Perturbative Triples Correction Research Articles

A new "gold standard": Perturbative triples corrections in unitary coupled cluster theory and prospects for quantum computing.

A major difficulty in quantum simulation is the adequate treatment of a large collection of entangled particles, synonymous with electron correlation in electronic structure theory, with coupled cluster (CC) theory being the leading framework for dealing with this problem. Augmenting computationally affordable low-rank approximations in CC theory with a perturbative account of higher-rank excitations is a tractable and effective way of accounting for the missing electron correlation in those approximations. This is perhaps best exemplified by the "gold standard" CCSD(T) method, which bolsters the baseline CCSD with the effects of triple excitations using considerations from many-body perturbation theory (MBPT). Despite this established success, such a synergy between MBPT and the unitary analog of CC theory (UCC) has not been explored. In this work, we propose a similar approach wherein converged UCCSD amplitudes are leveraged to evaluate energy corrections associated with triple excitations, leading to the UCCSD[T] method. In terms of quantum computing, this correction represents an entirely classical post-processing step that improves the energy estimate by accounting for triple excitation effects without necessitating new quantum algorithm developments or increasing demand for quantum resources. The rationale behind this choice is shown to be rigorous by studying the properties of finite-order UCC energy functionals, and our efforts do not support the addition of the fifth-order contributions as in the (T) correction. We assess the performance of these approaches on a collection of small molecules and demonstrate the benefits of harnessing the inherent synergy between MBPT and UCC theories.

Coupled cluster method tailored with quantum computing

Introducing an active space approximation is inevitable for the quantum computations of chemical systems. However, this approximation ignores the electron correlations related to nonactive orbitals. Here, we propose a computational method for correcting quantum computing results using a well-established classical theory called coupled cluster theory. Our approach efficiently extracts the quantum state from a quantum device by computational basis tomography. The extracted expansion coefficients of the quantum state are embedded into the coupled cluster ansatz within the framework of the tailored coupled cluster method. We demonstrate the performance of our method by verifying the potential energy curves of LiH, H2O, and N2 with a correlation-energy correction scheme. Our method demonstrates reasonable potential energy curves even when the standard coupled cluster fails. The sufficient numbers of measurements for tomography were also investigated. Furthermore, this method successfully estimated the activation energy of the Cope rearrangement reaction of 1,5-hexadiene together with perturbative triples correction. These demonstrations suggest that our approach has the potential for practical quantum chemical calculations using quantum computers. Published by the American Physical Society 2024

Electronic properties and collision cross sections of AgOkHm± (k, m = 1-4) aerosol ionic clusters.

Experimental evidence shows that hydroxylated metal ions are often produced during cluster synthesis by atmospheric pressure spark ablation. In this work, we predict the ground state equilibrium structures of AgOkHm± clusters (k and m = 1-4), which are readily produced when spark ablating Ag, using the coupled cluster with singles and doubles (CCSD) method. The stabilization energy of these clusters is calculated with respect to the dissociation channel having the lowest energy, by accounting perturbative triples corrections to the CCSD method. The interatomic interactions in each of the systems have been investigated using the frontier molecular orbital (FMO), natural bond orbital (NBO) and quantum theory of atoms in molecules (QTAIM) methods. Many of the ground states of these ionic clusters are found to be stable, corroborating experimental observations. We find that clusters having singlet spin states are more stable in terms of dissociation than the clusters that have doublet or triplet spin states. Our calculations also indicate a strong affinity of the ionic and neutral Ag atom towards water and hydroxyl radicals or ions. Many 3-center, 4-electron (3c/4e) hyperbonds giving rise to more than one resonance structure are identified primarily for the anionic clusters. The QTAIM analysis shows that the O-H and O-Ag bonds in the clusters of both polarities are respectively covalent and ionic. The FMO analysis indicates that the anionic clusters are more reactive than the cationic ones. Using the cluster structures predicted by the CCSD method, we calculate the collision cross sections of the AgOkHm± family, with k and m ranging from 1 to 4, by the trajectory method. In turn, we predict the electrical mobilities of these clusters when suspended in helium at atmospheric pressure and compare them with experimental measurements.

