MultiReference Double-Configuration

Multireference Briliouin-Wigner cou/ded cluster singles and doubles (MRBWCCSDJ and multireference doubles configuration interaction (MRD-CI) calculations for the Bergman cyclization reaction... 

Figure 1. The shape of the potential curve for nitrogen in a correlation-consistent polarized double-zeta basis set is presented for the variational 2-RDM method as well as (a) single-reference coupled cluster, (b) multireference second-order perturbation theory (MRPT) and single-double configuration interaction (MRCl), and full configuration interaction (FCl) wavefunction methods. The symbol 2-RDM indicates that the potential curve was shifted by the difference between the 2-RDM and CCSD(T) energies at equilibrium.

Another class of methods uses more than one Slater determinant as the reference wave function. The methods used to describe electron correlation within these calculations are similar in some ways to the methods listed above. These methods include multiconfigurational self-consistent field (MCSCF), multireference single and double configuration interaction (MRDCI), and /V-clcctron valence state perturbation theory (NEVPT) methods.5... 

MP (n = 2-4) n-th order of Mpller-Plesset correlation energy correction MRSDCI multireference single - - double configuration interaction... 

For longer polyenes, multireference double excitation configuration interaction (MRD-CI) approximations have been employed which select the most important electronic configurations and balance the effects of electron correlation in the ground and excited states. The MRD-CI methods provide results comparable to Q-CI or full -Cl calculations on short polyenes (Zoos and Ramasesha, 1984) and have allowed calculations to be extended to molecules with up to eight double bonds (Tavan and Schulten,... 

Chwee TS, Szilva AB, Lindh R, Carter EA (2008) Linear scaling multireference singles and doubles configuration interaction. J Chem Phys 128 224106-1/9... 

H + CH2 CH3 This reaction has been the subject of several experimental [11] and theoretical studies [12]. The published theoretical work calculated portions of the hindered rotation barriers for different values of Rh-C Ihe distance of the attacking H from CH2. This calculation employed a tzp basis set [13] with an multireference singles and doubles configuration interaction (MRSDCI) wavefunction and was carried out with the COLUMBUS program system [14]. This work has now been supplemented by a much more extensive mapping of the hindered rotational potential with a less expensive dzp basis set [13], Tests show that Vtr is not sensitive to dzp or tzp basis set selection. 

QDMBPT = quasi-degenerate many-body perturbation theory, (POL-) Cl = (polarization-) configuration interaction, MC SCF = multiconfiguration SCF, CAS SCF = complete active space SCF, MRD Cl = multireference double-excitation Cl, UHF = unrestricted Hartree-Fock, UMP2 = unrestricted Moller-Plesset perturbation method of second order. - An analytical, combined polynomial-exponential form for E(x) with x = (r-rg)/r and a figure for x= —0.98 to +0.04. 

CSF = configurational spin functions GUGA = graphical unitary group approach MRSDCl = multireference singles and doubles configuration interaction RCl = relativistic Cl RECP = relativistic effective core potential. 

Chwee TS, Carter EA. Valence Excited States in Large Molecules via Local Multireference Singles and Doubles Configuration Interaction. J Chem Theory Comput. 2010 7 103-111. 

Equilibrium Bond Distance and the Harmonic Frequency for N2 from the 2-RDM Method with 2-Positivity (DQG) Conditions Compared with Their Values from Coupled-Cluster Singles-Doubles with Perturbative Triples (CCD(T)), Multireference Second-Order Perturbation Theory (MRPT), Multireference Configuration Interaction with Single-Double Excitations (MRCI), and Full Configuration Interaction (FCI)". 

The calculations are not all at exactly the same bond length R. The basis set is indicated after the slash in the method. R, L, C, and T are basis sets of Slater-type functions. The aug-cc-pVDZ and aug-cc-pVTZ basis sets [360] are composed of Gaussian functions. SCF stands for self-consistent-field MC, for multiconfiguration FO, for first-order Cl, for configuration interaction MR, for multireference MPn, for nth-order Mpller-Plesset perturbation theory and SDQ, for singles, doubles, and quadruples. 

The second step of the calculation involves the treatment of dynamic correlation effects, which can be approached by many-body perturbation theory (62) or configuration interaction (63). Multireference coupled-cluster techniques have been developed (64—66) but they are computationally far more demanding and still not established as standard methods. At this point, we will only focus on configuration interaction approaches. What is done in these approaches is to regard the entire zeroth-order wavefunc-tion Tj) or its constituent parts double excitations relative to these reference functions. This produces a set of excited CSFs ( Q) that are used as expansion space for the configuration interaction (Cl) procedure. The resulting wavefunction may be written as... 

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