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Cluster perturbation (CP) theory was developed in Paper I [F. Pawłowski et al., J. Chem. Phys. 150, 134108 (2019)] for a coupled cluster (CC) target state and is extended in this paper to comprehend a cluster linear (CL) target state, for which the embedding of a CC parent state in the target excitation space is described using a linear parametrization. The theory is developed for determining the energy and molecular properties for a CL state. When CP theory is applied to a CL target state, a series of corrections is determined in orders of the CC parent-state similarity-transformed fluctuation potential, where the zeroth-order term is the energy or molecular property of the CC parent state and where the series formally converges to the energy or molecular property of the CL target state. The determination of energies and molecular properties is simpler for a CL state than for a CC state because the CL state is linearly parametrized. The amplitude equations are quadratic for a CL target state, while quartic for a CC target state, and molecular property expressions for a CL target state have the same simple structure as for a configuration interaction state. The linear parametrization introduces non-size-extensive contributions in the energy and molecular property expressions. However, since the linear parametrization describes the embedding of the CC parent state in the target excitation space, the energy and molecular properties for a CL state are weakly size-extensive. For the energy, weak size-extensivity means that non-size-extensive contributions enter in sixth and higher orders in the CP energy series, whereas for molecular properties, weak size-extensivity means that non-size-extensive contributions enter in second and higher orders. Weak size-extensivity therefore has a little or vanishing effect on calculated energies or molecular properties. The determination of the CP energy and molecular property corrections does not require that amplitude or response equations are solved explicitly for the target state and it becomes computationally tractable to use low-order corrections from these series to obtain energies and molecular properties of CL target state quality. For three simple molecules, HF, N 2 , and CH 2 , the accuracy of the CL approach for ground-state energies is tested using a parent state including single and double excitations (i.e., the CC singles-and-doubles state, CCSD) and a target state that includes triple excitations. It is found that the size-extensive fifth-order CL energies deviate by less than 0.0001 hartree from the energies of a target CC that includes triple excitations (i.e., the CC singles-doubles-and-triples state, CCSDT). CP theory with a CL target state therefore becomes a very attractive replacement of standard CC theory for high-accuracy energy and molecular property calculations, in which triple and higher excitation levels are considered.

We introduce a new class of perturbation models - the cluster perturbation (CP) models - where the major drawbacks of Møller-Plesset perturbation theory and coupled cluster perturbation theory have been eliminated. In CP theory, we consider a target excitation space relative to the Hartree-Fock state and partition the target excitation space into a parent and an auxiliary excitation space. The zeroth-order state is a coupled cluster (CC) state in the parent excitation space, and the target state is either a cluster linear or a CC state in the target excitation space. In CP theory, perturbation series are determined in orders of the CC parent state similarity-transformed fluctuation potential for the energy and for a molecular property, where the zeroth-order term in the series is the energy or a molecular property for the CC parent state and where the series formally converge to the energy or a molecular property for the target state. In CP theory, we use a generalized order concept, where the zeroth-order component of the extended parent-state Jacobian contains a fluctuation potential contribution, and use this new generalized order to treat internal relaxation in the parent excitation space at zeroth order and hence remove it from the perturbation calculation. Even more importantly, using this new generalized order concept, CP series can be determined for molecular properties of ground and excited states and for transition properties between these states, including excitation energies and energies of the excited states. The applicability of CP theory to both the energy and molecular properties and numerical results for the CP energy and molecular property series demonstrate the superiority of CP theory compared to previous perturbation models. Low-order corrections in the CP perturbation series can be expected soon to become state-of-the-art electronic structure models for the determination of energies and molecular properties of target-state quality for single-configuration dominated molecular systems.

The scope of this review article is to discuss the locality of occupied and virtual orthogonal Hartree-Fock orbitals generated by localization function optimization. Locality is discussed from the stand that an orbital is local if it is confined to a small region in space. Focusing on locality measures that reflects the spatial extent of the bulk of an orbital and the thickness of orbital tails, we discuss, with numerical illustrations, how the locality may be reported for individual orbitals as well as for sets of orbitals. Traditional and more recent orbital localization functions are reviewed, and the locality measures are used to compare the locality of the orbitals generated by the different localization functions, both for occupied and virtual orbitals. Numerical illustrations are given also for large molecular systems and for cases where diffuse functions are included in the atomic orbital basis. In addition, we have included a discussion on the physical and mathematical limitations on orbital locality.

In cluster perturbation (CP) theory, we consider a target excitation space relative to a Hartree-Fock state and partition the target excitation space into a parent excitation space and an auxiliary excitation space. The zeroth-order state is in CP theory a coupled cluster (CC) state in the parent excitation space, and the target state is a CC state in the target excitation space. In this paper, we derive CP series for excitation energies in orders of the CC parent-state similarity-transformed fluctuation potential where the zeroth-order term in the series is an excitation energy for the CC parent state response eigenvalue equation and where the series formally converge to an excitation energy for the CC target state response eigenvalue equation. We give explicit expressions for the lowest-order excitation energy corrections. We also report calculations for CP excitation energy series for various parent and target excitation spaces and examine how well the lower-order corrections can reproduce the total excitation energies. Considering the fast local convergence we have observed for the CP excitation energy series, it becomes computationally attractive to use low-order corrections in CP series to obtain excitation energies of CC target state quality. For the CPS(D-n) series, the first-order correction vanishes, the second-order correction becomes the CIS(D) model, and for the CPS(D-3) model, our calculations suggest that excitation energies of CCSD quality are obtained. The numerical results also suggest that a similar behavior can be seen for the low-order excitation energy corrections for CP series where the parent state contains more than a singles excitation space, e.g., for the CPSD(T) model. We therefore expect the low-order excitation energy corrections in CP series soon to become state-of-the-art models for determining excitation energies of CC target state quality.

