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Showing papers on "Coupled cluster published in 2011"


Journal ArticleDOI
TL;DR: It is demonstrated that the accuracy of this scheme can be significantly improved by including the close pair LMP2 amplitudes in the LCCSD equations, as well as in the perturbative treatment of the triples excitations.
Abstract: An efficient local coupled cluster method with single and double excitation operators and perturbative treatment of triple excitations [DF-LCCSD(T)] is described All required two-electron integrals are evaluated using density fitting approximations These have a negligible effect on the accuracy but reduce the computational effort by 1–2 orders of magnitude, as compared to standard integral-direct methods Excitations are restricted to local subsets of non-orthogonal virtual orbitals (domain approximation) Depending on distance criteria, the correlated electron pairs are classified into strong, close, weak, and very distant pairs Only strong pairs, which typically account for more than 90% of the correlation energy, are optimized in the LCCSD treatment The remaining close and weak pairs are approximated by LMP2 (local second-order Moller-Plesset perturbation theory); very distant pairs are neglected It is demonstrated that the accuracy of this scheme can be significantly improved by including the close pair LMP2 amplitudes in the LCCSD equations, as well as in the perturbative treatment of the triples excitations Using this ansatz for the wavefunction, the evaluation and transformation of the two-electron integrals scale cubically with molecular size If local density fitting approximations are activated, this is reduced to linear scaling The LCCSD iterations scale quadratically, but linear scaling can be achieved by neglecting some terms involving contractions of single excitations The accuracy and efficiency of the method is systematically tested using various approximations, and calculations for molecules with up to 90 atoms and 2636 basis functions are presented

253 citations


Journal ArticleDOI
TL;DR: The ability of the four families of basis sets to extrapolate SCF and correlation energies to the basis set limit has been investigated and the SCF energy extrapolation proposed by Petersson and co-workers is found to be effective.
Abstract: The performance of several families of basis sets for correlated wave function calculations on molecules is studied. The widely used correlation-consistent basis set family cc-pVXZ (n = D, T, Q, 5) is compared to a systematic series of atomic natural orbital basis sets (ano-pVXZ). These basis sets are built from the cc-pV6Z primitives in atomic multireference average coupled pair functional (MR-ACPF) calculations. Segmented basis sets optimized for self-consistent field calculations (def2-SVP, def2-TZVPP, and def2-QZVPP as well as “pc-n”, n = 1, 2, 3) were also tested. Reference Hartree−Fock energies are determined with the uncontracted aug-cc-pV6Z basis set for a set of 21 small molecules built from H, B, C, N, O, and F. Reference coupled cluster CCSD(T) correlation energies were determined from extrapolation at the cc-pV5Z/cc-pV6Z level. It is found that the ano-pVXZ basis sets outperform the other basis sets. The error in the SCF energies compared to cc-pVXZ basis sets is reduced by about a factor of 3...

228 citations


Journal ArticleDOI
TL;DR: Explicitly correlated MP2-F12 and CCSD(T)-F12 methods with orbital-pair-specific Slater-type geminals are proposed in this article, where the fixed amplitude ansatz of Ten-no is used, and different exponents of the Slater geminal functions can be chosen for core-core, core-valence, and valence-valences pairs.
Abstract: Explicitly correlated MP2-F12 and CCSD(T)-F12 methods with orbital-pair-specific Slater-type geminals are proposed. The fixed amplitude ansatz of Ten-no is used, and different exponents of the Slater geminal functions can be chosen for core–core, core–valence, and valence–valence pairs. This takes care of the different sizes of the correlation hole and leads to improved results when inner-shell orbitals are correlated. The complications and the extra computational cost as compared to corresponding calculations with a single geminal are minor. The improved accuracy of the method is demonstrated for spectroscopic properties of Br2, As2, Ga2, Cu2, GaCl, CuCl, and CuBr, where the d-orbitals are treated as core.

186 citations


Journal ArticleDOI
TL;DR: A general-order local coupled-cluster (CC) method is presented which has the potential to provide accurate correlation energies for extended systems and allows for a higher order description of the chemically more important segments of the molecule and a lower level treatment of the rest delivering further significant savings in computer time.
Abstract: A general-order local coupled-cluster (CC) method is presented which has the potential to provide accurate correlation energies for extended systems. Our method combines the cluster-in-molecule approach of Li and co-workers [J. Chem. Phys. 131, 114109 (2009)] with the frozen natural orbital (NO) techniques widely used for the cost reduction of correlation methods. The occupied molecular orbitals (MOs) are localized, and for each occupied MO a local subspace of occupied and virtual orbitals is constructed using approximate Moller-Plesset NOs. The CC equations are solved and the correlation energies are calculated in the local subspace for each occupied MO, while the total correlation energy is evaluated as the sum of the individual contributions. The size of the local subspaces and the accuracy of the results can be controlled by varying only one parameter, the threshold for the occupation number of NOs which are included in the subspaces. Though our local CC method in its present form scales as the fifth power of the system size, our benchmark calculations show that it is still competitive for the CC singles and doubles (CCSD) and the CCSD with perturbative triples [CCSD(T)] approaches. For higher order CC methods, the reduction in computation time is more pronounced, and the new method enables calculations for considerably bigger molecules than before with a reasonable loss in accuracy. We also demonstrate that the independent calculation of the correlation contributions allows for a higher order description of the chemically more important segments of the molecule and a lower level treatment of the rest delivering further significant savings in computer time.

