Vibrational modes in partially optimized molecular systems

The Amsterdam Modeling Suite

In this paper, we present the Amsterdam Modeling Suite (AMS), a comprehensive software platform designed to support advanced molecular and materials simulations across a wide range of chemical and physical systems. AMS integrates cutting-edge quantum chemical methods, including Density Functional Theory (DFT) and time-dependent DFT, with molecular mechanics, fluid thermodynamics, machine learning techniques, and more, to enable multi-scale modeling of complex chemical systems. Its design philosophy allows for seamless coupling between components, facilitating simulations that range from small molecules to complex biomolecular and solid-state systems, making it a versatile tool for tackling interdisciplinary challenges, both in industry and in academia. The suite also emphasizes user accessibility, with an intuitive graphical interface, extensive scripting capabilities, and compatibility with high-performance computing environments.

Local Bond-Stretch Coordinates for Anharmonic Vibrational Computations

The local bond-stretch (LBS) method is presented as a means of obtaining a set of localized, rectilinear vibrational modes. Three variants of the LBS method are considered: pure LBS, projected LBS (pLBS), and orthogonal, projected LBS (opLBS). These variants feature different degrees of localization and different coupling terms in the kinetic energy operator, such that the most localized method (LBS) has the largest number and magnitude of coupling terms, and the least localized (opLBS) has the least coupling terms. The different LBS variants are exemplified in computations on overtone vibrational spectra of water, nitroxyl (chemical formula HNO), formaldehyde, and 1,3-butadiene computed with a vibrational coupled cluster band Lanczos approach. These spectra are calculated using potential energy surfaces (PESs) obtained with the adaptive density-guided approach (ADGA). We observe faster convergence with respect to the coupling level in the PES when using the LBS variants compared to normal coordinates. Among the LBS variants, pLBS and opLBS appear most promising.

Assessing the Partial Hessian Approximation in QM/MM-Based Vibrational Analysis

The partial Hessian approximation is often used in vibrational analysis of quantum mechanics/molecular mechanics (QM/MM) systems because calculating the full Hessian matrix is computationally impractical. This approach aligns with the core concept of QM/MM, which focuses on the QM subsystem. Thus, using the partial Hessian approximation implies that the main interest is in the local vibrational modes of the QM subsystem. Here, we investigate the accuracy and applicability of the partial Hessian vibrational analysis (PHVA) approach as it is typically used within QM/MM, i.e., only the Hessian belonging to the QM subsystem is computed. We focus on solute-solvent systems with small, rigid solutes. To separate two of the major sources of errors, we perform two separate analyses. First, we study the effects of the partial Hessian approximation on local normal modes, harmonic frequencies, and harmonic IR and Raman intensities by comparing them to those obtained using full Hessians, where both partial and full Hessians are calculated at the QM level. Then, we quantify the errors introduced by QM/MM used with the PHVA by comparing normal modes, frequencies, and intensities obtained using partial Hessians calculated using a QM/MM-type embedding approach to those obtained using partial Hessians calculated at the QM level. Another aspect of the PHVA is the appearance of normal modes resembling the translation and rotation of the QM subsystem. These pseudotranslational and pseudorotational modes should be removed as they are collective vibrations of the atoms in the QM subsystem relative to a frozen MM subsystem and, thus, not well-described. We show that projecting out translation and rotation, usually done for systems in isolation, can adversely affect other normal modes. Instead, the pseudotranslational and pseudorotational modes can be identified and removed.

