Dynamical electron correlation nondynamical

Two different correlation effects can be distinguished. The first one, called dynamical electron correlation, comes from the fact that in the Hartree-Fock approximation the instantaneous electron repulsion is not taken into account. The nondynamical electron correlation arises when several electron configurations are nearly degenerate and are strongly mixed in the wave function. 

It is possible to divide electron correlation as dynamic and nondynamic correlations. Dynamic correlation is associated with instant correlation between electrons occupying the same spatial orbitals and the nondynamic correlation is associated with the electrons avoiding each other by occupying different spatial orbitals. Thus, the ground state electronic wave function cannot be described with a single Slater determinant (Figure 3.3) and multiconfiguration self-consistent field (MCSCF) procedures are necessary to include dynamic electron correlation. 

The simplest ab initio approach which can be used for the characterization of excited states is the configuration interaction with single excitations from the HF reference (CIS) [21]. The CIS method can be considered as the equivalent of the ground-state HF method for excited states. It does not account for so-called nondynamical electron correlation effects associated with the near degeneracy of electronic configurations, nor does it account for so-called dynamical electron correlation effects. The CIS method is computationally cheap and robust and can easily be applied to relatively large systems. 

Despite an effective treatment of nondynamical electron correlation, MCSCF calculations carried out in feasible active spaces7 do not produce quantitatively reliable results. The reason for this is the neglect of dynamical electron correlation involving the inactive occupied and virtual orbitals. Qualitatively,... 

As indicated, MC methods extend the application of HF theory to problems with strong nondynamic electron correlation. Therefore, the MC methods represent a separate class of correlation corrected methods, actually closer to HF than dynamic electron correlation methods. 

The theoretical study of accurate potential energy surfaces (PESs) has seen some essential progress in the last decade. Much of this progress can be attributed, at least in broad terms, to advancements in the ability to include nondynamical electron correlation equitably with dynamical electron correlation. Perhaps this point can be underscored by noting the tremendous response of the greater chemistry community to the CASPT2 (I) functionality in the widely... 

In situations in which physically well-motivated MR-CISD calculations are not computationally feasible, the need for adequate approximations of nondynamical and dynamical electron correlation must be balanced. One useful way of categorizing alternatives to MR-CISD is to focus on the sequence of treating nondynamical and dynamical correlation. One could address dynamical correlation for all, or part, of the model space first and, then, proceed to address the nondynamical correlation. This approach gives rise to an effective... 

Multiple PESs may be of simultaneous interest based not only on physical reasons, as emphasized in the previous paragraph, but also for mathematical or computational reasons. Consider the basic paradigm of state-selective methods the nondynamical electron correlation for a specific state is calculated within a model space and then the dynamical electron correlation is calculated. The implicit assumption is that the zero-order model space many-electron basis functions (MEBFs) (e.g., MCSCF functions and MCSCF complementary space... 

The major advantage of a 1-RDM formulation is that the kinetic energy is explicitly defined and does not require the construction of a functional. The unknown functional in a D-based theory only needs to incorporate electron correlation. It does not rely on the concept of a fictitious noninteracting system. Consequently, the scheme is not expected to suffer from the above mentioned limitations of KS methods. In fact, the correlation energy in 1-RDM theory scales homogeneously in contrast to the scaling properties of the correlation term in DPT [14]. Moreover, the 1-RDM completely determines the natural orbitals (NOs) and their occupation numbers (ONs). Accordingly, the functional incorporates fractional ONs in a natural way, which should provide a correct description of both dynamical and nondynamical correlation. 

J. Paldus and X. Li, Electron Correlation in Small Molecules Grafting Cl onto CC. In P. Surjan (Ed.) Correlation and Localization, Series in Topics in Current Chemistry, Vol. 203. (Springer, Berlin, 1999), pp. 1-20 X. Li and J. Paldus, Simultaneous Account of Dynamic and Nondynamic Correia,tions Based on Complementarity of Cl and CC Approaches. In M. R. Hoffmann and K. G. Dyall (Eds.) Low-Lying Potential Energy Surfaces, ACS Symposium Series No. 828 (ACS Books, Washington, 2002), pp. 10-30. 

Electron correlation plays a role in electrical response properties and where nondynamical correlation is important for the potential surface, it is likely to be important for electrical properties. It is also the case that correlation tends to be more important for higher-order derivatives. However, a deficient basis can exaggerate the correlation effect. For small, fight molecules that are covalently bonded and near their equilibrium structure, correlation tends to have an effect of 1 5% on the first derivative properties (electrical moments) [92] and around 5 15% on the second derivative properties (polarizabilities) [93 99]. A still greater correlation effect is possible, if not typical, for third derivative properties (hyperpolarizabilities). Ionic bonding can exhibit a sizable correlation effect on hyperpolarizabilities. For instance, the dipole hyperpolarizability p of LiH at equilibrium is about half its size with the neglect of correlation effects [100]. For the many cases in which dynamical correlation is not significant, the nondynamical correlation effect on properties is fairly well determined with MP2. For example, in five small covalent molecules chosen as a test set, the mean deviation of a elements obtained with MP2 from those obtained with a coupled cluster level of treatment was 2% [101]. 

For a general discussion of dynamic and nondynamic electron correlation, see, for example (a) DKW Mok, R Neumann, NC Handy. J Phys Chem 100 6225-6230, 1996. (b) MA Buijse, EJ Baerends. In ED EUis, ed. Density Functional Theory of Molecules, Clusters, and Solids. Dordrecht, The Netherlands Kluwer Academic, 1995, pp 1-46. 

On the Separation of Electron Correlation into Dynamical (D) and Nondynamical (ND)... 

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