175 citations


Journal ArticleDOI
TL;DR: A production level implementation of the high-spin open-shell (spin unrestricted) single reference coupled pair, quadratic configuration interaction and coupled cluster methods with up to doubly excited determinants in the framework of the local pair natural orbital (LPNO) concept is reported.
Abstract: A production level implementation of the high-spin open-shell (spin unrestricted) single reference coupled pair, quadratic configuration interaction and coupled cluster methods with up to doubly excited determinants in the framework of the local pair natural orbital (LPNO) concept is reported. This work is an extension of the closed-shell LPNO methods developed earlier [F. Neese, F. Wennmohs, and A. Hansen, J. Chem. Phys. 130, 114108 (2009)10.1063/1.3086717; F. Neese, A. Hansen, and D. G. Liakos, J. Chem. Phys. 131, 064103 (2009)10.1063/1.3173827]. The internal space is spanned by localized orbitals, while the external space for each electron pair is represented by a truncated PNO expansion. The laborious integral transformation associated with the large number of PNOs becomes feasible through the extensive use of density fitting (resolution of the identity (RI)) techniques. Technical complications arising for the open-shell case and the use of quasi-restricted orbitals for the construction of the referen...

169 citations


Journal ArticleDOI
TL;DR: The internally contracted multireference coupled cluster (icMRCC) method allows a highly accurate description of both static and dynamic correlation with a computational scaling similar to single reference coupled cluster theory and is in excellent agreement with CCSDTQ.
Abstract: The internally contracted multireference coupled cluster (icMRCC) method allows a highly accurate description of both static and dynamic correlation with a computational scaling similar to single reference coupled cluster theory. The authors show that the method can lose its orbital invariance and size consistency when no special care is taken in the elimination of redundant excitations. Using the BeH2 model system, four schemes are compared which differ in their treatment of linear dependencies between excitations of different rank (such as between singles and doubles). While the energy curves agree within tens of μEh when truncating the cluster operator at double excitations (icMRCCSD), inclusion of triple excitations (icMRCCSDT) leads to significant differences of more than 1 mEh. One scheme clearly yields the best results, while the others even turn out to be not size consistent. The former procedure uses genuine single and double excitations and discards those linear combinations of (spectator) doubl...

168 citations


Journal ArticleDOI
TL;DR: This work features an analysis for the acceleration technique DIIS that is standardly used in most of the important quantum chemistry codes, e.g. in DFT and Hartree–Fock calculations and in the Coupled Cluster method and shows that for the general nonlinear case, DIIS corresponds to a projected quasi-Newton/secant method.
Abstract: This work features an analysis for the acceleration technique DIIS that is standardly used in most of the important quantum chemistry codes, e.g. in DFT and Hartree–Fock calculations and in the Coupled Cluster method. Taking up results from Harrison (J Comput Chem 25:328, 2003), we show that for the general nonlinear case, DIIS corresponds to a projected quasi-Newton/secant method. For linear systems, we establish connections to the well-known GMRES solver and transfer according (positive as well as negative) convergence results to DIIS. In particular, we discuss the circumstances under which DIIS exhibits superlinear convergence behaviour. For the general nonlinear case, we then use these results to show that a DIIS step can be interpreted as step of a quasi-Newton method in which the Jacobian used in the Newton step is approximated by finite differences and in which the according linear system is solved by a GMRES procedure, and give according convergence estimates.

