Multireference double-excitation method

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,... 

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. 

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 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... 

In practice, one often has to restrict the active space to include only a few of the highest occupied and lowest unoccupied molecular orbitals. The correlation effects not included in the CASSCF calculation can then be recovered by a multireference Cl (MRCI) calculation, in which all single and double excitations from the CASSCF reference are taken into account [27], A computationally more efficient way of including dynamical electron correlation effects is perturbation theory with respect to the CASSCF reference. The most widely employed method of this type is the CASPT2 method developed by Roos and collaborators [28], The CASSCF and CASPT2 methods have been essential tools for the calculations described in this contribution. 

Modular FORTRAN programs for performing general ab initio multireference single- and double-excitation configuration interaction, averaged coupled-pair functional and linearized couple-cluster method calculations. Cray and other versions. 

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... 

Multireference State-Specific Coupled Cluster Theory with Complete Account of Single and Double Excitations The CASCCSD Method... 

It has not yet been possible to extend the CC approaches in a systematic way to the multiconfigurational regime. For small molecules it is possible in this case to use large multireference Cl methods, where the most important configurations in a CASSCF wave function are used as reference functions, and the Cl expansion comprises all single and double excitations from the occupied orbitals to virtual or other (partially) occupied orbitals. The size of such a Cl expansion grows, however, too quickly to be of interest for larger molecules. 

The calculations were performed with several different levels of correlation treatment Hartree-Fock (HF), configuration interaction with single and double excitations (SDCI), Multiconfiguration self consistent field (CAS), and multireference configuration interaction (MRCI). Relativistic efferts were accounted for using either the Douglas-Kroll method or a relativistic effective core potential approach (RECP). 

The calculations are CASSCF/multireference single and double excitation Cl (MRCI). The use of the MRCI method for computing potential energy surfaces is supported by full Cl studies as discussed by Bauschlicher, Langhoff, and Taylor in another article in this volume. The accuracy of this approach has also been demonstrated for reaction (2) by Walch [2], who showed that by systematically expanding the active space and basis set, the computed barrier height converged to the currently accepted value [14]. 

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