Multireference Moller-Plesset theory

Application of multireference Moller-Plesset theory confirmed the general tendency observed in carotenoids that the first transition of the dications of polyenes is at a higher energy (shorter m) than the intense transition of the radical cation and at a lower energy (longer Xmax) than the first allowed transition of the neutral species [141], cf. Fig. 23. 

MRMP multireference Moller—Plesset perturbation (jt-CI) theory (with -configuration interaction) NBO natural bond orbital (analysis)... 

The TDDFT excitation energies and oscillator strengths calculated for the lowest allowed excited states of MgP [138], ZnP [138, 140], and NiP [137, 138] complexes in their optimized D4h geometry, are reported in Table 15 and compared to CASPT2 [150] and Multireference Moller-Plesset perturbation (MRMP) theory [151] results. 

K. Nakayama, K. Hirao, R. Lindh, Different bases for different correlation effects Multireference Moller-Plesset perturbation theory in the extended basis function space, Chem. Phys. Lett. 300 (1999) 303. 

Witek HA, Choe Y, Finley IP, Hirao K (2002) Intruder state avoidance multireference Moller-Plesset perturbation theory. 1 Comput Chem 23 957... 

Hamiltonian proposed by Muller and Plesset gives rise to a very successful and efficient method to treat electron correlation effects in systems that can be described by a single reference wave function. However, for a multireference wave function the Moller-Plesset division can no longer be made and an alternative choice of B(0> is needed. One such scheme is the Complete Active Space See-ond-Order Perturbation Theory (CASPT2) developed by Anderson and Roos [3, 4], We will briefly resume the most important definitions of the theory one is referred to the original articles for a more extensive description of the method. The reference wave function is a CASSCF wave function that accounts for the largest part of the non-dynamical electron correlation. The zeroth-order Hamiltonian is defined as follows and reduces to the Moller-Plesset operator in the limit of zero active orbitals ... 

Configuration Interaction Density Functional Theory Equation of Motion CCSD Multiconfiguration-SCF Moller Plesset 2nd Order Multireference Cl Multistate CASPT2 Restricted Active Space SCF Restricted Hartree Fock Symmetry Adapted Cluster-CI Self Consistent Field Singlestate CASPT2... 

Figrire 8 An overview of quantum chemical methods for excited states. Bold-italic entries indicate methods that are currently applicable to large molecules. Important abbreviations used Cl (configuration Interaction), TD (time-dependent), CC (coupled-cluster), HF (Hartree-Fock), CAS (complete active space), RAS (restricted active space), MP (Moller-Plesset perturbation theory), S (singles excitation), SD (singles and doubles excitation), MR (multireference). Geometry optimizations of excited states for larger molecules are now possible with CIS, CASSCF, CC2, and TDDFT methods. 

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. 

---