Code generation in ORCA: progress, efficiency and tight integration.

An improved version of ORCA's automated generator environment (ORCA-AGE II) is presented. The algorithmic improvements and the move to C++ as the programming language lead to a performance gain of up to two orders of magnitude compared to the previously developed PYTHON toolchain. Additionally, the restructured modular design allows for far more complex code engines to be implemented readily. Importantly, we have realised an extremely tight integration with the ORCA host program. This allows for a workflow in which only the wavefunction Ansatz is part of the source code repository while all actual high-level code is generated automatically, inserted at the appropriate place in the host program before it is compiled and linked together with the hand written code parts. This construction ensures longevity and uniform code quality. Furthermore the new developments allow ORCA-AGE II to generate parallelised production-level code for highly complex theories, such as fully internally contracted multireference coupled-cluster theory (fic-MRCC) with an enormous number of contributing tensor contractions. We also discuss the automated implementation of nuclear gradients for arbitrary theories. All these improvements enable the implementation of theories that are too complex for the human mind and also reduce development times by orders of magnitude. We hope that this work enables researchers to concentrate on the intellectual content of the theories they develop rather than be concerned with technical details of the implementation.

SparseMaps-A systematic infrastructure for reduced-scaling electronic structure methods. VI. Linear-scaling explicitly correlated N-electron valence state perturbation theory with pair natural orbital.

In this work, a linear scaling explicitly correlated N-electron valence state perturbation theory (NEVPT2-F12) is presented. By using the idea of a domain-based local pair natural orbital (DLPNO), computational scaling of the conventional NEVPT2-F12 is reduced to near-linear scaling. For low-lying excited states of organic molecules, the excitation energies predicted by DLPNO-NEVPT2-F12 are as accurate as the exact NEVPT2-F12 results. Some cluster models of rhodopsin are studied using the new algorithm. Our new method is able to study systems with more than 3300 basis functions and an active space containing 12 π-electrons and 12 π-orbitals. However, even larger calculations or active spaces would still be feasible.

Implicit solvation in domain based pair natural orbital coupled cluster (DLPNO-CCSD) theory.

A nearly linear scaling implementation of coupled-cluster with singles and doubles excitations (CCSD) can be achieved by means of the domain-based local pair natural orbital (DLPNO) method. The combination of DLPNO-CCSD with implicit solvation methods allows the calculation of accurate energies and chemical properties of solvated systems at an affordable computational cost. We have efficiently implemented different schemes within the conductor-like polarizable continuum model (C-PCM) for DLPNO-CCSD in the ORCA quantum chemistry suite. In our implementation, the overhead due to the additional solvent terms amounts to less than 5% of the time the equivalent gas phase job takes. Our results for organic neutrals and open-shell ions in water show that for most systems, adding solvation terms to the coupled-cluster amplitudes equations and to the energy leads to small changes in the total energy compared to only considering solvated orbitals and corrections to the reference energy. However, when the solute contains certain functional groups, such as carbonyl or nitrile groups, the changes in the energy are larger and estimated to be around 0.04 and 0.02 kcal/mol for each carbonyl and nitrile group in the solute, respectively. For solutes containing metals, the use of accurate CC/C-PCM schemes is crucial to account for correlation solvation effects. Simultaneously, we have calculated the electrostatic component of the solvation energy for neutrals and ions in water for the different DLPNO-CCSD/C-PCM schemes. We observe negligible changes in the deviation between DLPNO-CCSD and canonical-CCSD data. Here, DLPNO-CCSD results outperform those for Hartree-Fock and density functional theory calculations.

Nudged Elastic Band Method for Molecular Reactions Using Energy-Weighted Springs Combined with Eigenvector Following.