Efficient Method for Numerical Calculations of Molecular Vibrational Frequencies by Exploiting Sparseness of Hessian Matrix

Molecular vibrational frequency analysis plays an important role in theoretical and computational chemistry. However, in many cases, the analytical frequencies are unavailable, whereas frequency calculations using conventional numerical methods are very expensive. In this work, we propose an efficient method to numerically calculate the frequencies. Our main strategies are to exploit the sparseness of the Hessian matrix and to construct the N-fold two-variable potential energy surfaces to fit the parabola parameters, which are later used for the construction of Hessian matrices. A set of benchmark calculations is performed for typical molecules of different sizes and complexities using the proposed method. The obtained frequencies are compared to those calculated with the analytical methods and conventional numerical methods. It is shown that the results yielded with the new method are in very good agreement with corresponding accurate values (with a maximum error of ∼20 cm-1), while the required computation resource is largely reduced compared to that required by conventional numerical methods. For medium-sized molecules, the calculational scaling is lowered to O(N1.6) (this work) from that of O(N2) (conventional numerical methods). For even larger molecules, more computational savings can be achieved, and the scaling is estimated to be quasilinear with respect to the molecular size.

Development of a universal method for vibrational analysis of the terminal alkyne C≡C stretch

The terminal alkyne C≡C stretch has a large Raman scattering cross section in the "silent" region for biomolecules. This has led to many Raman tag and probe studies using this moiety to study biomolecular systems. A computational investigation of these systems is vital to aid in the interpretation of these results. In this work, we develop a method for computing terminal alkyne vibrational frequencies and isotropic transition polarizabilities that can easily and accurately be applied to any terminal alkyne molecule. We apply the discrete variable representation method to a localized version of the C≡C stretch normal mode. The errors of (1) vibrational localization to the terminal alkyne moiety, (2) anharmonic normal mode isolation, and (3) discretization of the Born-Oppenheimer potential energy surface are quantified and found to be generally small and cancel each other. This results in a method with low error compared to other anharmonic vibrational methods like second-order vibrational perturbation theory and to experiments. Several density functionals are tested using the method, and TPSS-D3, an inexpensive nonempirical density functional with dispersion corrections, is found to perform surprisingly well. Diffuse basis functions are found to be important for the accuracy of computed frequencies. Finally, the computation of vibrational properties like isotropic transition polarizabilities and the universality of the localized normal mode for terminal alkynes are demonstrated.

The Role of Water in Carbon Dioxide Adsorption in Porphyrinic Metal-Organic Frameworks

Capturing and converting CO2 through artificial photosynthesis using photoactive, porous materials is a promising approach for addressing increasing CO2 concentrations. Porphyrinic Zr-based metal-organic frameworks (MOFs) are of particular interest as they incorporate a photosensitizer in the porous structure. Herein, the initial step of the artificial photosynthesis is studied: CO2 sorption and activation in the presence of water. A combined vibrational and visible spectroscopic approach was used to monitor the adsorption of CO2 into PCN-222 and PCN-223 MOFs, and the photophysical changes of the porphyrinic linker as a function of water concentration. A shift in CO2 sorption site and bending of the porphyrin macrocycle in response to humidity was observed, and CO2/H2O competition experiments revealed that the exchange of CO2 with H2O is pore-size dependent. Therefore, humidity and pore-size can be used to tune CO2 sorption, CO2 capacity, and light harvesting in porphyrinic MOFs, which are key factors for CO2 photoreduction.

A Comprehensive Review on Zeolite Chemistry for Catalytic Conversion of Biomass/Waste into Green Fuels

Numerous attempts have been made to produce new materials and technology for renewable energy and environmental improvements in response to global sustainable solutions stemming from fast industrial expansion and population growth. Zeolites are a group of crystalline materials having molecularly ordered micropore arrangements. Over the past few years, progress in zeolites has been observed in transforming biomass and waste into fuels. To ensure effective transition of fossil energy carriers into chemicals and fuels, zeolite catalysts play a key role; however, their function in biomass usage is more obscure. Herein, the effectiveness of zeolites has been discussed in the context of biomass transformation into valuable products. Established zeolites emphasise conversion of lignocellulosic materials into green fuels. Lewis acidic zeolites employ transition of carbohydrates into significant chemical production. Zeolites utilise several procedures, such as catalytic pyrolysis, hydrothermal liquefaction, and hydro-pyrolysis, to convert biomass and lignocelluloses. Zeolites exhibit distinctive features and encounter significant obstacles, such as mesoporosity, pore interconnectivity, and stability of zeolites in the liquid phase. In order to complete these transformations successfully, it is necessary to have a thorough understanding of the chemistry of zeolites. Hence, further examination of the technical difficulties associated with catalytic transformation in zeolites will be required. This review article highlights the reaction pathways for biomass conversion using zeolites, their challenges, and their potential utilisation. Future recommendations for zeolite-based biomass conversion are also presented.

