Keld L. Bak

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.

The accurate determination of molecular equilibrium structures

Equilibrium structures have been determined for 19 molecules using least-squares fits involving rotational constants from experiment and vibrational corrections from high-level electronic-structure calculations. Equilibrium structures obtained by this procedure have a uniformly high quality. Indeed, the accuracy of the results reported here likely surpasses that reported in most experimental determinations. In addition, the accuracy of equilibrium structures obtained by energy minimization has been calibrated for the following standard models of ab initio theory: Hartree–Fock, MP2, CCSD, and CCSD(T). In accordance with previous observations, CCSD(T) is significantly more accurate than the other models; the mean and maximum absolute errors for bond distances of the 19 molecules are 0.09 and 0.59 pm, respectively, in CCSD(T)/cc-pCVQZ calculations. The maximum error is obtained for ROO in H2O2 and is so large compared with the mean absolute error that an experimental reinvestigation of this molecule is warra...

Multiconfigurational self‐consistent field calculations of nuclear shieldings using London atomic orbitals

Nuclear shielding calculations are presented for multiconfigurational self‐consistent field wave functions using London atomic orbitals (gauge invariant atomic orbitals). Calculations of nuclear shieldings for eight molecules (H2O, H2S, CH4, N2, CO, HF, F2, and SO2) are presented and compared to corresponding individual gauges for localized orbitals (IGLO) results. The London results show better basis set convergence than IGLO, especially for heavier atoms. It is shown that the choice of active space is crucial for determination of accurate nuclear shielding constants.

Accuracy of atomization energies and reaction enthalpies in standard and extrapolated electronic wave function/basis set calculations

The accuracy of standard ab initio wave-function calculations of atomization energies and reaction enthalpies has been assessed by comparing with experimental data for 16 small closed-shell molecules and 13 isogyric reactions. The investigated wave-function models are Hartree–Fock (HF), Moller–Plesset second-order perturbation theory (MP2), coupled-cluster theory with singles and doubles excitations (CCSD) and CCSD with perturbative triple-excitation corrections [CCSD(T)]; the one-electron basis sets used are the correlation-consistent cc-pVxZ and cc-pCVxZ basis sets with cardinal numbers x=D, T, Q, 5, and 6. Results close to the basis-set limit have been obtained by using two-point extrapolations. In agreement with previous studies, it is found that the intrinsic error of the CCSD(T) method is less than chemical accuracy (≈4 kJ/mol) for both atomization energies and reaction enthalpies. The mean and maximum absolute errors of the best CCSD(T) calculations are 0.8 and 2.3 kJ/mol for the atomization energi...

Molecular equilibrium structures from experimental rotational constants and calculated vibration–rotation interaction constants

rotation interaction constants a r . The vibration‐rotation interaction constants have been calculated for 18 single-configuration dominated molecules containing hydrogen and first-row atoms at various standard levels of ab initio theory. Comparisons with the experimental data and tests for the internal consistency of the calculations show that the equilibrium structures generated using Hartree‐Fock vibration‐rotation interaction constants have an accuracy similar to that obtained by a direct minimization of the CCSD~T! energy. The most accurate vibration‐rotation interaction constants are those calculated at the CCSD~T!/cc-pVQZ level. The equilibrium bond distances determined from these interaction constants have relative errors of 0.02%‐0.06%, surpassing the accuracy obtainable either by purely experimental techniques ~except for the smallest systems such as diatomics! or by ab initio methods.

Hartree–Fock limit magnetizabilities from London orbitals

Molecular magnetizabilities have been calculated at the Hartree–Fock level for a series of diamagnetic molecules: H2O, NH3, CH4, PH3, H2S, CO2, CSO, CS2, and C3H4. Gauge invariance is imposed by the use of London atomic orbitals. The results are compared to those obtained with the IGLO (individual gauge for localized orbitals) method and are found to converge faster to the basis set limit. Magnetizabilities obtained from basis sets of different quality never differ by more than 4% for the London method, compared to 20% for IGLO. The Hartree–Fock limit may be approached using London basis sets of moderate size, in contrast to calculations of molecular polarizabilities which require large basis sets to be reliable. Comparison with experiment shows that the Hartree–Fock method overestimates experimental susceptibilities by 5%–10%.

Highly accurate calculations of molecular electronic structure

The highly accurate calculation of molecular electronic structure requires the expansion of the molecular electronic wavefunction to be as nearly complete as possible both in one- and n- electron space. In this review, we consider the convergence behaviour of computed electronic energies, in particular electronic enthalpies of reaction, as a function of the one-electron space. Based on the convergence behaviour, extrapolations to the limit of a complete one-electron basis are possible and such extrapolations are compared with the direct computation of electronic energies near the basis-set limit by means of explicitly correlated methods. The most elaborate and accurate computations are put into perspective with respect to standard and—from a computational point of view—inexpensive density functional, complete basis set (CBS) and Gaussian-2 calculations. Using the explicitly correlated coupled-cluster method including singles, doubles and non-iterative triples replacements, it is possible to compute (the electronic part of) enthalpies of reaction accurate to within 1 kJ mol 1 . To achieve this level of accuracy with standard coupled-cluster methods, large basis sets or extrapolations to the basis-set limit are necessary to exploit fully the intrinsic accuracy of the coupled-cluster methods.

Gauge‐origin independent multiconfigurational self‐consistent‐field theory for vibrational circular dichroism

Multiconfigurational self‐consistent‐field (MCSCF) theory is presented for the gauge‐origin independent calculation of vibrational circular dichroism. Origin independence is attained by the use of London atomic orbitals (LAO). MCSCF calculations on ammonia and its isotopomer NHDT demonstrate that atomic axial tensors and vibrational rotational strengths converge fast with the size of the basis set when LAOs are used. The correlation effects are significant both for the atomic tensors and the vibrational rotational strengths even for the single configuration dominated NHDT molecule.

Vibrational Raman optical activity calculations using London atomic orbitals

Ab initio calculations of Raman differential intensities are presented at the self-consistent field (SCF) level of theory. The electric dipole–electric dipole, electric dipole–magnetic dipole and electric dipole–electric quadrupole polarizability tensors are calculated at the frequency of the incident light, using SCF linear response theory. London atomic orbitals are employed, imposing gauge origin invariance on the calculations. Calculations have been carried out in the harmonic approximation for CFHDT and methyloxirane.

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...