Vertical ionization potential benchmark for unitary coupled-cluster and algebraic-diagrammatic construction methods.

The performance of several methods for the calculation of vertical ionization potentials (IPs) or, more generally, electron-detachment energies based on unitary coupled-cluster (UCC) theory and the algebraic-diagrammatic construction (ADC) scheme is evaluated with respect to benchmark data computed at the level of equation-of-motion coupled-cluster theory, including single, double, and triple excitations (IP-EOM-CCSDT). Based on a statistical evaluation of about 200 electron-detached states of 41 molecules, the second-order methods IP-ADC(2) and IP-UCC2 show modest accuracies with IP-EOM-CCSDT as reference, exposing a mean signed error and a standard deviation of the error of -0.54 ± 0.50 and -0.49 ± 0.54 eV, respectively, accompanied by a mean absolute error (MAE) of 0.61 and 0.58 eV, respectively. The strict third-order IP-ADC method demonstrates an accuracy of 0.26 ± 0.35 eV (MAE = 0.35 eV), while the IP-UCC3 method is slightly more accurate with 0.24 ± 0.26 eV (MAE = 0.29 eV). Employing the static self-energy computed using the Dyson expansion method (DEM) improves the IP-ADC(3) performance to 0.27 ± 0.28 eV, with the mean absolute error of this method being 0.32 eV. However, employing the simpler improved fourth-order scheme Σ(4+) for the static self-energy provides almost identical results as the DEM. Based on the quality of the present benchmark results, it therefore appears not necessary to use the computationally more demanding DEM.

Theoretical analysis and comparison of unitary coupled-cluster and algebraic-diagrammatic construction methods for ionization.

This article describes a novel approach for the calculation of ionization potentials (IPs), or, more generally, electron-detachment energies, based on a unitary coupled-cluster (UCC) parameterization of the ground-state wave function. Explicit working equations for a scheme referred to as IP-UCC3 are given, providing electron-detachment energies and spectroscopic amplitudes of electron-detached states dominated by one-hole excitations correct through third order. In the derivation, an expansion of the UCC transformed Hamiltonian involving Bernoulli numbers as expansion coefficients is employed. Both the secular matrix and the effective transition moments are shown to be essentially equivalent to the strict third-order algebraic-diagrammatic construction scheme for the electron propagator (IP-ADC). Interestingly, due to the Bernoulli expansion, neglecting triple substitutions in the UCC expansion manifold does not affect the third-order consistency of the IP-UCC effective transition moments. Finally, the equivalence between ADC and UCC excited-state schemes is shown to not hold in fourth or higher order due to a different treatment of the correlated excited-state basis.

Unitary coupled-cluster approach for the calculation of core-excited states and x-ray absorption spectra.

In this work, we present the core-valence separation (CVS) approximation applied to unitary coupled-cluster (UCC) theory for the calculation of core-excited states and the simulation of x-ray absorption spectroscopy (XAS). Excitation energies and oscillator strengths of small- to medium-sized organic molecules have been computed using the second-order and extended second-order UCC schemes (CVS-UCC2 and CVS-UCC2-x) as well as the third-order scheme (CVS-UCC3). All results are compared to the corresponding algebraic-diagrammatic construction methods and experimental data. The agreement between CVS-UCC and experimental data demonstrates its potential as a new approach for the calculation of XAS.

A Doubly Bridged Bis(phenylethynyl)benzene: Different from a Twisted Tolan.

The synthesis of a doubly bridged 1,4-bis(phenylethynyl)benzene is reported. The target displays photophysical properties, distinctly different from that of its congeners, the singly bridged tolans. Quantum-chemical calculations suggest a lack of planarization of the bridged bis(phenylethynyl)benzene in the first excited state.

Twisting and bending photo-excited phenylethynylbenzenes - a theoretical analysis.

