Chapter 5. Quantum chemistry in Molecular Modeling


5.1 Why use Quantum Chemical methods ?
Quantum-chemical methods are more general than empirical methods
5.2 The Schrödinger equation
The recipe for the calculation of the electronic wavefunction
5.3 Hartree-Fock SCF theory
Part a: The independent particle approximation
Part b:Molecular Orbitals, basis sets
5.4 Limitations of the HF method;
Electron correlation
CI, MP2 and MCSCF
5.5 Energy calculations
Conversion of absolute energies to heats of formation
Isodesmic reactions
5.6 Quality of ab initio results
Performance of low-level methods for organic molecules
5.7 Semi-empirical quantum chemistry
Further approximations and introduction of empirical parameters
5.8 Quality of semi-empirical results
Low-level ab initio methods are usually better, but much more time-consuming
5.9 Solvation
The medium can be represented as a dielectric continuum
5.10 Atomic charges
Not a physical concept !
Several methods exist for attributing charge to individual atoms
"For calculating molecular properties, quantum chemistry seems to be the obvious tool to use. Calculations that do not use the Schrödinger equation are acceptable only to the extent that they reproduce the results of high level quantum mechanical calculations."
(U. Burkert & N.L. Allinger, "Molecular Mechanics", 1982)


5.1 Why use Quantum Chemical methods ?

Many aspects of molecular structure and dynamics can be modeled using classical methods in the form of molecular mechanics and dynamics. The classical force field is based on empirical results, averaged over a large number of molecules. Because of this extensive averaging, the results can be good for standard systems, but there are many important questions in chemistry that can not at all be addressed by means of this empirical approach. If one wants to know more than just structure or other properties that are derived only from the potential energy surface, in particular properties that depend directly on the electron density distribution, one has to resort to a more fundamental and general approach : quantum chemistry. The same holds for all non-standard cases for which molecular mechanics is simply not applicable.

Quantum chemistry is based on the postulates of Quantum Mechanics. In this chapter we shall recall some basic aspects of the theory of quantum chemistry with an emphasis on their practical implications for the molecular modeler, and we will try to answer the questions of when to use a quantum chemical method instead of molecular mechanics, which quantum chemical method to choose, and what to expect from the quality of the results.

In quantum chemistry, the system is described by a wavefunction which can be found by solving the Schrödinger equation. This equation relates the stationary states of the system and their energies to the Hamiltonian operator, which can be viewed as the recipe for obtaining the energy associated with a wavefunction describing the positions of the nuclei and electrons in the system. In practice the Schršdinger equation cannot be solved exactly and approximations have to be made, as we shall see below. The approach is called "ab initio" when it makes no use of empirical information, except for the fundamental constants of nature such as the mass of the electron, Planck's constant etc., that are required to arrive at numerical predictions. Do not confuse "ab initio" with "exact" ! In spite of the necessary approximations, ab initio theory has the conceptual advantage of generality, and the practical advantage that (with experience) its successes and failures are more or less predictable.

The major disadvantage of ab initio quantum chemistry are the heavy demands on computer power. Therefore, further approximations have been applied for a long time which go together with the introduction of empirical parameters into the theoretical model. This has led to a number of semi-empirical quantum chemical methods, which can be applied to larger systems, and give reasonable electronic wavefunctions so that electronic properties can be predicted. Compared with ab initio calculations their reliability is less and their applicability is limited by the requirement for parameters, just like in molecular mechanics.

In general, one should apply quantum chemistry for "small" systems, which can be treated at a very high level, when electronic properties are sought (electric moments, polarizabilities, shielding constants in NMR and ESR, etc.) and for "non-standard" structures, for which no valid molecular mechanics parameters are available. Examples are conjugated pi systems, organometallic compounds and other systems with unusual bond or atom types, excited states, reactive intermediates, and generally structures with unusual electronic effects.

Quantum chemistry is the subject of many excellent textbooks.
The one by Levine [1] has a good reputation, and devotes much attention to practical computational methods.
Several chapters in the series Reviews in Computational Chemistry [2] put quantum chemical calculations in a molecular modeling perspective.
In the interesting book of G. Nàray-Szabò, P.R. Surjàn and J.G. Angyàn [3] theoretical chemistry is discussed in relation to experimental chemistry.
An account of the development of "model chemistries" based on ab initio calculations is given by W.J. Hehre, L. Radom, P. von R. Schleyer and J.A. Pople [4].
A more advanced textbook is that of Szabo and Ostlund [5].
Useful guides in the use of ab initio and semi-empirical quantum-chemical methods are the manual of Spartan [6] and the book published by Gaussian Inc. [7].

References:

  1. Levine Quantum Chemistry, 4th ed., 1991
  2. Reviews in Computational Chemistry, Volumes 1 to 4, K.B. Lipkowitz and D.B. Boyd, eds., VCH publishers.
  3. G. Nàray-Szabò, P.R. Surjàn and J.G. Angyàn Applied Quantum Chemistry, Reidel, 1987
  4. W.J. Hehre, L. Radom, P. von R. Schleyer and J.A. Pople Ab initio molecular orbital theory, Wiley, 1986
  5. Szabo and Ostlund Modern Quantum Chemistry, McGraw-Hill, 1989.
  6. Spartan User's Guide, version 3.0, Wavefunction, Inc., 1993.
  7. Foresman, J.B.; Frisch, A. Exploring Chemistry with Electronic Structure Methods: A Guide to Using Gaussian, Gaussian Inc., 1993.

Next paragraph, 5.2 The Schrödinger Equation
Back to Chapter 3 of the Computational Chemistry Course.
Chapter 5 MM Syllabus 1995 MODIFIED November 8, 1995
Fred Brouwer, Lab. of Organic Chemistry, University of Amsterdam.