Poul Jørgensen

BASIS-SET CONVERGENCE IN CORRELATED CALCULATIONS ON NE, N2, AND H2O

Valence and all-electron correlation energies of Ne, N2, and H2O at fixed experimental geometries are computed at the levels of second-order perturbation theory (MP2) and coupled cluster theory with singles and doubles excitations (CCSD), and singles and doubles excitations with a perturbative triples correction (CCSD(T)). Correlation-consistent polarized valence and core-valence basis sets up to sextuple zeta quality are employed. Guided by basis-set limits established by rij-dependent methods, a number of extrapolation schemes for use with the correlation-consistent basis sets are investigated. Among the schemes considered here, a linear least-squares procedure applied to the quintuple and sextuple zeta results yields the most accurate extrapolations.

The second-order approximate coupled cluster singles and doubles model CC2

Abstract An approximate coupled cluster singles and doubles model is presented, denoted CC2. The CC2 total energy is of second-order Moller-Plesset perturbation theory (MP2) quality. The CC2 linear response function is derived. Unlike MP2, excitation energies and transition moments can be obtained in CC2. A hierarchy of coupled cluster models, CCS, CC2, CCSD, CC3, CCSDT etc., is presented where CC2 and CC3 are approximate coupled cluster models defined by similar approximations. Higher levels give increased accuracy at increased computational effort. The scaling of CCS, CC2, CCSD, CC3 and CCSDT is N4, N5, N6, N7 and N8, respectively where N is th the number of orbitals. Calculations on Be, N2 and C2H4 are performed and results compared with those obtained in the second-order polarization propagator approach SOPPA.

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.

Basis-set convergence of the energy in molecular Hartree–Fock calculations

Abstract The basis-set convergence towards the numerical limit of the Hartree–Fock total energy and binding energy is investigated for the correlation-consistent cc-pVXZ basis sets. For both energies, solid improvements are obtained with each increment in X . The basis-set errors for the total energy (Δ E ) fit an exponential form better than a power form, and the total energy is better fitted than the binding energy. It is difficult to find generally reliable extrapolation schemes for the total energy. In most cases, the most successful scheme gives results extrapolated beyond a given X that are comparable to the cc-pV(X+1)Z results, but occasionally it fails dramatically for large X . Indeed, explicit calculation of the energy in a larger basis set, especially the cc-pV6Z set for which Δ E ⩽0.1 mE h , gives the most reliable estimate of the basis-set limit.

Response Functions from Fourier Component Variational Perturbation Theory Applied to a Time-Averaged Quasienergy

It is demonstrated that frequency-dependent response functions can conveniently be derived from the time-averaged quasienergy. The variational criteria for the quasienergy determines the time-evolution of the wave-function parameters and the time-averaged time-dependent Hellmann)Feynman theorem allows an identification of response functions as derivatives of the quasienergy. The quasienergy therefore plays the same role as the usual energy in time-independent theory, and the same techniques can be used to obtain computationally tractable expressions for response properties, as for energy derivatives in time-independent theory. This includes the use of the variational Lagrangian technique for obtaining expressions for molecular properties in accord with the 2 n q 1 and 2 n q 2 rules. The derivation of frequency-dependent response properties becomes a simple extension of variational perturbation theory to a Fourier component variational perturbation theory. The generality and simplicity of this approach are illustrated by derivation of linear and higher-order response functions for both exact and approximate wave functions and for both variational and nonvariational wave functions. Examples of approximate models discussed in this article are coupled-cluster, self- consistent field, and second-order Moller)Plesset perturbation theory. A discussion of symmetry properties of the response functions and their relation to molecular properties is also given, with special attention to the calculation of transition- and excited-state

The genetic basis of long QT and short QT syndromes: A mutation update†

Long QT and short QT syndromes (LQTS and SQTS) are cardiac repolarization abnormalities that are characterized by length perturbations of the QT interval as measured on electrocardiogram (ECG). Prolonged QT interval and a propensity for ventricular tachycardia of the torsades de pointes (TdP) type are characteristic of LQTS, while SQTS is characterized by shortened QT interval with tall peaked T‐waves and a propensity for atrial fibrillation. Both syndromes represent a high risk for syncope and sudden death. LQTS exists as a congenital genetic disease (cLQTS) with more than 700 mutations described in 12 genes (LQT1–12), but can also be acquired (aLQTS). The genetic forms of LQTS include Romano‐Ward syndrome (RWS), which is characterized by isolated LQTS and an autosomal dominant pattern of inheritance, and syndromes with LQTS in association with other conditions. The latter includes Jervell and Lange‐Nielsen syndrome (JLNS), Andersen syndrome (AS), and Timothy syndrome (TS). The genetics are further complicated by the occurrence of double and triple heterozygotes in LQTS and a considerable number of nonpathogenic rare polymorphisms in the involved genes. SQTS is a very rare condition, caused by mutations in five genes (SQTS1–5). The present mutation update is a comprehensive description of all known LQTS‐ and SQTS‐associated mutations. Hum Mutat 30:1486–1511, 2009.

Recent advances in wave function-based methods of molecular-property calculations.

Recent Advances in Wave Function-Based Methods of Molecular-Property Calculations Trygve Helgaker,* Sonia Coriani, Poul Jørgensen, Kasper Kristensen, Jeppe Olsen, and Kenneth Ruud Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway Dipartimento di Scienze Chimiche e Farmaceutiche, Universit a degli Studi di Trieste, Via Giorgieri 1, I-34127 Trieste, Italy Lundbeck Center for Theoretical Chemistry, Department of Chemistry, Aarhus University, 8000 Aarhus C, Denmark Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Tromsø, N-9037 Tromsø, Norway

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...

Passing the one-billion limit in full configuration-interaction (FCI) calculations

Abstract Full configuration-interaction calculations have been carried out using more than one-billion determinants. Such large eigenvalue calculations are possible because of advances in the direct CI technology and in the iterative technique used to solve the eigenvalue equations. The CPU time per direct CI iteration varies approximately linearly with the dimension of the matrix from one million to more than one billion. One direct CI iteration is found to take about 1.2-1.4 min per million determinants on an IBM 3090/VF.

EXCITATION ENERGIES OF H2O, N2 AND C2 IN FULL CONFIGURATION INTERACTION AND COUPLED CLUSTER THEORY

Abstract Singlet excitation energies of H2O, N2 and C2 have been calculated in full configuration interaction (FCI) and in the coupled cluster model hierarchy CCS, CC2, CCSD and CC3. Excitation energies are improved at each level in the coupled cluster hierarchy, with a decrease in the error compared to FCI of about a factor of three at each level. This decrease is in accordance with the fact that the excitations in CCS, CC2, CCSD and CC3 are correct through higher and higher order in the fluctuation potential, and that more and more completer cluster treatments are used. Non-iterative triples corrections to the CCSD excitation energies are compared with the iterative triples models CC3 and FCI. The CCSDR(3) approach recovers the major part of the correlation improvement obtained in the CC3 model.