Oligo(phenylethynyl)benzenes are a family of compounds that exhibit a rich photochemistry changing dramatically with different orientation of a phenyl group in the molecule. Quantum-chemical calculations have been performed to investigate different members of this family of compounds and compared to previous experimental and theoretical studies. 1,4-Bis(phenylethynyl)benzene (BPEB) has different optical properties than its smaller relative diphenylacetylene; however, upon twisting an outer phenyl ring of BPEB, its photochemistry becomes very similar. Fluorine substituents at the central benzene ring are shown to have only small effects on the optical properties of BPEB.

Unitary coupled cluster ground- and excited-state molecular properties.

A scheme for the calculation of molecular properties within the framework of unitary coupled-cluster (UCC) theory in both the electronic ground and excited states is presented. The scheme is based on an expectation-value ansatz, similar to the equation-of-motion coupled-cluster method or the intermediate state representation (ISR) approach of the algebraic-diagrammatic construction (ADC) scheme. Due to the UCC ansatz, the resulting equations cannot be given by closed-form expressions but need to be approximated. Explicit expressions for the expectation value of a general one-particle operator correct through second order in perturbation theory have been derived and coded for the electronic ground state as well as for excited states of predominant single-excitation character. The resulting equations are shown to be equivalent to those of the second-order ADC/ISR procedure. As first computational tests, the second-order UCC method (UCC2) and the one employing third-order amplitudes (also eigenvectors) together with the second-order density matrix, denoted as UCC3(2), are applied to the calculation of dipole moments for a series of small closed- and open-shell systems as well as 4-cyanoindole and 2,3-benzofuran and compared to full configuration interaction or experimental results. For the aromatic organic molecules, the UCC2 method is shown to be sufficient for the ground-state dipole moment, whereas the UCC3(2) scheme is superior for excited-state dipole moments.

Hermitian second-order methods for excited electronic states: Unitary coupled cluster in comparison with algebraic-diagrammatic construction schemes.

Employing an intermediate state representation (ISR) approach, Hermitian second-order methods for the calculation of electronic excitation energies are presented and compared in detail. These comprise the algebraic-diagrammatic construction scheme for the polarization propagator, a hybrid second-order ISR scheme based on traditional coupled-cluster theory as well as two similar approaches based on a unitary coupled-cluster (UCC) ansatz. Although in a strict perturbation-theoretical framework all prove to be identical, differences emerge when the corresponding converged cluster amplitudes are used and depending on how the similarity-transformed UCC Hamiltonian is evaluated. The resulting excitation energies, however, do not significantly differ for systems well described by means of perturbation theory.

Quinoidal Azaacenes: 99 % Diradical Character.

Quinoidal azaacenes with almost pure diradical character (y=0.95 to y=0.99) were synthesized. All compounds exhibit paramagnetic behavior investigated by EPR and NMR spectroscopy, and SQUID measurements, revealing thermally populated triplet states with an extremely low-energy gap ΔEST' of 0.58 to 1.0 kcal mol-1 . The species are persistent in solution (half-life≈14-21 h) and in the solid state they are stable for weeks.

Efficient implementation of the non-Dyson third-order algebraic diagrammatic construction approximation for the electron propagator for closed- and open-shell molecules.

A novel efficient implementation of the non-Dyson algebraic diagrammatic construction (ADC) scheme of the (N - 1)-part of the electron propagator up to third order of perturbation theory is presented. Due to the underlying spin-orbital formulation, for the first time, the computation of ionization potentials of open-shell radicals is thus possible via non-Dyson ADC schemes. Thorough evaluation of the accuracy, applicability, and capabilities of the new method reveals a mean error of 0.15 eV for closed- as well as open-shell atoms and molecules.

Algebraic-diagrammatic construction scheme for the polarization propagator including ground-state coupled-cluster amplitudes. I. Excitation energies.

