Reference functions, open-shell molecules

The fundamental difference between CN and Nj is simply that one molecule is centrosymmetric while the other is not. The lowest-energy UHF wave function in both cases suffers from unphysical spin localization, and it is illusory to believe that, 2 is the easier of the two molecules to calculate. The low spin-contamination solution to the UHF equations exists simply because of the molecular symmetry, while in CN the lower symmetry of the molecule allows the equations to converge to the lowest energy solution. This is a somewhat unappreciated difficulty in calculations on open-shell molecules. If one has appropriate elements of symmetry, then unphysical solutions can be avoided by enforcing the constraints on the wave function. Even if the constraints are not enforced, problems with the reference function are easily identifiable nonzero dipole moments along directions where the exact value must vanish by symmetry, unsymmetric spin densities, and so on. However, the issue is more diabolical in lower-symmetry species where localization does not break the framework molecular symmetry. In these cases, UHF and ROHF... 

The examples discussed above refer to adduct ion formation, where covalent bonds are formed in the Cl plasma. However, with the increasing importance of alternative ionization techniques, such as thermospray (TSI) and, in particular, electrospray ionization (ESI), a wealth of non-covalent ion/molecule adduct ions can be generated and studied nowadays. One recent example concerns the formation of ion/solvent adducts, [M- -So]+, with M including 3-aminophenol, 3-(methylamino)phenol and 3-(dimethylamino)phenol, and several hydroxypyrimidines, among other aromatic molecules. The relative abundances of ions [M- -H]+, [M -h So -h H]+ and [M - - 2 So - - H]+ were studied as a function of the temperature and the pH, with the solvents being mixtures of methanol/water and acetonitrile/water which may contain ammonium acetate as an additive . Quite in contrast to this empirical study on proton-bound ion/molecule complexes, the non-covalent, open-shell adduct ions [l + -h NH3] were investigated with respect to their intrinsic reactivity. These adduct ions were generated from phenol and ammonia by laser ionization of a... 

Because the full Cl (FCI) is the ultimate result in a given basis set, we can partly assess the comparative quality of different correlated methods by comparing with the limited number of full Cl results available for molecules. These are available for BH, FH, and H2O at the equilibrium bond length , 1.5 Re, and 2.0 in a DZP basis (see later). As discussed earlier, the RHF reference function separates incorrectly when going to open-shell fragments, so as bonds are stretched, it offers a particularly poor approximation to the correct answer. Because the FCI is the best possible answer, this behavior has no effect on those results, but for a truncated Cl, MBPT, or CC calculation, a poor... 

Paldus, elsewhere in this book, discusses that there is as yet no generally applicable, open-shell, size-extensive, coupled cluster method, and the same holds for open-shell S APT methods. Therefore, for the computation of potentials of open-shell van der Waals molecules one has the choice between CASSCF followed by a Davidson-corrected MRCl calculation of the interaction energy, or the single reference, high spin, method RCCSD(T). When the ground state of the open-shell monomer is indeed a high spin state, then RCCSD(T) is the method of choice. With regard to the latter method we recall that a major difficulty in open-shell systems is the adaptation of the wave function to the total spin operator S for the CCSD method a partial spin adaptation was published by Knowles et al. [219,220] who refer to their method as partially spin restricted . When non-iterative triple corrections [221] are included, the spin restricted CCSD(T) method, RCCSD(T), is obtained. 

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