Understanding the Catalytic Activity of Microporous and Mesoporous Zeolites in Cracking by Experiments and Simulations

Porous zeolite catalysts have been widely used in the industry for the conversion of fuel-range molecules for decades. They have the advantages of higher surface area, better hydrothermal stability, and superior shape selectivity, which make them ideal catalysts for hydrocarbon cracking in the petrochemical industry. However, the catalytic activity and selectivity of zeolites for hydrocarbon cracking are significantly affected by the zeolite topology and composition. The aim of this review is to survey recent investigations on hydrocarbon cracking and secondary reactions in micro- and mesoporous zeolites, with the emphasis on the studies of the effects of different porous environments and active site structures on alkane adsorption and activation at the molecular level. The pros and cons of different computational methods used for zeolite simulations are also discussed in this review.

Discrete Oligomers and Polymers of Chloride Monohydrate Can Form in Encapsulated Environments: Structures and Infrared Spectra of [Cl4 (H2 O)4 ]4- and {[Cl(H2 O)]- }∞

A discrete tetrachloride tetrahydrate cluster, [Cl₄ (H₂ O)₄ ]^4- , was obtained with a partially-fluorinated triaminocyclopropenium cation, [C₃ (N(CH₂ CF₃ )₂ )(NEt₂ )(NPr₂ )]⁺ . The cluster consists of a [Cl₂ (H₂ O)₂ ]^2- square with each Cl^- coordinated by another H₂ O bridged to another Cl^- . A 1D polymer of chloride monohydrate, {[Cl(H₂ O)]^- }_∞ , was obtained with [C₃ (N(CH₂ CF₃ )₂ )₂ (NBuMe)]⁺ . The tetrameric and polymeric structures were found to be computationally-unstable in the gas phase which indicates that an encapsulated environment is essential for their isolation. DFT and DFTB calculations were carried out on gas-phase [Cl₄ (H₂ O)₄ ]^4- to assist the infrared assignments. Anharmonically-corrected B3LYP transition frequencies were in close agreement with experiment, but DFTB models were only appropriate for qualitative interpretation. Solid-state DFTB calculations allowed the vibrational modes to be assigned. The results found are consistent with "discrete" chloride hydrates.

Partitioning of the Vibrational Free Energy

Vibrational energies are partitioned into the contributions of molecular parts called segments, for instance, residues in proteins. The fragment molecular orbital method is used to facilitate vibrational calculations of large systems at the DFTB and HF-3c levels. The vibrational analysis is combined with the partitioning of the electronic energy, yielding free-energy contributions of segments to the binding energy, pinpointing hot spots for drug discovery and other studies. The analysis is illustrated on two protein-ligand complexes in solution.

A revised formulation of the generalized subsystem vibrational analysis (GSVA)

In this work, a simplified formulation of our recently developed generalized subsystem vibrational analysis (GSVA) for obtaining intrinsic fragmental vibrations (J Chem Theory Comput 14:2558, 2018) is presented. In contrast to the earlier implementation, which requires the explicit definition of a non-redundant set of internal coordinate parameters to be constructed for the subsystem, the new implementation circumvents this process by employing massless Eckart conditions to the subsystem fragment paired with a Gram-Schmidt orthogonalization to span the same internal vibration space indirectly. This revised version of GSVA (rev-GSVA) can be applied to equilibrium structure as well as transition state structure, and it has been incorporated into the open-source package UniMoVib (https://github.com/zorkzou/UniMoVib).

