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The convergence of the recently developed cluster perturbation (CP) expansions [Pawlowski et al., J. Chem. Phys. 150, 134108 (2019)] is analyzed with the double purpose of developing the mathematical tools and concepts needed to describe these expansions at general order and to identify the factors that define the rate of convergence of CP series. To this end, the CP energy, amplitude, and Lagrangian multiplier equations as a function of the perturbation strength are developed. By determining the critical points, defined as the perturbation strengths for which the Jacobian becomes singular, the rate of convergence and the intruder and critical states are determined for five small molecules: BH, CO, H2O, NH3, and HF. To describe the patterns of convergence for these expansions at orders lower than the high-order asymptotic limit, a model is developed where the perturbation corrections arise from two critical points. It is shown that this model allows for rationalization of the behavior of the perturbation corrections at much lower order than required for the onset of the asymptotic convergence. For the H2O, CO, and HF molecules, the pattern and rate of convergence are defined by critical states where the Fock-operator underestimates the excitation energies, whereas the pattern and rate of convergence for BH are defined by critical states where the Fock-operator overestimates the excitation energy. For the NH3 molecule, both forms of critical points are required to describe the convergence behavior up to at least order 25.

We have extended cluster perturbation (CP) theory to comprehend the calculation of first order properties (FOPs). We have determined CP FOP series where FOPs are determined as a first energy derivative and also where the FOPs are determined as a generalized expectation value of the external perturbation operator over the coupled cluster state and its biorthonormal multiplier state. For S(D) orbital excitation spaces, we find that the CP series for FOPs that are determined as a first derivative, in general, in second order have errors of a few percent in the singles and doubles correlation contribution relative to the targeted coupled cluster (CC) results. For a SD(T) orbital excitation space, we find that the CP series for FOPs determined as a generalized expectation value in second order have errors of about ten percent in the triples correlation contribution relative to the targeted CC results. These second order models, therefore, constitute viable alternatives for determining high quality FOPs.

We present here a massively parallel implementation of the recently developed CPS(D-3) excitation energy model that is based on cluster perturbation theory. The new algorithm extends the one developed in Baudin et al. [J. Chem. Phys., 150, 134110 (2019)] to leverage multiple nodes and utilize graphical processing units for the acceleration of heavy tensor contractions. Furthermore, we show that the extended algorithm scales efficiently with increasing amounts of computational resources and that the developed code enables CPS(D-3) excitation energy calculations on large molecular systems with a low time-to-solution. More specifically, calculations on systems with over 100 atoms and 1000 basis functions are possible in a few hours of wall clock time. This establishes CPS(D-3) excitation energies as a computationally efficient alternative to those obtained from the coupled-cluster singles and doubles model.

We have extended cluster perturbation (CP) theory to comprehend the Lagrangian framework of coupled cluster (CC) theory and derived the CP Lagrangian energy series ( L CP) where the 2 n + 1/2 n + 2 rules for the cluster amplitudes and multipliers are used to get the energy corrections. We have also developed the variational CP [Formula: see text] series, where the total cluster amplitudes and multipliers are determined through the same orders as in the L CP series, but the energy is obtained by inserting the total cluster amplitudes and multipliers in the Lagrangian. The energies of the [Formula: see text] series have errors that are bilinear in the errors of the total cluster amplitudes and multipliers. Test calculations have been performed for S(D) and SD(T) orbital excitation spaces. With the exception of molecular systems that have a low lying doubly excited state compared to the electronic ground state configuration, we find that the fourth order models [Formula: see text]( D−4), [Formula: see text]( T−4), and L CPSD( T−4) give energies of CC target state quality. For the [Formula: see text]( D−4) model, CC target state quality is obtained as the [Formula: see text]( D−4) calculation determines more than 99.7% of the coupled cluster singles and doubles (CCSD) correlation energy as the numerical deviations of the [Formula: see text]( D−4) energy from the CCSD energy were more than an order of magnitude smaller than the triples correlation contribution. For the [Formula: see text]( T−4) and L CPSD( T−4) models, CC target state quality was obtained, given that the [Formula: see text]( T−4) and L CPSD( T−4) calculations recover more than 99% of the coupled cluster singles doubles and triples (CCSDT) correlation contribution and as the numerical deviations of the [Formula: see text]( T−4) and L CPSD( T−4) energies from the CCSDT energy were nearly and order of magnitude smaller than the quadruples correlation contribution. We, thus, suggest that the fourth order models may replace the full target CC models with no or very limited loss of accuracy.

