Intermediate State Representation Research Articles

Ab initio calculations of molecular double Auger decay rates.

We report on the application of the recently developed Fano-ADC(2,2) method to compute total and partial Auger decay widths of molecular core-hole states, including explicit evaluation of double Auger decay branching ratios. The method utilizes the fast-convergent intermediate state representation to construct many-electron wave functions and is readily applicable to atoms, molecules, and clusters. The ADC(2,2) scheme describes the initial and final states of the normal Auger decay consistently up to the second order of perturbation theory. In addition, excitations with two electrons in the continuum provide access to three-electron decay modes. The method yields decay widths and the Auger electron spectra in excellent agreement with the experiment, demonstrating the high accuracy of partial widths. The average relative error of double Auger decay branching ratios compared to available experimental data is about 30%, which should be evaluated as an excellent result considering the universality of the method, the complexity of the double decay process, and the neglection of nuclear motion in this study.

Two-Photon Absorption Strengths of Small Molecules: Reference CC3 Values and Benchmarks.

We present a large dataset of highly accurate two-photon transition strengths (δTPA) determined for standard small molecules. Our reference values have been calculated using the quadratic response implementation of the third-order coupled cluster method including iterative triples (Q-CC3). The aug-cc-pVTZ atomic basis set is used for molecules with up to five non-hydrogen atoms, while larger molecules are assessed with aug-cc-pVDZ; the differences due to the basis sets are discussed. This dataset, encompassing 82 singlet transitions of various characters (Rydberg, valence, and double excitations), enables a comprehensive benchmark of smaller basis sets and alternative wavefunction methods when Q-CC3 calculations become beyond reach as well as time-dependent density functional theory (TD-DFT) approaches. The evaluated wavefunction methods include quadratic response and equation-of-motion CCSD approximations, Q-CC2, and second-order algebraic diagrammatic construction in its intermediate state representation (I-ADC2). In the TD-DFT framework, a set of five commonly used exchange-correlation functionals are evaluted. This extensive analysis provides a quantitative assessment of these methods, revealing how different system sizes, response intensities, and types of transitions affect their performances.

Fourth-Order Algebraic Diagrammatic Construction for Electron Detachment and Attachment: The IP- and EA-ADC(4) Methods.

We present a non-Dyson fourth-order algebraic diagrammatic construction formulation of the electron propagator, featuring the distinct IP- and EA-ADC(4) schemes for the treatment of ionization and electron attachment processes. The algebraic expressions have been derived automatically using the intermediate state representation approach and implemented in the Q-Chem quantum-chemical program package. The performance of the novel methods is assessed with respect to high-level reference data for ionization potentials and electron affinities of closed- and open-shell systems. While only minor improvements over the corresponding third-order methods are observed for one-hole ionization and one-particle electron attachment processes from closed-shell systems (MAEIP-ADC(4) = 0.27 eV and MAEEA-ADC(4) = 0.05 eV), a significantly enhanced performance is found in case of open-shell reference states (MAEIP-ADC(4) = 0.11 eV and MAEEA-ADC(4) = 0.02 eV). A particularly appealing feature of the novel methods is their accurate treatment of satellite transitions. For closed-shell reference states, we obtain accuracies of MAEIP-ADC(4) = 0.81 eV and MAEEA-ADC(4) = 0.27 eV, while in case of open-shell reference states, mean absolute errors of MAEIP-ADC(4) = 0.15 eV and MAEEA-ADC(4) = 0.27 eV are found.

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. The new ADC/ISR methodology, employing the recently presented responsefun package, is applied to a test set of Ne and small molecules (H2, HF, O2, CO2, and benzene) and compared to data from the experiment as well as other ab initio methods. The presented theoretical ab initio ADC/ISR approach is a substantial extension of the available computational methods for the investigation of complex nonlinear properties, however, with a gauge origin dependence inherent to the method that decreases with increasing perturbation order.

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. Employing the novel responsefun package, we present the first ADC/ISR calculations of second-order hyperpolarizability tensors and three-photon-absorption matrix elements.

Algebraic Diagrammatic Construction Schemes Employing the Intermediate State Formalism: Theory, Capabilities, and Interpretation.

Algebraic diagrammatic construction (ADC) schemes represent a family of ab initio methods for the calculation of excited electronic states and electron-detached and -attached states. All ADC methods have been demonstrated to possess great potential for molecular applications, e.g., for the calculation of absorption or photoelectron spectra or electron attachment processes. ADC originates from Green's function or propagator theory; however, most recent ADC developments heavily rely on the intermediate state representation or effective Liouvillian formalisms, which comprise new ADC methods and computational schemes for high-order properties. The different approaches for the calculation of excitation energies, ionization potentials, and electron affinities are intimately related, and they provide a coherent description of these quantities at equivalent levels of theory and with comparable errors. Most quantum chemical program packages contain ADC methods; however, the most complete ADC suite of methods can be found in the recent release of Q-Chem.

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.

HyperTP: A unified approach for live hypervisor replacement in datacenters

Maintenance of virtualized datacenters is often needed for the purposes of introducing new features, fixing bugs or mitigating security problems. However, current maintenance methods are either highly disruptive to the operation of VMs, utilize large amounts of computing resources or require high development efforts.We build HyperTP, a generic framework which combines in a unified way two approaches: in-place server micro-reboot-based hypervisor transplant (noted InPlaceTP) and live VM migration-based hypervisor transplant (noted MigrationTP). HyperTP hinges on a VM state hierarchy for organizing different types of hypervisor memory states in terms of their relation to VM execution, and an Unified Intermediate State Representation that abstracts VM-relevant memory states between multiple different hypervisors. We describe our implementations of both approaches, including technical details of our UISR design and the transplant process. Our evaluation results show that HyperTP delivers satisfactory performance: (1) MigrationTP changes a VM's underlying hypervisor while taking the same time and impacting virtual machines (VMs) with the same performance degradation as normal live migration; and (2) InPlaceTP imposes minimal VM downtime, even under increasing number of VMs and memory sizes. Finally, we discuss how the combination of InPlaceTP and MigrationTP can be used to address the challenges of upgrading a hypervisor cluster, and to mitigate known unpatched hypervisor vulnerabilities.