The climbing image nudged elastic band method (CI-NEB) is used to identify reaction coordinates and to find saddle points representing transition states of reactions. It can make efficient use of parallel computing as the calculations of the discretization points, the so-called images, can be carried out simultaneously. In typical implementations, the images are distributed evenly along the path by connecting adjacent images with equally stiff springs. However, for systems with a high degree of flexibility, this can lead to poor resolution near the saddle point. By making the spring constants increase with energy, the resolution near the saddle point is improved. To assess the performance of this energy-weighted CI-NEB method, calculations are carried out for a benchmark set of 121 molecular reactions. The performance of the method is analyzed with respect to the input parameters. Energy-weighted springs are found to greatly improve performance and result in successful location of the saddle points in less than a thousand energy and force evaluations on average (about a hundred per image) using the same set of parameter values for all of the reactions. Even better performance is obtained by stopping the calculation before full convergence and complete the saddle point search using an eigenvector following method starting from the location of the climbing image. This combination of methods, referred to as NEB-TS, turns out to be robust and highly efficient as it reduces the average number of energy and force evaluations down to a third, to 305. An efficient and flexible implementation of these methods has been made available in the ORCA software.

The ORCA quantum chemistry program package.

In this contribution to the special software-centered issue, the ORCA program package is described. We start with a short historical perspective of how the project began and go on to discuss its current feature set. ORCA has grown into a rather comprehensive general-purpose package for theoretical research in all areas of chemistry and many neighboring disciplines such as materials sciences and biochemistry. ORCA features density functional theory, a range of wavefunction based correlation methods, semi-empirical methods, and even force-field methods. A range of solvation and embedding models is featured as well as a complete intrinsic to ORCA quantum mechanics/molecular mechanics engine. A specialty of ORCA always has been a focus on transition metals and spectroscopy as well as a focus on applicability of the implemented methods to "real-life" chemical applications involving systems with a few hundred atoms. In addition to being efficient, user friendly, and, to the largest extent possible, platform independent, ORCA features a number of methods that are either unique to ORCA or have been first implemented in the course of the ORCA development. Next to a range of spectroscopic and magnetic properties, the linear- or low-order single- and multi-reference local correlation methods based on pair natural orbitals (domain based local pair natural orbital methods) should be mentioned here. Consequently, ORCA is a widely used program in various areas of chemistry and spectroscopy with a current user base of over 22 000 registered users in academic research and in industry.

Improved survival in metastatic breast cancer: results from a 20-year study involving 1033 women treated at a single comprehensive cancer center.

PURPOSE: Diagnosis and treatment of breast cancer have changed profoundly over the past 25 years. The outcome improved dramatically and was well quantified for early stage breast cancer (EBC). However, progress in the treatment of metastatic disease has been less convincingly demonstrated. We have studied survival data of patients with metastatic breast cancer (MBC) from a large academic cancer center over a period of 20 years. METHODS: Data from 1033 consecutive MBC patients who were treated at the Department of Medical Oncology of the West German Cancer Center from January 1990 to December 2009 were retrospectively analyzed for overall survival (OS) and risk factors. Patients were grouped in 5-year cohorts, and survival parameters of each cohort were compared before and after adjustment for risk factors. RESULTS: Overall survival of patients with MBC treated at specialized center has significantly improved from 1990 to 2010 (hazard ratio 0.7, 95%CI 0.58-0.84). The increments in OS have become less profound over time (median OS 1990-1994: 24.2 months, 1995-1999: 29.6 months, 2000-2004: 36.5 months, 2005-2009: 37.8 months). CONCLUSION: Survival of patients with MBC has improved between 1990 and 2004, but less from 2005 to 2009. Either this suggests an unnoticed shift in the patient population, or a lesser impact of therapeutic innovations introduced in the most recent period.

Linear scaling perturbative triples correction approximations for open-shell domain-based local pair natural orbital coupled cluster singles and doubles theory [DLPNO-CCSD(T0/T)].

