Normal modes for large molecules with arbitrary link constraints in the mobile block Hessian approach.

In a previous paper [Ghysels et al., J. Chem. Phys. 126, 224102 (2007)] the mobile block Hessian (MBH) approach was presented. The method was designed to accurately compute vibrational modes of partially optimized molecular structures. The key concept was the introduction of several blocks of atoms, which can move as rigid bodies with respect to a local, fully optimized subsystem. The choice of the blocks was restricted in the sense that none of them could be connected, and also linear blocks were not taken into consideration. In this paper an extended version of the MBH method is presented that is generally applicable and allows blocks to be adjoined by one or two common atoms. This extension to all possible block partitions of the molecule provides a structural flexibility varying from very rigid to extremely relaxed. The general MBH method is very well suited to study selected normal modes of large macromolecules (such as proteins and polymers) because the number of degrees of freedom can be greatly reduced while still keeping the essential motions of the molecular system. The reduction in the number of degrees of freedom due to the block linkages is imposed here directly using a constraint method, in contrast to restraint methods where stiff harmonic couplings are introduced to restrain the relative motion of the blocks. The computational cost of this constraint method is less than that of an implementation using a restraint method. This is illustrated for the alpha-helix conformation of an alanine-20-polypeptide.

A Comparison of Barostats for the Mechanical Characterization of Metal-Organic Frameworks.

In this paper, three barostat coupling schemes for pressure control, which are commonly used in molecular dynamics simulations, are critically compared to characterize the rigid MOF-5 and flexible MIL-53(Al) metal-organic frameworks. We investigate the performance of the three barostats, the Berendsen, the Martyna-Tuckerman-Tobias-Klein (MTTK), and the Langevin coupling methods, in reproducing the cell parameters and the pressure versus volume behavior in isothermal-isobaric simulations. A thermodynamic integration method is used to construct the free energy profiles as a function of volume at finite temperature. It is observed that the aforementioned static properties are well-reproduced with the three barostats. However, for static properties depending nonlinearly on the pressure, the Berendsen barostat might give deviating results as it suppresses pressure fluctuations more drastically. Finally, dynamic properties, which are directly related to the fluctuations of the cell, such as the time to transition from the large-pore to the closed-pore phase, cannot be well-reproduced by any of the coupling schemes.

Mobile Block Hessian Approach with Adjoined Blocks: An Efficient Approach for the Calculation of Frequencies in Macromolecules.

In an earlier work, the authors developed a new method, the mobile block Hessian (MBH) approach, to accurately calculate vibrational modes for partially optimized molecular structures [ J. Chem. Phys. 2007 , 126 ( 22 ), 224102. ]. It is based on the introduction of blocks, consisting of groups of atoms, that can move as rigid bodies. The internal geometry of the blocks need not correspond to an overall optimization state of the total molecular structure. The standard MBH approach considers free blocks with six degrees of freedom. In the extended MBH approach introduced herein, the blocks can be connected by one or two adjoining atoms, which further reduces the number of degrees of freedom. The new approach paves the way for the normal-mode analysis of biomolecules such as proteins. It rests on the hypothesis that low-frequency modes of proteins can be described as pure rigid-body motions of blocks of consecutive amino acid residues. The method is validated for a series of small molecules and further applied to alanine dipeptide as a prototype to describe vibrational interactions between two peptide units; to crambin, a small protein with 46 amino acid residues; and to ICE/caspase-1, which contains 518 amino acid residues.

Calculating Reaction Rates with Partial Hessians: Validation of the Mobile Block Hessian Approach.

In an earlier paper, the authors have developed a new method, the mobile block Hessian (MBH), to accurately calculate vibrational modes for partially optimized molecular structures [J. Chem. Phys. 2007, 126 (22), 224102]. The proposed procedure remedies the artifact of imaginary frequencies, occurring in standard frequency calculations, when parts of the molecular system are optimized at different levels of theory. Frequencies are an essential ingredient in predicting reaction rate coefficients due to their input in the vibrational partition functions. The question arises whether the MBH method is able to describe the chemical reaction kinetics in an accurate way in large molecular systems where a full quantum chemical treatment at a reasonably high level of theory is unfeasible due to computational constraints. In this work, such a validation is tested in depth. The MBH method opens a lot of perspectives in predicting accurate kinetic parameters in chemical reactions where the standard full Hessian procedure fails.

Cartesian formulation of the mobile block Hessian approach to vibrational analysis in partially optimized systems.

Partial optimization is a useful technique to reduce the computational load in simulations of extended systems. In such nonequilibrium structures, the accurate calculation of localized vibrational modes can be troublesome, since the standard normal mode analysis becomes inappropriate. In a previous paper [A. Ghysels et al., J. Chem. Phys. 126, 224102 (2007)], the mobile block Hessian (MBH) approach was presented to deal with the vibrational analysis in partially optimized systems. In the MBH model, the nonoptimized regions of the system are represented by one or several blocks, which can move as rigid bodies with respect to the atoms of the optimized region. In this way unphysical imaginary frequencies are avoided and the translational/rotational invariance of the potential energy surface is fully respected. In this paper we focus on issues concerning the practical numerical implementation of the MBH model. The MBH normal mode equations are worked out for several coordinate choices. The introduction of a consistent group-theoretical notation facilitates the treatment of both the case of a single block and the case of multiple blocks. Special attention is paid to the formulation in terms of Cartesian variables, in order to provide a link with the standard output of common molecular modeling programs.

Vibrational modes in partially optimized molecular systems.

In this paper the authors develop a method to accurately calculate localized vibrational modes for partially optimized molecular structures or for structures containing link atoms. The method avoids artificially introduced imaginary frequencies and keeps track of the invariance under global translations and rotations. Only a subblock of the Hessian matrix has to be constructed and diagonalized, leading to a serious reduction of the computational time for the frequency analysis. The mobile block Hessian approach (MBH) proposed in this work can be regarded as an extension of the partial Hessian vibrational analysis approach proposed by Head [Int. J. Quantum Chem. 65, 827 (1997)]. Instead of giving the nonoptimized region of the system an infinite mass, it is allowed to move as a rigid body with respect to the optimized region of the system. The MBH approach is then extended to the case where several parts of the molecule can move as independent multiple rigid blocks in combination with single atoms. The merits of both models are extensively tested on ethanol and di-n-octyl-ether.