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Both density functional methods, one based on Gaussian basis sets and one based on plane waves, predict that the crossover from planarity to nonplanarity occurs at clusters larger than Au8, but both correlated ab initio methods predict that this crossover occurs between Au6 and Au8. This is because the density functional theory calculations cannot account for long-range interactions such as dispersion.

The accuracies of excitation energies of the cytosine molecule in the gas phase and in the aqueous solution calculated with noniterative and iterative coupled-cluster methods are discussed. It is shown that the inclusion of triply excited configurations has played a vital role in a proper description of the excitation energies of the cytosine molecule in realistic environment.

The article discusses the characterization of the signature absorption spectrum of a solvated hydroxyl OH radical as a solvent-to-solute charge transfer state. The intensity of such transfer is found to be dependent on the alignment of the molecular orbitals.

An asymptotic extrapolation scheme, based on the behavior of the electronic energies as functions of the cutoff factor for orbital energies corresponding to virtual orbitals is performed for the excited state large-scale calculations. The traditional coupled cluster (CC) method, in combination with the classical molecular dynamics is used to demonstrate the effects of the native environment and the dynamic fluctuations on the various biochemical systems, used frequently.

The completely renormalized [CR-CCSD (T)] method has been used to calculate the entire ground-state potential energy surface` (PES) for the Be + HF reaction. The study concluded that the single-reference 'black-box' CR-CCSD(T) method employing the spin- and symmetry-adapted RHF reference provides a highly accurate PES of the BeFH system, which is almost identical to the PES resulting form, the more expensive and more complicated MRCL(Q) calculations.

The theoretical results of the coupled-cluster, renormalized coupled cluster, and vibrational study on the trans-HNOO molecule are reported. The findings on HNOO are compared with the experimental results obtained by Ling, Boldyrev, Simons, and Wight (LBSW) and Laursen, Grace, DeKock, and Spronk (LGDS).

Photoelectron spectroscopy (PES) is a standard experimental method for material characterization, but its interpretation can be hampered by its reliance on standard materials. To facilitate the study of unknown systems, theoretical methods are desirable. Here, we present a real-time equation-of-motion coupled cluster (RT-EOM-CC) approach for valence PES, extending our core-level development. We demonstrate that RT-EOM-CC yields ionization energies and spectral functions in good agreement with experimental and CI-based results, even for some more correlated cases.

Since the advent of the first computers, chemists have been at the forefront of using computers to understand and solve complex chemical problems. As the hardware and software have evolved, so have the theoretical and computational chemistry methods and algorithms. Parallel computers clearly changed the common computing paradigm in the late 1970s and 80s, and the field has again seen a paradigm shift with the advent of graphical processing units. This review explores the challenges and some of the solutions in transforming software from the terascale to the petascale and now to the upcoming exascale computers. While discussing the field in general, NWChem and its redesign, NWChemEx, will be highlighted as one of the early codesign projects to take advantage of massively parallel computers and emerging software standards to enable large scientific challenges to be tackled.

In this paper, we present an efficient implementation for the analytical energy-dependent Green's function coupled-cluster with singles and doubles (GFCCSD) approach with our first practice being computing spectral functions of realistic molecular systems. Because of its algebraic structure, the presented method is highly scalable and is capable of computing spectral function for a given molecular system in any energy region. Several typical examples have been given to demonstrate its capability of computing spectral functions not only in the valence band but also in the core-level energy region. Satellite peaks have been observed in the inner valence band and core-level energy region where a many-body effect becomes significant and the single particle picture of ionization often breaks down. The accuracy test has been carried out by extensively comparing the computed spectral functions by our GFCCSD method with experimental photoelectron spectra as well as the theoretical ionization potentials obtained from other methods. It turns out the GFCCSD method is able to provide a qualitative or semiquantitative level of description of ionization processes in both the core and valence regimes. To significantly improve the GFCCSD results for the main ionic states, a larger basis set can usually be employed, whereas the improvement of the GFCCSD results for the satellite states needs higher-order many-body terms to be included in the GFCC implementation.

The stability and electron loss process of numerous multiply charged anions (MCAs) have been traditionally explained in terms of the classical Coulomb interaction between spatially separated charged groups. An understanding of these processes in MCAs with not well-separated excess charges is still lacking. We report the surprising properties and physical behavior of [B 12 X 12 ] 2- , X = F, Cl, Br, I, At, which are MCAs with not well-separated excess charges and cannot be described by the prevailing classical picture. In this series of MCAs, comprising a "boron core" surrounded by a "halogen shell", the sign of the total charge in these two regions changes along the halogen series from X = F-At. With the aid of experimental photoelectron spectroscopy and highly correlated ab initio electronic structure calculations, we demonstrate that the trend in the electronic stability of these MCAs is determined by the interplay between the Coulomb (de)stabilization originating from the "boron core" and "halogen shell" and the extension of the overlap between the orbitals from both regions. The second excess electron is always taken from the most positively charged region, viz., the "boron core" for X = F, Cl, and the surrounding "halogen shell" for X = I, At. This change in the physical behavior is attributed to the position of the highest occupied molecular orbital, which dwells in a region that is spatially separated from the one containing the excess negative charge. The unusual intrinsic electronic structure of the [B 12 X 12 ] 2- MCAs provides the basis for a molecular level understanding of their observed unique physical and chemical properties and a new paradigm for understanding the properties of these MCAs with not well-separated charges that departs from the prevailing model used for spatially separated charges that is based on their classical Coulomb interaction.

