Showing papers on "Coupled cluster published in 2020"

The DIRAC code for relativistic molecular calculations.

Abstract: DIRAC is a freely distributed general-purpose program system for 1-, 2- and 4-component relativistic molecular calculations at the level of Hartree--Fock, Kohn--Sham (including range-separated theory), multiconfigurational self-consistent-field, multireference configuration interaction, coupled cluster and electron propagator theory. At the self-consistent-field level a highly original scheme, based on quaternion algebra, is implemented for the treatment of both spatial and time reversal symmetry. DIRAC features a very general module for the calculation of molecular properties that to a large extent may be defined by the user and further analyzed through a powerful visualization module. It allows the inclusion of environmental effects through three different classes of increasingly sophisticated embedding approaches: the implicit solvation polarizable continuum model, the explicit polarizable embedding, and frozen density embedding models. DIRAC was one of the earliest codes for relativistic molecular calculations and remains a reference in its field.

Comprehensive Benchmark Results for the Domain Based Local Pair Natural Orbital Coupled Cluster Method (DLPNO-CCSD(T)) for Closed- and Open-Shell Systems

Abstract: In this study we examine the accuracy of domain-based local pair natural orbital coupled cluster theory with single, double, and perturbative triple excitations (DLPNO-CCSD(T)) on a large benchmark data set. To this end, we use the recently published GMTKN55 superset of molecules that contains 1505 relative energies and 2462 single-point calculations. To our knowledge this is the most comprehensive benchmark evaluation of any highly correlated wave function based ab initio method to date. In the first part of the study, canonical CCSD(T) reference calculations were carried out on the entire test set in order to guarantee that the reference data are of uniform quality. Second, DLPNO-CCSD(T) calculations were carried out under identical conditions. The main finding is that with the exception of two data sets, all data sets have a MAD of 0.4 kcal/mol or less and the majority of sets have a MAD of less than 0.2 kcal/mol. For open shells, the accuracy of the DLPNO calculations was significantly improved through an iterative version of the triples correction.

The DIRAC code for relativistic molecular calculations

Abstract: DIRAC is a freely distributed general-purpose program system for one-, two-, and four-component relativistic molecular calculations at the level of Hartree–Fock, Kohn–Sham (including range-separated theory), multiconfigurational self-consistent-field, multireference configuration interaction, electron propagator, and various flavors of coupled cluster theory. At the self-consistent-field level, a highly original scheme, based on quaternion algebra, is implemented for the treatment of both spatial and time reversal symmetry. DIRAC features a very general module for the calculation of molecular properties that to a large extent may be defined by the user and further analyzed through a powerful visualization module. It allows for the inclusion of environmental effects through three different classes of increasingly sophisticated embedding approaches: the implicit solvation polarizable continuum model, the explicit polarizable embedding model, and the frozen density embedding model.

Is the Trotterized UCCSD Ansatz Chemically Well-Defined?

Abstract: The variational quantum eigensolver (VQE) has emerged as one of the most promising near-term quantum algorithms that can be used to simulate many-body systems such as molecular electronic structures. Serving as an attractive ansatz in the VQE algorithm, unitary coupled cluster (UCC) theory has seen a renewed interest in recent literature. However, unlike the original classical UCC theory, implementation on a quantum computer requires a finite-order Suzuki-Trotter decomposition to separate the exponentials of the large sum of Pauli operators. While previous literature has recognized the nonuniqueness of different orderings of the operators in the Trotterized form of UCC methods, the question of whether or not different orderings matter at the chemical scale has not been addressed. In this Letter, we explore the effect of operator ordering on the Trotterized UCCSD ansatz, as well as the much more compact k-UpCCGSD ansatz recently proposed by Lee et al. [ J. Chem. Theory Comput. , 2019 , 15 , 311 . arXiv, 2019 , quant-ph:1909.09114. https://arxiv.org/abs/1909.09114 ]. We observe a significant, system-dependent variation in the energies of Trotterizations with different operator orderings. The energy variations occur on a chemical scale, sometimes on the order of hundreds of kcal/mol. This Letter establishes the need to define not only the operators present in the ansatz but also the order in which they appear. This is necessary for adhering to the quantum chemical notion of a "model chemistry", in addition to the general importance of scientific reproducibility. As a final note, we suggest a useful strategy to select out of the combinatorial number of possibilities, a single well-defined and effective ordering of the operators.

