Post Hartree-Fock

HyperChein perforins ab initio. SCK calculations generally. It also can calculate the coi relation energy (to he added to the total -SCK energy) hy a post Hartree-Fock procedure call. M P2 that does a Moller-Plesset secon d-order perturbation calculation. I he Ml 2 procedure is on ly available for sin gle poin t calculation s an d on ly produces a single tiuin ber, th e Ml 2 correlation energy, to be added to the total SCF en ergy at th at sin gle poin t con figuration of th e ti iiclei. 

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. 

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). 

DFT and post-Hartree-Fock ab initio studies on the different tautomers and rotamers of 2-hydroxy- (94) and 2,3-dihydroxypyrazine (95) indicate that the former species is stabilized by about -3 kcal/mol with respect to its keto tautomer in the gas phase [99JST229]. In solution the opposite appears to be true. For 95, the hydroxyoxo 95b and diketo tautomers 95c are most stable in the gas phase (Scheme 61). 

Trioxane 210 has been used as a model system by Gu and coworkers to study the antimalarial drug artemisinin 211 (Scheme 137) [97CPL234, 99JST103]. It is the boat/twist form rather than the chair conformer of 210 that describes the subunit in 211. Moreover, geometric parameters and vibrational frequencies can only reliably be computed at the DFT level and by post-Hartree-Fock methods. B3-LYP/6-31G calculations on the conformers of 3,3,6,6-tetramethyl-1,2,4,5-tetroxane show that the chair conformer is stabilized with respect to the twisted conformer by about -2.8 kcal/mol [00JST85]. No corresponding boat conformer was found. 

One of the simplest chemical reactions involving a barrier, H2 + H —> [H—H—H] —> II + H2, has been investigated in some detail in a number of publications. The theoretical description of this hydrogen abstraction sequence turns out to be quite involved for post-Hartree-Fock methods and is anything but a trivial task for density functional theory approaches. Table 13-7 shows results reported by Johnson et al., 1994, and Csonka and Johnson, 1998, for computed classical barrier heights (without consideration of zero-point vibrational corrections or tunneling effects) obtained with various methods. The CCSD(T) result of 9.9 kcal/mol is probably very accurate and serves as a reference (the experimental barrier, which of course includes zero-point energy contributions, amounts to 9.7 kcal/mol). 

Barone, V., Adamo, C., 1996, Proton Transfer in the Ground and Lowest Excited States of Malonaldehyde A Comparative Density Functional and Post-Hartree-Fock Study , J. Chem. Phys., 105, 11007. 

Bartlett, R. J., Stanton, J. F., 1995, Applications of Post-Hartree-Fock Methods A Tutorial , Rev. Comput. Chem., 5, 65. 

Kesyczynski, J. Goodman, L., Kwiatkowski, J. S., 1997, Density Functional Theory and Post-Hartree-Fock Studies on Molecular Structure and Harmonic Vibrational Spectrum of Formaldehyde , Theor. Chem. Acc., 97, 195. 

Sodupe, M., Bertran, J., Rodriguez-Santiago, L., Baerends, E. J., 1999, Ground State of the (H20)2 Radical Cation DFT versus Post-Hartree-Fock Methods , J. Phys. Chem. A, 103, 166. 

Bartlett RJ, Stanton JF (1994) Applications of post-hartree-fock methods a tutorial. In Lipkowitz KB Boyd DB (eds) Reviews in computational chemistry, vol. 5. Wiley-VCH, New York, pp 65—169... 

How does a rigorously calculated electrostatic potential depend upon the computational level at which was obtained p(r) Most ab initio calculations of V(r) for reasonably sized molecules are based on self-consistent field (SCF) or near Hartree-Fock wavefunctions and therefore do not reflect electron correlation in the computation of p(r). It is true that the availability of supercomputers and high-powered work stations has made post-Hartree-Fock calculations of V(r) (which include electron correlation) a realistic possibility even for molecules with 5 to 10 first-row atoms however, there is reason to believe that such computational levels are usually not necessary and not warranted. The Mpller-Plesset theorem states that properties computed from Hartree-Fock wave functions using one-electron operators, as is T(r), are correct through first order (Mpller and Plesset 1934) any errors are no more than second-order effects. 

It has been shown that the electrostatic potentials of formamide calculated at near-Hartree-Fock (HF/6-31G ) and post-Hartree-Fock (MP2/6-31G ) levels are qualitatively similar (Politzer and Murray 1991). Both computational approaches predict the oxygen to be the preferred site for electrophilic attack (Seminario, Murray, and Politzer 1991). It is further noteworthy that SCF results obtained with minimal basis sets (e.g., HF/STO-3G and HF/STO-5G) are also in good agreement with those calculated at the higher computational levels. 

Suhai128 investigated water dimer and an infinite chain of hydrogen-bonded water molecules by means of the DFT and post-Hartree-Fock calculations. For the infinite system, the DFT(BLYP), MP2, and MP4 binding energies were within 0.2 kcal/mol, whereas the corresponding interatomic distances were within 0.04 A. A similar agreement was reported for water dimer. 

The SCRF approach became a standard tool167 for estimating solvent effects and was combined with various quantum chemical methods that range from semi-empirical161 to the post-Hartree-Fock ab initio ones. It can also be combined with the Kohn-Sham formalism where the Kohn-Sham Hamiltonian (Eq. 4.2) is used for the gas-phase Hamiltonian in Eq. 4.15. The effective Kohn-Sham Hamiltonian for the system embedded in the dielectric environment takes the following form ... 

Schmiedenkamp, A. M., I. A. Topol, S. K. Burt, H. Razafinjanahary, H. Chermette, T. Pfatzgraff, and C. J. Michejda. 1994. Triazene Proton Affinities A comparison between Density Functional, Hartree-Fock, and Post-Hartree-Fock Methods. J. Comp. Chem. 875, 875. 

Kieninger, M., and S. Suhai. 1996. Conformational and Energetic Properties of the Ammonia Dimer-Comparison of Post-Hartree-Fock and Density Functional Methods. J. Comp. Chem. 17, 1508. 

Barone, V. and C. Adamo. 1994. Theoretical study of direct and water-assisted isomerization of formaldehyde radical cation. A comparison between density functional and post-Hartree-Fock approaches. Chem. Phys. Lett. 224, 432. 

---