Use Hückel theory to write the secular determinant and determine the energies of the pi orbitals...
Use Hückel theory to write the secular determinant and determine the energies of the pi orbitals and total energy of the pi system for hexatriene
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Use Hückel theory to write the secular determinant and determine
the energies of the pi orbitals...
(a) What is Hückel theory? Why is it used? What assumptions does it make? (b) Consider...
(a) What is Hückel theory? Why is it used? What assumptions does it make? (b) Consider hexatriene, how many molecular orbitals would you expect there to be? (C) Write the secular determinant for the hexatriene system. (d) Using Hückel approximations, re-write the Hückel secular determinant using the appropriate variables, and explain what the variable represent. (e) Determine the energies of the molecular orbitals (1) Determine the total energy of the -electronic energy in hexatriene (9) Hückel theory is meant as...
Q 2(a) [70 Marks] The secular equations for describing the overlap of the four unhybridised p orb...
Q 2(a) [70 Marks] The secular equations for describing the overlap of the four unhybridised p orbitals in butadiene (shown above) lead to a matrix of the form H11- ES ES12 H13- ES13H14-ES14 H21- ES21 H22- ES22 H23 - ES23 H24- ES24 H31- ES31 H32 - ES32 H33 - ES33 H34- ES34 41 - ES41 H42 - ES42 H43- ES43 H44- ES44 where Hy is the Hamiltonian integral for orbitals i and j and Sj is the overlap integral for...
The allyl cation C3H5+ has 2Pi electrons. Solving the Huckel MO secular equation yield E= {a+(sqrt2)*B,a,-(sqrt2)*B}...
The allyl cation C3H5+ has 2Pi electrons. Solving the Huckel MO secular equation yield E= {a+(sqrt2)*B,a,-(sqrt2)*B} a) write the secular determinant b) recalling that b,0, sketch the orbital energy diagram and fill in the Pi electrons. Indicate clearly which one is the HOMO and LUMO c) in terms of a and B what does the HMO theory predict the HOMO-LUMO gap in allyl cation to be ? d) what is the total energy of the molecule (in terms of a...
The ordering of the energies of the pi-molecular orbitals of benzene is shown in Fig. 1....
The ordering of the energies of the pi-molecular orbitals of benzene is shown in Fig. 1. Those energies can be approximated by a two-dimensional particle-in-a-box, in which the energy values take a form very similar to those of a one-dimensional box: E_n_x, n_y = n_x^2 + n_y^2) h^2/8mL^2 where n_x and n_y take non-zero integer values. For this model, the first few derived energy levels, indexed by (n_x, n_y) pairs, are diagrammed in Fig. 2. Approximating benzene as a square,...
b) Benzene and ar Please fint mPle in the Picte: ter ange) fxoni low Estimating the...
b) Benzene and ar Please fint mPle in the Picte: ter ange) fxoni low Estimating the delocalization energy within the Hückel appr tonian matrix Example 10E.2 Use the Hickel approxination to find the energies of the π s of cyclobutadiene, and estimate the delocalization αβ000 energy Method Set for butadiene, but note that atoms A and D are also now neigh bours Then solve for the roots of the secular equation and assess the total π-bond energy. For the delocalization...
calculation of geometries. Question 5 (8 points (2,3,3)) For a particular problem, the wavefunction is written...
calculation of geometries. Question 5 (8 points (2,3,3)) For a particular problem, the wavefunction is written as a superposition of two orthonormal functions (xi): Y = CX,+C2X2. The coefficients are determined with variation theory. The following integrals are given in eV): H, =Sxix, dt =-10 H2 = Sxixdr = -0.5 H,2 = xixdt =-1.0 a) Give the secular equations. b) Find the energies. c) Find the wavefunction for the state with the lowest energy (if you did not find the...
2. Using the Huckel model write the secular determinant for phenanthrene (see attached figure and use the graph paper grid. Leave blanks where there should be zeros and only put in the x'...
2. Using the Huckel model write the secular determinant for phenanthrene (see attached figure and use the graph paper grid. Leave blanks where there should be zeros and only put in the x's and 1's where you expect them.) 2 3 9 Il 5 5 7
2. Using the Huckel model write the secular determinant for phenanthrene (see attached figure and use the graph paper grid. Leave blanks where there should be zeros and only put in the x's and...
5. (5 pts) Consider the hybridization and bonding scheme for cis-1,2-dichloroethene, CH2Cl2, using valence bond theory....
5. (5 pts) Consider the hybridization and bonding scheme for cis-1,2-dichloroethene, CH2Cl2, using valence bond theory. (a) Complete the Lewis structure using the skeletal structure shown below: H H c-c CI CI (b) Use VSEPR theory to predict the electron domain geometry and the hybridization around carbon; (c) Draw an energy diagram showing the formation of hybrid orbitals from the atomic orbitals; (d) Sketch the molecule showing the orbitals and any overlapping orbitals to indicate covalent bonds; (e) Label all...
Question 4 [31] For a diatomic molecule, the electronic wavefunction was descri bed by CA +...