The coupled cluster method with single-, double-, and perturbative triple excitations [CCSD(T)] is considered to be one of the most reliable quantum chemistry theories. However, the steep scaling of CCSD(T) has limited its application to small or medium-sized systems for a long time. In our previous work, the linear scaling domain based local pair natural orbital CCSD variant (DLPNO-CCSD) has been developed for closed-shell and open-shell. However, it is known from extensive benchmark studies that triple-excitation contributions are important to reach chemical accuracy. In the present work, two linear scaling (T) approximations for open-shell DLPNO-CCSD are implemented and compared: (a) an algorithm based on the semicanonical approximation, in which off-diagonal Fock matrix elements in the occupied space are neglected [referred to as DLPNO-(T0)]; and (b) an improved algorithm in which the triples amplitudes are computed iteratively [referred to as DLPNO-(T)]. This work is based on the previous open-shell DLPNO-CCSD algorithm [M. Saitow et al., J. Chem. Phys. 146, 164105 (2017)] as well as the iterative (T) correction for closed-shell systems [Y. Guo et al., J. Chem. Phys. 148, 011101 (2018)]. Our results show that the new open-shell perturbative corrections, DLPNO-(T0/T), can predict accurate absolute and relative correlation energies relative to the canonical reference calculations with the same basis set. The absolute energies from DLPNO-(T) are significantly more accurate than those of DLPNO-(T0). The additional computational effort of DLPNO-(T) relative to DLPNO-(T0) is a factor of 4 on average. We report calculations on systems with more than 4000 basis functions.

Comparison and combination of "direct" and fragment based local correlation methods: Cluster in molecules and domain based local pair natural orbital perturbation and coupled cluster theories.

Local correlation theories have been developed in two main flavors: (1) "direct" local correlation methods apply local approximation to the canonical equations and (2) fragment based methods reconstruct the correlation energy from a series of smaller calculations on subsystems. The present work serves two purposes. First, we investigate the relative efficiencies of the two approaches using the domain-based local pair natural orbital (DLPNO) approach as the "direct" method and the cluster in molecule (CIM) approach as the fragment based approach. Both approaches are applied in conjunction with second-order many-body perturbation theory (MP2) as well as coupled-cluster theory with single-, double- and perturbative triple excitations [CCSD(T)]. Second, we have investigated the possible merits of combining the two approaches by performing CIM calculations with DLPNO methods serving as the method of choice for performing the subsystem calculations. Our cluster-in-molecule approach is closely related to but slightly deviates from approaches in the literature since we have avoided real space cutoffs. Moreover, the neglected distant pair correlations in the previous CIM approach are considered approximately. Six very large molecules (503-2380 atoms) were studied. At both MP2 and CCSD(T) levels of theory, the CIM and DLPNO methods show similar efficiency. However, DLPNO methods are more accurate for 3-dimensional systems. While we have found only little incentive for the combination of CIM with DLPNO-MP2, the situation is different for CIM-DLPNO-CCSD(T). This combination is attractive because (1) the better parallelization opportunities offered by CIM; (2) the methodology is less memory intensive than the genuine DLPNO-CCSD(T) method and, hence, allows for large calculations on more modest hardware; and (3) the methodology is applicable and efficient in the frequently met cases, where the largest subsystem calculation is too large for the canonical CCSD(T) method.

Communication: An improved linear scaling perturbative triples correction for the domain based local pair-natural orbital based singles and doubles coupled cluster method [DLPNO-CCSD(T)].

In this communication, an improved perturbative triples correction (T) algorithm for domain based local pair-natural orbital singles and doubles coupled cluster (DLPNO-CCSD) theory is reported. In our previous implementation, the semi-canonical approximation was used and linear scaling was achieved for both the DLPNO-CCSD and (T) parts of the calculation. In this work, we refer to this previous method as DLPNO-CCSD(T0) to emphasize the semi-canonical approximation. It is well-established that the DLPNO-CCSD method can predict very accurate absolute and relative energies with respect to the parent canonical CCSD method. However, the (T0) approximation may introduce significant errors in absolute energies as the triples correction grows up in magnitude. In the majority of cases, the relative energies from (T0) are as accurate as the canonical (T) results of themselves. Unfortunately, in rare cases and in particular for small gap systems, the (T0) approximation breaks down and relative energies show large deviations from the parent canonical CCSD(T) results. To address this problem, an iterative (T) algorithm based on the previous DLPNO-CCSD(T0) algorithm has been implemented [abbreviated here as DLPNO-CCSD(T)]. Using triples natural orbitals to represent the virtual spaces for triples amplitudes, storage bottlenecks are avoided. Various carefully designed approximations ease the computational burden such that overall, the increase in the DLPNO-(T) calculation time over DLPNO-(T0) only amounts to a factor of about two (depending on the basis set). Benchmark calculations for the GMTKN30 database show that compared to DLPNO-CCSD(T0), the errors in absolute energies are greatly reduced and relative energies are moderately improved. The particularly problematic case of cumulene chains of increasing lengths is also successfully addressed by DLPNO-CCSD(T).

