Fenske—Hall molecular orbital calculations

Its absorption spectrum shows one band at 320 nm (e = 2900 M 1cm 1), assigned to the cti - ct2 transition localized in the Au-Tl moiety. The emission spectrum in the solid state at 77 K shows a band at 602 nm, which is attributable to a transition between orbitals that appear as a result of the metal-metal interaction. In this sense, Fenske-Hall molecular orbital calculations indicate that the ground state is the result of the mixing of the empty 6s and 6pz orbitals of gold(I) with the filled 6,v and the empty 6pz orbitals of thallium(I). In frozen solution, this derivative shows a shift of the emission to 536 nm, which has been explained by a higher aggregation of [AuT1(MTP)2] units in the solid state if compared to the situation in solution. 

The absorption spectrum of the gold-lead complex shows two bands at 290 nm (e = 28598 M-1cm-1) and 385 nm (e = 7626 M-1cm-1), while the emission spectrum in the solid state shows only one band at 752 nm at room temperature. It was assigned to a transition between orbitals that appear as a result of the gold-lead interaction. Thus Fenske-Hall molecular orbital calculations indicated that the HOMO is constituted from the 6pz orbital of gold and 6s orbital of lead and the LUMO is entirely constituted from the 6pz orbitals of these atoms. 

The assignment that the emissions arise from a LMCT [E M4] excited state with mixing of a metal-centered d sjd p) state has been substantiated by ab initio and Fenske-Hall molecular orbital calculations performed for the silver(I) clusters. These results revealed that the HOMOs of the clusters are principally Ag—E bonding orbitals, while the LUMOs are metal-localized orbitals with predominantly 55 and 5p character. Furthermore, the calculated HOMO-LUMO energy gaps decrease in the order (13a) > (13b) > (13c), consistent with the observed trend for the emission energies of the complexes. 

Xiv,585-598 x 38,599,600 Synthesized. Fenske-Hall molecular orbital calculations... 

P(CH3)3. UV-photoelectron spectroscopy and Fenske-Hall molecular orbital calculations have been used to compare the species and its derivatives with the analogous cluster (p-H)2(CO)9-OS3CCO and its derivatives. The conclusions of the study are that when bound to a metal cluster, boron can act as pseudometal atom. Apparently the orbitals of the apical boron atom are less stable than those of an apical carbon atom and thus are in a better position to interact with high-lying metal orbitals [12]. 

Nonparametrized Fenske-Hall molecular orbital calculations on the carbyne complexes fra s-[CrX(CO)4(CR)] (X = Cl, Br, or I R = Me, Ph, or NEt2) support an earlier contention that nucleophilic additions to carbyne ligands are frontier orbital controlled rather than charge controlled. Thus, the only such complex to undergo nucleophilic addition to its carbyne carbon atom, namely, trans-[CrBr(CO)4(CC6H4Me-p)], is the only one whose LUMO corresponds to a Cr-carbyne ir-antibond. 

The results of Fenske-Hall molecular orbital calculations for transition metal thiophene complexes with the ligand bound in 1)5, T l-S-bound, 1)2,1 4 t 4-S-112 and ring-opened modes have been reported335. Formation of Ti -complexes such as [Cp Ir(Ti4-2,5-diinethylthiophene)]2+ was found to be favoured by the presence of elecron-rich metal centres and also to lead to activation of the ring with respect to a ring-opening reaction via a formal oxidative addition reaction. 

Recently SO2, CpMn(C0)2(S02), CpMn(CO)3 and (Me5-Cp)Mn(C0)2(S02) have been examined by Lichtenberger and Campbell " using photoelectron spectroscopy and Fenske-Hall molecular orbital methods. While the results are in basic agreement with previous calculations the following additional conclusions were drawn relative to SO2 binding. 

The first and most influential molecular-orbital calculation on metal-alkynyl complexes is that of Kostin and Fenske, who applied the Fenske-Hall method to the complexes FeCp(C=CH)(PH3)2 and FeCp-(C=CH)(C0)2 (11). They concluded that the M-CCH bonds in these complexes are nearly pure a in character. The large energy gap (ca. 15 eV) between the occupied metal orbitals and ir (C=CH) levels severely limits the ir-accepting quality of the latter, with the total electron population for the pair of tt orbitals being 0.22 e for FeCp(C=CH)(PH3)2 and 0.14 e" for FeCp(C=CH)(CO)2. The filled ir(C=CH) orbitals, in contrast, mix extensively with the higher-lying occupied metal orbitals these filled-filled interactions result in the destabilization of the metal-based orbitals. The HOMOs of both complexes possess substantial coefficients at the alkynyl jS-carbon this was noted to be consistent with the alkynyl-localized reactivity of these complexes. 

