Generalized Normal Coordinates for the Vibrational Analysis of Molecular Dynamics Simulations

Theoretical terahertz spectroscopy of free radical solutes in solution: an EPR spin probe in water

Free radical species are used as spin labels in electron paramagnetic resonance (EPR) spectroscopy of biomolecular systems in water, for instance in the frame of Overhauser dynamic nuclear polarization (ODNP) relaxometry to probe the local hydration water dynamics close to protein surfaces in aqueous environments. Widely used in this context are nitroxide spin probes such as TEMPO, PROXYL or MTSL derivatives. Here, we study the THz spectroscopy of HMI (2,2,3,4,5,5-HexaMethylImidazolidin-1-oxyl) in water at ambient conditions which has been recently investigated as to how its EPR properties depend on its solvation pattern in water. To enable theoretical THz spectroscopy of molecular radicals in solution, we have generalized well-established methodologies for THz spectral decomposition of closed-shell systems, namely the supermolecular solvation complex (SSC) and cross-correlation analysis (CCA) techniques, to open-shell polyatomic solute species in water. Based on this methodological advance, we have decomposed and assigned the THz response of HMI including its solvation shell by employing the generalized SSC and CCA methods to cope with the open-shell character of this free radical solute, in particular its unpaired electron localized at the nitroxy group. We reveal that the main modulations of the far-IR spectrum of HMI are dominated by the low-frequency intramolecular modes of the spin probe molecule itself while the solvation of its two hydrogen bonding sites contribute much less intensely in this spectral window. Finally, we have computed THz spectra of HMI with its local solvation water with an aim to provide a theoretical analogue of experimental THz difference spectroscopy. Beyond the specific case, our decomposition methodology that now is able to include open shells can be applied in future work to analyze the low-frequency vibrational response of the solvation shell of other free radicals in solution.

Exploring Conformational Landscapes Along Anharmonic Low-Frequency Vibrations

We aim to automatize the identification of collective variables to simplify and speed up enhanced sampling simulations of conformational dynamics in biomolecules. We focus on anharmonic low-frequency vibrations that exhibit fluctuations on time scales faster than conformational transitions but describe a path of least resistance toward structural change. A key challenge is that harmonic approximations are ill-suited to characterize these vibrations, which are observed at far-infrared frequencies and are easily excited by thermal collisions at room temperature. Here, we approached this problem with a frequency-selective anharmonic (FRESEAN) mode analysis that does not rely on harmonic approximations and successfully isolates anharmonic low-frequency vibrations from short molecular dynamics simulation trajectories. We applied FRESEAN mode analysis to simulations of alanine dipeptide, a common test system for enhanced sampling simulation protocols, and compared the performance of isolated low-frequency vibrations to conventional user-defined collective variables (here backbone dihedral angles) in enhanced sampling simulations. The comparison shows that enhanced sampling along anharmonic low-frequency vibrations not only reproduces known conformational dynamics but can even further improve the sampling of slow transitions compared to user-defined collective variables. Notably, free energy surfaces spanned by low-frequency anharmonic vibrational modes exhibit lower barriers associated with conformational transitions relative to representations in backbone dihedral space. We thus conclude that anharmonic low-frequency vibrations provide a promising path for highly effective and fully automated enhanced sampling simulations of conformational dynamics in biomolecules.

Infrared Spectroscopy of Li+ Solvation in Diglyme: Ab Initio Molecular Dynamics and Experiment

Infrared (IR) spectra of solutions of the lithium salt LiBF4 in diglyme, CH3O(CH2CH2O)2CH3, are studied via IR spectroscopy and ab initio molecular dynamics (AIMD) simulations. Experiments show that the major effects of LiBF4, compared to neat diglyme, are the appearance of a new broad band in the 250-500 cm-1 frequency region and a broadening and intensity enhancement of the diglyme band in the 900-1150 cm-1 region accompanied by a red-shift. Computational analysis indicates that hindered translational motions of Li+ in its solvation cage are mainly responsible for the new far-IR band, while the changes in the mid-IR are due to Li+-coordination-dependent B-F stretching vibrations of BF4- anions coupled with diglyme vibrations. Molecular motions in these and lower frequency regions are generally correlated, revealing the collective nature of the vibrational dynamics, which involve multiple ions/molecules. Herein, a detailed analysis of these features via AIMD simulations of the spectrum and its components, combined with analysis of the generalized normal modes of the solution components, is presented. Other minor spectral changes as well as diglyme conformational changes induced by the lithium salt are also discussed.