Multilevel Approaches within the Local Pair Natural Orbital Framework.

The linear-scaling local coupled cluster method DLPNO-CCSD(T) allows calculations on systems containing hundreds of atoms to be performed while reproducing canonical CCSD(T) energies typically with chemical accuracy (<1 kcal/mol). The accuracy of the method is determined by two main truncation thresholds that control the number of electron pairs included in the CCSD iterations and the size of the pair natural orbital virtual space for each electron pair, respectively. While the results of DLPNO-CCSD(T) calculations converge smoothly toward their canonical counterparts as the thresholds are tightened, the improved accuracy is accompanied by a fairly steep increase of the computational cost. Many applications study events that are confined to a relatively small region of the system of interest. Hence, it is viable to develop methods that allow the user to treat different parts of a large system at various levels of accuracy. In this work we present an extension to the native DLPNO method that fragments the system into preselected molecular parts and uses different thresholds or even different levels of theory for the interaction between individual fragments. Thereby chemical intuition can be used to focus computational resources on a more accurate evaluation of the properties at the center of interest, while permitting a less demanding description of the surrounding moieties. The strategy was implemented within the DLPNO-CCSD(T) framework. We tested the scheme for a series of realistic quantum chemical applications such as the calculation of the dimerization energies, potential energy surfaces, enantiomeric excess in organometallic catalysis, and the binding energy of the anticancer drug ellipticine to DNA. This work demonstrates the power of the approach and offers guidance to its setup.

A new near-linear scaling, efficient and accurate, open-shell domain-based local pair natural orbital coupled cluster singles and doubles theory.

The Coupled-Cluster expansion, truncated after single and double excitations (CCSD), provides accurate and reliable molecular electronic wave functions and energies for many molecular systems around their equilibrium geometries. However, the high computational cost, which is well-known to scale as O(N6) with system size N, has limited its practical application to small systems consisting of not more than approximately 20-30 atoms. To overcome these limitations, low-order scaling approximations to CCSD have been intensively investigated over the past few years. In our previous work, we have shown that by combining the pair natural orbital (PNO) approach and the concept of orbital domains it is possible to achieve fully linear scaling CC implementations (DLPNO-CCSD and DLPNO-CCSD(T)) that recover around 99.9% of the total correlation energy [C. Riplinger et al., J. Chem. Phys. 144, 024109 (2016)]. The production level implementations of the DLPNO-CCSD and DLPNO-CCSD(T) methods were shown to be applicable to realistic systems composed of a few hundred atoms in a routine, black-box fashion on relatively modest hardware. In 2011, a reduced-scaling CCSD approach for high-spin open-shell unrestricted Hartree-Fock reference wave functions was proposed (UHF-LPNO-CCSD) [A. Hansen et al., J. Chem. Phys. 135, 214102 (2011)]. After a few years of experience with this method, a few shortcomings of UHF-LPNO-CCSD were noticed that required a redesign of the method, which is the subject of this paper. To this end, we employ the high-spin open-shell variant of the N-electron valence perturbation theory formalism to define the initial guess wave function, and consequently also the open-shell PNOs. The new PNO ansatz properly converges to the closed-shell limit since all truncations and approximations have been made in strict analogy to the closed-shell case. Furthermore, given the fact that the formalism uses a single set of orbitals, only a single PNO integral transformation is necessary, which offers large computational savings. We show that, with the default PNO truncation parameters, approximately 99.9% of the total CCSD correlation energy is recovered for open-shell species, which is comparable to the performance of the method for closed-shells. UHF-DLPNO-CCSD shows a linear scaling behavior for closed-shell systems, while linear to quadratic scaling is obtained for open-shell systems. The largest systems we have considered contain more than 500 atoms and feature more than 10 000 basis functions with a triple-ζ quality basis set.