166 citations


Journal ArticleDOI
TL;DR: The COLUMBUS Program System as discussed by the authors allows high-level quantum chemical calculations based on the multiconfiguration self-consistent field, multireference configuration interaction with singles and doubles, and the multiireference averaged quadratic coupled cluster methods.
Abstract: The COLUMBUS Program System allows high-level quantum chemical calculations based on the multiconfiguration self-consistent field, multireference configuration interaction with singles and doubles, and the multireference averaged quadratic coupled cluster methods. The latter method includes size-consistency corrections at the multireference level. Nonrelativistic (NR) and spin–orbit calculations are available within multireference configuration interaction (MRCI). A prominent feature of COLUMBUS is the availability of analytic energy gradients and nonadiabatic coupling vectors for NR MRCI. This feature allows efficient optimization of stationary points and surface crossings (minima on the crossing seam). Typical applications are systematic surveys of energy surfaces in ground and excited states including bond breaking. Wave functions of practically any sophistication can be constructed limited primarily by the size of the CI expansion rather than by its complexity. A massively parallel CI step allows state-of-the art calculations with up to several billion configurations. Electrostatic embedding of point charges into the molecular Hamiltonian gives access to quantum mechanical/molecular mechanics calculations for all wave functions available in COLUMBUS. The analytic gradient modules allow on-the-fly nonadiabatic photodynamical simulations of interesting chemical and biological problems. Thus, COLUMBUS provides a wide range of highly sophisticated tools with which a large variety of interesting quantum chemical problems can be studied. © 2011 John Wiley & Sons, Ltd. WIREs Comput Mol Sci 2011 1 191-199 DOI: 10.1002/wcms.25

164 citations


Journal ArticleDOI
TL;DR: A formal analysis shows that the ic-MRCC method is invariant with respect to rotation among active orbitals, and that the orthogonalization procedure used to produce the set of linearly independent excitation operators plays a crucial role in guaranteeing the invariance properties.
Abstract: We have formulated and implemented an internally contracted multireference coupled cluster (ic-MRCC) approach aimed at solving two of the problems encountered in methods based on the Jeziorski–Monkhorst ansatz: (i) the scaling of the computational and memory costs with respect to the number of references, and (ii) the lack of invariance of the energy with respect to rotations among active orbitals. The ic-MRCC approach is based on a straightforward generalization of the single-reference coupled cluster ansatz in which an exponential operator is applied to a multiconfigurational wave function. The ic-MRCC method truncated to single and double excitations (ic-MRCCSD) yields very accurate potential energy curves in benchmark computations on the Be + H2 insertion reaction, the dissociation of hydrogen fluoride, and the symmetric double dissociation of water. Approximations of the ic-MRCC theory in which the Baker–Campbell–Hausdorff expansion is truncated up to a given number of commutators are found to conver...

155 citations


Journal ArticleDOI
TL;DR: LPNO-CEPA/1 holds great promise for the efficient ab initio treatment of weak intermolecular interactions and the global minimum on the PES obtained from the calculations agrees excellently with the experimentally determined crystal structure.
Abstract: A parallel implementation of the recently developed local pair natural orbital coupled electron pair approximation (LPNO-CEPA/n, n = Version 1, 2, or 3) and the corresponding LPNO coupled cluster method with single- and double excitations (LPNO−CCSD) is described. A detailed analysis alongside pseudocode is presented for the most important computational steps. The scaling with respect to the number of processors is reasonable and speedups of about 10 with 14 processors have been found in benchmark calculations (wall-clock time). The most important factor limiting the efficiency of the scaling with respect to the number of processors is probably the limited bandwidth of the presently prevailing multicore machines. The parallel LPNO methods were applied to study weak intermolecular interactions. Initially, the well-established S22 set of molecules was studied. The mean absolute error resulting from the use of the LPNO-CEPA/1 method relative to the most recent CCSD(T) reference data is found to be 0.24 kcal/...

140 citations


Journal ArticleDOI
TL;DR: Analysis of the systematic and random errors present in computational methods through the use of error probability density functions for computed interaction energies between chemical fragments comprising a protein-ligand complex concludes that statistical error analysis is a necessary addition to any scoring function attempting to produce reliable binding affinity predictions.
Abstract: A largely unsolved problem in computational biochemistry is the accurate prediction of binding affinities of small ligands to protein receptors. We present a detailed analysis of the systematic and random errors present in computational methods through the use of error probability density functions, specifically for computed interaction energies between chemical fragments comprising a protein−ligand complex. An HIV−II protease crystal structure with a bound ligand (indinavir) was chosen as a model protein−ligand complex. The complex was decomposed into 21 interacting fragment pairs, which were studied using a number of computational methods. The chemically accurate complete basis set coupled cluster theory (CCSD(T)/CBS) interaction energies were used as reference values to generate our error estimates. In our analysis, we observed significant systematic and random errors in most methods, which was surprising, especially for parametrized classical and semiempirical quantum mechanical calculations. After pr...

