First-row atom

Dunning T FI Jr 1970 Gaussian basis funotions for use in moleoular oaloulations I. Contraotion of (9s 5p) atomio basis sets for the first-row atoms J. Chem. Phys. 53 2823-33... 

Table 8-1 Energies (in hartrees) of First Row Atoms and Ions...

Normally, you would expects all 2p orbitals in a given first row atom to be identical, regardless of their occupancy. This is only true when you perform calculations using Extended Hiickel. The orbitals derived from SCE calculations depend sensitively on their occupation. Eor example, the 2px, 2py, and 2pz orbitals are not degenerate for a CNDO calculation of atomic oxygen. This is especially important when you look at d orbital splittings in transition metals. To see a clear delineation between t2u and eg levels you must use EHT, rather than other semiempirical methods. 

In the PPP model, each first-row atom such as carbon and nitrogen contributes a single basis functiqn to the n system. Just as in Huckel theory, the orbitals x, m e not rigorously defined but we can visualize them as 2p j atomic orbitals. Each first-row atom contributes a certain number of ar-electrons—in the pyridine case, one electron per atom just as in Huckel 7r-electron theory. 

In the TT-electron theories, each first-row atom contributes a single basis function. For the all valence electron models there is now an additional complication in at some of the basis functions could be on the same atomic centre. So how should we treat integrals involving basis functions all on the same atomic centre such as... 

And what if the basis functions are centred on different atoms The CNDO solution to the problem is to take all possible integrals such as those above to be equal, and to assume that they depend only on the atoms A and B on which the basis functions are centred. This satisfies the rotational invariance requirement. In CNDO theory, we write the two-electron integrals as pab and they are taken to have the same value irrespective of the basis functions on atom A and/or atom B. They are usually calculated exactly, but assuming that the orbital in question is a Is orbital (for hydrogen) or a 2s orbital (for a first row atom). 

Gaussian Basis Functions for use in Molecular Calculations III Contraction of (10s, 6p) Atomic Basis Sets for the First-Row Atoms T. FI. Dunning, Jr... 

The presence of a single polarization function (either a full set of the six Cartesian Gaussians dxx, d z, dyy, dyz and dzz, or five spherical harmonic ones) on each first row atom in a molecule is denoted by the addition of a. Thus, STO/3G means the STO/3G basis set with a set of six Cartesian Gaussians per heavy atom. A second star as in STO/3G implies the presence of 2p polarization functions on each hydrogen atom. Details of these polarization functions are usually stored internally within the software package. 

Here 1/ is the effective potential and a>i i is a nodeless pseudo-orbital that can be derived from Xi, in several different ways. For first-row atoms, Christiansen, Lee and Pitzer (1979) suggest... 

There is a nice point as to what we mean by the experimental energy. All the calculations so far have been based on non-relativistic quantum mechanics. A measure of the importance of relativistic effects for a given atom is afforded by its spin-orbit coupling parameter. This parameter can be easily determined from spectroscopic studies, and it is certainly not zero for first-row atoms. We should strictly compare the HF limit to an experimental energy that refers to a non-relativistic molecule. This is a moot point we can neither calculate molecular energies at the HF limit, nor can we easily make measurements that allow for these relativistic effects. 

Here the phosphorus atom has four shared electron pairs and one unshared pair, using five orbitals. (In PC15, eg, the transargononic phosphorus atom has five shared pairs in its outer shell.) However, because of the electroneutrality principle such a structure is allowed only for structure 1. Transargononic structures do not occur for first-row atoms, so this phenomenon is not found in NF3. These ideas concerning the bonding in NF3 and PF3 are implicit in the discussion by Marynick, Rosen and Liebman61 of the inversion barriers of these molecules. 

The new carbon-carbon double-bond distance corresponds to the value 0.87 for the double-bond factor. Moreover, there are now available three accurately known triple-bond distances 1.204 for C=C in acetylene, 1.154 A. for C=N in hydrogen cyanide, and 1.094 for N==N in the nitrogen molecule, whereas five years ago only the last was known. The ratios of these distances to the corresponding sums of single-bond radii are 0.782, 0.785, and 0.781, respectively. We accordingly now select 0.78 as the value of the triple-bond factor. Revised covalent radii26 for first-row atoms are given in Table XV. 

It is probable that the factors for atoms other than first-row atoms have values somewhat different from 0.87 and 0.78. Because of the small tendency of these atoms to form multiple bonds,... 

Once the number of valence electrons has been ascertained, it is necessary to determine which of them are found in covalent bonds and which are unshared. Unshared electrons (either a single electron or a pair) form part of the outer shell of just one atom, but electrons in a covalent bond are part of the outer shell of both atoms of the bond. First-row atoms (B, C, N, O, F) can have a maximum of eight valence electrons, and usually have this number, although some cases are known where a first-row atom has only six or seven. Where there is a choice between a structure that has six or seven electrons around a first-row atom and one in which all such atoms have an octet, it is the latter that generally has the lower energy and that consequently exists. For example, ethylene is... 

There are a few exceptions. In the case of the molecule O2, the structure 6=6 has a lower energy than 6=0. Although first-row atoms are limited to 8... 

Kendall, R.A., Dunning, T.H. Jr and Harrison, R.J. (1992) Electron affinities of the first-row atoms revisited. Systematic basis sets and wave functions. Journal of Chemical Physics, 96, 6796-6806. 

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