Implications of molecular orbital symmetries and energies for the electron delocalization of inorganic clusters.

Isostructural clusters exhibit contrasting magnetic properties when the number of electrons differs. Surprisingly, the same is true even for isoelectronic cages (e.g. O(h) B6H6(2-) is diatropic, whereas O(h) Si6(2-) is paratropic) or for those with different substitutents (e.g. T(d) B4H4 is paratropic, whereas T(d) B4F4 is diatropic). Indeed, the total nucleus-independent chemical shift (NICS) values, based on shieldings computed at cluster centers, may range considerably in magnitude and even change from diatropic (up-field shifted) to paratropic (down-field shifted). Similarly, individual dissected canonical molecular orbital contributions to the total NICS values computed at the "gauge-including atomic orbitals" (GIAO) level vary greatly. This contrasting behavior arises from molecular orbital energy differences, from the extent of orbital overlap, as well as from symmetry-based selection rules derived from group theory. Differences in magnetic properties may originate from the symmetry of the orbitals; specifically from the forbidden nature of the highest occupied molecular orbital --> lowest unoccupied molecular orbital (HOMO --> LUMO) electronic excitation weighted by the occupied-unoccupied orbital energy difference. Thus, HOMO-NICS values are generally highly paratropic if the HOMO --> LUMO rotational transition is allowed by symmetry selection rules.     

Relativistic ring currents in metallabenzenes: an analysis in terms of contributions of localised orbitals

Ring currents calculated in the ipsocentric CTOCD-DZ formalism are presented for four representative metallabenzenes, compounds in which a benzene CH group is formally replaced by a transition metal atom with ligands. Aromaticity is probed using ring currents computed using non-relativistic and relativistic orbitals (derived with relativistic effective core potentials or ZORA). Maps computed at different levels of relativistic theory turn out to be similar, showing that orbital nodal character is the main determinant of ring current. Diatropic/paratropic global ring currents in these compounds, and also circulations localised on the metal centre, are interpreted in terms of contributions of localised π-type orbitals and metal d-orbitals, respectively. All four considered metallabenzenes should be regarded as 6π electron species, despite the fact that three support diatropic ('aromatic') ring currents and one a paratropic ('anti-aromatic') current. The current-density maps determine the correct way to count electrons in these species: differential occupation of d-orbitals of formal π-symmetry contributes to circulation on the metal centre, but not around the benzenoid ring. The overall trend from strongly diatropic to weakly paratropic ring currents along the series 1 to 4 is explained by the increasing strength of interaction between formally non-bonding orbitals on the metal centre and C(5)H(5) moiety, which together make up the six-membered ring.     

Aromaticity of ortho and meta 8-Cycloparaphenylene and Their Dications: Induced Magnetic Field Analysis with Localized and Delocalized Orbitals in Strained Nanohoops

Dications of cycloparaphenyles ([n]CPPs) are known to exhibit in-plane global aromaticity, contained in a nanobelt structure. Recently synthesized ortho and meta isomers of [n]CPPs break the radial symmetry of π structure incorporating perpendicular oriented π orbitals. Herein we set to explore the aromaticity of neutral and dicationic ortho and meta isomers of [8]CPP by dissecting the induced magnetic field to contributions of the twofold radial/perpendicular π system using delocalized canonical molecular orbitals (CMO), and introducing the natural localized molecular orbitals (NLMO) analysis with DFT methods. The dications sustain a reduced global aromatic character of the radial π system under a perpendicular orientation of the external field which declines from ortho to meta isomer and reinforces local aromaticity of ortho ring while it destroys aromaticity of meta ring. Aromaticity variations are determined by symmetry governed rotational excitations of frontier π orbitals. The parallel orientation reveals a substantial reduction of local aromaticity verified with NICS_π analysis and electron delocalization indices.     

