Multiconfiguration self-consistent field 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. 

Complete multiconfiguration-self consistent-field (CMC-SCF) technique designates the method where a given occupied molecular orbital of the set is excited to all unoccupied molecular orbitals. If an occupied orbital is excited to one or more, but not all, of the unoccupied orbitals, the technique is described as incomplete MC-SCF (IMC-SCF). The reader is referred to refs. 13 and 14 for details of the derivation. The CMC-SCF formalism differs from most many body techniques presented to date insofar as the Hartree-Fock energy is not assumed to be the zero order energy. 

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. 

Simons, J., Size extensivity correction for complete active space multiconfiguration self-consistent-field configuration interaction energies, J. Phys. Chem. 93, 626-627 (1989). 

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... 

A. Energy Expressions for Multiconfiguration Self-consistent Field... 

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. 

In the 1980s and 1990s, multiconfigurational self-consistent field (MCSCF) reference perturbation theories [1-6,23-30] were proposed to overcome the defects of the singlereference PT and the QDPT, and now they are established as reliable methods that can be applied to wide variety of problems potential energies surfaces of chemical reactions, excited spectra of molecules, etc. In fact, they have many advantages ... 

C. Woywod, W. Domcke, A. L. Sobolewski, and H-J Werner, Characterization of the 5,-5 conical intersection in pyrazine using ab initio multiconfiguration self-consistent-field and multireference configuration-interaction methods, J. Chem. Phys. 100 1400 (1994) G Stock and W. Domcke, Femtosecond spectroscopy of ultrafast nonadiabatic excited-state dynamics on the basis of ab initio potential-energy surfaces the S2 state of pyrazine, J. Phys. Chem. 97 12466 (1993). 

We summarize below the photodissociation cross-section measurements of CH3S at 193 nm [58], The CH3S radicals are prepared by photodissociation of CH3SCH3. To rationalize the experimental observations, we have also examined the ab initio multiconfiguration-self-consistence field (MCSCF), potential-energy surfaces of CH3S along the CH3-S dissociation coordinate [58],... 

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