The theoretical foundation has been developed for establishing whether cluster perturbation (CP) series for the energy, molecular properties, and excitation energies are convergent or divergent and for using a two-state model to describe the convergence rate and convergence patterns of the higher-order terms in the CP series. To establish whether the perturbation series are convergent or divergent, a fictitious system is introduced, for which the perturbation is multiplied by a complex scaling parameter z. The requirement for convergent perturbation series becomes that the energy or molecular property, including an excitation energy, for the fictitious system is an analytic, algebraic function of z that has no singularities when the norm |z| is smaller than one. Examples of CP series for the energy and molecular properties, including excitation energies, are also presented, and the two-state model is used for the interpretation of the convergence rate and the convergence patterns of the higher-order terms in these series. The calculations show that the perturbation series effectively become a two-state model at higher orders.

A simple two-state model has previously been shown to be able to describe and rationalize the convergence of the most common perturbation method for including electron correlation, the Møller-Plesset expansion. In particular, this simple model has been able to predict the convergence rate and the form of the higher-order corrections for typical Møller-Plesset expansions of the correlation energy. In this paper, the convergence of nondegenerate perturbation expansions in the two-state model is analyzed in detail for a general form of two-state perturbation expansion by examining the analytic expressions of the corrections and series of the values of the corrections for various choices of the perturbation. The previous analysis that covered only a single form of the perturbation is thereby generalized to arbitrary forms of the perturbation. It is shown that the convergence may be described in terms of four characteristics: archetype, rate of convergence, length of recurring period, and sign pattern. The archetype defines the overall form of a plot of the energy-corrections, and the remaining characteristics specify details of the archetype. For symmetric (Hermitian) perturbations, five archetypes are observed: zigzag, interspersed zigzag, triadic, ripples, and geometric. Two additional archetypes are obtained for an asymmetric perturbation: zigzag-geometric and convex-geometric. For symmetric perturbations, each archetype has a distinctive pattern that recurs with a period which depends on the perturbation parameters, whereas no such recurrence exists for asymmetric perturbations from a series of numerical corrections. The obtained relations between the form of a two-state perturbation and the energy corrections allow us to obtain additional insights into the convergence behavior of the Møller-Plesset and other forms of perturbation expansions. This is demonstrated by analyzing several diverging or slowly converging perturbation expansions of ground state and excitation energies. It is demonstrated that the higher-order corrections of these expansions can be described using the two-state model and each expansion can therefore be described in terms of an archetype and the other three characteristics. Examples of all archetypes except the zigzag and convex-geometric archetypes are given. For each example, it is shown how the characteristics may be extracted from the higher-order corrections and used to identify the term in the perturbation that is the cause of the observed slow convergence or divergence.

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, MOller-Plesset, confi ...

Recent advances in orbital localization algorithms are used to minimize the Pipek–Mezey localization function for both occupied and virtual Hartree–Fock orbitals. Virtual Pipek–Mezey orbitals for large molecular systems have previously not been considered in the literature. For this work, the Pipek–Mezey (PM) localization function is implemented for both the Mulliken and a Lowdin population analysis. The results show that the standard PM localization function (using either Mulliken or Lowdin population analyses) may yield local occupied orbitals, although for some systems the occupied orbitals are only semilocal as compared to state-of-the-art localized occupied orbitals. For the virtual orbitals, a Lowdin population analysis shows improvement in locality compared to a Mulliken population analysis, but for both Mulliken and Lowdin population analyses, the virtual orbitals are seen to be considerably less local compared to state-of-the-art localized orbitals. © 2013 Wiley Periodicals, Inc.

Using the three-level energy optimization procedure combined with a refined version of the least-change strategy for the orbitals--where an explicit localization is performed at the valence basis level--it is shown how to more efficiently determine a set of local Hartree-Fock orbitals. Further, a core-valence separation of the least-change occupied orbital space is introduced. Numerical results comparing valence basis localized orbitals and canonical molecular orbitals as starting guesses for the full basis localization are presented. The results show that the localization of the occupied orbitals may be performed at a small computational cost if valence basis localized orbitals are used as a starting guess. For the unoccupied space, about half the number of iterations are required if valence localized orbitals are used as a starting guess compared to a canonical set of unoccupied Hartree-Fock orbitals. Different local minima may be obtained when different starting guesses are used. However, the different minima all correspond to orbitals with approximately the same locality.

We present a scalable cross-platform hybrid MPI/OpenMP/OpenACC implementation of the Divide–Expand–Consolidate (DEC) formalism with portable performance on heterogeneous HPC architectures. The Divide–Expand–Consolidate formalism is designed to reduce the steep computational scaling of conventional many-body methods employed in electronic structure theory to linear scaling, while providing a simple mechanism for controlling the error introduced by this approximation. Our massively parallel implementation of this general scheme has three levels of parallelism, being a hybrid of the loosely coupled task-based parallelization approach and the conventional MPI +X programming model, where X is either OpenMP or OpenACC. We demonstrate strong and weak scalability of this implementation on heterogeneous HPC systems, namely on the GPU-based Cray XK7 Titan supercomputer at the Oak Ridge National Laboratory. Using the “resolution of the identity second-order Moller–Plesset perturbation theory” (RI-MP2) as the physical model for simulating correlated electron motion, the linear-scaling DEC implementation is applied to 1-aza-adamantane-trione (AAT) supramolecular wires containing up to 40 monomers (2440 atoms, 6800 correlated electrons, 24 440 basis functions and 91 280 auxiliary functions). This represents the largest molecular system treated at the MP2 level of theory, demonstrating an efficient removal of the scaling wall pertinent to conventional quantum many-body methods.