Magnetic euripi in corannulene

Ab initio current densities induced by an external magnetic field have been computed for corannulene dianion, dication, and tetraanion. The pi-ring currents are found to be large with respect to benzene and to undergo remarkable changes in response to variations in the oxidation state. According to the results obtained here, the three corannulene ions plus the neutral species constitute a very special set that spans all of the possible patterns of rim and hub circulations: diatropic/hub-paratropic/rim (the dianion), paratropic/hub-paratropic/rim (the dication, assuming conformationally averaged current density), diatropic/hub-diatropic/rim (the tetraanion), and paratropic/hub-diatropic/rim (the neutral, as already reported by other authors). Orbital contributions and their breakdown into explicit contributions from virtual excitations have been analyzed. It is shown that the dianion and dication are both (2p) systems characterized by a single highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) rotationally allowed transition. For the dianion, this transition is responsible not only for the outer paratropic circulation but also for the inner diatropic circulation, a behavior that requires an extension of the few electron model based on orbital contributions to be fully rationalized. For the dication, the HOMO-LUMO transition provides a paratropic circulation localized on one indene subunit. However, because of the fast exchange of conformers, it is sensible to calculate an averaged current density field, which is characterized by con-rotating paratropic inner and outer ring currents. For the tetraanion, the calculated current pattern is in agreement with a previous indication, while the orbital analysis reveals that the HOMO and the HOMO - 1 contribute to both inner and outer circulations. Despite the small 6-31G** basis set employed to calculate current densities and magnetic properties, a satisfactory agreement between computed and available experimental (1)H and (13)C chemical shifts is found, providing a firm basis for the above conclusions. Remarkably, the "diamagnetic" corannulene dianion observed in NMR at low temperature is predicted to be a paramagnetic closed-shell species.     

Diamagnetic and paramagnetic ring currents in expanded porphyrins

Ipsocentric current density maps are computed at the coupled Hartree-Fock level in the 6-31G** basis set for the planar C(2v) B3LYP geometries of the expanded porphyrins, sapphyrin and orangarin. Both give clearly dominant global macrocyclic ring currents, but with opposite senses of circulation: in 22[small pi] sapphyrin, a diatropic current runs, with some bifurcation, around the conventional 22-centre delocalisation pathway; in 20[small pi] orangarin, a paratropic current runs around the inner 17-atom pathway. In agreement with the annulene analogy for these macrocycles, analysis of orbital contributions shows that in each case topology, energy and symmetry of the frontier orbitals together determine the macrocyclic ring current. In sapphryrin, 4-electron diamagnetism (aromaticity) arises from translationally allowed HOMO-LUMO excitations as in benzene itself; in orangarin, 2-electron paramagnetism (antiaromaticity) arises from rotationally allowed HOMO-LUMO excitations as in planarised cyclooctatetraene. The active orbitals invoked in the explanation of ring currents are those involved in the longstanding four-orbital model of porphyrin electronic spectra.     

Structure of the T1-state wave function of linear polyenes

Configuration interaction singles (CIS) calculations of the planar T₁ state of hexatriene, octatetraene, decapentaene, and dodecahexaene showed that the (HOMO−i)→(LUMO+i) type single excitations contribute significantly. This is attributed to the similarity of the HOMO, LUMO, and HOMO−i, LUMO+i overlap densities which stem from nodal properties of the π molecular orbitals. CASSCF calculations for hexatriene and octatetraene also showed remarkable contributions of the (HOMO−i)→(LUMO+i) type singly excited configurations. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 67: 101–106, 1998     

Chemisorption of CO on Pd(100): An lcgto-lsd cluster study

LCGTO-LSD model potential calculations have been performed for CO interacting with two-, four-, and eight-atom clusters of Pd, chosen to model the bridge site of the (100) surface. The geometry and vibrational frequencies are not very sensitive to the cluster size. For Pd₈ + CO we obtain d_C—O = 1.18 Å (1.13 ± 0.1 exp.), d_Pd—C = 1.87 Å (1.93 ± 0.07 exp.), and (uncoupled) estimates for ω_C—O = 1828 cm^?1 (1895 exp.) and ω_Pd—CO = 454 cm^?1 (339 exp.) Binding energies of 4.8, 3.8, and 2.6 eV are calculated, respectively, for Pd₂ + CO, Pd₄ + CO, and Pd₈ + CO which may be compared with the experimental initial heat of adsorption of 1.6 eV. Ionization potentials for CO-derived levels are in excellent agreement with experiment (relative to ?_F: 4σ (-11.0 eV, -11.2 exp.); 5σ (-8.0, ?8.2 exp.); 1π [?7.5 (b₁), ?7.3 (b₂), ?7.5 exp.]). The main negative ion states of 2π* character are calculated at 2.8 eV (b₁) and 2.7 eV (b₂) above E_F. Other states with appreciable 2π* character are found near 5 eV. These may be compared with inverse photoemission results which show a broad peak centered at 4.8 eV. Interactions of the 4σ, 5σ, 1π, and 2π* orbitals of CO with the metal are discussed. The 4σ and 5σ levels are highly mixed, each receiving appreciable contributions from the 4σ and 5σ orbitals of isolated CO. This is discussed in relation to the dispersion of the 4σ and 5σ levels observed in UPS and to the photon-energy dependent intensities of the 4σ and 5σ resonances. The 2π* component of the backbonding comes through several levels in the upper part of the d band which contain small 2π* contributions in bonding combination with Pd d orbitals. The main 2π* orbitals (contaminated by small antibonding contributions from the metal) are empty (see above).     

