Molecular quantum mechanical gradients within the polarizable embedding approach—Application to the internal vibrational Stark shift of acetophenone

We present an implementation of analytical quantum mechanical molecular gradients within the polarizable embedding (PE) model to allow for efficient geometry optimizations and vibrational analysis of molecules embedded in large, geometrically frozen environments. We consider a variational ansatz for the quantum region, covering (multiconfigurational) self-consistent-field and Kohn–Sham density functional theory. As the first application of the implementation, we consider the internal vibrational Stark effect of the C==O group of acetophenone in different solvents and derive its vibrational linear Stark tuning rate using harmonic frequencies calculated from analytical gradients and computed local electric fields. Comparisons to PE calculations employing an enlarged quantum region as well as to a non-polarizable embedding scheme show that the inclusion of mutual polarization between acetophenone and water is essential in order to capture the structural modifications and the associated frequency shifts observed in water. For more apolar solvents, a proper description of dispersion and exchange–repulsion becomes increasingly important, and the quality of the optimized structures relies to a larger extent on the quality of the Lennard-Jones parameters

Development of an Accurate and Efficient Method for Normal Mode Analysis in Extended Molecular Systems: the Mobile Block Hessian Method

Vibrational spectroscopy is an important technique for the structural characterization of (bio)molecules and (nano)materials. For example, it is particularly suited for studying proteins in their natural environment (i.e., in aqueous solution), and can be used in many cases where other techniques such as Xray crystallography and nuclear magnetic resonance spectroscopy cannot be employed. In particular infrared (IR) and Raman spectroscopy have been used extensively for gaining information on the secondary structure of polypeptides and proteins. Also in other fields, these techniques help to identify the functional groups in the material, or provide a unique “fingerprint” of the material, the so-called skeleton vibrations. A frequently encountered problem in spectroscopy is the precise interpretation of the obtained experimental spectra. Many of these nanostructured systems are characterized by very complex vibrational spectra and the assignment of specific bands to particular vibrations is difficult if based solely on experimental techniques. In this field theoretical predictions form an undeniable complement to the measured spectra. Each observed band in the spectrum consists of a number of close-lying normal modes, which result from normal mode analysis (NMA). This is the diagonalization of the full mass-weighted molecular Hessian matrix, which contains the second derivatives of the total potential energy with respect to Cartesian nuclear coordinates, evaluated in an equilibrium point on the potential energy surface (PES). By performing NMA, the system is approximated as a set of decoupled harmonic oscillators. The frequencies and modes contain information on the curvatures of the PES and the mass distribution in the system. NMA is a static approach that samples the PES exactly, if higher order derivatives, i.e. anharmonic corrections, are neglected, and is therefore an approximate analysis method complementary to molecular dynamics and Monte Carlo simulations. In extended molecular systems (like polypeptides, polymer chains, supramolecular assemblies, systems embedded in a solvent or molecules adsorbed within porous materials etc.), this procedure poses two major problems. First, the size of the relevant systems can easily reach a few hundreds or several ten thousands of atoms, and full calculations of such large systems are computationally demanding if not impossible with accurate methods. Second, even if possible, such calculations provide a large amount of data that will be increasingly difficult to interpret. Here lies the scope of this PhD work: The aim of this PhD is the calculation of accurate frequencies and modes in extended molecular systems in an efficient manner. Mainly two categories of approximate normal mode calculations can be identified: (1) the PES description is simplified; (2) the description of the PES is unchanged, but only a subset of the modes is calculated in an approximate way. This PhD work focuses on the latter category and presents the new Mobile Block Hessian (MBH) method and its variants. The key concept is the partitioning of the system into several blocks of atoms, which move as rigid bodies during the vibrational analysis with only rotational and translational degrees of freedom. The MBH has several variants according to the block choice and the way blocks are adjoined together. The MBH is currently implemented in the last upgrade of CHARMM and Q-Chem and the method will be available too in the next release of ADF. Outline PhD thesis In the introductory Chapter 1, normal mode analysis is presented as a technique to scan the potential energy surface within the harmonic oscillator approximation. The standard NMA equations with the full Hessian are revised. The problems brought up by nonstationary points motivate the necessity of a profound theoretical study of the NMA of partially optimized geometries as is the case for MBH. Chapter 2 elaborates the MBH theory in two sets of coordinates: internal coordinates and block parameters. For the extension of the MBH to all kind of blocks (including linear, single-atom blocks) and adjoined blocks (linked by a common “adjoining” atom), the general formulation in block parameters is also linked to Cartesian quantities (Cartesian Hessian, gradient). Five practical implementation schemes for MBH conclude this chapter. In Chapter 3, the MBH is assessed in its performance to reproduce accurate frequencies and normal modes. During my PhD, a large test set has three examples are outlined. The thanol molecule shows how MBH yields physical frequencies for a partially optimized structure, and that MBH is an improvement with respect to the Partial Hessian Vibrational Analysis (PHVA) because of the correct mass description of the block. The MBH is capable of reproducing accurate reaction rate constants given an acceptable block choice, as is illustrated with an aminophosphonate reaction in solvent. The usefulness of adjoined blocks is demonstrated with the calculation of the lowest normal modes of crambin, a small protein. Finally Chapter 4 gives some concluding remarks on the MBH’s performance. Perspectives for the further improvements of MBH include the optimization of the implementation in frequently used program packages, as well as several combined models for advanced NMA. Besides MBH there are other models in literature for the calculation of frequencies in extended systems. In particular, the vibrational subsystem analysis (VSA) method by B. R. Brooks is a competitive scheme. A comparative study of NMA methods based on Hessians of reduced dimension (partial Hessians) has been accomplished very recently in collaboration with prof. B. R. Brooks of the Laboratory of Computational Biology (National Institutes of Health) in Bethesda (Maryland). PHVA is found to be capable of reproducing localized modes. In addition to localized modes, the MBH can reproduce more global modes. VSA is most suited for the reproduction of the modes and frequencies in the lower spectrum. In partially optimized structures, PHVA and MBH can still yield physical frequencies. Moreover, by varying the size of the blocks, MBH can be used as an analysis tool of the spectrum. The comparative study is added in the Appendix. This PhD work has resulted in eight papers, six related to MBH – published, in press, or submitted – and two papers not directly related to MBH. All publications are included in the Appendix

