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

State-specific frozen natural orbital for reduced-cost algebraic diagrammatic construction calculations: The application to ionization problem

We have developed a reduced-cost algebraic diagrammatic construction (ADC) method based on state-specific frozen natural orbital and natural auxiliary functions. The newly developed method has been benchmarked on the GW100 test set for the ionization problem. The use of state-specific natural orbitals drastically reduces the size of the virtual space with a systematically controllable accuracy and offers a significant speedup over the standard ionization potential (IP)-ADC(3) method. The accuracy of the method can be controlled by two thresholds and nearly a black box to use. The inclusion of the perturbative correction significantly improves the accuracy of the calculated IP values, and the efficiency of the method has been demonstrated by calculating the IP of a molecule with 60 atoms and more than 2216 basis functions.

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.

Vertical Ionization Potentials and Electron Affinities at the Double-Hybrid Density Functional Level

The double-hybrid (DH) time-dependent density functional theory is extended to vertical ionization potentials (VIPs) and electron affinities (VEAs). Utilizing the density fitting approximation, efficient implementations are presented for the genuine DH ansatz relying on the perturbative second-order correction, while an iterative analogue is also elaborated using our second-order algebraic-diagrammatic construction [ADC(2)]-based DH approach. The favorable computational requirements of the present schemes are discussed in detail. The performance of the recently proposed spin-component-scaled and spin-opposite-scaled (SOS) range-separated (RS) and long-range corrected (LC) DH functionals is comprehensively assessed, while popular hybrid and global DH approaches are also discussed. For the benchmark calculations, up-to-date test sets are selected with high-level coupled-cluster references. Our results show that the ADC(2)-based SOS-RS-PBE-P86 approach is the most accurate and robust functional. This method consistently outperforms the excellent SOS-ADC(2) approach for VIPs, although the results are somewhat less satisfactory for VEAs. Among the genuine DH functionals, the SOS-ωPBEPP86 approach is also recommended for describing ionization processes, but its performance is even less reliable for electron-attached states. In addition, surprisingly good results are attained by the LC hybrid ωB97X-D functional, where the corresponding occupied (unoccupied) orbital energies are retrieved as VIPs (VEAs) within the present formalism.

Quantum self-consistent equation-of-motion method for computing molecular excitation energies, ionization potentials, and electron affinities on a quantum computer

Near-term quantum computers are expected to facilitate material and chemical research through accurate molecular simulations. Several developments have already shown that accurate ground-state energies for small molecules can be evaluated on present-day quantum devices. Although electronically excited states play a vital role in chemical processes and applications, the search for a reliable and practical approach for routine excited-state calculations on near-term quantum devices is ongoing. Inspired by excited-state methods developed for the unitary coupled-cluster theory in quantum chemistry, we present an equation-of-motion-based method to compute excitation energies following the variational quantum eigensolver algorithm for ground-state calculations on a quantum computer. We perform numerical simulations on H2, H4, H2O, and LiH molecules to test our quantum self-consistent equation-of-motion (q-sc-EOM) method and compare it to other current state-of-the-art methods. q-sc-EOM makes use of self-consistent operators to satisfy the vacuum annihilation condition, a critical property for accurate calculations. It provides real and size-intensive energy differences corresponding to vertical excitation energies, ionization potentials and electron affinities. We also find that q-sc-EOM is more suitable for implementation on NISQ devices as it is expected to be more resilient to noise compared with the currently available methods.

Non-Dyson Algebraic Diagrammatic Construction Theory for Charged Excitations in Solids

We present the first implementation and applications of non-Dyson algebraic diagrammatic construction theory for charged excitations in three-dimensional periodic solids (EA/IP-ADC). The EA/IP-ADC approach has a computational cost similar to the ground-state Møller-Plesset perturbation theory, enabling efficient calculations of a variety of crystalline excited-state properties (e.g., band structure, band gap, density of states) sampled in the Brillouin zone. We use EA/IP-ADC to compute the quasiparticle band structures and band gaps of several materials (from large-gap atomic and ionic solids to small-gap semiconductors) and analyze the errors of EA/IP-ADC approximations up to the third order in perturbation theory. Our work also reports the first-ever calculations of ground-state properties (equation-of-state and lattice constants) of three-dimensional crystalline systems using a periodic implementation of third-order Møller-Plesset perturbation theory (MP3).