Multiconfiguration SCF calculations

H. B. Gray Multiconfiguration SCF calculations by P. J. Hay indicate that the 166 -366 energy separation is over 1 eV, and there is no evidence for intervening states that could provide a facile intersystem pathway. Thus a relatively small singlet triplet intersystem crossing rate constant is not all that peculiar. 

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. 

This formalism may be extended to simple multiconfiguration SCF calculations using standard nonrelativistic computer codes (48). For instance, in the simplest case involving the two-electron promotion from one closed shell to another, the coupling is of the form... 

This section barely scratches the surface of many-electron atomic structure calculations. They have mushroomed in complexity to multiconfigurational SCF calculations in which linear combinations of atomic orbitals (LCAOs) are used for each of the spatial orbitals With atomic orbital basis sets of sufficient... 

The energy-gradient method was first put into practice for closed-shell HF calculations, but it has recently been extended to spin-unrestricted and restricted-HF calculations on open-shell systems and to certain types of multiconfigurational SCF calculations. A method has been developed, based on the perturbed HF theory, to calculate the derivatives of MO coefficients. With this in hand, one is now able to calculate the energy gradient for a... 

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. 

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 black box situation of SCF applications has not yet been reached for the multiconfigurational SCF theory. This constitutes a major problem, since MCSCF is a much better starting point for quantum chemical calculations on many interesting chemical problems (a good example is studies of transition states for chemical reactions). A development towards more automatized procedures can consequently be expectedto take place in MCSCF theory too. 

Potential energy surfaces for dissociation of SiH2 to SiH + H and Si + H2, from various states up to 8 eV excitation energy, have been calculated by multiconfiguration SCF + multireference Cl calculations252. 

Mainly high-level correlated ab initio calculations (multiconfiguration SCF, multireference Cl, and CC) and DFT. The emphasis is on highly accurate computations. .. accurate ab initio calculations can be performed for much larger molecules than with most other programs. An unusual feature is the inclusion of... 

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. 

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