Analytical Gradients for Electron-Attached and Ionized States for the Algebraic-Diagrammatic Construction Scheme for the Electron Propagator up to Third Order.

The derivation and implementation of analytical gradients for methods based on the non-Dyson algebraic diagrammatic construction for the electron propagator, IP-ADC and EA-ADC, up to the third order is presented. Using nuclear gradients, ground-state equilibrium structures for small open-shell systems are calculated. In addition, we investigated the performance of IP/EA-ADC methods for the calculation of adiabatic ionization potentials and electron affinities for medium-sized organic molecules.

Cotton-Mouton Effect Using Algebraic Diagrammatic Construction Schemes in the Intermediate State Representation Formalism.

The Cotton-Mouton effect is theoretically investigated for a selected set of molecules by using a novel computational methodology based on algebraic diagrammatic construction (ADC) schemes in the intermediate state representation (ISR) formulation. Therefore, the electronic contributions to the frequency-dependent polarizabilities and, for the first time, to the magnetizabilities as well as mixed electric and magnetic hypermagnetizabilities have been computed in the ADC/ISR framework. In addition to calculation of the Cotton-Mouton constant and the birefringence, the gauge origin dependence of the computed tensors and the applied methodology are thoroughly investigated.

responsefun: Fun with Response Functions in the Algebraic Diagrammatic Construction Framework.

We present the open-source responsefun package, which implements a universally applicable procedure for computing molecular response properties within the algebraic diagrammatic construction (ADC) framework, exploiting the intermediate state representation (ISR) approach. With symbolic mathematics, the user can simply enter textbook sum-over-states (SOS) expressions from time-dependent perturbation theory, which are then automatically translated into the corresponding symbolic ADC/ISR formulations. Using the data structures provided by the hybrid Python/C++ module adcc for calculating excited states with ADC, the specified response property is directly evaluated, and the result is returned to the user.

Solving response expressions in the ADC/ISR framework.

We present an implementation for the calculation of molecular response properties using the algebraic-diagrammatic construction (ADC)/intermediate state representation approach. For the second-order ADC model [ADC(2)], a memory-efficient ansatz avoiding the storage of double excitation amplitudes is investigated. We compare the performance of different numerical algorithms for the solution of the underlying response equations for ADC(2) and show that our approach also strongly improves the convergence behavior for the investigated algorithms compared with the standard implementation.

Magnetic circular dichroism within the algebraic diagrammatic construction scheme of the polarization propagator up to third order.

We present an implementation of the B term of Magnetic Circular Dichroism (MCD) within the Algebraic Diagrammatic Construction (ADC) scheme of the polarization propagator and its Intermediate State Representation. As illustrative results, the MCD spectra of the ADC variants ADC(2), ADC(2)-x, and ADC(3) of the molecular systems uracil, 2-thiouracil, 4-thiouracil, purine, hypoxanthine 1,4-naphthoquinone, 9,10-anthraquinone, and 1-naphthylamine are computed and compared with results obtained by using the Resolution-of-Identity Coupled-Cluster Singles and Approximate Doubles method, with literature Time-Dependent Density Functional Theory results, and with available experimental data.

Exploring the accuracy and usefulness of semi-empirically scaled ADC schemes by blending second and third order terms.

Different approaches to mixed-order algebraic-diagrammatic construction (ADC) schemes are investigated. The performance of two different strategies for scaling third-order contributions to the ADC secular matrix is evaluated. Both considered schemes employ a single tuning parameter and conserve general properties inherent to all ADC methods, such as hermiticity and size-consistency.

Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package.

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods.

Analytical gradients for core-excited states in the algebraic diagrammatic construction (ADC) framework.

Expressions for analytical molecular gradients of core-excited states have been derived and implemented for the hierarchy of algebraic diagrammatic construction (ADC) methods up to extended second-order within the core-valence separation (CVS) approximation. We illustrate the use of CVS-ADC gradients by determining relaxed core-excited state potential energy surfaces and optimized geometries for water, formic acid, and benzene. For water, our results show that in the dissociative lowest core-excited state, a linear configuration is preferred.

Excited-State Electronic Circular Dichroism Spectra Exploiting the Third-Order Algebraic-Diagrammatic Construction Scheme for the Polarization Propagator.

Excited-state rotatory strengths are reported for the first time at a correlated level, here with the algebraic diagrammatic construction scheme of the polarization propagator up to the third order. To demonstrate the capabilities of this computational approach, the gas phase S electronic circular dichroism spectra of the bicyclic ketones (1)-camphor, (1)-norcamphor, and (1)-fenchone have been calculated at the ADC(3) level of theory. Furthermore, the solution excited-state spectra of the energetically lowest conformer of -(+)-1,1'-bi(2-naphthol) have been computed with inclusion of a polarizable continuum model at the ADC(2) level of theory.

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.

Electronic circular dichroism spectra using the algebraic diagrammatic construction schemes of the polarization propagator up to third order.

Expressions for the calculation of rotatory strengths using the algebraic diagrammatic construction (ADC) scheme of the polarization propagator in both length and velocity gauges have been implemented. This enables the simulation of electronic circular dichroism (ECD) spectra at the ADC level up to third order of perturbation theory. The ADC(n) methods produce rotatory strengths of comparable accuracy to those obtained with coupled cluster methods of corresponding approximation levels, as evaluated for methyloxirane, methylthiirane, dimethyloxirane, dimethylthiirane, hydrogen peroxide, and dihydrogen disulfide.

