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Trygve Helgaker

Publications and source records attributed to Trygve Helgaker.

15 recordsLinked to original sources
PubMed2005

Density-functional theory study of electric and magnetic properties of hexafluorobenzene in the vapor phase.

A series of electric and magnetic properties of hexafluorobenzene have been calculated, including the electric dipole polarizability, magnetizability, electric quadrupole moment, and nonlinear mixed electric dipole-magnetic dipole-electric quadrupole hyperpolarizabilities needed to obtain estimates of the Kerr, Cotton-Mouton, Buckingham, Jones, and magnetoelectric birefringences in the vapor phase. Time-dependent density-functional theory was employed for the calculation of linear-, quadratic, and cubic response functions. A number of density functionals have been considered, along with Sadlej's triple-zeta basis set and the augmented correlation-consistent polarized valence double zeta and augmented correlation-consistent polarized valence triple zeta basis sets. Comparisons have been made with experiment where possible. The analysis of results allows for an assessment of the capability of time-dependent density-functional theory for high-order electromagnetic properties of an electron-rich system such as hexafluorobenzene.

Journal Article↗
PubMed2004

A closed-shell coupled-cluster treatment of the Breit-Pauli first-order relativistic energy correction.

First-order relativistic corrections to the energy of closed-shell molecular systems are calculated, using all terms in the two-component Breit-Pauli Hamiltonian. In particular, we present the first implementation of the two-electron Breit orbit-orbit integrals, thus completing the first-order relativistic corrections within the two-component Pauli approximation. Calculations of these corrections are presented for a series of small and light molecules, at the Hartree-Fock and coupled-cluster levels of theory. Comparisons with four-component Dirac-Coulomb-Breit calculations demonstrate that the full Breit-Pauli energy corrections represent an accurate approximation to a fully relativistic treatment of such systems. The Breit interaction is dominated by the spin-spin interaction, the orbit-orbit interaction contributing only about 10% to the total two-electron relativistic correction in molecules consisting of light atoms. However, the relative importance of the orbit-orbit interaction increases with increasing nuclear charge, contributing more than 20% in H(2)S.

Journal Article↗
PubMed2004

Coupled-cluster connected quadruples and quintuples corrections to the harmonic vibrational frequencies and equilibrium bond distances of HF, N(2), F(2), and CO.

Using the coupled-cluster method, we have examined the contributions from the connected quadruple and quintuple virtual excitations to the harmonic vibrational frequencies and equilibrium bond distances of HF, N(2), F(2), and CO. Whereas the largest quadruples contributions are -18.8 cm(-1) to the harmonic frequency of N(2) and 0.43 pm to the bond distance of F(2), the largest quintuples contributions are -3.9 cm(-1) to the harmonic frequency of N(2) and 0.03 pm to the bond distances of N(2) and F(2). As we improve the description by going from the coupled-cluster singles-and-doubles model with a perturbative triples correction [CCSD(T)] to the coupled-cluster singles-doubles-triples-and-quadruples model, the mean and maximum absolute errors in the calculated frequencies relative to experiment are reduced from 11.3 and 15.8 cm(-1), respectively, to 3.2 and 4.7 cm(-1); for the bond distances, the mean and maximum absolute errors are reduced from 0.16 and 0.47 pm, respectively, to 0.04 and 0.13 pm. The calculations presented here confirm previous observations that, to some extent, the relatively small errors in the CCSD(T) equilibrium bond distances and harmonic frequencies arise from a cancellation of errors in the approximate (perturbative) treatment of the connected triples and the neglect of higher-order connected excitations. Further inclusion of quintuples contributions, relativistic corrections, and adiabatic corrections reduces the mean and maximum absolute errors to 1.1 and 2.3 cm(-1), respectively, for the harmonic frequencies and to 0.02 and 0.05 pm, respectively, for the bond distances.

Journal Article↗
PubMed2004

The calculation of indirect nuclear spin-spin coupling constants in large molecules.