Frequency-Selective Anharmonic Mode Analysis of Thermally Excited Vibrations in Proteins

Low-frequency molecular vibrations at far-infrared frequencies are thermally excited at room temperature. As a consequence, thermal fluctuations are not limited to the immediate vicinity of local minima on the potential energy surface, and anharmonic properties cannot be ignored. The latter is particularly relevant in molecules with multiple conformations, such as proteins and other biomolecules. However, existing theoretical and computational frameworks for the analysis of molecular vibrations have so far been limited by harmonic or quasi-harmonic approximations, which are ill-suited to describe anharmonic low-frequency vibrations. Here, we introduce a fully anharmonic analysis of molecular vibrations based on a time correlation formalism that eliminates the need for harmonic or quasi-harmonic approximations. We use molecular dynamics simulations of a small protein to demonstrate that this new approach, in contrast to harmonic and quasi-harmonic normal modes, correctly identifies the collective degrees of freedom associated with molecular vibrations at any given frequency. This allows us to unambiguously characterize the anharmonic character of low-frequency vibrations in the far-infrared spectrum.

Spectroscopic and Chemical Properties of Ionic Liquids: Computational Study

A brief account is given of highlights of our computational efforts - often in collaboration with experimental groups - to understand spectroscopic and chemical properties of ionic liquids (ILs). Molecular dynamics, including their inhomogeneous character, responsible for key spectral features observed in dielectric absorption, infra-red (IR) and fluorescence correlation spectroscopy (FCS) measurements are elucidated. Mechanisms of chemical processes involving imidazolium-based ILs are illustrated for CO2 capture and related reactions, transesterification of cellulose, and Au nanocluster-catalyzed Suzuki cross-coupling reaction with attention paid to differing roles of IL ions. A comparison with experiments is also made.

Hydration and Hydrogen Bond Order of Octadecanoic Acid and Octadecanol Films on Water at 21 and 1 °C

The temperature-dependent hydration structure of long-chain fatty acids and alcohols at air-water interfaces has great significance in the fundamental interactions underlying ice nucleation in the atmosphere. We present an integrated theoretical and experimental study of the temperature-dependent vibrational structure and electric field character of the immediate hydration shells of fatty alcohol and acid headgroups. We use a combination of surface-sensitive infrared reflection-absorption spectroscopy (IRRAS), surface potentiometry, and ab initio molecular dynamics simulations to elucidate detailed molecular structures of the octadecanoic acid and octadecanol (stearic acid and stearyl alcohol) headgroup hydration shells at room temperature and near freezing. In experiments, the alcohol at high surface concentration exhibits the largest surface potential; yet we observe a strengthening of the hydrogen-bonding for the solvating water molecules near freezing for both the alcohol and the fatty acid IRRAS experiments. Results reveal that the hydration shells for both compounds screen their polar headgroup dipole moments reducing the surface potential at low surface coverages; at higher surface coverage, the polar headgroups become dehydrated, which reduces the screening, correlating to higher observed surface potential values. Lowering the temperature promotes tighter chain packing and an increase in surface potential. IRRAS reveals that the intra- and intermolecular vibrational coupling mechanisms are highly sensitive to changes in temperature. We find that intramolecular coupling dominates the vibrational relaxation pathways for interfacial water determined by comparing the H₂O and the HOD spectra. Using ab initio molecular dynamics (AIMD) calculations on cluster systems of propanol + 6H₂O and propionic acid + 10H₂O, a spectral decomposition scheme was used to correlate the OH stretching motion with the IRRAS spectral features, revealing the effects of intra- and intermolecular coupling on the spectra. Spectra calculated with AIMD reproduce the red shift and increase in intensity observed in experimental spectra corresponding to the OH stretching region of the first solvation shell. These findings suggest that intra- and intermolecular vibrational couplings strongly impact the OH stretching region at fatty acid and fatty alcohol water interfaces. Overall, results are consistent with ice templating behavior for both the fatty acid and the alcohol, yet the surface potential signature is strongest for the fatty alcohol. These findings develop a better understanding of the complex surface potential and spectral signatures involved in ice templating.

