Third-order Algebraic Diagrammatic Construction Research Articles

Theoretical study of electronic structure and ionization spectrum of γ-pyrone

The electronic structure and ionization spectrum of γ-pyrone (4 H -pyran-4-one) were studied using the third-order algebraic-diagrammatic construction method for a one-particle Green’s function [IP-ADC(3)] and a number of other high-level quantum chemical methods. The results of the calculations are used to interpret the recently obtained photoelectron spectra. A number of new assignments are proposed concerning the nature of the photoelectron maxima of γ-pyrone above 12 eV, where, according to our calculations, there is a significant violation of the single-electron ionization picture due to electron correlation effects. The results obtained significantly change the interpretation of the spectrum available in the literature.

Theoretical Study of the Electronic Structure and Ionization Spectrum of γ-Pyrone

The electronic structure and ionization spectrum of γ-pyrone (4H-pyran-4-one) were calculated using the third-order algebraic diagrammatic construction method for the single-particle Green function [IP-ADC(3)] and some other high-level quantum chemical methods. The results of calculations were used to interpret its recently recorded photoelectron spectra. New assignments have been proposed for the nature of a series of photoelectron maxima of γ-pyrone located above 12 eV, where, according to calculations, the one-electron ionization pattern is disturbed due to electron correlation effects. The obtained results significantly change the interpretation of the spectrum available in the literature.

Consistent third-order one-particle transition and excited-state properties within the algebraic-diagrammatic construction scheme for the polarization propagator.

The intermediate state representation (ISR) formalism allows for the straightforward calculation of excited state properties and state-to-state transition moments using the algebraic-diagrammatic construction (ADC) scheme for the polarization propagator. Here, the derivation and implementation of the ISR in third-order perturbation theory for the one-particle operator are presented, enabling, for the first time, the calculation of consistent third-order ADC [ADC(3)] properties. The accuracy of ADC(3) properties is evaluated with respect to high-level reference data and compared to the previously used ADC(2) and ADC(3/2) schemes. Oscillator strengths and excited state dipole moments are computed, and typical response properties are considered: dipole polarizabilities, first-order hyperpolarizabilities, and two-photon absorption strengths. The consistent third-order treatment of the ISR leads to an accuracy similar to that of the mixed-order ADC(3/2) method; the individual performance, however, depends on the property and molecule under investigation. ADC(3) produces slightly improved results in the case of oscillator strengths and two-photon absorption strengths, while excited state dipole moments, dipole polarizabilities, and first-order hyperpolarizabilities exhibit similar accuracy at ADC(3) and ADC(3/2) levels. Taking the significant increase of central processing unit time and memory requirements of the consistent ADC(3) approach into account, the mixed-order ADC(3/2) scheme offers a better compromise between accuracy and efficiency for the properties considered.

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.

CAP/EA-ADC method for metastable anions: Computational aspects and application to π* resonances of norbornadiene and 1,4-cyclohexadiene.

The second- and third-order algebraic-diagrammatic construction schemes for the electron propagator for studies of electron attachment processes [EA-ADC(2) and EA-ADC(3)] have been extended to include the complex absorbing potential (CAP) method for the treatment of electronic resonances. Theoretical and conceptual aspects of the new CAP/EA-ADC methodology are studied in detail at the example of the well-known 2Πg resonance of the nitrogen anion N2 -. The methodology is further applied to π* shape resonances, for which ethylene is considered as a prototype. Furthermore, the first many-body treatment of the π+ * and π- * resonances of norbornadiene and 1,4-cyclohexadiene is provided, which have served as model systems for the concept of through-space and through-bond interactions for a long time.

Efficient implementation of the single-reference algebraic diagrammatic construction theory for charged excitations: Applications to the TEMPO radical and DNA base pairs.

