Potential energy surface size-consistency

Equation to a general computational scheme. A theoretical models needs to be unique and well defined and, to the maximum extent possible, be unbiased by preconceived ideas. It should lead to Potential Energy Surfaces which are continuous. It is also desirable (but not required) that a theoretical model be Size Consistent and... 

The total difference in zero-point vibrational energies of the FH--FD and FD—FH complexes, displayed in the last row of Table 2.51, is 85 cm" at the SCF level, and 94 cm" at MP2. It is interesting that this difference is relatively insensitive to correlation. The size of the basis set is not crucial either, as earlier calculations with a smaller basis set " had obtained a value of 109 cm" . While the potential energy surface of the dimer can perhaps be calculated reasonably well, the biggest source of error in this analysis is the assumption of harmonic frequencies. Analysis of high resolution near-IR data for the Cl analogue is consistent with a stronger D-bond here as well C1D--C1H is more stable than C1H--C1D by 16 4 cm" . 

Size-extensivity can be seen to be of particular importance when a consistent description is needed over a large portion of a correlated potential energy surface. 

Here is the difference between the MRCI energy and the energy obtained with the reference CSFs, and Cj, is the coefficient of reference CSF R in the MRCI wave function. We shall use the notation i -I- Q) to denote the use of the corrections given by Eq. (7) or (8). A problem with such approximations is that as there are no useful bounds on the adjusted energy expression, some numerical noise can be introduced across a large set of calculations (say, for a potential energy surface), while the MRCI values themselves would be much smoother. " (This noise can also be a problem with those MRCI methods that apply selection to all CSFs used, rather than just reference CSFs.) A more sophisticated approach to the size-consistency problem is to... 

Among several types of the MCSCF method, the complete active space self-consistent field (CASSCF) method is commonly used at present. In fact, it has many attractive features (1) applicable to excited state as well as the ground state in a single framework (2) size-consistent (3) well defined on the whole potential energy surface if an appropriate active space is selected. However, CASSCF takes into account only nondynamic electron correlation and not dynamic correlation. The accuracy in the energy such as excitation energy and dissociation energy does not reach the chemical accuracy, that is, within several kcal/mol. A method is necessary which takes into account both the non-dynamic and dynamic correlations for quantitative description. 

Because of slow convergence, lack of size consistency, and disappointing results of CISD calculations. Cl calculations have lost their former dominance in correlation calculations, and several other correlation methods have been developed (Sections 15.18-15.20). However, multireference Cl calculations (MRCI) are widely used to explore potential-energy surfaces— for example in studying chemical reactions (Section 15.26). 

Now the expression (19) is an uncoupled formulation of the polarizability. We can replace it by a polarizability derived from coupled Hartree-Fock perturbation theory, which is more accurate, because it takes account of the reorganisation of the electron distribution in a self-consistent manner. Better still would be to evaluate the monomer polarizability by a method that takes account of electron correlation as well . But whatever the level of calculation, we can once again perform a much better calculation of the monomer property than is possible for the dimer. In this way we arrive at a description of the induction energy that is far more accurate than we can obtain through either intermolecular perturbation theory, where the perturbation is treated in an uncoupled fashion, or from a supermolecule calculation, where the size of the basis is limited by the need to perform calculations at a large number of points on the potential energy surface. 

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