Electronic Structures of Symmetric Diradical Systems

The diradical and ionic natures of open-shell singlet systems have been investigated using new definitions of the diradical and ionic characters as well as of their densities within the valence configuration interaction (VCI) model with two electrons in two active orbitals. The two-site symmetric and asymmetric diradical models are examined by using these diradical/ionic characters. For realistic compounds, we investigate a diradicaloid diphenalenyl and a rectangular graphene nanoflake in the presence of an external static electric field, as well as π-stacked phenalenyl-derivative dimers with varying the intermonomer distance, where the central carbon atoms in the phenalenyl rings are substituted by boron (B) and nitrogen (N) atoms, respectively. It is found that the increase of charge asymmetricity induced by the static electric field decreases the diradical character and finally induces an ionic character in the ground state, while the first excited state is changed from pure ionic to diradical-dominant as the field amplitude increases. On the other hand, when increasing the intermonomer distance, the B/N substitution in the phenalenyl dimer changes the electronic state from open-shell singlet with small diradical character to closed-shell with large ionic character. These results indicate that the application of a static electric field to diradicaloids and the asymmetric substitution of a pancake bonded π-dimer combined with the variation of intermonomer distance could tune the diradical/ionic characters and therefore control the nonlinear optical responses.

The open-shell diatomic molecular ion C2+ has acomplicated structure in which low-lying target statesrequire extensive configuration interaction (CI) to depictitaccurately. We present three-dimensional visualizationsin which the modulus of the CI coefficient is plotted againstthe CI label and its bond length. This form of visualizationis a major aid in identifying the dominant electron correlationconfigurations as the molecular ion dissociates, therebyproviding the key electron correlation configurations forcompact target wavefunctions used in scattering calculations.Electron scattering R-matrix calculations for phaseshiftswithin a six-state extended valence configuration interaction(VCI) model reveal the presence of several complex Rydbergresonance series between the closely separated target states ofthis cation. Interloping resonances disrupting the regularRydberg spectral patterns are present in the 3Πg and3Πu scattering symmetries and the prominent resonanceseries lying below the C2+(a 2Πu) threshold areanalysed in detail. Closed-channel, electron scatteringcalculations from the C2+ ion yield bound states ofthe neutral system. For the C2(a 3Πu) bound stateour VCI results show that the vertical ionization potentials tothe X 4Σg- and a 2Πu states of thecation are in suitable accord with more elaborate CI studies.

Fluoreno[2,1-a]fluorene, a molecule comprising fused ortho-quinodimethane units in a 1,5-napthoquinodimethane core, has been prepared and investigated with spectroscopy (UV-Vis-NIR, 1H-NMR and Raman), SQUID magnetometry, spectroelectrochemistry and quantum chemistry. While para-quinodimethanes with a 2,6-substitution pattern exist as closed-shell species and meta-quinodimethanes with 2,7-substitution favour a ground electronic state with very large diradical character, our 1,5-substituted ortho-naphthoquinodimethane-based system exhibits an intermediate degree of diradical character.

All‐electron ab initio Hartree–Fock (HF), valence configuration interaction (CI), and multiconfiguration self‐consistent‐field (CASSCF) calculations have been applied to investigate the electronic states of the CrC molecule. The molecule is predicted as having four low‐lying electronic states, 3∑−, 5∑−, 7∑−, and 9∑−, separated by an energy gap of 0.55 eV from the next higher‐lying state, 1∑−, which is followed by the states 5Π and 7Π. The four lowest‐lying electronic states are due to the coupling of the angular momenta of the 6Sg Cr+ ion with those of the 4Su C− anion. The chemical bond in the 3∑− ground state can be viewed as a quadruple bond composed of two σ and two π bonds. One σ bond is due to the formation of a molecular orbital that is doubly occupied. The remaining bonds, i.e., one σ and two π bonds, arise from valence‐bond couplings. The π bonds originate from the valence‐bond couplings of the electrons in the C 2pπ orbitals with those in the Cr 3dπ orbitals. The σ bond originates from the valence‐bond coupling of the C 2pσ electron with an electron in the Cr 4s, 4p hybrid that is polarized away from the C atom.