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.

When a set of orthogonal orbitals is localised using orthogonal transformations, the orbital metric is conserved as the unit matrix during the localisation. In this paper we describe how non-orthogonal orbitals may be localised by requiring that the orbital metric is conserved. In particular, we demonstrate how exponential mappings may be used to parametrise orbital transformations such that the orbital metric is conserved. Using this parametrisation, the localisation of non-orthogonal orbitals becomes a generalisation of the localisation for orthogonal orbitals, where the conservation of a unit metric is replaced by the conservation of a non-unit metric. As a result, standard orbital localisation functions and optimisation algorithms that have been used for localising orthogonal orbitals may also be used to localise non-orthogonal orbitals. Numerical illustrations show that the thickness of the orbital tails may be reduced when a set of non-orthogonal orbitals is localised compared to the orthogo...

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.

The Divide-Expand-Consolidate (DEC) scheme is a linear-scaling and massively parallel framework for high accuracy coupled cluster (CC) calculations on large molecular systems. It is designed as a black-box method, which ensures error control in the correlation energy and molecular properties. DEC is combined with a massively parallel implementation to fully utilize modern manycore architectures providing a fast time to solution. The implementation ensures performance portability and will straightforwardly benefit from new hardware developments. The DEC scheme has been applied to several levels of CC theory and extended the range of application of those methods. For further resources related to this article, please visit the WIREs website.

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 ...

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.

Excitation energies and oscillator strengths in the multiconfigurational time-dependent Hartree-Fock (MCTDHF) approximation are presented for the O2 molecule. Variations of excitation energies with respect to the diffuse character of the basis set are examined. The equivalence between oscillator strengths calculated in the dipole length and dipole velocity approximation in the MCTDHF approximation is investigated.

We derive the multiconfigurational random phase approximation (MCRPA) by requiring the equivalence between the length and velocity forms of the oscillator strength. The MCRPA is also justified in terms of the equations of motion (EOM) formalism. The final equations and techniques developed are the same as the multiconfigurational time dependent Hartree-Fock (MCTDHF). We explicitly demonstrate the validity of the energy-weighted sum rule for the MCRPA-MCTDHF. A modification of our previously derived MCTDHF technique is introduced. This involves the incorporation of additional CI states from different symmetry blocks than the symmetry block of the MCSCF reference state into the MCRPA equations. For a 50 STO calculation on O2 molecule, our results for the low-lying vertical excitation energies are in excellent agreement with experiment and with large-scale CI. Oscillator strengths, frequency dependent polarizabilities, and the energy weighted sum rule are also reported.

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.

The response equations as occurring in the Hartree–Fock, multiconfigurational self-consistent field, and Kohn–Sham density functional theory have identical matrix structures. The algorithms that are used for solving these equations are discussed, and new algorithms are proposed where trial vectors are split into symmetric and antisymmetric components. Numerical examples are given to compare the performance of the algorithms. The calculations show that the standard response equation for frequencies smaller than the highest occupied molecular orbital–lowest unoccupied molecular orbital gap is best solved using the preconditioned conjugate gradient or conjugate residual algorithms where trial vectors are split into symmetric and antisymmetric components. For larger frequencies in the standard response equation as well as in the damped response equation in general, the preconditioned iterative subspace approach with symmetrized trial vectors should be used. For the response eigenvalue equation, the Davidson algorithm with either paired or symmetrized trial vectors constitutes equally good options.

We propose a reformulation of the traditional (T) triples correction to the coupled cluster singles and doubles (CCSD) energy in terms of local Hartree-Fock (FM orbitals such that its structural form aligns with our recently developed linear-scaling divide expand consolidate (DEC) coupled cluster family of local correlation methods. In a DEC-CCSD(T) calculation, a basis of local occupied and virtual HF orbitals is used to partition the correlated calculation on the full system into a number of independent atomic fragment and pair fragment calculations, each performed within a truncated set of the complete Orbital space. In return, this leads to a massively parallel algorithm for the evaluation of the DEC-CCSD(T) correlation energy, which formally scales linearly with the site of the full system and has a tunable precision with respect to a conventional CCSD(T) calculation via a single energy-based input threshold. The theoretical developments are supported by proof of concept DEC-CCSD(T) calculations on a series of medium-sized molecular systems.