The representation and storage of two-electron integral tensors are vital in large-scale applications of accurate electronic structure methods. Low-rank representation and efficient storage strategy of integral tensors can significantly reduce the numerical overhead and consequently time-to-solution of these methods. In this work, by combining pivoted incomplete Cholesky decomposition (CD) with a follow-up truncated singular vector decomposition (SVD), we develop a decomposition strategy to approximately represent the two-electron integral tensor in terms of low-rank vectors. A systematic benchmark test on a series of 1-D, 2-D, and 3-D carbon-hydrogen systems demonstrates high efficiency and scalability of the compound two-step decomposition of the two-electron integral tensor in our implementation. For the size of the atomic basis set, N b , ranging from ∼100 up to ∼2,000, the observed numerical scaling of our implementation shows [Formula: see text] versus [Formula: see text] cost of performing single CD on the two-electron integral tensor in most of the other implementations. More importantly, this decomposition strategy can significantly reduce the storage requirement of the atomic orbital (AO) two-electron integral tensor from [Formula: see text] to [Formula: see text] with moderate decomposition thresholds. The accuracy tests have been performed using ground- and excited-state formulations of coupled cluster formalism employing single and double excitations (CCSD) on several benchmark systems including the C 60 molecule described by nearly 1,400 basis functions. The results show that the decomposition thresholds can be generally set to 10 -4 to 10 -3 to give acceptable compromise between efficiency and accuracy.

We study the vertical and adiabatic ionization potentials and electron affinities of bare and hydroxylated TiO 2 nanoclusters, as well as their fundamental gap and exciton binding energy values, to understand how the clusters' electronic properties change as a function of size and hydroxylation. In addition, we have employed a range of many-body methods; including G 0 W 0 , qsGW, EA/IP-EOM-CCSD, and DFT (B3LYP, PBE), to compare the performance and predictions of the different classes of methods. We demonstrate that, for bare clusters, all many-body methods predict the same trend with cluster size. The highest occupied and lowest unoccupied DFT orbitals follow the same trends as the electron affinity and ionization potentials predicted by the many-body methods, but are generally far too shallow and deep respectively in absolute terms. In contrast, the ΔDFT method is found to yield values in the correct energy window. However, its predictions depend upon the functional used and do not necessarily follow trends based on the many-body methods. Adiabatic potentials are predicted to be similar to their vertical counterparts and holes found to be trapped more strongly than excess electrons. The effect of hydroxylation on the clusters is to open up both the optical and fundamental gap. Finally, a simple microscopic explanation for the observed trends with cluster size and upon hydroxylation is proposed in terms of the onsite electrostatic potential.

In this paper, we apply equation-of-motion coupled cluster (EOM-CC) methods in the studies of the vertical ionization potentials (IPs) and electron affinities (EAs) for a series of single-walled carbon nanotubes (SWCNT). The EOM-CC formulations for IPs and EAs employing excitation manifolds spanned by single and double excitations (IP/EA-EOM-CCSD) are used to study the IPs and EAs of the SWCNTs as a function of the nanotube length. Several armchair nanotubes corresponding to C 20n H 20 models with n = 2-6 have been used in benchmark calculations. In agreement with previous studies, we demonstrate that the electronegativity of C 20n H 20 systems remains, to a large extent, independent of the nanotube length. We also compare IP/EA-EOM-CCSD results with those obtained with coupled cluster models with single and double excitations corrected by perturbative triples, CCSD(T), and density functional theory (DFT) using global and range-separated hybrid exchange-correlation functionals.

Criteria to assess charge-transfer (CT) and CT-like character of electronic excitations are examined. Time-dependent density functional theory (TDDFT) calculations with non-hybrid, hybrid, and tuned long-range corrected (LC) functionals are compared with coupled-cluster (CC) benchmarks. The test set comprises an organic CT complex, two push-pull donor-acceptor chromophores, a cyanine dye, and several polycyclic aromatic hydrocarbons. Proper CT is easily identified. Excitations with significant density changes upon excitation within regions of close spatial proximity can also be diagnosed. For such excitations, the use of LC functionals in TDDFT sometimes leads to dramatic improvements of the singlet energies, similar to proper CT. It is shown that such CT-like excitations do not have the characteristics of physical charge transfer, and improvements with LC functionals may not be obtained for the right reasons. The TDDFT triplet excitation energies are underestimated for all systems, often severely. For the CT-like candidates, the singlet-triplet (S/T) separation changes from negative with a non-hybrid functional to positive with a tuned LC functional. For the cyanine, the S/T separation is systematically too large with TDDFT, leading to better error compensation for the singlet energy with a non-hybrid functional.

