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The completely renormalized equation-of-motion coupled-cluster approach with singles, doubles, and noniterative triples [CR-EOMCCSD(T)] has proven to be a reliable tool in describing vertical excitation energies in small and medium size molecules. In order to reduce the high numerical cost of the genuine CR-EOMCCSD(T) method and make noniterative CR-EOMCCSD(T) approaches applicable to large molecular systems, two active-space variants of this formalism [the CR-EOMCCSd(t)-II and CR-EOMCCSd(t)-III methods], based on two different choices of the subspace of triply excited configurations employed to construct noniterative correction, are introduced. In calculations for green fluorescent protein (GFP) and free-base porphyrin, where the CR-EOMCCSD(T) results are available, we show good agreement between the active-space CR-EOMCCSD(T) (variant II) and full CR-EOMCCSD(T) excitation energies. For the oligoporphyrin dimer (P(2)TA) active-space CR-EOMCCSD(T) results provide reasonable agreement with experimentally inferred data. For all systems considered we demonstrated that the active-space CR-EOMCCSD(T) corrections lower the EOMCCSD (iterative equation-of-motion coupled-cluster method with singles and doubles) excitation energies by 0.2 and 0.3 eV, which leads to a better agreement with experiment. We also discuss the quality of basis sets used and compare EOMCC excitation energies with excitation energies obtained with other methods. In particular, we demonstrate that for GFP and FBP Sadlej's TZP and cc-pVTZ basis sets lead to a similar quality of the EOMCC results. The performance of the CR-EOMCCSD(T) implementation is discussed from the point of view of timings of iterative parts and scalability of the most expensive, N(7), part of the calculation. In the latter case the scalability across 34 008 processors is reported.

We report the study of microsolvated CN(-)(H(2)O)(n) (n=1-5) clusters in the gas phase using a combination of experimental and computational approaches. The hydrated cyanide clusters were produced by electrospray and their structural and energetic properties were probed using temperature-controlled photoelectron spectroscopy (PES) and ab initio electronic structure calculations. Comparison between the low temperature (LT,T=12 K) and the room-temperature (RT) spectra shows a 0.25 eV spectral blueshift in the binding energy of the n=1 cluster and a significant spectral sharpening and blueshift for n=2 and 3. The experimental results are complemented with ab initio electronic structure calculations at the MP2 and CCSD(T) levels of theory that identified several isomers on the ground state potential energy function arising from the ability of CN(-) to form hydrogen bonds with water via both the C and N ends. In all cases the N end seems to be the preferred hydration site for the water network. The excellent agreement between the low temperature measured PES spectra and the basis set- and correlation-corrected [at the CCSD(T) level of theory] calculated vertical detachment energies, viz., 3.85 versus 3.84 eV (n=0), 4.54 versus 4.54 eV (n=1), 5.20 versus 5.32 eV (n=2), 5.58 versus 5.50 eV (n=3), and 5.89 versus 5.87 eV (n=4), allow us to establish the hydration motif of cyanide. Its microsolvation pattern was found to be similar to that of the halide anions (Cl(-), Br(-), and I(-)) as well as other diatomic anions having cylindrical symmetry such as NO(-), resulting to structures in which the ion resides on the surface of a water cluster. The exception is CN(-)(H(2)O)(2), for which one water molecule is bound to either side of the anion resulting in a quasilinear structure. For the n=3 cluster the anion was found to freely "tumble" on the surface of a water trimer, since the inclusion of zero-point energy even at T=0 K stabilizes the configuration of C(3) symmetry with respect to the one having the anion tilted toward the water cluster. For n=4 this motion is more restricted since the corresponding barrier at RT is 1.2 kcal/mol. It is also possible that at RT other isomers (lying within approximately 0.6 kcal/mol above the global minima) are also populated, resulting in the further broadening of the PES spectra.

