Question

Draw a model of simplest molecule, H₂⁺ and labelwith all the important variable in solving Schrodinger equation. Then using those variables , express hamiltonian for the molecule

Answer 1

Hydrogen molecule ion (H2 +) by quantum mechanics. (Fig.14) Quantum mechanical hydrogen molecule ion (H2 +) ? First we need to know the quantum mechanical approach about hydrogen molecule ion (H2 +). Different from hydrogen atom, the wavefunction of H2 + molecule ion itself does NOT mean real probability density of electrons. So we cannot know the real states of an electron from this quantum mechanical H2 + molecule ion. (Eq.l) H2 + molecule ion Hamiltonian.H^cap psi = Epsi H^cap = plancks^2/2m_e nabla^2 - e^2/4piE_0 r_a - e^2/4piE_0 r_b + e^2/4piE_0 R Eq.l consists of kinetic energy of an electron and Coulomb interactions among one electron and two nuclei (a and b). Internuclear distance of H2 + is very long (= 1.057 times I0^10m). So it is natural that we think electron probability distribution around one nucleus is almost same as hydrogen atom. So they define H2 + wavefunction using the Is H and wavefunction follows. (Eq. 1) H2 + molecule ion