We present an efficient implementation of the second- and third-order single-reference algebraic diagrammatic construction (ADC) theory for electron attachment and ionization energies and spectra [EA/IP-ADC(n), n = 2, 3]. Our new EA/IP-ADC program features spin adaptation for closed-shell systems, density fitting for efficient handling of the two-electron integral tensors, and vectorized and parallel implementation of tensor contractions. We demonstrate capabilities of our efficient implementation by applying the EA/IP-ADC(n) (n = 2, 3) methods to compute the photoelectron spectrum of the (2,2,6,6-tetramethylpiperidin-1-yl)oxyl (TEMPO) radical, as well as the vertical and adiabatic electron affinities of TEMPO and two DNA base pairs (guanine-cytosine and adenine-thymine). The spectra and electron affinities computed using large diffuse basis sets with up to 1028 molecular orbitals are found to be in good agreement with the best available results from the experiment and theoretical simulations.

High-resolution vacuum ultraviolet absorption spectra of 2,3- and 2,5-dihydrofuran

Using a synchrotron-based Fourier-transform spectrometer, the high-resolution absorption spectra of the C1-symmetric 2,3-dihydrofuran (23DHF) and C2v-symmetric 2,5-dihydrofuran (25DHF) have been measured from 5.5 eV to 9.4 eV with an absolute absorption cross section scale. Oscillator strengths and vertical excitation energies of the lowest 18 states have been computed using the average of the second- and third-order algebraic diagrammatic construction polarization propagator method and the equation-of-motion coupled-cluster method at the level of singles and doubles model. These show that the bright valence transitions of ππ*-character are embedded into Rydberg transitions, whose oscillator strengths are at least one order of magnitude lower. To account for intensity borrowing, the first broad valence transition between 5.5 eV and 6.8 eV was simulated using a nuclear ensemble, and the agreement between experiment and theory is excellent. Whereas 23DHF only exhibits one broad valence transition followed by d/f Rydberg series converging to the ionization energy, the absorption spectrum of 25DHF has four bands, attributed to a valence nπσ → π*-transition, nπσ → 3px,z/3dxz transitions, a second valence nπ → π*-transition followed by d/f Rydberg series converging to the ionization energy, respectively. All Rydberg series converging to the ionization energy have been characterized in terms of their quantum defects.

Electronic Excited States and UV-Vis Absorption Spectra of the Dihydropyrene/Cyclophanediene Photochromic Couple: a Theoretical Investigation.

Dihydropyrene (DHP)/cyclophanediene (CPD) is a fascinating photoswitchable organic system displaying negative photochromism. Upon irradiation in the visible region, the colored DHP can be converted to its open-ring CPD colorless isomer, which can be converted back to DHP by UV light. DHP and CPD thus possess very different absorption spectra whose absorption bands have never been assigned in detail so far. In this work, we characterize the vertical electronic transitions of the first six and seven excited states of DHP and CPD, respectively, aiming for a realistic comparison with experiment. We used state-of-the-art electronic structure methods [e.g., complete active space second-order perturbation theory (CASPT2), n-electron valence-state perturbation theory (NEVPT2), extended multiconfigurational quasi-degenerate perturbation theory (XMCQDPT2), and third-order algebraic diagrammatic construction ADC(3)] capable of describing differential electron correlation. Vertical transition energies were also computed with time-dependent density functional theory (TD-DFT) and compared to these accurate methods. After the reliability of TD-DFT was validated for the main optical transitions, this efficient method was used to simulate the absorption spectra of DHP and CPD in the framework of the Franck-Condon Herzberg-Teller approximation and also using the nuclear ensemble approach. Overall, for both methods, the simulated absorption spectra reproduce nicely the main spectral features of the DHP and CPD isomers, that is, the main four absorption bands of increasing intensity of DHP and the absorption rise below 300 nm for CPD.

Intermediate state representation approach to physical properties of molecular electron-detached states. II. Benchmarking.

The third-order algebraic-diagrammatic construction method for studies of electron detachment processes within the electron propagator framework [IP-ADC(3)] was extended to treat the properties of molecular states with a detached electron using the intermediate state representation (ISR) formalism. The second-order ISR(2) equations for the one-particle (transition) density matrix have been derived and implemented as an extension of the IP-(U)ADC(3) method available in the Q-CHEM program. As a first systematic test of the present IP-(U)ADC(3)/ISR(2) method, the dipole moments of various electronic states of closed- and open-shell molecules have been computed and compared to full configuration interaction (FCI) results. The present study employing FCI benchmarks also provides the first rigorous estimates for the accuracy of electron detachment energies obtained using the IP-ADC(3) method.