The static dipole polarizabilities of water clusters (2

In this article we discuss the problem of proper balancing of the noniterative corrections to the ground- and excited-state energies obtained with approximate coupled cluster (CC) and equation-of-motion CC (EOMCC) approaches. It is demonstrated that for a class of excited states dominated by single excitations and for states with medium doubly excited component, the newly introduced nested variant of the method of moments of CC equations provides mathematically rigorous way of balancing the ground- and excited-state correlation effects. The resulting noniterative methodology accounting for the effect of triples is tested using its parallel implementation on the systems, for which iterative CC/EOMCC calculations with full inclusion of triply excited configurations or their most important subset are numerically feasible.

Static hyperpolarizabilities of molecules (water, acetonitrile, chloroform, and para-nitroaniline) are calculated with large basis sets using coupled-cluster response theory and compared to four common density functional theory methods. These results reveal which methods and basis sets are appropriate for nonlinear optical studies for different types of molecules and provide a means for estimating errors from the quantum chemical approximation when including vibrational contributions or solvent effects at the QM/MM level. The largest calculation reported, which was for 72 electrons in 812 functions at C(2v) symmetry, took only a few hours on 256 nodes demonstrating that even larger calculations are quite feasible using modern supercomputers.

New theoretical framework for the method of moments of coupled cluster equations (MMCC) [K. Kowalski and P. Piecuch, J. Chem. Phys. 113, 18 (2000)] that, in a natural way, assures the connected form of the resulting MMCC corrections is discussed. In order to maintain the validity of the proposed expansion in the presence of strong quasidegeneracy effects, the regularization of the correlated part (gamma) of the overlap between the exact and approximate coupled cluster wave functions is required. It is shown that related approximations accounting for the effect of triples require a rudimentary form of the gamma-regularization (based on the regularization of cluster amplitudes) in order to provide results of completely renormalized CCSD(T) or better quality in situations when a single bond is broken (the HF molecule). For strongly correlated systems (C(2)) more efficient regularization schemes are required especially for stretched internuclear distances. Discussed type of the regularization procedure can also prevent the unphysical propagation of strong correlation effects through the products of cluster operators toward highly excited sectors of the Hilbert space.

Vertical excitation energies in uracil in the gas phase and in water solution are investigated by the equation-of-motion coupled-cluster and multireference configuration interaction methods. Basis set effects are found to be important for converged results. The analysis of electronic wave functions reveals that the lowest singlet states are predominantly of a singly excited character and are therefore well described by single-reference equation-of-motion methods augmented by a perturbative triples correction to account for dynamical correlation.Our best estimates for the vertical excitation energies for the lowest singlet n --> pi* and pi --> pi* are 5.0 +/- 0.1 eV and 5.3 +/- 0.1 eV, respectively. The solvent effects for these states are estimated to be +0.5 eV and +/- 0.1 eV, respectively. We attribute the difference between the computed vertical excitations and the maximum of the experimental absorption to strong vibronic interaction between the lowest A" and A' states leading to intensity borrowing by the forbidden transition.

The need for inclusion higher-order correlation effects for adequate description of the excitation energies of the DNA bases became clear in the past few years. In particular, we demonstrated that the inclusion of triply excited configurations may play an important role in a proper description of the excitation energies of the cytosine molecule in realistic environment. In this paper we discuss the accuracies of excitation energies for the cystosine molecule in the gas phase and in the aqueous solution calculated with noniterative and iterative coupled-cluster methods that include the effect of triply excited configurations.

Dynamic polarizabilities for open- and closed-shell molecules were obtained by using coupled-cluster (CC) linear response theory with full treatment of singles, doubles, and triples (CCSDT-LR) with large basis sets utilizing the NWChem software suite. By using four approximate CC methods in conjunction with augmented cc-pVNZ basis sets, we are able to evaluate the convergence in both many-electron and one-electron spaces. For systems with primarily dynamic correlation, the results for CC3 and CCSDT are almost indistinguishable. For systems with significant static correlation, the CC3 tends to overestimate the triples contribution, while the PS(T) approximation [J. Chem. Phys. 127, 164105 (2007)] produces mixed results that are heavily dependent on the accuracies provided by noniterative approaches used to correct the equation-of-motion CCSD excitation energies. Our results for open-shell systems show that the choice of reference (restricted open-shell Hartree-Fock versus unrestricted Hartree-Fock) can have a significant impact on the accuracy of polarizabilities. A simple extrapolation based on pentuple-zeta CCSD calculations and triple-zeta CCSDT calculations reproduces experimental results with good precision in most cases.

