Correlation problem

Ldwdin P O 1959 Correlation problem in many-eleotron quantum meohanios Adv. Chem. Phys. 2 207-32... 

Cizek J 1966 On the correlation problem in atomic and molecular systems. 

Paldus J, Cizek J and Shavitt I 1972 Correlation problems in atomic and... 

Bartlett R J and Purvis G D 1978 Many-body perturbation theory coupled-pair many-electron theory and the importance of quadruple excitations for the correlation problem int. J. Quantum Chem. 14 561-81... 

Martinez T J and Carter E A 1995 Pseudospectral methods applied to the electron correlation problem Modem Electronic Structure Theory yo 2, ed D R Yarkony (Singapore World Scientific) pp 1132-65... 

Further prerequisites depend on the chemical problem to be solved. Some chemical effects have an undesired influence on the structure descriptor if the experimental data to be processed do not account for them. A typical example is the conformational flexibility of a molecule, which has a profound influence on a 3D descriptor based on Cartesian coordinates. In particular, for the application of structure descriptors with structure-spectrum correlation problems in... 

In principle, this set of equations can be solved for the various constants, a through Q, just as a and b were obtained previously. In practice, however, the actual numerical evaluation involves considerable computation in all but the simplest examples. Computer solution by matrix techniques designed specifically to handle this type of data correlation problem is usually required. 

Krug et al. have shown that a plot of AG against AH [see Eq. (7-75)] is not subject to the error correlation problem of the AH vs. AS plot provided AG is evaluated at the harmonic mean temperature of the experimental range. (The harmonic mean is the reciprocal of the mean of the reciprocals, i.e., = <1/... 

Any method which goes beyond SCF in attempting to treat this phenomenon properly is known as an electron correlation method (despite the fact that Hartree-Fock theory does include some correlation effects) or a post-SCT method. We will look briefly at two different approaches to the electron correlation problem in this section. 

CORRELATION PROBLEM IN MANY-ELECTRON QUANTUM MECHANICS ... 

An entirely different approach to the correlation problem is taken in the plasma model (Bohm and Pines 1953, Pines 1954, 1955), in which the electrons in a metal are approximated by a free-electron gas moving in a uniform positive background. According to classical discharge theory, such a plasma is characterized by an oscillatory behavior having a frequency... 

Unfortunately, the omission of the hydrogen-like continuum has in the literature led to several misleading conclusions and wrong results, and this question is still being discussed in connection with the correlation problem (Taylor and Parr 1952, Gerhauser and Mat sen 1955). 

The projection operator formalism also gives interesting aspects on the correlation problem. Previously one mainly used the secular equation (Eq. III.21) for investigating the symmetry properties of the solutions, and one was often satisfied with those approximate wave functions which were the simplest linear combinations of the basic functions having the correct symmetry. In our opinion, this problem is now better solved by means of the projection operators, and the use of the secular equations can be reserved for handling actual correlation effects. This implies also that, in place of the ordinary Slater determinants (Eq. III.17), we will essentially consider the projections of these functions as our basis. 

Variational principle on the correlation problem, 213, 318, 320, 326 Vibrational electronic modes, 12 Vibrational entropy in dilute solutions, 133... 

Correlation Problem in Many-Electron Quantum Mechanics. I. 

If we except the Density Functional Theory and Coupled Clusters treatments (see, for example, reference [1] and references therein), the Configuration Interaction (Cl) and the Many-Body-Perturbation-Theory (MBPT) [2] approaches are the most widely-used methods to deal with the correlation problem in computational chemistry. The MBPT approach based on an HF-SCF (Hartree-Fock Self-Consistent Field) single reference taking RHF (Restricted Hartree-Fock) [3] or UHF (Unrestricted Hartree-Fock ) orbitals [4-6] has been particularly developed, at various order of perturbation n, leading to the widespread MPw or UMPw treatments when a Moller-Plesset (MP) partition of the electronic Hamiltonian is considered [7]. The implementation of such methods in various codes and the large distribution of some of them as black boxes make the MPn theories a common way for the non-specialist to tentatively include, with more or less relevancy, correlation effects in the calculations. 

London, F., 1937, Quantum Theory of Interatomic Currents in Aromatic Compounds , J. Phys. Radium, 8,397. Lowdin, P.-O., 1959, Correlation Problem in Many-Electron Quantum Mechanics , Adv. Chem. Phys., 2, 207. 

In analytical calibration, there exists - strictly speaking - no correlation problem for the following two reasons ... 

Many-Electron Quantum Mechanics, Correlation Problem in. I (Lowdin), II (Yoshizumi). ... 

Quantum Theory of Many-Electron Systems and the Correlation Problem (Lowdin). ... 

Miller, E.C. and Miller, J.A. (1971). The mutagenicity of chemical carcinogens correlations, problems and interpretations. In Chemical Mutagens, Principles and Methods for Their Detection (Hollaender, A., Ed.), Vol. 1. Plenum Press, New York, pp. 83-120. 

Evaluation in the Unitary Group Approach to the Electron Correlation Problem. 

Langenbucher F. Handling of computational in vitro/in vivo correlation problems by Microsoft Excel, part II. Distribution functions and moments. Eur J Pharm Biopharm 2002 53 1—7. 

The correlation problem alluded to in the Introduction has most often been approached through the use of determinantal wave functions, that is, by writing Peiec as a linear combination of Hartree-Fock-like functions, [6]... 

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