Proton in the ring: spectroscopy and dynamics of proton bonding in macrocycle cavities

The proton bond is a paradigmatic quantum molecular interaction and a major driving force of supramolecular chemistry. The ring cavities of crown ethers provide an intriguing environment, promoting competitive proton sharing with multiple coordination anchors. This study shows that protons confined in crown ether cavities form dynamic bonds that migrate to varying pairs of coordinating atoms when allowed by the flexibility of the macrocycle backbone. Prototypic native crown ethers (12-crown-4, 15-crown-5 and 18-crown-6) and aza-crown ethers (cyclen, 1-aza-18-crown-6 and hexacyclen) are investigated. For each system, Infrared action spectroscopy experiments and ab initio Molecular Dynamics computations are employed to elucidate the structural effects associated with proton diffusion and its entanglement with the conformational and vibrational dynamics of the protonated host.

Direct Observation of the Orientational Anisotropy of Buried Hydroxyl Groups inside Muscovite Mica

Muscovite mica (001) is a widely used model surface for controlling molecular assembly and a common substrate for environmental adsorption processes. The mica (001) surface displays near-trigonal symmetry, but many molecular adsorbates-including water-exhibit unequal probabilities of alignment along its three nominally equivalent lattice directions. Buried hydroxyl groups within the muscovite structure are speculated to be responsible, but direct evidence is lacking. Here, we utilize vibrational sum frequency generation spectroscopy (vSFG) to characterize the orientation and hydrogen-bonding environment of near-surface hydroxyls inside mica. Multiple distinct peaks are detected in the O-H stretch region, which we attribute to Si/Al substitution in the SiO₄ tetrahedron and K⁺ ion adsorption above the hydroxyls based on density functional theory simulations. Our findings demonstrate that vSFG can identify the absolute orientation of -OH groups and, hence, the surface termination at a mica surface, providing a means to investigate how -OH groups influence molecular adsorption and better understand mica stacking-sequences and physical behavior.

Elucidating the Nuclear Quantum Dynamics of Intramolecular Double Hydrogen Transfer in Porphycene

We address the double hydrogen transfer (DHT) dynamics of the porphycene molecule, a complex paradigmatic system in which the making and breaking of H-bonds in a highly anharmonic potential energy surface require a quantum mechanical treatment not only of the electrons but also of the nuclei. We combine density functional theory calculations, employing hybrid functionals and van der Waals corrections, with recently proposed and optimized path-integral ring-polymer methods for the approximation of quantum vibrational spectra and reaction rates. Our full-dimensional ring-polymer instanton simulations show that below 100 K the concerted DHT tunneling pathway dominates but between 100 and 300 K there is a competition between concerted and stepwise pathways when nuclear quantum effects are included. We obtain ground-state reaction rates of 2.19 × 10¹¹ s^–1 at 150 K and 0.63 × 10¹¹ s^–1 at 100 K, in good agreement with experiment. We also reproduce the puzzling N–H stretching band of porphycene with very good accuracy from thermostated ring-polymer molecular dynamics simulations. The position and line shape of this peak, centered at around 2600 cm^–1 and spanning 750 cm^–1, stem from a combination of very strong H-bonds, the coupling to low-frequency modes, and the access to cis-like isomeric conformations, which cannot be appropriately captured with classical-nuclei dynamics. These results verify the appropriateness of our general theoretical approach and provide a framework for a deeper physical understanding of hydrogen transfer dynamics in complex systems.

Simulating structure and dynamics in small droplets of 1-ethyl-3-methylimidazolium acetate

To investigate the structure and dynamics of small ionic liquid droplets in gas phase, we performed a DFT-based ab initio molecular dynamics study of several 1-ethyl-3-methylimidazolium acetate clusters in vacuum as well as a bulk phase simulation. We introduce an unbiased criterion for average droplet diameter and density. By extrapolation of the droplet densities, we predict the experimental bulk phase density with a deviation of only a few percent. The hydrogen bond geometry between cations and anions is very similar in droplets and bulk, but the hydrogen bond dynamics is significantly slower in the droplets, becoming slower with increasing system size, with hydrogen bond lifetimes up to 2000 ps. From a normal mode analysis of the trajectories, we identify the modes of the ring proton C-H stretching, which are strongly affected by hydrogen bonding. From analyzing these, we find that the hydrogen bond becomes weaker with increasing system size. The cations possess an increased concentration inside the clusters, whereas the anions show an excess concentration on the outside. Almost all anions point towards the droplet center with their carboxylic groups. Ring stacking is found to be a very important structural motif in the droplets (as in the bulk), but side chain interactions are only of minor importance. By using Voronoi tessellation, we define the exposed droplet surface and find that it consists mainly of hydrogen atoms from the cation's and anion's methyl and ethyl groups. Polar atoms are rarely found on the surface, such that the droplets appear completely hydrophobic on the outside.