The ANI-1ccx and ANI-1x data sets, coupled-cluster and density functional theory properties for molecules

Abstract: Maximum diversification of data is a central theme in building generalized and accurate machine learning (ML) models. In chemistry, ML has been used to develop models for predicting molecular properties, for example quantum mechanics (QM) calculated potential energy surfaces and atomic charge models. The ANI-1x and ANI-1ccx ML-based general-purpose potentials for organic molecules were developed through active learning; an automated data diversification process. Here, we describe the ANI-1x and ANI-1ccx data sets. To demonstrate data diversity, we visualize it with a dimensionality reduction scheme, and contrast against existing data sets. The ANI-1x data set contains multiple QM properties from 5 M density functional theory calculations, while the ANI-1ccx data set contains 500 k data points obtained with an accurate CCSD(T)/CBS extrapolation. Approximately 14 million CPU core-hours were expended to generate this data. Multiple QM calculated properties for the chemical elements C, H, N, and O are provided: energies, atomic forces, multipole moments, atomic charges, etc. We provide this data to the community to aid research and development of ML models for chemistry. Machine-accessible metadata file describing the reported data: https://doi.org/10.6084/m9.figshare.12046440

A Mountaineering Strategy to Excited States: Highly Accurate Energies and Benchmarks for Medium Sized Molecules

Abstract: Following our previous work focussing on compounds containing up to 3 non-hydrogen atoms [\emph{J. Chem. Theory Comput.} {\bfseries 14} (2018) 4360--4379], we present here highly-accurate vertical transition energies obtained for 27 molecules encompassing 4, 5, and 6 non-hydrogen atoms. To obtain these energies, we use equation-of-motion coupled cluster theory up to the highest technically possible excitation order for these systems (CC3, EOM-CCSDT, and EOM-CCSDTQ), selected configuration interaction (SCI) calculations (with tens of millions of determinants in the reference space), as well as the multiconfigurational $n$-electron valence state perturbation theory (NEVPT2) method. All these approaches are applied in combination with diffuse-containing atomic basis sets. For all transitions, we report at least CC3/\emph{aug}-cc-pVQZ vertical excitation energies as well as CC3/\emph{aug}-cc-pVTZ oscillator strengths for each dipole-allowed transition. We show that CC3 almost systematically delivers transition energies in agreement with higher-level methods with a typical deviation of $\pm 0.04$ eV, except for transitions with a dominant double excitation character where the error is much larger. The present contribution gathers a large, diverse and accurate set of more than 200 highly-accurate transition energies for states of various natures (valence, Rydberg, singlet, triplet, $n \rightarrow \pi^*$, $\pi \rightarrow \pi^*$, \ldots). We use this series of theoretical best estimates to benchmark a series of popular methods for excited state calculations: CIS(D), ADC(2), CC2, STEOM-CCSD, EOM-CCSD, CCSDR(3), CCSDT-3, CC3, as well as NEVPT2. The results of these benchmarks are compared to the available literature data.

Iterative Qubit Coupled Cluster Approach with Efficient Screening of Generators.

Abstract: An iterative version of the qubit coupled cluster (QCC) method [I. G. Ryabinkin et al., J. Chem. Theory Comput. 2019, 14, 6317] is proposed. The new method seeks to find ground electronic energies ...

Quantum orbital-optimized unitary coupled cluster methods in the strongly correlated regime: Can quantum algorithms outperform their classical equivalents?

Abstract: The Coupled Cluster (CC) method is used to compute the electronic correlation energy in atoms and molecules and often leads to highly accurate results. However, due to its single-reference nature, standard CC in its projected form fails to describe quantum states characterized by strong electronic correlations and multi-reference projective methods become necessary. On the other hand, quantum algorithms for the solution of many-electron problems have also emerged recently. The quantum unitary variant of CC (UCC) with singles and doubles (q-UCCSD) is a popular wavefunction Ansatz for the variational quantum eigensolver algorithm. The variational nature of this approach can lead to significant advantages compared to its classical equivalent in the projected form, in particular, for the description of strong electronic correlation. However, due to the large number of gate operations required in q-UCCSD, approximations need to be introduced in order to make this approach implementable in a state-of-the-art quantum computer. In this work, we evaluate several variants of the standard q-UCCSD Ansatz in which only a subset of excitations is included. In particular, we investigate the singlet and pair q-UCCD approaches combined with orbital optimization. We show that these approaches can capture the dissociation/distortion profiles of challenging systems, such as H4, H2O, and N2 molecules, as well as the one-dimensional periodic Fermi-Hubbard chain. These results promote the future use of q-UCC methods for the solution of challenging electronic structure problems in quantum chemistry.

