Andreas Köhn

Efficient use of the correlation consistent basis sets in resolution of the identity MP2 calculations

The convergence of the second-order Moller–Plesset perturbation theory (MP2) correlation energy with the cardinal number X is investigated for the correlation consistent basis-set series cc-pVXZ and cc-pV(X+d)Z. For the aug-cc-pVXZ and aug-cc-pV(X+d)Z series the convergence of the MP2 correlation contribution to the dipole moment is studied. It is found that, when d-shell electrons cannot be frozen, the cc-pVXZ and aug-cc-pVXZ basis sets converge much slower for third-row elements then they do for first- and second-row elements. Based on the results of these studies criteria are deduced for the accuracy of auxiliary basis sets used in the resolution of the identity (RI) approximation for electron repulsion integrals. Optimized auxiliary basis sets for RI-MP2 calculations fulfilling these criteria are reported for the sets cc-pVXZ, cc-pV(X+d)Z, aug-cc-pVXZ, and aug-cc-pV(X+d)Z with X=D, T, and Q. For all basis sets the RI error in the MP2 correlation energy is more than two orders of magnitude smaller than...

Transition moments and excited-state first-order properties in the coupled-cluster model CC2 using the resolution-of-the-identity approximation

An implementation of transition moments and excited-state first-order properties is reported for the approximate coupled-cluster singles-and-doubles model (CC2) using the resolution of the identity (RI) approximation. In parallel to the previously reported code for the ground- and excited-state amplitude equations, we utilize a partitioned form of the CC2 equations and thus eliminate the need to store any N 4 intermediates. This opens the perspective for applications on molecules with 30 and more atoms. The accuracy of the RI approximation is tested for a set of 29 molecules for the aug-cc -p V X Z (X=D,T,Q) basis sets in connection with the recently optimized auxiliary basis sets. These auxiliary basis sets are found to be sufficient even for the description of diffuse states. The RI error is compared to the usual basis set error and is demonstrated to be insignificant.

Explicitly Correlated Electrons in Molecules

Explicitly Correlated Electrons in Molecules Christof H€attig, Wim Klopper,* Andreas K€ohn, and David P. Tew Lehrstuhl f€ur Theoretische Chemie, Ruhr-Universit€at Bochum, D-44780 Bochum, Germany Abteilung f€ur Theoretische Chemie, Institut f€ur Physikalische Chemie, Karlsruher Institut f€ur Technologie, KIT-Campus S€ud, Postfach 6980, D-76049 Karlsruhe, Germany Institut f€ur Physikalische Chemie, Johannes Gutenberg-Universit€at Mainz, D-55099 Mainz, Germany School of Chemistry, University of Bristol, Bristol BS8 1TS, United Kingdom

Analytic gradients for excited states in the coupled-cluster model CC2 employing the resolution-of-the-identity approximation

The derivation and implementation of excited state gradients is reported for the approximate coupled-cluster singles and doubles model CC2 employing the resolution-of-the-identity approximation for electron repulsion integrals. The implementation is profiled for a set of examples with up to 1348 basis functions and exhibits no I/O bottlenecks. A test set of sample molecules is used to assess the performance of the CC2 model for adiabatic excitation energies, excited state structure constants and vibrational frequencies. We find very promising results, especially for adiabatic excitation energies, though the need of a single-reference ground state and a single-replacement dominated excited state puts some limits on the applicability of the method. Its reliability, however, can always be tested on grounds of diagnostic measures. As an example application, we present calculations on the π*←π excited state of trans-azobenzene.

Communications: Accurate and efficient approximations to explicitly correlated coupled-cluster singles and doubles, CCSD-F12

We propose a novel explicitly correlated coupled-cluster singles and doubles method CCSD(F12(*)), which retains the accuracy of CCSD-F12 while the computational costs are only insignificantly larger than those for a conventional CCSD calculation.