Question 4 [31] For a diatomic molecule, the electronic wavefunction was descri bed by CA + €pB R (a)Express energy expectation value as a function of c, Ca and integral constants [3] (b) Derive and explain their chemical implications of Coulombic integral (a), Resonance Integral (B), and Overlap Integral (s). [3] (c)What are the key Hückel's approximations for a homonuclear molecule? [4] Question 4 [31]; Contin ued Propene Cyclopropene Cyclopropenyl Cation Using the Hückel molecular orbital theory, wavefunction of electrons...
Use the following figure of atomic orbital energies to explain what you observed in the switch...
Use the following figure of atomic orbital energies to explain
what you observed in the switch of the pz sigma (g) and the
pi(u)
Changes in molecular orbital energy levels for ground state homonuclear diatomic molecules Energy *(2p) 7 "(2p) ----- - 0,*(2p) (2p) ------ ++ +++ *,*(2) z_(20) ++ titt - ## ## Ho # ## ,127) 5,20 # 0,123) # # # o #.....# # 0,4(25) 9412) B2 Assuming that the criterion you determined in the previous question...
(a) What is Hückel theory? Why is it used? What assumptions does it make? (b) Consider hexatriene, how many molecular orbitals would you expect there to be? (C) Write the secular determinant for the hexatriene system. (d) Using Hückel approximations, re-write the Hückel secular determinant using the appropriate variables, and explain what the variable represent. (e) Determine the energies of the molecular orbitals (1) Determine the total energy of the -electronic energy in hexatriene (9) Hückel theory is meant as...
Q 2(a) [70 Marks] The secular equations for describing the overlap of the four unhybridised p orbitals in butadiene (shown above) lead to a matrix of the form H11- ES ES12 H13- ES13H14-ES14 H21- ES21 H22- ES22 H23 - ES23 H24- ES24 H31- ES31 H32 - ES32 H33 - ES33 H34- ES34 41 - ES41 H42 - ES42 H43- ES43 H44- ES44 where Hy is the Hamiltonian integral for orbitals i and j and Sj is the overlap integral for...
The ordering of the energies of the pi-molecular orbitals of benzene is shown in Fig. 1. Those energies can be approximated by a two-dimensional particle-in-a-box, in which the energy values take a form very similar to those of a one-dimensional box: E_n_x, n_y = n_x^2 + n_y^2) h^2/8mL^2 where n_x and n_y take non-zero integer values. For this model, the first few derived energy levels, indexed by (n_x, n_y) pairs, are diagrammed in Fig. 2. Approximating benzene as a square,...
b) Benzene and ar Please fint mPle in the Picte: ter ange) fxoni low Estimating the delocalization energy within the Hückel appr tonian matrix Example 10E.2 Use the Hickel approxination to find the energies of the π s of cyclobutadiene, and estimate the delocalization αβ000 energy Method Set for butadiene, but note that atoms A and D are also now neigh bours Then solve for the roots of the secular equation and assess the total π-bond energy. For the delocalization...
calculation of geometries. Question 5 (8 points (2,3,3)) For a particular problem, the wavefunction is written as a superposition of two orthonormal functions (xi): Y = CX,+C2X2. The coefficients are determined with variation theory. The following integrals are given in eV): H, =Sxix, dt =-10 H2 = Sxixdr = -0.5 H,2 = xixdt =-1.0 a) Give the secular equations. b) Find the energies. c) Find the wavefunction for the state with the lowest energy (if you did not find the...
2. Using the Huckel model write the secular determinant for phenanthrene (see attached figure and use the graph paper grid. Leave blanks where there should be zeros and only put in the x's and 1's where you expect them.) 2 3 9 Il 5 5 7
2. Using the Huckel model write the secular determinant for phenanthrene (see attached figure and use the graph paper grid. Leave blanks where there should be zeros and only put in the x's and...
5. (5 pts) Consider the hybridization and bonding scheme for cis-1,2-dichloroethene, CH2Cl2, using valence bond theory. (a) Complete the Lewis structure using the skeletal structure shown below: H H c-c CI CI (b) Use VSEPR theory to predict the electron domain geometry and the hybridization around carbon; (c) Draw an energy diagram showing the formation of hybrid orbitals from the atomic orbitals; (d) Sketch the molecule showing the orbitals and any overlapping orbitals to indicate covalent bonds; (e) Label all...
Question 4 [31] For a diatomic molecule, the electronic wavefunction was descri bed by CA + €pB R (a)Express energy expectation value as a function of c, Ca and integral constants [3] (b) Derive and explain their chemical implications of Coulombic integral (a), Resonance Integral (B), and Overlap Integral (s). [3] (c)What are the key Hückel's approximations for a homonuclear molecule? [4] Question 4 [31]; Contin ued Propene Cyclopropene Cyclopropenyl Cation Using the Hückel molecular orbital theory, wavefunction of electrons...
Use the following figure of atomic orbital energies to explain
what you observed in the switch of the pz sigma (g) and the
pi(u)
Changes in molecular orbital energy levels for ground state homonuclear diatomic molecules Energy *(2p) 7 "(2p) ----- - 0,*(2p) (2p) ------ ++ +++ *,*(2) z_(20) ++ titt - ## ## Ho # ## ,127) 5,20 # 0,123) # # # o #.....# # 0,4(25) 9412) B2 Assuming that the criterion you determined in the previous question...
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