The theoretical foundation for solving coupled cluster singles and doubles (CCSD) amplitude equations to a desired precision in terms of independent fragment calculations using restricted local orbital spaces is reinvestigated with focus on the individual error sources. Four different error sources are identified theoretically and numerically and it is demonstrated that, for practical purposes, local orbital spaces for CCSD calculations can be identified from calculations at the MP2 level. The development establishes a solid theoretical foundation for local CCSD calculations for the independent fragments, and thus for divide–expand–consolidate coupled cluster calculations for large molecular systems with rigorous error control. Based on this theoretical foundation, we have developed an algorithm for determining the orbital spaces needed for obtaining the single fragment energies to a requested precision and numerically demonstrated the robustness and precision of this algorithm.

The accuracy at which total energies of open-shell atoms and organic radicals may be calculated is assessed for selected coupled cluster perturbative triples expansions, all of which augment the coupled cluster singles and doubles (CCSD) energy by a non-iterative correction for the effect of triple excitations. Namely, the second- through sixth-order models of the recently proposed CCSD(T-n) triples series [J. Chem. Phys. 140, 064108 (2014)] are compared to the acclaimed CCSD(T) model for both unrestricted as well as restricted open-shell Hartree-Fock (UHF/ROHF) reference determinants. By comparing UHF- and ROHF-based statistical results for a test set of 18 modest-sized open-shell species with comparable RHF-based results, no behavioral differences are observed for the higher-order models of the CCSD(T-n) series in their correlated descriptions of closed- and open-shell species. In particular, we find that the convergence rate throughout the series towards the coupled cluster singles, doubles, and triples (CCSDT) solution is identical for the two cases. For the CCSD(T) model, on the other hand, not only its numerical consistency, but also its established, yet fortuitous cancellation of errors breaks down in the transition from closed- to open-shell systems. The higher-order CCSD(T-n) models (orders n>3) thus offer a consistent and significant improvement in accuracy relative to CCSDT over the CCSD(T) model, equally for RHF, UHF, and ROHF reference determinants, albeit at an increased computational cost., 22 pages, 5 figures, 1 table, 1 supporting information (attached as an ancillary file)

We consider two distinct coupled cluster (CC) perturbation series that both expand the difference between the energies of the CCSD (CC with single and double excitations) and CCSDT (CC with single, double, and triple excitations) models in orders of the M{\o}ller-Plesset fluctuation potential. We initially introduce the E-CCSD(T-$n$) series, in which the CCSD amplitude equations are satisfied at the expansion point, and compare it to the recently developed CCSD(T-$n$) series [J. Chem. Phys. 140, 064108 (2014)], in which not only the CCSD amplitude, but also the CCSD multiplier equations are satisfied at the expansion point. The computational scaling is similar for the two series, and both are term-wise size extensive with a formal convergence towards the CCSDT target energy. However, the two series are different, and the CCSD(T-$n$) series is found to exhibit a more rapid convergence up through the series, which we trace back to the fact that more information at the expansion point is utilized than for the E-CCSD(T-$n$) series. The present analysis can be generalized to any perturbation expansion representing the difference between a parent CC model and a higher-level target CC model. In general, we demonstrate that, whenever the parent parameters depend upon the perturbation operator, a perturbation expansion of the CC energy (where only parent amplitudes are used) differs from a perturbation expansion of the CC Lagrangian (where both parent amplitudes and parent multipliers are used). For the latter case, the bivariational Lagrangian formulation becomes more than a convenient mathematical tool, since it facilitates a different and faster convergent perturbation series than the simpler energy-based expansion., Comment: 26 pages, 1 figure, 1 supporting information (attached as an ancillary file)

Review of ab initio wave-function based approaches for calculation of molecular (response) properties

We present a Lagrangian approach for the calculation of molecular (quadratic) response properties that can be expressed as geometric gradients of a generic linear response function, its poles, and its residues. The approach is implemented within an atomic-orbital-based formalism suitable for linear scaling at the level of self-consistent time-dependent Hartree−Fock and density functional theory. Among the properties that can be obtained using this formalism are the gradient of the frequency-dependent polarizability (e.g., Raman intensities) and that of the one-photon transition dipole moment (entering the Herzberg−Teller factors), in addition to the excited-state molecular forces required for excited-state geometry optimizations. Geometric derivatives of ground-state first-order properties (e.g., IR intensities) and excited-state first-order property expressions are also reported as byproducts of our implementation. The one-photon transition moment gradient is the first analytic implementation of the one-photon transition moment derivative at the DFT level of theory. Besides offering a simple solution to overcome phase (hence, sign) uncertainties connected to the determination of the Herzberg−Teller corrections by numerical derivatives techniques based on independent calculations, our approach also opens the possibility to determine, for example by a mixed analytic−numerical approach, the one-photon transition dipole Hessian, and thus to investigate vibronic effects beyond the linear Herzberg−Teller approximation. As an illustrative application, we report a DFT study of the vibronic fine structure of the one-photon (1A1g) − (1B2u) transition in the absorption spectrum of benzene, which is Franck−Condon-forbidden in the electric dipole approximation and hence determined by the Herzberg−Teller integrals and electronic transition dipole-moment derivatives.

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. © 2009 Wiley-Liss, Inc.

