An excited state coupled-cluster study on indigo dyes

In the present study, the domain-based pair natural orbital implementation of the similarity-transformed equation of motion method is employed to reproduce the vibrationally resolved absorption spectra of indigo dyes. After an initial investigation of multireference, basis set and implicit solvent effects, our calculated 0–0 transition energies are compared to a benchmark set of experimental absorption band maxima. It is established that the agreement between our method and experimental results is well below the desired 0.1 eV threshold in virtually all cases and that the shift in excitation energies upon chemical substitution is also well reproduced. Finally, the entire spectra of some of the main components of the Tyrian purple dye mixture are reproduced and it is found that our computed spectra match the experimental ones without an empirical shift

A perturbative approach to multireference equation-of-motion coupled cluster

We introduce a variant of the multireference equation-of-motion coupled-cluster (MR-EOMCC) method where the amplitudes used for the similarity transformations are estimated from perturbation theory. Consequently, the new variant retains the many-body formalism, a reliance on at most two-body densities, and the state-universal character. As a non-iterative variant, computational costs are reduced, and no convergence difficulties with near-singular amplitudes can arise. Its performance was evaluated on several test sets covering transition metal atoms, small diatomics, and organic molecules against (near-)full CI quality reference data. We further highlight its efficacy on the weakly avoided crossing of LiF and place MR-EOMCC and the new variant into context with linear response theory. The accuracy of the variant was found to be at least on par with expectations for multireference perturbation theories, judging by the NEVPT2 method. The variant can be especially useful in multistate situations where the high accuracy of the iterative MR-EOMCC method is not required

Fragment-Based Local Coupled Cluster Embedding Approach for the Quantification and Analysis of Noncovalent Interactions: Exploring the Many-Body Expansion of the Local Coupled Cluster Energy

Herein, we introduce a fragment-based local coupled cluster embedding approach for the accurate quantification and analysis of noncovalent interactions in molecular aggregates. Our scheme combines two different expansions of the domain-based local pair natural orbital coupled cluster (DLPNO-CCSD(T)) energy: the many-body expansion (MBE) and the local energy decomposition (LED). The low-order terms in the MBE are initially computed in the presence of an environment that is treated at a low level of theory. Then, LED is used to decompose the energy of each term in the embedded MBE into additive fragment and fragment-pairwise contributions. This information is used to quantify the total energy of the system while providing at the same time in-depth insights into the nature and cooperativity of noncovalent interactions. Two different approaches are introduced and tested, in which the environment is treated at different levels of theory: the local coupled cluster in the Hartree–Fock (LCC-in-HF) method, in which the environment is treated at the HF level; and the electrostatically embedded local coupled cluster method (LCC-in-EE), in which the environment is replaced by point charges. Both schemes are designed to preserve as much as possible the accuracy of the parent local coupled cluster method for total energies, while being embarrassingly parallel and less memory intensive. These schemes appear to be particularly promising for the study of large and complex molecular aggregates at the coupled cluster level, such as condensed phase systems and protein–ligand interactions

Statistical phase estimation and error mitigation on a superconducting quantum processor

Quantum phase estimation (QPE) is a key quantum algorithm, which has been widely studied as a method to perform chemistry and solid-state calculations on future fault-tolerant quantum computers. Recently, several authors have proposed statistical alternatives to QPE that have benefits on early fault-tolerant devices, including shorter circuits and better suitability for error-mitigation techniques. However, experimental investigations of the algorithm on real quantum processors are lacking. Here, we implement statistical phase estimation on Rigetti’s superconducting processors. Specifically, we use a modification of the Lin and Tong [PRX Quantum 3, 010318 (2022)] algorithm with the improved Fourier approximation of Wan et al. [Phys. Rev. Lett. 129, 030503 (2022)] and apply a variational-compilation technique to reduce the circuit depth. We then incorporate error-mitigation strategies including zero-noise extrapolation and readout-error mitigation with bit-flip averaging. We propose a new method to estimate energies from the statistical phase estimation data, which is found to improve the accuracy in the final energy estimates by 1–2 orders of magnitude with respect to prior theoretical bounds, reducing the cost of performing accurate phase-estimation calculations. We apply these methods to chemistry problems for active spaces up to four electrons in four orbitals, including the application of a quantum embedding method, and use them to correctly estimate energies within chemical precision. Our work demonstrates that statistical phase estimation has a natural resilience to noise, particularly after mitigating coherent errors, and can achieve far higher accuracy than suggested by previous analysis, demonstrating its potential as a valuable quantum algorithm for early fault-tolerant devices

Accurate Treatment of Large Supramolecular Complexes by Double-Hybrid Density Functionals Coupled with Nonlocal van der Waals Corrections

In this work, we present a thorough assessment of the performance of some representative double-hybrid density functionals (revPBE0-DH-NL and B2PLYP-NL) as well as their parent hybrid and GGA counterparts, in combination with the most modern version of the nonlocal (NL) van der Waals correction to describe very large weakly interacting molecular systems dominated by noncovalent interactions. Prior to the assessment, an accurate and homogeneous set of reference interaction energies was computed for the supramolecular complexes constituting the L7 and S12L data sets by using the novel, precise, and efficient DLPNO-CCSD(T) method at the complete basis set limit (CBS). The correction of the basis set superposition error and the inclusion of the deformation energies (for the S12L set) have been crucial for obtaining precise DLPNO-CCSD(T)/CBS interaction energies. Among the density functionals evaluated, the double-hybrid revPBE0-DH-NL and B2PLYP-NL with the three-body dispersion correction provide remarkably accurate association energies very close to the chemical accuracy. Overall, the NL van der Waals approach combined with proper density functionals can be seen as an accurate and affordable computational tool for the modeling of large weakly bonded supramolecular systems.Financial support by the “Ministerio de Economía y Competitividad” (MINECO) of Spain and European FEDER funds through projects CTQ2011-27253 and CTQ2012-31914 is acknowledged. The support of the Generalitat Valenciana (Prometeo/2012/053) is also acknowledged. J.A. thanks the EU for the FP7-PEOPLE-2012-IEF-329513 grant. J.C. acknowledges the “Ministerio de Educación, Cultura y Deporte” (MECD) of Spain for a predoctoral FPU grant

Single‐reference coupled cluster methods for computing excitation energies in large molecules: The efficiency and accuracy of approximations

While methodological developments in the last decade made it possible to compute coupled cluster (CC) energies including excitations up to a perturbative triples correction for molecules containing several hundred atoms, a similar breakthrough has not yet been reported for excited state computations. Accurate CC methods for excited states are still expensive, although some promising candidates for an efficient and accurate excited state CC method have emerged recently. This review examines the various approximation schemes with particular emphasis on their performance for excitation energies and summarizes the best state‐of‐the‐art results which may pave the way for a robust excited state method applicable to molecules of hundreds of atoms. Among these, special attention will be given to exploiting the techniques of similarity transformation, perturbative approximations as well as integral decomposition, local and embedding techniques within the equation of motion CC framework

A local similarity transformed equation of motion approach for calculating excited states

The efficient and accurate calculation of excitation energies and properties for large molecular systems remains a challenge. In this perspective, local implementation of the similarity‐transformed equation of motion‐coupled cluster method will be briefly outlined, and its current uses and future potentials will be shortly summarized. The available calculations using this new method suggest that it can be applied to a variety of large systems, for which it delivers accurate results