Is ADC(3) as Accurate as CC3 for Valence and Rydberg Transition Energies?

The search for new models rapidly delivering accurate excited-state energies and properties is one of the most active research lines of theoretical chemistry. Along with these developments, the performance of known methods is constantly reassessed on the basis of new benchmark values. In this Letter, we show that the third-order algebraic diagrammatic construction, ADC(3), does not yield transition energies of the same quality as the third-order coupled cluster method, CC3. This is demonstrated by extensive comparisons with several hundred high-quality vertical transition energies obtained with FCI, CCSDTQ, and CCSDT. Direct comparisons with experimental 0-0 energies of small- and medium-size molecules support the same conclusion, which holds for both valence and Rydberg transitions. Considering these results, we introduce a composite approach, ADC(2.5), which consists of averaging the ADC(2) and ADC(3) excitation energies. Although ADC(2.5) does not match the CC3 accuracy, it significantly improves the ADC(3) results, especially for vertical energies.

Third-order algebraic diagrammatic construction theory for electron attachment and ionization energies: Conventional and Green's function implementation.

We present implementation of second- and third-order algebraic diagrammatic construction (ADC) theory for efficient and accurate computations of molecular electron affinities (EA), ionization potentials (IP), and densities of states [EA-/IP-ADC(n), n = 2, 3]. Our work utilizes the non-Dyson formulation of ADC for the single-particle propagator and reports working equations and benchmark results for the EA-ADC(2) and EA-ADC(3) approximations. We describe two algorithms for solving EA-/IP-ADC equations: (i) conventional algorithm that uses iterative diagonalization techniques to compute low-energy EA, IP, and density of states and (ii) Green's function algorithm (GF-ADC) that solves a system of linear equations to compute density of states directly for a specified spectral region. To assess the accuracy of EA-ADC(2) and EA-ADC(3), we benchmark their performance for a set of atoms, small molecules, and five DNA/RNA nucleobases. As our next step, we demonstrate the efficiency of our GF-ADC implementation by computing core-level K-, L-, and M-shell ionization energies of a zinc atom without introducing the core-valence separation approximation. Finally, we use EA- and IP-ADC methods to compute the bandgaps of equally spaced hydrogen chains Hn with n up to 150, providing their estimates near thermodynamic limit. Our results demonstrate that EA-/IP-ADC(n) (n = 2, 3) methods are efficient and accurate alternatives to widely used electronic structure methods for simulations of electron attachment and ionization properties.

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.

Electronically excited state geometries and vibrational frequencies calculated using the algebraic diagrammatic construction scheme for the polarization propagator

• The aug-cc-pVTZ basis set shows convergence for the properties and methods tested. • Geometries using ADC methods are similar in accuracy to TDDFT. • Harmonic frequencies are well treated by ADC methods and improve with the order. • Scaling factors can be used to improve ADC harmonic frequencies. • Spin-Opposite-Scaling further improves the frequency match for the ADC(2). The algebraic diagrammatic construction (ADC) scheme for the polarization propagator provides a series of ab initio methods for the calculation of electronically excited states. Here we examine the accuracy of these methods for calculating excited state geometries and excited state harmonic vibrational frequencies for open-shell singlet excited states. A range of ADC methods have been assessed up to third-order, including both the strict and extended second-order schemes and spin-opposite scaling. Third-order ADC is found to provide a high level of agreement for both the experimental excited state geometry and frequency values, while second-order ADC is improved using spin-opposite scaling.

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.

Electron Propagator Methods for Vertical Electron Detachment Energies of Anions: Benchmarks and Case Studies.