An ad hoc modification of the algebraic-diagrammatic construction (ADC) scheme for the polarization propagator is presented. Within this approach, all first-order Møller-Plesset correlation coefficients occurring in the second-order ADC secular matrix are replaced by amplitudes obtained from a coupled cluster doubles (CCD) calculation. This new hybrid method, denoted CCD-ADC(2), has been tested on a series of small diatomic and triatomic molecules and benchmarked with respect to Thiel's benchmark set of medium-sized organic molecules. For the latter, the calculation of 134 singlet and 71 triplet states has shown that CCD-ADC(2) exhibits a mean error and standard deviation of 0.15 ± 0.34 eV for singlet states and 0.0 ± 0.17 eV for triplet states with respect to the provided theoretical best estimates, whereas standard ADC(2) has a mean error and standard deviation of 0.22 ± 0.30 eV for singlet and 0.12 ± 0.16 eV for triplet states. The corresponding extended second-order schemes ADC(2)-x and CCD-ADC(2)-x revealed accuracies of -0.70 ± 0.32 eV and -0.76 ± 0.33 eV for singlet states and -0.55 ± 0.20 eV and -0.67 ± 0.22 eV for triplet states, respectively. Furthermore, the investigation of excited-state potential energy curves along the dissociation of the N2 molecule has shown that the higher reliability of the ground-state CCD method as compared to MP2 is also inherent to the excited states. While the curves obtained at the ADC(2) level break down at around 2 Å, the ones obtained at CCD-ADC(2) remain reasonable up to about 3.5 Å.

Algebraic-diagrammatic construction scheme for the polarization propagator including ground-state coupled-cluster amplitudes. II. Static polarizabilities.

The modification of the algebraic-diagrammatic construction (ADC) scheme for the polarization propagator using ground-state coupled-cluster (CC) instead of Møller-Plesset (MP) amplitudes, referred to as CC-ADC, is extended to the calculation of molecular properties, in particular, dipole polarizabilities. Furthermore, in addition to CC with double excitations (CCD), CC with single and double excitations (CCSD) amplitudes can be used, also in the second-order transition moments of the ADC(3/2) method. In the second-order CC-ADC(2) variants, the MP correlation coefficients occurring in ADC are replaced by either CCD or CCSD amplitudes, while in the F/CC-ADC(2) and F/CC-ADC(3/2) variants, they are replaced only in the second-order modified transition moments. These newly implemented variants are used to calculate the static dipole polarizability of several small- to medium-sized molecules, and the results are compared to the ones obtained by full configuration interaction or experiment. It is shown that the results are consistently improved by the use of CC amplitudes, in particular, for aromatic systems such as benzene or pyridine, which have proven to be difficult cases for standard ADC approaches. In this case, the second-order CC-ADC(2) and F/CC-ADC(2) variants yield significantly better results than the standard third-order ADC(3/2) method, at a computational cost amounting to only about 1% of the latter.

Similarities and differences of the Lagrange formalism and the intermediate state representation in the treatment of molecular properties.

When dealing with approximate wave functions, molecular properties can be computed either as expectation values or as derivatives of the energy with respect to a corresponding perturbation. In this work, the intermediate state representation (ISR) formalism for the computation of expectation values is compared to the Lagrange formalism following a derivative ansatz, which are two alternative approaches of which neither one can be considered superior in general. Within the ISR formalism, terms are included up to a given order of perturbation theory only, while in the Lagrange formalism, all terms are accounted for arising through the differentiation. Similarities and differences of the Lagrange and ISR formalism are illustrated using explicit working equations for selected methods and analyzing numerical results for a range of coupled-cluster as well as algebraic-diagrammatic construction (ADC) methods for excited states. The analysis explains why the ADC(3/2) method is able to yield a large amount of the orbital-relaxation effects for p-h states in contrast to ADC(2) although the same second-order ISR is used to represent the corresponding operator.

Phenylene Bridged Cyclic Azaacenes: Dimers and Trimers.

