Hartree-Fock performance

The application of density functional theory to isolated, organic molecules is still in relative infancy compared with the use of Hartree-Fock methods. There continues to be a steady stream of publications designed to assess the performance of the various approaches to DFT. As we have discussed there is a plethora of ways in which density functional theory can be implemented with different functional forms for the basis set (Gaussians, Slater type orbitals, or numerical), different expressions for the exchange and correlation contributions within the local density approximation, different expressions for the gradient corrections and different ways to solve the Kohn-Sham equations to achieve self-consistency. This contrasts with the situation for Hartree-Fock calculations, wlrich mostly use one of a series of tried and tested Gaussian basis sets and where there is a substantial body of literature to help choose the most appropriate method for incorporating post-Hartree-Fock methods, should that be desired. 

There are also ways to perform relativistic calculations explicitly. Many of these methods are plagued by numerical inconsistencies, which make them applicable only to a select set of chemical systems. At the expense of time-consuming numerical integrations, it is possible to do four component calculations. These calculations take about 100 times as much CPU time as nonrelativistic Hartree-Fock calculations. Such calculations are fairly rare in the literature. 

Ab initio calculations can be performed at the Hartree-Fock level of approximation, equivalent to a self-consistent-field (SCF) calculation, or at a post Hartree-Fock level which includes the effects of correlation — defined to be everything that the Hartree-Fock level of approximation leaves out of a non-relativistic solution to the Schrodinger equation (within the clamped-nuclei Born-Oppenhe-imer approximation). 

Single point energy calculations can be performed at any level of theory and with small or large basis sets. The ones we ll do in this chapter will be at the Hartree-Fock level with medium-sized basis sets, but keep in mind that high accuracy energy computations are set up and interpreted in very much the same way. 

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. ... 

In order to do so, you will need to perform Hartree-Fock NMR calculations using the 6-311+G(2d,p) basis set. Compute the NMR properties at geometries optimized with the B3LYP method and the 6-31G(d) basis set. This is a recommended model for reliable NMR predictions by Cheeseman and coworkers. Note that NMR calculations typically benefit from an accurate geometry and a large basis set. 

Perform a low-level geometry optimization with a medium-sized basis set, for example, a Hartree-Fock or B3LYP Density Functional Theory calculation with the 6-31G(d) basis set. (For very large systems, a smaller basis set might be necessary.)... 

The first cell in the last tow of the table represents the Hartree-Fock limit the best approximation that can be achieved without taking electron correlation into account. Its location on the chart is rather far from the exact solution. Although in some cases, quite good results can be achieved with Hartree-Fock theory alone, in many others, its performance ranges from orfly fair to quite poor. We ll look at some these cases in Chapters 5 and 6. 

Optimize the structure of acetyl radical using the 6-31G(d) basis set at the HF, MP2, B3LYP and QCISD levels of theory. We chose to perform an Opt Freq calculation at the Flartree-Fock level in order to produce initial force constants for the later optimizations (retrieved from the checkpoint file via OptsReadFC). Compare the predicted spin polarizations (listed as part of the population analysis output) for the carbon and oxygen atoms for the various methods to one another and to the experimental values of 0.7 for the C2 carbon atom and 0.2 for the oxygen atom. Note that for the MP2 and QCISD calculations you will need to include the keyword Density=Current in the job s route section, which specifies that the population analysis be performed using the electron density computed by the current theoretical method (the default is to use the Hartree-Fock density). 

CBS models typically include a Hartree-Fock calculation with a very large basis set, an MP2 calculation with a medium-sized basis set (and this is also the level where the CBS extrapolation is performed), and one or more higher-level calculations with a medium-to-modest basis set. The following table outlines the components of the CBS-4 and CBS-Q model chemistries ... 

In order to save computation time, set up the second and subsequent jobs to extract the electron density from the checkpoint file by using the Geom=Checlcpoint and Densiiy=(Checkpoint/AP2) keywords in the route section. You will also need to include Den iiy=MP2 for the first job, which specifies that the population analysis should be performed using the electron density computed at the MP2 level (the default is to use the Hartree-Fock density). 

AMI benefits from the same cancellation of errors for the first reaaion as Hartree-Fock theory. However, it performs even more poorly for the other two reactions. ... 

Both the MP2 Onsager calculation and the IPCM calculaton are in good agreement with experiment. The SCI-PCM and Hartree-Fock Onsager SCRF calculations perform significantly less well for this problem. ... 

In actual practice, self-consistent Kohn-Sham DFT calculations are performed in an iterative manner that is analogous to an SCF computation. This simiBarity to the methodology of Hartree-Fock theory was pointed out by Kohn and Sham. 

Ab initio Hartree-Fock and density functional theory calculations were performed to study the transition state geometry in intramolecular Diels-Alder cycloaddition of azoalkenes 55 to give 2-substituted 3,4,4u,5,6,7-hexahydro-8//-pyrido[l,2-ft]pyridazin-8-ones 56 (01MI7). 

The answer to this question as well as the question of the precise meaning of the term ab initio itself in the context of quantum chemistry seems to differ considerably according to the particular researcher that one might consult.3 Some authors I have questioned claim that the two terms are used interchangeably to mean calculations performed without recourse to any experimental measurement. This would include Hartree-Fock, and many of the DFT functionals, along with quantum Monte Carlo and Cl methods. 

One Important aspect of the supercomputer revolution that must be emphasized Is the hope that not only will It allow bigger calculations by existing methods, but also that It will actually stimulate the development of new approaches. A recent example of work along these lines Involves the solution of the Hartree-Fock equations by numerical Integration In momentum space rather than by expansion In a basis set In coordinate space (2.). Such calculations require too many fioatlng point operations and too much memory to be performed In a reasonable way on minicomputers, but once they are begun on supercomputers they open up several new lines of thinking. 

All the eleetronie calculations were performed with the GAUSSIAN/90 [18] and GAUSSIAN/92 [19] eodes and the vibrational studies by the DiNa package [16]. Eleetronie wave funetions were generated by the Unrestrieted Hartree-Fock (UHF) formalism,... 

All three states were described by a single set of SCF molecular orbitals based on the occupied canonical orbitals of the X Z- state and a transformation of the canonical virtual space known as "K-orbitals" [10] which, among other properties, approximate the set of natural orbitals. Transition moments within orthogonal basis functions are easier to derive. For the X state the composition of the reference space was obtained by performing two Hartree-Fock single and double excitations (HFSD-CI) calculations at two typical intemuclear distances, i.e. R. (equilibrium geometry) and about 3Re,and adding to the HF... 

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