Sparse maps--A systematic infrastructure for reduced-scaling electronic structure methods. II. Linear scaling domain based pair natural orbital coupled cluster theory.

Domain based local pair natural orbital coupled cluster theory with single-, double-, and perturbative triple excitations (DLPNO-CCSD(T)) is a highly efficient local correlation method. It is known to be accurate and robust and can be used in a black box fashion in order to obtain coupled cluster quality total energies for large molecules with several hundred atoms. While previous implementations showed near linear scaling up to a few hundred atoms, several nonlinear scaling steps limited the applicability of the method for very large systems. In this work, these limitations are overcome and a linear scaling DLPNO-CCSD(T) method for closed shell systems is reported. The new implementation is based on the concept of sparse maps that was introduced in Part I of this series [P. Pinski, C. Riplinger, E. F. Valeev, and F. Neese, J. Chem. Phys. 143, 034108 (2015)]. Using the sparse map infrastructure, all essential computational steps (integral transformation and storage, initial guess, pair natural orbital construction, amplitude iterations, triples correction) are achieved in a linear scaling fashion. In addition, a number of additional algorithmic improvements are reported that lead to significant speedups of the method. The new, linear-scaling DLPNO-CCSD(T) implementation typically is 7 times faster than the previous implementation and consumes 4 times less disk space for large three-dimensional systems. For linear systems, the performance gains and memory savings are substantially larger. Calculations with more than 20 000 basis functions and 1000 atoms are reported in this work. In all cases, the time required for the coupled cluster step is comparable to or lower than for the preceding Hartree-Fock calculation, even if this is carried out with the efficient resolution-of-the-identity and chain-of-spheres approximations. The new implementation even reduces the error in absolute correlation energies by about a factor of two, compared to the already accurate previous implementation.

Magnetic resonance imaging findings of the lumbar spine in elite horseback riders: correlations with back pain, body mass index, trunk/leg-length coefficient, and riding discipline.

BACKGROUND: Most orthopaedic problems experienced by competitive horseback riders are related to pain in the lower back, hip joint, and hamstring muscles. Riders-especially, show jumpers-are frequently hampered in their performance because of lumbar pain. To date, there has been no research into lumbar disk degeneration in elite competitive riders. HYPOTHESIS: Competitive horseback riding accelerates lumbar disk degeneration. STUDY DESIGN: Cross-sectional study; Level of evidence, 3. METHODS: Fifty-eight elite riders (18 men, 40 women; mean age, 32.4 years) and a control group of 30 nonriding volunteers (17 men, 13 women; mean age, 28.7 years) were evaluated for lumbar disk degeneration, cross-sectional area of paraspinal muscles, spondylolysis, and spondylolisthesis, using magnetic resonance imaging (MRI). The prevalence of disk degeneration between the 2 groups was compared, and the relationship was investigated between low back pain (LBP), riding discipline, body mass index (BMI), trunk/leg-length coefficient, and MRI results. RESULTS: Eighty-eight percent of elite riders (n = 51) had a history of LBP, versus 33% of the controls (P < .05). There was no statistical difference for the prevalence of LBP among the different riding disciplines. However, there was a high rate of pathologic T2 signal intensity of the lumbar intervertebral disk among riders-specifically, dressage riders-yet no significant increase when compared with controls. History of LBP symptoms, riding discipline, BMI, and trunk/leg-length ratio had no significant effect on the development of lumbar disk degeneration. Occult fractures of the pars interarticularis and manifest spondylolysis were not seen for any rider. Two controls had spondylolisthesis Meyerding grade 1 not associated with back pain. CONCLUSION: Although riders have a high prevalence of LBP, there is no conclusive MRI evidence to suggest that the cause lies in undue disk degeneration, spondylolysis, spondylolisthesis, or pathologic changes of the paraspinal muscles of the lumbar spine.

Local adaptation in the monocarpic perennial Carlina vulgaris at different spatial scales across Europe.