Ab initio electron propagator methods are efficient and accurate means of calculating vertical electron detachment energies of closed-shell, molecular anions with nuclei from the first three periods. Basis set extrapolations enable definitive comparisons between electron propagator results and benchmarks defined by total energy differences obtained with coupled-cluster, single, double, plus perturbative triple substitution theory. The best compromises of accuracy and efficiency are provided by the renormalized, partial third-order, diagonal (P3+) self-energy and by the nondiagonal, renormalized, second-order (NR2) approximation. The outer-valence Green function, the two-particle-one-hole Tamm-Dancoff approximation, the third-order algebraic diagrammatic construction, and the renormalized third-order methods also are examined. A detailed analysis of errors for small anions is performed. Case studies include F-(H2O) and Cl-(H2O) complexes, C5H5-, two P2N3- pentagonal rings, and a superhalide, Al(BO2)4-, whose electron detachment energy is more than double those of the halide anions. These applications illustrate the versatility of electron propagator methods, their utility for interpreting negative-ion photoelectron spectra, and their promise in the discovery of unusual properties and patterns of chemical bonding. Composite methods, which combine basis set effects calculated at the relatively efficient diagonal, second-order level and higher correlation effects calculated with small basis sets, provide excellent estimates of basis set-extrapolated P3+ or NR2 results and facilitate applications to large molecules. In the P3+ and NR2 methods, a judicious choice of low-order couplings between hole operators that correspond to the assumptions of Koopmans's theorem and operators that describe final-state relaxation and polarization and initial-state correlation leads to predictive accuracy, computational efficiency, and interpretive lucidity.

An experimental and theoretical study of the photoelectron spectra of cis-dichloroethene: Valence shell vertical ionization and vibronic coupling in the low-lying cationic states.

The valence shell photoelectron spectrum of cis-dichloroethene has been studied both experimentally and theoretically. Photoelectron spectra have been recorded with horizontally and vertically plane polarized synchrotron radiation, thereby allowing the anisotropy parameters, characterizing the angular distributions, to be determined. The third-order algebraic-diagrammatic construction approximation scheme for the one-particle Green's function has been employed to compute the complete valence shell ionization spectrum. In addition, the vertical ionization energies have been calculated using the outer valence Green's function (OVGF) method and the equation-of-motion coupled-cluster, with single and double substitutions for calculating ionization potentials (EOM-IP-CCSD) model. The theoretical results have enabled assignments to be proposed for most of the structure observed in the experimental spectra, including the inner-valence regions dominated by satellite states. The linear vibronic coupling model has been employed to study the vibrational structure of the lowest photoelectron bands, using parameters obtained from ab initio calculations. The ground state optimized geometries and vibrational frequencies have been computed at the level of the second-order Møller-Plesset perturbation theory, and the dependence of the ionization energies on the nuclear configuration has been evaluated using the OVGF method. While the adiabatic approximation holds for the 2B1 state photoelectron band, the 2B2, 2A1, and 2A2 states interact vibronically and form a complex photoelectron band system with four distinct maxima. The 2B1 and 2B2 states also interact vibronically with each other. The potential energy surface of the 2B1 state is predicted to have a double-minimum shape with respect to the out-of-plane a2 deformations of the molecular structure. The single photoelectron band resulting from this interaction is characterized by a highly irregular structure, reflecting the non-adiabatic nuclear dynamics occurring on the two coupled potential energy surfaces forming a conical intersection close to the minimum of the 2B2 state.

Unitary coupled-cluster based self-consistent polarization propagator theory: A third-order formulation and pilot applications.

In this article, the development of a third-order self-consistent polarization propagator method based on unitary coupled-cluster (UCC) parametrization of the ground-state wavefunction and the excitation manifold comprising unitary-transformed excitation operators, hereafter referred to as UCC3, is reported. The UCC3 method is designed to provide excitation energies correct up to the third order for excited states dominated by single excitations. An expansion for the UCC transformed Hamiltonian involving Bernoulli numbers as expansion coefficients is adopted in the derivation of UCC3 working equations. Interestingly, UCC-based polarization propagator theory offers an alternative derivation for the strict version of the third-order algebraic diagrammatic construction [ADC(3)-s] method. The UCC3 results for the excitation energies of excited states in H2O, HF, N2, Ne, CH2, BH, and C2 molecules are compared with benchmark full configuration interaction values as well as ADC(3) and equation-of-motion coupled-cluster singles and doubles results to demonstrate the accuracy of the UCC3 method. UCC-based self-consistent polarization propagator theory appears to be a promising framework for developing non-perturbative hermitian formulations for treating electronically excited states.

