An electron moving in a conjugated pi framework of a molecule (such as an alkene like polyacetylene) can be approximated as an electron in a box of length L. If an externally applied electric field of strength e = ee that is oriented along the x axis (the length of the box), it interacts with the negatively charged electron via the following perturbation to the potential energy VE еє х — where x is the position of the electron in the box, e is the field strength, and e is the electron charge. Calculate the first order perturbation to the energy of the ground-state wavefunction.

A normalized valence bond wavefunction turned out to have the form ψ = 0.8891ψcon + 0.458ψion. What is the chance that. in 1000 inspections of the molecule, both electrons of the bond will be found on one atom?

A point charge q with a charge of 7.3µC is held at the origin. A second point charge 92 with a charge of -1.2µC is held 4.5cm away. Let the potential energy be zero at an infinite separation between the two charges. What is the electric potential energy stored in this configuration? (Include the appropriate SI Unit) PE

3. Hydrogen atoms (ignore spin) are first at a basic state. At the time t > 0, atoms experience the electric field Ae-bt with A> 0 and b>0, and is a unit vector in the z direction. Determine the probability of transition to the first excitation state at the time t → ∞.

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-.

Write the valence bond wavefunction for the one cr andtwo n bonds in a nitrogen molecule, N2 .

for C2H2   1- Calculate the separation at which the minimum of the potential energy occur.2- verify that at this minimum the potential energy V = ─  .3- Choose values of r such that all characteristic points and areas are shown clearly on the graph. Let the x-axis be r in pm

The particle on a ring can be used as a model for the motion of electrons around the [18]-annulene ring. See a 2-D representation of the [18]-annulene molecule below; the dashed line around the periphery of the molecule indicates the electron path. H H H H H H H H H H H H H H H We may treat the structure as a circular ring of radius 840 pm, with 18 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.

Write the valence-bond wavefunction for the single bond in HCl?

Treat a vibrating HI molecule as a hydrogen atom oscillating towards and away from a stationary iodine atom. Given the force constant of the HI bond is 314 N m-1, calculate the vibrational frequency of the molecule.