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A multistate local CC2 response method for the calculation of orbital-relaxed first order properties is presented for ground and electronically excited states. It enables the treatment of excited state properties including orbital relaxation for extended molecular systems and is a major step on the way towards analytic gradients with respect to nuclear displacements. The Laplace transform method is employed to partition the eigenvalue problem and the lambda equations, i.e., the doubles parts of these equations are inverted on-the-fly, leaving only the corresponding effective singles equations to be solved iteratively. Furthermore, the state specific local approximations are adaptive. Density-fitting is utilized to decompose the electron-repulsion integrals. The accuracy of the local approximation is tested and the efficiency of the new code is demonstrated on the example of an organic sensitizer for solar-cell applications, which consists of about 100 atoms. [ABSTRACT FROM AUTHOR]

A local method based on orbital specific virtuals (OSVs) for calculating the perturbative triples correction in local coupled cluster calculations is presented. In contrast to the previous approach based on projected atomic orbitals (PAOs), described by Schütz [J. Chem. Phys. 113, 9986 (2000)], the new scheme works without any ad hoc truncations of the virtual space to domains. A single threshold defines the pair and triple specific virtual spaces completely and automatically. It is demonstrated that the computational cost of the method scales linearly with molecular size. Employing the recommended threshold a similar fraction of the correlation energy is recovered as with the original PAO method at a somewhat lower cost. A benchmark for 52 reactions demonstrates that for reaction energies the intrinsic accuracy of the coupled cluster with singles and doubles excitations and a perturbative treatment of triples excitations method can be reached by OSV-local coupled cluster theory with singles and doubles and perturbative triples, provided a MP2 correction is applied that accounts for basis set incompleteness errors as well as for remaining domain errors. As an application example the interaction energies of the guanine-cytosine dimers in the Watson-Crick and stacked arrangements are investigated at the level of local coupled cluster theory with singles and doubles and perturbative triples. Based on these calculations we propose new complete-basis-set-limit estimates for these interaction energies at this level of theory. [ABSTRACT FROM AUTHOR]

We present a density fitted local configuration interaction singles (CIS) method for calculating optical bandgaps in 3D-periodic systems. We employ an Ewald technique to carry out infinite lattice summations for the exciton-exciton interaction, and robust product-density specific local density fitting in direct space for the electron-hole interaction. Moreover, we propose an alternative to the usual cyclic model with Born-von Karman periodic boundary conditions, the so called Wigner-Seitz supercell truncated infinite model, which exhibits much improved convergence of the CIS excitation energy with respect to the size of the supercell. Test calculations on a series of prototypical systems demonstrate that the method at the present stage can be used to calculate the excitonic bandgaps of 3D periodic systems with up to a dozen atoms in the unit cell, ranging from wide-gap insulators to semiconductors. [ABSTRACT FROM AUTHOR]

An efficient method for the calculation of nuclear magnetic resonance (NMR) shielding tensors is presented, which treats electron correlation at the level of second-order Mo\ller-Plesset perturbation theory. It uses spatially localized functions to span occupied and virtual molecular orbital spaces, respectively, which are expanded in a basis of gauge including atomic orbitals (GIAOs or London atomic orbitals). Doubly excited determinants are restricted to local subsets of the virtual space and pair energies with an interorbital distance beyond a certain threshold are omitted. Furthermore, density fitting is employed to factorize the electron repulsion integrals. Ordinary Gaussians are employed as fitting functions. It is shown that the errors in the resulting NMR shielding constant, introduced (i) by the local approximation and (ii) by density fitting, are very small or even negligible. The capabilities of the new program are demonstrated by calculations on some extended molecular systems, such as the cyclobutane pyrimidine dimer photolesion with adjacent nucleobases in the native intrahelical DNA double strand (ATTA sequence). Systems of that size were not accessible to correlated ab initio calculations of NMR spectra before. The presented method thus opens the door to new and interesting applications in this area. [ABSTRACT FROM AUTHOR]

We extend the orbital-specific-virtual tensor factorization, introduced for local Mo\ller-Plesset perturbation theory in Ref. [J. Yang, Y. Kurashige, F. R. Manby and G. K. L. Chan, J. Chem. Phys. 134, 044123 (2011)], to local coupled cluster singles and doubles theory (OSV-LCCSD). The method is implemented by modifying an efficient projected-atomic-orbital local coupled cluster program (PAO-LCCSD) described recently, [H.-J. Werner and M. Schütz, J. Chem. Phys. 135, 144116 (2011)]. By comparison of both methods we find that the compact representation of the amplitudes in the OSV approach affords various advantages, including smaller computational time requirements (for comparable accuracy), as well as a more systematic control of the error through a single energy threshold. Overall, the OSV-LCCSD approach together with an MP2 correction yields small domain errors in practical calculations. The applicability of the OSV-LCCSD is demonstrated for molecules with up to 73 atoms and realistic basis sets (up to 2334 basis functions). [ABSTRACT FROM AUTHOR]