This paper discusses practical scheme for correcting the linear response coupled cluster with singles and doubles (CCSD) equations by shifting the poles corresponding to the equation-of-motion CCSD excitation energies by adding noniterative corrections due to triples. A simple criterion is derived for the excited states to be corrected in the spectral resolution of similarity transformed Hamiltonian on the CCSD level. Benchmark calculations were performed to compare the accuracies of static and dynamic polarizabilities obtained in this way with the CC3 and CCSDT counterparts.

Coupled-cluster theory with single and double excitations is applied to the calculation of optical properties of large polyaromatic hydrocarbons. Dipole polarizabilities are reported for benzene, pyrene, and the oligoacenes sequence n=2-6. Dynamic polarizabilities were calculated on polyacences as large as pentacene for a single frequency and for benzene and pyrene at many frequencies. The basis set effect was studied for benzene using a variety of basis sets in the Pople [Theor. Chim. Acta 28, 213 (1973)] and Dunning [J. Chem. Phys. 90, 1007 (1989)] families up to aug-cc-pVQZ and the Sadlej pVTZ basis [Collect. Czech. Chem. Commun. 53, 1995 (1998)], which was used exclusively for the largest molecules. Geometries were optimized using HF, B3LYP, PBE0, and MP2 and compared to experiment to measure method dependence and the possible role of bond-length alternation. Finally, the polarizability results were compared to four common density functionals (B3LYP, BLYP, PBE0, PBE).

Evolution of the excited state energies of cytosine base in the native DNA environment was investigated using a hybrid coupled cluster and classical molecular dynamics approach. The time averaged excitation energies obtained with the variant of the completely renormalized equation-of-motion with singles, doubles, and non-iterative triples approach that includes a bulk of the correlation effects for excited states, are compared with the analogous calculations in the gas phase. Significant blue shifts for the two lowest singlet excitation energies can be observed as a result of the interaction of the quantum system with the surrounding environment.

In this paper we discuss a simple extrapolation scheme based on the asymptotic behavior of the electronic energies considered as functions of cutoff factor for orbital energies corresponding to virtual orbitals. The performance of this approach is illustrated in the context of large-scale dynamic simulations for excitation energies of the cytosine molecule in its native DNA environment. We demonstrate that the extrapolation errors are significantly smaller than the excitation-energy fluctuations, due to the fluctuating environment.

The stationary conditions obtained from approximate coupled-cluster functional derived from the numerator-denominator connected expansion (NDC) [K. Kowalski and P. Piecuch, J. Chem. Phys. 122, 074107 (2005)] are employed to calculate the linear response of cluster amplitudes. A simple scheme that involves singly and doubly excited amplitudes, termed locally renormalized equation-of-motion approach with singles and doubles (LR-EOMCCSD), is compared with other excited-state methods that include up to two-body operators in the wave function expansion. In particular, the impact of the local denominators on the excitation energies is discussed in detail. Several benchmark calculations on the CH(+), C(2), N(2), O(3), and ClOCl molecules are presented to illustrate the performance of the LR-EOMCCSD approach.

