Electron correlation models

It is likely that different quantum chemical models will perform differently in each of these situations. Processes which involve net loss or gain of an electron pair are likely to be problematic for Hartree-Fock models, which treat the electrons as essentially independent particles, but less so for density functional models and MP2 models, which attempt to account for electron correlation. Models should fare better for processes in which reactants and products are similar and benefit from cancellation of errors, than those where reactants and products are markedly different. The only exception might be for semi-empirical models, which have been explicitly parameterized to reproduce individual experimental heats of formation, and might not be expected to benefit from error cancellation. 

The inconsistency between predictions made by MO REPEs and VB REPEs may be attributed to the different natures of simple MO and VB theories, i.e., the simple MO theory is a one-electron model, free of electron correlation, but VB theory is a many-electron, correlation model. This difference may result in the different topological dependence of -conjugation in MO and VB models, as illustrated by the [n]phenanthrene series. 

Methods and Algorithms of Quantum Chemistry, Proceedings, Second ed., J. Grotendorst, Ed., John von Neumann Institute for Computing, Jiilich, Germany, NIC Series, Vol. 3, 2000, pp. 593-638. Tensors in Electronic Structure Theory Basic Concepts and Applications to Electron Correlation Models. 

Gallagher Feeder S M and Jonas D 1999 Two-dimensional electronic correlation and relaxation spectra theory and model calculations J. Phys. Chem. A 102 10 489-505... 

A. R. Leach, Molecular Modelling Principles and Applications Longman, Essex (1996). P. Fulde, Electron Correlations in Molecules and Solids Third Enlarged Edition Springer,... 

A variation on MNDO is MNDO/d. This is an equivalent formulation including d orbitals. This improves predicted geometry of hypervalent molecules. This method is sometimes used for modeling transition metal systems, but its accuracy is highly dependent on the individual system being studied. There is also a MNDOC method that includes electron correlation. 

DFT methods are attractive because they include the effects of electron correlation—the fact that electrons in a molecular system react to one another s motion and attempt to keep out of one another s way—in their model. Hartree-Fock calculations consider this effect only in an average sense—each electron sees and... 

As a final note, be aware that Hartree-Fock calculations performed with small basis sets are many times more prone to finding unstable SCF solutions than are larger calculations. Sometimes this is a result of spin contamination in other cases, the neglect of electron correlation is at the root. The same molecular system may or may not lead to an instability when it is modeled with a larger basis set or a more accurate method such as Density Functional Theory. Nevertheless, wavefunctions should still be checked for stability with the SCF=Stable option. ... 

Each cell in the chart defines a model chemistry. The columns correspond to differcni theoretical methods and the rows to different basis sets. The level of correlation increases as you move to the right across any row, with the Hartree-Fock method jI the extreme left (including no correlation), and the Full Configuration Interaction method at the right (which fuUy accounts for electron correlation). In general, computational cost and accuracy increase as you move to the right as well. The relative costs of different model chemistries for various job types is discussed in... 

As we have seen throughout this book, the Hartree-Fock method provides a reasonable model for a wide range of problems and molecular systems. However, Hartree-Fock theory also has limitations. They arise principally from the fact that Hartree-Fock theory does not include a full treatment of the effects of electron correlation the energy contributions arising from electrons interacting with one another. For systems and situations where such effects are important, Hartree-Fock results may not be satisfactory. The theory and methodology underlying electron correlation is discussed in Appendix A. 

A variety of theoretical methods have been developed which include some effects of electron correlation. Traditionally, such methods are referred to as post-SCF methods because they add correlation corrections to the basic Hartree-Fock model. As of this writing, there are many correlation methods available in Gaussian, including the following ... 

Hartree-Fock theory is very useful for providing initial, first-level predictions for many systems. It is also reasonably good at computing the structures and vibrational frequencies of stable molecules and some transition states. As such, it is a good base-level theory. However, its neglect of electron correlation makes it unsuitable for some purposes. For example, it is insufficient for accurate modeling of the energetics of reactions and bond dissociation. 

All of the model chemistries predict acetaldehyde to the lower energy isomer. The methods including electron correlation all produce good estimates of the isomerization energy. However, it turns out that the MP2 value is fortuitously good increasing the basis set size would produce a poorer result at the MP2 level. For the... 

J. B. Foresman, T. A. Keith, K. B. Wiberg, J. Snoonian and M. J. Frisch, Solvent Effects. 5. The Influence of Cavity Shape, Truncation of Electrostatics, and Electron Correlation on Ab Initio Reaction Field Calculations, J. Phys. Chem., submitted (1996). [Discusses the IPCM SCRF model.]... 

Density functional theory-based methods ultimately derive from quantum mechanics research from the 1920 s, especially the Thomas-Fermi-Dirac model, and from Slater s fundamental work in quantum chemistry in the 1950 s. The DFT approach is based upon a strategy of modeling electron correlation via general functionals of the electron density. 

Chapter 6, Selecting an Appropriate Theoretical Method, discusses the model chemistry concept introduced in Chapter 1 in detail. It covers the strengths, computational cost and limitations of a variety of popular methods, beginning with semi-empirical models and continuing through Hartree-Fock, Density Functional Theory, and electron correlation methods. 

The remarkable thing is that the HF model is so reliable for the calculation of very many molecular properties, as 1 will discuss in Chapters 16 and 17. But for many simple applications, a more advanced treatment of electron correlation is essential and in any case there are very many examples of spectroscopic states that caimot be represented as a single Slater determinant (and so cannot be treated using the standard HF model). In addition, the HF model can only treat the lowest-energy state of any given symmetry. 

Theoretical Models Incorporating Electron Correlation John A. Pople, J. Stephen Binkley and Rolf Seeger International Journal of Quantum Theory, Symp. No. 10 (1976) 1... 

Some methods of describing electron correlation are compared from the point of view of requirements for theoretical chemical models. The perturbation approach originally introduced by Mpller and Plesset, terminated at finite order, is found to satisfy most of these requirements. It is size consistent, that is applicable to an ensemble of isolated systems in an additive manner. On the other hand, it does not provide an upper bound for the electronic energy. ... 

---