Christof Hättig

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...

CC2 excitation energy calculations on large molecules using the resolution of the identity approximation

A new implementation of the approximate coupled cluster singles and doubles method CC2 is reported, which is suitable for large scale integral-direct calculations. It employs the resolution of the identity (RI) approximation for two-electron integrals to reduce the CPU time needed for calculation and I/O of these integrals. We use a partitioned form of the CC2 equations which eliminates the need to store double excitation cluster amplitudes. In combination with the RI approximation this formulation of the CC2 equations leads to a reduced scaling of memory and disk space requirements with the number of correlated electrons (n) and basis functions (N) to, respectively, O(N2) and O(nN2), compared to O(n2N2) in previous implementations. The reduced CPU, memory and disk space requirements make it possible to perform CC2 calculations with accurate basis sets on large molecules, which would not be accessible with conventional implementations of the CC2 method. We present an application to vertical excitation ene...

The Dalton quantum chemistry program system

Dalton is a powerful general‐purpose program system for the study of molecular electronic structure at the Hartree–Fock, Kohn–Sham, multiconfigurational self‐consistent‐field, Møller–Plesset, configuration‐interaction, and coupled‐cluster levels of theory. Apart from the total energy, a wide variety of molecular properties may be calculated using these electronic‐structure models. Molecular gradients and Hessians are available for geometry optimizations, molecular dynamics, and vibrational studies, whereas magnetic resonance and optical activity can be studied in a gauge‐origin‐invariant manner. Frequency‐dependent molecular properties can be calculated using linear, quadratic, and cubic response theory. A large number of singlet and triplet perturbation operators are available for the study of one‐, two‐, and three‐photon processes. Environmental effects may be included using various dielectric‐medium and quantum‐mechanics/molecular‐mechanics models. Large molecules may be studied using linear‐scaling and massively parallel algorithms. Dalton is distributed at no cost from http://www.daltonprogram.org for a number of UNIX platforms.

Response Functions from Fourier Component Variational Perturbation Theory Applied to a Time-Averaged Quasienergy

It is demonstrated that frequency-dependent response functions can conveniently be derived from the time-averaged quasienergy. The variational criteria for the quasienergy determines the time-evolution of the wave-function parameters and the time-averaged time-dependent Hellmann)Feynman theorem allows an identification of response functions as derivatives of the quasienergy. The quasienergy therefore plays the same role as the usual energy in time-independent theory, and the same techniques can be used to obtain computationally tractable expressions for response properties, as for energy derivatives in time-independent theory. This includes the use of the variational Lagrangian technique for obtaining expressions for molecular properties in accord with the 2 n q 1 and 2 n q 2 rules. The derivation of frequency-dependent response properties becomes a simple extension of variational perturbation theory to a Fourier component variational perturbation theory. The generality and simplicity of this approach are illustrated by derivation of linear and higher-order response functions for both exact and approximate wave functions and for both variational and nonvariational wave functions. Examples of approximate models discussed in this article are coupled-cluster, self- consistent field, and second-order Moller)Plesset perturbation theory. A discussion of symmetry properties of the response functions and their relation to molecular properties is also given, with special attention to the calculation of transition- and excited-state

Geometry optimizations with the coupled-cluster model CC2 using the resolution-of-the-identity approximation

An implementation of the gradient for the second-order coupled-cluster singles-and-doubles model CC2 is reported, which employs the resolution-of-the-identity (RI) approximation for electron repulsion integrals. The performance of the CC2 model for ground state equilibrium geometries and harmonic frequencies is investigated and compared with experiment and other ab initio methods. It is found that CC2 equilibrium geometries have a similar accuracy to those calculated with second-order Moller–Plesset perturbation theory (MP2), but the bond lengths are larger. In particular, double and triple bonds and bonds in electron-rich compounds are elongated by 0.5–1.5 pm. Thereby CC2 slightly outperforms MP2 for single bonds, in particular in electron-rich compounds, but for strong double and triple bonds CC2 is somewhat inferior to MP2. The results for harmonic frequencies go in parallel with the results for equilibrium structures. The error introduced by the RI approximation is found to be negligible compared to t...

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.

Optimization of auxiliary basis sets for RI-MP2 and RI-CC2 calculations: Core–valence and quintuple-ζ basis sets for H to Ar and QZVPP basis sets for Li to Kr

An implementation of analytic basis set gradients is reported for the optimization of auxiliary basis sets in resolution-of-the-identity second-order Moller–Plesset perturbation theory (RI-MP2) and approximate coupled-cluster singles-and-doubles (RI-CC2) calculations. The analytic basis set gradients are applied in the optimization of auxiliary basis sets for a number of large one-electron orbital basis sets which provide correlation energies close to the basis set limit: the core–valence basis sets cc-pwCVXZ (B–Ne, Al–Ar) with X = D, T, Q, 5, the quintuple-ζ basis sets cc-pV5Z (H–Ar) and cc-pV(5 + d)Z (Al–Ar) and the doubly-polarized valence quadruple-ζ basis sets QZVPP for Li–Kr. The quality of the optimized auxiliary basis sets is evaluated for several test sets with small and medium sized molecules.

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.

Structure Optimizations for Excited States with Correlated Second-Order Methods: CC2 and ADC(2)

Abstract The performance of the second-order methods for excitation energies CC2 and ADC(2) is investigated and compared with the more approximate CIS and CIS(D) methods as well as with the coupled-cluster models CCSD, CCSDR(3) and CC3. As a by-product of this investigation the first implementation of analytic excited state gradients for ADC(2) and CIS(D∞) is reported. It is found that for equilibrium structures and vibrational frequencies the second-order models CIS(D), ADC(2) and CC2 give often results close to those obtained with CCSD. The main advantage of CCSD lies in its robustness with respect to strong correlation effects. For adiabatic excitation energies CC2 is found to give from all second-order methods for excitation energies (including CCSD) the smallest mean absolute errors. ADC(2) and CIS(D∞) are found to give almost identical results. An advantage of ADC(2) compared to CC2 is that the excitation energies are obtained as eigenvalues of a Hermitian secular matrix, while in coupled-cluster response the excitation energies are obtained as eigenvalues of a non-Hermitian Jacobi matrix. It is shown that, as a consequence of the lack of Hermitian symmetry, the latter methods will in general not give a physically correct description of conical intersections between states of the same symmetry. This problem does not appear in ADC(2).