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

Monte Carlo simulations to understand 'breathing' phenomenon of metal organic frameworks

Metal Organic Frameworks (MOFs) are a new class of porous materials synthesized from metal clusters connected by organic linkers. One of the promising applications of MOFs is carbon capture from fuel gasses, where CO2 is adsorbed in the pores of the material. In this presentation, we explore framework flexibility as a possible mechanism for selective and reversible CO2 adsorption by means of Monte Carlo simulations. Most MOFs are fairly rigid structures, in the sense that they undergo small changes in volume when external stress is applied. Typical volume changes are of the order of a few percent only. Nevertheless, some MOF materials have an unexpectedly high flexibility and impressively shrink or swell under pressure, temperature or adsorption changes. A well-known example is MIL-53, a structure that shows volume changes of over 40%. In an adsorption experiment, the gas pressure is gradually increased while the amount of adsorbed material in the pores is measured. For MIL-53, the measured adsorption isotherm shows interesting features: when MIL-53 is brought into contact with a gas at increasing pressure, the framework's pores constrict, while at even higher pressures, the pores return to their original geometry. The process, referred to as "breathing", is reversible and shows hysteresis. Based on Monte Carlo runs, we have constructed a mean-field model to gain insight in the thermodynamics of the breathing. The model shows that the behavior is the result of the different factors at play in a (Nmof,μ,P,T) ensemble (constant amount of MOF material, constant gas chemical potential, constant gas pressure, constant temperature), i.e. the entropy, the pressure and the resistance given by the adsorbed particles. We further investigate how the MOFs' flexibility could be exploited to design an efficient pressure swing setup

An efficient approach for the calculation of frequencies in macromolecules

I. INTRODUCTION. Conformational changes of macromolecules are essential in the understanding of e.g. proteins and drug design. The theoretical prediction is far from trivial, especially for large molecules. In many cases, collective motions are present which occur on a timescale (~ms) that is too long to be accessible through molecular dynamics simulations. Normal mode analysis (NMA) has been proven succesful in exploring the potential energy surface (PES) within the harmonic oscillator approximation. The lowest frequency modes contribute the most to a conformational change. This paper presents a computationally attractive method that selects modes from the lower spectrum

Normal mode analysis of macromolecular systems with the Mobile Block Hessian method

Until recently, normal mode analysis (NMA) was limited to small proteins, not only because the required energy minimization is a computationally exhausting task, but also because NMA requires the expensive diagonalization of a 3Na 3Na matrix with Na the number of atoms. A series of simplified models has been proposed, in particular the Rotation-Translation Blocks (RTB) method by Tama et al. for the simulation of proteins. It makes use of the concept that a peptide chain or protein can be seen as a subsequent set of rigid components, i.e. the peptide units. A peptide chain is thus divided into rigid blocks with six degrees of freedom each. Recently we developed the Mobile Block Hessian (MBH) method, which in a sense has similar features as the RTB method. The main difference is that MBH was developed to deal with partially optimized systems. The position/orientation of each block is optimized while the internal geometry is kept fixed at a plausible – but not necessarily optimized – geometry. This reduces the computational cost of the energy minimization. Applying the standard NMA on a partially optimized structure however results in spurious imaginary frequencies and unwanted coordinate dependence. The MBH avoids these unphysical effects by taking into account energy gradient corrections. Moreover the number of variables is reduced, which facilitates the diagonalization of the Hessian. In the original implementation of MBH, atoms could only be part of one rigid block. The MBH is now extended to the case where atoms can be part of two or more blocks. Two basic linkages can be realized: (1) blocks connected by one link atom, or (2) by two link atoms, where the latter is referred to as the hinge type connection. In this work we present the MBH concept and illustrate its performance with the crambin protein as an example

A theoretical and experimental spectroscopy study on methanol and ethanol conversion over H-SAPO-34

The elucidation of the structure-activity relation of zeolites or zeotype materials remains very challenging. Recent advances in both theoretical and experimental techniques provide new opportunities to study these complex materials and any catalytic reaction occurring inside. In order to establish new active reaction routes, the knowledge of formed intermediates is crucial. The characterization of such intermediates can be done using a variety of spectroscopic techniques. In this contribution, methanol and ethanol conversion over H-SAPO-34 is investigated using IR and UV-VIS measurements. Calculated adsorption enthalpies of methanol and ethanol in a large SAPO 44T finite cluster show the stronger adsorption of the larger alcohol by 14 kJ mol-1. Dispersion contributions are found to be crucial. IR spectra are calculated for the clusters containing the adsorbed alcohols and matched with experimental data. In addition, the cluster is also loaded with singly methylated cationic hydrocarbons as these are representative reaction intermediates. A detailed normal mode analysis is performed, enabling to separate the framework-guest contributions. Based on the computed data in situ DRIFT experimental peaks could be assigned. Finally, contemporary DFT functionals such as CAM-B3LYP seem promising to compute gas phase UV-VIS spectra