TMB: Automatic Differentiation and Laplace Approximation

TMB is an open source R package that enables quick implementation of complex nonlinear random effect (latent variable) models in a manner similar to the established AD Model Builder package (ADMB, admb-project.org). In addition, it offers easy access to parallel computations. The user defines the joint likelihood for the data and the random effects as a C++ template function, while all the other operations are done in R; e.g., reading in the data. The package evaluates and maximizes the Laplace approximation of the marginal likelihood where the random effects are automatically integrated out. This approximation, and its derivatives, are obtained using automatic differentiation (up to order three) of the joint likelihood. The computations are designed to be fast for problems with many random effects (~10^6) and parameters (~10^3). Computation times using ADMB and TMB are compared on a suite of examples ranging from simple models to large spatial models where the random effects are a Gaussian random field. Speedups ranging from 1.5 to about 100 are obtained with increasing gains for large problems. The package and examples are available at http://tmb-project.org

Combining Parameterizations, Sobolev Methods and Shape Hessian Approximations for Aerodynamic Design Optimization

Aerodynamic design optimization, considered in this thesis, is a large and complex area spanning different disciplines from mathematics to engineering. To perform optimizations on industrially relevant test cases, various algorithms and techniques have been proposed throughout the literature, including the Sobolev smoothing of gradients. This thesis combines the Sobolev methodology for PDE constrained flow problems with the parameterization of the computational grid and interprets the resulting matrix as an approximation of the reduced shape Hessian. Traditionally, Sobolev gradient methods help prevent a loss of regularity and reduce high-frequency noise in the derivative calculation. Such a reinterpretation of the gradient in a different Hilbert space can be seen as a shape Hessian approximation. In the past, such approaches have been formulated in a non-parametric setting, while industrially relevant applications usually have a parameterized setting. In this thesis, the presence of a design parameterization for the shape description is explicitly considered. This research aims to demonstrate how a combination of Sobolev methods and parameterization can be done successfully, using a novel mathematical result based on the generalized Faà di Bruno formula. Such a formulation can yield benefits even if a smooth parameterization is already used. The results obtained allow for the formulation of an efficient and flexible optimization strategy, which can incorporate the Sobolev smoothing procedure for test cases where a parameterization describes the shape, e.g., a CAD model, and where additional constraints on the geometry and the flow are to be considered. Furthermore, the algorithm is also extended to One Shot optimization methods. One Shot algorithms are a tool for simultaneous analysis and design when dealing with inexact flow and adjoint solutions in a PDE constrained optimization. The proposed parameterized Sobolev smoothing approach is especially beneficial in such a setting to ensure a fast and robust convergence towards an optimal design. Key features of the implementation of the algorithms developed herein are pointed out, including the construction of the Laplace-Beltrami operator via finite elements and an efficient evaluation of the parameterization Jacobian using algorithmic differentiation. The newly derived algorithms are applied to relevant test cases featuring drag minimization problems, particularly for three-dimensional flows with turbulent RANS equations. These problems include additional constraints on the flow, e.g., constant lift, and the geometry, e.g., minimal thickness. The Sobolev smoothing combined with the parameterization is applied in classical and One Shot optimization settings and is compared to other traditional optimization algorithms. The numerical results show a performance improvement in runtime for the new combined algorithm over a classical Quasi-Newton scheme

Synthesis, characterization and vibrational studies of p-chlorosulfinylaniline

p-Cholorosulfinylaniline was prepared by the reaction of p-chloroaniline and SOCl2. The structural, conformational and configurational properties of the obtained liquid compound were studied by Raman and infrared spectroscopy in the liquid state. The assignment of the vibrational spectra was carried out with the help of data obtained by quantum chemical calculations at the harmonic oscillator approximation and using anharmonic vibrational self-consistent field (VSCF) method as well. The 1H and 13C NMR chemical shifts of the molecule were calculated by Gauge including orbital (GIAO) method (DFT/B3LYP approximation using 6-311 + G (df), 6-311++G (df,pd) and cc-pVTZ basis sets) and compared to the experimental values. Natural Bond Orbital analysis provides an explanation of the stability of the molecule and its electronic properties upon charge delocalization.Fil: Chemes, Doly María. Universidad Nacional de Tucumán. Facultad de Bioquímica, Química y Farmacia; ArgentinaFil: Alonso de Armiño, Diego Javier. Universidad Nacional de Tucumán. Facultad de Bioquímica, Química y Farmacia; ArgentinaFil: Cutin, Edgardo Hugo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tucumán. Instituto de Química del Noroeste. Universidad Nacional de Tucumán. Facultad de Bioquímica, Química y Farmacia. Instituto de Química del Noroeste; ArgentinaFil: Oberhammer, Heinz. Universitat Tübingen; AlemaniaFil: Robles, Norma Lis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tucumán. Instituto de Química del Noroeste. Universidad Nacional de Tucumán. Facultad de Bioquímica, Química y Farmacia. Instituto de Química del Noroeste; Argentin