All-DFTB Approach to the Parametrization of the System-Bath Hamiltonian Describing Exciton-Vibrational Dynamics of Molecular Assemblies

Spectral density functions are central to the simulation of complex many body systems. Their determination requires making approximations not only to the dynamics but also to the underlying electronic structure theory. Here, blending different methods bears the danger of an inconsistent description. To solve this issue we propose an all-DFTB approach to determine spectral densities for the description of Frenkel excitons in molecular assemblies. The protocol is illustrated for a model of a PTCDI crystal, which involves the calculation of monomeric excitation energies and Coulomb couplings between monomer transitions, as well as their spectral distributions due to thermal fluctuations of the nuclei. Using dynamically defined normal modes, a mapping onto the standard harmonic oscillator spectral densities is achieved.

Monitoring transient events in infrared spectra using local mode analysis

Time-resolved Fourier transformed infrared (FTIR) spectroscopy of chemical reactions is highly sensitive to minimal spatiotemporal changes. Structural features are decoded and represented in a comprehensible manner by combining FTIR spectroscopy with biomolecular simulations. Local mode analysis (LMA) is a tool to connect molecular motion based on a quantum mechanics simulation with infrared (IR) spectral features and vice versa. Here, we present the python-based software tool of LMA and demonstrate the novel feature of LMA to extract transient structural details and identify the related IR spectra at the case example of malonaldehyde (MA). Deuterated MA exists in two almost equally populated tautomeric states separated by a low barrier for proton transfer so IR spectra represent a mixture of both states. By state-dependent LMA, we obtain pure spectra for each tautomeric state occurring within the quantum mechanics trajectory. By time-resolved LMA, we obtain a clear view of the transition between states in the spectrum. Through local mode decomposition and the band-pass filter, marker bands for each state are identified. Thus, LMA is beneficial to analyze the experimental spectra based on a mixture of states by determining the individual contributions to the spectrum and motion of each state.

Understanding the scale of the single ion free energy: A critical test of the tetra-phenyl arsonium and tetra-phenyl borate assumption

The tetra-phenyl arsonium and tetra-phenyl borate (TATB) assumption is a commonly used extra-thermodynamic assumption that allows single ion free energies to be split into cationic and anionic contributions. The assumption is that the values for the TATB salt can be divided equally. This is justified by arguing that these large hydrophobic ions will cause a symmetric response in water. Experimental and classical simulation work has raised potential flaws with this assumption, indicating that hydrogen bonding with the phenyl ring may favor the solvation of the TB^- anion. Here, we perform ab initio molecular dynamics simulations of these ions in bulk water demonstrating that there are significant structural differences. We quantify our findings by reproducing the experimentally observed vibrational shift for the TB^- anion and confirm that this is associated with hydrogen bonding with the phenyl rings. Finally, we demonstrate that this results in a substantial energetic preference of the water to solvate the anion. Our results suggest that the validity of the TATB assumption, which is still widely used today, should be reconsidered experimentally in order to properly reference single ion solvation free energy, enthalpy, and entropy.

Tagging effects on the mid-infrared spectrum of microsolvated protonated methane

Although bare protonated methane is by now essentially understood at the level of intramolecular large-amplitude motion, scrambling dynamics and broadband vibrational spectra, the microsolvated species still offer plenty of challenges. One aspect is the effect of the attached solvent molecules on the infrared absorption spectra of microsolvated CH₅⁺ complexes compared to the bare parent molecule. In this study we analyze, based on ab initio molecular dynamics simulations, protonated methane molecules that have been microsolvated with up to three hydrogen molecules, i.e. CH₅⁺·(H₂) _n . In particular, upon introducing a novel multi-channel maximum entropy methodology described herein, we are able to decompose the infrared spectra of these weakly-bound complexes in the frequency window from 1000 to 4500 cm^-1 into additive single mode contributions. Detailed comparisons to the bare CH₅⁺ parent reveal that these perturbed modes encode distinct features that depend on the exact microsolvation pattern. Beyond the specific case, such understanding is relevant to assess tagging artifacts in vibrational spectra of parent molecules based on messenger predissociation action spectroscopy.