Fermionic neural-network states for ab-initio electronic structure.

Abstract: Neural-network quantum states have been successfully used to study a variety of lattice and continuous-space problems. Despite a great deal of general methodological developments, representing fermionic matter is however still early research activity. Here we present an extension of neural-network quantum states to model interacting fermionic problems. Borrowing techniques from quantum simulation, we directly map fermionic degrees of freedom to spin ones, and then use neural-network quantum states to perform electronic structure calculations. For several diatomic molecules in a minimal basis set, we benchmark our approach against widely used coupled cluster methods, as well as many-body variational states. On some test molecules, we systematically improve upon coupled cluster methods and Jastrow wave functions, reaching chemical accuracy or better. Finally, we discuss routes for future developments and improvements of the methods presented. Despite the importance of neural-network quantum states, representing fermionic matter is yet to be fully achieved. Here the authors map fermionic degrees of freedom to spin ones and use neural-networks to perform electronic structure calculations on model diatomic molecules to achieve chemical accuracy.

Automated Fitting of Neural Network Potentials at Coupled Cluster Accuracy: Protonated Water Clusters as Testing Ground

Abstract: Highly accurate potential energy surfaces are of key interest for the detailed understanding and predictive modeling of chemical systems. In recent years, several new types of force fields, which are based on machine learning algorithms and fitted to ab initio reference calculations, have been introduced to meet this requirement. Here, we show how high-dimensional neural network potentials can be employed to automatically generate the potential energy surface of finite sized clusters at coupled cluster accuracy, namely CCSD(T*)-F12a/aug-cc-pVTZ. The developed automated procedure utilizes the established intrinsic properties of the model such that the configurations for the training set are selected in an unbiased and efficient way to minimize the computational effort of expensive reference calculations. These ideas are applied to protonated water clusters from the hydronium cation, H3O+, up to the tetramer, H9O4+, and lead to a single potential energy surface that describes all these systems at essentially converged coupled cluster accuracy with a fitting error of 0.06 kJ/mol per atom. The fit is validated in detail for all clusters up to the tetramer and yields reliable results not only for stationary points but also for reaction pathways and intermediate configurations as well as different sampling techniques. Per design, the neural network potentials (NNPs) constructed in this fashion can handle very different conditions including the quantum nature of the nuclei and enhanced sampling techniques covering very low as well as high temperatures. This enables fast and exhaustive exploration of the targeted protonated water clusters with essentially converged interactions. In addition, the automated process will allow one to tackle finite systems much beyond the present case.

eT 1.0: An open source electronic structure program with emphasis on coupled cluster and multilevel methods.

Abstract: The eT program is an open source electronic structure package with emphasis on coupled cluster and multilevel methods. It includes efficient spin adapted implementations of ground and excited singlet states, as well as equation of motion oscillator strengths, for CCS, CC2, CCSD, and CC3. Furthermore, eT provides unique capabilities such as multilevel Hartree-Fock and multilevel CC2, real-time propagation for CCS and CCSD, and efficient CC3 oscillator strengths. With a coupled cluster code based on an efficient Cholesky decomposition algorithm for the electronic repulsion integrals, eT has similar advantages as codes using density fitting, but with strict error control. Here, we present the main features of the program and demonstrate its performance through example calculations. Because of its availability, performance, and unique capabilities, we expect eT to become a valuable resource to the electronic structure community.

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

Abstract: 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.

Jastrow-type Decomposition in Quantum Chemistry for Low-Depth Quantum Circuits

Abstract: We propose an efficient O(N2)-parameter ansatz that consists of a sequence of exponential operators, each of which is a unitary variant of Neuscamman's cluster Jastrow operator. The ansatz can also be derived as a decomposition of T2 amplitudes of the unitary coupled cluster with generalized singles and doubles, which gives a near full-CI energy. The proposed ansatz therefore can reproduce the uCCGSD energy, or rather will reach the exact full-CI energy because of the exponential operator product form. Because the cluster Jastrow operators are expressed by a product of number operators and the derived Pauli operator products, namely, the Jordan-Wigner strings, are all commutative, it does not require the Trotter approximation to implement to a quantum circuit and should be a good candidate for the variational quantum eigensolver algorithm of a near-term quantum computer. The accuracy of the ansatz was examined for dissociation of a nitrogen dimer, and compared with other existing O(N2)-parameter ansatzs. Not only the original ansatzs defined in the second-quantization form but also their Trotter-splitting variants, in which the cluster amplitudes are optimized to minimize the energy obtained with a few, typically single, Trotter steps, were examined by quantum circuit simulators.

