Upper (<em>V</em>₊) and lower (<em>V</em>₋) PECs for the BrCN⁺^2Pi _{frac{1}{2}} and ^2Pi _{frac{3}{2}} states determined by applying the FSCC method in combination with the Dirac–Coulomb Hamiltonian (DC-FSCC)

<p><strong>Figure 3.</strong> Upper (<em>V</em>₊) and lower (<em>V</em>₋) PECs for the BrCN⁺^2\Pi _{\frac{1}{2}} and ^2\Pi _{\frac{3}{2}} states determined by applying the FSCC method in combination with the Dirac–Coulomb Hamiltonian (DC-FSCC).</p> <p><strong>Abstract</strong></p> <p>In this work, we present the four-component quadratic vibronic coupling model for the description of the Renner–Teller effect (RTE) in the presence of the spin–orbit coupling. The interaction of the two potential energy surfaces emerging from the cationic ²Π states of singly ionized linear triatomic molecules is described by the quadratic coupling constant <em>c</em> for the genuine RT repulsion and the second parameter, <em>d</em>, for a nonconstant spin–orbit coupling varying with the bond angle of the triatomic. The emergence of a linear RT constant in the presence of the spin–orbit operator was originally shown by Poluyanov and Domcke (2004 <em>Chem. Phys.</em> <strong>301</strong> 111–27) and is based on the application of the Breit–Pauli Hamiltonian in combination with nonrelativistic wavefunctions. In contrast to this methodology, we generate the diabatic RT Hamiltonian in a 4-spinor basis where the symmetry transformation properties of the electronic and vibrational wavefunctions completely determine the RT matrix structure. Explicit access to highly correlated wavefunctions is not required in our approach. In addition, the four-component vibronic coupling model takes into account the full spatial orbital relaxation upon the inclusion of the spin–orbit coupling and is therefore well suited for heavy systems. The third parameter, <em>p</em>, accounting for a possible pseudo-Jahn–Teller interaction is not considered here, but it does not introduce a principal difficulty. As the initial systems for this study, we considered the BrCN⁺ and ClCN⁺ cations and determined the <em>c</em> and <em>d</em> parameters by a numerical fit to accurate adiabatic potential energy surfaces obtained by the relativistic Fock-space coupled-cluster method. New values for the computed linear RT parameter <em>d</em> amount to 14.7 ± 0.5 cm⁻¹ for ClCN⁺ and 73.2 ± 0.7 cm⁻¹ for BrCN⁺.</p

Geometry parameters, vibrational frequencies and RT parameters for the BrCN⁺ cation

<p><b>Table 1.</b> Geometry parameters, vibrational frequencies and RT parameters for the BrCN⁺ cation. Hereby, bond lengths are given in Å, vibrational frequencies (ω) and RT parameters <em>c</em> and <em>d</em> are given in wavenumbers for the NR, scalar relativistic (SF) and four-component (DC) treatment. For the DC case the distances for the lower and (upper) surface are both listed, where ε is dimensionless. <em>c</em>_calc and <em>c</em>_fit denote the values obtained by equations (<a href="http://iopscience.iop.org/0953-4075/46/12/125101/article#jpb469975eqn28" target="_blank">28</a>), (<a href="http://iopscience.iop.org/0953-4075/46/12/125101/article#jpb469975eqn29" target="_blank">29</a>) and via the fit. The parameter <em>d</em> does not apply in the absence of the SO coupling.</p> <p><strong>Abstract</strong></p> <p>In this work, we present the four-component quadratic vibronic coupling model for the description of the Renner–Teller effect (RTE) in the presence of the spin–orbit coupling. The interaction of the two potential energy surfaces emerging from the cationic ²Π states of singly ionized linear triatomic molecules is described by the quadratic coupling constant <em>c</em> for the genuine RT repulsion and the second parameter, <em>d</em>, for a nonconstant spin–orbit coupling varying with the bond angle of the triatomic. The emergence of a linear RT constant in the presence of the spin–orbit operator was originally shown by Poluyanov and Domcke (2004 <em>Chem. Phys.</em> <strong>301</strong> 111–27) and is based on the application of the Breit–Pauli Hamiltonian in combination with nonrelativistic wavefunctions. In contrast to this methodology, we generate the diabatic RT Hamiltonian in a 4-spinor basis where the symmetry transformation properties of the electronic and vibrational wavefunctions completely determine the RT matrix structure. Explicit access to highly correlated wavefunctions is not required in our approach. In addition, the four-component vibronic coupling model takes into account the full spatial orbital relaxation upon the inclusion of the spin–orbit coupling and is therefore well suited for heavy systems. The third parameter, <em>p</em>, accounting for a possible pseudo-Jahn–Teller interaction is not considered here, but it does not introduce a principal difficulty. As the initial systems for this study, we considered the BrCN⁺ and ClCN⁺ cations and determined the <em>c</em> and <em>d</em> parameters by a numerical fit to accurate adiabatic potential energy surfaces obtained by the relativistic Fock-space coupled-cluster method. New values for the computed linear RT parameter <em>d</em> amount to 14.7 ± 0.5 cm⁻¹ for ClCN⁺ and 73.2 ± 0.7 cm⁻¹ for BrCN⁺.</p