Mode specific THz spectra of solvated amino acids using the AMOEBA polarizable force field

We have used the AMOEBA model to simulate the THz spectra of two zwitterionic amino acids in aqueous solution, which is compared to the results on these same systems using ab initio molecular dynamics (AIMD) simulations. Overall we find that the polarizable force field shows promising agreement with AIMD data for both glycine and valine in water. This includes the THz spectral assignments and the mode-specific spectral decomposition into intramolecular solute motions as well as distinct solute-water cross-correlation modes some of which cannot be captured by non-polarizable force fields that rely on fixed partial charges. This bodes well for future studies for simulating and decomposing the THz spectra for larger solutes such as proteins or polymers for which AIMD studies are presently intractable. Furthermore, we believe that the current study on rather simple aqueous solutions offers a way to systematically investigate the importance of charge transfer, nuclear quantum effects, and the validity of computationally practical density functionals, all of which are needed to fully quantitatively capture complex dynamical motions in the condensed phase.

Spin-state dependence of the structural and vibrational properties of solvated iron(ii) polypyridyl complexes from AIMD simulations: aqueous [Fe(bpy)3]Cl2, a case study

LS and HS IR spectra of aqueous [Fe(bpy)₃]²⁺ and corresponding HS–LS difference IR spectrum as obtained from state-of-the-art ab initio molecular dynamics simulations applied to the determination of the structural and vibrational properties of the solvated complex.

Aqueous TMAO solutions as seen by theoretical THz spectroscopy: hydrophilic versus hydrophobic water

All THz resonances of aqueous TMAO solutions are computed and assigned based on ab initio molecular dynamics simulations.

On-the-Fly ab Initio Semiclassical Calculation of Glycine Vibrational Spectrum

We present an on-the-fly ab initio semiclassical study of vibrational energy levels of glycine, calculated by Fourier transform of the wavepacket correlation function. It is based on a multiple coherent states approach integrated with monodromy matrix regularization for chaotic dynamics. All four lowest-energy glycine conformers are investigated by means of single-trajectory semiclassical spectra obtained upon classical evolution of on-the-fly trajectories with harmonic zero-point energy. For the most stable conformer I, direct dynamics trajectories are also run for each vibrational mode with energy equal to the first harmonic excitation. An analysis of trajectories evolved up to 50 000 atomic time units demonstrates that, in this time span, conformers II and III can be considered as isolated species, while conformers I and IV show a pretty facile interconversion. Therefore, previous perturbative studies based on the assumption of isolated conformers are often reliable but might be not completely appropriate in the case of conformer IV and conformer I for which interconversion occurs promptly.

Local Mode Analysis: Decoding IR Spectra by Visualizing Molecular Details

Integration of experimental and computational approaches to investigate chemical reactions in proteins has proven to be very successful. Experimentally, time-resolved FTIR difference-spectroscopy monitors chemical reactions at atomic detail. To decode detailed structural information encoded in IR spectra, QM/MM calculations are performed. Here, we present a novel method which we call local mode analysis (LMA) for calculating IR spectra and assigning spectral IR-bands on the basis of movements of nuclei and partial charges from just a single QM/MM trajectory. Through LMA the decoding of IR spectra no longer requires several simulations or optimizations. The novel approach correlates the motions of atoms of a single simulation with the corresponding IR bands and provides direct access to the structural information encoded in IR spectra. Either the contributions of a particular atom or atom group to the complete IR spectrum of the molecule are visualized, or an IR-band is selected to visualize the corresponding structural motions. Thus, LMA decodes the detailed information contained in IR spectra and provides an intuitive approach for structural biologists and biochemists. The unique feature of LMA is the bidirectional analysis connecting structural details to spectral features and vice versa spectral features to molecular motions.

