Open Electron Shells

El predominantly creates singly charged ions from the precursor neutral. If the neutral was a molecule as in most cases, it started as having an even number of electrons, i.e., it was an even-electron (closed-shelT) molecule. The molecular ion formed must then be a radical cation or an odd-electron open-shell) ion as these species are termed, e.g., for methane we obtain ... 

The only known tt-excessive 12-membered ring is the multiply annulated thiaannulene (30) (70JA5284). It is an unconventional molecule insofar as it incorporates an odd number of electrons (13) within an even-membered frame. As a result, its central tt-ribbon cannot be mobilized into 7r-delocalization without becoming exposed to the adversity of an electronic open shell (78AHC(23)55). The molecule s natural resistance to do so is borne out by its UV and XH NMR characteristics which are clearly implicative of a nonplanar, strictly atropic central skeleton. 

It appears that the only known representative of this family is the heavily annulated substance depicted in 65, which was synthesized as shown.82 Being an even-membered ring and incorporating but a single -excessive heteroatom in its periphery, the twelve-membered monocyclic moiety of 65 is somewhat unorthodox in the sense that it contains an odd number of electrons, thirteen to be exact. As a result, the central 17-ribbon of 65 cannot sustain delocalization without experiencing the ill effects of a w-electronic open shell. It is hardly surprising, therefore, to find that 65 exhibits UV and 1H NMR characteristics that are indicative of a nonplanar, strictly atropic, central frame. 

It is noteworthy that the development of a -electronic open shell predicted for peripherally delocalized 65 may, in principle, be prevented through simple electron transfer to or from the remote n centers of the system s peri-fused naphthalene tail. Derivatives of 65 with strongly electron-withdrawing, e.g., CN, N02, or electron-releasing, e.g., OMe, NH2, substituents attached to the para position(s) of the naphthalene appendage would certainly be of interest. 

We saw that numerous ionization techniques exist that yield radical cations or radical anions, protonated or deprotonated molecules, and various adducts. These ions yield fragments with an even number of electrons (closed shell) or with an odd number of electrons (open shell). Even though the radical cations derived from electron ionization sources retain a privileged status in common mass spectrometry, the other ionization methods become increasingly common. Electron ionization is not possible for many categories of molecules. Therefore, we will not limit the discussion to radical cations. 

We now return to the problem of implementing our earlier result the solution of the equations vjhich determine the orbitals of the optimum single-determinant wavefunction for an n-electron system. This necessarily involves electronic "open shells . 

Neutral molecules are the polynitrogen species of main interest because they represent pure polymerized nitrogen without the esthetic distraction of a counterion, because they have been the most difficult to realize experimentally, and because being pure nitrogen they are in principle the best candidates for high-energy-density materials. Closed-shell species would seem to be of particular interest, because most stable molecules fall into this class, but radicals and even-electron open-shell molecules will also be mentioned where appropriate. We will consider N3, N4, N5, Ne, N7, Ng, and larger molecules . 

A practical instrument for many-electron open shell system is still the MCDF method. There are several modifications of it implemented into computational codes of Desclaux [57], developed further by Indelicato [36], of Grant [58] and Frose-Fisher [59]. Based on the Cl technique, the MCDF method accounts for most of the correlation effects while retaining a relatively small number of configurations. It can treat a large number of open shell configurations and can be applied to elements with any number of valence electrons. It omits, however, dynamic correlation, since excitations of the type (nj) n j) cannot be handled, and some core polarization, which makes it less accurate than the DC(B) CC methods. An average error for IP of heavy elements is about 1 eV. Calculations for many heaviest and superheavy elements were performed with the use of the AL version [23-31], as well as with a more accurate OL one [36]. 

Having considered the closed-shell CSFs, we now turn our attention to the two-electron open-shell CSFs (10.1.4)-(10.1.7). The singlet and triplet CSFs may be written in the general form... 

We conclude that, for closed-shell and high-spin states, second-order optimizations can be carried out in the AO basis at a cost of n for each trial-vector transformation (10.8.8). For other open-shell CSF states, it is more difficult to simplify the construction of the Q matrix in order to carry out a second-order optimization in the AO basis. However, with the possible exception of the two-electron open-shell singlet state (10.1.7), Hartree-Fock wave functions for oth than high-spin states are of little interest except for systems of high spatial symmetry. In Exercise 10.7, an STO-3G Hartree-Fock wave function for HeH is calculated using Newton s method. 

The spherical shell model can only account for tire major shell closings. For open shell clusters, ellipsoidal distortions occur [47], leading to subshell closings which account for the fine stmctures in figure C1.1.2(a ). The electron shell model is one of tire most successful models emerging from cluster physics. The electron shell effects are observed in many physical properties of tire simple metal clusters, including tlieir ionization potentials, electron affinities, polarizabilities and collective excitations [34]. 

WFth all semi-empirical methods, IlyperChem can also perform psendo-RIfF calculations for open -shell systems. For a doublet stale, all electrons except one are paired. The electron is formally divided into isvo "half electron s" with paired spins. Each halfelec-... 

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. ... 

Total spin den sity reflects th e excess probability of fin din g a versus P electrons in an open-shell system. Tor a system m which the a electron density is equal to the P electron density (for example, a closed-shell system), the spin density is zero. 

Another way of constructing wave functions for open-shell molecules is the restricted open shell Hartree-Fock method (ROHF). In this method, the paired electrons share the same spatial orbital thus, there is no spin contamination. The ROHF technique is more difficult to implement than UHF and may require slightly more CPU time to execute. ROHF is primarily used for cases where spin contamination is large using UHF. 

For an open-shell system, try converging the closed-shell ion of the same molecule and then use that as an initial guess for the open-shell calculation. Adding electrons may give more reasonable virtual orbitals, but as a general rule, cations are easier to converge than anions. 

Both HF and DFT calculations can be performed. Supported DFT functionals include LDA, gradient-corrected, and hybrid functionals. Spin-restricted, unrestricted, and restricted open-shell calculations can be performed. The basis functions used by Crystal are Bloch functions formed from GTO atomic basis functions. Both all-electron and core potential basis sets can be used. 

This program is excellent for high-accuracy and sophisticated ah initio calculations. It is ideal for technically difficult problems, such as electronic excited states, open-shell systems, transition metals, and relativistic corrections. It is a good program if the user is willing to learn to use the more sophisticated ah initio techniques. 

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