Biomedical subjects

Trygve Helgaker

Publications and source records attributed to Trygve Helgaker.

At least 19 recordsLinked to original sources

PubMed2006

A second-quantization framework for the unified treatment of relativistic and nonrelativistic molecular perturbations by response theory.

A formalism is presented for the calculation of relativistic corrections to molecular electronic energies and properties. After a discussion of the Dirac and Breit equations and their first-order Foldy-Wouthuysen [Phys. Rev. 78, 29 (1950)] transformation, we construct a second-quantization electronic Hamiltonian, valid for all values of the fine-structure constant alpha. The resulting alpha-dependent Hamiltonian is then used to set up a perturbation theory in orders of alpha(2), using the general framework of time-independent response theory, in the same manner as for geometrical and magnetic perturbations. Explicit expressions are given to second order in alpha(2) for the Hartree-Fock model. However, since all relativistic considerations are contained in the alpha-dependent Hamiltonian operator rather than in the wave function, the same approach may be used for other wave-function models, following the general procedure of response theory. In particular, by constructing a variational Lagrangian using the alpha-dependent electronic Hamiltonian, relativistic corrections can be calculated for nonvariational methods as well.

Journal Article↗

PubMed2006

Benchmarking two-photon absorption with CC3 quadratic response theory, and comparison with density-functional response theory.

We present a detailed study of the effects of electron correlation on two-photon absorption calculated by coupled cluster quadratic response theory. The hierarchy of coupled cluster models CCS, CC2, CCSD, and CC3 has been used to investigate the effects of electron correlation on the two-photon absorption cross sections of formaldehyde (CH2O), diacetylene (C4H2), and water (H2O). In particular, the effects of triple excitations on two-photon transition cross sections are determined for the first time. In addition, we present a detailed comparison of the coupled cluster results with those obtained from Hartree-Fock and density-functional response theories. We have investigated the local-density approximation, the pure Becke-Lee-Yang-Parr (BLYP) functional, the hybrid Becke-3-parameter-Lee-Yang-Parr (B3LYP), and the Coulomb-attenuated B3LYP (CAM-B3LYP) functionals. Our results show that the CAM-B3LYP functional, when used in conjuction with a one-particle basis-set containing diffuse functions, has much promise; however, care must still be exercised for diffuse Rydberg-type states.

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PubMed2006

The equilibrium structure of ferrocene.

The molecular structures of ferrocene in the eclipsed (equilibrium) and staggered (saddle-point) conformations have been determined by full geometry optimizations at the levels of second-order Møller-Plesset (MP2) theory, coupled-cluster singles-and-doubles (CCSD) theory, and CCSD theory with a perturbative triples correction [CCSD(T)] in a TZV2P+f basis set. Existing experimental results are reviewed. The agreement between the CCSD(T) results and experiment is in all cases excellent; the calculated structure parameters and the barrier to internal rotation of the ligand rings differ from the most accurate experimental values by less than two estimated standard deviations. The CCSD(T) calculations for single-configuration-dominated transition metal complexes such as ferrocene thus appear to have an accuracy comparable to that observed for molecules containing only first- and second-row atoms, and to be of a quality similar to that obtained experimentally. A comparison with previous DFT results indicates that the B3LYP model gives overall the best DFT results, with a deviation of around 2 pm for the metal-carbon distance and smaller errors for the cyclopentadienyl rings.

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PubMed2005

Quadratic response functions in a second-order polarization propagator framework.

The linear and quadratic response functions have been derived for an exact state, based on an exponential parametrization of the time evolution consisting of products of exponentials for orbital rotations and for higher-order excitations. Truncating the linear response function such that the response function itself and its pole structure is correct to second order in Møller-Plesset perturbation theory, we arrive at the second-order polarization propagator approximation (SOPPA). Previous derivations of SOPPA have used the superoperator formalism, making the extension of SOPPA to quadratic and higher order response functions difficult. The derivation of the quadratic response function is described in detail, allowing molecular properties such as hyperpolarizabilities, two-photon cross sections, and excited-state properties to be calculated using the SOPPA model.

Journal Article↗

PubMed2005

Assessment of a Coulomb-attenuated exchange-correlation energy functional.

The recently proposed CAM-B3LYP exchange-correlation energy functional, based on a partitioning of the r operator in the exchange interaction into long- and short-range components, is assessed for the determination of molecular thermochemistry, structures, and second order response properties. Rydberg and charge transfer excitation energies and static electronic polarisabilities are notably improved over the standard B3LYP functional; classical reaction barriers also improve. Ionisation potentials, bond lengths, NMR shielding constants and indirect spin-spin coupling constants are comparable with the two functionals. CAM-B3LYP atomisation energies and diatomic harmonic vibrational wavenumbers are less accurate than those of B3LYP. Future research directions are outlined.

Journal Article↗

PubMed2005

Calculations of two-photon charge-transfer excitations using Coulomb-attenuated density-functional theory.

In this work, we show that an implementation of Coulomb-attenuated density-functional theory leads to considerably better prospects than hitherto for modeling two-photon absorption cross sections for charge-transfer species. This functional, which corrects for the effect of poor asymptotic dependence of commonly used functionals, essentially brings down the widely different results for larger charge-transfer species between Hartree-Fock and density-functional theory (DFT)-B3LYP into a closer range. The Coulomb-attenuated functional, which retains the best aspects of the Hartree-Fock and DFT-B3LYP methods, proves to be very promising for further modeling design of multiphoton materials with technical applications.