Supplementary Information

The online version contains supplementary material available at 10.1007/s00214-021-02727-y.

Coupled transport of electrons and protons in a bacterial cytochrome c oxidase-DFT calculated properties compared to structures and spectroscopies

After a general introduction to the features and mechanisms of cytochrome c oxidases (CcOs) in mitochondria and aerobic bacteria, we present DFT calculated physical and spectroscopic properties for the catalytic reaction cycle compared with experimental observations in bacterial ba3 type CcO, also with comparisons/contrasts to aa3 type CcOs. The Dinuclear Complex (DNC) is the active catalytic reaction center, containing a heme a3 Fe center and a near lying Cu center (called CuB) where by successive reduction and protonation, molecular O2 is transformed to two H2O molecules, and protons are pumped from an inner region across the membrane to an outer region by transit through the CcO integral membrane protein. Structures, energies and vibrational frequencies for Fe-O and O-O modes are calculated by DFT over the catalytic cycle. The calculated DFT frequencies in the DNC of CcO are compared with measured frequencies from Resonance Raman spectroscopy to clarify the composition, geometry, and electronic structures of different intermediates through the reaction cycle, and to trace reaction pathways. X-ray structures of the resting oxidized state are analyzed with reference to the known experimental reaction chemistry and using DFT calculated structures in fitting observed electron density maps. Our calculations lead to a new proposed reaction pathway for coupling the PR → F → OH (ferryl-oxo → ferric-hydroxo) pathway to proton pumping by a water shift mechanism. Through this arc of the catalytic cycle, major shifts in pKa's of the special tyrosine and a histidine near the upper water pool activate proton transfer. Additional mechanisms for proton pumping are explored, and the role of the CuB+ (cuprous state) in controlling access to the dinuclear reaction site is proposed.

A Series of Discrete Dichloride Dihydrates: Characterisation and Symmetry Effects

A series of three discrete dichloride dihydrates [Cl₂ (H₂ O)₂ ]^2- have been isolated with different triaminocyclopropenium (TAC) cations and with different crystallographic symmetries. The cluster exhibits D_2h symmetry with the tris(dimethylamino)cyclopropenium cation [C₃ (NMe₂ )₃ ]⁺ , C_2h symmetry with the fluorinated cation [C₃ (N(CH₂ CF₃ )₂ )(NBu₂ )₂ ]⁺ (containing two 2,2,2-trifluoroethyl substituents) and C_2v symmetry with the more fluorinated [C₃ (N(CH₂ CF₃ )₂ )₂ (NBu₂ )]⁺ cation. The effect of symmetry on the infrared spectra of the dichloride ion-pair clusters, as well as deuterated analogues, has been investigated. The D_2h - and C_2h -symmetric clusters each exhibit two stretching bands in the infrared at 3427 and 3368 cm^-1 for D_2h symmetry and 3444 and 3392 cm^-1 for C_2h symmetry, whereas the C_2v -symmetric cluster exhibits three bands at 3475, 3426 and 3373 cm^-1 . Computational studies were carried out on a [Cl₂ (H₂ O)₂ ]^2- cluster with C_2v symmetry to aid the infrared band assignments.

DFT Fea3-O/O-O Vibrational Frequency Calculations over Catalytic Reaction Cycle States in the Dinuclear Center of Cytochrome c Oxidase