Unveiling the Photophysical Properties of Boron-dipyrromethene Dyes Using a New Accurate Excited State Coupled Cluster Method

Abstract: Boron-dipyrromethene (BODIPY) molecules form a class of fluorescent dyes known for their exceptional photoluminescence properties. Today, they are used extensively in various applications from fluorescent imaging to optoelectronics. The ease of altering the BODIPY core has allowed scientists to synthesize dozens of analogues by exploring chemical substitutions of various kinds or by increasing the length of conjugated groups. However, predicting the impact of any chemical change accurately is still a challenge, especially as most computational methods fail to describe correctly the photophysical properties of BODIPY derivatives. In this study, the recently developed coupled cluster method called "domain-based local pair natural orbital similarity transformed equation of motion-coupled cluster singles and doubles" (DLPNO-STEOM-CCSD) is employed to compute the lowest vertical excitation energies of more than 50 BODIPY molecules. The method performs remarkably well yielding an accuracy of about 0.06 eV compared to the experimental absorption maxima. We also provide an estimate to the error made by neglecting vibronic effects in the computed spectra. The dyes selected for investigation here span a large range of molecular sizes and chemical functionalities and are embedded in solvents with different polarities. We have also investigated if the method is able to correctly reproduce the impact of a single chemical modification on the absorption energy. To characterize the method in more specific terms, we have studied four large BODIPY analogues used in real-life applications due to their interesting chemical properties. These examples should illustrate the capacity of the DLPNO-STEOM-CCSD procedure to become a method of choice for the study of photophysical properties of medium to large organic compounds.

Detailed Pair Natural Orbital–based Coupled Cluster Studies of Spin Crossover Energetics

Abstract: In this work, a detailed study of spin-state splittings in three spin crossover model compounds with DLPNO-CCSD(T) is presented. The performance in comparison to canonical CCSD(T) is assessed in detail. It was found that spin-state splittings with chemical accuracy, compared to the canonical results, are achieved when the full iterative triples (T1) scheme and TightPNO settings are applied and relativistic effects are taken into account. Having established the level of accuracy that can be reached relative to the canonical results, we have undertaken a detailed basis set study in the second part of the study. The slow convergence of the results of correlated calculations with respect to basis set extension is particularly acute for spin-state splittings for reasons discussed in detail in this Article. In fact, for some of the studied systems, 5Z basis sets are necessary in order to come close to the basis set limit that is estimated here by basis set extrapolation. Finally, the results of the present work are compared to available literature. In general, acceptable agreement with previous CCSD(T) results is found, although notable deviations stemming from differences in methodology and basis sets are noted. It is noted that the published CASPT2 numbers are far away from the extrapolated CCSD(T) numbers. In addition, dynamic quantum Monte Carlo results differ by several tens of kcal/mol from the CCSD(T) numbers. A comparison to DFT results produced with a range of popular density functionals shows the expected scattering of results and showcases the difficulty of applying DFT to spin-state energies.

Ground State Energy Functional with Hartree-Fock Efficiency and Chemical Accuracy.

Abstract: We introduce the deep post Hartree-Fock (DeePHF) method, a machine learning-based scheme for constructing accurate and transferable models for the ground-state energy of electronic structure problems. DeePHF predicts the energy difference between results of highly accurate models such as the coupled cluster method and low accuracy models such as the Hartree-Fock (HF) method, using the ground-state electronic orbitals as the input. It preserves all the symmetries of the original high accuracy model. The added computational cost is less than that of the reference HF or DFT and scales linearly with respect to system size. We examine the performance of DeePHF on organic molecular systems using publicly available data sets and obtain the state-of-art performance, particularly on large data sets.

Efficient Step-Merged Quantum Imaginary Time Evolution Algorithm for Quantum Chemistry.

