Figure 1 Setting the charge in HF 2 -.

Transcription

1 Self-Stud Problems / Eam Preparation compute the orbitals for (linear) -, draw and annotate a MO diagram consistent with the MOs ou observe o if ou have problems setting up the calculation, select Be and create a molecule of Be, then replace the Be with and replace the s with s. o don t forget to add the charge, put - in the charge bo on the methods page in calculation setup, igure igure Setting the charge in -. o the deep saos are around -4.6 hartree, which is ver deep, these orbitals are so contracted that the have the same radius as the van der Waals radius given the atoms b gaussview the visualisation program, the will be ignored as we want to draw a valence MO diagram o the ke orbitals are the valence orbitals emploing AOs from the principle quantum number n= shell, ie the s and p AOs of the atom, appear at above -.0 hartree o the computed MOs are depicted in igure. o the dividing line between the OMO and LUMO is shown. o degenerate orbitals are easil identified b their identical energies, and orbital shapes that differ onl b a rotation around the nuclear bond ais o to build this MO diagram we start with the fragment, but with the orbitals well separated and therefor with ver little overlap, igure 3 o the small overlap means there is ver little stabilisation or destabilisation on interaction. o notice that from our calculation that MO3 and MO4 lie much deeper ( hartree) than the orbitals in the OMO region ( hartree) this is due to the large s-p gap for elements on the right hand side of the periodic table. o the large s-p gap means that the aao will interact with - the p AO rather than the s AOs which lie too deep in igure computed MOs for energ, this is confirmed b eamining MO5 of igure. is ver electronegative, thus the p AOs of will lie lower in energ than the s AO of.

2 AO contributions are equal because the fragments orbitals are degenerate p the MO splitting is etremel small becuase the l atoms are far apart p these orbitals should not touch... the atoms are two far apart. lies to the right of the PT, therefor the s-p splitting is ver large s s the MO splitting is etremel small becuase the atoms are far apart, and these are saos (which are dense and do not etend far from the nucleus) igure 3 MO diagram to form the fragment orbitals for --- in 3s e 6e 5e igure 4 MO diagram to for o igure 4 shows the MO diagram for - side b side with the computed MOs. o notice how MO looks more like our LUMO from the qualitative MO diagram. The computed LUMO differs from that we might epect, this is not unusual, unoccupied orbitals are often more diffuse than epected and can energ order differentl as well. This LUMO looks to be a combination of 3s AOs from the - fragment.

3 using the formula which allows the energ of the fragment orbitals to differ, (also assuming S ab =0) what happens to the MO energ levels as gets larger? E = b a E = ab o the splitting energ is proportional to ab squared divided b the energ difference between the two AOs, as increases the stabilisation and destabilisation energ decrease until it is essentiall ero (ionic bonding situation). As this occurs the O contributions will start out essentiall even and then become increasingl localised on one fragment until the energ gap is ver large, at which point electron transfer occurs from one O to the other. E = ab energ igure 5 effect of increasing when is S ab likel to be small? o S ab is the orbital overlap it is highl distance dependents and will be ero if the orbitals ψ a and ψ b are "far apart" in realit this means, for first row atoms, if the atoms are more than one bond length apart. owever, if the orbitals are diffuse the etend into space further and there can be through space overlap. o S ab will also be ero if the orbitals are orthogonal Show that c= when S ab =0 c = (± S ab ) if S ab c = (± 0) = 3

4 (advanced for eperts) irst, solve the secular determinant for 3 overlapping p orbitals on a 3- atom chain (energies and wavefunctions). Draw the relevant MOs based on our mathematical equations. Then, draw a MO diagram (using the processes described in this course) using two p AOs as one fragment and a single p AO as the other fragment. inall, check our answers b computing the MOs of the allene anion ( 5 ). ompare the maths, MO theor and computational results. basis set 3pAOs α E β β 3 β α E β 3 β 3 β 3 α 3 E = α E β 0 0 igure 6 allene anion paos α E β 0 β α E β 0 β α E ( i i) (i 0 i) 0(i 0 i ) 3 ( ) or = ± and,± normalised = = = 0 0 = 0 = = = summar = = = 0 = 0 = = = = 4 = = summar = = = 4

5 = 0 = 0 = = = = 4 = = summar = = = () σ v () E σ v () σ v () - - a through space antibonding σ v () b a b a pao reference b b through space bonding E σ v () σ v () - - b igure 7 MO diagram o note that the smmetr is v and the principle ais must be the -ais, therefore the out-ofplane pao are actuall p AOs o in addition the orbital coefficients predicted b MO theor are not eactl the same as those predicted via ückel theor o below are the computed OMO-, OMO and OMO4 for the allene anion. 5