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. All routines are implemented in an open-source Python library.

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. The first approach, scaled-matrix ADC[(2) + x(3)], scales all contributions first occurring in ADC(3) equally and leads to an improvement of the accuracy of excitation energies compared to ADC(3) for x = 0.4-0.5. However, with respect to excited state dipole moments, this method provides lower accuracy than ADC(3). The second scaling approach, MP[(1) + x(2)] - ISR(3), scales the second order contributions of the ground-state wavefunction and derives a rigorous ADC scheme via the intermediate state representation formalism. Although the error in excitation energies is not improved, this method provides insight into the relevance of the individual terms of the ADC(3) matrix and indicates that the MP(2) wavefunction is, indeed, the optimal reference wavefunction for deriving a third-order single-reference ADC scheme.

Intermediate state representation approach to physical properties of molecular electron-attached states: Theory, implementation, and benchmarking.

Computational schemes for comprehensive studies of molecular electron-attached states and the calculation of electron affinities (EAs) are formulated and implemented employing the intermediate state representation (ISR) formalism and the algebraic-diagrammatic construction approximation for the electron propagator (EA-ADC). These EA-ADC(n)/ISR(m) schemes allow for a consistent treatment of not only electron affinities and pole strengths up to third-order of perturbation theory (n = 3) but also one-electron properties of electron-attached states up to second order (m = 2). The EA-ADC/ISR equations were implemented in the Q-Chem program for Ŝz-adapted intermediate states, allowing also open-shell systems to be studied using unrestricted Hartree-Fock references. For benchmarking of the EA-(U)ADC/ISR schemes, EAs and dipole moments of various electron-attached states of small closed- and open-shell molecules were computed and compared to full configuration interaction data. As an illustrative example, EA-ADC(3)/ISR(2) has been applied to the thymine-thymine (6-4) DNA photolesion.

A complex absorbing potential electron propagator approach to resonance states of metastable anions

An earlier developed electron propagator method for the treatment of electron attachment to molecules within the non-Dyson algebraic-diagrammatic construction framework (EA-ADC) is extended by inclusion of the complex absorbing potential (CAP). The resulting method allows for the investigation of resonance states of metastable anions. Approximation schemes up to third-order perturbation theory for the electron propagator (EA-ADC(3)) are implemented. The CAP operator is treated up to second-order using the intermediate state representation formalism (ISR(2)) and the subspace projection technique. The CAP/EA-ADC(3) method is tested in first applications to the resonances in CO and N2 molecules associated with electron attachment to their low-lying π*-orbitals. The results of the calculations agree well with the available experimental and theoretical data and demonstrate the CAP-augmented EA-ADC modeling can become a useful tool for theoretical studies of metastable electron-attached states.

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.

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 C6 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. We exemplify the approach using illustrative model systems and compare it to results from other ab initio methods and from experiments.

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.

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.

Intermediate state representation approach to physical properties of molecular electron-detached states. I. Theory and implementation.

The third-order non-Dyson algebraic-diagrammatic construction approach to the electron propagator [IP-ADC(3)] is extended using the intermediate state representation (ISR) formalism, allowing the wave functions and properties of molecular states with detached electron to be studied. The second-order ISR equations [ISR(2)] for the one-particle (transition) density matrix have been derived and implemented in the Q-CHEM program. The approach is completely general and enables evaluation of arbitrary one-particle operators and interpretation of electron detachment processes in terms of density-based quantities. The IP-ADC(3)/ISR(2) equations were implemented for Ŝz-adapted intermediate states, allowing open-shell molecules to be studied using unrestricted Hartree-Fock references. As a first test for computations of ground state properties, dipole moments of various closed- and open-shell molecules have been computed by means of electron detachment from the corresponding anions. The results are in good agreement with experimental data. The potential of IP-ADC(3)/ISR(2) for the interpretation of photoelectron spectra is demonstrated for the galvinoxyl free radical.

Restricted Correlation Space B-Spline ADC Approach to Molecular Ionization: Theory and Applications to Total Photoionization Cross-Sections.

Herein is presented a new approach to the ab initio algebraic diagrammatic construction (ADC) schemes for the polarization propagator, which is explicitly designed to accurately and efficiently describe molecular ionization. The restricted correlation space (RCS) version of the ADC methods up to second order of perturbation theory is derived via the intermediate state representation (ISR) and implemented in the multicenter B-spline basis set for the electronic continuum. Remarkably a general close-coupling structure of the RCS-ADC many-electron wave function, connecting the N-particle to the ( N - 1)-particle ADC intermediate states, emerges naturally as a nontrivial result of the RCS ansatz. Moreover, the introduced RCS-ADC schemes prove to be particularly manageable from a computational point of view, overcoming the practical limitations of the conventional ADC approaches. The quality of the new RCS-ADC( n) approaches is verified by performing a series of total photoionization cross-section calculations on a test set of molecules. The excellent agreement of the results with existing accurate benchmarks demonstrates that the RCS versions of the ADC schemes are optimal and quantitatively accurate methods for studying multichannel molecular photoionization.

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.