Abstract: We develop a resource-efficient step-merged quantum imaginary time evolution approach (smQITE) to solve for the ground state of a Hamiltonian on quantum computers This heuristic method features a fixed shallow quantum circuit depth along the state evolution path We use this algorithm to determine the binding energy curves of a set of molecules, including H2, H4, H6, LiH, HF, H2O, and BeH2, and find highly accurate results The required quantum resources of smQITE calculations can be further reduced by adopting the circuit form of the variational quantum eigensolver (VQE) technique, such as the unitary coupled cluster ansatz We demonstrate that smQITE achieves a similar computational accuracy as VQE at the same fixed-circuit ansatz, without requiring a generally complicated high-dimensional nonconvex optimization Finally, smQITE calculations are carried out on Rigetti quantum processing units, demonstrating that the approach is readily applicable on current noisy intermediate-scale quantum devices

Accurate Computation of the Absorption Spectrum of Chlorophyll a with Pair Natural Orbital Coupled Cluster Methods.

Abstract: The ability to accurately compute low-energy excited states of chlorophylls is critically important for understanding the vital roles they play in light harvesting, energy transfer, and photosynthetic charge separation. The challenge for quantum chemical methods arises both from the intrinsic complexity of the electronic structure problem and, in the case of biological models, from the need to account for protein-pigment interactions. In this work, we report electronic structure calculations of unprecedented accuracy for the low-energy excited states in the Q and B bands of chlorophyll a. This is achieved by using the newly developed domain-based local pair natural orbital (DLPNO) implementation of the similarity transformed equation of motion coupled cluster theory with single and double excitations (STEOM-CCSD) in combination with sufficiently large and flexible basis sets. The results of our DLPNO-STEOM-CCSD calculations are compared with more approximate approaches. The results demonstrate that, in contrast to time-dependent density functional theory, the DLPNO-STEOM-CCSD method provides a balanced performance for both absorption bands. In addition to vertical excitation energies, we have calculated the vibronic spectrum for the Q and B bands through a combination of DLPNO-STEOM-CCSD and ground-state density functional theory frequency calculations. These results serve as a basis for comparison with gas-phase experiments.

Coupled cluster theory in materials science

Abstract: In this tutorial-style review we discuss basic concepts of coupled cluster theory and recent developments that increase its computational efficiency for calculations of molecules, solids and materials in general. We will touch upon the connection between coupled cluster theory and the random-phase approximation that is widely used in the field of solid-state physics. We will discuss various approaches to improve the computational performance without compromising on accuracy. These approaches include large-scale parallel design as well as techniques that reduce the pre-factor of the computational complexity. A central part of this article discusses the convergence of calculated properties to the thermodynamic limit, which is of significant importance for reliable predictions of materials properties and constitutes an additional challenge compared to calculations of large molecules. We mention technical aspects of computer code implementations of periodic coupled cluster theories in different numerical frameworks of the one-electron orbital basis; the projector-augmented-wave formalism using a plane wave basis set and the numeric atom-centered-orbital (NAO) with resolution-of-identity. We will discuss results and the possible scope of these implementations and how they can help advance the current state of the art in electronic structure theory calculations of materials.

Qubit coupled cluster singles and doubles variational quantum eigensolver ansatz for electronic structure calculations

Abstract: Variational quantum eigensolver (VQE) for electronic structure calculations is believed to be one major potential application of near term quantum computing. Among all proposed VQE algorithms, the unitary coupled cluster singles and doubles excitations (UCCSD) VQE ansatz has achieved high accuracy and received a lot of research interest. However, the UCCSD VQE based on fermionic excitations needs extra terms for the parity when using Jordan-Wigner transformation. Here we introduce a new VQE ansatz based on the particle preserving exchange gate to achieve qubit excitations. The proposed VQE ansatz has gate complexity up-bounded to $O(n^4)$ where $n$ is the number of qubits of the Hamiltonian. Numerical results of simple molecular systems such as BeH$_2$, H$_2$O, N$_2$, H$_4$ and H$_6$ using the proposed VQE ansatz gives very accurate results within errors about $10^{-3}$ Hartree.

Equation-of-motion coupled-cluster theory to model L-edge x-ray absorption and photoelectron spectra

Abstract: We present an extension of the equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) theory for computing X-ray L-edge spectra, both in the absorption (XAS) and in the photoelectron (XPS) regimes. The approach is based on the perturbative evaluation of spin-orbit couplings using the Breit-Pauli Hamiltonian and nonrelativistic wave functions described by the fc-CVS-EOM-CCSD ansatz (EOM-CCSD within the frozen-core core-valence separated (fc-CVS) scheme). The formalism is based on spinless one-particle density matrices. The approach is illustrated by modeling XAS and XPS of several model systems ranging from Ar to small molecules containing sulfur and silicon.