Several new variants of the locally-renormalized coupled-cluster (CC) approaches that account for the effect of triples (LR-CCSD(T)) have been formulated and implemented for arbitrary reference states using the TENSOR CONTRACTION ENGINE functionality, enabling the automatic generation of an efficient parallel code. Deeply rooted in the recently derived numerator-denominator-connected (NDC) expansion for the ground-state energy [K. Kowalski and P. Piecuch, J. Chem. Phys. 122, 074107 (2005)], LR-CCSD(T) approximations use, in analogy to the completely renormalized CCSD(T) (CR-CCSD(T)) approach, the three-body moments in constructing the noniterative corrections to the energies obtained in CC calculations with singles and doubles (CCSD). In contrast to the CR-CCSD(T) method, the LR-CCSD(T) approaches discussed in this paper employ local denominators, which assure the additive separability of the energies in the noninteracting system limit when the localized occupied spin-orbitals are employed in the CCSD and LR-CCSD(T) calculations. As clearly demonstrated on several challenging examples, including breaking the bonds of the F2, N2, and CN molecules, the LR-CCSD(T) approaches are capable of providing a highly accurate description of the entire potential-energy surface (PES), while maintaining the characteristic N(7) scaling of the ubiquitous CCSD(T) approach. Moreover, as illustrated numerically for the ozone molecule, the LR-CCSD(T) approaches yield highly competitive values for a number of equilibrium properties including bond lengths, angles, and harmonic frequencies.

The general-purpose open-shell implementation of the completely renormalized equation-of-motion coupled-cluster approach with singles, doubles, and noniterative triples [CR-EOMCCSD(T)] is reported. Benchmark calculations for the low-lying doublet and quartet states of the CH radical show that the CR-EOMCCSD(T) method is capable of providing a highly accurate description of ground and excited states of open-shell molecules. This includes states with strong double excitation character, for which the conventional EOMCCSD approach fails.

The recently developed completely renormalized (CR) coupled-cluster (CC) methods with singles, doubles, and noniterative triples or triples and quadruples [CR-CCSD(T) or CR-CCSD(TQ), respectively], which are based on the method of moments of CC equations (MMCC) [K. Kowalski and P. Piecuch, J. Chem. Phys. 113, 18 (2000)], eliminate the failures of the standard CCSD(T) and CCSD(TQ) methods at larger internuclear separations, but they are not rigorously size extensive. Although the departure from strict size extensivity of the CR-CCSD(T) and CR-CCSD(TQ) methods is small, it is important to examine the possibility of formulating the improved CR-CC methods, which are as effective in breaking chemical bonds as the existing CR-CCSD(T) and CR-CCSD(TQ) approaches, which are as easy to use as the CR-CCSD(T) and CR-CCSD(TQ) methods, and which can be made rigorously size extensive. This may be particularly useful for the applications of CR-CC methods and other MMCC approaches in calculations of potential energy surfaces of large many-electron systems and van der Waals molecules, where the additive separability of energies in the noninteracting limit is very important. In this paper, we propose different types of CR-CC approximations, termed the locally renormalized (LR) CCSD(T) and CCSD(TQ) methods, which become rigorously size extensive if the orbitals are localized on nointeracting fragments. The LR-CCSD(T) and LR-CCSD(TQ) methods rely on the form of the energy expression in terms of the generalized moments of CC equations, derived in this work, termed the numerator-denominator-connected MMCC expansion. The size extensivity and excellent performance of the LR-CCSD(T) and LR-CCSD(TQ) methods are illustrated numerically by showing the results for the dimers of stretched HF and LiH molecules and bond breaking in HF and H2O.

The single-reference ab initio methods for high accuracy calculations of potential energy surfaces (PESs) of excited electronic states, termed the completely renormalized equation-of-motion coupled-cluster approaches with singles, doubles, and noniterative triples [CR-EOMCCSD(T)], are developed. In the CR-EOMCCSD(T) methods, which are based on the formalism of the method of moments of coupled-cluster equations, the suitably designed corrections due to triple excitations are added, in a state-selective manner, to the excited-state energies obtained in the standard equation-of-motion coupled-cluster calculations with singles and doubles (EOMCCSD). It is demonstrated that the CR-EOMCCSD(T) approaches, which can be regarded as the excited-state analogs of the ground-state CR-CCSD(T) theory, provide a highly accurate description of excited states dominated by double excitations, excited states displaying a manifestly multireference character, and PESs of excited states along bond breaking coordinates with the ease of the ground-state CCSD(T) or CR-CCSD(T) calculations. The performance of the CR-EOMCCSD(T) methods is illustrated by the results of calculations for the excited states of CH+, HF, N2, C2, and ozone.