Accelerating Coupled-Cluster Calculations with GPUs: An Implementation of the Density-Fitted CCSD(T) Approach for Heterogeneous Computing Architectures Using OpenMP Directives.

An algorithm is presented for the coupled-cluster singles, doubles, and perturbative triples correction [CCSD(T)] method based on the density fitting or the resolution-of-the-identity (RI) approximation for performing calculations on heterogeneous computing platforms composed of multicore CPUs and graphics processing units (GPUs). The directive-based approach to GPU offloading offered by the OpenMP application programming interface has been employed to adapt the most compute-intensive terms in the RI-CCSD amplitude equations with computational costs scaling as , , and (where NO and NV denote the numbers of correlated occupied and virtual orbitals, respectively) and the perturbative triples correction to execute on GPU architectures. The pertinent tensor contractions are performed using an accelerated math library such as cuBLAS or hipBLAS. Optimal strategies are discussed for splitting large data arrays into tiles to fit them into the relatively small memory space of the GPUs, while also minimizing the low-bandwidth CPU-GPU data transfers. The performance of the hybrid CPU-GPU RI-CCSD(T) code is demonstrated on pre-exascale supercomputers composed of heterogeneous nodes equipped with NVIDIA Tesla V100 and A100 GPUs and on the world's first exascale supercomputer named "Frontier", the nodes of which consist of AMD MI250X GPUs. Speedups within the range 4-8× relative to the recently reported CPU-only algorithm are obtained for the GPU-offloaded terms in the RI-CCSD amplitude equations. Applications to polycyclic aromatic hydrocarbons containing 16-66 carbon atoms demonstrate that the acceleration of the hybrid CPU-GPU code for the perturbative triples correction relative to the CPU-only code increases with the molecule size, attaining a speedup of 5.7× for the largest circumovalene molecule (C66H20). The GPU-offloaded code enables the computation of the perturbative triples correction for the C60 molecule using the cc-pVDZ/aug-cc-pVTZ-RI basis sets in 7 min on Frontier when using 12,288 AMD GPUs with a parallel efficiency of 83.1%.

Electronic Structure, Stability, and Electrical Mobility of Cationic Silver Oxide Atomic Clusters.

Silver oxide cluster cations (AgnOm+) can readily be produced by a number of methods including atmospheric-pressure spark ablation of pure silver electrodes when trace amounts of oxygen are present in the carrier gas. Here we determine the equilibrium geometries of AgnOm+ clusters (n = 1-4; m = 1-5) using accurate coupled cluster with singles and doubles (CCSD) method, while the stabilization energies are calculated with additional perturbative triples correction (CCSD(T)). Although a number of stable states have been identified, our results show that the AgnOm+ clusters with m = 1 are more stable than those with m ≥ 2 due to the absence of the terminally attached O2 molecule, corroborating recent observations by mass spectrometry. Using the computed structures, we calculate the electrical mobilities of the AgnOm+ clusters and label the values on a respective experimentally determined spectrum in an attempt to better interpret the occurrence of the peaks and troughs in the measurements.

Reconciling Local Coupled Cluster with Multireference Approaches for Transition Metal Spin-State Energetics

