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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- Assume that you are evaluating the integral of products of functions having symmetry labels in exercise 13.60, parts a-d. Which integrals, if any, are exactly zero due to symmetry considerations?Write a Slater determinant for the lithide ion, Li.Construct the symmetry-adapted linear combination molecular orbitals for hydrogen sulfide, H2S.
- Find the representatives of the operations of the group D2h in a basis of the four H1s orbitals of ethene. Take the molecule as lying in the xy-plane, with x directed along the C–C bond.A set of basis functions is found to span a reducible representation of the group Oh with characters 6,0,0,2,2,0,0,0,4,2 (in the order of operations in the character table in the Resource section). What irreducible representations does it span?Show that all three sigma v operations in the group D3h belong to the same class.
- Find the representatives of the operations of the group Td in a basis of four H1s orbitals, one at each apex of a regular tetrahedron (as in CH4). You need give the representative for only one member of each class.A set of basis functions is found to span a reducible representation of the group D2 with characters 6,−2,0,0 (in the order of operations in the character table in the Resource section). What irreducible representations does it span?The algebraic forms of the f orbitals are a radial function multiplied by one of the factors (a) z(5z2 − 3r2), (b) y(5y2 − 3r2), (c) x(5x2 − 3r2), (d) z(x2 − y2), (e) y(x2 − z2), (f) x(z2 − y2), (g) xyz. Identify the irreducible representations spanned by these orbitals in the point group C2v.
- 4. Show that the function x y z has symmetry species A1 in pt group D2,Consider the character table given below for the point group D3h, which includes molecules like cyclopropane and BF3. Suppose has been already determined a reducible representation for the collective motions of one such molecule, Γ(3N). What combination of irreps should we remove from it to account for translations & rotations, thereby yielding the purely vibrational representation, Γvib?P10C.8 Consider the molecule F2C=CF2 (point group D2h), and take it as lying in the xy-plane, with x directed along the C–C bond. (a) Consider a basis formed from the four 2pz orbitals from the fluorine atoms: show that the basis spans B1u, B2g, B3g, and Au. (b) By applying the projection formula to one of the 2pz orbitals, generate the SALCs with the indicated symmetries. (c) Repeat the process for a basis formed from four 2px orbitals (the symmetry species will be different from those for 2pz).