Coupled-perturbed multiconfigurational

RPA, and CPHF. Time-dependent Hartree-Fock (TDFIF) is the Flartree-Fock approximation for the time-dependent Schrodinger equation. CPFIF stands for coupled perturbed Flartree-Fock. The random-phase approximation (RPA) is also an equivalent formulation. There have also been time-dependent MCSCF formulations using the time-dependent gauge invariant approach (TDGI) that is equivalent to multiconfiguration RPA. All of the time-dependent methods go to the static calculation results in the v = 0 limit. 

Here we will skip the notation details, as the relation established to the Coupled Perturbed frame allow us the shortcut of passing the references to the comprehensive works devoted to the analytic derivatives of molecular energy [9]. The recent advances in the analytic derivatives and Coupled Perturbed equations into multiconfigurational second order quasi-degenerate perturbation theory is the premise of further development in the ab initio approach of vibronic constants of JT effects [10]. 

Analytical second derivatives for closed-shell (or unrestricted Hartree-Fock (UHF)) SCF wavefunctions are used routinely now. The extension to the MCSCF case is relatively new, however. In contrast to the first derivatives, the coupled perturbed SCF equations have to be solved in order to calculate the second and third energy derivatives. The closed-shell case is relatively straightforward, and will be discussed. The multiconfigurational formalism is... 

However, until today no systematic comparison of methods based on MpUer-Plesset perturbation (MP) and Coupled Cluster theory, the SOPPA or multiconfigurational linear response theory has been presented. The present study is a first attempt to remedy this situation. Calculations of the rotational g factor of HF, H2O, NH3 and CH4 were carried out at the level of Hartree-Fock (SCF) and multiconfigurational Hartree-Fock (MCSCF) linear response theory, the SOPPA and SOPPA(CCSD) [40], MpUer-Plesset perturbation theory to second (MP2), third (MP3) and fourth order without the triples contributions (MP4SDQ) and finally coupled cluster singles and doubles theory. The same basis sets and geometries were employed in all calculations for a given molecule. The results obtained with the different methods are therefore for the first time direct comparable and consistent conclusions about the performance of the different methods can be made. 

DFT is the modern alternative to the wave-function based ab initio methods and allows to obtain accurate results at low computational cost, that also helps to understand the chemical origin of the effect. DFT, like Hartree-Fock (HF) methods, exploit molecular symmetry which is crucial in the case of computational studies of the JT effect. It also includes correlation effects into the Hamiltonian via the exchange-correlation functional. HF and many-body perturbation methods are found to perform poorly in the analysis of JT systems for obvious reasons, at contrast to the methods based on DFT, or multiconfigurational SCF and coupled cluster based methods [73]. The later are very accurate but have some drawbacks, mainly the very high computational cost that limits the applications to the smaller systems only. Another drawback is the choice of the active space which involves arbitrariness. 

A particular advantage of the Cl approach, as opposed to coupled-cluster or perturbation theoretic techniques, is that it can be readily formulated to handle the case in which is multiconfigurational in character. Corresponding multireference CC or perturbation theory approaches are much less well developed. As we shall see, there are many important chemical applications in which a multireference approach is mandatory, and we shall therefore concentrate mainly on the Cl method in this article. 

The all-orders relativistic many-body perturbation theory approach [82], [83], the combination of this approach with the multiconfiguration Dirac - Fock method [84] or the relativistic coupled-cluster approach [85] allow for the evaluation of the energy levels for valence electrons with accuracy of the order of... 

The development of multireference methods represents important progress in electronic stmcture theory in the last decades. The multiconfiguration self-consistent field (MCSCF) method, and configuration interaction (Cl), coupled cluster (CC), and perturbation methods based on the MCSCF functions play a central role in the studies of electronic stmcture of molecules and chemical reaction mechanisms, especially in those concerned with electronic excited states. 

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