MCSCF method coupled perturbed

Importantly for direct dynamics calculations, analytic gradients for MCSCF methods [124-126] are available in many standard quantum chemistiy packages. This is a big advantage as numerical gradients require many evaluations of the wave function. The evaluation of the non-Hellmann-Feynman forces is the major effort, and requires the solution of what are termed the coupled-perturbed MCSCF (CP-MCSCF) equations. The large memory requirements of these equations can be bypassed if a direct method is used [233]. Modem computer architectures and codes then make the evaluation of first and second derivatives relatively straightforward in this theoretical framework. 

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. 

The accurate calculation of these molecular properties requires the use of ab initio methods, which have increased enormously in accuracy and efficiency in the last three decades. Ab initio methods have developed in two directions first, the level of approximation has become increasingly sophisticated and, hence, accurate. The earliest ab initio calculations used the Hartree-Fock/self-consistent field (HF/SCF) methodology, which is the simplest to implement. Subsequently, such methods as Mpller-Plesset perturbation theory, multi-configuration self-consistent field theory (MCSCF) and coupled-cluster (CC) theory have been developed and implemented. Relatively recently, density functional theory (DFT) has become the method of choice since it yields an accuracy much greater than that of HF/SCF while requiring relatively little additional computational effort. 

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. 

PHF methods can, in turn, be classified as the variational and nonvariational ones. In the former gronp of methods the coefficients in linear combination of Slater determinants and in some cases LCAO coefficients in HF MOs are optimized in the PHF calculations, in the latter such an optimization is absent. To the former group of PHF methods one refers different versions of the configuration interaction (Cl) method, the multi-configuration self-consistent field (MCSCF) method, the variational coupled cluster (CC) approach and the rarely used valence bond (VB) and generaUzed VB methods. The nonvariational PHF methods inclnde the majority of CC reaUza-tions and many-body perturbation theory (MBPT), called in its molecular realization the MoUer-Plessett (MP) method. In MP calculations not only RHF but UHF MOs are also used [107]. 

Passing now to the analytical calculations of the y " tensor elements in solution, there are several SCRF methods in use we quote here some major examples, referring for more details to the relevant papers. " All the quoted methods use spherical or ellipsoidal cavities, with the exception of the PCM version which can treat cavities of general shape, and work at a QM level ranging from semiempirical to MCSCF methods. A MPE approach is generally used to describe solvent effects, with the exception of PCM again, which uses an ASC method. The evaluation of the y " tensor elements is made either with finite differences, response theory and SOS methods, or with coupled perturbed Hartree-Fock (CPHF) methods. ... 

Solutions to the eigenvalue equation (16) can be obtained by any of the standard quantum chemical methods, such as Hartree-Fock SCF, multiconfiguration SCF (MCSCF), Mpller-Plesset perturbation, coupled cluster, or density functional theories. The matrix elements of Hr, a one-electron operator, are readily computed, thus formally the inclusion of solvent effects in the quantum mechanical description of the solute molecule appears quite simple. Moreover, gradients of the eigenvalue E are readily computed. 

A number of types of calculations begin with a HF calculation and then correct for correlation. Some of these methods are Moller-Plesset perturbation theory (MPn, where n is the order of correction), the generalized valence bond (GVB) method, multi-conhgurational self-consistent held (MCSCF), conhgu-ration interaction (Cl), and coupled cluster theory (CC). As a group, these methods are referred to as correlated calculations. 

The use of Cl methods has been declining in recent years, to the profit of MP and especially CC methods. It is now recognized that size extensivity is important for obtaining accurate results. Excited states, however, are somewhat difficult to treat by perturbation or coupled cluster methods, and Cl or MCSCF based methods have been the prefen ed methods here. More recently propagator or equation of motion (Section 10.9) methods have been developed for coupled cluster wave functions, which allows calculation of exited state properties. 

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. 

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