Spatial variation in environmental conditions can lead to local adaptation of plant populations, particularly if gene flow among populations is low. Many studies have investigated adaptation to contrasting environmental conditions, but little is known about the spatial scale of adaptive evolution. We studied population differentiation and local adaptation at two spatial scales in the monocarpic grassland perennial Carlina vulgaris. We reciprocally transplanted seedlings among five European regions (northwestern Czech Republic, central Germany, Luxembourg, southern Sweden and northwestern Switzerland) and among populations of different sizes within three of the regions. We recorded survival, growth and reproduction over three growing periods. At the regional scale, several performance traits and the individual fitness of C. vulgaris were highest if the plants were grown in their home region and they decreased with increasing transplant distance. The effects are likely due to climatic differences that increased with the geographical distance between regions. At the local scale, there were significant interactions between the effects of the population of origin and the transplant site, but these were not due to an enhanced performance of plants at their home site and they were not related to the geographical or environmental distance between the site of origin and the transplant site. The size of the population of origin did not influence the strength of local adaptation. The results of our study suggest that C. vulgaris consists of regionally adapted genotypes, and that distance is a good predictor of the extent of adaptive differentiation at large scales ( > 200 km) but not at small scales. We conclude that patterns of local adaptation should be taken into account for the efficient preservation of genetic resources, when assessing the status of a plant species and during conservation planning.

Phenotypic plasticity in Carlina vulgaris: effects of geographical origin, population size, and population isolation.

If phenotypic plasticity is under genetic control, it may vary in amount and pattern on a geographical scale, e.g. among different regions of a species' distribution. It may also differ between large and small or between less and more isolated populations, due to differences in genetic diversity. In a 2-year common garden study, the responses of several traits to drought and fertilizer treatments were studied in the grassland herb Carlina vulgaris. Individuals originating from populations of different size and degree of isolation in six European countries, representing "central" and "marginal" regions, were compared. Fertilizing had a negative effect on early plant survival, as well as on flowering probability in surviving plants. However, in those plants that flowered, fertilizing strongly increased mean number of flowerheads, flowerhead area (a correlate of seed number), and seed mass. Drought had generally weaker effects but enhanced survivorship, indicating that this treatment was closer to optimal conditions than were non-drought conditions. For some traits there were significant interactions of region x fertilizer, but the geographical pattern of reaction norms was inconsistent and lent no support to the hypothesis that central and marginal populations differ in overall plasticity. Population size and isolation had hardly any influence on treatment responses, but populations within regions differed in their mean response to fertilizing with regard to survival and flowering probabilities, as well as in their response to drought with regard to survival and total flowerhead area. It is concluded that response to raised nutrient levels is highly variable within populations, ranging from death to strongly increased reproductive output, but also among populations irrespective of size or isolation. This also goes for the response to water supply, though this variation shows a more unclear pattern. There is no evidence that small or isolated/marginal populations are less plastic than large or non-isolated/central populations, and the explanation for differences in treatment responses among plant populations should be sought in other population characteristics.

Modulation of angiogenesis-related protein synthesis by valproic acid.

Recent studies have attested to the antiangiogenic effects of HDAC inhibitors on solid human tumors. The HDAC inhibitor butyrate has been reported to impair tumor-cell-induced angiogenesis. However, due to its poor bioavailability in vivo, the therapeutic use of butyrate is limited. On the other hand, valproic acid has inhibitory effects on carcinoma cells, is known to be well tolerated, and has an excellent bioavailability. We therefore set out to investigate whether the HDAC inhibitor valproic acid also impairs angiogenesis. Our findings indicate that valproic acid represses the relevant angiogenic factors VEGF and FGF in Caco-2 cells. Both, protein expression as well as mRNA levels of VEGF, were reduced to a similar degree. Suppression of ubiquitin-proteasome activity could be a possible reason for valproic acid effects on regulatory angiogenesis proteins. These results suggest that the HDAC inhibitor valproic acid could become a valuable new addition in the attempt to develop alternative therapeutic approaches in the treatment of colon carcinomas.