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.

Deciphering the Electronic Transitions of Thiophene-Based Donor-Acceptor-Donor Pentameric Ligands Utilized for Multimodal Fluorescence Microscopy of Protein Aggregates.

Anionic pentameric thiophene acetates can be used for fluorescence detection and diagnosis of protein amyloid aggregates. Replacing the central thiophene unit by benzothiadiazole (BTD) or quinoxaline (QX) leads to large emission shifts and basic spectral features have been reported [Chem. Eur.

Evaluation of Single-Reference DFT-Based Approaches for the Calculation of Spectroscopic Signatures of Excited States Involved in Singlet Fission.

Singlet fission (SF) has the potential to dramatically increase solar cell efficiency by converting one singlet exciton to two free triplet excitons via a correlated triplet pair intermediate. Identification and characterization of excited states involved in SF are of great importance for understanding the fundamentals of SF. Despite their importance, it is still nontrivial to distinguish various species in transient absorption spectra due to their spectral overlaps and ultrashort lifetimes.

Complex excited state polarizabilities in the ADC/ISR framework.

We present the derivation and implementation of complex, frequency-dependent polarizabilities for excited states using the algebraic-diagrammatic construction for the polarization propagator (ADC) and its intermediate state representation. Based on the complex polarizability, we evaluate C dispersion coefficients for excited states. The methodology is implemented up to third order in perturbation theory in the Python-driven adcc toolkit for the development and application of ADC methods.

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.

Nuclear dynamics in resonant inelastic X-ray scattering and X-ray absorption of methanol.

We report on a combined theoretical and experimental study of core-excitation spectra of gas and liquid phase methanol as obtained with the use of X-ray absorption spectroscopy (XAS) and resonant inelastic X-ray scattering (RIXS). The electronic transitions are studied with computational methods that include strict and extended second-order algebraic diagrammatic construction [ADC(2) and ADC(2)-x], restricted active space second-order perturbation theory, and time-dependent density functional theory-providing a complete assignment of the near oxygen K-edge XAS. We show that multimode nuclear dynamics is of crucial importance for explaining the available experimental XAS and RIXS spectra.

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.

Analytic nuclear gradients of the algebraic-diagrammatic construction scheme for the polarization propagator up to third order of perturbation theory.

Analytic gradient expressions for the algebraic diagrammatic construction (ADC) scheme for the polarization propagator up to third order are derived using a Lagrangian approach. An implementation within the Q-CHEM electronic structure package for excited-state nuclear gradients of the ADC(2), ADC(2)-x, and ADC(3) models based on restricted and unrestricted Hartree-Fock references is presented. Details of the implementation and the applicability of the newly derived gradients for geometry optimizations and the quality of the resulting structures are discussed.

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.

Characterizing Bonding Patterns in Diradicals and Triradicals by Density-Based Wave Function Analysis: A Uniform Approach.

Density-based wave function analysis enables unambiguous comparisons of the electronic structure computed by different methods and removes ambiguity of orbital choices. We use this tool to investigate the performance of different spin-flip methods for several prototypical diradicals and triradicals. In contrast to previous calibration studies that focused on energy gaps between high- and low spin-states, we focus on the properties of the underlying wave functions, such as the number of effectively unpaired electrons.

Resonant Inelastic X-ray Scattering Amplitudes and Cross Sections in the Algebraic Diagrammatic Construction/Intermediate State Representation (ADC/ISR) Approach.

A scheme has been derived and implemented to gain computational access to the full electronic part of the Kramers-Heisenberg-Dirac (KHD) expression for resonant and nonresonant inelastic scattering amplitudes. Our implementation of this scheme is based on the complex polarization propagator in the algebraic diagrammatic construction (ADC) framework and within its intermediate state representation (ISR). The hierarchy of the second- and third-order ADC/ISR computational schemes known as ADC(2), ADC(2)-x, and ADC(3/2) is considered, and the calculated resonant inelastic X-ray scattering (RIXS) amplitudes and transition strengths for water are in excellent agreement with recent experimental data.

Benchmarking Post-Hartree-Fock Methods To Describe the Nonlinear Optical Properties of Polymethines: An Investigation of the Accuracy of Algebraic Diagrammatic Construction (ADC) Approaches.

Third-order nonlinear optical (NLO) properties of polymethine dyes have been widely studied for applications such as all-optical switching. However, the limited accuracy of the current computational methodologies has prevented a comprehensive understanding of the nature of the lowest excited states and their influence on the molecular optical and NLO properties. Here, attention is paid to the lowest excited-state energies and their energetic ratio, as these characteristics impact the figure-of-merit for all-optical switching.

Accurate adiabatic singlet-triplet gaps in atoms and molecules employing the third-order spin-flip algebraic diagrammatic construction scheme for the polarization propagator.

For the calculation of adiabatic singlet-triplet gaps (STG) in diradicaloid systems the spin-flip (SF) variant of the algebraic diagrammatic construction (ADC) scheme for the polarization propagator in third order perturbation theory (SF-ADC(3)) has been applied. Due to the methodology of the SF approach the singlet and triplet states are treated on an equal footing since they are part of the same determinant subspace. This leads to a systematically more accurate description of, e.