecular axis). For0.4255319a.u.≤γ≤10a.u. the equilibrium configuration is not neither the vertical configuration nor the parallel configuration. With increasing the field strength the angle of the equilibrium configuration decreases. All configurations are stable in weak magnetic fields with respect to the dissociation H+p. With increasing the field strength, more and more configurations with large inclination become unstable. The potential energy curve of1u at θ=0°is composed by two parts, one of which belongs to the Instate of H2+in parallel magnetic field while the other belongs to the Instate. This is attributed to the cross of the potential energy curves of the two states in magnetic field.