Polaritonic coupled-cluster theory

Abstract: We develop coupled-cluster theory for systems of electrons strongly coupled to photons, providing a promising theoretical tool in polaritonic chemistry with a perspective of application to all types of fermion-boson coupled systems. We show benchmark results for model molecular Hamiltonians coupled to cavity photons. By comparing to full configuration interaction results for various ground-state properties and optical spectra, we demonstrate that our method captures all key features present in the exact reference, including Rabi splittings and multiphoton processes. Furthermore, a path on how to incorporate our bosonic extension of coupled-cluster theory into existing quantum chemistry programs is given.

Excitons in Solids from Periodic Equation-of-Motion Coupled-Cluster Theory.

Abstract: We present an ab initio study of electronically excited states of three-dimensional solids using Gaussian-based periodic equation-of-motion coupled-cluster theory with single and double excitations...

Hardware Efficient Quantum Algorithms for Vibrational Structure Calculations

Abstract: We introduce a framework for the calculation of ground and excited state energies of bosonic systems suitable for near-term quantum devices and apply it to molecular vibrational anharmonic Hamiltonians. Our method supports generic reference modal bases and Hamiltonian representations, including the ones that are routinely used in classical vibrational structure calculations. We test different parametrizations of the vibrational wave function, which can be encoded in quantum hardware, based either on heuristic circuits or on the bosonic Unitary Coupled Cluster Ansatz. In particular, we define a novel compact heuristic circuit and demonstrate that it provides the best compromise in terms of circuit depth, optimization costs, and accuracy. We evaluate the requirements, number of qubits and circuit depth, for the calculation of vibrational energies on quantum hardware and compare them with state-of-the-art classical vibrational structure algorithms for molecules with up to seven atoms.

A New Benchmark Set for Excitation Energy of Charge Transfer States: Systematic Investigation of Coupled Cluster Type Methods.

Abstract: The numerous existing publications on benchmarking quantum chemistry methods for excited states rarely include Charge Transfer (CT) states, although many interesting phenomena in, e.g., biochemistr...

Finding chemical concepts in the Hilbert space: Coupled cluster analyses of noncovalent interactions

Abstract: Noncovalent interactions (NCIs) play a major role in essentially all fields of chemical research. Energy decomposition analysis (EDA) schemes provide in‐depth insights into their nature by decomposing interaction energies into additive contributions, such as electrostatics, polarization, and London dispersion. Although modern local variants of the “gold standard” coupled‐cluster singles and doubles method plus perturbative triples (CCSD(T)) have made it possible to accurately quantify NCIs for relatively large systems, extracting chemically meaningful energy terms from such high level electronic structure calculations has been a long lasting challenge in computational chemistry. This review describes basic principles, interpretative aspects and applications of recently developed coupled cluster‐based EDAs for the analysis of NCIs. The focus is on computationally efficient methods for systems with a few hundred atoms, for example, the recently introduced local energy decomposition analysis. In order to draw connections between different interpretative frameworks, these schemes are compared with other popular approaches for the quantification and analysis of NCIs, such as Symmetry Adapted Perturbation Theory and supermolecular EDAs based on mean‐field as well as correlated approaches. Strengths and limitations of the various techniques are discussed.

Protein Matrix Control of Reaction Center Excitation in Photosystem II.