Geometry parameters for the XCN (X=Cl, Br) molecules as used in equations (25) and (27)

<p><strong>Figure 1.</strong> Geometry parameters for the XCN (X=Cl, Br) molecules as used in equations (<a href="http://iopscience.iop.org/0953-4075/46/12/125101/article#jpb469975eqn25" target="_blank">25</a>) and (<a href="http://iopscience.iop.org/0953-4075/46/12/125101/article#jpb469975eqn27" target="_blank">27</a>).</p> <p><strong>Abstract</strong></p> <p>In this work, we present the four-component quadratic vibronic coupling model for the description of the Renner–Teller effect (RTE) in the presence of the spin–orbit coupling. The interaction of the two potential energy surfaces emerging from the cationic ²Π states of singly ionized linear triatomic molecules is described by the quadratic coupling constant <em>c</em> for the genuine RT repulsion and the second parameter, <em>d</em>, for a nonconstant spin–orbit coupling varying with the bond angle of the triatomic. The emergence of a linear RT constant in the presence of the spin–orbit operator was originally shown by Poluyanov and Domcke (2004 <em>Chem. Phys.</em> <strong>301</strong> 111–27) and is based on the application of the Breit–Pauli Hamiltonian in combination with nonrelativistic wavefunctions. In contrast to this methodology, we generate the diabatic RT Hamiltonian in a 4-spinor basis where the symmetry transformation properties of the electronic and vibrational wavefunctions completely determine the RT matrix structure. Explicit access to highly correlated wavefunctions is not required in our approach. In addition, the four-component vibronic coupling model takes into account the full spatial orbital relaxation upon the inclusion of the spin–orbit coupling and is therefore well suited for heavy systems. The third parameter, <em>p</em>, accounting for a possible pseudo-Jahn–Teller interaction is not considered here, but it does not introduce a principal difficulty. As the initial systems for this study, we considered the BrCN⁺ and ClCN⁺ cations and determined the <em>c</em> and <em>d</em> parameters by a numerical fit to accurate adiabatic potential energy surfaces obtained by the relativistic Fock-space coupled-cluster method. New values for the computed linear RT parameter <em>d</em> amount to 14.7 ± 0.5 cm⁻¹ for ClCN⁺ and 73.2 ± 0.7 cm⁻¹ for BrCN⁺.</p

Split upper (<em>V</em>₊) and lower (<em>V</em>₋) PECs of the BrCN⁺²Π state determined by applying FSCC in combination with an NR Hamiltonian

<p><strong>Figure 2.</strong> Split upper (<em>V</em>₊) and lower (<em>V</em>₋) PECs of the BrCN⁺²Π state determined by applying FSCC in combination with an NR Hamiltonian. The SF curves look almost identical and are not plotted separately.</p> <p><strong>Abstract</strong></p> <p>In this work, we present the four-component quadratic vibronic coupling model for the description of the Renner–Teller effect (RTE) in the presence of the spin–orbit coupling. The interaction of the two potential energy surfaces emerging from the cationic ²Π states of singly ionized linear triatomic molecules is described by the quadratic coupling constant <em>c</em> for the genuine RT repulsion and the second parameter, <em>d</em>, for a nonconstant spin–orbit coupling varying with the bond angle of the triatomic. The emergence of a linear RT constant in the presence of the spin–orbit operator was originally shown by Poluyanov and Domcke (2004 <em>Chem. Phys.</em> <strong>301</strong> 111–27) and is based on the application of the Breit–Pauli Hamiltonian in combination with nonrelativistic wavefunctions. In contrast to this methodology, we generate the diabatic RT Hamiltonian in a 4-spinor basis where the symmetry transformation properties of the electronic and vibrational wavefunctions completely determine the RT matrix structure. Explicit access to highly correlated wavefunctions is not required in our approach. In addition, the four-component vibronic coupling model takes into account the full spatial orbital relaxation upon the inclusion of the spin–orbit coupling and is therefore well suited for heavy systems. The third parameter, <em>p</em>, accounting for a possible pseudo-Jahn–Teller interaction is not considered here, but it does not introduce a principal difficulty. As the initial systems for this study, we considered the BrCN⁺ and ClCN⁺ cations and determined the <em>c</em> and <em>d</em> parameters by a numerical fit to accurate adiabatic potential energy surfaces obtained by the relativistic Fock-space coupled-cluster method. New values for the computed linear RT parameter <em>d</em> amount to 14.7 ± 0.5 cm⁻¹ for ClCN⁺ and 73.2 ± 0.7 cm⁻¹ for BrCN⁺.</p