Propagator quantum chemical study of S-cis-(Z)-2-(2-formylethenyl)pyrrole: electronic structure and aspects of intramolecular hydrogen bond manifestation in ionization spectra

For the purpose of investigation of the electronic structures of functionalized pyrroles with potential biological activity the electronic structures and ionization spectra of S-cis-(Z)-2-(2-formylethenyl)pyrrole (FP) were calculated by the propagator quantum chemical method. The calculations were performed using the third-order algebraic diagrammatic construction method (ADC(3)) for one-particle Green´s function (electronic propagator) and the 6–31G** basis set. Going from FP (possessing the intramolecular hydrogen bond H⋯O) to its conformation FPR (without H⋯O bonding), the O1s-ionization energy and the ionization energy of the σ-type lone electron pair orbital of the O atom decrease by ~0.2 eV, which is a consequence of stopping the electron density transfer from the O atom. A strong electron density transfer through the hydrogen bond from the O atom to the NH group occurs in the nitrogen core level ionization spectrum as evidenced by a lower N1s-ionization energy of FP (by ~0.7 eV ) compared to that of FPR. The valence shell ionization spectra of FP and FPR calculated using the ADC(3) method are characterized by a high density of the satellite states. The results obtained indicate that the electronic structures of the compounds of the considered class are characterized by pronounced effects of electron correlation.

An experimental and theoretical study of the valence shell photoelectron spectra of 2-chloropyridine and 3-chloropyridine.

The valence shell photoelectron spectra of 2-chloropyridine and 3-chloropyridine have been studied both experimentally and theoretically. Synchrotron radiation has been employed to record angle resolved photoelectron spectra in the photon energy range 20-100 eV, and these have enabled anisotropy parameters and branching ratios to be derived. The experimental results have been compared with theoretical predictions obtained using the continuum multiple scattering Xα approach. This comparison shows that the anisotropy parameter associated with the nominally chlorine lone-pair orbital lying in the molecular plane is strongly affected by the atomic Cooper minimum. In contrast, the photoionization dynamics of the second lone-pair orbital, orientated perpendicular to the molecular plane, seem relatively unaffected by this atomic phenomenon. The outer valence ionization has been studied theoretically using the third-order algebraic-diagrammatic construction (ADC(3)) approximation scheme for the one-particle Green's function, the outer valence Green's function method, and the equation-of-motion (EOM) coupled cluster (CC) theory at the level of the EOM-IP-CCSD and EOM-EE-CC3 models. The convergence of the results to the complete basis set limit has been investigated. The ADC(3) method has been employed to compute the complete valence shell ionization spectra of 2-chloropyridine and 3-chloropyridine. The relaxation mechanism for ionization of the nitrogen σ-type lone-pair orbital (σN LP) has been found to be different to that for the corresponding chlorine lone-pair (σCl LP). For the σN LP orbital, π-π* excitations play the main role in the screening of the lone-pair hole. In contrast, excitations localized at the chlorine site involving the chlorine πCl LP lone-pair and the Cl 4p Rydberg orbital are the most important for the σCl LP orbital. The calculated photoelectron spectra have allowed assignments to be proposed for most of the structure observed in the experimental spectra. The theoretical work also highlights the formation of satellite states, due to the breakdown of the single particle model of ionization, in the inner valence region.

The Spin-Flip Variant of the Algebraic-Diagrammatic Construction Yields the Correct Topology of S1/S0 Conical Intersections.

While the conventional variants of the algebraic-diagrammatic construction (ADC) scheme for the polarization propagator are generally incapable of correctly describing the topology of S1/S0 conical intersections (CIs), its corresponding spin-flip (SF) variant of third-order ADC (ADC(3)) is herein demonstrated to successfully reproduce the S1/S0 minimum-energy CI (MECI) of twisted formaldinium (H2C═NH2+). Analytical nuclear excited-state gradients of ADC have been used in combination with the CIOpt program for the optimization of the MECI without the need for nonadiabatic-coupling vectors. For comparison, MS-CASPT2 calculations were performed via conventional CI optimization employing analytical nonadiabatic-coupling vectors. It is shown that SF-ADC(3) yields the correct dimensionality of the CI and overall compares very favorably to the MS-CASPT2 results.