We have investigated the description of excited state relaxation in naked and hydrated TiO2 nanoparticles using Time-Dependent Density Functional Theory (TD-DFT) with three common hybrid exchange-correlation (XC) potentials: B3LYP, CAM-B3LYP and BHLYP. Use of TD-CAM-B3LYP and TD-BHLYP yields qualitatively similar results for all structures, which are also consistent with predictions of coupled-cluster theory for small particles. TD-B3LYP, in contrast, is found to make rather different predictions; including apparent conical intersections for certain particles that are not observed with TD-CAM-B3LYP nor with TD-BHLYP. In line with our previous observations for vertical excitations, the issue with TD-B3LYP appears to be the inherent tendency of TD-B3LYP, and other XC potentials with no or a low percentage of Hartree-Fock like exchange, to spuriously stabilize the energy of charge-transfer (CT) states. Even in the case of hydrated particles, for which vertical excitations are generally well described with all XC potentials, the use of TD-B3LYP appears to result in CT problems during excited state relaxation for certain particles. We hypothesize that the spurious stabilization of CT states by TD-B3LYP even may drive the excited state optimizations to different excited state geometries from those obtained using TD-CAM-B3LYP or TD-BHLYP. Finally, focusing on the TD-CAM-B3LYP and TD-BHLYP results, excited state relaxation in small naked and hydrated TiO2 nanoparticles is predicted to be associated with a large Stokes' shift.

The coupled cluster singles and doubles (CCSD) algorithm in the NWChem software package has been optimized to alleviate the communication bottleneck. This optimization provided a 2-fold to 5-fold speedup in the CCSD iteration time depending on the problem size and available memory, and improved the CCSD scaling to 20 000 nodes of the NCSA Blue Waters supercomputer. On 20 000 XE6 nodes of Blue Waters, a complete conventional CCSD(T) calculation of a system encountering 1042 basis functions and 103 occupied correlated orbitals obtained a performance of 0.32 petaflop/s and took 5 h and 24 min to complete. The reported time and performance included all stages of the calculation from initialization to termination for iterative single and double excitations as well as perturbative triples correction. In perturbative triples alone, the computation sustained a rate of 1.18 petaflop/s. The CCSD and (T) phases took approximately (3)/4 and (1)/4 of the total time to solution, respectively, showing that CCSD is the most time-consuming part at the large scale. The MP2, CCSD, and CCSD(T) computations in 6-311++G** basis set performed on guanine-cytosine deoxydinucleotide monophosphate probed the conformational energy difference between the A- and B-conformations of single stranded DNA. Good agreement between MP2 and coupled cluster methods has been obtained, suggesting the utility of MP2 for conformational analysis in these systems. The study revealed a significant discrepancy between the quantum mechanical and classical force field predictions, suggesting a need to improve the dihedral parameters.

In this paper we discuss the application of novel parallel implementation of the coupled cluster (CC) and equation-of-motion coupled cluster methods (EOMCC) in calculations of excitation energies of triplet states in β-carotene. Calculated excitation energies are compared with experimental data, where available. We also provide a detailed description of the new parallel algorithms for iterative CC and EOMCC models involving singles and doubles excitations.

We have investigated the suitability of Time-Dependent Density Functional Theory (TD-DFT) to describe vertical low-energy excitations in naked and hydrated titanium dioxide nanoparticles. Specifically, we compared TD-DFT results obtained using different exchange-correlation (XC) potentials with those calculated using Equation-of-Motion Coupled Cluster (EOM-CC) quantum chemistry methods. We demonstrate that TD-DFT calculations with commonly used XC potentials (e.g., B3LYP) and EOM-CC methods give qualitatively similar results for most TiO 2 nanoparticles investigated. More importantly, however, we also show that, for a significant subset of structures, TD-DFT gives qualitatively different results depending upon the XC potential used and that only TD-CAM-B3LYP and TD-BHLYP calculations yield results that are consistent with those obtained using EOM-CC theory. Moreover, we demonstrate that the discrepancies for such structures originate from a particular combination of defects that give rise to charge-transfer excitations, which are poorly described by XC potentials that do not contain sufficient Hartree-Fock like exchange. Finally, we consider that such defects are readily healed in the presence of ubiquitously present water and that, as a result, the description of vertical low-energy excitations for hydrated TiO 2 nanoparticles is nonproblematic.

