Modelling chemistry

Frisch M J, G W Trucks and J R Cheeseman 1996. Systematic Model Chemistries Based on Density Functional Theory Comparison with Traditional Models and with Experiment. Theoretical and Computational Chemistry (Recent Developments and Applications of Modem Density Functional Theory) 4 679-707. 

The implementation of such a theoretical model is termed a theoretical-model chemistry, or simply a model chemistry. 

Other desirable features of a model chemistry include ... 

Gaussian includes many different model chemistries. The theoretical model chemistries in Gaussian have been subjected to the testing procedure described previously and so may be recommended for general use with any system for which they are computationally feasible. 

Model chemistries are characterized by the combination of theoretical procedure and basis set. Every calculation performed with Gaussian must specify the desired theoretical model chemistry in addition to specifying the molecular system to consider and which results to compute for it. 

Although not strictly part of a model chemistry, there is a third component to every Gaussian calculation involving how electron spin is handled whether it is performed using an open shell model or a closed shell model the two options are also referred to as unrestricted and restricted calculations, respectively. For closed shell molecules, having an even number of electrons divided into pairs of opposite spin, a spin restricted model is the default. In other words, closed shell calculations use doubly occupied orbitals, each containing two electrons of opposite spin. 

Traditional electronic structure energy calculations consist of a single job. However, a calculation at a very accurate level of theory can take a very long time to complete. In an effort to achieve high accuracy results at less computational cost, several new model chemistries have been defined as a series of calculations to be run and a... 

Shielding constants reported in experimental studies are usually shifts relative to a standard compound, often tetramethylsilane (TMS). In order to compare predicted values to experimental results, we also need to compute the absolute shielding value for TMS, using exactly the same model chemistry. Here is the relevant output for TMS ... 

The structures are quite similar for all of the model chemistries we are considering. The second isomer is characterized by a very long bridging carbon distance, indicating that the two carbons are no longer bonded (which is why we refer to it as the open form). 

A better theoretical model is required to adequately study this problem (although this is fairly unlikely as the HF/3-21G model chemistry generally performs well on systems of this type). 

This hypothetical sequence of jobs should give you a sense of how a real study might proceed. We ll begin this part of the book by looking at each of the components of a model chemistry in more detail. 

In the first chapter, we described a model chemistry as an unbiased, uniquely defined, and uniformly applicable theoretical model for predicting the properties of chemical systems. A model chemistry generally consists of the combination of a theoretical method with a basis set. Each such unique pairing of method with basis set represents... 

The chart below lists various model chemistries definable via traditional ab iniiin methods and standard basis sets ... 

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... 

Chapter 6 (page 122) the relative accuracies of various model chemistries is discussed in Chapter 7 (page 146). See Appendix A for a discussion of the approximation techniques used by the various methods. 

Choosing a model chemistry almost always involves a trade-off between accuracy and computational cost. More accurate methods and larger basis sets make jobs run longer. We ll provide some specific examples of these effects throughout the chapters in this part of the book. 

We will designate model chemistries using this naming convention (which we have already used in earlier chapters without comment) ... 

The following table summarizes some recommended research-level model chemistries for predicting total energies for molecular systems of various sizes (the details of the reasons behind these choices will unfold along with the chapters in this part of the book), arranged in order of increasing computational cost ... 

Model Chemistry Range of MAD /Max. Error Applicability on G2 Molecule Set [ heavy atoms] Relative Cost... 

Zero-point and thermal energy corrections are usually computed with the same model chemistry as the geometry optimization. However, you may also choose to follow the common practice of always using the HF/6-31G(d) model chemistry for predicting zero-point and thermal energies (see page 149). Of course, such frequency calculations must follow a HF/6-31G(d) geometry optimization. 

All of the geometries predicted with the 6-31IG basis set are quite accurate. Adding two sets of diffuse functions yields a more accurate structure. However, adding additional polarization functions does not significantly affect the results. 6-311++G(d,p) thus appears to achieve the basis set limit for this model chemistry. ... 

With these results, we see an example of a phenomenon that occurs from time to time a less accurate model chemistry will produce a better answer than more accurate ones. In our case, fortuitous cancellation of errors at the HF/STO-3G levels leads to the correct identification of the planar conformation as a transition state. However, a more accurate model chemistry is needed to properly study this system. ... 

Run a single-point energy calculation on methanol using the HF/6-31++G(d,p) model chemistry, including the GFPrint and GFinput keywords in the route section which request that the basis set information be included in the output file (in tabular and input format, respectively). Examine the basis set output and identify its main components. 

The 6-3 IGt basis set is defined as part of the Complete Basis Set model chemistry (described in detail in Chapter 7). This basis set attempts to remedy some deficiencies in the standard 6-31 G(d) basis set. 

In this chapter, we will consider the other half of a model chemistry definition the theoretical method used to model the molecular system. This chapter will serve as an introductory survey of the major classes of electronic structure calculations. The examples and exercises will compare the strengths and weaknesses of various specific methods in more detail. The final section of the chapter considers the CPU, memory and disk resource requirements of the various methods. 

We will complete our consideration of model chemistries in Chapter 7, which describes compound methods for computing very accurate energies. It also includes a section discussing the relative accuracies of various model chemistries, as measured by their performance on the G2 set of test computations (see page 146). 

Compute the isomerization energy between two forms of C4Hjq iso-butane and n-butane using AMI, PM3 and HF/6-31G(d). How does each model chemistry compare with the observed energy difference (iso-butane minus n-butane) of -1.64 kcal-moT ... 

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