Spin-state energetics of transition metal complexes remain one of the most challenging targets for electronic structure methods. Among single-reference wave function approaches, local correlation approximations to coupled cluster theory, most notably the domain-based local pair natural orbital (DLPNO) approach, hold the promise of bringing the accuracy of coupled cluster theory with single, double, and perturbative triple excitations, CCSD(T), to molecular systems of realistic size with acceptable computational cost. However, recent studies on spin-state energetics of iron-containing systems raised doubts about the ability of the DLPNO approach to adequately and systematically approximate energetics obtained by the reference-quality complete active space second-order perturbation theory with coupled-cluster semicore correlation, CASPT2/CC. Here, we revisit this problem using a diverse set of iron complexes and examine several aspects of the application of the DLPNO approach. We show that DLPNO-CCSD(T) can accurately reproduce both CASPT2/CC and canonical CCSD(T) results if two basic principles are followed. These include the consistent use of the improved iterative (T1) versus the semicanonical perturbative triple corrections and, most importantly, a simple two-point extrapolation to the PNO space limit. The latter practically eliminates errors arising from the default truncation of electron-pair correlation spaces and should be viewed as standard practice in applications of the method to transition metal spin-state energetics. Our results show that reference-quality results can be readily achieved with DLPNO-CCSD(T) if these principles are followed. This is important also in view of the applicability of the method to larger single-reference systems and multinuclear clusters, whose treatment of dynamic correlation would be challenging for multireference-based approaches.

Limitations of perturbative coupled-cluster approximations for highly accurate investigations of Rb2+

We reveal limitations of several standard coupled-cluster (CC) methods with perturbation-theory based noniterative or approximate iterative treatments of triple excitations when applied to the determination of highly accurate potential energy curves (PECs) of ionic dimers, such as the XΣg+2 electronic ground state of Rb2 +. Such computations are of current interest for the understanding of ion-atom interactions in the ultracold regime. We demonstrate that these CC methods lead to an unphysical long-range barrier for the Rb2 + system. The barrier is small but spoils the long-range behavior of the PEC. The effect is also found for other X2 + systems, such as X = Li, Na, and K. Calculations using a flexible framework for obtaining leading perturbative triples corrections derived using an analytic CC singles and doubles energy derivative formulation demonstrate that the origin of this problem lies in the use of T̂3 amplitudes obtained from approximate CC singles, doubles, and triples amplitude equations. It is shown that the unphysical barrier is related to a symmetry instability of the underlying Hartree-Fock mean-field solution, leading to orbitals representing two +0.5-fold charged ions in the limit of separated fragments. This, in turn, leads to a wrong 1/R asymptote of the interaction potential computed by perturbation-based CC approximations. Physically meaningful perturbative corrections in the long-range tail of the PEC may instead be obtained using symmetry-broken reference determinants.

Externally Corrected CCSD with Renormalized Perturbative Triples (R-ecCCSD(T)) and the Density Matrix Renormalization Group and Selected Configuration Interaction External Sources.

We investigate the renormalized perturbative triples correction together with the externally corrected coupled-cluster singles and doubles (ecCCSD) method. We use the density matrix renormalization group (DMRG) and heat-bath CI (HCI) as external sources for the ecCCSD equations. The accuracy is assessed for the potential energy surfaces of H2O, N2, and F2. We find that the triples correction significantly improves upon ecCCSD, and we do not see any instability of the renormalized triples with respect to dissociation. We explore how to balance the cost of computing the external source amplitudes against the accuracy of the subsequent CC calculation. In this context, we find that very approximate wave functions (and their large amplitudes) serve as an efficient and accurate external source. Finally, we characterize the domain of correlation treatable using the ecCCSD and renormalized triples combination studied in this work via a well-known wave function diagnostic.

Scalable Electron Correlation Methods. 8. Explicitly Correlated Open-Shell Coupled-Cluster with Pair Natural Orbitals PNO-RCCSD(T)-F12 and PNO-UCCSD(T)-F12.

