Correlating orbitals

Finally, we also account for an explicit relaxation of both lone pairs of H2COby the inclusion of corresponding correlating orbitals [50] and treat them at a GVB-like level. 

The methodology presented here expands the recent CASPT2 approach to more flexible zeroth-order variational spaces for a multireference perturbation, either in the Moller-Plesset scheme or in Epsein-Nesbet approach [70-72]. Furthermore, it allows for the use of a wide set of possible correlated orbitals. These two last points were discussed elsewhere [34]. 

A CAS, (4220) or (62), which consists of the valence orbitals which would be occupied in a Hartree-Fock calculation, (2110) or (31), and exactly one unoccupied, so-called correlating, orbital for each of the occupied ones included in the active space. In CH4 this is the same as the valence CAS. 

A CAS, (6331) or (94), which was chosen according to the MP2 natural orbital occupation numbers [71]. They turn out to be slightly larger than a CAS which includes two correlating orbitals for each HF occupied orbital, (6330) or (93). 

The number No of occupied valence SCF orbitals in a molecule is typically less than the total number Nmb of orbitals in the minimal valence basis sets of all atoms. The full valence MCSCF wavefunction is the optimal expansion in terms of all configurations that can be generated from N b molecular orbitals. Closely related is the full MCSCF wavefunction of all configurations that can be generated from Ne orbitals, where Nc is the number of valence electrons, i.e. each occupied valence orbital has a correlating orbital, as first postulated by Boys (48) and also presumed in perfect pairing models (49,50), We shall call these two types of frill spaces FORS 1 and FORS 2. In both, the inner shell remains closed. 

In consequence, the most expensive steps of the ground- and excited-state calculations using methods based on the MMCC(2,3) approximation are essentially identical to the n nf noniterative steps of the ground-state CCSD(T) calculations uo and are the numbers of occupied and unoccupied correlated orbitals, respectively). Similar remarks apply to the memory and disk-space requirements. Clearly, these are great simplifications in the computer effort, compared to the higher-level EOMCC approaches, such as EOMCCSDT [43,44,55,56], particularly if we realize that we only have to use the Ti and T2 clusters, obtained in the CCSD calculations, to construct matrix elements of that enter 9Jt (2), Eqs. (58) and (59). In... 

CV and valence calculations leads to almost insuperable linear dependence problems in the resulting basis set [97], We should note that these problems axe perhaps at their worst for the first row. For heavier elements the separation between the valence shell and the core (meaning the next innermost shell here) is not as great, so the disparities in correlating orbital occupation number are less. Suitable ANO sets can often be obtained by correlating all the desired electrons [48, 98]. 

Generalized Valence Bond method with one pair of correlated orbitals... 

In order to illustrate some computational features of the response methods we show in this section convergence behavior of results for SOC with respect to correlating orbital spaces and basis sets. For this purpose we choose the particular case of the A 3Ej - b1 magnetic dipole transition in O2, partially presented in ref. [8]. 

Adamowicz, L., NNO—HCl complex. Ab initio calculations with the coupled cluster method and first-order correlation orbitals, Chem. Phys. Lett. 176, 249—254 (1991). 

In 1984, Adamowicz and Bartlett used a linear combination simple spherical Gaussians (FSGOs) for constructing correlation orbitals. They performed SCF calculation with extended basis sets of M functions, which give resulting Woccupied (index a, h,. .. ) and M-N virtual orbitals (index i,j,. . . ). Then, the second order perturbation energy can be expressed as. 

The choice of the active orbital space for the CASSCF calculations is a crucial step, and has turned out to be especially difficult in these proteins and other systems containing a Cu-thiolate bond. From earlier studies it was known that in complexes with first-row transition metal ions with many 3d electrons, the active space should include one correlating orbital for each of the doubly occupied 3d orbitals [28]. Therefore the starting active space contains 10 orbitals 3d and 3d"). In addition, it is necessary to add the 3p orbitals on Scys to describe correctly the covalent character of the Cu-Scys bond and also 2p and 3p orbitals on nitrogen and sulphur to describe charge-transfer states. The final active space therefore contain 11 or 12 active orbitals (12 active orbitals are at present the upper limit for the CASPT2 method). 

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