The OpenMolcas Web: A Community-Driven Approach to Advancing Computational Chemistry

The developments of the open-source OpenMolcas chemistry software environment since spring 2020 are described, with a focus on novel functionalities accessible in the stable branch of the package or via interfaces with other packages. These developments span a wide range of topics in computational chemistry and are presented in thematic sections: electronic structure theory, electronic spectroscopy simulations, analytic gradients and molecular structure optimizations, ab initio molecular dynamics, and other new features. This report offers an overview of the chemical phenomena and processes OpenMolcas can address, while showing that OpenMolcas is an attractive platform for state-of-the-art atomistic computer simulations

Zeta-Functions of Two-Sided Ideals in Arithmetic Orders

78 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1984.The thesis deals with the theory of two-sided ideals in arithmetic orders. The theory and techniques developed by Bushnell and Reiner are used.The work begins with an introduction to the theory of Z - and L-series. The basic plan is to compare these series with a Z-integral whose analytic properties are more accessible, and then use these properties to obtain some analogous ones of Z- and L-series. Next the theory of two-sided ideals is studied. First we translate the general theory just developed to our context; then we obtain explicit formulas for the zeta functions for some particular classes of orders, and we give some examples. We also study, in the simple case, the behavior of the zeta-functions at their largest pole. The thesis ends with discussion of some possible generalizations of the prime ideal theorem to two-sided ideals of arithmetic orders in simple algebras.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD

Restricted-Variance Constrained, Reaction Path, and Transition State Molecular Optimizations Using Gradient-Enhanced Kriging

Gaussian process regression has recently been explored as an alternative to standard surrogate models in molecular equilibrium geometry optimization. In particular, the gradient-enhanced Kriging approach in association with internal coordinates, restricted-variance optimization, and an efficient and fast estimate of hyperparameters has demonstrated performance on par or better than standard methods. In this report, we extend the approach to constrained optimizations and transition states and benchmark it for a set of reactions. We compare the performance of the newly developed method with the standard techniques in the location of transition states and in constrained optimizations, both isolated and in the context of reaction path computation. The results show that the method outperforms the current standard in efficiency as well as in robustness

Restricted-Variance Constrained, Reaction Path, and Transition State Molecular Optimizations Using Gradient-Enhanced Kriging

Gaussian process regression has recently been explored as an alternative to standard surrogate models in molecular equilibrium geometry optimization. In particular, the gradient-enhanced Kriging approach in association with internal coordinates, restricted-variance optimization, and an efficient and fast estimate of hyperparameters has demonstrated performance on par or better than standard methods. In this report, we extend the approach to constrained optimizations and transition states and benchmark it for a set of reactions. We compare the performance of the new developed method with the standard techniques in the location of transition states and in constrained optimizations, both isolated and in the context of reaction path computation. The results show that the method outperforms the current standard in efficiency as well as in robustness.<br /

The -(+) and -(+) constructions for biset functors

In this article we define the $-_+$-construction and the $-^+$-construction, that was crucial in the theory of canonical induction formulas (see \cite{Boltje1998b}), in the setting of biset functors, thus providing the necessary framework to define and construct canonical induction formulas for representation rings that are most naturally viewed as biset functors. Additionally, this provides a unified approach to the study of a class of functors including the Burnside ring, the monomial Burnside ring and global representation ring

Halogen bond of halonium ions : Benchmarking DFT methods for the description of NMR chemical shifts