We present explicitly correlated open-shell pair natural orbital local coupled-cluster methods, PNO-RCCSD(T)-F12 and PNO-UCCSD(T)-F12. The methods are extensions of our previously reported PNO-R/UCCSD methods (J. Chem. Theory Comput., 2020, 16, 3135-3151, https://pubs.acs.org/doi/10.1021/acs.jctc.0c00192) with additions of explicit correlation and perturbative triples corrections. The explicit correlation treatment follows the spin-orbital CCSD-F12b theory using Ansatz 3*A, which is found to yield comparable or better basis set convergence than the more rigorous Ansatz 3C in computed ionization potentials and reaction energies using double- to quaduple-ζ basis sets. The perturbative triples correction is adapted from the spin-orbital (T) theory to use triples natural orbitals (TNOs). To address the coupling due to off-diagonal Fock matrix elements, the local triples amplitudes are iteratively solved using small domains of TNOs, and a semicanonical (T0) domain correction with larger domains is applied to reduce the domain errors. The performance of the methods is demonstrated through benchmark calculations on ionization potentials, radical stabilization energies, reaction energies of fragmentations and rearrangements in radical cations, and spin-state energy differences of iron complexes. For a few test sets where canonical calculations are feasible, PNO-RCCSD(T)-F12 results agree with the canonical ones to within 0.4 kcal mol-1, and this maximum error is reduced to below 0.2 kcal mol-1 when large local domains are used. For larger systems, results using different thresholds for the local approximations are compared to demonstrate that 1 kcal mol-1 level of accuracy can be achieved using our default settings. For a couple of difficult cases, it is demonstrated that the errors from individual approximations are only a fraction of 1 kcal mol-1, and the overall accuracy of the method does not rely on error compensations. In contrast to canonical calculations, the use of spin-orbitals does not lead to a significant increase of computational time and memory usage in the most expensive steps of PNO-R/UCCSD(T)-F12 calculations. The only exception is the iterative solution of the (T) amplitudes, which can be avoided without significant errors by using a perturbative treatment of the off-diagonal coupling, known as (T1) approximation. For most systems, even the semicanonical approximation (T0) leads only to small errors in relative energies. Our program is well parallelized and capable of computing accurate correlation energies for molecules with 100-200 atoms using augmented triple-ζ basis sets in less than a day of elapsed time on a small computer cluster.

Gas-Phase Thermochemistry of MX3 and M2X6 (M = Sc, Y; X = F, Cl, Br, I) from a Composite Reaction-Based Approach: Homolytic versus Heterolytic Cleavage.

A domain-based local-pair natural-orbital coupled-cluster approach with single, double, and improved linear-scaling perturbative triple correction via an iterative algorithm, DLPNO-CCSD(T1), was applied within the framework of the Feller-Peterson-Dixon approach to derive gas-phase heats of formation of scandium and yttrium trihalides and their dimers via a set of homolytic and heterolytic dissociation reactions. All predicted heats of formation moderately depend on the reaction type with the most and least negative values obtained for homolytic and heterolytic dissociation, respectively. The basis set size dependence, as well as the influence of static correlation effects not covered by the standard (DLPNO-)CCSD(T) approach, suggests that exploitation of the heterolytic dissociation reactions with the formation of M3+ and X- ions leads to the most robust heats of formation. The gas-phase formation enthalpies ΔHf°(0 K)/ΔHf°(298.15 K) and absolute entropies S°(298.15 K) were obtained for the first time for the Sc2F6, Sc2Br6, and Sc2I6 species. For ScBr3, ScI3, Sc2Cl6, and Y2Cl6, we suggest a reexamination of the experimental heats of formation available in the literature. For other compounds, the predicted values were found to be in good agreement with the experimental estimates. Extracted MX3 (M = Sc, Y; X = F, Cl, Br, and I) 0 K atomization enthalpies indicate weaker bonding when moving from fluorine to iodine and from yttrium to scandium. Likewise, the stability of yttrium trihalide dimers degrades when going from fluorine to iodine. Respective scandium trihalide dimers are less stable, with 0 K dimer dissociation energy decreasing in the row fluorine - chlorine - bromine ≈ iodine. Correlation of the (n - 1)s2p6 electrons on bromine and iodine, inclusion of zero-point energy, relativistic effects, and the effective-core-potential correction as well as amelioration of the DLPNO localization inaccuracy are shown to be of similar magnitude, which is critical if accurate heats of formation are a goal.

Energetic degeneracy and electronic structures of germanium trimers doped with titanium.