Brugada syndrome (BrS) is a condition characterized by a distinct ST-segment elevation in the right precordial leads of the electrocardiogram and, clinically, by an increased risk of cardiac arrhythmia and sudden death. The condition predominantly exhibits an autosomal dominant pattern of inheritance with an average prevalence of 5:10,000 worldwide. Currently, more than 100 mutations in seven genes have been associated with BrS. Loss-of-function mutations in SCN5A, which encodes the α-subunit of the Nav1.5 sodium ion channel conducting the depolarizing INa current, causes 15–20% of BrS cases. A few mutations have been described in GPD1L, which encodes glycerol-3-phosphate dehydrogenase-1 like protein; CACNA1C, which encodes the α-subunit of the Cav1.2 ion channel conducting the depolarizing IL,Ca current; CACNB2, which encodes the stimulating β2-subunit of the Cav1.2 ion channel; SCN1B and SCN3B, which, in the heart, encodes β-subunits of the Nav1.5 sodium ion channel, and KCNE3, which encodes the ancillary inhibitory β-subunit of several potassium channels including the Kv4.3 ion channel conducting the repolarizing potassium Ito current. BrS exhibits variable expressivity, reduced penetrance, and “mixed phenotypes,” where families contain members with BrS as well as long QT syndrome, atrial fibrillation, short QT syndrome, conduction disease, or structural heart disease, have also been described. Hum Mutat 30:1–11, 2009. © 2009 Wiley-Liss, Inc.

A Lagrangian approach has been used to derive gauge-origin independent expressions for two properties that rationalize magneto-optical activity, namely the Verdet constant V(ω) of the Faraday effect and the ℬ term of magnetic circular dichroism. The approach is expressed in terms of an atomic-orbital density-matrix based formulation of response theory and use London atomic orbitals to parametrize the magnetic field dependence. It yields a computational procedure which is both gauge-origin independent and suitable for linear-scaling at the level of time-dependent Hartree-Fock and density functional theory. The formulation includes a modified preconditioned conjugated gradient algorithm, which projects out the excited state component from the solution to the linear response equation. This is required when solving one of the response equations for the determination of the ℬ term and divergence is encountered if this component is not projected out. Illustrative results are reported for the Verdet constant of H2, HF, CO, N2O, and CH3CH2CH3 and for the ℬ term of pyrimidine, phosphabenzene, and pyridine. The results are benchmarked against gauge-origin independent CCSD values.

The presenilin-1 (PS-1)/S 182 gene at chromosome 14q24.3 is, when mutated, the most common disease gene in autosomal dominant early-onset Alzheimer's disease. Substitution of methionine 146 of the gene product for either valine or leucine co-segregates with Alzheimer's disease with the age of onset in the late thirties or early forties. Here we describe a new substitution of methionine 146 for isoleucine that co-segregates with Alzheimer's disease with age of the onset in the early forties. All identified missense mutations in methionine codon 146 replace one hydrophobic amino acid (Met) with another (Val, Leu, Ile) and correspond to any nucleotide change at the first or third position of the codon. Second position mutations invariably lead to replacement of the hydrophobic methionine with a hydrophilic amino acid that may severely affect the function of the protein. The fact that no second position mutations have been identified so far may support the hypothesis that the protein product of PS-1 plays a crucial role during development.

Molecular response properties for ground and excited states and for transitions between these states are defined by solving the time-dependent Schrödinger equation for a molecular system in a field of a time-periodic perturbation. In equation of motion coupled cluster (EOM-CC) theory, molecular response properties are commonly obtained by replacing, in configuration interaction (CI) molecular response property expressions, the energies and eigenstates of the CI eigenvalue equation with the energies and eigenstates of the EOM-CC eigenvalue equation. We show here that EOM-CC molecular response properties are identical to the molecular response properties that are obtained in the coupled cluster–configuration interaction (CC-CI) model, where the time-dependent Schrödinger equation is solved using an exponential (coupled cluster) parametrization to describe the unperturbed system and a linear (configuration interaction) parametrization to describe the time evolution of the unperturbed system. The equivalence between EOM-CC and CC-CI molecular response properties only holds when the CI molecular response property expressions—from which the EOM-CC expressions are derived—are determined using projection and not using the variational principle. In a previous article [F. Pawłowski, J. Olsen, and P. Jørgensen, J. Chem. Phys. 142, 114109 (2015)], it was stated that the equivalence between EOM-CC and CC-CI molecular response properties only held for a linear response function, whereas quadratic and higher order response functions were mistakenly said to differ in the two approaches. Proving the general equivalence between EOM-CC and CC-CI molecular response properties is a challenging task, that is undertaken in this article. Proving this equivalence not only corrects the previous incorrect statement but also first and foremost leads to a new, time-dependent, perspective for understanding the basic assumptions on which the EOM-CC molecular response property expressions are founded. Further, the equivalence between EOM-CC and CC-CI molecular response properties highlights how static molecular response properties can be obtained from finite-field EOM-CC energy calculations.

We compare the numerical performance of various non-iterative coupled cluster (CC) quadruples models. The results collectively show how approaches that attempt to correct the CC singles and doubles energy for the combined effect of triple and quadruple excitations all fail at recovering the correlation energy of the full CC singles, doubles, triples, and quadruples (CCSDTQ) model to within sufficient accuracy. Such a level of accuracy is only achieved by models that make corrections to the full CC singles, doubles, and triples (CCSDT) energy for the isolated effect of quadruple excitations of which the CCSDT(Q–3) and CCSDT(Q–4) models of the Lagrangian-based CCSDT(Q–n) perturbation series are found to outperform alternative models that add either of the established [Q] and (Q) corrections to the CCSDT energy.

We propose the Same Number Of Optimized Parameters (SNOOP) scheme as an alternative to the counterpoise method for treating basis set superposition errors in calculations of intermolecular interaction energies. The key point of the SNOOP scheme is to enforce that the number of optimized wave function parameters for the noninteracting system is the same as for the interacting system. This ensures a delicate balance between the quality of the monomer and dimer finite basis set calculations. We compare the SNOOP scheme to the uncorrected and counterpoise schemes theoretically as well as numerically. Numerical results for second-order Møller-Plesset perturbation theory (MP2) and coupled-cluster with single, double, and approximate triple excitations (CCSD(T)) show that the SNOOP scheme in general outperforms the uncorrected and counterpoise approaches. Furthermore, we show that SNOOP interaction energies calculated using a given basis set are of similar quality as those determined by basis set extrapolation of counterpoise-corrected results obtained at a similar computational cost.