Identification of Plasmons in Molecules with Scaled Ab Initio Approaches

For the electronic excitations in metallic systems under periodic boundary conditions, momentum conservation and a uniform electron–electron interaction imply a clear distinction of plasmons and single-particle excitations. For finite molecular systems, this distinction is less clear, but excitations formed by a coherent superposition of elementary particle–hole transitions that show a collective oscillation of the transition electron density have nevertheless been identified as plasmons in molecules. To aid this distinction, a scaling approach [Bernadotte, S.; Evers, F.; Jacob, C. R. <i>J. Phys. Chem. C</i> <b>2013</b>, <i>117</i>, 1863] has recently been developed that is based on the observation that, in contrast to single-particle excitations, plasmonic excitation energies strongly depend on the electron–electron interaction. In this work, we adapt the proposed scaling scheme to ab initio models, specifically configuration interaction singles and the second-order algebraic diagrammatic construction scheme of the polarization propagator. The resulting approach is applied to a series of linear polyenes and the characterization based on the scaling method is confirmed by inspection of the eigenvector components, transition density patterns, and transition strengths

Gold Phenolate Complexes: Synthesis, Structure, and Reactivity

Seven different NHC gold­(I) phenolate complexes were synthesized. Structural data, including X-ray crystal structure analyses, could be obtained for each of them. An investigation by computational chemistry, including NBO analysis, indicates three-center–four-electron hyperbonds among the carbene carbon, the gold atom, and the oxygen atom of the phenolate with an approximate 60:40 distribution of the bonding interaction in favor of the carbene–gold bond. The new class of complexes shows only moderate catalytic activity

Gold Phenolate Complexes: Synthesis, Structure, and Reactivity

Seven different NHC gold­(I) phenolate complexes were synthesized. Structural data, including X-ray crystal structure analyses, could be obtained for each of them. An investigation by computational chemistry, including NBO analysis, indicates three-center–four-electron hyperbonds among the carbene carbon, the gold atom, and the oxygen atom of the phenolate with an approximate 60:40 distribution of the bonding interaction in favor of the carbene–gold bond. The new class of complexes shows only moderate catalytic activity

Single-molecule studies on the quenching of TMR-bipy-DNA by CuSO₄.

<p>(A) Confocal fluorescence image of single ATTO620-bipy-DNA molecules immobilized on glass cover slides via biotin/streptavidin. Image (30×15 µm²) taken using pulsed excitation with a diode laser emitting at 635 nm with a repetition rate of 80 MHz at an average excitation power of 5.5 µW in presence of 0.1 µM CuSO₄. Time-resolved traces of single immobilized dye-bipy-DNA molecules labeled with TMR (B), ATTO 620 (C) and ATTO 633 (D) recorded under the same conditions show discrete dark states due to reversible complexation of Cu²⁺ and bipyridine which leads to intramolecular quenching of the fluorescence emission.</p

Fluorescence and UV/VIS studies on the quenching of TMR-bipy-DNA by CuSO₄.

<p>(A) Stern-Volmer plot of TMR-bipy-DNA fluorescence quenching by CuSO₄ (closed circles) shows a pronounced negative deviation from the Stern-Volmer law for collisional quenching (solid line) that can be explained using the model from eq. (1) for fitting the data (dashed line). (B) Absorption of TMR-bipy-DNA shows only a very weak dependency on the addition of CuSO₄.</p

Gold Catalysis: Hydrolysis of Di(alkoxy)carbenium Ion Intermediates as a Sensor for the Electronic Properties of Gold(I) Complexes

Six different cationic gold(I) complexes LAu⁺ were converted to the corresponding di(alkoxy)carbenium ions by reaction with ethyl 2,5-dimethylhexa-2,3-dienoate. These conversions were monitored by in situ IR spectroscopy; at room temperature they proceeded in only a few seconds. The ligands L are based on the most popular ligand types in gold catalysis: phosphanes, phosphites, carbenes, and isonitriles. The di(alkoxy)carbenium ions were stable, not short-lived intermediates, and could be characterized. This allowed the kinetic study of the next step, the hydrolytic cleavage to the Hammond-type vinylgold species. Depending on the ligand on gold, large rate differences were detected. Computational chemistry revealed a correlation of the experimental reaction rates with the LUMO energies of the di(alkoxy)carbenium species and the direct influence of the ligand on gold on these LUMO energies. Thus, the di(alkoxy)carbenium ion could be utilized as an easy to use benchmark system for the electronic characterization of LAu⁺ catalysts by theory, spectroscopy, and kinetic experiments