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.

Vapor phase OH-stretching overtone spectra of ethylene glycol were recorded to investigate weak intramolecular hydrogen bonding. The spectra were recorded with conventional absorption spectroscopy and laser photoacoustic spectroscopy in the first to fourth OH-stretching overtone regions. The room-temperature spectra are dominated by two conformers that show weak intramolecular hydrogen bonding. A less abundant third conformer, with no sign of hydrogen bonding, is also observed. Vapor phase spectra of the ethylene-d(4) glycol isotopomer were also recorded and used to identify an interfering resonance between CH-stretching and OH-stretching states in the fourth overtone. Anharmonic oscillator local mode calculations of the OH-stretching transitions have provided an accurate simulation of the observed spectra. The local mode parameters were calculated with coupled cluster ab initio methods. The calculations facilitate assignment of the different conformers in the spectra and illustrate the effect of the intramolecular hydrogen bonding.

The static and frequency-dependent hyperpolarizabilities of the N2 molecule have been calculated using the coupled cluster approximate triples model CC3. The CC3 basis-set limit of the hyperpolarizability has been estimated. Considering the zero-point vibrational correction and neglecting the relativistic contributions (which are found to be small) the best estimate of the static hyperpolarizability is 912.9 ± 4.3 a.u. (the uncertainty of 4.3 a.u. does not account for correlation effects beyond CC3). The effect of triples is important and increases with frequency. The hyperpolarizabilities calculated at the CC3 level agree well with experiment, the discrepancies being of 0.1–2.2%. The largest CC3 calculations employed 326 basis functions.

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.

Quantum chemical methods for the calculation of molecular properties to chemical accuracy are reviewed. We begin by reviewing wave-function based electronic structure theory, with emphasis on coupled-cluster theory and the description of electron correlation in terms of virtual excitations from occupied to virtual molecular orbitals. Next, we discuss the expansion of molecular orbitals in atomic orbitals and the design of one-electron basis sets for correlated calculations at the coupled-cluster level of theory. In particular, we discuss the convergence of the electronic energy in the principal expansion as realized in the correlation-consistent basis sets. Following this theoretical introduction, we consider the accurate calculation of atomization energies, reaction enthalpies, dipole moments and spectroscopic constants such as bond distances and harmonic and anharmonic force constants. For each property, we identify what levels of theory in terms of basis set (the one-electron description) and virtual excitation level (the N-electron description) are needed for agreement with experiment to chemical accuracy, that is, about 1 kcal mol−1 (1 kcal = 4.184 kJ) for atomization energies and reaction enthalpies, about 0.1 pm for bond distances and about 1 cm−1 for vibrational frequencies. In each case, we consider in detail the direction and magnitude of the changes in the calculated properties with improvements in the one- and N-electron descriptions of the electronic system, paying particular attention to the cancellation of errors arising from the simultaneous truncations of the coupled-cluster expansion and the one-electron basis set. We emphasize that agreement with experiment, even with chemical accuracy, for a few selected properties is by itself no guarantee of quality and should never be taken as indicative of an accurate description of the electronic system. To ensure such a description, the errors arising from the truncations of the one- and N-electron expansions must be controlled by carrying out sequences of calculations, where the different levels of theory are systematically varied and where convergence is carefully monitored. Copyright © 2004 John Wiley & Sons, Ltd.

The computation of first-order relativistic corrections to electrical response properties has been implemented into the Dalton program at the level of closed-shell coupled-cluster theory, within the framework of the direct perturbation theory (DPT) of relativistic effects. Calculations of the first-order relativistic DPT corrections to the static and frequency-dependent dipole polarizability (α) and second dipole hyperpolarizability (γ) of the Ne atom illustrate possible applications of the new code.