Journal Article↗

PubMed2005

The accuracy of ab initio molecular geometries for systems containing second-row atoms.

The performance of the standard hierarchy of ab initio models--that is, Hartree-Fock theory, second-order Moller-Plesset theory, coupled-cluster singles-and-doubles theory, and coupled-cluster singles-doubles-approximate-triples theory--in combination with correlation-consistent basis sets is investigated for equilibrium geometries of molecules containing second-row elements. From an analysis on a collection of 31 molecules (yielding statistical samples of 41 bond distances and 13 bond angles), the statistical errors (mean deviation, mean absolute deviation, standard deviation, and maximum absolute deviation) are established at each level of theory. The importance of core correlation is examined by comparing calculations in the frozen-core approximation with calculations where all electrons are correlated.

Journal Article↗

PubMed2005

A computational study of some electric and magnetic properties of gaseous BF3 and BCl3.

We present the results of an extended computational study of the electric and magnetic properties connected to Cotton-Mouton birefringences, on the trifluoro- and trichloroborides in the gas phase. The electric dipole polarizabilities, magnetizabilities, quadrupole moments, and higher-order hypersusceptibilities--expressed as quadratic and cubic frequency-dependent response functions--are computed within Hartree-Fock, density-functional, and coupled-cluster response theories employing singly and doubly augmented correlation-consistent basis sets and London orbitals in the magnetic property calculations. The results, which illustrate the capability of time-dependent density-functional theory for electron-rich systems, are compared with available experimental data. Revised values of both experimentally derived quadrupole moment of BF3, 2.72 +/- 0.15 a.u., and magnetizability anisotropy of BCl3, -0.45 +/- 0.09 a.u., both obtained in birefringence experiments that neglect the effects of higher-order hypersusceptibilities, are presented. In the theoretical limit the traceless quadrupole moments of BF3 and BCl3 are determined to be 3.00 +/- 0.01 and 0.71 +/- 0.01 a.u., respectively.

Journal Article↗

PubMed2005

The trust-region self-consistent field method in Kohn-Sham density-functional theory.

The trust-region self-consistent field (TRSCF) method is extended to the optimization of the Kohn-Sham energy. In the TRSCF method, both the Roothaan-Hall step and the density-subspace minimization step are replaced by trust-region optimizations of local approximations to the Kohn-Sham energy, leading to a controlled, monotonic convergence towards the optimized energy. Previously the TRSCF method has been developed for optimization of the Hartree-Fock energy, which is a simple quadratic function in the density matrix. However, since the Kohn-Sham energy is a nonquadratic function of the density matrix, the local energy functions must be generalized for use with the Kohn-Sham model. Such a generalization, which contains the Hartree-Fock model as a special case, is presented here. For comparison, a rederivation of the popular direct inversion in the iterative subspace (DIIS) algorithm is performed, demonstrating that the DIIS method may be viewed as a quasi-Newton method, explaining its fast local convergence. In the global region the convergence behavior of DIIS is less predictable. The related energy DIIS technique is also discussed and shown to be inappropriate for the optimization of the Kohn-Sham energy.

Algorithms↗

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↗

PubMed2005

Theoretical studies of nuclear magnetic resonance parameters for the proton-exchange pathways in porphyrin and porphycene.

The nuclear magnetic resonance (NMR) parameters in porphyrin and porphycene have been calculated to investigate their changes during the process of proton exchange, using density-functional theory (DFT) for both the spin-spin coupling constants and the shielding constants. In addition, in calculations on the smaller 1,3-bis(arylimino)isoindoline molecule, we have tested the performance of our computational approach against experimental data. The calculated nuclear spin-spin coupling constants and shielding constants have been analyzed as functions of the progress of the proton transfer between two nitrogen atoms. The one-bond couplings between proton and nitrogen, dominated by the Fermi-contact term, decay steeply as the internuclear distance increases. The small changes in the intramolecular J(HH) coupling between two inner protons are mainly determined by the sum of relatively large spin-orbit terms. The isotropic shielding constant shows a strong deshielding of the nitrogen nuclei as the proton migrates away. Both the isotropic shielding of the exchanged protons and the shielding anisotropy exhibit a minimum close to the transition states.

Journal Article↗

PubMed2005

Atmospheric chemistry of CHF2CHO: study of the IR and UV-vis absorption cross sections, photolysis, and OH-, Cl-, and NO3-initiated oxidation.

The infrared and ultraviolet-visible absorption cross sections, effective quantum yield of photolysis, and OH, Cl, and NO3 reaction rate coefficients of CHF2CHO are reported. Relative rate measurements at 298 +/- 2 K and 1013 +/- 10 hPa gave kOH = (1.8 +/- 0.4) x 10(-12) cm3 molecule(-1) s(-1) (propane as reference compound), kCl = (1.24 +/- 0.13) x 10(-11) cm3 molecule(-1) s(-1) (ethane as reference compound), and kNO3 = (5.9 +/- 1.7) x 10(-17) cm3 molecule(-1) s(-1) (trans-dichloroethene as reference compound). The photolysis of CHF2CHO has been investigated under pseudonatural tropospheric conditions in the European simulation chamber, Valencia, Spain (EUPHORE), and an effective quantum yield of photolysis equal to 0.30 +/- 0.05 over the wavelength range 290-500 nm has been extracted. The tropospheric lifetime of CHF2CHO is estimated to be around 1 day and is determined by photolysis. The observed photolysis rates of CH3CHO, CHF2CHO, and CF3CHO are discussed on the basis of results from quantum chemical calculations.

Absorption↗

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.

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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↗