Correlation dynamical

Radiation probes such as neutrons, x-rays and visible light are used to see the structure of physical systems tlirough elastic scattering experunents. Inelastic scattering experiments measure both the structural and dynamical correlations that exist in a physical system. For a system which is in thennodynamic equilibrium, the molecular dynamics create spatio-temporal correlations which are the manifestation of themial fluctuations around the equilibrium state. For a condensed phase system, dynamical correlations are intimately linked to its structure. For systems in equilibrium, linear response tiieory is an appropriate framework to use to inquire on the spatio-temporal correlations resulting from thennodynamic fluctuations. Appropriate response and correlation functions emerge naturally in this framework, and the role of theory is to understand these correlation fiinctions from first principles. This is the subject of section A3.3.2. 

For these reasons, in the MCSCF method the number of CSFs is usually kept to a small to moderate number (e.g. a few to several thousand) chosen to describe essential correlations (i.e. configuration crossings, near degeneracies, proper dissociation, etc, all of which are often tenned non-dynamicaI correlations) and important dynamical correlations (those electron-pair correlations of angular, radial, left-right, etc nature that are important when low-lying virtual orbitals are present). 

As larger atomic basis sets are employed, the size of the CSF list used to treat a dynamic correlation increases rapidly. For example, many of the above methods use singly- and doubly-excited CSFs for this purpose. For large basis sets, the number of such CSFs (N ) scales as the number of electrons squared uptimes the number... 

There are two types of electron correlations static and dynamic. Static correlation refers to a near degeneracy of a given state a dynamic correlation refers to the in stantaneous avoidance of electrons with each other. 

BD. Dynamical correlations in suspensions of charged rod-like particles were simulated [121]. 

RHF to UHF, or to a TCSCF, is almost pure static correlation. Increasing the number of configurations in an MCSCF will recover more and more of the dynamical correlation, until at the full Cl limit, the correlation treatment is exact. As mentioned above, MCSCF methods are mainly used for generating a qualitatively correct wave function, i.e. recovering the static part of the correlation. 

The structure on the left is biradical, while the two others are ionic, corresponding to both electrons being at the same carbon. The simplest CASSCF wave function which qualitatively can describe this system has two electrons in two orbitals, giving the three configurations shown above. The dynamical correlation between die two active electrons will tend to keep them as far apart as possible, i.e. favouring the biradical structure. Now... 

A more balanced description requires MCSCF based methods where the orbitals are optimized for each particular state, or optimized for a suitable average of the desired states (state averaged MCSCF). It should be noted that such excited state MCSCF solutions correspond to saddle points in the parameter space for the wave function, and second-order optimization techniques are therefore almost mandatory. In order to obtain accurate excitation energies it is normally necessarily to also include dynamical Correlation, for example by using the CASPT2 method. 

Hochhaus G, Barrett JS, Derendorf H. Evolution of pharmacokinetics and phar-macokinetic/dynamic correlations during the 20th century. J Clin Pharmacol. 2000 Sep 40(9) 908-17. 

Obviously, this cannot be dynamical correlation because at rHH — °o we have two independent hydrogen atoms with only one electron at each center and no electron-electron interaction whatsoever (because l/rHH —> 0). To understand this wrong dissociation behavior... 

Becke, A. D., 1996a, Density-Functional Thermochemistry. IV. A New Dynamical Correlation Functional and Implications for Exact-Exchange Mixing , J. Chem. Phys., 104, 1040. 

The electronic structure method used to provide the energies and gradients of the states is crucial in photochemistry and photophysics. Ab initio electronic structure methods have been used for many years. Treating closed shell systems in their ground state is a problem that, in many cases, can now be solved routinely by chemists using standardized methods and computer packages. In order to obtain quantitative results, electron correlation (also referred to as dynamical correlation) should be included in the model and there are many methods available for doing this based on either variational or perturbation principles [41],... 

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