Stephan P. A. Sauer

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.

Benchmarks for electronically excited states: CASPT2, CC2, CCSD, and CC3.

A benchmark set of 28 medium-sized organic molecules is assembled that covers the most important classes of chromophores including polyenes and other unsaturated aliphatic compounds, aromatic hydrocarbons, heterocycles, carbonyl compounds, and nucleobases. Vertical excitation energies and one-electron properties are computed for the valence excited states of these molecules using both multiconfigurational second-order perturbation theory, CASPT2, and a hierarchy of coupled cluster methods, CC2, CCSD, and CC3. The calculations are done at identical geometries (MP26-31G*) and with the same basis set (TZVP). In most cases, the CC3 results are very close to the CASPT2 results, whereas there are larger deviations with CC2 and CCSD, especially in singlet excited states that are not dominated by single excitations. Statistical evaluations of the calculated vertical excitation energies for 223 states are presented and discussed in order to assess the relative merits of the applied methods. CC2 reproduces the CC3 reference data for the singlets better than CCSD. On the basis of the current computational results and an extensive survey of the literature, we propose best estimates for the energies of 104 singlet and 63 triplet excited states.

Benchmarks for electronically excited states: time-dependent density functional theory and density functional theory based multireference configuration interaction.

Time-dependent density functional theory (TD-DFT) and DFT-based multireference configuration interaction (DFT/MRCI) calculations are reported for a recently proposed benchmark set of 28 medium-sized organic molecules. Vertical excitation energies, oscillator strengths, and excited-state dipole moments are computed using the same geometries (MP2/6-31G(*)) and basis set (TZVP) as in our previous ab initio benchmark study on electronically excited states. The results from TD-DFT (with the functionals BP86, B3LYP, and BHLYP) and from DFT/MRCI are compared against the previous high-level ab initio results, and, in particular, against the proposed best estimates for 104 singlet and 63 triplet vertical excitation energies. The statistical evaluation for the latter reference data gives the lowest mean absolute deviations for DFT/MRCI (0.22 eV for singlets and 0.24 eV for triplets) followed by TD-DFT/B3LYP (0.27 and 0.44 eV, respectively), whereas TD-DFT/BP86 and TD-DFT/BHLYP are significantly less accurate. The energies of singlet states with double excitation character are generally overestimated by TD-DFT, whereas triplet state energies are systematically underestimated by the currently investigated DFT-based methods.

The effect of lone pairs and electronegativity on the indirect nuclear spin–spin coupling constants in CH2X (X=CH2, NH, O, S): Ab initio calculations using optimized contracted basis sets

The indirect nuclear spin–spin coupling constants of C2H4, CH2NH, CH2O, and CH2S were investigated by means of correlated ab initio calculations at the level of the second order polarization propagator approximation (SOPPA) and the second order polarization propagator approximation with coupled cluster singles and doubles amplitudes—SOPPA(CCSD) using large basis sets, which are optimized for the calculation of coupling constants. It is found that at the self-consistent-field (SCF) level CH2NH and CH2S exhibit triplet instabilities whereas CH2CH2 and CH2O show triplet quasi-instabilities, which renders the SCF results meaningless. Our best results deviate between 0.3 and 2.7 Hz from the experimental values. We find that although the one-bond C–H and Y–H couplings as well as the two- and three-bond H–H couplings are dominated by the Fermi contact term, significant contributions of the orbital paramagnetic and sometimes even spin–dipolar terms are observed for the one-bond C–Y and two-bond C–H and Y–H coupli...

Benchmarks of electronically excited states: Basis set effects on CASPT2 results

Vertical excitation energies and one-electron properties are computed for the valence excited states of 28 medium-sized organic benchmark molecules using multistate multiconfigurational second-order perturbation theory (MS-CASPT2) and the augmented correlation-consistent aug-cc-pVTZ basis set. They are compared with previously reported MS-CASPT2 results obtained with the smaller TZVP basis. The basis set extension from TZVP to aug-cc-pVTZ causes rather minor and systematic shifts in the vertical excitation energies that are normally slightly reduced (on average by 0.11 eV for the singlets and by 0.09 eV for the triplets), whereas the changes in the calculated oscillator strengths and dipole moments are somewhat more pronounced on a relative scale. These basis set effects at the MS-CASPT2 level are qualitatively and quantitatively similar to those found at the coupled cluster level for the same set of benchmark molecules. The previously proposed theoretical best estimates (TBE-1) for the vertical excitation energies for 104 singlet and 63 triplet excited states of the benchmark molecules are upgraded by replacing TZVP with aug-cc-pVTZ data that yields a new reference set (TBE-2). Statistical evaluations of the performance of density functional theory (DFT) and semiempirical methods lead to the same ranking and very similar quantitative results for TBE-1 and TBE-2, with slightly better performance measures with respect to TBE-2. DFT/MRCI is most accurate among the investigated DFT-based approaches, while the OMx methods with orthogonalization corrections perform best at the semiempirical level.