Density functional vibrational frequency calculations have been performed on eight geometry optimized cytochrome c oxidase (CcO) dinuclear center (DNC) reaction cycle intermediates and on the oxymyoglobin (oxyMb) active site. The calculated Fe-O and O-O stretching modes and their frequency shifts along the reaction cycle have been compared with the available resonance Raman (rR) measurements. The calculations support the proposal that in state A[Fea33+-O2-•···CuB+] of CcO, O2 binds with Fea32+ in a similar bent end-on geometry to that in oxyMb. The calculations show that the observed 20 cm-1 shift of the Fea3-O stretching mode from the PR to F state is caused by the protonation of the OH- ligand on CuB2+ (PR[Fea34+═O2-···HO--CuB2+] → F[Fea34+═O2-···H2O-CuB2+]), and that the H2O ligand is still on the CuB2+ site in the rR identified F[Fea34+═O2-···H2O-CuB2+] state. Further, the observed rR band at 356 cm-1 between states PR and F is likely an O-Fea3-porphyrin bending mode. The observed 450 cm-1 low Fea3-O frequency mode for the OH active oxidized state has been reproduced by our calculations on a nearly symmetrically bridged Fea33+-OH-CuB2+ structure with a relatively long Fea3-O distance near 2 Å. Based on Badger's rule, the calculated Fea3-O distances correlate well with the calculated νFe-O-2/3 (νFe-O is the Fea3-O stretching frequency) with correlation coefficient R = 0.973.

Measuring Local Electric Fields and Local Charge Densities at Electrode Surfaces Using Graphene-Enhanced Raman Spectroscopy (GERS)-Based Stark-Shifts

We report spectroscopic measurements of the local electric fields and local charge densities at electrode surfaces using graphene-enhanced Raman spectroscopy (GERS) based on the Stark-shifts of surface-bound molecules and the G band frequency shift in graphene. Here, monolayer graphene is used as the working electrode in a three-terminal potentiostat while Raman spectra are collected in situ under applied electrochemical potentials using a water immersion lens. First, a thin layer (1 Å) of copper(II) phthalocyanine (CuPc) molecules are deposited on monolayer graphene by thermal evaporation. GERS spectra are then taken in an aqueous solution as a function of the applied electrochemical potential. The shifts in vibrational frequencies of the graphene G band and CuPc are obtained simultaneously and correlated. The upshifts in the G band Raman mode are used to determine the free carrier density in the graphene sheet under these applied potentials. Of the three dominant peaks in the Raman spectra of CuPc (i.e., 1531, 1450, and 1340 cm^-1), only the 1531 cm^-1 peak exhibits Stark-shifts and can, thus, be used to report the local electric field strength at the electrode surface under electrochemical working conditions. Between applied electrochemical potentials from -0.8 V to 0.8 V vs NHE, the free carrier density in the graphene electrode spans a range from -4 × 10¹² cm^-2 to 2 × 10¹² cm^-2. Corresponding Stark-shifts in the CuPc peak around 1531 cm^-1 are observed up to 1.0 cm^-1 over a range of electric field strengths between -3.78 × 10⁶ and 1.85 × 10⁶ V/cm. Slightly larger Stark-shifts are observed in a 1 M KCl solution, compared to those observed in DI water, as expected based on the higher ion concentration of the electrolyte. Based on our data, we determine the Stark shift tuning rate to be 0.178 cm^-1/ (10⁶ V/cm), which is relatively small due to the planar nature of the CuPc molecule, which largely lies perpendicular to the electric field at this electrode surface. Computational simulations using density functional theory (DFT) predict similar Stark shifts and provide a detailed atomistic picture of the electric field-induced perturbations to the surface-bound CuPc molecules.

Observation of an oxonium ion intermediate in ethanol dehydration to ethene on zeolite

Zeolite-catalyzed dehydration of ethanol offers promising perspectives for the sustainable production of ethene. Complex parallel-consecutive pathways are proposed to be involved in the reaction network of ethanol dehydration on zeolites, where the initial step of ethanol dehydration is still unclear particularly for the favorable production of ethene at lower temperature. Here we report the observation of a triethyloxonium ion (TEO) in the dehydration of ethanol on zeolite H-ZSM-5 by using ex situ and in situ solid-state NMR spectroscopy. TEO is identified as a stable surface species on the working catalyst, which shows high reactivity during reaction. Ethylation of the zeolite by TEO occurs at lower temperature, leading to the formation of surface ethoxy species and then ethene. The TEO-ethoxide pathway is found to be energetically preferable for the dehydration of ethanol to ethene in the initial stage, which is also supported by theoretical calculations.