Journal ArticleDOI
TL;DR: The results indicate that a direct comparison of the experimental absorption maxima and the theoretical vertical excitations is not possible due to the presence of nonvertical transitions, and that the B2PLYP scheme gives excitations in satisfactory agreement with CC3 and DMC, significantly improving on the generalized gradient and hybrid approximations.
Abstract: The simplest cyanine dye series [H2N(CH)nNH2]+ with n = 1, 3, 5, 7, and 9 appears to be a challenge for all theoretical excited-state methods since the experimental spectra are difficult to predict and the observed deviations cannot be easily explained with standard arguments. We compute here the lowest vertical excitation energies of these dyes using a variety of approaches, namely, complete active space second-order perturbation theory (CASPT2), quantum Monte Carlo methods (QMC), coupled cluster linear response up to third approximate order (CC3), and various flavors of time-dependent density functional theory (TDDFT), including the recently proposed perturbative correction scheme (B2PLYP). In our calculations, all parameters such as basis set, active space, and geometry dependence are carefully analyzed. We find that all wave function methods give reasonably close excitation energies, with CASPT2 yielding the lowest values, and that the B2PLYP scheme gives excitations in satisfactory agreement with CC3 and DMC, significantly improving on the generalized gradient and hybrid approximations. Finally, to resolve the remaining discrepancy between predicted excitation energies and experimental absorption spectra, we also investigate the effect of excited-state relaxation. Our results indicate that a direct comparison of the experimental absorption maxima and the theoretical vertical excitations is not possible due to the presence of nonvertical transitions. The apparent agreement of earlier CASPT2 calculations with experiments was an artifact of the choice of active space and the use of an older definition of the zero-order Hamiltonian.

Journal ArticleDOI
TL;DR: This work compares a large variety of density functionals against the equation of motion coupled cluster singles and doubles (EOM-CCSD) method for the calculation of oscillator strengths to confirm that there is a large difference between the functionals.
Abstract: In this work, we compare a large variety of density functionals against the equation of motion coupled cluster singles and doubles (EOM-CCSD) method for the calculation of oscillator strengths. Valence and Rydberg states are considered for a test set composed of 11 small organic molecules. In our previous work, the same systems and methods were tested against experimental results for the excitation energies. The results from this investigation confirm our previous findings, i.e., that there is a large difference between the functionals. For the oscillator strength, the average best agreement with EOM-CCSD is provided by CAM-B3LYP followed by LC-ωPBE and, to a lesser extent, B3P86 and LC-BLYP.

Journal ArticleDOI
TL;DR: A new combined quantum mechanics/molecular mechanics (QM/MM) method based on a self-consistent polarizable embedding (PE) scheme is formulated and the relative importance of multipoles and polarizabilities in the description of two-photon absorption activity for formamide in aqueous solution is investigated.
Abstract: We formulate a new combined quantum mechanics/molecular mechanics (QM/MM) method based on a self-consistent polarizable embedding (PE) scheme. For the description of the QM region, we apply the popular coupled cluster (CC) method detailing the inclusion of electrostatic and polarization effects into the CC Lagrangian. Also, we consider the transformations required to obtain molecular properties from the linear and quadratic response functions and provide an implementation for the calculation of excitation energies, one- and two-photon absorption properties, polarizabilities and hyperpolarizabilities all coupled to a polarizable MM environment. In the process, we identify CC densitylike intermediates that allow for a very efficient implementation retaining a computational low cost of the QM/MM terms even when the number of MM sites increases. The strengths of the new implementation are illustrated by property calculations on different systems representing the frontier of the capabilities of the CC/MM method. We combine our method with a molecular dynamics sampling scheme such that statistical averages of different excited state solvated properties may be obtained. Especially, we systematically investigate the relative importance of multipoles and polarizabilities in the description of two-photon absorption activity for formamide in aqueous solution. Also, we demonstrate the strengths of the CC hierarchies by incorporating correlation effects both at the CC2, CCSD, and at the triples level in the so-called PE-CCSDR(3) model. Finally, we utilize the presented method in the description of a full protein by investigating the shift of the intense electronic excitation energy of the photoactive yellow protein due to the surrounding amino acids.

Journal ArticleDOI
TL;DR: The multi-ionization equation-of-motion coupled-cluster (CC) method is developed for multireference (MR) problems, depending upon a formal matrix diagonalization step to define the coefficients in the wavefunction in an unbiased way that allows for important MR character.
Abstract: The multi-ionization equation-of-motion coupled-cluster (CC) method is developed for multireference (MR) problems. It is operationally single reference, depending upon a formal matrix diagonalization step to define the coefficients in the wavefunction in an unbiased way that allows for important MR character. The method is illustrated for the autoisomerization of cyclobutadiene, which has a very large multireference effect and compared to other MR-CC results. The newly implemented methods are also used to obtain the vertical double ionization (DI) potentials of several small molecules (H2O, CO, C2H2, C2H4). Also, the performance of the new methods is analyzed by plotting the potential energy curve for twisted ethylene as a function of a dihedral angle between two methylenes. Evaluation of the total molecular energy via MR-DI-CC calculations makes it possible to avoid an unphysical cusp.