Orbital mechanism of upright CO activation on Fe(100)

The knowledge of bond activation forms a cornerstone for modern chemistry, wherein symmetry rules of electronic activation lie in the heart of bond activation. However, the question as to how a chemical bond is activated remains elusive. By taking CO activated on Fe(100), herein, we have resolved the long-standing fundamental question; we have found that excitations in the adsorbate feature the bond activation. We essentially have discovered contrasting electronic processes in respective σ and π electron systems of the adsorbed CO molecule. The σ electron system is involved in reversible hidden excitations/deexcitations between two occupied σ orbitals, whereas the π electron system is subject to irreversible π to π* excitations dispersed along the d-band region, which is coupled to the rotational 2π electron couplings depending on the strength of molecule-metal interactions. The σ excitations pertain to the Pauli repulsion mediated quantum nature with energy and entropy marked by the two energy levels, whereas the π to π* excitations fall into a new category of electronic excitations contributing to energy and entropy exchanges in a wide and continuous d-band region. The findings that the internal states of the adsorbate are excited and that fundamental connections between the frontier orbitals and low-lying orbitals are established as the molecule comes to the surface may open up new channels to realize more efficient bond activation and renew our thinking on probing the quantum mechanical nature of bond activation at surfaces with further possible impact on manipulation of orbital activation in femtochemistry and attochemistry.     

A unified orbital model of delocalised and localised currents in monocycles, from annulenes to azabora-heterocycles

Why are some (4n+2)π systems aromatic, and some not? The ipsocentric approach to the calculation of the current density induced in a molecule by an external magnetic field predicts a four‐electron diatropic (aromatic) ring current for (4n+2)π carbocycles and a two‐electron paratropic (antiaromatic) current for (4n)π carbocycles. With the inclusion of an electronegativity parameter, an ipsocentric frontier‐orbital model also predicts the transition from delocalised currents in carbocycles to nitrogen‐localised currents in alternating azabora‐heterocycles, which rationalises the differences in (magnetic) aromaticity between these isoelectronic π‐conjugated systems. Ab initio valence‐bond calculations confirm the localisation predicted by the naïve model, and coupled‐Hartree–Fock calculations give current‐density maps that exhibit the predicted delocalised‐to‐localised/carbocycle–heterocycle transition.     

Induced currents and electron counting in aromatic boron wheels: B8(2-) and B9-)

The newly discovered atom-centered polygonal wheels B8(2-) and B9- are predicted to show ring currents characteristic of aromatic systems. Ipsocentric mapping of induced current density for both molecules attributes a pi diatropic current to the four electrons of the doubly degenerate pi HOMO and a sigma diatropic current to the four electrons of the doubly degenerate sigma HOMO, each orbital pair having an available transition to corresponding LUMO orbitals in which the angular node count increases by one. Thus, on the magnetic criterion, B8(2-) and B9- are each both pi- and sigma-aromatic as a consequence of the nodal properties of the frontier orbitals of the pi- and sigma-stacks.     