The hemicapped cluster is an eight electron system and a Fenske-Hall type molecular orbital calculation shows that in addition to the six M—bonding electrons comparable to those in the bicapped species, an additional electron pair occupies an orbital which is weakly M—M bonding, in agreement with the observed shortening of the W—W bond length. 

Figure 50. Molecular orbital energy diagrams resulting from a Fenske-Hall calculation on Movi(S2C2H2)3 [adapted from (410)] and DFT calculations [unpublished work of the authors] on Movi(S2C2H2)3 and MoIY(S2C2H2)3. Occupied MOs are in bold.

FIGURE 1. Molecular orbital diagram for (CO)3Co( -C3H3) based on Fenske-Hall calculations ... 

For alkynes bonded to higher nuclearity clusters no overall molecular orbital treatment encompassing all the variations in geometry has appeared yet. However, there are a small number of examples of specific alkyne-substituted clusters which have been analyzed by one type of molecular orbital treatment or another, and a number of these have been mentioned in Section III,G because photoelectron spectroscopy has been used as an aid to assignments. CNDO calculations (397) on Fe3(CO)9(EtCCEt) (390) and M3(CO)9(/i-H)(CCR) (M = Ru, Os) (391) and Fenske-Hall calculations (398) on Co4(CO)10(PhCCH) (389) indicate that there is net back donation into alkyne n orbitals, which increases as the number of metal atoms to which the ligand is bonded increases. The normally accepted view of considering the interaction... 

F. Fenske. We demonstrate for transition metal complexes that the non-empirical Fenske-Hall (FH) approach provides qualitative results that are quite similar to the more rigorous treatment given by density functional theory (DFT) and are quite different from Hartree-Fock-Roothaan (HFR) calculations which have no electron correlation. For example, the highest occupied molecular orbital of ferrocene is metal based for both DFT and FH while it is ligand (cyclopentadienyl) based for HFR. In the doublet (S = 1/2) cluster, Cp2Ni2(pi-S)2(MnCO)3, the unpaired electron is delocalized over the complex in agreement with the DFT and FH results, but localized on Mn in the HFR calculation. A brief description of the theory of FH calculations is used to rationalize the origin of its similarity to DFT. 

Early hints that Fenske-Hall (FH) calculations had some advantage over full HFR calculations came from comparisons of the FH molecular orbital energies with the experimental ionization energies from gas-phase ultraviolet photoelectron spectroscopy [2,7,8], where the order of MOs paralleled the order of states from the PES better for FH calculations than for HFR calculations. In other words, Koopmans theorem [9] seemed to work better for Fenske-Hall than for HFR calculations. 

Some more rigorous, non-parametric calculations also confirm the validity of the isolobal principle. Fenske-Hall LCAO-MO-SCF calculations of the structure of B5H9 and some of its ferroborane derivatives, i.e. l-Fe(CO)3B4Hs, 2-Fe(CO)3B4Hs and l,2-[Fe(CO)3]2B3H3 have been completed. A summary of a qualitative description of the properties of frontier molecular orbitals in... 

Molecular orbital (MO) theory includes a series of quantum mechanical methods for describing the behavior of electrons in molecules by combining the familiar s, p, d, and / atomic orbitals (AOs) of the individual atoms to form MOs that extend over the molecule as a whole. The accuracy of the calculations critically depends on the way the interactions between the electrons (electron correlation) are handled. More exact treatments generally require more computer time, so the problem is to find methods that give acceptable accuracy for systems of chemical interest without excessive use of computer time. For many years, the extended Hiickel (EH) method was widely used in organometallic chemistry, largely thanks to the exceptionally insightful contributions of Roald Hoffmann. The EH method allowed structural and reactivity trends to be discussed in terms of the interactions of specific molecular orbitals. Fenske-Hall methods also proved very useful in this period. ... 

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