Journal ArticleDOI
TL;DR: The potential of the method is demonstrated for five reactions of biochemical or pharmacological interest which include molecules with up to 61 atoms, and calculations show that molecules of this size can now be treated routinely and yield results that are close to the CCSD(T) complete basis set limits.
Abstract: A new explicitly correlated local coupled-cluster method with single and double excitations and a perturbative treatment of triple excitations [DF-LCCSD(T0)-F12x (x = a,b)] is presented. By means of truncating the virtual orbital space to pair-specific local domains (domain approximation) and a simplified treatment of close, weak and distant pairs using LMP2-F12 (pair approximation) the scaling of the computational cost with molecular size is strongly reduced. The basis set incompleteness errors as well as the errors due to the domain approximation are largely eliminated by the explicitly correlated terms. All integrals are computed using efficient density fitting (DF) approximations. The accuracy of the method is investigated for 52 reactions involving medium size molecules. A comparison of DF-LCCSD(T0)-F12x reaction energies with canonical CCSD(T)-F12x calculations shows that the errors introduced by the domain approximation are indeed very small. Care must be taken to keep the errors due to the additio...

Journal ArticleDOI
TL;DR: The quadratically convergent orbital-optimization procedure converges quickly for OMP2, and provides molecular properties that are somewhat different than those of MP2 for most of the test cases considered (although they are similar for H(2)O).
Abstract: Using a Lagrangian-based approach, we present a more elegant derivation of the equations necessary for the variational optimization of the molecular orbitals (MOs) for the coupled-cluster doubles (CCD) method and second-order Moller-Plesset perturbation theory (MP2). These orbital-optimized theories are referred to as OO-CCD and OO-MP2 (or simply “OD” and “OMP2” for short), respectively. We also present an improved algorithm for orbital optimization in these methods. Explicit equations for response density matrices, the MO gradient, and the MO Hessian are reported both in spin-orbital and closed-shell spin-adapted forms. The Newton-Raphson algorithm is used for the optimization procedure using the MO gradient and Hessian. Further, orbital stability analyses are also carried out at correlated levels. The OD and OMP2 approaches are compared with the standard MP2, CCD, CCSD, and CCSD(T) methods. All these methods are applied to H2O, three diatomics, and the O4+ molecule. Results demonstrate that the CCSD and...

Journal ArticleDOI
TL;DR: In the case of Ne, HF, and C(2), the alternative coupled cluster approaches yield almost identical bond length, harmonic vibrational frequency, and anharmonic constant, which are more accurate than those from traditional coupled cluster theory.
Abstract: We report a general implementation of alternative formulations of single-reference coupled cluster theory (extended, unitary, and variational) with arbitrary-order truncation of the cluster operator. These methods are applied to compute the energy of Ne and the equilibrium properties of HF and C(2). Potential energy curves for the dissociation of HF and the BeH(2) model computed with the extended, variational, and unitary coupled cluster approaches are compared to those obtained from the multireference coupled cluster approach of Mukherjee et al. [J. Chem. Phys. 110, 6171 (1999)] and the internally contracted multireference coupled cluster approach [F. A. Evangelista and J. Gauss, J. Chem. Phys. 134, 114102 (2011)]. In the case of Ne, HF, and C(2), the alternative coupled cluster approaches yield almost identical bond length, harmonic vibrational frequency, and anharmonic constant, which are more accurate than those from traditional coupled cluster theory. For potential energy curves, the alternative coupled cluster methods are found to be more accurate than traditional coupled cluster theory, but are three to ten times less accurate than multireference coupled cluster approaches. The most challenging benchmark, the BeH(2) model, highlights the strong dependence of the alternative coupled cluster theories on the choice of the Fermi vacuum. When evaluated by the accuracy to cost ratio, the alternative coupled cluster methods are not competitive with respect to traditional CC theory, in other words, the simplest theory is found to be the most effective one.

Journal ArticleDOI
TL;DR: This work implements different variants of the random phase approximation to the correlation energy derived from closed-shell ring-diagram approximations to coupled cluster doubles theory in range-separated density-functional theory, i.e., by combining the long-range random phase approximation with short-range density- functional approxIMations.
Abstract: We explore different variants of the random phase approximation (RPA) to the correlation energy derived from closed-shell ring-diagram approximations to coupled cluster doubles theory. We implement these variants in range-separated density-functional theory, i.e. by combining the long-range random phase approximations with short-range density-functional approximations. We perform tests on the rare-gas dimers He_2, Ne_2, and Ar_2, and on the weakly interacting molecular complexes of the S22 set of Jurecka et al. [Phys. Chem. Chem. Phys. 8, 1985 (2006)]. The two best variants correspond to the ones originally proposed by Szabo and Ostlund [J. Chem. Phys. 67, 4351 (1977)]. With range separation, they reach mean absolute errors on the equilibrium interaction energies of the S22 set of about 0.4 kcal/mol, corresponding to mean absolute percentage errors of about 4 %, with the aug-cc-pVDZ basis set.