The benzene–Ar lowest energy triplet state T1 intermolecular potential energy surface is evaluated using coupled cluster methods and the aug-cc-pVDZ basis set extended with a set of 3s3p2d1f1g midbond functions. This surface is characterized by an absolute minimum of −392.5 cm−1, where the argon atom is located on the benzene C6 axis at a distance of 3.5153 A, and has a general shape very close to the ground state S0 and the first singlet S1 excited state surfaces. Using the T1 potential, the intermolecular vibrational energy levels were evaluated and the results compared to those for the ground S0 and the excited S1 states. The calculated fundamental frequencies for the bending and the stretching modes are lower than those in the S1 state. The calculated data for the T1 state is expected to have the same accuracy as previously calculated data for the S1 state.

Recently, we proposed a novel Lagrangian-based perturbation series-the CCSD(T-n) series-which systematically corrects the coupled cluster singles and doubles (CCSD) energy in orders of the Møller-Plesset fluctuation potential for effects due to triple excitations. In the present study, we report numerical results for the CCSD(T-n) series up through fourth order which show the predicted convergence trend throughout the series towards the energy of its target, the coupled cluster singles, doubles, and triples (CCSDT) model. Since effects due to the relaxation of the CCSD singles and doubles amplitudes enter the CCSD(T-n) series at fourth order (the CCSD(T-4) model), we are able to separate these effects from the total energy correction and thereby emphasize their crucial importance. Furthermore, we illustrate how the ΛCCSD[T]/(T) and CCSD[T]/(T) models, which in slightly different manners augment the CCSD energy by the [T] and (T) corrections rationalized from many-body perturbation theory, may be viewed as approximations to the second-order CCSD(T-2) model. From numerical comparisons with the CCSD(T-n) models, we show that the extraordinary performance of the ΛCCSD[T]/(T) and CCSD[T]/(T) models relies on fortuitous, yet rather consistent, cancellations of errors. As a side product of our investigations, we are led to reconsider the asymmetric ΛCCSD[T] model due to both its rigorous theoretical foundation and its performance, which is shown to be similar to that of the CCSD(T) model for systems at equilibrium geometry and superior to it for distorted systems. In both the calculations at equilibrium and distorted geometries, however, the ΛCCSD[T] and CCSD(T) models are shown to be outperformed by the fourth-order CCSD(T-4) model.

Udgivelsesdato: 2002-Aug-16 We describe a new human isoform, GFAP epsilon, of the intermediary filament protein GFAP (glial fibrillary acidic protein). GFAP epsilon mRNA is the result of alternative splicing and a new polyadenylation signal, and thus GFAP epsilon has a new C-terminal protein sequence. This provides GFAP epsilon with the capacity for specific binding of presenilin proteins in yeast and in vitro. Our observations suggest a direct link between the presenilins and the cytoskeleton where GFAP epsilon is incorporated. Mutations in GFAP and presenilins are associated with Alexander disease and Alzheimer's disease, respectively. Accordingly, GFAP epsilon should be taken into consideration when studying neurodegenerative diseases.

The equation-of-motion coupled cluster (EOM-CC) framework has been used for deriving a novel series of perturbative corrections to the coupled cluster singles and doubles energy that formally con- verges towards the full configuration interaction energy limit. The series is based on a Møller-Plesset partitioning of the Hamiltonian and thus size extensive at any order in the perturbation, thereby rem- edying the major deficiency inherent to previous perturbation series based on the EOM-CC ansatz. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4873138]

Using the coupled cluster Lagrangian technique, we have determined perturbative corrections to the coupled cluster singles and doubles (CCSD) energy that converge towards the coupled cluster singles, doubles, and triples (CCSDT) and coupled cluster singles, doubles, triples, and quadruples (CCSDTQ) energies, considering the CCSD state as the unperturbed reference state and the fluctua- tion potential as the perturbation. Since the Lagrangian technique is utilized, the energy corrections satisfy Wigner’s 2n + 1 rule for the cluster amplitudes and the 2n + 2 rule for the Lagrange multi- pliers. The energy corrections define the CCSD perturbation series, CCSD(T–n) and CCSD(TQ–n), which are term-wise size extensive to any order in the perturbation. A detailed comparison of the CCSD(TQ–n) series and the CC(2)PT(n) series of Hirata et al. [J. Chem. Phys. 114, 3919 (2001)] has been performed, revealing some deficiencies of the latter related to the target energy of the series and its lack of size extensivity. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4862501]

The activator of stromelysin 1 gene transcription, SPBP, interacts with the RING finger protein RNF4. Both proteins are ubiquitously expressed and localized in the nucleus. RNF4 facilitates accumulation of specific SPBP-DNA complexes in vitro and acts as a positive cofactor in SPBP-mediated transactivation. SPBP harbors an internal zinc finger of the PHD/LAP type. This domain can form intra-chain protein-protein contacts in SPBP resulting in negative modulation of SPBP-RNF4 interaction.