We present calculations of indirect nuclear spin-spin coupling constants in large molecular systems, performed using density functional theory. Such calculations, which have become possible because of the use of linear-scaling techniques in the evaluation of the Coulomb and exchange-correlation contributions to the electronic energy, allow us to study indirect spin-spin couplings in molecules of biological interest, without having to construct artificial model systems. In addition to presenting a statistical analysis of the large number of short-range coupling constants in large molecular systems, we analyse the asymptotic dependence of the indirect nuclear spin-spin coupling constants on the internuclear separation. In particular, we demonstrate that, in a sufficiently large one-electron basis set, the indirect spin-spin coupling constants become proportional to the inverse cube of the internuclear separation, even though the diamagnetic and paramagnetic spin-orbit contributions to the spin-spin coupling constants separately decay as the inverse square of this separation. By contrast, the triplet Fermi contact and spin-dipole contributions to the indirect spin-spin coupling constants decay exponentially and as the inverse cube of the internuclear separation, respectively. Thus, whereas short-range indirect spin-spin coupling constants are usually dominated by the Fermi contact contribution, long-range coupling constants are always dominated by the negative diamagnetic spin-orbit contribution and by the positive paramagnetic spin-orbit contribution, with small spin-dipole and negligible Fermi contact contributions.

Crystallography, X-Ray↗
PubMed2004

Polarization consistent basis sets. V. The elements Si-Cl.

Polarization consistent basis sets, optimized for density functional calculations, are proposed for the elements Si-Cl. Their performance for atomization energies, equilibrium geometries, harmonic vibrational frequencies, and associated infrared intensities is compared with other commonly used basis sets. Atomization energies can be predicted to within 0.01 kJ/mol per atom of the basis set limit by extrapolation of the pc-2, -3, and -4 results. Equilibrium bond distances and harmonic vibrational frequencies can be calculated to within 10(-5) A and 0.5 cm(-1), respectively, of the basis set limit. The pc-n basis sets are shown to give comparable or better accuracy than other alternatives, while containing fewer or equal number of primitive basis functions.

Journal Article↗
PubMed2004

Linear-scaling formation of Kohn-Sham Hamiltonian: application to the calculation of excitation energies and polarizabilities of large molecular systems.

We present calculations of excitation energies and polarizabilities in large molecular systems at the local-density and generalized-gradient approximation levels of density-functional theory (DFT). Our results are obtained using a linear-scaling DFT implementation in the program system DALTON for the formation of the Kohn-Sham Hamiltonian. For the Coulomb contribution, we introduce a modification of the fast multipole method to calculations over Gaussian charge distributions. It affords a simpler implementation than the original continuous fast multipole method by partitioning the electrostatic Coulomb interactions into "classical" and "nonclassical" terms which are explicitly evaluated by linear-scaling multipole techniques and a modified two-electron integral code, respectively. As an illustration of the code, we have studied the singlet and triplet excitation energies as well as the static and dynamic polarizabilities of polyethylenes, polyenes, polyynes, and graphite sheets with an emphasis on the trends observed with system size.

Journal Article↗
PubMed2004

The trust-region self-consistent field method: towards a black-box optimization in Hartree-Fock and Kohn-Sham theories.

The trust-region self-consistent field (TRSCF) method is presented for optimizing the total energy E(SCF) of Hartree-Fock theory and Kohn-Sham density-functional theory. In the TRSCF method, both the Fock/Kohn-Sham matrix diagonalization step to obtain a new density matrix and the step to determine the optimal density matrix in the subspace of the density matrices of the preceding diagonalization steps have been improved. The improvements follow from the recognition that local models to E(SCF) may be introduced by carrying out a Taylor expansion of the energy about the current density matrix. At the point of expansion, the local models have the same gradient as E(SCF) but only an approximate Hessian. The local models are therefore valid only in a restricted region-the trust region-and steps can only be taken with confidence within this region. By restricting the steps of the TRSCF model to be inside the trust region, a monotonic and significant reduction of the total energy is ensured in each iteration of the TRSCF method. Examples are given where the TRSCF method converges monotonically and smoothly, but where the standard DIIS method diverges.