The valence electronic excited states of trans-1,3-butadiene and trans, trans-1,3,5-hexatriene from generalized valence bond and configuration interact

Theoretical studies of the bonding of sulfur to models of the (100) surface of nickel

In this work, theoretical methods of quantum chemistry are employed to estimate the effects that the structural modification of 1,5- and 9,10-anthraquinone molecules might produce in their electronic structure, in the pursuit of a common strategy to improve the electrochemical and singlet fission features of conjugated quinones. The proposed modifications are the following: (i) substitution of the carbonyl oxygen atom, (ii) insertion of heteroatoms in the carbon backbone, and (iii) introduction of electron-withdrawing and electron-donating substituents in different positions of the rings. This work shows how specific modifications of the electronic structure can be used to tune the electrochemistry and photophysics of the quinones, improving their suitability to be singlet fission sensitizers and cathode materials. As it was previously known, intermediate diradical characters favor the accomplishment of the singlet fission process. This can be achieved for 1,5-anthraquinone by introduction of B and Si atoms and electron-donating groups in low spin density positions of the carbon backbone or N atoms in high spin density positions. The introduction of heteroatoms or substituents in 9,10-anthraquinone hardly facilitates the singlet fission process. Regarding the electrochemistry, it is observed that the reduction potentials greatly depend on the nature of the modification rather than on the diradical character.

In a theoretical study of the gas phase insertion of transition-metal cations into the C–H and C–C bonds of simple alkanes, an unusual aspect of the metal-carbon bond was discovered. Using ab initio methods (generalized valence bond and configuration interaction), it was found that the two methyl groups in Co(CH3)2+ do not bond to equivalent sd hybrid orbitals as one might expect. Instead, using a single valence bond (VB) spin coupling, we found two distinctly different bonds: one to a Co 4s-like orbital and the other to a 3d-like orbital, leading to a distortion of the molecule from its symmetrical geometry. With the resonance of two valence bond configurations, the bond distances become equivalent and symmetry is restored, however, the bonding orbitals in each configuration remain quite inequivalent. Similar behavior was observed on the potential-energy surface of CoH2+ and this description was found to carry over to Co(H)(CH3)+, where one VB configuration dominates: the hydrogen bonds to the Co 4s orbital while the methyl group bonds to a 3d orbital. The behavior of the cobalt complexes contrasts dramatically with that of the isoelectronic complexes Rh(R1)(R2)+ and Ir(R1)(R2)+ (R1,R2=H,CH3), in which the ligands form bonds to sd hybrid orbitals. These orbitals are essentially the same in the case of R1=H and R2=CH3 and strictly equivalent in the case of R1=R2.

The configuration interaction (CI) method dates back to the earliest days of quantum mechanics, and is the most straightforward and versatile approach for dealing with electron correlation. The earliest applications typically involved 2–10 terms, while modern molecular CI calculations often employ many millions of configuration state functions (CSFs). In addition to the enormous increase in computer power over the last fifty years, many theoretical developments have contributed to the evolution of the CI approach, including the development of efficient algorithmic tools for the various computational steps and the exploration and optimization of the choices of basis sets, orbitals, and the structure of the CI expansion. Among the milestones in these developments have been the introduction of efficient matrix eigenvalue methods, the introduction of multireference CI expansions, the formulation of various corrections and modifications to overcome the major fault of CI, its lack of extensivity, and particularly the introduction of direct CI, which greatly increased the length of accessible CI expansions by eliminating the need to store the Hamiltonian matrix. Unitary group and related methods have helped make direct CI calculations particularly efficient. Specialized computer programs for full CI calculations have become very efficient and are producing benchmark results which are extremely useful for evaluating other methodologies. Although it has lost ground to the very attractive coupled cluster methods, CI still has an important role to play in quantum chemistry.

