Multiconfiguration self-consistent field electronic energy

Our present focus is on correlated electronic structure methods for describing molecular systems interacting with a structured environment where the electronic wavefunction for the molecule is given by a multiconfigurational self-consistent field wavefunction. Using the MCSCF structured environment response method it is possible to determine molecular properties such as (i) frequency-dependent polarizabilities, (ii) excitation and deexcitation energies, (iii) transition moments, (iv) two-photon matrix elements, (v) frequency-dependent first hyperpolarizability tensors, (vi) frequency-dependent polarizabilities of excited states, (vii) frequency-dependent second hyperpolarizabilities (y), (viii) three-photon absorptions, and (ix) two-photon absorption between excited states. 

We start out with a section on the energy functionals and Hamiltonians that are relevant for molecular systems interacting with a structured environment. We continue with a section that briefly describes the correlated electron structure method, the multiconfigurational self-consistent field (MCSCF) electronic structure method. In the following section we cover the procedure for obtaining the correlated MCSCF response equations for the two different models describing molecules in structured environments. The final sections provide a brief overview of the results obtained using the two methods and a conclusion. 

The adiabatic potential energy curves for these electronic states calculated in the Born-Oppenhelmer approximation, are given in Figure 1. Since we have discussed the choice of basis functions and the choice of configurations for these multiconfiguration self-consistent field (MCSCF) computations (12) previously (] - ), we shall not explore these questions in any detail here. Suffice it to say that the basis set for Li describes the lowest 2s and 2p states of the Li atom at essentially the Hartree-Fock level of accuracy, and includes a set of crudely optimized d functions to accommodate molecular polarization effects. The basis set we employed for calculations involving Na is somewhat less well optimized than is the Li basis in particular, so molecular orbitals are not as well described for Na2 (relatively speaking) as they are for LI2. 

The present contribution concerns an outline of the response tlieory for the multiconfigurational self-consistent field electronic structure method coupled to molecular mechanics force fields and it gives an overview of the theoretical developments presented in the work by Poulsen et al. [7, 8, 9], The multiconfigurational self-consistent field molecular mechanics (MCSCF/MM) response method has been developed to include third order molecular properties [7, 8, 9], This contribution contains a section that describes the establisment of the energy functional for the situation where a multiconfigurational self-consistent field electronic structure method is coupled to a classical molecular mechanics field. The second section provides the necessary background for forming the fundamental equations within response theory. The third and fourth sections present the linear and quadratic, respectively, response equations for the MCSCF/MM response method. The fifth 283... 

Our multireference M0Uer-Plesset (MRMP) perturbation method [1-4] and MC-QDPT quasi-degenerate perturbation theory (QDPT) with multiconfiguration self-consistent field reference functions (MC-QDPT) [5,6] are perturbation methods of such a type. Using these perturbation methods, we have clarified electronic stmctures of various systems and demonstrated that they are powerful tools for investigating excitation spectra and potential energy surfaces of chemical reactions [7-10]. In the present section, we review these multireference perturbation methods as well as a method for interpreting the electronic structure in terms of valence-bond resonance structure based on the CASSCF wavefunction. 

Figure 4.6 Potential energy curves for six electronic states of NaH. The curve labeled "ionic" is the function e / ne R. approaching the energy of Na + H at infinite separation. From multiconfigurational self-consistent field calculations by E. S. Sachs, J. Hinze, and N. H. Sabelli, J. Chem. Phys. 62 3367 (1975) used with permission.

Calculations of core hole states and core electron binding energies have mostly concerned state-by-state optimization using open-shell Hartree-Fock, multiconfiguration self-consistent field, and configuration interaction techniques, while propagator techniques have been of restricted use owing to the relaxation problem ... 

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