Journal Article↗
PubMed2004

Density-functional generalized-gradient and hybrid calculations of electromagnetic properties using Slater basis sets.

In this paper we extend our density-functional theory calculations, with generalized gradient approximation and hybrid functionals, using Slater-type orbitals (STOs), to the determination of second-order molecular properties. The key to the entire methodology involves the fitting of all STO basis function products to an auxiliary STO basis, through the minimization of electron-repulsion integrals. The selected properties are (i) dipole polarizabilities, (ii) nuclear magnetic shielding constants, and (iii) nuclear spin-spin coupling constants. In all cases the one-electron integrals involving STOs were evaluated by quadrature. The implementation for (ii) involved some complexity because we used gauge-including atomic orbitals. The presence of two-electron integrals on the right-hand side of the coupled equations meant that the fitting procedure had to be implemented. For (iii) in the hybrid case, fitting procedures were again required for the exchange contributions. For each property we studied a number of small molecules. We first obtained an estimate of the basis set limit using Gaussian-type orbitals (GTOs). We then showed how it is possible to reproduce these values using a STO basis set. For (ii) a regular TZ2P quality STO basis was adequate; for (i) the addition of one set of diffuse functions (determined by Slater's rules) gave the required accuracy; for (iii) it was necessary to add a set of 1s functions, including one very tight function, to give the desired result. In summary, we show that it is possible to predict second-order molecular properties using STO basis sets with an accuracy comparable with large GTO basis sets. We did not encounter any major difficulties with either the selection of the bases or the implementation of the procedures. Although the energy code (especially in the hybrid case) may not be competitive with a regular GTO code, for properties we find that STOs are more attractive.

Journal Article↗
PubMed2004

Density-functional theory calculations of optical rotatory dispersion in the nonresonant and resonant frequency regions.

The complex linear response function, which can be employed for calculations of second-order molecular properties in regions of strong absorption, is here extended to encompass the mixed electric-dipole-magnetic-dipole polarizability. The mixed electric-dipole-magnetic-dipole polarizability determines the optical rotation and, when absorption is taken into account, the full anomalous optical rotatory dispersion (ORD) spectra of chiral molecules can be calculated using first-principle quantum-chemical methods. Gauge-origin independence of the results is ensured through the use of London atomic orbitals. To illustrate the importance of taking the absorption process properly into account, we here apply this methodology to the study of the anomalous ORD of hydrogen peroxide, 3R-methylcyclohexanone, 4R-1,1-dimethyl-[3]-(1,2)-ferrocenophan-2-on, and the D(2) isomer of the C(84) fullerene.

Journal Article↗
PubMed2004

Calculation of electric dipole hypershieldings at the nuclei in the Hellmann-Feynman approximation.

The third-rank electric hypershieldings at the nuclei of four small molecules have been evaluated at the Hartree-Fock level of theory in the Hellmann-Feynman approximation. The nuclear electric hypershieldings are closely related to molecular vibrational absorption intensities and a generalization of the atomic polar tensors (expanded in powers of the electric field strength) is proposed to rationalize these intensities. It is shown that the sum rules for rototranslational invariance and the constraints imposed by the virial theorem provide useful criteria for basis-set completeness and for near Hartree-Fock quality of nuclear shieldings and hypershieldings evaluated in the Hellmann-Feynman approximation. Twelve basis sets of different size and quality have been employed for the water molecule in an extended numerical test on the practicality of the proposed scheme. The best results are obtained with the R12 and R12+ basis sets, designed for the calculation of electronic energies by the explicitly correlated R12 method. The R12 basis set is subsequently used to investigate three other molecules, CO, N2, and NH3, verifying that the R12 basis consistently performs very well.

Journal Article↗
PubMed2004

The performance of hybrid density functional theory for the calculation of indirect nuclear spin-spin coupling constants in substituted hydrocarbons.

