First and Second Row Molecules

The molecular orbital description of He 2 predicts two electrons in a bonding orbital and two electrons in an antibonding orbital, with a bond order of zero—in other words, no bond. This is what is observed experimentally. The noble gas He has no significant tendency to form diatomic molecules and, like the other noble gases, exists in the form of free atoms. He2 has been detected only in very low pressure and low temperature molecular beams. It has a very low binding energy, approximately 0.01 J/mol for comparison, H2 has a bond energy of 436 kJ/mol. 

Be2 has the same number of antibonding and bonding electrons and consequently a bond order of zero. Hence, like Hc2, Be2 is not a stable chemical species. 

Here is an example in which the MO model has a distinct advantage over the Lewis dot picture. B2 is found only in the gas phase solid boron is found in several very hard forms with complex bonding, primarily involving B12 icosahedra. B2 is paramagnetic. This behavior can be explained if its two highest energy electrons occupy separate it orbitals as shown. The Lewis dot model cannot account for the paramagnetic behavior of this molecule. 

B2 is also a good example of the energy level shift caused by the mixing of 5 and p orbitals. In the absence of mixing, the (Tg 2p) orbital is expected to be lower in energy than the orbitals and the resulting molecule would be diamagnetic. Howev- 

Note Oxygen-oxygen distances in O2 and 02 are influenced by the cation. This influence is especially strong in the case of 02 and is one factor in its unusually long bond distance. 

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These composite approaches have been, overall, very successful. For example, recent variants of G3 give the heats of formation of a test set of 222 molecules, many having second-row atoms, with overall mean absolute deviations of about 1 kcal/mole [42,43], Atomization reactions were used. The results are nearly as good when third-row atoms are included [44]. Similarly, the CBS-QB3 procedure, for 147 first- and second-row molecules, produced a mean average deviation of 1.08 kcal/mole [38]. A few molecules, often containing halogens, do give problems [38,42-44], but the errors are rarely more than 5 kcal/mole. However the size limitations mentioned above must be kept in mind. 

Several points should be mentioned in this context. First, while we use QCISD(T) in our basic dehnition of G2 and G3 theories, analogous methods have been defined where the CCSD(T) method replaces QCISD(T). Both variations seem to yield very similar mean absolute deviations in most cases. However, in our most recent work on transition metal systems [78], it appears that CCSD(T) has a clear advantage over QCISD(T) and will thus become the preferred method. For the first- and second-row molecules, however, there is no clear preference. The key point to note is that the accuracy and predictive capability of these methods comes from the inherent accuracy of QCISD(T) or CCSD(T). Finally, this is one of the steps in the calculation and is likely to be rate-limiting if carried out with very large basis sets. Indeed, it is the bottleneck in CCSD(T) calculations with large correlation-consistent basis sets. In G2 theory, QCISD(T) calculations are carried out with a polarized valence triple-zeta basis set. This is a very modest basis set and this makes it possible to carry out G2 calculations on molecules of the size of naphthalene on small workstations. In our later work on G3 theory, we use even smaller 6-31G(d) calculations that makes these methods applicable for even larger molecules. 

Cohen and Tantirungrotechai97 have investigated the performance of new exchange-correlation functionals within the usual electron density schemes and compared calculated dipoles and multipoles for first and second row molecules with those obtained by established ab initio and electron density methods. The results obtained with the new functionals compare favourably with those of the previous methods and, in particular, give a value for the dipole moment of CO which is in good agreement with experiment. 

Curtiss L A, K Raghavachari, P C Redfem, V Rassolov eind J A Pople 1998. Gaussian-3 (G3) Theory for Molecules Containing First and Second-row Atoms. Journal of Chemical Physics 109 7764-7776. 

There is a second point to note in dementi s paper above where he speaks of 3d and 4f functions. These atomic orbitals play no part in the description of atomic electronic ground states for first- and second-row atoms, but on molecule formation the atomic electron density distorts and such polarization functions are needed to accurately describe the distortion. 

Diamondoids, when in the solid state, melt at much higher temperatures than other hydrocarbon molecules with the same number of carbon atoms in their structures. Since they also possess low strain energy, they are more stable and stiff, resembling diamond in a broad sense. They contain dense, three-dimensional networks of covalent bonds, formed chiefly from first and second row atoms with a valence of three or more. Many of the diamondoids possess structures rich in tetrahedrally coordinated carbon. They are materials with superior strength-to-weight ratio. 

Methods such as G3 and CBS-QB3 do reach the goal of chemical accuracy (generally defined as 1 kcal/mol) on average, but worst-case errors for problematic molecules may exceed this criterion by almost an order of magnitude. In addition, almost all of these approaches involve some level of parameterization and/or empirical correction against experimental data. While this is by and large possible (albeit not without pitfalls) in the kcal/mol accuracy range for first-and second-row compounds, experimental data of sub-kcal/mol accuracy are thin on the... 

Curtiss, L. A., Raghavachari, K., Redfern, P. C., Rassolov, V., and Pople, J. A. 1998. Gaiissian-3 (G3) Theory for Molecules Containing First and Second-row Atoms , J. Chem. Phys. 109, 7764. Feller, D. and Davidson, E. R. 1990. Basis Sets for Ab Initio Molecular Orbital Calculations and... 

A G2 subset (32 molecules containing only first-row atoms, see Johnson, GiU, and Pople 1993), 6-311G(d,p) basis set unless otherwise specified B (108 molecules including first- and second-row atoms, see Scheiner, Baker, and Andzelm 1997), 6-31G(d,p) basis set C (40 molecules containing third-row atoms Ga-Kr, see Redfern, Blaudeau, and Curtiss 1997). 

Some molecular orbital results for first- and second-row diatomic molecules, as well as relevant experimental data, are summarized in Table S.5. 

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