Geometries and electronic structures of germanium trimer clusters doped with titanium TiGe3 -/0 were studied making use of the complete active space self-consistent field followed by second-order perturbation theory explicitly correlated coupled cluster singles and doubles method with perturbative triples corrections CCSD(T)-F12 and Tao-Perdew-Staroverov-Scuseria methods. Two electronic states (2A' and 2A″) of the anion (pyramid shape) were determined to be nearly degenerate and energetically competing for the anionic ground state of TiGe3 -. These two anionic states are believed to be concurrently populated in the experiment and induce six observed anion photoelectron bands. Total 14 electronic transitions starting from the 2A' and 2A″ states were assigned to five out of six visible bands in the experimental anion photoelectron spectrum of TiGe3 -. Each band was proven to be caused by multiple one-electron detachments from two populated anionic states. The last experimental band with the highest detachment energy is believed to be the result of various inner one-electron removals.

Connected three-body terms in single-reference unitary many-body theories: Iterative and perturbative approximations.

This work introduces various approaches to include connected three-body terms in unitary many-body theories, focusing on the driven similarity renormalization group (DSRG). Starting from the least approximate method-the linearized DSRG truncated to one-, two-, and three-body operators [LDSRG(3)]-we develop several approximate LDSRG(3) models with reduced computational cost. Through a perturbative analysis, we motivate a family of iterative LDSRG(3)-n and -n' (n = 1, 2, 3, 4) methods that contain a subset of the LDSRG(3) diagrams. Among these variants, the LDSRG(3)-2 scheme has the same computational complexity of coupled cluster theory with singles, doubles, and triples (CCSDT), but it outperforms CCSDT in the accuracy of the predicted correlation energies. We also propose and implement two perturbative triples corrections based on the linearized DSRG truncated to one- and two-body operators augmented with recursive semi-quadratic commutators [qDSRG(2)]. The resulting qDSRG(2)+(T) approach matches the accuracy of the "gold-standard" coupled cluster theory with singles, doubles, and perturbative triples model on the energetics of twenty-eight closed-shell atoms and small molecules.

Near-Linear Scaling in DMRG-Based Tailored Coupled Clusters: An Implementation of DLPNO-TCCSD and DLPNO-TCCSD(T).

We present a new implementation of density matrix renormalization group based tailored coupled clusters method (TCCSD), which employs the domain-based local pair natural orbital approach (DLPNO). Compared to the previous local pair natural orbital (LPNO) version of the method, the new implementation is more accurate, offers more favorable scaling, and provides more consistent behavior across the variety of systems. On top of the singles and doubles, we include the perturbative triples correction (T), which is able to retrieve even more dynamic correlation. The methods were tested on three systems: tetramethyleneethane, oxo-Mn(Salen), and iron(II)-porphyrin model. The first two were revisited to assess the performance with respect to LPNO-TCCSD. For oxo-Mn(Salen), we retrieved between 99.8 and 99.9% of the total canonical correlation energy which is an improvement of 0.2% over the LPNO version in less than 63% of the total LPNO runtime. Similar results were obtained for iron(II)-porphyrin. When the perturbative triples correction was employed, irrespective of the active space size or system, the obtained energy differences between two spin states were within the chemical accuracy of 1 kcal/mol using the default DLPNO settings.

Improved and simplified orthogonalisation scheme and connected triples correction within the internally contracted multireference coupled-cluster method

The internally contracted multireference coupled-cluster theory (icMRCC) is reviewed, providing additional insights that we have gained over recent years. In addition, several modifications are presented that lead to an overall improvement in the method. These include a simpler and size extensive way to generate the excitation manifold and therefore determine the cluster amplitudes. Modifications and approximations are also introduced to the perturbative triples correction, icMRCCSD(T), which lead to a small improvement over the previous manifestation, at a reduced computational cost. With these reformulated methods, we can approach sub-chemical accuracy results.

