Qualitative MO Research Articles

D-orbital energy levels in planar [MIIF4]2-, [MII(NH3)4]2+ and [MII(CN)4]2- complexes: the nature of M-L π bonding and the implications for ligand field theory.

Qualitative MO theory predicts degenerate dπ orbitals for planar coordination complexes with formally σ-only ligands and the splitting energy, ΔEπ = E(dxy) - E(dxz,dyz), should be zero. For π-donor ligands, ΔEπ should be positive (dxy > dxz,yz) while for π-acceptors, ΔEπ should be negative (dxy < dxz,yz). However, experimental d-d spectra, ab initio ligand field theory (AI LFT) and crystal field theory for σ-only [M(NH3)4]2+ complexes give pronounced dπ splittings with ΔEπ around +2500 cm-1 for first-row, divalent metal ions. AI LFT further suggests ΔEπ values around +4500 cm-1 for [MF4]2- and +1000 cm-1 for [M(CN)4]2- species. The origins of these dπ orbital splittings can be traced to the effects of the ligand field potential surrounding the metal centre which includes not only the intrinsic metal-ligand π bonding but also substantial contributions from the 'void' regions above and below the molecular plane. The π component of the 'void cell' potentials increases ΔEπ which, if not explicitly taken into account, artificially enhances the apparent π-donor strength of the ligands. With the inclusion of void cell π interactions, even though the AI LFT d orbital sequence always places dxz,yz below dxy, the ligand field analysis provides a chemically-reasonable description of the M-L π interactions with cyanide being a weak π acceptor, ammonia being π-neutral and fluoride being a strong π donor. In the case of [Ni(CN)4]2-, ligand field calculations further show that, contrary to the recent claims of Oppenheim et al. (Inorg. Chem., 2019, 58, 15202) the sequence of the many-electron excited states is not a definitive guide to the underlying order of one-electron d orbital energies and that the observed sequence of nA2g > nEg > nB1g, n = 1 or 3, does not guarantee a d-orbital sequence of dxy < dxz,yz < dz2.

Valence Virtual Orbitals: An Unambiguous ab Initio Quantification of the LUMO Concept.

Many chemical concepts hinge on the notion of an orbital called the lowest unoccupied molecular orbital, or LUMO. This hypothetical orbital and the much more concrete highest occupied molecular orbital (HOMO) constitute the two "frontier orbitals", which rationalize a great deal of chemistry. A viable LUMO candidate should have a sensible energy value, a realistic shape with amplitude on those atoms where electron attachment or reduction or excitation processes occur, and often an antibonding correspondence to one of the highest occupied MOs. Unfortunately, today's quantum chemistry calculations do not yield useful empty orbitals. Instead, the empty canonical orbitals form a large sea of orbitals, where the interesting valence antibonds are scrambled with the basis set's polarization and diffuse augmentations. The LUMO is thus lost within a continuum associated with a detached electron, as well as many Rydberg excited states. A suitable alternative to the canonical orbitals is proposed, namely, the valence virtual orbitals. VVOs are found by a simple algorithm based on singular value decomposition, which allows for the extraction of all valence-like orbitals from the large empty canonical orbital space. VVOs are found to be nearly independent of the working basis set. The utility of VVOs is demonstrated for construction of qualitative MO diagrams, for prediction of valence excited states, and as starting orbitals for more sophisticated calculations. This suggests that VVOs are a suitable realization of the LUMO, LUMO + 1, ... VVO generation requires no expert knowledge, as the number of VVOs sought is found by counting s-block atoms as having only a valence s orbital, transition metals as having valence s and d, and main group atoms as being valence s and p elements. Closed shell, open shell, or multireference wave functions and elements up to xenon may be used in the present program.

Gerhard Quinkert (1927-2015).

Gerhard Quinkert (1927-2015).