Because of their anisotropic electron distribution and electron deficiency, halonium ions are unusually strong halogen-bond donors that form strong and directional three-center, four-electron halogen bonds. These halogen bonds have received considerable attention owing to their applicability in supramolecular and synthetic chemistry and have been intensely studied using spectroscopic and crystallographic techniques over the past decade. Their computational treatment faces different challenges to those of conventional weak and neutral halogen bonds. Literature studies have used a variety of wave functions and DFT functionals for prediction of their geometries and NMR chemical shifts, however, without any systematic evaluation of the accuracy of these methods being available. In order to provide guidance for future studies, we present the assessment of the accuracy of 12 common DFT functionals along with the Hartree–Fock (HF) and the second-order Møller–Plesset perturbation theory (MP2) methods, selected from an initial set of 36 prescreened functionals, for the prediction of 1H, 13C, and 15N NMR chemical shifts of [N–X–N]+ halogen-bond complexes, where X = F, Cl, Br, and I. Using a benchmark set of 14 complexes, providing 170 high-quality experimental chemical shifts, we show that the choice of the DFT functional is more important than that of the basis set. The M06 functional in combination with the aug-cc-pVTZ basis set is demonstrated to provide the overall most accurate NMR chemical shifts, whereas LC-ωPBE, ωB97X-D, LC-TPSS, CAM-B3LYP, and B3LYP to show acceptable performance. Our results are expected to provide a guideline to facilitate future developments and applications of the [N–X–N]+ halogen bond

Restricted-Variance Molecular Geometry Optimization Based on Gradient-Enhanced Kriging

Machine learning techniques, specifically gradient-enhanced Kriging (GEK), have been implemented for molecular geometry optimization. GEK-based optimization has many advantages compared to conventional-step-restricted second-order truncated expansion-molecular optimization methods. In particular, the surrogate model given by GEK can have multiple stationary points, will smoothly converge to the exact model as the number of sample points increases, and contains an explicit expression for the expected error of the model function at an arbitrary point. Machine learning is, however, associated with abundance of data, contrary to the situation desired for efficient geometry optimizations. In this paper, we demonstrate how the GEK procedure can be utilized in a fashion such that in the presence of few data points, the surrogate surface will in a robust way guide the optimization to a minimum of a potential energy surface. In this respect, the GEK procedure will be used to mimic the behavior of a conventional second-order scheme but retaining the flexibility of the superior machine learning approach. Moreover, the expected error will be used in the optimizations to facilitate restricted-variance optimizations. A procedure which relates the eigenvalues of the approximate guessed Hessian with the individual characteristic lengths, used in the GEK model, reduces the number of empirical parameters to optimize to two: the value of the trend function and the maximum allowed variance. These parameters are determined using the extended Baker (e-Baker) and part of the Baker transition-state (Baker-TS) test suites as a training set. The so-created optimization procedure is tested using the e-Baker, full Baker-TS, and S22 test suites, at the density functional theory and second-order Moller-Plesset levels of approximation. The results show that the new method is generally of similar or better performance than a state-of-the-art conventional method, even for cases where no significant improvement was expected

Restricted-Variance Molecular Geometry Optimization Based on Gradient-Enhanced Kriging

Machine learning techniques, specifically gradient-enhanced Kriging (GEK), have been implemented for molecular geometry optimization. GEK-based optimization has many advantages compared to conventional - step-restricted second-order truncated expansion - molecular optimization methods. In particular, the surrogate model given by GEK can have multiple stationary points, will smoothly converge to the exact model as the number of sample points increases, and contains an explicit expression for the expected error of the model function at an arbitrary point. Machine learning is, however, associated with abundance of data, contrary to the situation desired for efficient geometry optimizations. In the paper we demonstrate how the GEK procedure can be utilized in a fashion such that in the presence of few data points, the surrogate surface will in a robust way guide the optimization to a minimum of a potential energy surface. In this respect the GEK procedure will be used to mimic the behavior of a conventional second-order scheme, but retaining the flexibility of the superior machine learning approach. Moreover, the expected error will be used in the optimization to facilitate restricted-variance optimizations (RVO). A procedure which relates the eigenvalues of the approximate guessed Hessian with the individual characteristic lengths, used in the GEK model, reduces the number of empirical parameters to optimize to two - the value of the trend function and the maximum allowed variance. These parameters are determined using the extended Baker (e-Baker) and part of the Baker transition-state (Baker-TS) test suites as a training set. The so-created optimization procedure is tested using the e-Baker, the full Baker-TS, and the S22 test suites, at the density-functional-theory and second order Møller-Plesset levels of approximation. The results show that the new method is generally of similar or better performance than a state-of-the-art conventional method, even for cases where no significant improvement was expected