Multiconfiguration SCF method

Shepard R (1987) In Lawley KP (ed) Ab initio methods in quantum chemistry part II the multiconfiguration SCF method. Wiley, Chichester... 

Actually, there is no necessity to use SCF MOs in a Cl calculation. Any set of MOs calculated from the basis set will produce the same final wave function provided a full Cl calculation is carried out. Moreover, if the non-SCF MOs are well chosen, they can produce much faster convergence to the true wave function than is obtained with SCF MOs, thereby allowing substantially fewer CSFs to be included in Two approaches that use this idea are the multiconfiguration SCF method and the method of natural orbitals. 

All of the Cl methods described so far are considered single determinant wavefunctions. Multiconfigurational SCF methods use multiple determinantsP " . In these methods, the coeffficients that multiply each state in Eq. (A21) and also the molecular orbital coefficients used to construct the determinants must also be optimized. This involves an iterative SCF-like approach. 

As in the Hartree-Fock molecular orbital theory, which is based on the independent particle model, the above Hartree product method also lacks enough correlation among the orbitals, and thereby the resultant accuracy is limited. To overcome the drawback, one can take account of the interaction among possible configurations (or the Hartree products) as in the configuration interaction method and multiconfiguration SCF methods in electronic structure theory. The multiconfigulational time-dependent Hartree... 

In this exercise, we will introduce the Complete Active Space Multiconfiguration SCF (CASSCF) method, using it to compute the excitation energy for the first excited state of acrolein (a singlet). The CIS job we ran in Exercise 9.3 predicted an excitation energy of 4.437 eV, which is rather for from the experimental value of 3.72 eV. We ll try to improve this prediction here. 

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. 

The standard method for selecting the 4>j is to ask for the <)>i which maximize the importance of one or more terms in the sum. This gives the self-consistent-field (SCF) or multiconfiguration SCF (MC-SCF) equations. If each < >. is expanded as a linear combination of some fixed set of basis functions f - the coefficients can be found by an extension of the Roothaan SCF equations. 

B.O.Roos, The Multiconfigurational (MC) SCF Method, in Methods in Computational Physics (G.H.F Diercksen and S.Wilson, eds), D.Reidel Publishing Company, Dordrecht (1983). 

As a first application of a new analytical gradient method employing UHF reference functions, seven different methods for inclusion of correlation effects were employed to optimize the geometry and calculate the harmonic vibrational frequencies and dipole moments of the lowest open-shell states for three simple hydrides including 3Z i SiH2228. As the degree of correlation correction increased, results approached those from the best multiconfiguration SCF calculation. 

The Valence Bond Self-Consistent Field (VBSCF) method has been devised by Balint-Kurti and van Lenthe (32), and was further modified by Verbeek (6,33) who also developed an efficient implementation in a package called TURTLE (11). Basically, the VBSCF method is a multiconfiguration SCF procedure that allows the use of nonorthogonal orbitals of any type. The wave function is given as a linear combination of VB structures, (Eq. 9.7). 

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. 

In order to make up for those imperfections one needs to turn to post-Hartree-Fock methods. Two variational techniques are worth discussing due to their popularity the configuration-interaction (SCF Cl) method and the multiconfiguration self-consistent-field (MC SCF) method. 

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