The atomic orbital basis set limit is approached in periodic correlated calculations for solid LiH. The valence correlation energy is evaluated at the level of the local periodic second order Mo\ller-Plesset perturbation theory (MP2), using basis sets of progressively increasing size, and also employing 'bond'-centered basis functions in addition to the standard atom-centered ones. Extended basis sets, which contain linear dependencies, are processed only at the MP2 stage via a dual basis set scheme. The local approximation (domain) error has been consistently eliminated by expanding the orbital excitation domains. As a final result, it is demonstrated that the complete basis set limit can be reached for both HF and local MP2 periodic calculations, and a general scheme is outlined for the definition of high-quality atomic-orbital basis sets for solids. [ABSTRACT FROM AUTHOR]

We present a density fitted local configuration interaction singles (CIS) method for calculating optical band gaps in 1D-periodic systems. The method is based on the Davidson diagonalization procedure, carried out in the reciprocal space. The one-electron part of the matrix-vector products is also evaluated in the reciprocal space, where the diagonality of the Fock matrix can be exploited. The contraction of the CIS vectors with the two electron integrals is performed in the direct space in the basis of localized occupied (Wannier) and virtual (projected atomic) orbitals. The direct space approach allows to utilize the sparsity of the integrals due to the local representation and locality of the exciton. The density fitting approximation employed for the two electron integrals reduces the nominal scaling with unit cell size to O(N4). Test calculations on a series of prototypical systems demonstrate that the method in its present stage can be used to calculate the excitonic band gaps of polymers with up to a few dozens of atoms in the cell. The computational cost depends on the locality of the exciton, but even relatively delocalized excitons occurring in the polybiphenyl in the parallel orientation, can be routinely treated with this method. [ABSTRACT FROM AUTHOR]

A new multistate local CC2 response method for calculating excitation energies and first-order properties of excited triplet states in extended molecular systems is presented. The Laplace transform technique is employed to partition the left/right local CC2 eigenvalue problems as well as the linear equations determining the Lagrange multipliers needed for the properties. The doubles part in the equations can then be inverted on-the-fly and only effective equations for the singles part must be solved iteratively. The local approximation presented here is adaptive and state-specific. The density-fitting method is utilized to approximate the electron-repulsion integrals. The accuracy of the new method is tested by comparison to canonical reference values for a set of 12 test molecules and 62 excited triplet states. As an illustrative application example, the lowest four triplet states of 3-(5-(5-(4-(bis(4-(hexyloxy)phenyl)amino)phenyl)thiophene-2-yl)thiophene-2-yl)-2-cyanoacrylic acid, an organic sensitizer for solar-cell applications, are computed in the present work. No triplet charge-transfer states are detected among these states. This situation contrasts with the singlet states of this molecule, where the lowest singlet state has been recently found to correspond to an excited state with a pronounced charge-transfer character having a large transition strength. [ABSTRACT FROM AUTHOR]

The lowest electronically excited states of the aniline dimer and trimer related to the lowest π*←π transition of the monomer are investigated by applying time-dependent coupled cluster theory, primarily at the level of the (spin-component-scaled) CC2 model. Minimum energy structures in the vicinity of the Franck-Condon points were determined on the individual potential energy surfaces. For the dimer we find an excimer and a head-to-tail configuration (with the monomers substantially displaced relative to the ground state minimum) for the lowest (dark) and second lowest (bright) states, respectively. The excitation is delocalized on both chromophores for both of these states. For the trimer three distinct minima with quite different hydrogen-bonding arrangements are found for the three lowest states. In strong contrast to the dimer the excitation here is clearly localized on the individual aniline chromophores for each of these three states. One of the three geometries is rather similar to the ground state minimum, while the two others are rather different and thus have presumably quite small Franck-Condon factors. It can be expected that only the electronic origin of the first conformer can eventually be detected in the absorption spectrum of the trimer, provided that it is separated by high-enough barriers from other, energetically lower configurations. [ABSTRACT FROM AUTHOR]

The aniline dimer and trimer are investigated in their electronic ground state. The potential energy surface was thoroughly searched for low lying minima by applying global optimizations on a model potential, which is recalibrated on-the-fly by ab initio calculations (spin-component-scaled LMP2) at relevant configurations. The most stable structure of the dimer corresponds to a head-to-tail arrangement with both aniline monomers being nearly equivalent. DFT-SAPT calculations reveal that the interaction energy is dominated by van der Waals dispersion, which is of comparable size as for the benzene dimer, but with a much larger total interaction energy than for the latter. The global minimum of the aniline trimer corresponds to a hydrogen bonding arrangement involving three directional NH–N hydrogen bonds, with the individual monomers being clearly distinguishable. Nonadditive three-body dispersion contributions appear to play a minor role for the trimer. [ABSTRACT FROM AUTHOR]