Vibrational Spectroscopy of Ionic Liquids

Vibrational spectroscopy has continued use as a powerful tool to characterize ionic liquids since the literature on room temperature molten salts experienced the rapid increase in number of publications in the 1990's. In the past years, infrared (IR) and Raman spectroscopies have provided insights on ionic interactions and the resulting liquid structure in ionic liquids. A large body of information is now available concerning vibrational spectra of ionic liquids made of many different combinations of anions and cations, but reviews on this literature are scarce. This review is an attempt at filling this gap. Some basic care needed while recording IR or Raman spectra of ionic liquids is explained. We have reviewed the conceptual basis of theoretical frameworks which have been used to interpret vibrational spectra of ionic liquids, helping the reader to distinguish the scope of application of different methods of calculation. Vibrational frequencies observed in IR and Raman spectra of ionic liquids based on different anions and cations are discussed and eventual disagreements between different sources are critically reviewed. The aim is that the reader can use this information while assigning vibrational spectra of an ionic liquid containing another particular combination of anions and cations. Different applications of IR and Raman spectroscopies are given for both pure ionic liquids and solutions. Further issues addressed in this review are the intermolecular vibrations that are more directly probed by the low-frequency range of IR and Raman spectra and the applications of vibrational spectroscopy in studying phase transitions of ionic liquids.

Ab Initio Transient Vibrational Spectral Analysis

Pump probe spectroscopy techniques have enabled the direct observation of a variety of transient molecular species in both ground and excited electronic states. Time-resolved vibrational spectroscopy is becoming an indispensable tool for investigating photoinduced nuclear dynamics of chemical systems of all kinds. On the other hand, a complete picture of the chemical dynamics encoded in these spectra cannot be achieved without a full temporal description of the structural relaxation, including the explicit time-dependence of vibrational coordinates that are substantially displaced from equilibrium by electronic excitation. Here we present a transient vibrational analysis protocol combining ab initio direct molecular dynamics and time-integrated normal modes introduced in this work, relying on the recent development of analytic time-dependent density functional theory (TDDFT) second derivatives for excited states. Prototypical molecules will be used as test cases, showing the evolution of the vibrational signatures that follow electronic excitation. This protocol provides a direct route to assigning the vibrations implicated in the (photo)dynamics of several (photoactive) systems.

A polarizable QM/MM approach to the molecular dynamics of amide groups solvated in water

The infrared (IR) spectra of polypeptides are dominated by the so-called amide bands. Because they originate from the strongly polar and polarizable amide groups (AGs) making up the backbone, their spectral positions sensitively depend on the local electric fields. Aiming at accurate computations of these IR spectra by molecular dynamics (MD) simulations, which derive atomic forces from a hybrid quantum and molecular mechanics (QM/MM) Hamiltonian, here we consider the effects of solvation in bulk liquid water on the amide bands of the AG model compound N-methyl-acetamide (NMA). As QM approach to NMA we choose grid-based density functional theory (DFT). For the surrounding MM water, we develop, largely based on computations, a polarizable molecular mechanics (PMM) model potential called GP6P, which features six Gaussian electrostatic sources (one induced dipole, five static partial charge distributions) and, therefore, avoids spurious distortions of the DFT electron density in hybrid DFT/PMM simulations. Bulk liquid GP6P is shown to have favorable properties at the thermodynamic conditions of the parameterization and beyond. Lennard-Jones (LJ) parameters of the DFT fragment NMA are optimized by comparing radial distribution functions in the surrounding GP6P liquid with reference data obtained from a "first-principles" DFT-MD simulation. Finally, IR spectra of NMA in GP6P water are calculated from extended DFT/PMM-MD trajectories, in which the NMA is treated by three different DFT functionals (BP, BLYP, B3LYP). Method-specific frequency scaling factors are derived from DFT-MD simulations of isolated NMA. The DFT/PMM-MD simulations with GP6P and with the optimized LJ parameters then excellently predict the effects of aqueous solvation and deuteration observed in the IR spectra of NMA. As a result, the methods required to accurately compute such spectra by DFT/PMM-MD also for larger peptides in aqueous solution are now at hand.

Some studies on generalized coordinate sets for polyatomic molecules

Generalized coordinates are widely used in various analyses of the trajectories of polyatomic molecules from molecular dynamics simulations, such as normal mode analysis and force distribution analysis. Here, we presented detailed discussions on the properties of some specific sets of generalized coordinates, which separate translational, rotational, and vibrational motions of a molecule from one another once the trajectories of dynamical systems are known. Efficient methods were suggested for estimating the transformation matrix between generalized and Cartesian coordinates. Some properties of the well-known BAT coordinates (bond length, angle, and torsional coordinates) were discussed as well.