Density functional theory, in particular, with the Becke-3-parameter-Lee-Yang-Parr (B3LYP) hybrid functional, has been shown to be a promising method for the calculation of indirect nuclear spin-spin coupling constants. However, no systematic investigation has so far been undertaken to evaluate the capability of B3LYP to calculate these coupling constants accurately, taking properly into account the vibrational contributions. In this work, vibrationally corrected indirect spin-spin coupling constants were calculated using the B3LYP functional for 10 rigid unsubstituted and substituted hydrocarbons: ethyne, ethene, allene, cyclopropene, cyclopropane, cyclobutene, pyrrole, furan, thiophene and benzene. The resulting spin-spin constants were compared with the available experimental values. The basis sets in these calculations give indirect nuclear spin-spin coupling constants of ethyne that are almost converged to the basis-set limit, making the intrinsic error of the computational method and the error in equilibrium geometry the main sources of error. On average, the B3LYP functional overestimates the indirect nuclear spin-spin coupling constants in hydrocarbons by 10%.

Journal Article↗
PubMed2004

Models of fragmentations induced by electron attachment to protonated peptides.

Invoking a number of theoretical levels ranging from HF/STO-3G to CCSD(T)/aug-cc-pVQZ, we have made a detailed survey of six potential energy surfaces (NH4+, NH4*, [CH3CONHCH3]H+, [CH3CONHCH3]H*, [HCONHCH2CONH2]H+, [HCONHCH2CONH2]H*). In conjunction with this, ab inito direct dynamics calculations have been conducted, tracing out several hundred reaction trajectories to reveal details of the electron-capture dissociation mechanism. The model calculations suggest the possibility of a bimodal pattern where some of the radicals, formed upon recombination, dissociate almost directly within one picosecond, the remaining radicals being subject to complete energy redistribution with a subsequent dissociation occurring at the microsecond timescale. Both processes give rise to c and z backbone fragments, resulting from cleavage of N-Calpha bonds of the peptide chain.

Electrons↗
PubMed2002

Four-component relativistic Kohn-Sham theory.

A four-component relativistic implementation of Kohn-Sham theory for molecular systems is presented. The implementation is based on a nonredundant exponential parametrization of the Kohn-Sham energy, well suited to studies of molecular static and dynamic properties as well as of total electronic energies. Calculations are presented of the bond lengths and the harmonic and anharmonic vibrational frequencies of Au(2), Hg(2+)(2), HgAu(+), HgPt, and AuH. All calculations are based on the full four-component Dirac-Coulomb Hamiltonian, employing nonrelativistic local, gradient-corrected, and hybrid density functionals. The relevance of the Coulomb and Breit operators for the construction of relativistic functionals is discussed; it is argued that, at the relativistic level of density-functional theory and in the absence of a vector potential, the neglect of current functionals follows from the neglect of the Breit operator.

Journal Article↗
PubMed2002

Software news and updates. Basis-set completeness profiles in two dimensions.

A two-electron basis-set completeness profile is proposed by analogy with the one-electron profile introduced by D. P. Chong (Can J Chem 1995, 73, 79). It is defined as Y(alpha, beta) = sigmam sigman (Galpha(1)Gbeta(2)/(1/r12)/ psim(1)psin(2)) (psim(1)psin(2)/r12/Galpha(1)Gp(2)) and motivated by the expression for the basis-set truncation correction that occurs in the framework of explicitly correlated methods (Galpha is a scanning Gaussian-type orbital of exponent alpha and [psim] is the orthonormalized one-electron basis under study). The two-electron basis-set profiles provide a visual assessment of the suitability of basis sets to describe electron-correlation effects. Furthermore, they provide the opportunity to assess the quality of the basis set as a whole--not only of the individual angular momentum subspaces, as is the case for the one-electron basis-set profiles. The two-electron completeness profiles of the cc-pVXZ (X = D, T, Q), aug-cc-pVTZ, cc-pCVTZ, and SVP-auxiliary basis sets for the carbon atom are presented as illustrative examples.

Journal Article↗