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Permeability is a key property in various fields such as membrane technology for chemical separation and transport of substances through cell membranes. At the molecular scale, the counting method uses the number of membrane crossings in a conventional unbiased molecular dynamics simulation to predict the permeability. This contribution investigates under which conditions the counting method has insufficient statistics. An equation is derived for a compartmental model based on the inhomogeneous solubility–diffusion (Smoluchowski) model, giving insight into how the flux correlates with the solubility of permeants. This equation shows that a membrane crossing is a rare event not only when the membrane forms a large free energy barrier but also when the membrane forms a deep free energy well that traps permeants. Such a permeant trap has a high permeability; yet, the counting method suffers from poor statistics. To illustrate this, coarse-grained MD was run for 16 systems of dipalmitoylphosphatidylcholine bilayer membranes with different permeant types. The composition rule for permeability is shown to also hold for fluxes, and it is highlighted that the considered thickness of the membrane causes uncertainty in the permeability calculation of highly permeable membranes. In conclusion, a high permeability in itself is not an effective indicator of the sampling efficiency of the counting method, and caution should be taken for permeants whose solubility varies greatly over the simulation box. A practical consequence relevant in, e.g., drug design is that a drug with high membrane permeability might get trapped by membranes thus reducing its efficacy. [ABSTRACT FROM AUTHOR]

Permeation of many small molecules through lipid bilayers can be directly observed in molecular dynamics simulations on the nano- and microsecond timescale. While unbiased simulations provide an unobstructed view of the permeation process, their feasibility for computing permeability coefficients depends on various factors that differ for each permeant. The present work studies three small molecules for which unbiased simulations of permeation are feasible within less than a microsecond, one hydrophobic (oxygen), one hydrophilic (water), and one amphiphilic (ethanol). Permeabilities are computed using two approaches: counting methods and a maximum-likelihood estimation for the inhomogeneous solubility diffusion (ISD) model. Counting methods yield nearly model-free estimates of the permeability for all three permeants. While the ISD-based approach is reasonable for oxygen, it lacks precision for water due to insufficient sampling and results in misleading estimates for ethanol due to invalid model assumptions. It is also demonstrated that simulations using a Langevin thermostat with collision frequencies of 1/ps and 5/ps yield oxygen permeabilities and diffusion constants that are lower than those using Nosé–Hoover by statistically significant margins. In contrast, permeabilities from trajectories generated with Nosé–Hoover and the microcanonical ensemble do not show statistically significant differences. As molecular simulations become more affordable and accurate, calculation of permeability for an expanding range of molecules will be feasible using unbiased simulations. The present work summarizes theoretical underpinnings, identifies pitfalls, and develops best practices for such simulations. [ABSTRACT FROM AUTHOR]

A Fourier-based method is presented to relate changes of the molecular structure during a molecular dynamics simulation with fluctuations in the electronic excitation energy. The method implies sampling of the ground state potential energy surface. Subsequently, the power spectrum of the velocities is compared with the power spectrum of the excitation energy computed using timedependent density functional theory. Peaks in both spectra are compared, and motions exhibiting a linear or quadratic behavior can be distinguished. The quadratically active motions are mainly responsible for the changes in the excitation energy and hence cause shifts between the dynamic and static values of the spectral property. Moreover, information about the potential energy surface of various excited states can be obtained. The procedure is illustrated with three case studies. The first electronic excitation is explored in detail and dominant vibrational motions responsible for changes in the excitation energy are identified for ethylene, biphenyl, and hexamethylbenzene. The proposed method is also extended to other low-energy excitations. Finally, the vibrational fingerprint of the excitation energy of a more complex molecule, in particular the azo dye ethyl orange in a water environment, is analyzed. [ABSTRACT FROM AUTHOR]

An efficient protocol is presented to compensate for the basis set superposition error (BSSE) in DFT molecular dynamics (MD) simulations using localized Gaussian basis sets. We propose a classical correction term that can be added a posteriori to account for BSSE. It is tested to what extension this term will improve radial distribution functions (RDFs). The proposed term is pairwise between certain atoms in different molecules and was calibrated by fitting reference BSSE data points computed with the counterpoise method. It is verified that the proposed exponential decaying functional form of the model is valid. This work focuses on hydrogen-bonded liquids, i.e., methanol, and more specific on the intermolecular hydrogen bond, but in principle the method is generally applicable on any type of interaction where BSSE is significant. We evaluated the relative importance of the Grimme-dispersion versus BSSE and found that they are of the same order of magnitude, but with an opposite sign. Upon introduction of the correction, the relevant RDFs, obtained from MD, have amplitudes equal to experiment. [ABSTRACT FROM AUTHOR]

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 α-helix conformation of an alanine-20-polypeptide. [ABSTRACT FROM AUTHOR]

A new vibrational subsystem analysis (VSA) method is presented for coupling global motion to a local subsystem while including the inertial effects of the environment. The premise of the VSA method is a partitioning of a system into a smaller region of interest and a usually larger part referred to as environment. This method allows the investigation of local-global coupling, a more accurate estimation of vibrational free energy contribution for parts of a large system, and the elimination of the “tip effect” in elastic network model calculations. Additionally, the VSA method can be used as a probe of specific degrees of freedom that may contribute to free energy differences. The VSA approach can be employed in many ways, but it will likely be most useful for estimating activation free energies in QM/MM reaction path calculations. Four examples are presented to demonstrate the utility of this method. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A Fourier-based method is presented to relate changes of the molecular structure during a molecular dynamics simulation with fluctuations in the electronic excitation energy. The method implies sampling of the ground state potential energy surface. Subsequently, the power spectrum of the velocities is compared with the power spectrum of the excitation energy computed using time-dependent density functional theory. Peaks in both spectra are compared, and motions exhibiting a linear or quadratic behavior can be distinguished. The quadratically active motions are mainly responsible for the changes in the excitation energy and hence cause shifts between the dynamic and static values of the spectral property. Moreover, information about the potential energy surface of various excited states can be obtained. The procedure is illustrated with three case studies. The first electronic excitation is explored in detail and dominant vibrational motions responsible for changes in the excitation energy are identified for ethylene, biphenyl, and hexamethylbenzene. The proposed method is also extended to other low-energy excitations. Finally, the vibrational fingerprint of the excitation energy of a more complex molecule, in particular the azo dye ethyl orange in a water environment, is analyzed.