The synthesis and characterization of novel macrocyclic, phenylene-bridged azaacenes is reported. These species were obtained either by a conventional benzoin- diamine condensation, as shown for the case of the cyclotrimers, in which the azaacene units are separated by meta-connected phenylene bridges, or by a Buchwald-Hartwig-type Pd-catalyzed coupling, which employs 1,2,5,6-tetrabromodibenzocyclooctatetraene as the substrate and bis-TIPS-ethynylated diaminobenzene, -naphthalene or -anthracene as the coupling partner to give the double coupling products azaacene-annulated dibenzocyclooctatetraenes in moderate yields. The macrocycles show strong emission and light emitting diodes have been built with brightnesses exceeding 1600 cd m-2 . We evaluated the optical and electronic properties and the solid-state structures of the molecules and discuss their properties through comparison with their linear and tetrameric N-heteroacene counterparts.

Azaacenes Bearing Five-Membered Rings.

We report the synthesis of processible (dihydro)pyracyclene- and acenaphthylene-substituted azaacenes using condensation reactions in solution. The targets are characterized via cyclic voltammetry, X-ray crystallography, UV/Vis, fluorescence spectroscopy and DFT/NICS calculations. Formal hydrogenation of the annulated five-membered ring surprisingly alters emission in the solid-state as a consequence of modulation of aromaticity and HOMO-LUMO overlap. Five highly fluorescent, crystalline azaacenes were investigated as emitters in organic light-emitting diodes, and their performance with respect to luminance and efficiency was compared to that of structurally related azaacenes.

Alkyne-Substituted N-Heterophenes.

The synthesis and characterization of novel S-shaped N-heterophenes is reported. The targets contain a central anthracene connected to two heterophenanthrene units. N-Heterophenes are synthesized by reacting Boldt's 1,2,6,7-anthracenetetraone with different dialkynylated ortho-diaminobenzenes. The condensation yields range from 63 to 75 %; all of the N-heterophenes are stable and isolable.

Third-Order Unitary Coupled Cluster (UCC3) for Excited Electronic States: Efficient Implementation and Benchmarking.

The efficient implementation of the third-order unitary coupled-cluster scheme (UCC3) for the calculation of excited electronic states is reported. The UCC3 scheme and its second-order UCC2 variant have been benchmarked and compared to Jacquemin's recently introduced, as well as Thiel's well-established, benchmark sets for excitation energies and oscillator strengths. For the latter, the calculation of 134 excited singlet and 71 excited triplet states of 28 small- to medium-sized organic molecules has revealed that UCC2 exhibits a mean error and standard deviation of 0.36 ± 0.41 eV for singlet states and 0.22 ± 0.21 eV for triplet states, whereas UCC3 revealed an accuracy of 0.06 ± 0.27 eV for singlet and -0.22 ± 0.15 eV for triplet states. In addition, the oscillator strengths obtained with effective transition moments correct through second order in perturbation theory are in very good agreement with literature data.

Simulation of Vacuum UV Absorption and Electronic Circular Dichroism Spectra of Methyl Oxirane: The Role of Vibrational Effects.

Vibrationally resolved one-photon absorption and electronic circular dichroism spectra of (R)-methyl oxirane were calculated with different electronic and vibronic models selecting, through an analysis of the convergence of the results, the best compromise between reliability and computational cost. Linear-response TD-DFT/CAM-B3LYP/SNST electronic computations in conjunction with the simple vertical gradient vibronic model were chosen and employed for systematic comparison with the available experimental data. Remarkable agreement between simulated and experimental spectra was achieved for both one-photon absorption and circular dichroism concerning peak positions, relative intensities, and general spectral shapes considering the computational efficiency of the chosen theoretical approach. The significant improvement of the results with respect to smearing of vertical electronic transitions by phenomenological Gaussian functions and the possible inclusion of solvent effects by polarizable continuum models at a negligible additional cost paves the route toward the simulation and analysis of spectral shapes of complex molecular systems in their natural environment.