The inclusion of dynamical and static electron correlation (SEC) is mandatory for accurate quantum chemistry (QC). SEC is particularly difficult to calculate and hence a qualitative understanding is ...important to judge the applicability of approximate QC methods. Existing scalar SEC diagnostics, however, lack the important information where the SEC effects occur in a molecule. We introduce an analysis tool based on a fractional occupation number weighted electron density (ρFOD) that is plotted in 3D for a pre‐defined contour surface value. The scalar field is obtained by finite‐temperature DFT calculations with pre‐defined electronic temperature (e.g. TPSS at 5000 K). FOD plots only show the contribution of the “hot” (strongly correlated) electrons. We discuss illustrative plots for a broad range of chemical systems from small molecules to large conjugated molecules with polyradicaloid character. Spatial integration yields a single number which can be used to globally quantify SEC.
Hot FOD: The inclusion of static electron correlation (SEC) is mandatory for accurate quantum chemistry yet is particularly difficult to calculate. An analysis tool is developed based on a fractional occupation number weighted electron density (ρFOD) that is plotted as an isosurface and shows the “hot” (strongly correlated) electrons. Spatial integration of ρFOD yields a single number which can be used to globally quantify SEC.
Mean-field electronic structure methods like Hartree–Fock, semilocal density functional approximations, or semiempirical molecular orbital (MO) theories do not account for long-range electron ...correlation (London dispersion interaction). Inclusion of these effects is mandatory for realistic calculations on large or condensed chemical systems and for various intramolecular phenomena (thermochemistry). This Review describes the recent developments (including some historical aspects) of dispersion corrections with an emphasis on methods that can be employed routinely with reasonable accuracy in large-scale applications. The most prominent correction schemes are classified into three groups: (i) nonlocal, density-based functionals, (ii) semiclassical C 6-based, and (iii) one-electron effective potentials. The properties as well as pros and cons of these methods are critically discussed, and typical examples and benchmarks on molecular complexes and crystals are provided. Although there are some areas for further improvement (robustness, many-body and short-range effects), the situation regarding the overall accuracy is clear. Various approaches yield long-range dispersion energies with a typical relative error of 5%. For many chemical problems, this accuracy is higher compared to that of the underlying mean-field method (i.e., a typical semilocal (hybrid) functional like B3LYP).
Aims.
The Chemical Evolution of
R
-process Elements in Stars (CERES) project aims to provide a homogeneous analysis of a sample of metal-poor stars (Fe/H < –1.5). We present the stellar parameters ...and the chemical abundances of elements up to Zr for a sample of 52 giant stars.
Methods.
We relied on a sample of high signal-to-noise UVES spectra. We determined stellar parameters from
Gaia
photometry and parallaxes. Chemical abundances were derived using spectrum synthesis and model atmospheres.
Results.
We determined chemical abundances of 26 species of 18 elements: Na, Mg, Al, Si, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Sr, Y, and Zr. For several stars, we were able to measure both neutral and ionised species, including Si, Sc, Mn, and Zr. We have roughly doubled the number of measurements of Cu for stars at Fe/H ≤ −2.5. The homogeneity of the sample made it possible to highlight the presence of two Zn-rich stars (Zn/Fe ∼ +0.7), one
r
-rich and the other
r
-poor. We report the existence of two branches in the Zn/Fe versus Ni/Fe plane and suggest that the high Zn/Fe branch is the result of hypernova nucleosynthesis. We discovered two stars with peculiar light neutron-capture abundance patterns: CES1237+1922 (also known as BS 16085-0050), which is ∼1 dex underabundant in Sr, Y, and Zr with respect to the other stars in the sample, and CES2250-4057 (also known as HE 2247-4113), which shows a ∼1 dex overabundance of Sr with respect to Y and Zr.
Conclusions.
The high quality of our dataset allowed us to measure hardly detectable ions. This can provide guidance in the development of line formation computations that take deviations from local thermodynamic equilibrium and hydrodynamical effects into account.