Magnetically induced current densities in Al4 (2-) and Al4 (4-) species studied at the coupled-cluster level

Magnetically induced current densities in the four-membered rings of Al4(2-) and Al4(4-) species have been calculated at the coupled-cluster singles and doubles (CCSD) level by applying the recently developed gauge-including magnetically induced current (GIMIC) method. The strength of the ring-current susceptibilities were obtained by numerical integration of the current densities passing through a cross section perpendicular to the Al4 ring. The GIMIC calculations support the earlier notion that Al4 (2-) with formally two pi electrons sustains a net diatropic ring current. The diatropic contribution to the ring-current susceptibility is carried by the electrons in both the sigma (16.7 nAT) and the pi (11.3 nAT) orbitals. The induced ring current in the Al4 (4-) compounds, with four pi electrons, consists of about equally strong diatropic sigma and paratropic pi currents of about 14 and -17 nAT, respectively. The net current susceptibilities obtained for Al4Li-, Al4Li2, Al4Li3(-), and Al4Li4 at the CCSD level using a triple-zeta basis set augmented with polarization functions are 28.1, 28.1, -5.9, and -3.1 nAT, respectively. The corresponding diatropic (paratropic) contributions to the ring-current susceptibilities are 32.4 (0.0), 36.7 (0.0), 18.9 (-19.9), and 18.6 (-16.8) nAT, respectively. For the Al4(2-) and Al4(4-) species, the net currents circling each Li+ cation is estimated to 4.3 and 2.4 nAT, respectively.     

The phenalenyl motif: a magnetic chameleon

The 12pi cation (3) and 14pi anion (4) derived from the phenalenyl radical (2) support diatropic ("aromatic") perimeter ring currents, but isoelectronic replacement of the central atom by either boron (5) or nitrogen (6) leads to paratropic ("antiaromatic") current; the ipsocentric approach to molecular magnetic response accounts for all four patterns in terms of competition between translationally and rotationally allowed virtual pi-pi* excitations.     

Perimeter Effects on Ring Currents in Polycyclic Aromatic Hydrocarbons: Circumcoronene and Two Hexabenzocoronenes

Current‐density maps are calculated at an ab initio level for the three symmetrical polycyclic aromatic hydrocarbons, circumcoronene [ 1 (D_6h)], hexabenzo[bc,ef,hi,kl,no,qr]coronene [ 2 a (D_6h) and 2 b (D_3d)], and hexabenzo[a,d,g,j,m,p]coronene [ 3 a (D_6h), 3 b (D₆) and 3 c (D_3d)], all of which can be formally derived by annelation of benzene rings to a coronene core. Whilst 1 is planar, 2 has a non‐planar minimum that is effectively isoenergetic with its planar form, and 3 has a well defined non‐planar structure. The shape of the molecular boundary rather than the planarity of the molecule plays the critical rôle in the character of the predicted currents. Formal deletion of outer hexagons from circumcoronene ( 1 ) in two different ways produces either hexabenzocoronene 2 with a prediction of disjoint local benzenoid diatropic currents linked by a global perimeter, or 3 with a giant diatropic perimeter current enclosing a weak paramagnetic circulation on the central hexagon. The current density map of 1 is effectively a superposition of those of 2 and 3 . Its strong diatropic perimeter current subsumes the six weaker diatropic benzenoid circulations evident in 2 , and bifurcates in the six outer benzenoid rings that form the corners of the giant hexagon; its benzene “hub” sustains a diatropic current, as would be expected from the partial cancellation of the strong diatropic hub current of 2 by the weaker paratropic hub current of 3 . The relationship between the three molecules is rationalised by considering orbital contributions to their current density maps.     

The Pi‐Nature of Methyl Obtained by the Natural Bond Orbital Method: Orbital‐Based Rationalizations of Site‐Dependent Substitution Effects on Fine Color‐Tuning of Luminescence

Both C‐H bonding and antibonding (σ_CH and σ*_CH) of a methyl group would contribute to the highest occupied or lowest unoccupied molecular orbitals (HOMO or LUMO) in methylated derivatives of Ir(ppz)₂ 3 iq (ppz = 1‐phenylpyrazole and 3iq = isoquinoline‐3‐carboxylate). This is found by analysis of HOMO (or LUMO) formed by linear combination of bond orbitals using the natural bond orbital (NBO) method. The elevated level of HOMO (or LUMO) uniformly found for each methylated derivative, indicating the σ_CH‐destabilization outweighs the σ*_CH‐stabilization. To broaden the HOMO‐LUMO gap, methylation at a carbon having smaller contribution to HOMO and/or larger contribution to LUMO is suggested.     