Pilot applications of internally contracted multireference coupled cluster theory, and how to choose the cluster operator properly

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 BeH(2) 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 μE(h) when truncating the cluster operator at double excitations (icMRCCSD), inclusion of triple excitations (icMRCCSDT) leads to significant differences of more than 1 mE(h). 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) double and triple excitations which have the same effect on the reference function. With this approach, the equilibrium structure and harmonic vibrational frequencies of ozone obtained with icMRCCSDT are in excellent agreement with CCSDTQ. The authors further apply icMRCC methods to potential energy surfaces of HF, LiF, N(2), and to the singlet-triplet splitting of benzynes. In particular, the latter calculations have been made possible by implementing the method with the proper formal scaling using automated techniques.

Implementation of the full explicitly correlated coupled-cluster singles and doubles model CCSD-F12 with optimally reduced auxiliary basis dependence

An implementation of the full explicitly correlated coupled-cluster singles and doubles model CCSD-F12 using a single Slater-type geminal has been obtained with the aid of automated term generation and evaluation techniques. In contrast to a previously reported computer code [T. Shiozaki et al., J. Chem. Phys. 129, 071101 (2008)], our implementation features a reduced dependence on the auxiliary basis set due to the use of a reformulated evaluation of the so-called Z-intermediate rather than straight forward insertion of an auxiliary basis expansion, which allows an unambiguous comparison to more approximate CCSD-F12 models. First benchmark results for total correlation energies and reaction energies indicate an excellent performance of the much cheaper CCSD(F12) model.

Explicitly correlated connected triple excitations in coupled-cluster theory

A way to incorporate explicit electron correlation into connected triple excitations in coupled-cluster theory is proposed. The new ansatz is applied to the coupled-cluster singles and doubles model with noniterative triple excitations [CCSD(T)] and does not introduce any further sets of equations to be solved. A first implementation using automated generation and string-based evaluation of the explicit expressions is reported. The results demonstrate that the ansatz significantly enhances the basis set convergence of the noniterative triple excitation correction and thus improves upon previous approaches to explicitly correlated CCSD(T).

Solvent Effects on Electronically Excited States Using the Conductor-Like Screening Model and the Second-Order Correlated Method ADC(2)

The conductor-like screening model (COSMO) is used to treat solvent effects on excited states within a correlated method based on the algebraic-diagrammatic construction through second-order ADC(2). The origin of solvent effects is revisited, and it is pointed out that two types of contributions have to be considered. One effect is due to the change of the solutes charge distribution after excitation, which triggers a reorganization of the solvent. Initially, only the electronic degrees of freedom adapt to the new charge distribution (nonequilibrium case); for sufficiently long-lived states, the reorientation of the solvent molecules contributes, as well (equilibrium case). The second effect is the coupling of the transition densities to the fast (purely electronic) response of the solvent molecules, which can be viewed as excitonic coupling between solute and solvent molecules. This interaction is also responsible for the screening of excitonic couplings between spatially separated chromophores. While most previous implementations of comparable continuum solvation models only include either of both effects, we argue that both contributions should be taken into account. Both effects can significantly influence the excitation energy and excited state properties of the solute, as exemplified for the π-π* and n-π* excitations of acrolein, and no a priori reason exists to neglect either. The implementation is also tested for the excitonic coupling of the ethene dimer where linear response contributions are indispensable for recovering the screening effects due to the solvent. Example applications to larger cases are provided, too. We discuss the excitonic coupling in a linked dyad consisting of two perylene-tetracarboxy-diimide chromophores, and the solvent effects on an intramolecular charge-transfer state of 4-(N,N-dimethylamino)benzonitrile.

First-order properties for triplet excited states in the approximated coupled cluster model CC2 using an explicitly spin coupled basis

An implementation is reported for first-order properties of excited triplet states within the approximate coupled cluster model CC2 using an explicitly spin coupled basis for the triplet excitation manifold and the resolution of the identity (RI) approximation for the electron repulsion integrals. Results are presented for the change of the second moment of charge upon excitation in the ππ* valence and n=3 Rydberg states of benzene. Employing large basis sets with up to 828 functions, we obtain results close to the CC2 basis set limit and are able to resolve an uncertainty in the assignment of the lowest 1E1u states. It is found that the often used %T1 measure for the single excitation contribution to excited states is not reliable for a comparison across different excitation operator manifolds. An alternative diagnostic is proposed which provides a unique measure for the single excitation contribution that is independent of the chosen representation of the excitation operator manifold.