Post-SCF calculations

DISP Dispersion energy. An interaction resembling London forces, present only in post-SCF calculations. 

The efforts to extend the direct SCF methodology to post-SCF calculations began with the paper by Taylor.Soon afterward, practical implementations of the direct MP2 method were published, almost simultaneously, by Pople s and Almlof s groups. The latter report also considered the direct MP3 method and presented an example of an MP2 calculation with 318 basis functions. The direct post-SCF methods are discussed later in this review. 

Results from self-consistent field (SCF) molecular orbital calculations, in combination with gas-phase photoelectron data and results from post-SCF calculations have provided a basis for descriptions of the valence electronic structure of gas-phase nucleotides and of nucleotides in water-counterion clusters. These descriptions contain values for 11 to 14 of the lowest energy ionization events in the DNA nucleotides 5 -dGMP , 5 -dAMP, 5 -dCMP and 5 -dTMP . When used with an evaluation of the difference between the Gibbs free energies of hydration for the initial and final states associated with ionization, this approach also describes the influence of hydration on the energetic ordering of ionization events in nucleotides. 

When described at the ab initio SCF level with a split-valence basis set the valence orbital electronic structure of 5 -dTMP" is localized like those of the previously examined nucleotides 5 -dCMP , 5 -dAMP and 5 -dGMP. This localized orbital structure of nucleotides makes it possible to employ PE data and results from post-SCF calculations on model anions to correct nucleotide valence IPs obtained from SCF... 

The HE, GVB, local MP2, and DFT methods are available, as well as local, gradient-corrected, and hybrid density functionals. The GVB-RCI (restricted configuration interaction) method is available to give correlation and correct bond dissociation with a minimum amount of CPU time. There is also a GVB-DFT calculation available, which is a GVB-SCF calculation with a post-SCF DFT calculation. In addition, GVB-MP2 calculations are possible. Geometry optimizations can be performed with constraints. Both quasi-Newton and QST transition structure finding algorithms are available, as well as the SCRF solvation method. 

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). 

Calculations for rutile and anatase were performed using both LDA level of DFT and the gradient corrected form of the exchange-correlation potential (GGA). The GGA approach is implemented self-consistently as described in 18 and not as a post-SCF correction. 

The cc correlation energy is determined by the single and double amplitudes and the two-electron MO integrals. However, the recent progress in computational methods is largely influenced by DFT. One primary advantage of DFT over conventional HF-SCF procedures is that the former includes electron correlation fairly adequately (some times too much) at a fractional cost compared to a typical post-SCF (Cl, MBPT, or CC) calculation. 

Density-Functional Theory. Transition metals pose a problem for classical quantum chemical methods like self-consistent field (SCF), perturbation theory, configuration interaction (Cl), and variations on these methods, because of the very large electron correlation. SCF underestimates binding substantially, and post-SCF methods are so expensive for transition metals that one can do a calculation only on models with few atoms. DFT on the other hand is relatively cheap it is about as expensive as SCF. Moreover, with the development of the generalized-gradient approximations it is also reasonably accurate. A large majority of quantum chemical... 

Quantum mechanics (QM) can be further divided into ab initio and semiempiri-cal methods. The ab initio approach uses the Schrodinger equation as the starting point with post-perturbation calculation to solve electron correlation. Various approximations are made that the wave function can be described by some functional form. The functions used most often are a linear combination of Slater-type orbitals (STO), exp (-ax), or Gaussian-type orbitals (GTO), exp (-ax2). In general, ab initio calculations are iterative procedures based on self-consistent field (SCF) methods. Self-consistency is achieved by a procedure in which a set of orbitals is assumed and the electron-electron repulsion is calculated. This energy is then used to calculate a new set of orbitals, and these in turn are used to calculate a new repulsion energy. The process is continued until convergence occurs and self-consistency is achieved. 

All the calculations have been made with the Gaussian 94 [5] or the Gaussian 98 [6] program. Molecular structures for all molecules studied here have been calculated by geometry optimization within the procedures of the restricted Hartree-Fock method (HF) but good agreement with experimental structures is obtained only accidentally with HF when using small basis sets, so that Post-SCF... 

Tsipis [73] gives extensive tabulations of M-L bond energies. The vast majority of post-HF calculations are restricted to simple ML or ML2 systems where L is monatomic (H, O or halide) or a small ligand such as CO, CH3, NH3, PH3 or C2H4. These molecules are small enough to facilitate the necessary correlation treatment. Multi Reference Cl and Complete Active Space SCF are the most popular correlated methods and appear capable of good accuracy (i.e. to within 5-10 kcal/mole). 

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