Multiconfiguration SCF MCSCF

When the HF wave function gives a very poor description of the system, i.e. when nondynamical electron correlation is important, the multiconfigurational SCF (MCSCF) method is used. This method is based on a Cl expansion of the wave function in which both the coefficients of the Cl and those of the molecular orbitals are variationally determined. The most common approach is the Complete Active Space SCF (CASSCF) scheme, where the user selects the chemically important molecular orbitals (active space), within which a full Cl is done. 

The various response tensors are identified as terms in these series and are calculated using numerical derivatives of the energy. This method is easily implemented at any level of theory. Analytic derivative methods have been implemented using self-consistent-field (SCF) methods for a, ft and y, using multiconfiguration SCF (MCSCF) methods for ft and using second-order perturbation theory (MP2) for y". The response properties can also be determined in terms of sum-over-states formulation, which is derived from a perturbation theory treatment of the field operator — [iE, which in the static limit is equivalent to the results obtained by SCF finite field or analytic derivative methods. 

An example of a multireference technique is the multiconfigurational SCF (MCSCF) approach, where the wave function is obtained by simultaneously optimizing both the molecular orbitals and the configuration coefficients, thereby blending the different resonance structures together. [28] Historically, the MCSCF approach has been used extensively to provide qualitatively accurate representations of surfaces however, this method still suffers two primary drawbacks (1) the ambiguous choice of configurations and (2) the lack of dynamical correlation. 

The Section on More Quantitive Aspects of Electronic Structure Calculations introduces many of the computational chemistry methods that are used to quantitatively evaluate molecular orbital and configuration mixing amplitudes. The Hartree-Fock self-consistent field (SCF), configuration interaction (Cl), multiconfigurational SCF (MCSCF), many-body and Mpller-Plesset perturbation theories,... 

The Cl procedure just described uses a fixed set of orbitals in the functions An alternative approach is to vary the forms of the MOs in each determinantal function O, in (1.300), in addition to varying the coefficients c,. One uses an iterative process (which resembles the Hartree-Fock procedure) to find the optimum orbitals in the Cl determinants. This form of Cl is called the multiconfiguration SCF (MCSCF) method. Because the orbitals are optimized, the MCSCF method requires far fewer configurations than ordinary Cl to get an accurate wave function. A particular form of the MCSCF approach developed for calculations on diatomic molecules is the optimized valence configuration (OVC) method. 

Variational optimization of equation (11.9), where we are concerned with only one projection of tp corresponding to a particular electronic eigenstate, has been extensively studied. There are at least two well-developed techniques for such situations, namely, the multiconfiguration SCF (MCSCF) and iterative natural spin-orbital (INSO) approaches. 

With respect to the multiconfiguration SCF (MCSCF), the virtues and the drawbacks of this method99-101 have been described in the literature on several occasions (see e.g. Ref.5 ). In our opinion, the MCSCF still remains much more suited... 

Finally, we should mention some approximate calculations on H2. Jug77 has developed a semi-empirical version of the multiconfiguration SCF (MCSCF) method, using CNDO- and INDO-type approximations, and has reported the results of a double-configuration approach to Ha. It was shown that the eigenvalues of the EHF operator have physically interpretable characteristics and follow dissociation properly. Further results of this method should be very interesting. 

Multiconfiguration SCF (MCSCF) Theory and Complete Active Space SCF (CASSCF) Theory... 

Efficient techniques for optimizing orbitals have been elaborated in multiconfiguration SCF (MCSCF) theory (see e.g. the book by McWeeny [134] and refs, therein). Since the APSG wave function represents a special class among MCSCF functions, these procedures can be applied to determine the optimal Arai-subspaces [65],... 

An improvement of the RPA would be obtained if we could remove the possibility of instabilities from the reference state 0>, i.e. make sure that the Hessian is positive definite. The multiconfigurational SCF (MCSCF) wave-function for the ground state fulfils this requirement. Furthermore, MCSCF introduces a much higher level of electronic correlation into the propagator method. Also, away from equilibrium (bond breaking, etc.), where the SCF reference state is very poor or perhaps even gives an incorrect description of... 

The inclusion of closed-shell configurations in spin-coupled calculations is most easily accomplished by carrying out a self-consistent field (SCF) (or small multiconfiguration SCF (MCSCF)) step first. The integrals over the basis functions are transformed to the molecular-orbital representation and input to the spin-coupled program. The use of MOs as basis functions also shows directly which of them are significant in the spin-coupled wavefunction. 

It should be pointed out, however, that the size of the Cl expansion used in a CASSCF calculation is almost always much larger than those normally used in earlier applications of the multiconfigurational SCF (MCSCF) method . It was only when the graphical unitary group approach (GUGA) for full Cl calculations was invented in the years 1975-78 that an efficient computational procedure for CASSCF calculations could be developed ". ... 

The multiconfigurational SCF (MCSCF) model [43,44] is a generalization of the Hartree-Fock model to several configurations ... 

A b initio quantum chemical studies of hyperfine structures (hfs) were initiated some 25 years ago, with the pioneering work of Meyer and others [127]. However, results from the early Hartee-Fock-based methods deviated considerably from experimentally determined hf parameters. It was not until the configuration interaction (Cl) techniques were fully developed for hfs calculations, that theoretical predictions of high accuracy were possible for atomic and molecular radicals [20]. This is mainly associated with the importance of electron correlation and with the development of new and fax larger basis sets. In later years, hfs calculations have also been carried out with great success using various levels of multiconfiguration SCF (MCSCF) [21], multireference Cl (MRCI) [22] and coupled cluster (CC) theory [23]. 

In the multiconfiguration SCF (MCSCF) method, one writes the molecular wave function as a linear combination of CSFs <5, and varies not only the expansion coefficients = 2, but also the forms of the molecular orbitals in the CSFs. 

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