P3F92–: An All-Pseudo-π* 2π-Aromatic

A qualitative MO analysis suggests (PH3)3(2-) as a candidate for an all-pseudo-π* 2π-aromatic; however computational studies rule out its existence. Fluorine substitution which increases the contribution of p orbitals on P in the pseudo-π* MO makes (PF3)3(2-) a minimum and an aromatic. The 2π aromaticity arising from the bonding combination of the three pseudo-π* fragment MOs is comparable to that in C3O3(2-) and is another example for the analogy between CO and PF3. The dianion (PF3)3(2-) forms the first example of a three-membered ring with all the vertices constituted by pentacoordinate phosphorus. The ability of PF3 to form the all-pseudo-π* 2π-aromatic system is not shared by the heavier analogues, AsF3 and SbF3.

Howard E. Zimmerman (1926-2012)

Howard E. Zimmerman (1926-2012)

Conformational and Bonding Analysis of C&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;H&amp;lt;sub&amp;gt;4&amp;lt;/sub&amp;gt;&amp;lt;sup&amp;gt;2+&amp;lt;/sup&amp;gt;

In this report, different models of bonding and structure such as Lewis, VSEPR, Ligand close packing (LCP), VB, qualitative MO and QTAIM have been applied to analyze the Bonds and structures of two equilibrium geometries (planar D2h and perpendicular D2d) of C2H42+. The geometries were optimized at near RHF and MP2 limit using ccpVTZ basis set. While the above bonding models are successfully applied for predicting the low energy isomers of molecules, prior to solving the Schr?dinger equation, it is shown that the cited models fail in predicting the existence of perpendicular, D2d form of C2H42+. In this regard the interpretations of significant energetic stabilization of D2d form over planar isomer has also been revisited. This is attributed to the hidden effect of the Pauli Exclusion principle.

Diamagnetic Group 6 Tetrakis(di-tert-butylketimido)metal(IV) Complexes

The addition of 4 equiv of LiN=C-t-Bu(2) to CrCl(3), MoCl(5), and WCl(6) in diethyl ether produced the complexes M(N=C-t-Bu(2))(4) (M = Cr, Mo, W). Single-crystal X-ray diffraction studies revealed that the molecules have flattened tetrahedral geometries with virtual D(2d) symmetry in the solid state. (1)H and (13)C NMR spectra indicated that the complexes are diamagnetic, and a qualitative MO analysis showed that the orthogonal π-donor and -acceptor orbitals of the ketimide ligand cooperatively split the d(xy) and d(z2) orbitals sufficiently to allow spin pairing in the d(xy) orbital. A more sophisticated quantum-mechanical analysis of Cr(N=C-t-Bu(2))(4) using density functional/molecular mechanics methods confirmed the qualitative analysis by showing that the singlet state is 27 kcal/mol more stable than the triplet state.

Comparative Analysis of the Multicenter, Long Bond in [TCNE]·−and Phenalenyl Radical Dimers: A Unified Description of Multicenter, Long Bonds

The nature of the multicenter, long bond in neutral phenalenyl dimers is analyzed in detail and compared to the multicenter, long bond in [TCNE](2)(2-). These dimers are prototypes of multicenter, long bond in dimers of neutral and anion radicals. This was done by examining the number of electrons (m) and atomic centers (c) involved in the long bond for these dimers, as well as identifying the dominant attractive components of their interaction energy (SOMO-SOMO bonding, dispersion, and the sum of the exchange-repulsion and electrostatic components) in accord with Pauling's focus on total bond energies. The long bond in [TCNE](2)(2-) is a 2e(-)/4c bond, the electrostatic component is repulsive, and the dominant attractive component is the dispersion component (-27.7 kcal/mol), about two times larger than the bonding component. In phenalenyl dimers the dispersion component (-31.7 kcal/mol) is about 2.5 times stronger (than the SOMO-SOMO bonding component; hence, the multicenter, long bond in these dimers is closer to a van der Waals bond than to a covalent bond. Consequently, it possesses a two-electrons/fourteen center 2e(-)/14c bond, rather than the 2e(-)/12c bond suggested by the SOMO-SOMO bonding component. The covalent-like properties in phenalenyl dimers result from the dominant dispersion component that enable the fragments to approach each other so that their SOMOs overlap and produce a qualitative MO diagram identical to that found in conventional covalent bonds.