Use of Density Functional Based Tight Binding Methods in Vibrational Circular Dichroism

Vibrational circular dichroism (VCD) is a spectroscopic technique used to resolve the absolute configuration of chiral systems. Obtaining a theoretical VCD spectrum requires computing atomic polar and axial tensors on top of the computationally demanding construction of the force constant matrix. In this study we evaluated a VCD model in which all necessary quantities are obtained with density functional based tight binding (DFTB) theory. The analyzed DFTB parametrizations fail at providing accurate vibrational frequencies and electric dipole gradients but yield reasonable normal modes at a fraction of the computational cost of density functional theory (DFT). Thus, by applying DFTB in composite methods along with DFT, we show that it is possible to obtain accurate VCD spectra at a much lower computational demand.

Frequency Range Selection Method for Vibrational Spectra

Theoretical calculations of vibrational properties are widely used to explain and predict experimental spectra. However, with standard quantum chemical methods all molecular motions are considered, which is rather time-consuming for large molecules. Because typically only a specific spectral region is of experimental interest, we propose here an efficient method that allows calculation of only a selected frequency interval. After a computationally cheap low-level estimate of the molecular motions, the computational time is proportional to the number of normal modes needed to describe this frequency range. Results for a medium-sized molecule show a reduction in computational time of up to 1 order of magnitude with negligible loss in accuracy. We also show that still larger computational savings are possible by using an additional intensity-selection procedure.

Brønsted/Lewis acid sites synergistically promote the initial C-C bond formation in the MTO reaction

The Lewis acid site combined with a Brønsted acid site in zeolite catalysts facilitates first C–C bond formation in the initiation step of the MTO reaction.

The methanol-to-olefin (MTO) reaction is an active field of research due to conflicting mechanistic proposals for the initial carbon–carbon (C–C) bond formation. Herein, a new methane–formaldehyde pathway, a Lewis acid site combined with a Brønsted acid site in zeolite catalysts can readily activate dimethyl ether (DME) to form ethene, is identified theoretically. The mechanism involves a hydride transfer from Al–OCH₃ on the Lewis acid site to the methyl group of the protonated methanol molecule on the adjacent Brønsted acid site leading to synchronous formation of methane and Al–COH₂⁺ (which can be considered as formaldehyde (HCHO) adsorbed on the Al³⁺ Lewis acid sites). The strong electrophilic character of the Al–COH₂⁺ intermediate can strongly accelerate the C–C bond formation with CH₄, as indicated by the significant decrease of activation barriers in the rate-determining-step of the catalytic processes. These results highlight a synergy of extra-framework aluminum (EFAl) Lewis and Brønsted sites in zeolite catalysts that facilitates initial C–C bond formation in the initiation step of the MTO reaction via the Al–COH₂⁺ intermediate.

Identifying the effective phosphorous species over modified P-ZSM-5 zeolite: a theoretical study

In this work, a density functional theory (DFT) study was carried out to address the fundamental description of the effective phosphorous species that could improve the framework stability and reduce the coke deposition formation on the P-ZSM-5 zeolite.

Metal-organic and covalent organic frameworks as single-site catalysts

Heterogeneous single-site catalysts consist of isolated, well-defined, active sites that are spatially separated in a given solid and, ideally, structurally identical. In this review, the potential of metal-organic frameworks (MOFs) and covalent organic frameworks (COFs) as platforms for the development of heterogeneous single-site catalysts is reviewed thoroughly. In the first part of this article, synthetic strategies and progress in the implementation of such sites in these two classes of materials are discussed. Because these solids are excellent playgrounds to allow a better understanding of catalytic functions, we highlight the most important recent advances in the modelling and spectroscopic characterization of single-site catalysts based on these materials. Finally, we discuss the potential of MOFs as materials in which several single-site catalytic functions can be combined within one framework along with their potential as powerful enzyme-mimicking materials. The review is wrapped up with our personal vision on future research directions.