Linear scaling perturbative triples correction approximations for open-shell domain-based local pair natural orbital coupled cluster singles and doubles theory [DLPNO-CCSD(T0/T)

The coupled cluster method with single-, double-, and perturbative triple excitations [CCSD(T)] is considered to be one of the most reliable quantum chemistry theories. However, the steep scaling of CCSD(T) has limited its application to small or medium-sized systems for a long time. In our previous work, the linear scaling domain based local pair natural orbital CCSD variant (DLPNO-CCSD) has been developed for closed-shell and open-shell. However, it is known from extensive benchmark studies that triple-excitation contributions are important to reach chemical accuracy. In the present work, two linear scaling (T) approximations for open-shell DLPNO-CCSD are implemented and compared: (a) an algorithm based on the semicanonical approximation, in which off-diagonal Fock matrix elements in the occupied space are neglected [referred to as DLPNO-(T0)]; and (b) an improved algorithm in which the triples amplitudes are computed iteratively [referred to as DLPNO-(T)]. This work is based on the previous open-shell DLPNO-CCSD algorithm [M. Saitow et al., J. Chem. Phys. 146, 164105 (2017)] as well as the iterative (T) correction for closed-shell systems [Y. Guo et al., J. Chem. Phys. 148, 011101 (2018)]. Our results show that the new open-shell perturbative corrections, DLPNO-(T0/T), can predict accurate absolute and relative correlation energies relative to the canonical reference calculations with the same basis set. The absolute energies from DLPNO-(T) are significantly more accurate than those of DLPNO-(T0). The additional computational effort of DLPNO-(T) relative to DLPNO-(T0) is a factor of 4 on average. We report calculations on systems with more than 4000 basis functions.

Iterative multireference configuration interaction

Iterative multireference configuration interaction (IMRCI) is proposed. It is exploited to compute the electronic energies of H2O and CH2 (singlet and triplet states) at equilibrium and non-equilibrium geometries. The potential energy curves of H2O, CH2 (singlet and triplet states) and N2 have also been calculated with IMRCI as well as the Møller Plesset perturbation theory (MP2, MP3, and MP4), the coupled cluster method with single and double substitutions (CCSD), and CCSD with perturbative triples correction (CCSD(T)). These calculations demonstrate that IMRCI results are independent of the initial guess of configuration functions in the reference space and converge quickly to the results of the full configuration interaction. The IMRCI errors relative to the full configuration interaction results are at the order of magnitude of 10−5 hartree within just 2–4 iterations. Further, IMRCI provides an efficient way to find on the potential energy surface the leading electron configurations which, as correct reference states, will be very helpful for the single-reference and multireference theoretical models to obtain accurate results.

Domain-based local pair natural orbital CCSD(T) calculations of strongly correlated electron systems: Examination of dynamic equilibrium models based on multiple intermediates in S1 state of photosystem II

ABSTRACT Domain-based local pair natural orbital (DLPNO) coupled cluster single and double (CCSD) methods with perturbative triples (T) correction with NormalPNO were used to compute energies for twelve different S1 structures of the CaMn4O5 cluster in the oxygen evolving complex (OEC) of photosystem II (PSII). The DLPNO-CCSD(T0) calculations with TightPNO for the important six structures among them revealed that the right (R)-opened S1XYZW structures were more stable than the corresponding left (L)-opened structures (X = O(5), Y = W2, Z = W1, and W = O(4)) of CaMn4O5. The three different S1 structures belonging to the R-opened type (S1acca, S1bbca, and S1abcb, where O2- = a, OH- = b and H2O = c) were found nearly degenerated in energy, indicating the possibility of the coexistence of different structures in the S1 state. The DLPNO-CCSD(T0) calculations with TightPNO supported the proposal of a dynamic equilibrium model based on the multi-intermediate structures for the S1 state, which is also in agreement with EPR and other experimental and hybrid DFT computational results. Implications of the computational results are discussed in relation to scope and applicability of NormalPNO and TightPNO for the CCSD(T0) calculations of strongly correlated electron systems such as 3d transition-metal complexes.

Exploring Nature and Predicting Strength of Hydrogen Bonds: A Correlation Analysis Between Atoms-in-Molecules Descriptors, Binding Energies, and Energy Components of Symmetry-Adapted Perturbation Theory.

