Hartree-Fock level

On the basis of their data, Szalewicz et al. estimate that the SCF interaction energy for the water dimer is -3.73 + 0.05 kcal/mol. The reader is again reminded that this represents a frozen-molecule estimate. The binding energy is likely to increase a small amount if this restriction is removed, primarily due to stretching of the bridging O —H bond. 

Szalewicz et al. point out that is the leading term in the correlated 

This same quantity was calculated also using a coupled-cluster method, which includes single and double excitations, and a triple-excitation correction, the so-called CCSD-T technique. The results were found to be quire similar to the MP4 values for each basis set examined. The authors suggest that because of the small contributions from infinite summations, SDTQ-MBPT(4) is much more cost effective than is CCSD-T. 

The best estimate obtained for the correlation contribution to the interaction energy with the many-body approach, the counterpoise-corrected result with the largest basis set (150 functions), is - 0.70 kcal/mol. This value required 9 hr of Cray X-MP time to compute even so, it recovers only some 70% of the total correlation effect. Smaller sets yield only half the true value. In summary, the authors were pessimistic about the ability of computing very accurate correlation contributions, especially for systems larger than the water dimer. 

Comparison of the first and second columns of data does indeed verify the close correspondence between second-order MP correlation and full cumulative terms up through fourth-order. The exceptions again are the minimal basis sets. As the basis sets are improved, the third and fourth-order terms tend to shrink in magnitude. 

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Ah initio calculation s can be performetl at th e Ilartree-Fock level of approximation, equivalent to a self-con sisten t-field (SCK) calculation. or at a post llartree-Fock level which includes the effects of correlation —defined to be everything that the Hartree-Fock level of appi oxiniation leaves out of a n on-relativistic solution to the Schrddinger ec nation (within the clamped-nuclei Born-Oppenh e-imer approximation ). 

Having the Slater atomic orbitals, the linear combination approximation to molecular orbitals, and the SCF method as applied to the Fock matrix, we are in a position to calculate properties of atoms and molecules ab initio, at the Hartree-Fock level of accuracy. Before doing that, however, we shall continue in the spirit of semiempirical calculations by postponing the ab initio method to Chapter 10 and invoking a rather sophisticated set of approximations and empirical substitutions... 

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. 

Here we give the molecule specification in Cartesian coordinates. The route section specifies a single point energy calculation at the Hartree-Fock level, using the 6-31G(d) basis set. We ve specified a restricted Hartree-Fock calculation (via the R prepended to the HF procedure keyword) because this is a closed shell system. We ve also requested that information about the molecular orbitals be included in the output with Pop=Reg. 

The total energy of the system, computed at the Hartree-Fock level, is given by this line of the output ... 

We win run this job on methane at the Hartree-Fock level using the 6-31G(d) basis our molecule specification is the result of a geometry optimization using the B3LYP Density Functional Theory method with the same basis set. This combination is cited... 

FuUerene compounds have receieved a lot of attention in recent years. In this exercise we predict the energy of Cgg and look at its highest occupied molecular orbital, predicted at the Hartree-Fock level with the 3-21G basi set. Include SCF=1ight in the route section of the job. 

Raw frequency values computed at the Hartree-Fock level contain known systematic errors due to the neglect of electron correlation, resulting in overestimates of about 10%-12%. Therefore, it is usual to scale frequencies predicted at the Hartree-Fock level by an empirical factor of 0.8929. Use of this factor has been demonstrated to produce very good agreement with experiment for a wide range of systems. Our values must be expected to deviate even a bit more from experiment because of our choice of a medium-sized basis set (by around 15% in all). 

Optimize these three molecules at the Hartree-Fock level, using the LANL2DZ basis set, LANL2DZ is a double-zeta basis set containing effective core potential (ECP) representations of electrons near the nuclei for post-third row atoms. Compare the Cr(CO)5 results with those we obtained in Chapter 3. Then compare the structures of the three systems to one another, and characterize the effect of changing the central atom on the overall molecular structure. 

Step 1. Produce an initial equilibrium structure at the Hartree-Fock level using the 6-31G(d) basis set. Verify that it is a minimum with a frequency calculation and predict the zero-point energy (ZPE). This quantity is scaled by 0.8929. 

Run your study at the Hartree-Fock level, using the 6-31+G(d) basis set. Use a step size of 0.2 amu bohr for the IRC calculation (i.e., include IRC=(RCFC, StepSize=20) in the route section). You will also find the ColcFC option helpful in the geometry optimizations. 

A problem with studies on inert gas is that the interactions are so weak. Alkali halides are important commercial compounds because of their role in extractive metallurgy. A deal of effort has gone into corresponding calculations on alkali halides such as LiCl, with a view to understanding the structure and properties of ionic melts. Experience suggests that calculations at the Hartree-Fock level of theory are adequate, provided that a reasonable basis set is chosen. Figure 17.7 shows the variation of the anisotropy and incremental mean pair polarizability as a function of distance. 

Usually, geometries of transition states are significantly more sensitive with respect to method than are stmctures of stable species. Since electron correlation effects are of particular importance for these stmctures, the determination of transition states at the Hartree-Fock level should be avoided. It is recommended to compare the stmctural parameters of transition states obtained from different methods (for instance DFT and MP2) in order not to be misled. 

Pairing properties of 2-hydroxyadenine and 8-oxoadenine with four standard DNA bases were studied at the Hartree-Fock level [99JST59] and adenine-hydrogen peroxide complexes at the MP2 and DFT levels [99JPC(A)4755]. 

Rotational barriers and intramolecular S - - - O interactions were studied for acyliminothiadiazolines at the Hartree-Fock level [98JA3104]. 

Most studies concerning pyrimidines originate from biochemical questions. Since these systems are dominated by hydrogen-bonding and/or dispersion contributions, methods beyond the Hartree-Fock level are mandatory. The success of quantum chemical studies in this field is impressive and many effects could be explained on the basis of these theoretical investigations. 

We have chosen the C20 poly-yne ring as a reasonable representative for a large chain molecule. The bond lengths optimized at the Hartree-Fock level are 1.37 A and 1.20 A, respectively. The same values are found for the experimental bond lengths in 1,3-buta-di-yne CHg-C C-C C-H, indicating that there is very little n conjugation in the system. 

It is apparent that the Hartree-Fock level is characterized by an enormous average deviation from experiment, but standard post-HF methods for including correlation effects such as MP2 and QCISD also err to an extent that renders their results completely useless for this kind of thermochemistry. We should not, however, be overly disturbed by these errors since the use of small basis sets such as 6-31G(d) is a definite no-no for correlated wave function based quantum chemical methods if problems like atomization energies are to be addressed. It suffices to point out the general trend that these methods systematically underestimate the atomization energies due to an incomplete recovery of correlation effects, a... 

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