Polarized self-consistent field function

The addition of these terms gives a trial function known as the polarized self-consistent field (PSCF) function ... 

Many problems in force field investigations arise from the calculation of Coulomb interactions with fixed charges, thereby neglecting possible mutual polarization. With that obvious drawback in mind, Ulrich Sternberg developed the COSMOS (Computer Simulation of Molecular Structures) force field [30], which extends a classical molecular mechanics force field by serai-empirical charge calculation based on bond polarization theory [31, 32]. This approach has the advantage that the atomic charges depend on the three-dimensional structure of the molecule. Parts of the functional form of COSMOS were taken from the PIMM force field of Lindner et al., which combines self-consistent field theory for r-orbitals ( nr-SCF) with molecular mechanics [33, 34]. 

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. 

Non-additive terms effects of polarization in the potential function. Polarization effects induced by the ionic presence on the ion-molecule system have been investigated. We use the expression by Lybrand and Kollman24 that includes in the potential function a self-consistent field (SCF) polarization energy Upoi based on classical electrostatics, given by ... 

Hyperfine couplings, in particular the isotropic part which measures the spin density at the nuclei, puts special demands on spin-restricted wave-functions. For example, complete active space (CAS) approaches are designed for a correlated treatment of the valence orbitals, while the core orbitals are doubly occupied. This leaves little flexibility in the wave function for calculating properties of this kind that depend on the spin polarization near the nucleus. This is equally true for self-consistent field methods, like restricted open-shell Hartree-Fock (ROHF) or Kohn-Sham (ROKS) methods. On the other hand, unrestricted methods introduce spin contamination in the reference (ground) state resulting in overestimation of the spin-polarization. 

Shortly after the above was written, a paper by Jaszuhski et al. [47] on FH appeared. They used the polarization propagator technique (a Danish tradition ) and calculated the QRF using a multi-configurational-self-consistent-field reference state (the previously unimplemented formalism had been developed by Olsen and Jprgensen [48]). They also took into account zero-point-vibrational averaging. For p(SHG) at X = 6943 A, and using CAS 4220 functions (more than 125000 determinants), their final value was (in the Ward convention) -7.8 a.u. or 71% of the experimental value they considered that Sekino and Bartlett s [38] estimate to be an exaggeration of "how close to experiment theory can get". However, their own value is, in fact, within the limits that Sekino and Bartlett proposed. 

SM calculations are broadly based on either the (i) Hartree-Fock method (ii) Post-Hartree-Fock methods like the Mpller-Plesset level of theory (MP), configuration interaction (Cl), complete active space self-consistent field (CASSCF), coupled cluster singles and doubles (CCSD) or (iii) methods based on DFT [24-27]. Since the inclusion of electron correlation is vital to obtain an accurate description of nearly all the calculated properties, it is desirable that SM calculations are carried out at either the second-order Mpller-Plesset (MP2) or the coupled cluster with single, double, and perturbative triple substitutions (CCSD(T)) levels using basis sets composed of both diffuse and polarization functions. 

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