An overview of the electronic structure in trigonal bipyramidal clusters of main elements or mixed with transition metals

Equatorial/apical bond repartitioning in TBP clusters, formed by main group elements only (e.g., B5H5 2−, B3H3N2, etc.) or mixed with metal atoms (e.g., [(L2M)3S2] n , [(L3M)3S2] n , [(CpM)3S2] n ), is critically analyzed from the horizontal comparison of the experimental structures and in terms of basic MO concepts. The ideas are double-checked through specific DFT calculations or existing ab initio results. Based on the Wade’s rules for closo-clusters, the five vertices systems are normally characterized by six skeletal electron pairs. In the main group clusters, the electron delocalization at the equatorial edges depends on the electronegativity of the apical groups and for the Beq–Beq bonds an inverse relationship between bond strength and bond length is remarked. In [(L2M)3S2] n compounds with a total electron count (TEC) of 48, the six bonding electron pairs localize at the apical M–S bonds. In [(L3M)3S2] n or [(CpM)3S2] n , also with TEC = 48, the effective atomic number rule predicts three single M–M single bonds besides the six M–S apical ones. In actuality, only partial M–M bonding can be considered due to the intermediation of the capping sulphur atoms, that help shifting the antibonding character of populated radial levels with that of the vacant tangential ones (bonding). The qualitative MO arguments are supported by the topological nature of the calculated DFT wave functions. Moreover, the MO nature of three lowest LUMOs for 48e− species help to rationalize experimental structural trends observed for the addition of up to five electrons.

Parallel disulfido bridges in bi- and poly-nuclear transition metal compounds: Bonding flexibility induced by redox chemistry

We recently studied an elongated S 4 2 - rectangle bridging transition metals such as Ir, Rh, Cu, or Fe and found that its formation is related to the oxidation of parallel S 2 2 - molecules. The removal of two electrons can occur either externally or by an internal metal–ligand redox process that implies depopulation of the high-lying S 4 σ ∗ MO and population of a lower metal level. Thus, the interaction may be described as metal back-donation. However, sufficiently electropositive metals can more easily reach higher oxidation states and this reverses the direction of the two-electron interaction. In such a case, the system may be viewed as formed by two uncoupled disulfides donating an additional electron pair to the metals. In this paper, we analyze the aspects of the 2 S 2 2 - / S 4 2 - dichotomy through DFT calculations and qualitative MO analysis of the known bimetallic MS 4M cores having either triple-decker (TD) or chair-type structures. We correlate the extent of the disulfide coupling with the nature (electronegativity) of the terminal metal fragments (the metals range from Group IV to X) beside their electron configuration. We find that the formation of an S 4 2 - unit is favored by metals which cannot stabilize high oxidation states ( e.g. Fe(IV) or Cu(III)), whereas the two S 2 2 - units remain substantially uncoupled with early transition metal in high oxidation states ( e.g. Ti(IV)).

The electronic structure and spectra of spin-triplet ground state bis(biuretato)cobalt(iii) coordination compounds

The planar coordination compounds of cobalt(III) with bis(biuretato) ligands are highly unusual due to their intermediate spin triplet ground state. Density functional theory (DFT) and time-dependent DFT have been applied in a study of the structure and electronic spectroscopy of this type of coordination compounds. The investigations included prediction and spectroscopic measurements of the absorption and circular dichroism (CD), as well as an experimental study of the magnetic CD. The results obtained by TD-DFT were in excellent agreement with the observed spectral features, both regarding the d-d and the charge transfer regions. There was noted a systematic blue-shift of the TD-DFT results compared to experiment, corresponding to an offset of ca. 0.5 microm(-1) and a scaling factor of 1.25 for the transition energies. The DFT results are rationalized in terms of a qualitative MO analysis.

