Internal contraction

Brodzinsky R, Singh HB. 1982. Volatile organic chemicals in the atmosphere An assessment of available data. Menlo Park, CA Atmospheric Science Center, SRI International. Contract no. 68-02-3452, 107-108. 

Werner H-J, Knowles PJ (1988) An efficient internally contracted multiconfiguration reference Cl method. J Chem Phys 89 5803... 

Equation [1] is an internally contracted configuration space, doubly excited with respect to the CAS reference function 0) = G4SSCF) one or two of the four indices p,q,r,s must be outside the active space. The functions of Eq. [1] are linear combinations of CFs and span the entire configuration space that interacts with the reference function. Labeling the compound index pqrs as (i or v, we can write the first-order equation as... 

The second approximate scheme we will discuss here is the internally contracted Cl (ICCI) method. In this method correlating configurations are formed by applying excitation operators (the generators of the unitary group) directly on the full reference Cl vector. The four types of configurations thus formed can be written as,... 

H.-J. Werner and P.J. Knowles, An Efficient Internally Contracted Multiconfiguration Reference Configuration Interaction Method, J. Chem. Phys. 89, 5803 (1988). 

Spin-Orbit Matrix Elements for Internally Contracted Multireference Configuration Interaction Wavefunctions. 

Platelets are contractile blood elements with a specialized task in the arrest of bleeding. The fundamental mechanisms of this specific hmction involve adhesion, aggregation, internal contraction and secretion. Furthermore, the phospholipids present in the platelet membranes play a key role in the development of coagulation mechanisms. 

Werner and co-workers [2, 21, 34] used internally-contracted multi-reference configuration-interaction (IC-MRCI) calculations, based on state-averaged (three-state) multi-configuration, self-consistent-field (MCSCF) calculations with large atomic orbital basis sets, to determine the three electronically adiabatic C1(F)+H2 PESs in the reactant arrangement L4, 2A, and lA. These all correlate with X( P) + H2. These three adiabatic electronic states are the IC-MRCI approximations to the three lowest eigenfunctions of Hgi, namely... 

An alternative contraction scheme which has received more attention is internally contracted multireference CISD (usually denoted simply CMRCI), which was first discussed by Meyer99 and Siegbahn.100 This method applies the single and double excitation operators to a single multiconfigurational reference wavefunction as a whole, including the reference coefficients. Thus, if the reference wavefunction is... 

Once again, the contraction has dramatically reduced the number of variational parameters. One difficulty with the internally contracted multireference Cl method is that the relevant coupling coefficients become considerably more difficult to calculate. Werner and Knowles101 alleviate this problem by leaving internal and singly-external configurations uncontracted, i.e.,... 

III. The Internally Contracted Multiconfiguration Reference Self-consistent... 

III. THE INTERNALLY CONTRACTED MULTICONFIGURATION REFERENCE SELF-CONSISTENT ELECTRON-PAIR METHOD... 

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. ... 

In principle, the advantage of applying the internal contraction scheme... 

Comparison of correlation energies" for internally contracted and uncontracted MCSCF-SCEP wavefunctions (from Ref. 63). 

The number of variational parameters in internally contracted MCSCF-SCEP wavefunctions rarely exceeds 10 even if large basis sets and complex reference wavefunctions are employed. In contrast to the number of variational parameters, the number of coupling coefficients depends on the number of reference configurations, and can become very large if CASSCF references are used. The main problem is, therefore, the calculation and storage of the coupling coefficients. It would be very helpful if at least part of them could be recalculated each time they are needed. As will be discussed in Section 111.I, this would also allow one to relax the contraction coefficients in each direct Cl iteration, thereby improving the quality of the wavefunction. 

Internally contracted singly excited and semi-internal doubly excited configurations can be defined as... 

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