We have calculated the equilibrium geometry, formation energy, and bulk modulus of two molecular bulk crystals, NH3 and CO2, at the periodic post-Hartree–Fock correlated level. The dependence of the results on the basis set has been analyzed, by employing basis sets up to aug-cc-pVQZ quality. In the calculations, we used the periodic local Mo\ller–Plesset second order perturbation theory (LMP2), implemented in the CRYSCOR program. Multipolar expansion techniques, as well as density fitting, are employed in this code to reduce the number of and to factorize the required electron repulsion integrals; as a consequence of that, the computational cost for the correlation part of the calculations is comparable to that of the Hartree–Fock. Auxiliary calculations performed on molecular dimers are also reported to verify the accuracy of the LMP2 approach and of the basis sets used. Furthermore, the effect of spin-component scaling has been investigated for the two crystals. One intention of the present paper is also to lay out and specify the computational setup, which is generally applicable for accurate CRYSCOR calculations on molecular crystals. [ABSTRACT FROM AUTHOR]

A new Laplace transform based multistate local CC2 response method for calculating excitation energies of extended molecular systems is presented. By virtue of the Laplace transform trick, the eigenvalue problem involving the local CC2 Jacobian is partitioned along the doubles-doubles block (which is diagonal in the parental canonical method) without losing the sparsity in the integral, amplitude, and amplitude response supermatrices. Hence, only an effective eigenvalue problem involving singles vectors has to be solved, while the doubles part can be computed on-the-fly. Within this framework, a multistate treatment of excited states with state specific and adaptive local approximations imposed on the doubles part is straightforwardly possible. Furthermore, in the context of the density fitting approximation of the two-electron integrals, a procedure to specify the local approximation, i.e., the restricted pair lists and domains, on the basis of an analysis of the object to be approximated itself is proposed. Performance and accuracy of the new Laplace transformed density fitted local CC2 (LT-DF-LCC2) response method are tested for set of different test molecules and states. It turns out that LT-DF-LCC2 response is much more robust than the earlier local CC2 response method proposed before, which failed to find some excited states in difficult cases. [ABSTRACT FROM AUTHOR]

The potential energy surfaces of the S0 and S1(π*←π) states of the 2-naphthol(H2O)n, n∈{1,2} clusters were explored at the level of coupled cluster (CC2) response theory. In the electronic ground state two different types of hydrogen-bonding networks coexist for n=2, (i) a cyclic one [similar to those of the water trimer and phenol(H2O)2] where the hydroxy group of the aryl alcohol acts simultaneously as H donor for the first, and as H acceptor for the second water molecule, and (ii) a hydrogen-bonding arrangement where the aromatic π system is taking over the role as H acceptor. In the S1 state, on the other hand, the cyclic conformers are unstable. Consequently, the first group of cyclic ground state conformers gives rise to broad unstructured band shapes in the absorption spectrum, whereas the second group of conformers involving the aromatic π system gives rise to nicely structured band shapes. Based on these results the puzzling absorption spectrum of the n=2 cluster can properly be interpreted. [ABSTRACT FROM AUTHOR]

A hybrid scheme for the computation of reaction energies in large molecular systems is proposed. The approach is based on localized orbitals and allows for the treatment of different parts of a molecule at different computational levels. The localized orbitals are assigned to regions, and then different local correlation methods, such as local MP2 or local CCSD(T), can be applied to different regions. In contrast to previous hybrid schemes, the molecule does not have to be split into parts and, therefore, it is not necessary to saturate dangling bonds using link atoms. For fixed region sizes, the cost of the high-level calculation becomes independent of the molecular size, and it is demonstrated that O(1) scaling can be achieved. Illustrative applications are presented and the convergence of the results with respect to the size of the regions is investigated for reaction energies, barrier heights, and weakly bound complexes. [ABSTRACT FROM AUTHOR]

The S1(π*←π) state surfaces of the phenol-water1<=n<=3 clusters are reexplored at the level of coupled cluster response theory. The global minima for n=2 and n=3 so obtained are qualitatively different from those reported so far, which were obtained with methods such as configuration interaction singles or complete active space self-consistent field lacking dynamical electron correlation effects. Furthermore, the minimum-energy points on the conical intersection seams were located in this work. The results of these calculations offer a qualitative explanation for the anomalous photophysical behavior (broad congested absorption band structure, low quantum yield, short lifetime) of n=2 and the observed predissociation of n=3 at excess energies beyond ≈100 cm-1, resolving a disagreement between theory and experiment which persisted for almost a decade [ABSTRACT FROM AUTHOR]