Multielectron photoreduction of a bridged ruthenium dimer, [(phen)2Ru(tatpp)Ru(phen)2][PF6]4: aqueous reactivity and chemical and spectroelectrochemical identification of the photoproducts.

The dinuclear ruthenium(II) complex [(phen)(2)Ru(tatpp)Ru(phen)(2)][PF(6)](4) (P) (where phen is 1,10-phenanthroline and tatpp is 9,11,20,22-tetraazatetrapyrido[3,2-a:2'3'-c:3' ',2' '-l:2' ",3' "]pentacene) is shown to accept up to four electrons and two protons on the central tatpp bridging ligand via a combination of stoichiometric chemical reductions and protonations and spectroelectrochemistry (SEC) in acetonitrile. The absorption spectra of seven distinct species related by reduction and/or protonation of the central tatpp ligand were obtained and the two sequential photoproducts obtained from visible irradiation of P in acetonitrile (with 0.25 M triethylamine (TEA)) thus identified as P(-) (singly reduced, nonprotonated P) and HP(-) (doubly reduced, monoprotonated P), respectively. Importantly, the photochemical activity is maintained in mixed water-acetonitrile (1:4) solutions under basic conditions, and the protonation state of the photoproducts is readily controlled by varying the solution pH between 8 and 12. Absorption spectra obtained by SEC under similar solvent conditions were virtually identical to those obtained photochemically, and thus the doubly reduced photoproducts were identified as P(2)(-) (pH 12), HP(-) (pH 10), and H(2)()P (pH 8). This last photoproduct, H(2)()P, is particularly promising with respect to solar hydrogen production in that it can be produced in the presence of water and its dehydrogenation under appropriate conditions could yield H(2) and regenerate P. A qualitative MO diagram is presented as a framework for understanding the observed optical transitions as a function of oxidation and protonation state.

DFT study of the geometry and energy order of the low singlet and triplet states of [d4-eta5-CpMo(CO)2X] 16-electron complexes (X = halogen, CN, H, and CH3).

DFT methods have been used to investigate the dependence of the geometry and energy order of the low energy states of [d(4)-eta(5)-CpMo(CO)(2)X] 16-electron complexes on X (X = halogen, CN, H and CH(3)). The calculations use a double-zeta plus polarization valence basis set on all atoms and utilize relativistic ECPs on Mo and the heavier halogens. In every case two singlet and two triplet electronic states have been considered and minimized at the B3LYP level. For X = Cl, additional calculations were carried out at the BPW91, CCSD(T), and CASSCF levels. In the C(s) point group, the singlet states are from the (1a')(2)(1a'')(2) and (1a')(2)(2a')(2) configurations of the valence d(4) electrons of the metal, and are denoted (1)A'-a and (1)A'-b, respectively. The triplet species are for the lowest (3)A'' and (3)A' states from the (1a')(2)(2a')(1)(1a'')(1) and (1a'')(2)(1a')(1)(2a')(1) d(4) configurations. For all substituents, the geometry of both the singlet and triplet states is found to distort substantially from the uniform 3-leg piano-stool structural motif, a behavior that can be related to Jahn-Teller effects. When X is a halogen or a methyl, (1)A'-b is predicted to be lower than (1)A'-a, while the reverse order of these two singlet states is calculated for X = H and CN. For all substituents (3)A' is substantially higher than (3)A''. In turn, the energy of (3)A'' is calculated to be comparable to the lower singlet state of each complex. Attempts are made to rationalize some of these results using qualitative MO theory.

