Reduced multi-reference

The S-T splitting is obtained as a difference of the two separate individual energy calculations for the singlet and triplet. Those individual singlet and triplet calculations do not necessarily have to be by the same method, and in fact, the majority of the results in Table 1 use composite methods in which the singlet and triplet are treated by two different methods (primarily the singlet as a MR state while the triplet is SR). RMR indicates the reduced multi-reference approach of Li and Paldus [58]. The TD-CCSD of Baikova and Bartlett [54], an early SU-CCSD application, provides two roots simultaneously at each geometry. This SU-CCSD calculation introduced GVB CCSD as a two-determinant reference. The MR-BW is a state-specific MR... 

Density Functional Theory, DFT (B3LYP), CASSCF (Complete Active-State Self-Consistent Field) and MRSD-CI (Multi-Reference Single-Double Correlation Interaction) calculations on the diatomic units AuO, AuO", AuO " and AuO " clearly show that stability of Au-0 bond reduces in this order. This trend is consistent with the molecular orbital diagram of AuO molecule presented in Fig. 10. 

The first-order interacting space restriction is generally used to reduce the number of double substitutions included in single- or multi-reference CISD... 

The effects of intruder states are generally more severe for molecules than for atoms, due to more dense energy levels. Therefore, even if there are ways of avoiding - or at least reducing - the effect of intruder states in the multi-reference approach, it is when the interest lies entirely in one or a few particular states, more advantageous to study one state at a time in a state-specific approach. 

Aspects of size extensivity in unitary group adapted multi-reference coupled cluster theories the role of cumulant decomposition of spin-free reduced density matrices... 

In the early 90s, a second improvement in the field of computational photochemistry took place. The Roos group proposed and implemented the multi-reference second-order perturbation theory (CASPT2), which reduced the CASSCF errors to the level of the accepted chemical accuracy (0.2 eV). This promoted the computational photochemistry to a new stage. Since then, the CASSCF/CASPT2 method is the most general and robust method for qualitative and quantitative accurate studies of any type of photochemical or photophysical process. 

Matrix elements of the reaction operator, Va, could be determined by using eq. (4.245) including the terms contained in the braces. .. after convergence has been achieved. However, it can be shown that in the case p = 1, i.e. the singlereference case, eq. (4.245) reduces to the familiar and widely used AfP2 expression. In the multi-reference case, eq. (4.245) is independent of the exact ground state energy, o, and becomes... 

Several attempts have been made to remove the pervasive failing of the perturbative CC approximations at large internuclear separations. The representative examples include the externally-corrected SRCC methods (6,10,63-74), the active-space SRCC approaches (14,19, 75-86), the orbital-optimized SRCC methods (39,87,88), and the perturbative CC approaches based on the partitioning of the similarity-transformed Hamiltonian (89,90) (see ref 91 for the original idea). Of all these approaches, the reduced MRCCSD (RMRCCSD) method (68-74), which uses the multi-reference configuration interaction (MRCI) wave Unctions to extract information about triply and quadruply excited clusters, and the active-space CCSDt and CCSDtq methods (19,85,86) and their earlier state-selective (SS) CCSD(T) and CCSD(TQ) analogs (14, 75-84) are particularly promising. The RMRCCSD approach can be used to success-... 

The above-mentioned targets refer to general advantages of micro reactors [42, 80, 100, 114, 119]. Enhanced transfer and better controlled residence time improve conversion and selectivity. The tools have small internal volumes, allowing one to generate flexibly a multitude of samples in serial or parallel fashion. Synthesis can be combined with a multi-step procedure. The economy of micro-reactor processes has not really been analyzed so far however, it is clear that as laboratory tools they allow in a number of cases technical expenditure, personnel and costs to be reduced. 

Such a wave function is represented by a linear combination of wave functions for more than one electron configuration, and is called a "multi-configurational" wave function. The consideration of more than one configuration can reduce the correlation error. Such an approach is referred to as the method of configuration interaction (Cl) . 

As shown in Fig. 22, the resulting procedure, referred to as a multi-block experiment, produces a two-dimensional data set, such as an array of FIDs (its exact nature depends upon the signal acquisition method). The data of each x-block are then reduced to a single quantity, S(t) which should be proportional either to the total sample magnetization Ma(x) or to one of its components. Since the vertical scale of the relaxation curve is irrelevant, we can identify S(t) with Ma(x) at the exact time of detection (usually just after the first excitation pulse). 

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