We have developed a multiplex reverse transcription-polymerase chain reaction (RT-PCR) reaction, which enables us to detect 29 translocations/chromosomal aberrations in patients with acute lymphoid leukemia (ALL) and acute myeloid leukemia (AML). Through the construction and optimization of specific primers for each translocation, we have been able to reduce the set-up to 8 parallel multiplex PCR reactions, thus greatly decreasing the amount of work and reagents. We show the value of our set-up in a retrospective analysis on cryopreserved material from 102 AML and 62 ALL patients. The multiplex RT-PCR detected a hybrid mRNA resulting from a structural chromosomal aberration in 45 of 102 (44%) of the AML and in 28 of 62 (45%) of the pediatric ALL cases. Importantly, in 33% of AML and in 47% of the ALL cases with cytogenetic data, submicroscopic chromosomal aberrations or masked translocations were shown that were not detected in the cytogenetic analysis either for structural reasons or because of an insufficient number of metaphases obtained. This multiplex RT-PCR system, which can handle up to 10 patients with a response time of 2 working days, is thus an important tool that complements cytogenetic analysis in the up-front screening of acute leukemia patients and should provide a rapid and efficient characterization of leukemia cells, even in situations with sparse patient material.

Orbital localization of occupied and virtual Hartree-Fock orbitals generated from basis sets augmented with diffuse functions is performed using the Pipek-Mezey, Boys, powers of the second central moment, and powers of the fourth central moment localizations. The locality of the obtained orbital sets are presented in terms of second and fourth moment orbital spreads. The results show that both local occupied and virtual orbitals may be obtained when using powers of the second central moment and powers of the fourth central moment localizations, while the Pipek-Mezey and Boys localizations fail to produce sets of local virtual orbitals. The locality of the fourth central moment virtual orbitals exhibits a locality similar to the locality of a Boys localization for non-augmented basis sets.

Using a valence double-zeta polarization basis, full configuration-interaction (FCI) calculations are carried out on water at its equilibrium geometry and at geometries where the OH bond lengths are stretched until dissociation. At the same geometries and with the same basis set configuration interaction calculations at excitation levels up to hextuples, multireference singles doubles configuration interaction calculations, coupled cluster calculations at excitation levels up to quadruples, Møller-Plesset perturbation theory calculations through order fifteen, and complete active space second-order perturbation theory calculations are also carried out. The static correlation contribution increase with increasing bond length. The calculations show that the coupled cluster approach has a remarkable ability to describe even relatively large static correlation contributions. The single reference perturbation expansion breaks down for larger OH bond length, while the multireference approach preserves the accuracy for the whole potential curve. At the equilibrium geometry, FCI calculations have also been carried out for the lowest state of2A1,2B1, and2B2symmetry of H2O+, and the results compared with state of the art correlation results for total energies and ionization potentials (IP's). Differential energies (IP's) are obtained more accurately than absolute (total) energies in the size extensive coupled cluster and perturbation approaches. For the nonsize extensive configuration interaction method errors are obtained of the same size for differential and absolute energies. © 1996 American Institute of Physics.

Transduction of primer binding site-impaired Akv murine leukemia virus-based retroviral vectors from the murine packaging cell lines psi-2 and omega E was studied. The efficiency of transduction of the neo marker of all mutated constructs was found to decrease by 5 to 6 orders of magnitude compared with that of the wild-type vector. Thirty-two of 60 transduced proviruses analyzed harbored a primer binding site sequence matching a glutamine tRNA primer. Sequence analysis of the regions flanking the glutamine tRNA primer binding site revealed a distinct pattern of nucleotide differences from the Akv-based vector, suggesting the involvement of a specific endogenous virus-like sequence in patch repair rescue of the primer binding site mutants. The putative recombination partner RNA was found in virions from psi-2 cells as detected by analysis of glutamine tRNA-initiated cDNA and by sequence analysis of regions at or around the glutamine tRNA primer binding site. We propose that the forced recombination of primer binding site mutants involves initial priming on endogenous viral sequences and requires template switching during minus-strand synthesis in the region between the neo gene and the mutated primer binding site to allow correct second-strand transfer in reverse transcription. The system thereby selects for a reverse transcriptase-mediated recombination event in the 5' untranslated region. A panel of sequence differences between the recombination partners in this region has allowed mapping of the site of recombination for each transduction event. Interestingly, the majority of the recombination events were clustered within a narrow, 33-nucleotide region though to be involved in genomic RNA dimerization.

For large molecular systems conventional implementations of second order Moller–Plesset (MP2) theory encounter a scaling wall, both memory- and time-wise. We describe how this scaling wall can be removed. We present a massively parallel algorithm for calculating MP2 energies and densities using the divide–expand–consolidate scheme where a calculation on a large system is divided into many small fragment calculations employing local orbital spaces. The resulting algorithm is linear-scaling with system size, exhibits near perfect parallel scalability, removes memory bottlenecks and does not involve any I/O. The algorithm employs three levels of parallelisation combined via a dynamic job distribution scheme. Results on two molecular systems containing 528 and 1056 atoms (4278 and 8556 basis functions) using 47,120 and 94,240 cores are presented. The results demonstrate the scalability of the algorithm both with respect to the number of cores and with respect to system size. The presented algorithm is thus hi...

We extend our assessment of the potential of perturbative coupled cluster (CC) expansions for a test set of open-shell atoms and organic radicals to the description of quadruple excitations. Namely, the second- through sixth-order models of the recently proposed CCSDT(Q-n) quadruples series [J. Chem. Phys. 140, 064108 (2014)] are compared to the prominent CCSDT(Q) and lambda-CCSDT(Q) models. From a comparison of the models in terms of their recovery of total CC singles, doubles, triples, and quadruples (CCSDTQ) energies, we find that the performance of the CCSDT(Q-n) models is independent of the reference used (unrestricted or restricted (open-shell) Hartree-Fock), in contrast to the CCSDT(Q) and lambda-CCSDT(Q) models, for which the accuracy is strongly dependent on the spin of the molecular ground state. By further comparing the ability of the models to recover relative CCSDTQ atomization energies, the discrepancy between them is found to be even more pronounced, stressing how a balanced description of both closed- and open-shell species - as found in the CCSDT(Q-n) models - is indeed of paramount importance if any perturbative CC model is to be of chemical relevance for high-accuracy applications. In particular, the third-order CCSDT(Q-3) model is found to offer an encouraging alternative to the existing choices of quadruples models used in modern computational thermochemistry, since the model is still only of moderate cost, albeit markedly more costly than, e.g., the CCSDT(Q) and lambda-CCSDT(Q) models., 18 pages, 3 figures, 1 supporting information (attached as an ancillary file)

