Open-shell computations

A more complete coverage of the literature on electronic spectra of radicals is presented in our paper submitted for publication in Fortschr. Chem. Forsch. (Topics in Current Chemistry), where theafi initio studies are also reviewed and the existing open-shell computational procedures discussed. Recently we performed semiempirical all-valence-electron calculations on ground-state properties and electronic spectra of small radicals (Zahradnik, R., and P. Carsky, Theoret, Chim. Acta, 27, 121 (1972) and Carsky, P., M. Machacek, and R. Zahradnik, Coll. Czech. Chem. Commun., in press) and on equilibrium constants of dimerization reactions of small radicals (Zahradnik, R., Z. Slanina, and P. (5arsky, to be published). 

Although LHF is often a better theoretical treatment of open-shell systems than the RHF (half-electron) methods, it takes longer to compute. Separate matrices for electrons of each spin roughly double the length of the calculation. ... 

Nearly every technical difficulty known is routinely encountered in transition metal calculations. Calculations on open-shell compounds encounter problems due to spin contamination and experience more problems with SCF convergence. For the heavier transition metals, relativistic effects are significant. Many transition metals compounds require correlation even to obtain results that are qualitatively correct. Compounds with low-lying excited states are difficult to converge and require additional work to ensure that the desired states are being computed. Metals also present additional problems in parameterizing semi-empirical and molecular mechanics methods. 

LORG (localized orbital-local origin) technique for removing dependence on the coordinate system when computing NMR chemical shifts LSDA (local spin-density approximation) approximation used in more approximate DFT methods for open-shell systems LSER (linear solvent energy relationships) method for computing solvation energy... 

Next, you choose a UHF or RHF calculation. HyperChem can compute open-shell (non-singlet) systems with either the half-electron RHF or the UHF method (see Hartree-Fock Wave Functions on page 37). 

From the above it should be clear that UHF wave functions which are spin contaminated (more than a few percent deviation of (S ) from the theoretical value of S S + 1)) have disadvantages. For closed-shell systems an RHF procedure is therefore normally preferred. For open-shell systems, however, the UHF method has been heavily used. It is possible to use an ROHF type wave function for open-shell systems, but this leads to computational procedures which are somewhat more complicated than for the UHF case when electron correlation is introduced. 

From the point of view of the present state of computational possibilities, an extension of open-shell methods to a and a + rr electronic systems is rather tempting. This extension is easy for the method of Longuet-Higgins and Pople e.g., the CNDO/2 method is amenable to radicals having one nondegenerate open shell if in the original terms for F matrix elements (66),... 

Rotational Barrier in Ethylene. It is well known that the rotational barrier of the ethylene molecule cannot be adequately described by a single reference Hartree-Fock calculation SCF calculations on this level resulted in values of 126 kcal/mole (30) and 129 kcal/mole (31) whereas the experimental value is 65 kcal/mole (32). Open-shell ab initio calculations of double zeta+polarization quality give the more acceptable value of 48 kcal/mole (33). Inclusion of correlation such as in CEPA calculations yield theoretical results within the experimental error bar (34), albeit at a considerable computational cost. 

The representation of an essentially infinite framework by a finite SCF treated cluster of atoms, (with or without point-ions), inevitably leads to the problem of how to truncate the model-molecule . Previous attempts at this have included using hydrogen atoms l and ghost atoms . Other possibilities include leaving the electron from the broken bond in an open shell, or closing this shell to form an ionic cluster. A series of calculations were performed to test which was the host physically realistic, and computationally viable, solution to this problem for this system. 

The determination of the electronic structure of lanthanide-doped materials and the prediction of the optical properties are not trivial tasks. The standard ligand field models lack predictive power and undergoes parametric uncertainty at low symmetry, while customary computation methods, such as DFT, cannot be used in a routine manner for ligand field on lanthanide accounts. The ligand field density functional theory (LFDFT) algorithm23-30 consists of a customized conduct of nonempirical DFT calculations, extracting reliable parameters that can be used in further numeric experiments, relevant for the prediction in luminescent materials science.31 These series of parameters, which have to be determined in order to analyze the problem of two-open-shell 4f and 5d electrons in lanthanide materials, are as follows. 

Because of the inherent limitations of such semiempirical procedures, they can only be relied upon for yielding predictions for a limited set of data, the range of which includes the set of experimental data used for their parametrization. As such data are less abundant for open-shell species, such as radical ions, it is not surprising that there are examples of dramatic failures of semiempirical methods in predicting their electronic spectra, some of which will be discussed later. Ab initio methods are not burdened by these limitations but, as mentioned above, they require additional computations to account for dynamic electron correlation. 

The identification of unknown chemical compounds isolated in inert gas matrices is nowadays facilitated by comparison of the measured IR spectra with those computed at reliable levels of ab initio or density functional theory (DFT). Furthermore, the observed reactivity of matrix isolated species can in some instances be explained with the help of computed reaction energies and barriers for intramolecular rearrangements. Hence, electronic structure methods developed into a useful tool for the matrix isolation community. In this chapter, we will give an overview of the various theoretical methods and their limitations when employed in carbene chemistry. For a more detailed qualitative description of the merits and drawbacks of commonly used electronic structure methods, especially for open-shell systems, the reader is referred to the introductory guide of Bally and Borden.29... 

The closed-shell Ai state of 4a is computed to be less stable than the open-shell 1A2 state by ca. 9 kcal/mol at the CASPT2 level,57 and by 5 kcal/mol at the TC-CCSD level.55 The latter value is likely to be the more accurate energy difference, since CASPT2 probably overestimates the stability of open-shell... 

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