Journal ArticleDOI
TL;DR: The T1 diagnostics of coupled cluster theory and further energy-based criteria demonstrate that all investigated systems exhibit predominantly a (1)A(g) singlet closed-shell electronic ground state and a vanishing S(0)-T(1) energy gap, in the limit of an infinitely large polyacene.
Abstract: A benchmark theoretical study of the electronic ground state and of the vertical and adiabatic singlet–triplet (ST) excitation energies of n-acenes (C4n+2H2n+4) ranging from octacene (n = 8) to undecacene (n = 11) is presented. The T1 diagnostics of coupled cluster theory and further energy-based criteria demonstrate that all investigated systems exhibit predominantly a 1Ag singlet closed-shell electronic ground state. Singlet–triplet (S0–T1) energy gaps can therefore be very accurately determined by applying the principle of a focal point analysis (FPA) onto the results of a series of single-point and symmetry-restricted calculations employing correlation consistent cc-pVXZ basis sets (X = D, T, Q, 5) and single-reference methods [HF, MP2, MP3, MP4SDQ, CCSD, and CCSD(T)] of improving quality. According to our best estimates, which amount to a dual extrapolation of energy differences to the level of coupled cluster theory including single, double, and perturbative estimates of connected triple excitations...

Journal ArticleDOI
TL;DR: In this article, the effects of solvents on electronic spectra can be treated efficiently by combining an accurate quantum mechanical (QM) method for the solute with an efficient and accurate method for solvent molecules.
Abstract: The effects of solvents on electronic spectra can be treated efficiently by combining an accurate quantum mechanical (QM) method for the solute with an efficient and accurate method for the solvent molecules. One of the most sophisticated approaches for treating solvent effects is the effective fragment potential (EFP) method. The EFP method has been interfaced with several QM methods, including configuration interaction, time-dependent density functional theory, multiconfigurational methods, and equations-of-motion coupled cluster methods. These combined QM–EFP methods provide a range of efficient and accurate methods for studying the impact of solvents on electronic excited states. An energy decomposition analysis in terms of physically meaningful components is presented in order to analyze these solvent effects. Several factors that must be considered when one investigates solvent effects on electronic spectra are discussed, and several examples are presented.

Journal ArticleDOI
TL;DR: This study uses high-level coupled cluster calculations with core-valence correlation and complete basis set (CBS) limit extrapolation as a reference, for assessing the performance of popular density functional theory approximations for a variety of Au(I)/Au(III) complexes with unsaturated aliphatic hydrocarbon CnHm substrates.
Abstract: Gold–substrate interaction is essential in gold-catalyzed organic transformations. This study uses high-level coupled cluster calculations with core–valence correlation and complete basis set (CBS) limit extrapolation as a reference, for assessing the performance of popular density functional theory (DFT) approximations for a variety of Au(I)/Au(III) complexes with unsaturated aliphatic hydrocarbon CnHm substrates (ethene, ethyne, and allene). The tested functionals cover from LDA to GGA and meta-GGA, and to hybrids and double hybrids (LSDA, PBE, M06-L, TPSS, B3LYP, PBE0, M06, M06-2X, TPSSh, B2-PLYP, B2GP-PLYP). Both the geometry and bond dissociation energy (De) of the Au–CnHm complexes are studied. Our findings show that B2GP-PLYP, PBE0, and B2-PLYP are the best performing functionals for this set of Au–CnHm complexes. DFT dispersion correction (DFT-D3), though very helpful for some functionals (e.g., B3LYP and B2-PLYP), does not uniformly improve the results of all functionals. Ab initio methods like M...