Vibrational intensities in the mobile block Hessian approximation

Herein we present a proof of concept for the recovery of vibrational intensities from density functional theory vibrational calculations performed in the Mobile Block Hessian (MBH) approximation, which constrains the internal degrees of freedom of designated subsets of a molecule. We compare and contrast the behaviour of this methodology with respect to conventional vibrational calculations, and characterise the performance and accuracy of our method with respect to the size of MBH constrained regions within a variety of species. We demonstrate the viability of this method as a means by which to obtain vibrational intensities for regions of interest within a molecule whilst potentially dramatically reducing computational expense with respect to conventional all-atom vibrational calculations, and discuss caveats for application.

External or internal surface of H-ZSM-5 zeolite, which is more effective for the Beckmann rearrangement reaction?

The influence of Brønsted acid site location on the Beckmann rearrangement reaction over H-ZSM-5 zeolite has been explored.

Anharmonic Theoretical Vibrational Spectroscopy of Polypeptides

Because of the size of polypeptides and proteins, the quantum-chemical prediction of their vibrational spectra presents an exceptionally challenging task. Here, we address one of these challenges, namely, the inclusion of anharmonicities. By performing the expansion of the potential energy surface in localized-mode coordinates instead of the normal-mode coordinates, it becomes possible to calculate anharmonic vibrational spectra of polypeptides efficiently and reliably. We apply this approach to calculate the infrared, Raman, and Raman optical activity spectra of helical alanine polypeptides consisting of up to 20 amino acids. We find that while anharmonicities do not alter the band shapes, simple scaling procedures cannot account for the different shifts found for the individual bands. This closes an important gap in theoretical vibrational spectroscopy by making it possible to quantify the anharmonic contributions and opens the door to a first-principles calculation of multidimensional vibrational spectra.

Predicting accurate absolute binding energies in aqueous solution: thermodynamic considerations for electronic structure methods

Recent predictions of absolute binding free energies of host-guest complexes in aqueous solution using electronic structure theory have been encouraging for some systems, while other systems remain problematic. In this paper I summarize some of the many factors that could easily contribute 1-3 kcal mol(-1) errors at 298 K: three-body dispersion effects, molecular symmetry, anharmonicity, spurious imaginary frequencies, insufficient conformational sampling, wrong or changing ionization states, errors in the solvation free energy of ions, and explicit solvent (and ion) effects that are not well-represented by continuum models. While I focus on binding free energies in aqueous solution the approach also applies (with minor adjustments) to any free energy difference such as conformational or reaction free energy differences or activation free energies in any solvent.

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.

Multi-scaled normal mode analysis method for dynamics simulation of protein-membrane complexes: A case study of potassium channel gating motion correlations

Membrane proteins play critically important roles in many cellular activities such as ions and small molecule transportation, signal recognition, and transduction. In order to fulfill their functions, these proteins must be placed in different membrane environments and a variety of protein-lipid interactions may affect the behavior of these proteins. One of the key effects of protein-lipid interactions is their ability to change the dynamics status of membrane proteins, thus adjusting their functions. Here, we present a multi-scaled normal mode analysis (mNMA) method to study the dynamics perturbation to the membrane proteins imposed by lipid bi-layer membrane fluctuations. In mNMA, channel proteins are simulated at all-atom level while the membrane is described with a coarse-grained model. mNMA calculations clearly show that channel gating motion can tightly couple with a variety of membrane deformations, including bending and twisting. We then examined bi-channel systems where two channels were separated with different distances. From mNMA calculations, we observed both positive and negative gating correlations between two neighboring channels, and the correlation has a maximum as the channel center-to-center distance is close to 2.5 times of their diameter. This distance is larger than recently found maximum attraction distance between two proteins embedded in membrane which is 1.5 times of the protein size, indicating that membrane fluctuation might impose collective motions among proteins within a larger area. The hybrid resolution feature in mNMA provides atomic dynamics information for key components in the system without costing much computer resource. We expect it to be a conventional simulation tool for ordinary laboratories to study the dynamics of very complicated biological assemblies. The source code is available upon request to the authors.

