Active-space reference

Multireference State-Specific Coupled Cluster Theory with a Complete Active Space Reference... 

Theory for Large Restricted and Selective Active Space Reference Wave Functions. 

Abstract The purpose of this paper is to introduce a second-order perturbation theory derived from the mathematical framework of the quasiparticle-based multi-reference coupled-cluster approach (Rolik and Kallay in J Chem Phys 141 134112, 2014). The quasiparticles are introduced via a unitary transformation which allows us to represent a complete active space reference function and other elements of an orthonormal multi-reference basis in a determinant-like form. The quasiparticle creation and annihilation operators satisfy the fermion anti-commutation relations. As the consequence of the many-particle nature of the applied unitary transformation these quasiparticles are also many-particle objects, and the Hamilton operator in the quasiparticle basis contains higher than two-body terms. The definition of the new theory strictly follows the form of the single-reference many-body perturbation theory and retains several of its beneficial properties like the extensivity. The efficient implementation of the method is briefly discussed, and test results are also presented. 

Anderson K, Malmqvist PA, Roos BO (1992) Second-order perturbation-theory with a complete active space self-consistent field reference function. J Chem Phys 96 1218... 

The calorimeter response (the emf-time curve or the thermogram) is, of course, proportional at any time to the temperature difference which exists between two definite values of the space variable ri and r2 where the active and reference junctions of the thermoelement are located ... 

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... 

Figure 2. Initial ( (/a) and final ( J/b) state potential-energy contours for the complete (two-mode) active space the abscissa refers to the inner-sphere mode and the ordinate governs the low-frequency active solvent mode. The difference in frequencies leads to a curved reaction path. Equilibrium coordinate values for the reactant ( j/A) and product ( J/b) states are labeled qA and qB, respectively. For the case of qin, qB° - qA° = Aqin°, as given by Eq. 16.

The method can be also applied to open-shell Cl references. It has been applied for the first time to the calculation of the outer valence IPs of CO. This is a classic but by no means simple problem of theoretical studies of PES. The formalism used was the one-state one-root (SC) dressing approach. Small MR-SDCI have been used along with common sets of MOs for both the neutral and cationic systems. The results are also good, and we can reasonably expect to obtain improved results for similar problems in the future using MOs previously adapted to each ionized state. The selection of small sets of active MOs for the CAS is important to avoid very large SDCI matrices, but the results can be very sensitive to the choice of the active space. 

Figure 1. Multireference problems involve both dynamical and nondynamical correlation. The nondynamical correlation is accounted for by the CASCI/CASSCF/DMRG wavefunction, which is made of multiple configurations generated in the active space with a fixed number of active electrons. The dynamical correlation is recovered on top of the multiconfigurational reference by correlating the active orbitals with orbitals in the external space (i.e., core and virtual orbitals.)...

Step 1. Given the electronic Hamiltonian H (Eq. (1)), determine the reference function in the active space (e.g., CASSCF, CASCI, or HF). 

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