Rebuttal to the Bickelhaupt–Baerends Case for Steric Repulsion Causing the Staggered Conformation of Ethane

Two tenets of qualitative MO theory suggest contradictory explanations of ethane torsional barriers, but only one stands up to rigorous examination (see energy level diagrams). Bickelhaupt and Baerends' defense of the neo-steric “four-electron destabilization” concept (right) is shown to be as illusory as its predecessors.

Structural and electronic features of Group 8 metal complexes containing one α-diiminobenzene chelate ligand

Known complexes of general formula L n M( diim), where diim=C 6H 4(NH) 2- o, α-diiminobenzene, n=3, 4 and M is a metal of Group 8 (Ru(II), in particular) are analyzed in terms of their electronic structure and associated energetics. The newly synthesized compound [(CO) 2(PPh 3)BrRu(C 6H 4(NH) 2- o)]Br, 1, is a new member of the category. This is confirmed by the X-ray structure of 1 that is presented together with electrochemical measurements and other spectroscopic characterization. At variance with the isoelectronic L 4M( o-phenylenediamido) compounds (M=Group 6 metal) that are affected by structural deformations, 1 and similar complexes have a regular pseudo-octahedral structure. Density functional theory calculations and qualitative MO arguments provide an explanation for the different electronic trends as well as for the diimino/diamido dichotomy of the non-innocent chelate ligand. The latter is affected, not only by the nature of the metal (energy of d orbitals), but also by the surrounding environment (three or four coligands). Moreover, the calculations allow to outline the stability trends for the loss of one coligand from L 4M( diim) systems when the Ru(II) complexes are chemically or electrochemically reduced.

Synthesis, structure and magnetic properties of the S=1/2, one-dimensional antiferromagnet, Y 5Re 2O 12

Single crystals of Y 5Re 2O 12 have been grown, and the crystal structure has been determined by X-ray diffraction. This compound crystallizes in space group C2/ m with cell dimensions of a=12.4081(10) Å b=5.6604(5) Å, c=7.4951(6) Å, β=107.837(3)°, Z=2. The final refinement led to R1=0.0238, WR2=0.0459 for 1053 observed reflections with F>4 σ( F 0). Edge-sharing ReO 6 octahedra form infinite linear [ReO 2O 4/2] n chains along the b direction with alternating short and long Re–Re distances. Three crystallographically independent yttrium atoms surround O2 to form OY 4 tetrahedra, which share edges and corners in the ab plane to form a two-dimensional Y 5O 4 network which separates the [ReO 2O 4/2] n magnetic chains. This compound is therefore isostructural with the series Ln 5Re 2O 12 Ln=Gd–Lu, which have been known since 1969. The average Re oxidation state is +4.5 in the chains and a reasonable, if qualitative MO scheme results in one unpaired electron per Re dimer. Consistent with this, magnetic susceptibility data can be fitted to the one-dimensional antiferromagnetic Heisenberg model with S=1/2 and parameters J intra/ k=−89(1) K, g=2.15(4) and χ(TIP)=5(1)×10 −4 emu/mol. There is no sign of long-range magnetic order down to 2 K. These results are contrasted with those for the isostructural Y 5Mo 2O 12.

Does back-bonding involve bonding orbitals in boryl complexes? A theoretical DFT study.

Theoretical calculations at the DFT (B3LYP) level have been undertaken on tris- and bis(boryl) complexes. Two model d(6) complexes [Rh(PH(3))(3)(BX(2))(3) and Rh(PH(3))(4)(BX(2))(2)(+), X = OH and H] have been studied. In the model tris(boryl) complex (X = OH) we find a fac structure as a minimum, in accordance with the experimental data. The mer geometries are found to be higher in energy. Analysis of the energetic ordering in mer isomers shows that back-bonding in these complexes involves a bonding Rh-B orbital (and not a d-block orbital as usual). This surprising behavior is rationalized through a qualitative MO analysis and quantitative NBO analysis. Results on the bis(boryl) complex confirm the preceding analysis. Full optimization of unsubstituted (X = H) complexes leads to structures in which the BH(2) moieties are coupled. In the optimal geometry of the bis(boryl) complex, the B(2)H(4) ligand resembles the transition state of the C(2v)-->D(2d) interconversion of the isolated B(2)H(4) species. In the tris(boryl) complex, we find a B(3)H(6) ligand in which the B(3) atoms define an isosceles triangle with one hydrogen bridging the shorter B-B bond.