Near-Infrared-III-Absorbing and -Emitting Dyes: Energy-Gap Engineering of Expanded Porphyrinoids via Metallation

The synthesis of organometallic complexes of modified 26π-conjugated hexaphyrins with absorption and emission capabilities in the third near-infrared region (NIR-III) is described. Symmetry alteration of the frontier molecular orbitals (MOs) of bis-Pd^II and bis-Pt^II complexes of hexaphyrin via N-confusion modification led to substantial metal d_π–p_π interactions. This MO mixing, in turn, resulted in a significantly narrower HOMO–LUMO energy gap. A remarkable long-wavelength shift of the lowest S₀→S₁ absorption beyond 1700 nm was achieved with the bis-Pt^II complex, t -Pt₂-3 . The emergence of photoacoustic (PA) signals maximized at 1700 nm makes t -Pt₂-3 potentially useful as a NIR-III PA contrast agent. The rigid bis-Pd^II complexes, t -Pd₂-3 and c -Pd₂-3 , are rare examples of NIR emitters beyond 1500 nm. The current study provides new insight into the design of stable, expanded porphyrinic dyes possessing NIR-III-emissive and photoacoustic-response capabilities.     

Ab initio calculations on urea

Multiconfiguration wave functions constructed from contracted Gaussian-lobe functions have been found for the ground and valence-excited states of urea. ICSCF molecular orbitals of the excited states were used as the parent configurations for the CI calculations except for the ¹A₁(π → π*) state. The ¹A₁(π → π*) state used as its parent configuration an orthogonal linear combination of natural orbitals obtained from the second root of a three-configuration SCF calculation. The lowest excited states are predicted to be the n π → π* and π → π* triplet states. The lowest singlet state is predicted to be the n π → π* state with an energy in good agreement with the one known UV band at 7.2 eV. The π → π* singlet state is predicted to be about 1.9 eV higher, contrary to several previous assignments which assumed the lowest band was a π → π* amide resonance band. The predicted ionization energy of 9.0 eV makes this and higher states autoionizing.     

Synthesis and characterization of π-extended thienoacenes with up to 13 fused aromatic rings

π-Extended thienoacenes that comprise alternatively arranged anthracene and thieno[3,2-b]thiophene moieties and have 8 or 13 aromatic rings were synthesized. The delocalization of their HOMO and LUMO orbitals is over the entire molecules, and low-lying HOMO levels endow them good stability.     

n→π*-Übergänge in Dicarbonylverbindungen Der Einfluss der n,n- und π*, π*-Wechselwirkung

By CNDO-CI calculations we have found that dicarbonyl compounds exhibit only two n → π* transitions in the visible or near UV. region, instead of four as expected from simpler MO-models. The dominant features of the long-wavelength electronic spectra may be characterized by the relative energy of the two n and the two lowest π* orbitals. In general we distinguish between three cases:

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Electronic Push–Pull Modulation by Peripheral Substituents in Pentaaryl Boroles

Establishing access to a bulky tetraaryl dilithiobutadiene (Ph*C)₄Li₂ (Ph*=3,5-tBu₂(C₆H₃)) allowed for the synthesis of five-membered heterocycles with incorporated main-group elements. Along with an amino borole, a set of substituted pentaaryl boroles (Ph*C)₄BAr has been synthesized. The examination of their absorption spectra and computational studies by means of DFT granted insight into the influence of peripheral substituents on the electronic features of the parent pentaphenyl borole (PhC)₄BPh. Introduction of the more electron-rich Ph* residue at the carbon atoms increases the HOMO energy, redshifting the visible π/π*-absorption bands compared with the parent pentaphenyl borole. The influence on the frontier orbitals of three different boron-bound aryls with electronically modulating substituents in the remote 3,5-positions Ar=3,5-R₂-C₆H₃ (R=Me, H, CF₃) was studied. The substituents were found to increase (+I effect, Me) or decrease (−I effect, CF₃) the LUMO energy, thus directly affecting the visible absorption spectra. This represents the first study on HOMO–LUMO-gap adjustments by a combined push–pull approach of a substituted pentaphenylborole.