Journal ArticleDOI
TL;DR: This work has investigated using CCSD(T)-F12 contributions to correct the i-FCIQMC results and found much faster convergence with respect to basis set size may be achieved for both the electron affinities and the FCIQMC ionization potentials.
Abstract: For the atoms with Z ⩽ 11, energies obtained using the “initiator” extension to full configuration interaction quantum Monte Carlo (i-FCIQMC) come to within statistical errors of the FCIQMC results. As these FCIQMC values have been shown to converge onto FCI results, the i-FCIQMC method allows similar accuracy to be achieved while significantly reducing the scaling with the size of the Slater determinant space. The i-FCIQMC electron affinities of the Z ⩽ 11 atoms in the aug-cc-pVXZ basis sets are presented here. In every case, values are obtained to well within chemical accuracy [the mean absolute deviation (MAD) from the relativistically corrected experimental values is 0.41 mEh], and significantly improve on coupled cluster with singles, doubles and perturbative triples [CCSD(T)] results. Since the only remaining source of error is basis set incompleteness, we have investigated using CCSD(T)-F12 contributions to correct the i-FCIQMC results. By doing so, much faster convergence with respect to basis set size may be achieved for both the electron affinities and the FCIQMC ionization potentials presented in a previous paper. With this F12 correction, the MAD can be further reduced to 0.13 mEh for the electron affinities and 0.31 mEh for the ionization potentials.

Journal ArticleDOI
TL;DR: Only at the highest level of theory involving complete basis set extrapolation, triple excitation contributions as well as relativistic and solvent effects, the bis-(μ-oxo) isomer is found to be slightly more stable than the peroxo structure.
Abstract: Owing to the availability of large-scale computing facilities and the development of efficient new algorithms, wave function-based ab initio calculations are becoming more common in bioinorganic chemistry. In principle they offer a systematic route toward high accuracy. However, these calculations are by no means trivial. In this contribution we address some pertinent points through a systematic theoretical study for the equilibrium between the peroxo- and bis-(μ-oxo) isomers of the [{Cu(C2H8N2)}2O2](2+) complex. While this system is often regarded as a prototypical multireference case, we treat it with the single reference local-pair natural orbital coupled cluster method and reiterate that the multireference character in this system is very limited. A set of intermediate structures, for the interconversion between the two isomers, is calculated through a relaxed surface scan thus allowing the calculation of an energetic profile that cleanly connects the bis-(μ-oxo) and side-on peroxo minima on the ground-state potential energy surface. Only at the highest level of theory involving complete basis set extrapolation, triple excitation contributions as well as relativistic and solvent effects, the bis-(μ-oxo) isomer is found to be slightly more stable than the peroxo structure. This is in agreement with the experimental findings. The effects of basis set, triples excitation, relativity, and solvent contribution have all been analyzed in detail. Finally, the ab initio results are compared with density functional calculations using various functionals. It is demonstrated that the largest part of the discrepancies of the results reported in the literature are due to an inconsistent handling of relativistic effects, which are large in both ab initio and density functional theory calculations.

Journal ArticleDOI
TL;DR: The locality analysis shows that a CC calculation on a large molecular system may be carried out in terms of CC calculations on small orbital fragments of the total molecular system, where the sizes of the orbital fragment spaces are determined in a black box manner to ensure that the CC correlation energy is calculated to a preset energy threshold.
Abstract: We present a thorough locality analysis of the divide-expand-consolidate amplitude equations for second-order Moller-Plesset perturbation theory and the coupled cluster singles doubles (CCSD) model, which demonstrates that the amplitude equations are local when expressed in terms of a set of local occupied and local unoccupied Hartree-Fock orbitals, such as the least-change molecular basis. The locality analysis thus shows that a CC calculation on a large molecular system may be carried out in terms of CC calculations on small orbital fragments of the total molecular system, where the sizes of the orbital fragment spaces are determined in a black box manner to ensure that the CC correlation energy is calculated to a preset energy threshold. A practical implementation of the locality analysis is described, and numerical results are presented, which demonstrate that both the orbital fragment sizes and the relative energy error compared to a full CC calculation are independent of the molecular system size.

Journal ArticleDOI
TL;DR: These calculations simulate the laser-driven correlated many-electron dynamics in molecular systems and explore the limits for the numerical stability of the current TD-CCSD implementation, which uses time-independent molecular orbitals to form excited configurations.
Abstract: We report explicitly time-dependent coupled cluster singles doubles (TD-CCSD) calculations, which simulate the laser-driven correlated many-electron dynamics in molecular systems. Small molecules, i.e., HF, H(2)O, NH(3), and CH(4), are treated mostly with polarized valence double zeta basis sets. We determine the coupled cluster ground states by imaginary time propagation for these molecules. Excited state energies are obtained from the Fourier transform of the time-dependent dipole moment after an ultrashort, broadband laser excitation. The time-dependent expectation values are calculated from the complex cluster amplitudes using the corresponding configuration interaction singles doubles wave functions. Also resonant laser excitations of these excited states are simulated, in order to explore the limits for the numerical stability of our current TD-CCSD implementation, which uses time-independent molecular orbitals to form excited configurations.