Previously, we have introduced the linear scaling coupled cluster (CC) divide-expand-consolidate (DEC) method, using an occupied space partitioning of the standard correlation energy. In this article, we show that the correlation energy may alternatively be expressed using a virtual space partitioning, and that the Lagrangian correlation energy may be partitioned using elements from both the occupied and virtual partitioning schemes. The partitionings of the correlation energy leads to atomic site and pair interaction energies which are term-wise invariant with respect to an orthogonal transformation among the occupied or the virtual orbitals. Evaluating the atomic site and pair interaction energies using local orbitals leads to a linear scaling algorithm and a distinction between Coulomb hole and dispersion energy contributions to the correlation energy. Further, a detailed error analysis is performed illustrating the error control imposed on all components of the energy by the chosen energy threshold. This error control is ultimately used to show how to reduce the computational cost for evaluating dispersion energy contributions in DEC.

The trust region method has been applied to the minimization of localization functions, and it is shown that both local occupied and local virtual Hartree-Fock (HF) orbitals can be obtained. Because step sizes are size extensive in the trust region method, large steps may be required when the method is applied to large molecular systems. For an exponential parametrization of the localization function only small steps are allowed, and the standard trust radius update therefore has been replaced by a scheme where the direction of the step is determined using a conservative estimate of the trust radius and the length of the step is determined from a line search along the obtained direction. Numerical results for large molecular systems have shown that large steps can then safely be taken, and a robust and nearly monotonic convergence is obtained.

We present a new orbital localization function based on the sum of the fourth central moments of the orbitals. To improve the locality, we impose a power on the fourth central moment to act as a penalty on the least local orbitals. With power two, the occupied and virtual Hartree-Fock orbitals exhibit a more rapid tail decay than orbitals from other localization schemes, making them suitable for use in local correlation methods. We propose that the standard orbital spread (the square root of the second central moment) and fourth moment orbital spread (the fourth root of the fourth central moment) are used as complementary measures to characterize the locality of an orbital, irrespective of localization scheme.

Divide-Expand-Consolidate (DEC) is a local correlation method where the inherent locality of the electron correlation problem is used to express the correlated calculation on a large molecular system in terms of small independent fragment calculations employing small subsets of local HF orbitals. A crucial feature of the DEC scheme is that the sizes of the local orbital spaces are determined in a black box manner during the calculation. In this way it is ensured that the correlation energy has been determined to a predefined precision compared to a conventional calculation. In the present work we apply the DEC scheme to calculate the correlation energy as well as the electron density matrix for the insulin molecule using second order Moller–Plesset (MP2) theory. This is the first DEC calculation on a molecular system which is too large to be treated using a conventional MP2 implementation. The fragmentation errors for the insulin DEC calculation are carefully analyzed using internal consistency checks. It is demonstrated that size-intensive properties are determined to the same precision for small and large molecules. For example, the percentage of correlation energy recovered and the error per electron in the correlated density matrix depend only on the predefined precision and not on the molecular size.

Udgivelsesdato: 1994-Sep Integrated retroviruses or retroviral vectors may be transcriptionally inactive although their promoter-enhancer regions are able to direct transcription in the host cell. We have used single-gene retroviral vectors with a long terminal repeat-directed neo marker gene to determine if the level of transcription relates to the susceptibility of a provirus to inactivation. We used two isogenic vectors, carrying long terminal repeats with a strong and a weak transcriptional enhancer derived from SL3-3 and Akv murine leukemia viruses, respectively. Nonselected cell clones of the murine lymphoid cell line L691 with single integrated vector proviruses exhibiting a 20-fold range of initial expression levels were studied. The basal expression level of a given cell clone with a single provirus did not show any pattern of correlation with the long-term stability of expression, as monitored for periods up to 150 days. Our results thus indicate that the inactivation mechanism operates independently of the initial transcriptional activity of the provirus.

It is demonstrated that a set of local orthonormal Hartree-Fock (HF) molecular orbitals can be obtained for both the occupied and virtual orbital spaces by minimizing powers of the orbital variance using the trust-region algorithm. For a power exponent equal to one, the Boys localization function is obtained. For increasing power exponents, the penalty for delocalized orbitals is increased and smaller maximum orbital spreads are encountered. Calculations on superbenzene, C(60), and a fragment of the titin protein show that for a power exponent equal to one, delocalized outlier orbitals may be encountered. These disappear when the exponent is larger than one. For a small penalty, the occupied orbitals are more local than the virtual ones. When the penalty is increased, the locality of the occupied and virtual orbitals becomes similar. In fact, when increasing the cardinal number for Dunning's correlation consistent basis sets, it is seen that for larger penalties, the virtual orbitals become more local than the occupied ones. We also show that the local virtual HF orbitals are significantly more local than the redundant projected atomic orbitals, which often have been used to span the virtual orbital space in local correlated wave function calculations. Our local molecular orbitals thus appear to be a good candidate for local correlation methods.

The atomic axial tensor (AAT) of vibrational circular dichroism is expressed as the frequency derivative at zero frequency of a linear response function for operators referencing a nuclear displacement and a magnetic field. This is used in the density matrix-based quasienergy derivative Lagrangian approach of Thorvaldsen et al. [J. Chem. Phys., 2008, 129, 214108] to express the AAT in a form where the need to solve response equations for the nuclear displacements is removed, significantly reducing the computation cost compared to existing formulations. The density matrix-based quasienergy derivative Lagrangian approach also allows us straightforwardly to use London atomic orbitals to remove the gauge-origin dependence and to account for the atomic orbitals' dependence on the nuclear coordinates. The formalism is entirely based on atomic-orbital density and integral matrices and therefore amenable to linear scaling for sufficiently sparse matrices and given a linearly scaling response solver.

