Multi-configurational SCF

Within the SCF-CI method a fixed set of molecular orbitals is used. This means that during the calculation (leading to slow convergence) the individual molecular orbitals remain unchanged. A method where the linear expansion coefficients and the LCAO coefficients are optimized simultaneously is the multi-configuration SCF (MCSCF). 

MCSCF (multi-configuration SCF) methods are Cl in which not only the coefficients of the linear combination are optimized but also the MOs from which the excited configurations are constructed. Usually, the MOs are divided into active (FOs and some other nearby MOs) and inactive. If all the configurations generated from the active orbitals are taken into consideration, the model is called CASSCF (complete active space SCF).24... 

In any of these methods, the system itself can be described with varying degrees of sophistication, from simple models to extensive ab initio multi-configuration SCF descriptions. 

The more difficult multi-configuration SCF method, which has already been... 

In optimized multi-configuration or multi-configuration SCF (MCSCF) methods the coefficients Ci and the orbitals from which the are constructed are varied simultaneously. This is in principle a much more satisfactory process. It achieves energies comparable with those from configuration interaction calculations and yet provides much simpler wavefunctions (i.e. fewer configurations) however, the variation problem is non-linear, and the resulting technical difficulties have inhibited wide use of the method. 

In certain cases, a single determinant does not offer an adequate representation of the electronic structure. In such cases, it is useful to perform a Multi-Configuration SCF calculation (MCSCF) wherein a number of different configurations are chosen as important, and their adjustable parameters (orbital coefficients, etc.) are variationally optimized . 

Multi-configuration SCF wavefunctions for the ground and some low-lying excited states of AlO reproduce the measured geometrical parameters for this molecule quite well.398... 

Table 3. SCF and multi-configuration SCF calculations of observables in diatomic...

The structure and bonding in dilithiomethane 3 was reexamined recently in detail by Streitwiescr (electron density analysis) and Harrison (Multi-Configuration SCF calculations), essentially confirming the previous results. 

Hartree -Fock or Self-Consistent Field (SCF) Method Spin Optimized Self-Consistent Field Method Configuration Interaction Iterative Natural Orbital Method Multi-Configuration SCF Many Body Perturbation Theory Valence-Bond Method Pair-Function or Geminal Method... 

The Cl and INO calculations discussed above yield very unwieldy wave-functions which do not provide any simple qualitative picture of the bonding. An alternative approach is to pick a reasonably small number of configurations and to try to find, not only the best coefficients CK in the Cl wavefunction of (15), but also to vary the molecular orbitals so as to obtain the optimum orbitals for the chosen form of the wavefunction. This method is known as the multi-configuration SCF method (MC-SCF). The configurations chosen will normally include the Hartree-Fock configuration, plus those additional configurations which add the most important types of... 

In the mean time McLean and Yoshimine had completely rewritten the linear molecule code McL-Yosh Linear Molecular Program. L available also from QCPE. At the end of 1967, The Tables of Linear Molecule Wave Functions were available [61], with the introductory comment that these were a prelude to forthcoming tables at the Multi-Configuration-SCF level , following Das and Wahl [62], Clementi and Veillard [54,60], and J. Hinze [63] (at LMSS) works. At that time the San Jose collaboration on MC-SCF with B. Roos group had not yet started the idea to invest on the MC-SCF path was widely accepted in quantum chemistry. 

The situation is different for the multi-configurational SCF (MC-SCF) case. Although DIIS has been used successfully for simpler cases [36], the strong coupling between orbital rotations and configuration interaction (Cl) coefficients mandates the use of second-order or approximate second-order methods (see the reviews [3,... 

MCSCF multi-configurational SCF. Electronic wavefunction is a linear combina-... 

As indicated above, neither the SCF nor the DFT method is able to treat the Van der Waals interaction. This is well established for the SCF approximation [14, 15]. The Van der Waals interaction is a typical correlation effect therefore, its description requires the use of a correlated method . In wave function based ab initio methods correlation effects are described by adding singly, doubly and higher excited configurations to the SCF or to a multi-configuration SCF (MC-SCF or complete active space SCF, CASSCF) wave function. This can be done by means of perturbation theory (PT),by configuration interaction (Cl)... 

Further extensions of the END method to incorporate ionization channel and time-dependent electromagnetic fields (photon absorption and emission), as well as a multi-configurational SCF for the electronic state, are underway. This will provide the opening of a variety of processes to be treated within the same framework, END. 

Analytic gradient methods became widely used as a result of their implementation for closed-shell self-consistent field (SCF) wavefunctions by Pulay, who has reviewed the development of this topic. Since then, these methods have been extended to deal with all types of SCF wavefunctions, - as well as multi-configuration SCF (MC-SCF), - " configuration-interaction (Cl) wavefunctions, and various non-variational methods such as MoUer-Plesset (MP) perturbation theory - - and coupled-cluster (CC) techniques. - In short, it is possible to obtain analytic energy derivatives for virtually all the standard ab initio approaches. The main use of analytic gradient methods is, and will remain, the location of stationary points on a potential energy siuface, to obtain equilibrium and transition-state geometries. However, there is a specialized use in the calculation of quantities such as dipole derivatives. 

The construction of NOs (PNOs) requires either knowledge of the pair function —the NOs are then obtained by diagonalizing the corresponding C matrix—or the solution of a multi-configuration SCF (MCSCF) problem, i.e. it requires the simultaneous optimizing of D, and in (27) or (28). However, very efficient methods have been developed to determine good approxim-... 

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