In this paper, the possibility is explored to speed up Hartree–Fock and hybrid density functional calculations by forming the Coulomb and exchange parts of the Fock matrix by different ...approximations. For the Coulomb part the previously introduced Split-RI-J variant (F. Neese, J. Comput. Chem. 24 (2003) 1740) of the well-known ‘density fitting’ approximation is used. The exchange part is formed by semi-numerical integration techniques that are closely related to Friesner’s pioneering pseudo-spectral approach. Our potentially linear scaling realization of this algorithm is called the ‘chain-of-spheres exchange’ (COSX). A combination of semi-numerical integration and density fitting is also proposed. Both Split-RI-J and COSX scale very well with the highest angular momentum in the basis sets. It is shown that for extended basis sets speed-ups of up to two orders of magnitude compared to traditional implementations can be obtained in this way. Total energies are reproduced with an average error of <0.3kcal/mol as determined from extended test calculations with various basis sets on a set of 26 molecules with 20–200 atoms and up to 2000 basis functions. Reaction energies agree to within 0.2kcal/mol (Hartree–Fock) or 0.05kcal/mol (hybrid DFT) with the canonical values. The COSX algorithm parallelizes with a speedup of 8.6 observed for 10 processes. Minimum energy geometries differ by less than 0.3pm in the bond distances and 0.5° in the bond angels from their canonical values. These developments enable highly efficient and accurate self-consistent field calculations including nonlocal Hartree–Fock exchange for large molecules. In combination with the RI-MP2 method and large basis sets, second-order many body perturbation energies can be obtained for medium sized molecules with unprecedented efficiency. The algorithms are implemented into the ORCA electronic structure system.
We introduce the new MOR41 benchmark set consisting of 41 closed-shell organometallic reactions resembling many important chemical transformations commonly used in transition metal chemistry and ...catalysis. It includes significantly larger molecules than presented in other transition metal test sets and covers a broad range of bonding motifs. Recent progress in linear-scaling coupled cluster theory allowed for the calculation of accurate DLPNO-CCSD(T)/CBS(def2-TZVPP/def2-QZVPP) reference energies for 3d,4d,5d-transition metal compounds with up to 120 atoms. Furthermore, 41 density functionals, including seven GGAs, three meta-GGAs, 14 hybrid functionals, and 17 double-hybrid functionals combined with two different London dispersion corrections, are benchmarked with respect to their performance for the newly compiled MOR41 reaction energies. A few wave function-based post-HF methods as, e.g., MP2 or RPA with similar computational demands are also tested and in total, 90 methods were considered. The double-hybrid functional PWPB95-D3(BJ) outperformed all other assessed methods with an MAD of 1.9 kcal/mol, followed by the hybrids ωB97X-V (2.2 kcal/mol) and mPW1B95-D3(BJ) (2.4 kcal/mol). The popular PBE0-D3(BJ) hybrid also performs well (2.8 kcal/mol). Within the meta-GGA class, the recently published SCAN-D3(BJ) functional as well as TPSS-D3(BJ) perform best (MAD of 3.2 and 3.3 kcal/mol, respectively). Many popular methods like BP86-D3(BJ) (4.9 kcal/mol) or B3LYP-D3(BJ) (4.9 kcal/mol) provide significantly worse reaction energies and are not recommended for organometallic thermochemistry considering the availability of better methods with the same computational cost. The results regarding the performance of different functional approximations are consistent with conclusions from previous main-group thermochemistry benchmark studies.
Coupled-electron pair approximations (CEPAs) and coupled-pair functionals (CPFs) have been popular in the 1970s and 1980s and have yielded excellent results for small molecules. Recently, interest in ...CEPA and CPF methods has been renewed. It has been shown that these methods lead to competitive thermochemical, kinetic, and structural predictions. They greatly surpass second order Moller-Plesset and popular density functional theory based approaches in accuracy and are intermediate in quality between CCSD and CCSD(T) in extended benchmark studies. In this work an efficient production level implementation of the closed shell CEPA and CPF methods is reported that can be applied to medium sized molecules in the range of 50-100 atoms and up to about 2000 basis functions. The internal space is spanned by localized internal orbitals. The external space is greatly compressed through the method of pair natural orbitals (PNOs) that was also introduced by the pioneers of the CEPA approaches. Our implementation also makes extended use of density fitting (or resolution of the identity) techniques in order to speed up the laborious integral transformations. The method is called local pair natural orbital CEPA (LPNO-CEPA) (LPNO-CPF). The implementation is centered around the concepts of electron pairs and matrix operations. Altogether three cutoff parameters are introduced that control the size of the significant pair list, the average number of PNOs per electron pair, and the number of contributing basis functions per PNO. With the conservatively chosen default values of these thresholds, the method recovers about 99.8% of the canonical correlation energy. This translates to absolute deviations from the canonical result of only a few kcal mol(-1). Extended numerical test calculations demonstrate that LPNO-CEPA (LPNO-CPF) has essentially the same accuracy as parent CEPA (CPF) methods for thermochemistry, kinetics, weak interactions, and potential energy surfaces but is up to 500 times faster. The method performs best in conjunction with large and flexible basis sets. These results open the way for large-scale chemical applications.
