Correlation, configuration orbital

Unfortunately, these methods require more technical sophistication on the part of the user. This is because there is no completely automated way to choose which configurations are in the calculation (called the active space). The user must determine which molecular orbitals to use. In choosing which orbitals to include, the user should ensure that the bonding and corresponding antibonding orbitals are correlated. The orbitals that will yield the most correlation... 

In recent years density-functional methods32 have made it possible to obtain orbitals that mimic correlated natural orbitals directly from one-electron eigenvalue equations such as Eq. (1.13a), bypassing the calculation of multi-configurational MP or Cl wavefunctions. These methods are based on a modified Kohn-Sham33 form (Tks) of the one-electron effective Hamiltonian in Eq. (1.13a), differing from the HF operator (1.13b) by inclusion of a correlation potential (as well as other possible modifications of (Fee(av))-... 

Alternatively, if results of ab initio theory at the single-configuration orbital level are used to define the parameters of a semi-empirical model, it would be proper to use the semi-empirical orbitals in a subsequent higher-level treatment of electron correlations. 

Among the sequence of N-heterocycles, n.b. the 1,2,3,4 N-substituted azabenzenes, the response investigations have focussed on pyridine, pyrazine, pyridazine, pyrimidine, s-triazine, and s-tetrazine [151]. The calculations of phosphorescence of these compounds utilize x type complete active spaces, the general rule of thumb has been to use one correlating x orbital for each occupied x orbital. All azabenzenes, except pyridazine, take the same Hartree-Fock orbital configuration in C2V symmetry Ilai,7b2,2bi,la2, including 18 and 3 doubly occupied a and x orbitals, respectively. For pyridazine it reads 10ai,8b2,2bi,la2. 

The second possible contraction scheme was first proposed by Meyer , and discussed in the context of the direct Cl method by Siegbahn ". In this case all configurations which have the same external but different internal parts are contracted, and the scheme is therefore called the internal contraction. The internally contracted configurations are generated by applying pair excitation operators to the complete MCSCF reference function. Therefore, the number of contracted configurations and variational parameters is independent of the number of reference configurations. It only depends on the number of correlated internal orbitals and the size of the basis set. ... 

It is important to repeat that in making the selection of the correlation configurations in initial and final states, NON considerations between the two sets of orbitals are applied. This implies that even though the dipole operator is a one-electron operator, certain configurations that differ by more than one orbital can indeed be selected and added to the total wavefunctions of initial and final states [26b, 45]. 

From the correlation between orbitals we can derive the correlation between electron configurations. The results are given in Fig. 5. The broken arrows correlate electron configurations. However, electron repulsion prevents states of the same symmetry from crossing, and the full arrows represent correlations between the states. It appears that the... 

M k = 0, 2, and 4. They also considered the effect of additional configurations on the spin-orbit interaction to produce the electrostatically correlated spin-orbit interaction. 

Late Dr. Isaiah Shavitt has been the champion of configuration-interaction (Cl) theory [1-4], which is the first systematically accurate, ab initio electron-correlated molecular orbital (MO) theory. Although today its usage may be diminished with the advent of coupled-cluster (CC) theory [5], its predictions have overturned some experimental conclusions [6, 7] and helped computational quantum chemistry be accepted by a broader community of chemists as a vital engine of chemical research. 

The wavefunctions for the initial bound state the resonant states , and the neutral thresholds are generated in separate valence RCI calculations. The valence RCI calculation for the resonant state yields energy positions of unperturbed resonant states, i.e., the E s in equation 1.3. Since virtual orbitals are used for the correlation configurations that capture not only the bound orbitals but also a portion of the continuum orbitals, it s important to avoid in cj) the correlation configurations that are equivalent to the continuum state. For example, in Ce [5], 4/ 5d 6s vp and 4/ 5d 6s vf were excluded from the basis set for resonant state 4/ 5d 6p. Otherwise, the variational optimization for 4/ 5d 6s 6p may collapse into the continuum 4/ 5d 6s ep (f) in which it lies. 

The mean-field potential and the need to improve it to aohieve reasonably aeourate solutions to the true eleotronio Selirodinger equation introduoe three oonstniots that oharaoterize essentially all ab initio quantum ohemioal methods orbitals, configurations and electron correlation. 

In this example, tlie two non-orthogonal polarized orbital pairs involve mixing the k and k orbitals to produce two left-right polarized orbitals as depicted in figure B3.1.7. Here one says that the n electron pair undergoes left-right correlation when the (n configuration is introduced. 

Atomic natural orbital (ANO) basis sets [44] are fonned by contracting Gaussian fiinctions so as to reproduce the natural orbitals obtained from correlated (usually using a configuration interaction with... 

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). 

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