Björn O. Roos (1937-2010)

An ab initio cluster study of the magnetic properties of the CoO(0 0 1) surface

Ab initio spin-flip configuration interaction (SF-CI) methods with the finite-field (FF) scheme are applied to the calculation of static second hyperpolarizabilities (γ) of several singlet diradical systems, i.e., the model H2 molecule under dissociation, p-quinodimethane, o-quinoid five-membered ring, and 1,4-bis(imidazole-2-ylidene)cyclohexa-2,5-diene (BI2Y) models. The SF-CI method using the UHF reference wave function provides the qualitatively correct diradical character (y) dependence of γ in a wide range of a diradical character region for H2 under dissociation and p-quinodimethane as well as o-quinoid five-membered ring models. For BI2Y, which is a real diradical system, a non-negligible spin contamination is found in the spin-unrestricted Hartree-Fock (UHF) triplet state, which results in overestimations (SF-CIS) or underestimations (SF-CIS(D)) of γ. Such deficiencies are significantly reduced when using the pure spin state, i.e., the restricted open-shell HF (ROHF) triplet wave function as the reference wave function. These results indicate the applicability of the FF-SF-CI method starting with a pure or a nearly pure high-spin state to provide qualitative or semiquantitative γ for large-size diradical systems. For selected systems, these SF-CI results are also compared to the SF equation of motion coupled cluster singles and doubles (SF-EOM-CCSD) and to SF time-dependent density functional theory (SF-TDDFT) schemes. In particular, large amounts of Hartree-Fock exchange in the functional are required to obtain qualitatively correct dependence of γ on y in the case of p-quinodimethane.

Using spin-unrestricted density functional theory, the longitudinal static second hyperpolarizability γ has been investigated for an asymmetric azulene-like open-shell condensed-ring molecule (1) as well as for its symmetric almost closed-shell and open-shell analogues (pentacene (2) and its dicyclopenta- (3) and dicyclohepta-fused (4) analogues). It is found that the symmetric systems, 3 and 4, having intermediate diradical characters show a 6–9 times enhancement of γ as compared to 2, but that this enhancement is even larger (by a factor of 30) for the asymmetric diradicaloid, 1. Geometrical, electronic, and magnetic descriptors have shown that in 1 the terminal seven- and five-membered rings display a cooperative push–pull effect, leading to a large dipole moment, that seems to reinforce its aromaticity as well as its ionic character, whereas 3 and 4 are mostly neutral diradicaloids and are less aromatic. These features have been rationalized by resorting to an asymmetric two-site model within the vale...

Thermal decomposition of oxetan-2-one molecule in the light of DFT and CASPT2 modelling

Quantum chemistry has become one of the most reliable tools for characterizing the thermochemical underpinnings of reactions, such as bond dissociation energies (BDEs). The accurate prediction of these particular properties (BDEs) are challenging for ab initio methods based on perturbative corrections or coupled cluster expansions of the single-determinant Hartree-Fock wave function: the processes of bond breaking and forming are inherently multi-configurational and require an accurate description of non-dynamical electron correlation. To this end, we present a systematic ab initio approach for computing BDEs that is based on three components: 1) multi-reference single and double excitation configuration interaction (MRSDCI) for the electronic energies; 2) a two-parameter scheme for extrapolating MRSDCI energies to the complete basis set limit; and 3) DFT-B3LYP calculations of minimum-energy structures and vibrational frequencies to account for zero point energy and thermal corrections. We validated our methodology against a set of reliable experimental BDE values of CC and CH bonds of hydrocarbons. The goal of chemical accuracy is achieved, on average, without applying any empirical corrections to the MRSDCI electronic energies. We then use this composite scheme to make predictions of BDEs in a large number of hydrocarbon molecules for which there are no experimental data, so as to provide needed thermochemical estimates for fuel molecules.