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Trygve Helgaker

Publications and source records attributed to Trygve Helgaker.

26 records · Page 2Linked to original sources
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.

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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.

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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%.

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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.

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