MC SCF calculations

Density functional theory and MC-SCF calculations have been applied to competing concerted and stepwise mechanisms of cycloaddition reactions. ... 

Density functional theory and MC-SCF calculations have been applied to a number of pericyclic reactions including cycloadditions and electrocyclizations. It has been established that the transition states of thermally allowed electrocyclic reactions are aromatic. Apparently they not only have highly delocalized structures and large resonance stabilizations, but also strongly enhanced magnetic susceptibilities and show appreciable nucleus-independent chemical-shift values. 

P. Pulay and T.P. Hamilton, UHF Natural Orbitals for Defining and Starting MC-SCF Calculations, J.Chem. Phys. 88, 4926 (1988). 

MC-SCF calculations on polyatomic molecules are still rather rare, although there have been many such calculations on triatomic and diatomic molecules. Levy45 has described the results of such calculations using a minimal STO basis set for CH4, C2H4, and CjjHa. A quadratically convergent method was described and the results of localizing the orbitals were investigated. 

The Fle-Fle system has generated considerable interest. MC-SCF calculations have been performed for Fle-Fle [224], Cl calculations were... 

UV spectra usually involve electronic state transitions, so that simple Hartree-Fock and DFT calculations often are not sufficient PCM has been recently extended also to multi-configurational (MC-SCF) calculations [113] and to time-dependent approaches, allowing for the description of excited states and then the prediction of the so-called solvatochromic effects on these spectra. Nuclear magnetic resonance (NMR) and electron spin resonance (EPR) spectra are even more influenced by solute-solvent interactions moreover, the interpretation of experimental data is often very difficult without the support of reliable ab initio calculation, especially for EPR which is usually applied to unstable radical species. 

It is also possible to use perturbation theory in conjunction with Cl and MC-SCF calculations. The more important configurations are handled according to the Cl or MC-SCF method and the contribution of the less important configurations is estimated using perturbation theory.133-135... 

The first multiconfigurational (MC) SCF calculation was probably performed by Hartree and co-workers in 1939 [9]. They realized (as discussed above) that for the state of the oxygen atom there where two possible configurations, s and p , and constructed the two configurational wave function... 

As long as a satisfactory multireference coupled-cluster theory is missing, there are various options for states that need a zeroth-order multiconfiguration wave function. One possibility is to start from an MC-SCF calculation and to improve this by selected Cl. Since the MC-SCF part is basically extensive, while the Cl part is not, and since one can hardly go beyond external double excitations, one tends to include as many configurations in the MC-SCF part as possible. However, MC-SCF is usually of CAS (complete active space) [154] type, e.g. like full Cl, which restricts the possible size of the active space. Such multireference Cl scheme have been very popular for describing excited states, reaction barriers, dissociation processes etc. 

Though more complicated than the equivalent matrices for SCF wavefunctions (Eqs. (33) or (57)), the left-hand side of the MC-CHF equations is not a major problem as it consists of combinations of quantities that must be formed in a normal MC-SCF calculation of the energy. The right-hand side, however, causes more difficulty. This is... 

This problem has been investigated at the at initio level by Borden et alP using two different wavefunctions a two-configuration wavefunction (TC-SCF) and a wavefunction consisting of 52 Ag spin-adapted configurations (MC-SCF). Calculations have been carried out using both STO-3G and 3-2IG basis sets. Because the MC-SCF computations with the 3-21G basis required too much computer memory, the calculations were simulated by using ALIS to find the optimal orbitals. These optimized orbitals have been used to perform a full six-electron, six-orbital Cl. 

In order to improve the energetics, MC-SCF calculations have also been carried out at the previously optimized geometries with a valence space that consisted of the HOMO-LUMO out-of-plane it orbitals as weU, corresponding to eight valence orbitals. This calculation should account for some of the dynamic correlation of the delocalized n system. 

Fig. 10.8. CAS SCF, a method of construction of the Slater determinants in the MC SCF expansion. The inner shell orbitals are usually inactive, i.e. are doubly oecupied in each Slater determinant Within the active space + inactive spinorbitals we create the eomplete set of possible Slater determinants to be used in the MC SCF calculations. The spinorbitals of energy higher than a certain selected threshold are entirely ignored in the calculations.

An operator 6 is idempotent over a domain if 6 = 6 for any g Such coefficients may result from a configuration interaction (Cl) or multiconfiguration SCF (MC-SCF) calculation, for example. 

An ab initio MC SCF calculation of the spin-orbit coupling constant [30] and an SCF calculation of the A-doubling constant [18] are available. 

An ab initio MC-SCF calculation using a relativistic effective core potential treated the two 66 hole states Fg and F j mentioned above and two gg hole states, and E+, at higher energies [5]. Bonding in the Pd2 molecule was also found to be essentially due to the 5s electrons coming from the excited atomic configurations (4d 5s) [5, 6]. 

HF/CI calculations yielded De = 0.93eV (90 kJ/mol) relative to Pd atoms in their excited 4d 5s states (excitation energy 0.95 eV for each). 0 = 1.18 eV was obtained without correction for a basis set superposition error. for dissociation into ground-state atoms would thus become negative [1, 3]. Dq = 1.1 eV (106 kJ/mol) followed from an MP-LSD calculation [12]. Dissociation energies (of Fg, F, and two aa hole states) were based on MC-SCF calculations using a relativistic effective potential [5]. 

The j-dependent REP may be averaged over the quantum number ] = l 1/2, whereby spin-orbit contributions are suppressed [11, pp. 359, 374] and the more familiar A-S coupling scheme may be used [2, 14]. Such an averaged potential (AREP) was applied in a CAS-MC-SCF calculation (for CAS see [15]), followed by a first-order Cl treatment (FOCI) [9]. Spin-orbit effects were later introduced by a relativistic Cl method (RCI, first applied in [14, 16])... 

Another type of averaged REP was based upon the effective core potential (ECP) introduced by Kahn et al. [17], see also [11, p. 363], and was obtained by using j-independent one-component relativistic atomic orbitals [18, 19] see also [11, p. 374] and a review on these RECP s by Kahn [20]. Such potentials were used in another CAS-MC-SCF calculation... 

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