We apply damped response theory to the phenomenon of magnetic circular dichroism (MCD), and we investigate how the numerical instability associated with the simulation of the MCD spectrum from individually calculated A and B terms for close lying states can be remedied by the use of damped response theory. We also present a method for calculating the Faraday A term, formulated as a double residue of the quadratic response function.

Udgivelsesdato: 1993-Dec Two Akv murine leukemia virus-based retroviral vectors with primer binding sites matching tRNA(Gln-1) and tRNA(Lys-3) were constructed. The transduction efficiency of these mutated vectors was found to be comparable to that of a vector carrying the wild-type primer binding site matching tRNA(Pro). Polymerase chain reaction amplification and sequence analysis of transduced proviruses confirmed the transfer of vectors with mutated primer binding sites and further showed that tRNA(Gln-2) may act efficiently in conjunction with the tRNA(Gln-1) primer binding site. We conclude that murine leukemia virus can replicate by using various tRNA molecules as primers and propose primer binding site-tRNA primer interactions to be of major importance for tRNA primer selection. However, efficient primer selection does not require perfect Watson-Crick base pairing at all 18 positions of the primer binding site.

Udgivelsesdato: 1993-Oct-11 Identical transcription units inserted at different positions of mammalian chromosomes may vary widely in transcriptional activity. We have used a set of ten cell clones with random unselected single integrations of retroviral vectors to study such position effects. The vector used carries a neo gene driven by the Akv murine leukemia virus long terminal repeat that has only a weak promoter-enhancer activity in the target cell, the lymphoid cell line L691. Under transient expression conditions, the strength of the Akv promoter-enhancer in the L691 cells is increased by dexamethasone. In cell clones with single vector integrations, a correlation is observed between the non-induced expression levels and the degree of dexamethasone induction. The strongest relative induction is found for the integrated vectors with the lowest non-induced expression levels and approaches the inducibility under transient expression. These results indicate that expression levels are composed of distinct contributions from the integrated vector and from the site of integration and are best explained in terms of a model in which the sites of chromosomal integration exert variable positive enhancer effects upon vector transcription.

Udgivelsesdato: 1992-Aug The enhancer region of Akv murine leukemia virus contains the sequence motif ACAGATGG. This sequence is homologous to the E-box motif originally defined as a regulatory element in the enhancers of immunoglobulin mu and kappa genes. We have used double-stranded oligonucleotide probes, corresponding to the E box of the murine leukemia virus Akv, to screen a randomly primed lambda gt11 cDNA expression library made from mouse NIH 3T3 fibroblast RNA. We have identified seven lambda clones expressing DNA-binding proteins representing two different genes termed ALF1 and ALF2. The results of sequencing ALF2 cDNA suggests that we have recovered the gene for the basic-helix-loop-helix transcription factor A1, the murine analog of the human transcription factor E47. The cDNA sequence of ALF1 codes for a new member of the basic-helix-loop-helix protein family. Two splice variants of ALF1 cDNA have been found, differing by a 72-bp insertion, coding for putative proteins of 682 and 706 amino acids. The two ALF1 mRNAs are expressed at various levels in mouse tissues. In vitro DNA binding assays, using prokaryotically expressed ALF1 proteins, demonstrated specific binding of the ALF1 proteins to the Akv murine leukemia virus E-box motif ACAGATGG. Expression in NIH 3T3 fibroblasts of GAL4-ALF1 chimeric protein stimulated expression from a minimal promoter linked to a GAL4 binding site, indicating the existence of a transcriptional activator domain in ALF1.

We present a theory for the analytic calculation of frequency-dependent polarizability gradients, and apply the methodology to the calculation of coherent anti-Stokes Raman scattering (CARS). The formalism used is based on an open-ended theory for the calculation of frequency-dependent molecular response properties of arbitrary order, also including contributions from perturbation-dependent basis sets. An important feature of our approach is the close connection between the formalism--which is fully matrix-based in an atomic orbital basis--and the implementation, allowing for the rapid implementation of higher-order molecular properties. Care is taken to allow the formalism to be utilized with linearly-scaling Hartree-Fock and density-functional theory codes. By avoiding the evaluation of responses due to geometry distortions, only 9 response equations need to be solved for the calculation of the CARS intensities, independent of the size of the molecular system. The theory is illustrated by calculations on a set of polyaromatic hydrocarbons using a DFT/B3LYP force field and Hartree-Fock polarizability gradients. Good agreement with the experimental CARS spectra of these compounds is obtained.

A general method is presented for the calculation of molecular properties to arbitrary order at the Kohn-Sham density functional level of theory. The quasienergy and Lagrangian formalisms are combined to derive response functions and their residues by straightforward differentiation of the quasienergy derivative Lagrangian using the elements of the density matrix in the atomic orbital representation as variational parameters. Response functions and response equations are expressed in the atomic orbital basis, allowing recent advances in the field of linear-scaling methodology to be used. Time-dependent and static perturbations are treated on an equal footing, and atomic basis sets that depend on the applied frequency-dependent perturbations may be used, e.g., frequency-dependent London atomic orbitals. The 2n+1 rule may be applied if computationally favorable, but alternative formulations using higher-order perturbed density matrices are also derived. These may be advantageous in order to minimize the number of response equations that needs to be solved, for instance, when one of the perturbations has many components, as is the case for the first-order geometrical derivative of the hyperpolarizability.