Second-order polarization propagator approximation with coupled-cluster singles and doubles amplitudes - SOPPA(CCSD): the polarizability and hyperpolarizability of

A new modification of the second-order polarization propagator approximation (SOPPA) is presented. In the new method, called SOPPA(CCSD), all first-order Moller - Plesset doubles and second-order Moller - Plesset singles correlation coefficients are replaced with the corresponding coupled-cluster singles and doubles (CCSD) and amplitudes. This is in contrast to the earlier coupled-cluster polarization propagator approximation (CCSDPPA) in which only one of the doubles correlation coefficients was replaced in the unrelaxed second-order density matrix. The importance of this modification is investigated for the dipole polarizability, dipole oscillator strength sum rules and second hyperpolarizability of , which is known to be a difficult case for perturbative methods. The SOPPA(CCSD) values are compared with previous and new full CI results for the same basis sets.

Atomic integral driven second order polarization propagator calculations of the excitation spectra of naphthalene and anthracene

An atomic integral direct implementation of the second order polarization propagator approximation (SOPPA) for the calculation of electronic excitation energies and oscillator strengths is presented. The SOPPA equations are solved iteratively using an integral direct approach and, contrary to previous implementations, the new algorithm does not require two-electron integrals in the molecular orbital basis. The linear transformation of trial vectors are calculated directly from integrals in the atomic orbital basis. In addition, the eigenvalue solver is designed to work efficiently with only three trial vectors per eigenvalue. Both of these modifications dramatically reduce the amount of disk space required, thus, increasing the range of applicability of the SOPPA method. Calculations of the lowest singlet excitation energies and corresponding dipole oscillator strengths for naphthalene and anthracene employing basis sets of 238 and 329 atomic orbitals, respectively, are presented. The overall agreement of...

Nuclear spin–spin coupling in the acetylene isotopomers calculated from ab initio correlated surfaces for 1J(C, H), 1J(C, C), 2J(C, H), and 3J(H, H)

Ab initio calculated coordinate and internal valence coordinate coefficients for each of the four spin–spin coupling surfaces of the acetylene molecule—1J(C, H), 1J(C, C), 2J(C, H), and 3J(H, H) are presented. Calculations were carried out at the SOPPA(CCSD) level using a large basis set. Couplings were calculated at 35 geometries (including equilibrium) giving 35 distinct sites on the 1J(C, C) and 3J(H, H) surfaces and 53 distinct sites on the 1J(C, H) and 2J(C, H) surfaces. The results were fitted to fourth order in Taylor series expansions and are presented to second order in the coordinates. All couplings are sensitive to geometry with the principal features being (a) an even steeper increase of J(C1, H1) with CC bond stretching than with CH bond stretching—an example of “unexpected differential sensitivity” (or UDS), (b) very opposite variations of 2J(C1, H2) with variations of the CC and C2H2 bond lengths, (c) very opposite variations of 1J(C, C) with a CC stretch and a CH stretch and (d) very oppos...

Basis set effects on coupled cluster benchmarks of electronically excited states: CC3, CCSDR(3) and CC2

Vertical electronic excitation energies and one-electron properties of 28 medium-sized molecules from a previously proposed benchmark set are revisited using the augmented correlation-consistent triple-zeta aug-cc-pVTZ basis set in CC2, CCSDR(3), and CC3 calculations. The results are compared to those obtained previously with the smaller TZVP basis set. For each of the three coupled cluster methods, a correlation coefficient greater than 0.994 is found between the vertical excitation energies computed with the two basis sets. The deviations of the CC2 and CCSDR(3) results from the CC3 reference values are very similar for both basis sets, thus confirming previous conclusions on the intrinsic accuracy of CC2 and CCSDR(3). This similarity justifies the use of CC2- or CCSDR(3)-based corrections to account for basis set incompleteness in CC3 studies of vertical excitation energies. For oscillator strengths and excited-state dipole moments, CC2 calculations with the aug-cc-pVTZ and TZVP basis sets give correlation coefficients of 0.966 and 0.833, respectively, implying that basis set convergence is slower for these one-electron properties.

Benchmarks for Electronically Excited States: A Comparison of Noniterative and Iterative Triples Corrections in Linear Response Coupled Cluster Methods: CCSDR(3) versus CC3.

CCSDR(3) calculations of vertical excitation energies are reported for a set of 24 molecules and 121 excited valence singlet states from a recently published benchmark of organic molecules. The same geometries (MP2/6-31G*) and basis set (TZVP) were employed as in our previous linear response CC2, CCSD, and CC3 calculations. The CCSDR(3) results are compared against the CCSD and CC3 results. Statistical evaluation of all CCSDR(3) excitation energies gives mean absolute deviations of 0.09 eV from CC3 and 0.30 eV from CCSD. For excited states, which are dominated by single excitations, the absolute mean deviation from CC3 is reduced to 0.02 eV and the maximum deviation is 0.09 eV. CCSDR(3) is thus a very cost-effective accurate alternative to CC3.