In this paper, we discuss the performance of several simplified variants of equation-of-motion coupled cluster method (EOMCC) with iterative inclusion of singles, doubles, and active-space triples (EOMCCSDt). In particular, we explore simplified EOMCCSDt approaches that enable one to generate the triply excited amplitudes in an on-the-fly manner. The original EOMCCSDt formulation has already demonstrated great success in encapsulating the most important excited-state correlation effects due to triples. In analogy to the original EOMCCSDT-3 formulation, the proposed approach can bypass the typical bottlenecks associated with the need for storing triply excited amplitudes. In this paper, we illustrate the performance of several approximate EOMCCSDt methods, named EOMCCSDt-3̅ and EOMCCSDt-3̅, on typical benchmark systems including C2, N2, ozone, ethene, and E-butadiene molecules. These new methods yield excitation energies close to the EOMCCSDt ones. The extrapolation of excitation energies for basis sets ranging from cc-pVDZ to cc-pV6Z for N2 and C2 shows very good convergence to the experimental results for states dominated by single excitations. The performance of the EOMCCSDt-3̅x approach is also compared with the results obtained with popular CCSDR(3) and CC3 approaches.

A novel parallel algorithm for noniterative multireference coupled cluster (MRCC) theories, which merges recently introduced reference-level parallelism (RLP) [Bhaskaran-Nair, K.; Brabec, J.; Aprà, E.; van Dam, H. J. J.; Pittner, J.; Kowalski, K. J. Chem. Phys.2012, 137, 094112] with the possibility of accelerating numerical calculations using graphics processing units (GPUs) is presented. We discuss the performance of this approach applied to the MRCCSD(T) method (iterative singles and doubles and perturbative triples), where the corrections due to triples are added to the diagonal elements of the MRCCSD effective Hamiltonian matrix. The performance of the combined RLP/GPU algorithm is illustrated on the example of the Brillouin-Wigner (BW) and Mukherjee (Mk) state-specific MRCCSD(T) formulations.

A novel algorithm for implementing a general type of multireference coupled-cluster (MRCC) theory based on the Jeziorski-Monkhorst exponential ansatz [Jeziorski, B.; Monkhorst, H. J. Phys. Rev. A1981, 24, 1668] is introduced. The proposed algorithm utilizes processor groups to calculate the equations for the MRCC amplitudes. In the basic formulation, each processor group constructs the equations related to a specific subset of references. By flexible choice of processor groups and subset of reference-specific sufficiency conditions designated to a given group, one can ensure optimum utilization of available computing resources. The performance of this algorithm is illustrated on the examples of the Brillouin-Wigner and Mukherjee MRCC methods with singles and doubles (BW-MRCCSD and Mk-MRCCSD). A significant improvement in scalability and in reduction of time to solution is reported with respect to recently reported parallel implementation of the BW-MRCCSD formalism [Brabec, J.; van Dam, H. J. J.; Kowalski, K.; Pittner, J. Chem. Phys. Lett.2011, 514, 347].

The details of the graphical processing unit (GPU) implementation of the most computationally intensive (T)-part of the recently introduced regularized CCSD(T) (Reg-CCSD(T)) method [ Kowalski , K. ; Valiev , M. J. Chem. Phys. 2009 , 131 , 234107 ] for calculating electronic energies of strongly correlated systems are discussed. Parallel tests performed for several molecular systems show very good scalability of the triples part of the Reg-CCSD(T) approach. We also discuss the performance of the Reg-CCSD(T) GPU implementation as a function of the parameters defining the partitioning of the spinorbital domain (tiling structure). The accuracy of the Reg-CCSD(T) method is illustrated on three examples: the methyfluoride molecule, dissociation of dodecane, and open-shell Spiro cation (5,5'(4H,4H')-spirobi[cyclopenta[c]pyrrole] 2,2',6,6'-tetrahydro cation), which is a frequently used model to study electron transfer processes. It is demonstrated that a simple regularization of the cluster amplitudes used in the noniterative corrections accounting for the effect of triply excited configurations significantly improves the accuracies of ground-state energies in the presence of strong quasidegeneracy effects. For methylfluoride, we compare the Reg-CCSD(T) results with the CR-CC(2,3) and CCSDT energies, whereas for Spiro cation we compare Reg-CCSD(T) results with the energies obtained with completely renormalized CCSD(T) method. Performance tests for the Spiro, dodecane, and uracil molecules are also discussed.

Ab initio electronic structure theory calculations on cluster models support the characterization of the signature absorption spectrum of a solvated hydroxyl OH radical as a solvent-to-solute charge transfer state modulated by the hydrogen-bonding environment. Vertical excited states in OH(H2O)n clusters (n = 0-7, 16) calculated at the TDDFT level of theory (with companion calculations at the EOM-CCSD level of theory for n