This work studies the underlying nature of H-bonds (HBs) of different types and strengths and tries to predict binding energies (BEs) based on the properties derived from wave function analysis. A total of 42 HB complexes constructed from 28 neutral and 14 charged monomers were considered. This set was designed to sample a wide range of HB strengths to obtain a complete view about HBs. BEs were derived with the accurate coupled cluster singles and doubles with perturbative triples correction (CCSD(T))(T) method and the physical components of the BE were investigated by symmetry-adapted perturbation theory (SAPT). Quantum theory of atoms-in-molecules (QTAIM) descriptors and other HB indices were calculated based on high-quality density functional theory wave functions. We propose a new and rigorous classification of H-bonds (HBs) based on the SAPT decomposition. Neutral complexes are either classified as "very weak" HBs with a BE ≥ -2.5 kcal/mol that are mainly dominated by both dispersion and electrostatic interactions or as "weak-to-medium" HBs with a BE varying between -2.5 and -14.0 kcal/mol that are only dominated by electrostatic interactions. On the other hand, charged complexes are divided into "medium" HBs with a BE in the range of -11.0 to -15.0 kcal/mol, which are mainly dominated by electrostatic interactions, or into "strong" HBs whose BE is more negative than -15.0 kcal/mol, which are mainly dominated by electrostatic together with induction interactions. Among various explored correlations between BEs and wave function-based HB descriptors, a fairly satisfactory correlation was found for the electron density at the bond critical point (BCP; ρBCP ) of HBs. The fitted equation for neutral complexes is BE/kcal/mol = - 223.08 × ρBCP /a. u. + 0.7423 with a mean absolute percentage error (MAPE) of 14.7%, while that for charged complexes is BE/kcal/mol = - 332.34 × ρBCP /a. u. - 1.0661 with a MAPE of 10.0%. In practice, these equations may be used for a quick estimation of HB BEs, for example, for intramolecular HBs or large HB networks in biomolecules. © 2019 Wiley Periodicals, Inc.

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

AbstractWhile 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.This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods Structure and Mechanism > Molecular Structures

Accurate Prediction of Hyperfine Coupling Tensors for Main Group Elements Using a Unitary Group Based Rigorously Spin-Adapted Coupled-Cluster Theory.

We present the development of a perturbative triples correction scheme for the previously reported unitary group based spin-adapted combinatoric open-shell coupled-cluster (CC) singles and doubles (COS-CCSD) approach and report on the applications of the newly developed method, termed "COS-CCSD(T)", to the calculation of hyperfine coupling (HFC) tensors for radicals consisting of hydrogen, second- and third-row elements. The COS-CCSD(T) method involves a single noniterative step with [Formula: see text] scaling of the computational cost for the calculation of triples corrections to the energy. The key feature of this development is the use of spatial semicanonical orbitals generated from standard restricted open-shell Hartree-Fock (ROHF) orbitals, which allows the unperturbed Hamiltonian operator to be defined in terms of a diagonal spin-free Fock operator. The HFC tensors are computed as a first-order property via implementation of an analytic derivative scheme. The required one-particle spin density matrix is computed by using one- and two-particle spin-free density matrices that are obtained from the analytic derivative implementation, in this way avoiding the use of any spin-dependent operator and maintaining spin adaptation of the CC wavefunction. Benchmark calculations of HFC tensors for a set of 21 radicals indicate reasonably good agreement of the COS-CCSD(T) results with experiment and a consistent improvement over the COS-CCSD method. We demonstrate that the accuracies of the isotropic hyperfine coupling constants obtained in unrestricted HF (UHF) reference based spin-orbital CCSD(T) calculations deteriorate when spin contamination in the UHF wavefunction is large, and the results may even become qualitatively incorrect when spin polarization is the driving mechanism. Within a similar noniterative perturbative treatment of triple excitations, the spin-adapted COS-CCSD(T) approach produces accurate results, thus ensuring cost-effectiveness together with reliability.