Structural and Electronic Features of o-Phenylenediamido Complexes of Group 6 Metals in Different Oxidation States

Reported complexes of general formula L 4 M(phenylenediamido-o), where M is a metal of group 6 in various oxidation states (VI, IV, II and 0), are analyzed. The possible structural deviations from the most symmetric pseudo-octahedral structure (the one with the chelate in the equatorial plane) are evaluated, case by case, in view of their electronic origin. The analysis is based on systematic DFT calculations and their qualitative MO interpretation based on perturbation theory concepts.

Do Divalent [{HC(CR′NR′′)2}E] Compounds Contain E(I) or E(III) (E = B, Al, Ga, In)? On the Correspondence of Formal Oxidation Numbers, Lewis Structures, and Reactivity

Very recently, carbene-analogous aluminum and gallium compounds have been obtained in beautiful synthetic work giving rise to interesting theoretical questions in the framework of qualitative MO theory. We analyze the concept of oxidation numbers and the stabilities of these [{HC(CR′NR′′)2}E] compounds, 1(E), with E being boron, aluminum, gallium, and indium. Population analyses and the electron localization function are used as analytical tools for the elucidation of the electronic density distribution. Singlet-triplet splitting energies, and model reactions probing donor and acceptor properties of the atom E, yield criteria for the reactivity of the cyclic molecules. It is demonstrated that a unique class of Lewis structures can be selected from the large number of chemically reasonable Lewis structures in order to achieve a sufficiently good mapping of the quantum chemical results on simple chemical concepts. The analysis yields that 1(E), where E = In, is expected to have similar properties as the experimentally known compounds 1(Al) and 1(Ga), while the boron homologue is expected to be highly reactive, such that its synthesis appears to be difficult. (© Wiley-VCH Verlag GmbH, 69451 Weinheim, Germany, 2002)

Reaction of [Pt{Fe(CO) 3(NO)} 2(PhCN) 2] with diphenyl(2-pyridyl)phosphine selenide. Crystal structure of [(CO) 3Fe(μ 3-Se){Pt(CO)P(2-C 5H 4N)Ph 2} 2] and its theoretical study

The reaction between the linear trinuclear complex [Pt{Fe(CO) 3(NO)} 2(PhCN) 2] and Ph 2(2-C 5H 4N)PSe led to the isolation and characterization of the 46-electron cluster [(CO) 3Fe(μ 3-Se){Pt(CO)P(2-C 5H 4N)Ph 2} 2] ( 1), whose structure has been determined by X-ray diffraction methods. The cluster typology, which consists of an open triangle PtFePt capped by a μ 3-Se atom, is rather rare. The chemical bonding in 1 and in similar systems has been analyzed through density functional theory (DFT) and qualitative MO approaches. A strict analogy with the well understood L 2M(μ-acetylene)ML 2 systems is invoked by considering 1 as formed by the (CO) 3FeSe tetrahedral unit stabilized by sidewise interactions of the triple bond with two d 10-L 2M fragments. Otherwise, the 18-electron (CO) 3FeSe monomer is unstable as an isolate molecule. This is confirmed by our DFT calculations that indicate how the well characterized dimer (CO) 3Fe(μ-Se 2)Fe(CO) 3 lies as much as, approximately, 58 kcal mol −1 deeper in energy. Finally, by considering an analogy with [L 2M(μ-dichalcogen)ML 2] 0, +2 redox systems (M=Pd, Pt), reduction of 1 to a dianion has been hypothesized and the structure of the latter has been tentatively explored by DFT calculations.