Journal ArticleDOI
TL;DR: This paper presents the implementation of the spin-free CCD equations in which the entire iterative procedure is evaluated on the GPU, and shows that the GPU-accelerated algorithm readily achieves a factor of 4-5 speedup relative to the multithreaded CPU algorithm on same-generation hardware.
Abstract: The coupled cluster (CC) ansatz is generally recognized as providing one of the best wave function-based descriptions of electronic correlation in small- and medium-sized molecules. The fact that the CC equations with double excitations (CCD) may be expressed as a handful of dense matrix-matrix multiplications makes it an ideal method to be ported to graphics processing units (GPUs). We present our implementation of the spin-free CCD equations in which the entire iterative procedure is evaluated on the GPU. The GPU-accelerated algorithm readily achieves a factor of 4-5 speedup relative to the multithreaded CPU algorithm on same-generation hardware. The GPU-accelerated algorithm is approximately 8-12 times faster than Molpro, 17-22 times faster than NWChem, and 21-29 times faster than GAMESS for each CC iteration. Single-precision GPU-accelerated computations are also performed, leading to an additional doubling of performance. Single-precision errors in the energy are typically on the order of 10(-6) hartrees and can be improved by about an order of magnitude by performing one additional iteration in double precision.

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TL;DR: This work finds that the range-separated family of functionals addresses the well-documented TDDFT failures in describing these low-lying singlet excited states to a large extent and are as about as accurate as results from EOMCCSD on average.
Abstract: The low-lying excited states (La and Lb) of polyacenes from naphthalene to heptacene (N = 2-7) are studied using various time-dependent computational approaches. We perform high-level excited-state calculations using equation of motion coupled cluster with singles and doubles (EOMCCSD) and completely renormalized equation of motion coupled cluster with singles, doubles, and perturbative triples (CR-EOMCCSD(T)) and use these results to evaluate the performance of various range-separated exchange-correlation functionals within linear-response (LR) and real-time (RT) time-dependent density functional theories (TDDFT). As has been reported recently, we find that the range-separated family of functionals addresses the well-documented TDDFT failures in describing these low-lying singlet excited states to a large extent and are as about as accurate as results from EOMCCSD on average. Real-time TDDFT visualization shows that the excited state charged densities are consistent with the predictions of the perimeter free electron orbital (PFEO) model. This corresponds to particle-on-a-ring confinement, which leads to the well-known red-shift of the excitations with acene length. We also use time-dependent semiempirical methods like TD-PM3 and TD-ZINDO, which are capable of handling very large systems. Once reparametrized to match the CR-EOMCCSD(T) results, TD-ZINDO becomes roughly as accurate as range-separated TDDFT, which opens the door to modeling systems such as large molecular assemblies.

Journal ArticleDOI
TL;DR: Applications to the bond-stretching potential energy surfaces for N(2), CO, and the low-lying electronic states of C(2) indicate clear improvements of the results using the many-body residuals over the conventional projected residual equations.
Abstract: A state-specific partially internally contracted multireference coupled cluster approach is presented for general complete active spaces with arbitrary number of active electrons. The dominant dynamical correlation is included via an exponential parametrization of internally contracted cluster operators (T) which excite electrons from a multideterminantal reference function. The remaining dynamical correlation and relaxation effects are included via a diagonalization of the transformed Hamiltonian H¯=e−THeT in the multireference configuration interaction singles space in an uncontracted fashion. A new set of residual equations for determining the internally contracted cluster amplitudes is proposed. The second quantized matrix elements of H¯, expressed using the extended normal ordering of Kutzelnigg and Mukherjee, are used as the residual equations without projection onto the excited configurations. These residual equations, referred to as the many-body residuals, do not have any near-singularity a...

Journal ArticleDOI
TL;DR: It is demonstrated that the number of significant excited state PNOs scales asymptotically linearly with the system size in the worst case of completely delocalized excitations and sub-linearly whenever the chromophore does not increase with theSystem size.
Abstract: We explore how in response calculations for excitation energies with wavefunction based (e.g., coupled cluster) methods the number of double excitation amplitudes can be reduced by means of truncated pair natural orbital (PNO) expansions and localized occupied orbitals. Using the CIS(D) approximation as a test model, we find that the number of double excitation amplitudes can be reduced dramatically with minor impact on the accuracy if the excited state wavefunction is expanded in state-specific PNOs generated from an approximate first-order guess wavefunction. As for ground states, the PNO truncation error can also for excitation energies be controlled by a single threshold related to generalized natural occupation numbers. The best performance is found with occupied orbitals which are localized by the Pipek-Mezey localization. For a large test set of excited states we find with this localization that already a PNO threshold of 10−8–10−7, corresponding to an average of only 40–80 PNOs per pair, is suffic...