The static and frequency-dependent hyperpolarizability of Ne is calculated using the coupled cluster approximate triples model CC3 and a large correlation-consistent basis set. Relativisitic contributions are taken into account through first-order. Analyzing in details the one- and N -electron errors, the uncertainty of the results is estimated to be about one atomic unit, an accuracy which for the first time is obtained for a many electron system in ab initio calculations of frequency-dependent second hyperpolarizabilities. For the static hyperpolarizability of Ne we obtain a best theoretical estimate of 107.6 ± 1.0 a.u. The frequency-dependent hyperpolarizability of Ne is also calculated at the lower levels of the coupled cluster hierarchy – CCS, CC2, and CCSD – and compared to CC3 to illustrate the importance of the inclusion of the triple excitations in coupled cluster wavefunctions for an accurate determination of hyperpolarizabilities. The results at the CC3 level agree well with the latest experimental results.

The gauge invariance of the oscillator strength is examined for the lowest dipole transitions in Ne, N2 and H2O using the coupled cluster model hierarchy, CCS, CC2, CCSD, and CC3, and a variety of correlation consistent basis sets. The deviations between the oscillator strengths in the different gauges decrease from CCSD to CC3 (where connected triples are included) by about the same factor as they decrease from CCS to CC2 (where connected doubles are included). The deviations are very similar in CC2 and CCSD. The quality of the oscillator strengths is improved significantly at each level in coupled cluster hierarchy, also from CC2 to CCSD, where the equivalence between the oscillator strengths in the different gauges is very similar.

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.

CC3 is a member of the coupled-cluster model hierarchy CCS, CC2, CCSD, CC3, and CCSDT which is especially designed to describe frequency-dependent properties. CCS is the coupled-cluster singles model, in CCSD doubles are added and in CC2 the doubles of the CCSD model are approximated using the same strategy as for triples when CCSDT is approximated to give CC3. Excitation energies have been calculated successfully using this hierarchy. The error in the excitation energies is reduced by about a factor 3 at each level for the models CCS, CC2, CCSD, and CC3, and the CC3 excitation energies closely approximate the ones of the CCSDT model. 14 Calculation of frequency-dependent polarizabilities and hyperpolarizabilities have shown similar systematic improvements to the excitation energies. 15‐17

A total of six high-resolution FT-IR spectra for trans-glyoxal-d2, trans-glyoxal-d1 and trans-glyoxal-13C2 were recorded with a resolution ranging from 0.003 to 0.004 cm−1. By means of a simultaneous ground state combination difference analysis for each of these isotopologues using the Watson Hamiltonian in A-reduction and Ir-representation the ground state rotational constants are obtained. An empirical equilibrium structure is determined for trans-glyoxal using these experimental ground state rotational constants and vibration–rotation interaction constants calculated at the CCSD(T)/cc-pVTZ level of theory. The least-squares fit yields the following structural parameters for trans-glyoxal: re(C–C) = 1.51453(38) A, re(C–H) = 1.10071(26) A, re(CO) = 1.20450(27) A, αe(CCH) = 115.251(24)°, and αe(HCO) = 123.472(19)° in excellent agreement with theoretical predictions at the CCSD(T)/cc-pVQZ level of theory.

The direct inversion of the iterative subspace (DIIS) convergence acceleration algorithm is used in most electronic structure programs to solve the nonlinear coupled cluster amplitude equations. When the DIIS algorithm is used, the storage of previous trial vectors may become a bottleneck and the discarding of trial vectors may lead to a degradation of the convergence or even divergence. We discuss an alternative way of storing information from trial vectors where only the last three trial vectors are needed to maintain the convergence of the full set of previous trial vectors, and which requires only minor modifications of an existing DIIS code.

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.

The calculation of first-order one-electron molecular properties is discussed for an orbital nonrelaxed CCSD(T) (coupled cluster singles and doubles with perturbative triples corrections) wave function model. The conventional CCSD(T) triples amplitude equations have been generalized to contain terms that depend explicitly on the perturbation to compensate for the fact that the Hartree–Fock molecular orbitals are not allowed to relax. Results of sample calculations are presented, including the molecular electric quadrupole moment of benzene in the d-aug-cc-pVTZ basis set, which contains 564 contracted basis functions.