Advances in theory and their application within the field of zeolite chemistry

Zeolites are versatile and fascinating materials which are vital for a wide range of industries, due to their unique structural and chemical properties, which are the basis of applications in gas separation, ion exchange and catalysis. Given their economic impact, there is a powerful incentive for smart design of new materials with enhanced functionalities to obtain the best material for a given application. Over the last decades, theoretical modeling has matured to a level that model guided design has become within reach. Major hurdles have been overcome to reach this point and almost all contemporary methods in computational materials chemistry are actively used in the field of modeling zeolite chemistry and applications. Integration of complementary modeling approaches is necessary to obtain reliable predictions and rationalizations from theory. A close synergy between experimentalists and theoreticians has led to a deep understanding of the complexity of the system at hand, but also allowed the identification of shortcomings in current theoretical approaches. Inspired by the importance of zeolite characterization which can now be performed at the single atom and single molecule level from experiment, computational spectroscopy has grown in importance in the last decade. In this review most of the currently available modeling tools are introduced and illustrated on the most challenging problems in zeolite science. Directions for future model developments will be given.

Correcting for the free energy costs of bond or angle constraints in molecular dynamics simulations

BACKGROUND

Free energy simulations are an important tool in the arsenal of computational biophysics, allowing the calculation of thermodynamic properties of binding or enzymatic reactions. This paper introduces methods to increase the accuracy and precision of free energy calculations by calculating the free energy costs of constraints during post-processing. The primary purpose of employing constraints for these free energy methods is to increase the phase space overlap between ensembles, which is required for accuracy and convergence.

METHODS

The free energy costs of applying or removing constraints are calculated as additional explicit steps in the free energy cycle. The new techniques focus on hard degrees of freedom and use both gradients and Hessian estimation. Enthalpy, vibrational entropy, and Jacobian free energy terms are considered.

RESULTS

We demonstrate the utility of this method with simple classical systems involving harmonic and anharmonic oscillators, four-atomic benchmark systems, an alchemical mutation of ethane to methanol, and free energy simulations between alanine and serine. The errors for the analytical test cases are all below 0.0007kcal/mol, and the accuracy of the free energy results of ethane to methanol is improved from 0.15 to 0.04kcal/mol. For the alanine to serine case, the phase space overlaps of the unconstrained simulations range between 0.15 and 0.9%. The introduction of constraints increases the overlap up to 2.05%. On average, the overlap increases by 94% relative to the unconstrained value and precision is doubled.

CONCLUSIONS

The approach reduces errors arising from constraints by about an order of magnitude. Free energy simulations benefit from the use of constraints through enhanced convergence and higher precision.

GENERAL SIGNIFICANCE

The primary utility of this approach is to calculate free energies for systems with disparate energy surfaces and bonded terms, especially in multi-scale molecular mechanics/quantum mechanics simulations. This article is part of a Special Issue entitled Recent developments of molecular dynamics.

Long Timestep Molecular Dynamics on the Graphical Processing Unit

Molecular dynamics (MD) simulations now play a key role in many areas of theoretical chemistry, biology, physics, and materials science. In many cases, such calculations are significantly limited by the massive amount of computer time needed to perform calculations of interest. Herein, we present Long Timestep Molecular Dynamics (LTMD), a method to significantly speed MD simulations. In particular, we discuss new methods to calculate the needed terms in LTMD as well as issues germane to a GPU implementation. The resulting code, implemented in the OpenMM MD library, can achieve a significant 6-fold speed increase, leading to MD simulations on the order of 5 μs/day using implicit solvent models.