Abstract: Photosystem II (PSII) is a multisubunit pigment-protein complex that uses light-induced charge separation to power oxygenic photosynthesis. Its reaction center chromophores, where the charge transfer cascade is initiated, are arranged symmetrically along the D1 and D2 core polypeptides and comprise four chlorophyll (PD1, PD2, ChlD1, ChlD2) and two pheophytin molecules (PheoD1 and PheoD2). Evolution favored productive electron transfer only via the D1 branch, with the precise nature of primary excitation and the factors that control asymmetric charge transfer remaining under investigation. Here we present a detailed atomistic description for both. We combine large-scale simulations of membrane-embedded PSII with high-level quantum-mechanics/molecular-mechanics (QM/MM) calculations of individual and coupled reaction center chromophores to describe reaction center excited states. We employ both range-separated time-dependent density functional theory and the recently developed domain based local pair natural orbital (DLPNO) implementation of the similarity transformed equation of motion coupled cluster theory with single and double excitations (STEOM-CCSD), the first coupled cluster QM/MM calculations of the reaction center. We find that the protein matrix is exclusively responsible for both transverse (chlorophylls versus pheophytins) and lateral (D1 versus D2 branch) excitation asymmetry, making ChlD1 the chromophore with the lowest site energy. Multipigment calculations show that the protein matrix renders the ChlD1 → PheoD1 charge-transfer the lowest energy excitation globally within the reaction center, lower than any pigment-centered local excitation. Remarkably, no low-energy charge transfer states are located within the "special pair" PD1-PD2, which is therefore excluded as the site of initial charge separation in PSII. Finally, molecular dynamics simulations suggest that modulation of the electrostatic environment due to protein conformational flexibility enables direct excitation of low-lying charge transfer states by far-red light.

A Generalized Variational Principle with Applications to Excited State Mean Field Theory.

Abstract: We present a generalization of the variational principle that is compatible with any Hamiltonian eigenstate that can be specified uniquely by a list of properties. This variational principle appears to be compatible with a wide range of electronic structure methods, including mean field theory, density functional theory, multireference theory, and quantum Monte Carlo. Like the standard variational principle, this generalized variational principle amounts to the optimization of a nonlinear function that, in the limit of an arbitrarily flexible wave function, has the desired Hamiltonian eigenstate as its global minimum. Unlike the standard variational principle, it can target excited states and select individual states in cases of degeneracy or near-degeneracy. As an initial demonstration of how this approach can be useful in practice, we employ it to improve the optimization efficiency of excited state mean field theory by an order of magnitude. With this improved optimization, we are able to demonstrate that the accuracy of the corresponding second-order perturbation theory rivals that of singles-and-doubles equation-of-motion coupled cluster in a substantially broader set of molecules than could be explored by our previous optimization methodology.

Resource-Efficient Chemistry on Quantum Computers with the Variational Quantum Eigensolver and the Double Unitary Coupled-Cluster Approach.

Abstract: Applications of quantum simulation algorithms to obtain electronic energies of molecules on noisy intermediate-scale quantum (NISQ) devices require careful consideration of resources describing the complex electron correlation effects. In modeling second-quantized problems, the biggest challenge confronted is that the number of qubits scales linearly with the size of the molecular basis. This poses a significant limitation on the size of the basis sets and the number of correlated electrons included in quantum simulations of chemical processes. To address this issue and enable more realistic simulations on NISQ computers, we employ the double unitary coupled-cluster (DUCC) method to effectively downfold correlation effects into the reduced-size orbital space, commonly referred to as the active space. Using downfolding techniques, we demonstrate that properly constructed effective Hamiltonians can capture the effect of the whole orbital space in small-size active spaces. Combining the downfolding preprocessing technique with the variational quantum eigensolver, we solve for the ground-state energy of H2, Li2, and BeH2 in the cc-pVTZ basis using the DUCC-reduced active spaces. We compare these results to full configuration-interaction and high-level coupled-cluster reference calculations.

Development of nuclear basis sets for multicomponent quantum chemistry methods.

Abstract: The nuclear-electronic orbital (NEO) framework provides a practical approach for directly incorporating nuclear quantum effects and non-Born-Oppenheimer effects of specified nuclei, typically protons, into quantum chemistry calculations. Multicomponent wave function based methods, such as NEO coupled cluster singles and doubles, and multicomponent density functional theory (DFT), such as NEO-DFT, require the appropriate selection of electronic and nuclear basis sets. Although a wide array of electronic basis sets are available, systematically developed nuclear basis sets that balance accuracy and efficiency have been lacking. Herein, a series of nuclear basis sets are developed and shown to be accurate and efficient for describing both ground and excited state properties of multicomponent systems in which electrons and specified protons are treated quantum mechanically. Three series of Gaussian-type nuclear basis sets, denoted PB4, PB5, and PB6, are developed with varying levels of angular momentum. A machine-learning optimization procedure relying on the Gaussian process regression method is utilized to accelerate the optimization process. The basis sets are validated in terms of predictions of ground state energies, proton densities, proton affinities, and proton vibrational excitation energies, allowing the user to select the desired balance between accuracy and efficiency for the properties of interest. These nuclear basis sets will enhance the tractability of NEO methods for applications to a wide range of chemical systems.