Kasper Hald

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.

Controlling the alignment of neutral molecules by a strong laser field

A strong nonresonant nanosecond laser pulse is used to align neutral iodine molecules. The technique, applicable to both polar and nonpolar molecules, relies on the interaction between the strong laser field and the induced dipole moment of the molecules. The degree of alignment is enhanced by lowering the initial rotational energy of the molecules or by increasing the laser intensity. The alignment is measured by photodissociating the molecules with a femtosecond laser pulse and detecting the direction of the photofragments by imaging techniques. The strongest degree of alignment observed is 〈cos2 θ〉=0.81.

Implementation of RI-CC2 triplet excitation energies with an application to trans-azobenzene

Triplet excitation energies within the approximate coupled cluster singles and doubles model CC2 have been implemented using an explicitly spin coupled basis and the resolution of the identity approximation for two-electron integrals. This approach reduces substantially the requirements for CPU time, disk space and memory, and extends the applicability of CC2 for triplet excited states to molecules that could not be studied before with this method. We report an application to the lowest singlet and triplet vertical excitation energies of trans-azobenzene. An accurate ab initio geometry optimized at the MP2/cc-pVTZ level is presented, and CC2 calculations in the aug-cc-pVTZ basis set with 874 basis functions are combined with coupled cluster singles and doubles (CCSD) calculations in modest basis sets to obtain the best possible estimates for the vertical excitation energies. The results show that recently reported SOPPA calculations are unreliable. Good agreement with experiment is obtained for the lowest excited singlet state S1, but for the lowest triplet state T1 the results indicate a large difference between the vertical excitation energy and the experimentally observed transition.

Triplet excitation energies in full configuration interaction and coupled-cluster theory

Triplet excitation energies have been calculated for Ne, H2O, HF, BH, N2, and C2 using the full configuration interaction (FCI) model and the coupled-cluster model hierarchy CCS, CC2, CCSD, CC3, and CCSDT, where CCS, CCSD, and CCSDT are the standard coupled-cluster models where singles, doubles and triples are successively added and where CC2 and CC3 are approximations to the CCSD and CCSDT models where approximations are introduced in the highest amplitude equations. Comparing the coupled-cluster excitation energies with the FCI results shows that the excitation energies are improved at each level in the hierarchy up to CC3. The CC3 and CCSDT excitation energies have similar accuracy for the single excitation dominated excitation energies, whereas the double excitation dominated excitation energies are significantly improved also from CC3 to CCSDT. Singlet excitation energies have also been calculated for HF using the coupled-cluster hierarchy up to CCSDT. Triplet and singlet excitation energies with sim...

A Lagrangian, integral-density direct formulation and implementation of the analytic CCSD and CCSD(T) gradients

Using a Lagrangian formulation an integral-density direct implementation of the analytic CCSD(T) molecular gradient is presented, which circumvents the bottleneck of storing either O(N4) two-electron integrals or O(N4) density matrix elements on disk. Canonical orbitals are used to simplify the implementation of the frozen-core approximation and the CCSD gradient is obtained as a special case. Also a new, simplified approach to (geometrical) derivative integrals is presented. As a first application we report a full geometry optimization for the most stable isomer of SiC3 using the cc-pV5Z basis set with 368 contracted basis functions and the frozen-core approximation.

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.

Calculation of frequency-dependent polarizabilities using the approximate coupled-cluster triples model CC3

CC3 is a member of the coupled-cluster model hierarchy CCS, CC2, CCSD, CC3, and CCSDT which is especially designed to describe frequency-dependent properties. CCS is the coupled-cluster singles model, in CCSD doubles are added and in CC2 the doubles of the CCSD model are approximated using the same strategy as for triples when CCSDT is approximated to give CC3. Excitation energies have been calculated successfully using this hierarchy. The error in the excitation energies is reduced by about a factor 3 at each level for the models CCS, CC2, CCSD, and CC3, and the CC3 excitation energies closely approximate the ones of the CCSDT model. 14 Calculation of frequency-dependent polarizabilities and hyperpolarizabilities have shown similar systematic improvements to the excitation energies. 15‐17

An analysis and implementation of a general coupled cluster approach to excitation energies with application to the B2 molecule

A general scheme is presented for the calculation of excitation energies using the standard coupled cluster hierarchy and a simple implementation is described for the higher standard models. An error analysis is performed to find to what order excitation energies in different coupled cluster models are correct. The analysis includes both the standard coupled cluster hierarchy as well as the approximate models and considers excitations to states that are dominated by one, two, and three electron replacements compared to the reference state. Calculations are presented up to the quadruple excitation level for the open shell B2 molecule using an excited closed shell state as reference state to emphasize the usefulness of the order analysis. The coupled cluster excitation energies are compared to full configuration interaction results.

Triplet excitation energies in the coupled cluster singles and doubles model using an explicit triplet spin coupled excitation space

Triplet excitation energies are calculated from the response eigenvalue equation for the coupled cluster singles and doubles (CCSD) model using an integral direct approach and an explicit spin coupled triplet excitation space. The cost of one linear transformation for the triplet excitation energy is about two times the cost of one linear transformation for the singlet excitation energy. The triplet excitation spectrum of benzene is calculated using from 147 to 432 basis functions. The calculated triplet excitation energies are compared with experimental and other theoretical values.

Implementation of electronic ground states and singlet and triplet excitation energies in coupled cluster theory with approximate triples corrections

An implementation of triples corrections for the calculation of the electronic ground states and for singlet and triplet excitation energies within the CC3 model is discussed. At most objects of size V2O2 and V3O are kept in memory and on disc, respectively (V is the number of virtual orbital and O is the number of occupied orbitals). The used strategy means that more terms that scales as V4O3 has to be calculated than if the triples amplitudes are kept on disc but it allows larger cases to be handled. Sample calculations are presented for the triplet excitation energies of benzene.