A new ab initio method for calculating transition strengths and orbital-unrelaxed first-order properties of singlet ground and excited states of extended molecular systems is presented. It is based on coupled cluster response theory at the level of the CC2 model with local approximations introduced to the doubles-excitation part of the wave function. Density fitting is employed for the calculation of the electron repulsion integrals, so that—with the exception of doubles amplitudes—only three-indexed objects do occur in the formalism. The new method was tested by performing calculations for a set of various molecules and excited states and by comparing the results with corresponding canonical (nonlocal) calculations. It turned out that for calculating transition strengths and properties of excited states the ordinary Boughton-Pulay domains are insufficient in numerous cases. To circumvent this problem a new scheme for extending domains is proposed, which is based on the solution of the coupled perturbed localization and Hartree-Fock equations. When such extended domains are used, a satisfactory agreement between canonical and local results is achieved. [ABSTRACT FROM AUTHOR]

A new local method for the computation of electronic excitation energies of singlet states in extended molecular systems is presented. It is based on the CC2 model and local approximations to the wave functions. In the proposed method the singles excitations are treated nonlocally and local restrictions are imposed on doubles amplitudes only. The accuracy of the new method was tested by calculating several lowest excited states for 14 molecules and comparing them with canonical CC2 values. Deviations of the local excitation energies from the canonical reference values do not exceed 0.05 eV for all test molecules and all states in the lower energy range investigated in this work. The method uses the density-fitting approximation for all two-electron integrals, which considerably simplifies the computational complexity of the individual diagrams. A combination of the local approximations and the powerful density-fitting technique leads to a low-scaling method, capable to treat molecular systems comprised of 100 atoms and more in a basis of a polarized double zeta quality. A test calculation for a system consisting of 127 atoms and 370 active electrons without symmetry is presented to show the efficiency of the new method. [ABSTRACT FROM AUTHOR]

An efficient method to compute analytical energy derivatives for local second-order Møller–Plesset perturbation energy is presented. Density fitting approximations are employed for all 4-index integrals and their derivatives. Using local fitting approximations, quadratic scaling with molecular size and cubic scaling with basis set size for a given molecule is achieved. The density fitting approximations have a negligible effect on the accuracy of optimized equilibrium structures or computed energy differences. The method can be applied to much larger molecules and basis sets than any previous second-order Møller–Plesset gradient program. The efficiency and accuracy of the method is demonstrated for a number of organic molecules as well as for molecular clusters. Examples of geometry optimizations for molecules with 100 atoms and over 2000 basis functions without symmetry are presented. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Successful restoration of semi‐natural grasslands on grasslands previously subject to intensive management needs to overcome manifold barriers. These include high soil fertility, the dominance of a few fast‐growing plant species, degraded soil faunal communities and missing propagules of the targeted above‐ and below‐ground flora and fauna. A combination of removing the topsoil and introducing propagules of target plants has become one of the major tools for nature conservation agencies and practitioners to reduce soil fertility and restore former species‐rich grasslands in various European countries.Using topsoil removal as a restoration measure has provoked an ongoing debate between supporting nature conservation and rejecting soil protection agencies. Although it favours species‐rich plant communities, it strongly disturbs soil communities and affects physical and chemical soil properties and processes. Currently, there is a lack of long‐term data to assess how restored grassland ecosystems develop and recover after topsoil removal. Here, we used two well‐established bioindicators, soil nematodes and plants, to quantify restoration success of topsoil removal in comparison with alternative restoration measures and target communities 22 years after intervention.The nematode community composition indicated reduced nutrient availability in the restored systems, as was aimed at by topsoil removal. Nevertheless, after this 22‐year period following topsoil removal, nematode composition and structure revealed successful recovery.Plant communities benefitted from the reduction of soil nutrients after topsoil removal as indicated by higher numbers of plant species and higher Shannon diversity. Furthermore, topsoil removal strongly promoted the re‐establishment of plant species of the target plant community.Synthesis and applications. Overall, our study demonstrates how a massive intervention by topsoil removal proved successful in converting intensively managed into species‐rich grasslands. This contrasts with the mild intervention of repeated mowing and removing of the harvested plant material. We show that, in the long run, potential negative effects of topsoil removal on the soil fauna can be successfully overcome and plant communities can develop into targeted species‐rich grassland. Overall, our study demonstrates how a massive intervention by topsoil removal proved successful in converting intensively managed into species‐rich grasslands. This contrasts with the mild intervention of repeated mowing and removing of the harvested plant material. We show that, in the long run, potential negative effects of topsoil removal on the soil fauna can be successfully overcome and plant communities can develop into targeted species‐rich grassland. [ABSTRACT FROM AUTHOR]