444Computational Chemistry

[120]M. J. S. Dewar, “A Semiempirical Life,” American Chemical Society, Washington, DC, 1992, p. 162.

[121](a) Z. Zhou and R. G. Parr, J. Am. Chem. Soc., 1989, 111, 7371. (b) Z. Zhou, R. G. Parr, and J. F. Garst, Tetrahedron Lett., 1988, 29, 4843.

[122]Reference [9], p. 101.

[123](a) Reference [10], part B, and references therein. (b) G. Frenking, J. Chem. Soc., Dalton Trans., 1997, 1653.

[124](a) S. Kyistyan and P. Pulay, Chem. Phys. Lett., 1994, 229, 175. (b) J. M. Perez-Jorda and

A.D. Becke, Chem. Phys. Lett., 1995, 233, 134.

[125](a) M. Lozynski, D. Rusinska-Roszak, and H.-G. Mack, J. Phys. Chem. A, 1998, 102, 2899. (b) C. Adamo and V. Barone in “Recent Advances in Density Functional Methods. Part II,” D. P. Chong, Ed., World Scientific, Singapore, 1997. (c) F. Sim, A. St.-Amant,

I.Papai, and D. R. Salahub, J. Am. Chem. Soc., 1992, 114, 4391.

EASIER QUESTIONS

1.State the arguments for and against, regarding DFT as being more a semiempirical than an ab initio-like theory.

2.What is the essential difference between wavefunction theory and DFT? What is it that, in principle anyway, makes DFT simpler than wavefunction theory?

3.Why can’t current DFT calculations be improved in a stepwise, systematic way, as can ab initio calculations?

4.Which of these prescriptions for dealing with a function are functionals: (1) square root of

5.For which class(es) of functions is the nth derivative of a functional?

6.Explain why a kind of molecular orbital is found in current DFT, although DFT is touted as an alternative to wavefunction theory.

7.What is fundamentally wrong with functionals that are not gradient-corrected?

8.The ionization energy of a molecule can be regarded as the energy required to remove an electron from its HOMO. How then would a pure density functional theory, with no orbitals, be able to calculate ionization energy?

9.Label these statements true or false: (1) For each molecular wavefunction there is

an electron density function. (2) Since the electron density function has only as its variables, DFT necessarily ignores spin. (3) DFT is good for transition metal compounds because it has been specifically parameterized to handle them. (4) In the limit of a sufficiently large basis set, a DFT calculation represents an exact solution of the Schrödinger equation. (5) The use of very large basis sets is essential with DFT. (6) A major problem in density functional theory is the prescription for going from the molecular electron density function to the energy.

10.Explain in words the meaning of the terms electronegativity, hardness, and the Fukui function.

Density Functional Calculations 445

HARDER QUESTIONS

1.It is sometimes said that electron density is physically more real than a wavefunction. Do you agree? Is something that is more easily grasped intuitively necessarily more real?

2.A functional is a function of a function. Explore the concept of a function of a functional.

3.Why is it that the HF Slater determinant is an inexact representation of the wavefunction, but the DFT determinant for a system of noninteracting electrons is exact for this particular wavefunction?

4. Why do we expect the “unknown” term in the energy equation in Eq. (7.21)) to be small?

5.Merrill et al. have said that “while solutions to the [HF equations] may be viewed as exact solutions to an approximate description, the [KS equations] are approximations to an exact description!” Explain.

6. Electronegativity is the ability of an atom or molecule to attract electrons Why is it then (from one definition) the average of the ionization energy and the electron affinity (Eq. (7.14)), rather than simply the electron affinity?

7.Given the wavefunction of a molecule, it is possible to calculate the electron density function. Is it possible in principle to go in the other direction? Why or why not?

8.The multielectronwavefunction is a function of the spatial and spin coordinates of all the electrons. Physicists say that for any system tells us all that can be known

about the system. Do you think the electron densiity function tells us everything that can be known about a system? Why or why not?

9.If the electron density function concept is mathematically and conceptually simpler than the wavefunction concept, why did DFT come later than wavefunction theory?

10.For a spring or a covalent bond, the concepts of force and force constant can be expressed in terms of first and second derivatives of energy with respect to extension. If we let a “charge space” N replace the real space of extension of the spring or bond, what are the analogous concepts to force and force constant? Using the SI, derive the units of electronegativity and of hardness.

This page intentionally left blank