What is the number of primitive functions in a calculation of an H2S molecule using a 8-41G(d) basis set? NOTE: For the d orbitals, assume the use of spherical harmonics.
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What is the number of primitive functions in a calculation of an H2S molecule using a 8-41G(d) basis set?
NOTE: For the d orbitals, assume the use of spherical harmonics.
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- Write a Slater determinant for the lithide ion, Li.What are the energies and angular momenta of the first five energy levels of benzene in the 2-D rotational motion approximation? Use the mass of the electron and a radius of 1.51A to determine I.What are the degeneracies of the H atom wavefunctions when spin is accounted for? Give a general formula.
- 5. Using a table of Hermite Polynomials, provide the property normalized 42. You may 1 (as verify your answer with: n(x) = (21)² H₂ (α²x) e-x² 2nn! 2.Construct the Slater determinant for the 6C atom.The cyclobutadienyl cation (C4H4+) may be treated using the Huckel MO approach. The roots to the secular determinant are α+ 2β, α and α- 2β. The middle level is doubly degenerate. (a) Determine the energy for this system in terms of α and β. (b) The ionization energy for C4H4 has been determined to be 0.22 eV. Calculate α in kJ mol-1. (c) Predict the ground state multiplicities for C4H4, C4H4+, and C4H4-.
- Consider the real part of the spherical harmonic Y2,+2. At which values of ϕ do angular nodes occur? Identify the positions of the corresponding planes. Repeat the process for the imaginary part.1) The Hückel matrix for molecule; x 10 H = 1 x 1 where x = - a-E В is The secular equation is HC=0 which is used to 0 1 x find Huckel molecular orbitals of the above molecule where E is the energy(eigenvalue), a and ß are constants. Find the energy values(eigenvalues) in terms of a and B, then find the normalized eigenvectors (vector C).2. Consider a helium atom. (a) Sketch the system and write the Hamiltonian. Denote the term(s) in the operator that make(s) the Schrödinger equation unsolvable. (b) Given an excited-state configuration 1s 2s', express all possible excited-state wavefunctions in terms of spatial and spin functions for the two electrons. For each, denote the symmetry of the overall wavefunction, the spatial component, and the spin component with respect to exchange.
- 6. The particle on a ring is a useful model for the motion of electrons around the coronene ring. See a 2-D representation of the coronene molecule below; the dashed line around the periphery of the molecule indicates the electron path. We may treat the structure as a circular ring of radius 420 pm, with 14 electrons in the conjugated system moving along the perimeter of the ring. Assuming that, in the ground state of the molecule, each state is occupied by two electrons, (a) calculate the energy and angular momentum of an electron in the highest occupied level, and (b) calculate the frequency of radiation that can induce a transition between the highest occupied and lowest unoccupied levels.2. Commuting operators. (a) Show whether the operator of the kinetic energy operator K and the momentum operator Px for a one-dimensional system commute (show every step). (b) What does the result mean (physical interpretation)?For a He atom in the excited state with atomic electronic configuration 1s1 2s1: write out the symmetric and antisymmetric spatial wavefunctions. These two are linear combination of ψ1s and ψ2s each with an electron in them. combine each spatial wavefunction with the appropriate spin wavefunctions for two electrons (there are four of them) such that the total wavefunction is antisymmetric.