Chapter 2 Self-test questions

1. Consider a molecule of chlorobenzene, C₆H₅Cl. How many coordinates do you need in order to specify the absolute position in space of all of the nuclei making up this molecule?

12

3

30

36

2. Consider a molecule of chlorobenzene, C₆H₅Cl. How many coordinates do you need in order to specify the absolute position in space of all of the electrons making up this molecule?

174

58

17

212

3. The fundamental approximation that is made in Hartree-Fock theory is that:

The motion of each electron is in some sense independent of the motion of all the other electrons.

Electron-electron Coulomb interactions are not accounted for.

Electrons move at the speed of light so we can ignore their specific positions.

The spin of electrons is assumed to be described by either the α or the β spin state.

4. Which of the following methods is not used to improve the convergence behaviour when solving the Hartree-Fock equations?

Modifying the energy of the virtual orbitals when constructing the Fock operator, through level-shifting.

Combining the results of multiple steps to estimate the most accurate Fock operator matrix for the following step.

Carefully choosing the initial set of coefficients c_ij within equation (2.11), so that this 'guess' for the wavefunction is as close as possible to the final Hartree-Fock wavefunction.

Re-calculating some of the two-electron integrals of eq. (2.13) at each step.

5. The Hartree-Fock energy calculated for chlorobenzene using the STO-3G family of basis sets is of −681.8957 hartree. Bearing in mind the approximate nature of the HF/STO-3G method, which of the following is true?

The heat of formation of chlorobenzene is roughly −681.8957 hartree.

The Hartree-Fock method is so inaccurate that we do not learn anything about the energy of chlorobenzene from this calculation.

Forming chlorobenzene from its separated nuclei and electrons releases roughly 1.8 million kJ mol⁻¹.

The energy required to split chlorobenzene up into six carbon atoms, five hydrogen atoms, and one chlorine atom is about 1.8 million kJ mol⁻¹.

6. Consider the bis(benzene)chromium complex Cr(η⁶-C₆H₆)₂, which has a closed-shell electronic ground state. How many occupied spatial molecular orbitals will there be in the Hartree-Fock wavefunction for this species?

108

33

54

23

7. What is the total number of contracted basis functions (s, p_x, p_y and p_z) used when carrying out a Hartree-Fock calculation on fluorobenzene C₆H₅F using the 6-31G basis set?

73

108

100

82

8. Which of the following gives the correct values for the expectation value of the S² operator for non spin-contaminated wavefunctions for singlet, doublet, triplet, quartet and quintet states?

0, 0.5, 1., 1.5, 2.

1, 2, 3, 4, 5

0, 0.75, 2., 3.75, 6.

0, 2, 6, 12, 20

9. Most modern electronic structure codes use Gaussian functions as basis functions with which to expand the molecular orbitals. Which of the following statements is not correct:

The commonly-used 'Slater-Type Orbital' family of basis sets uses Slater functions.

For a given number of basis functions, it would be more accurate to use Slater functions instead of Gaussian functions

The integrals over basis functions needed to carry out Hartree-Fock calculations are more difficult to evaluate for Slater functions than for Gaussian functions

Some combinations of multiple Gaussian functions are quite similar to Slater functions.

10. For the isovalue surface representation of the HOMO-1 of camphor shown in Fig. 2.3, which of the following statements is most correct?

The delocalized nature of the MO indicates that bonding is very delocalized also, due to participation by many resonance forms.

The black regions correspond to regions with positive charge, whereas those in lighter grey correspond to negatively charged regions.

The low amplitude near the C=O carbonyl group suggests that this is a very electron-deficient region of the molecule.

The HOMO-1 is rather delocalized across the molecule; this orbital has a number of nodal surfaces across which its sign changes.

Chapter 2 Self-test questions

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