Diffuse orbitals

There are two basic differences of (sic) free atoms and chemically bound atoms. First, the more diffuse an AO, the stronger it is perturbed in molecular and condensed matter. The (n + )s AOs of the transition metal atoms, especially of the earlier ones, are not of primary importance for chemical bonding. Their relevance is comparable to that of the diffuse orbitals of main group elements ([34], p 653). 

In a previous work [1,2], we were interested in the calculation of second order hyperpolarizabilities of eonjugated systems including substituted benzenes, pyridine N-oxydes and vinyl oligomers, in relation with non linear optical activity [3]. We showed that MNDO ealeulations were in good agreement with SCF ab initio results obtained using a double zeta basis set plus polarization and diffuse orbitals. 

These compounds have been the subject of several theoretical [7,11,13,20)] and experimental[21] studies. Ward and Elliott [20] measured the dynamic y hyperpolarizability of butadiene and hexatriene in the vapour phase by means of the dc-SHG technique. Waite and Papadopoulos[7,ll] computed static y values, using a Mac Weeny type Coupled Hartree-Fock Perturbation Theory (CHFPT) in the CNDO approximation, and an extended basis set. Kurtz [15] evaluated by means of a finite perturbation technique at the MNDO level [17] and using the AMI [22] and PM3[23] parametrizations, the mean y values of a series of polyenes containing from 2 to 11 unit cells. At the ab initio level, Hurst et al. [13] and Chopra et al. [20] studied basis sets effects on and y. It appeared that diffuse orbitals must be included in the basis set in order to describe correctly the external part of the molecules which is the most sensitive to the electrical perturbation and to ensure the obtention of accurate values of the calculated properties. 

The starting point is our previously performed calculations [3] using the Huzinaga basis set [20] (9s) for Be and (4s) for H, triple-zeta contracted, supplemented by the three 2p orbitals proposed for Be by Ahlrichs and Taylor [21] with exponents equal to 1.2, 0.3 and 0.05 respectively. This initial basis set, noted I, includes one s-type bond-function the exponent of which is equal to 0.5647. Several sets of diffuse orbitals have then been added to this basis I. Their corresponding exponents were determined by downward extrapolation from the valence basis set, using the Raffenetti [22] and Ahlrichs [21] procedure. Three supplementary basis sets noted II, III and IV containing respectively one, two and three... 

As we can see, the diffuse orbitals play a dramatic part in the description of the magnetic properties of BeH not less two sets of these orbitals (basis set III) are necessary to obtain an accurate and converging value of the susceptibility. The BeH-anion should be diamagnetic and its mean susceptibility is of the order of -2.10- erg.G-2.mol"L Note that the use of a single set of supplementary diffuse orbitals is not sufficient to bring to light this magnetic property. 

For MgH", we have extended the previously defined basis set, noted 1, by means of one and two sets of diffuse orbitals, the exponents of which have been computed by downward extrapolation. These basis sets are reported in Table 4. 

Our results indicate that the basis set i cannot describe correctly MgH- and that the ma etic susceptibility of this anion is strongly depending on the inclusion of diffuse orbitals in the basis set. We notice that the basis set 11 permits to obtain reliable results, its further extension by extra diffuse functions (basis set 111) leading approximately to the same results. MgH- should be diamagnetic, and its mean susceptibility is of the order of -22. 10-6 erg.G-2.mol". ... 

Because Rydberg states are peculiar states with a core resembling the positive ion and one electron in a diffuse orbital, the A] Rydberg states have been recalculated with orbitals optimized for the ion, with the same MCSCF/SD expansion. An improvement of 0.2 eV is obtained, arguing for the use of this type of MOs for Rydberg A, states. 

The different struetures and transitions states of interest in the neutral and negative ion reaetions are represented in Fig. 2. A first approach was done at the SCF level, using the split-valence 4-3IG basis set. In order to provide a better estimation of the energy differences implied in this reaction schemes, extensive calculations have been performed at the MP2 level of theory using the 6-311++G basis set which contains the diffuse orbitals necessary to quantitatively describe the negative ions. 

The 15 trivalent lanthanide, or/ -block, ions La3+, Ce3+, Pr3+, Nd3+, Pm3+, Sm3+, Eu3+, Gd3+, Tb3+, Dy3+, Ho3+, Er3+, Tm3+, Yb3+, and Lu3+, which may be collectively denoted Ln3+, represent the most extended series of chemically similar metal ions. The progressive filling of the 4/orbitals from La3 + to Lu3 + is accompanied by a smooth decrease in rM with increase in atomic number as a consequence of the increasingly strong nuclear attraction for the electrons in the diffuse / orbitals (the lanthanide contraction). Thus, the nine-coordinate rM decrease from 121.6 to 103.2 pm from La3+ to Lu3+, and the eight-coordinate ionic radii decrease from 116.0 to 97.7 pm from La3+ to Lu3+ (2). Ligand field effects are small by comparison with those observed for the first-... 

We saw in Section 12.2.3.1 that the presence of additional chalcogen atoms in BEDT-TTF/TCNQ promotes interstack interactions, suppressing the Peierls distortion and imparting upon the salt increased dimensionality compared to TTF/TCNQ. The result of including a different chalcogen into the TTF/TCNQ structure is shown in Table 2. Despite losing donor efficiency compared to TTF (Table 1) the TCNQ complexes of m/trans-diselenadithiafulvalene (DSDTF, 55/56) and TSF show an improvement in conductivity when two or four selenium atoms are incorporated. The reduced metal-insulator transition suggests that this effect is also caused by a suppression of the Peierls distortion. Increased Se-Se interstack contacts add dimensionality to the structure and limit the co-facial dimerisation typical of Peierls distortion. Wider conduction bands are afforded from the improved overlap of diffuse orbitals. 

RET spectroscopy is based on the transfer of electrons from highly excited atoms into diffuse orbitals of polar systems and provides a useful method for the discrimination between different geometrical conhgurations. 

Early calculations (Pitzer, K. S. J. Am. Chem. Soc. 1948, 70, 2140) are usually mentioned in connection with the double-bond rule, predicting a small overlap due to the diffuse orbitals of the heavy atoms from the second or lower long row of the periodic table. 

When systems are pushed together, nonbonded electrons, on the other hand, tend to retreat toward the system that has the more diffuse orbitals. In this case that is C, B, or Be. Since the nonbonded electrons are generally in orbitals less far out, this effect occurs at closer distances and, according to our calculations, wins out at equilibrium distances for CO and BF. This is the only effect for BeNe, and the moment is in the same direction at all of the distances we show. This retreat of electrons is definitely a result of the Pauli exclusion principle. 

---