Multiconfigurational self-consistent field wavefunction

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. 

IV. Configuration State Function Expansion Spaces for Multiconfiguration Self-consistent Field Wavefunctions... 

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

IV. CONFIGURATION STATE FUNCTION EXPANSION SPACES FOR MULTICONFIGURATION SELF-CONSISTENT FIELD WAVEFUNCTIONS... 

The Multireference Space. The calculations of the embedded-cluster wavefunctions have a first step where multiconfigurational self-consistent field wavefunctions and energies are calculated using complete and/or restricted active spaces (CASSCF [32-34] and/or RASSCF [35,36]). The lanthanide 4/, 5d, and 6s shells must be included in the active space for the calculation of the 4/, 4f 5d, and manifolds, N being the num-... 

Multiconfiguration self-consistent field (MCSCF) theory aims to optimize simultaneously the LCAO coefficients and the Cl expansion coefficients in a wavefunction such as... 

Finally, we note that if we retain two-particle operators in the effective Hamiltonian, but restrict A to single-particle form, we recover exactly the orbital rotation formalism of the multiconfigurational self-consistent field. Indeed, this is the way in which we obtain the CASSCF wavefunctions used in this work. 

The multiconfigurational self-consistent field (MCSCF) method in which the expectation value /is treated variationally and simultaneously made stationary with respect to variations in the Q and Cv,i coefficients subject to the constraints that the spin-orbitals and the full N-electron wavefunction remain normalized ... 

For the construction of spin eigenfunctions see, for example, Ref. [22], There are obviously many parallels to the multiconfiguration self-consistent field (MCSCF) methods of MO theory, such as the restriction to a relatively small active space describing the chemically most interesting features of the electronic structure. The core wavefunction for the inactive electrons, 4>core, may be taken from prior SCF or complete active space self-consistent field (CASSCF) calculations, or may be optimised simultaneously with the and cat. 

The generalization of the HF methods toward degenerate or nearly degenerate systems is known as multiconfigurational self-consistent field (MCSCF). In this method, the MCSCF wavefunction is initially expanded in a set of many particle basis functions (Slater determinants or CSFs) [65],... 

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. 

For the MFP approach, most calculations have used SCF wavefunctions. However, very recently, Bak et al. have implemented the MFP theoretical approach at the correlated multiconfigurational self-consistent-field level by using the complete active space wavefunctions (CASSCF) expressed over conventional and gauge invariant basis sets. 

The multiconfigurational self-consistent field method (MCSCF) is the generalization of the Hartree-Fock method in the sense that the wavefunction... 

MP) perturbation theory, linearized coupled cluster and multiconfigurational self-consistent field (MCSCF) wavefunctions are commonly employed as approximate reference states in polarization propagator approximations and will be discussed in Sections 10.3 and 10.4. 

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. 

Further extension of reference wavefunctions—quasi-degenerate perturbation theory with general-multiconfiguration space self-consistent field reference functions (GMC-QDPT) [36]... 

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