This paper reports results from three studies concerning outdoor recreation participation and trends during the COVID-19 pandemic in Sweden. The studies, undertaken at national, regional and local ...levels, used surveys, interviews and PPGIS approaches, to build a solid knowledge base. Results are analyzed with particular attention given to management and policy implications based on the following observations: increased outdoor recreation participation, changes in lifestyle and routines, new visitor profiles and activity trends, spatial changes, visitor displacement, spatial redistribution, and indications of post-pandemic outdoor recreation behavior. The Swedish case is of special interest because of high accessibility to nature areas and few restrictions to recreate in nature due to the pandemic. Hence, this study could serve as a reference for other countries with more COVID-19 related restrictions and less accessible nature for recreation.
This paper contributes with a better understanding of recreational landscapes as a conceptual coupling that lacks clarity and cementation as a legitimate and integrated concept in landscape and ...outdoor recreation-related disciplines, especially within Nordic landscape and outdoor recreation research. The approach in the paper is an explorative-theoretical one with a base in a literature review. The results show 294 identified texts using the conceptual coupling 'recreation(al) landscape(s)' in any of its variants and published in 155 different journals. Only a few of the texts offer detailed description of its meaning. Consequently, in an attempt to further the understanding of recreational landscapes, the conceptual coupling is explored and discussed in more detail with special attention given to different landscape relations, human-nature encounters and the relationship between landscape and place. A conclusion is that recreational landscapes must receive more attention and better anchoring in various landscape and outdoor recreation-related disciplines.
Special-purpose classical force fields (FFs) provide good accuracy at very low computational cost, but their application is limited to systems for which potential energy functions are available. This ...excludes most metal-containing proteins or those containing cofactors. In contrast, the GFN2-xTB semiempirical quantum chemical method is parametrized for almost the entire periodic table. The accuracy of GFN2-xTB is assessed for protein structures with respect to experimental X-ray data. Furthermore, the results are compared with those of two special-purpose FFs, HF-3c, PM6-D3H4X, and PM7. The test sets include proteins without any prosthetic groups as well as metalloproteins. Crystal packing effects are examined for a set of smaller proteins to validate the molecular approach. For the proteins without prosthetic groups, the special purpose FF OPLS-2005 yields the smallest overall RMSD to the X-ray data but GFN2-xTB provides similarly good structures with even better bond-length distributions. For the metalloproteins with up to 5000 atoms, a good overall structural agreement is obtained with GFN2-xTB. The full geometry optimizations of protein structures with on average 1000 atoms in wall-times below 1 day establishes the GFN2-xTB method as a versatile tool for the computational treatment of various biomolecules with a good accuracy/computational cost ratio.
A production level implementation of the high-spin open-shell (spin unrestricted) single reference coupled pair, quadratic configuration interaction and coupled cluster methods with up to doubly ...excited determinants in the framework of the local pair natural orbital (LPNO) concept is reported. This work is an extension of the closed-shell LPNO methods developed earlier F. Neese, F. Wennmohs, and A. Hansen, J. Chem. Phys. 130, 114108 (2009); F. Neese, A. Hansen, and D. G. Liakos, J. Chem. Phys. 131, 064103 (2009). The internal space is spanned by localized orbitals, while the external space for each electron pair is represented by a truncated PNO expansion. The laborious integral transformation associated with the large number of PNOs becomes feasible through the extensive use of density fitting (resolution of the identity (RI)) techniques. Technical complications arising for the open-shell case and the use of quasi-restricted orbitals for the construction of the reference determinant are discussed in detail. As in the closed-shell case, only three cutoff parameters control the average number of PNOs per electron pair, the size of the significant pair list, and the number of contributing auxiliary basis functions per PNO. The chosen threshold default values ensure robustness and the results of the parent canonical methods are reproduced to high accuracy. Comprehensive numerical tests on absolute and relative energies as well as timings consistently show that the outstanding performance of the LPNO methods carries over to the open-shell case with minor modifications. Finally, hyperfine couplings calculated with the variational LPNO-CEPA∕1 method, for which a well-defined expectation value type density exists, indicate the great potential of the LPNO approach for the efficient calculation of molecular properties.
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