Simulating the vibrational spectra of ionic liquid systems: 1-ethyl-3-methylimidazolium acetate and its mixtures

The vibrational spectra of the ionic liquid 1-ethyl-3-methylimidazolium acetate and its mixtures with water and carbon dioxide are calculated using ab initio molecular dynamics simulations, and the results are compared to experimental data. The new implementation of a normal coordinate analysis in the trajectory analyzer TRAVIS is used to assign the experimentally observed bands to specific molecular vibrations. The applied computational approaches prove to be particularly suitable for the modeling of bulk phase effects on vibrational spectra, which are highly important for the discussion of the microscopic structure in systems with a strong dynamic network of intermolecular interactions, such as ionic liquids.

Exploring the vibrational fingerprint of the electronic excitation energy via molecular dynamics

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.

Asymmetric environmental effects on the structure and vibrations of cis-[Pt(NH3)2Cl2] in condensed phases

We report the structural and vibrational properties of anticancer drug cisplatin (cis-[Pt(NH3)2Cl2]) in gas phase, in solid phase, and in aqueous solution using density functional theory (DFT) calculations, quantum mechanical/molecular mechanical (QM/MM) molecular dynamics, and effective normal modes analysis. In contrast with the gas-phase case, asymmetric hydrogen bonding environments are found in both solid phase and aqueous solution. It is shown that the discrepancy of the molecular geometry between previous gas phase calculations and the X-ray crystal structure can be resolved by considering intermolecular hydrogen bonds in the calculations of solid phase. In addition, our simulations in solid phase and aqueous solution reveal that asymmetric environmental effects lead to several spectral features observed in experiments, such as the blue-shift in the N-H stretching region and the frequency splitting of NH3 symmetric deformation modes. Furthermore, a similar decoupling and localization of several vibrational modes of cisplatin is found in solid phase and aqueous solution, in comparison to those of O-H stretching modes of water molecules in liquid water [ J. Phys. Chem. Lett. 2013 , 4 ( 19 ), 3245 - 3250 ].

Aqueous Cation-Amide Binding: Free Energies and IR Spectral Signatures by Ab Initio Molecular Dynamics

Understanding specific ion effects on proteins remains a considerable challenge. N-methylacetamide serves as a useful proxy for the protein backbone that can be well characterized both experimentally and theoretically. The spectroscopic signatures in the amide I band reflecting the strength of the interaction of alkali cations and alkaline earth dications with the carbonyl group remain difficult to assign and controversial to interpret. Herein, we directly compute the infrared (IR) shifts corresponding to the binding of either sodium or calcium to aqueous N-methylacetamide using ab initio molecular dynamics simulations. We show that the two cations interact with aqueous N-methylacetamide with different affinities and in different geometries. Because sodium exhibits a weak interaction with the carbonyl group, the resulting amide I band is similar to an unperturbed carbonyl group undergoing aqueous solvation. In contrast, the stronger calcium binding results in a clear IR shift with respect to N-methylacetamide in pure water.

Coupling density functional theory to polarizable force fields for efficient and accurate Hamiltonian molecular dynamics simulations

Hybrid molecular dynamics (MD) simulations, in which the forces acting on the atoms are calculated by grid-based density functional theory (DFT) for a solute molecule and by a polarizable molecular mechanics (PMM) force field for a large solvent environment composed of several 10(3)-10(5) molecules, pose a challenge. A corresponding computational approach should guarantee energy conservation, exclude artificial distortions of the electron density at the interface between the DFT and PMM fragments, and should treat the long-range electrostatic interactions within the hybrid simulation system in a linearly scaling fashion. Here we describe a corresponding Hamiltonian DFT/(P)MM implementation, which accounts for inducible atomic dipoles of a PMM environment in a joint DFT/PMM self-consistency iteration. The long-range parts of the electrostatics are treated by hierarchically nested fast multipole expansions up to a maximum distance dictated by the minimum image convention of toroidal boundary conditions and, beyond that distance, by a reaction field approach such that the computation scales linearly with the number of PMM atoms. Short-range over-polarization artifacts are excluded by using Gaussian inducible dipoles throughout the system and Gaussian partial charges in the PMM region close to the DFT fragment. The Hamiltonian character, the stability, and efficiency of the implementation are investigated by hybrid DFT/PMM-MD simulations treating one molecule of the water dimer and of bulk water by DFT and the respective remainder by PMM.