Adiabatic Separation Research Articles

Attachment of Hydrogen Molecules to Atomic Ions (Na+, Cl-): Examination of an Adiabatic Separation of the H2 Rotational Motion.

Interactions between molecular hydrogen and ions are of interest in cluster science, astrochemistry and hydrogen storage. In dynamical simulations, H2 molecules are usually modelled as point particles, an approximation that can fail for anisotropic interactions. Here, we apply an adiabatic separation of the H2 rotational motion to build effective pseudoatom-ion potentials and in turn study the properties of (H2)nNa+/Cl- clusters. These interaction potentials are based on high-level ab initio calculations and Improved Lennard-Jones parametrizations, while the subsequent dynamics has been performed by quantum Monte Carlo calculations. By comparisons with simulations explicitly describing the molecular rotations, it is concluded that the present adiabatic model is very adequate. Interestingly, we find differences in the cluster stabilities and coordination shells depending on the spin isomer considered (para- or ortho-H2), especially for the anionic clusters.

The effect of the adiabatic assumption on asteroseismic scaling relations for luminous red giants

ABSTRACT Although stellar radii from asteroseismic scaling relations agree at the per cent level with independent estimates for main sequence and most first-ascent red giant branch (RGB) stars, the scaling relations over-predict radii at the tens of per cent level for the most luminous stars ($R \gtrsim 30 \, \mathrm{R}_{\odot }$). These evolved stars have significantly superadiabatic envelopes, and the extent of these regions increase with increasing radius. However, adiabaticity is assumed in the theoretical derivation of the scaling relations as well as in corrections to the large frequency separation. Here, we show that a part of the scaling relation radius inflation may arise from this assumption of adiabaticity. With a new reduction of Kepler asteroseismic data, we find that scaling relation radii and Gaia radii agree to within at least 2 per cent for stars with $R \lesssim 30\, \mathrm{R}_{\odot }$, when treated under the adiabatic assumption. The accuracy of scaling relation radii for stars with $50\, \mathrm{R}_{\odot }\lesssim R \lesssim 100\, \mathrm{R}_{\odot }$, however, is not better than $10~{{\ \rm per \, cent}}-15~{{\ \rm per \, cent}}$ using adiabatic large frequency separation corrections. We find that up to one third of this disagreement for stars with $R \approx 100\, \mathrm{R}_{\odot }$ could be caused by the adiabatic assumption, and that this adiabatic error increases with radius to reach 10 per cent at the tip of the RGB. We demonstrate that, unlike the solar case, the superadiabatic gradient remains large very deep in luminous stars. A large fraction of the acoustic cavity is also in the optically thin atmosphere. The observed discrepancies may therefore reflect the simplified treatment of convection and atmospheres.

An interoperable implementation of collective-variable based enhanced sampling methods in extended phase space within the OpenMM package.

Collective variable (CV)-based enhanced sampling techniques are widely used today for accelerating barrier-crossing events in molecular simulations. A class of these methods, which includes temperature accelerated molecular dynamics (TAMD)/driven-adiabatic free energy dynamics (d-AFED), unified free energy dynamics (UFED), and temperature accelerated sliced sampling (TASS), uses an extended variable formalism to achieve quick exploration of conformational space. These techniques are powerful, as they enhance the sampling of a large number of CVs simultaneously compared to other techniques. Extended variables are kept at a much higher temperature than the physical temperature by ensuring adiabatic separation between the extended and physical subsystems and employing rigorous thermostatting. In this work, we present a computational platform to perform extended phase space enhanced sampling simulations using the open-source molecular dynamics engine OpenMM. The implementation allows users to have interoperability of sampling techniques, as well as employ state-of-the-art thermostats and multiple time-stepping. This work also presents protocols for determining the critical parameters and procedures for reconstructing high-dimensional free energy surfaces. As a demonstration, we present simulation results on the high dimensional conformational landscapes of the alanine tripeptide in vacuo, tetra-N-methylglycine (tetra-sarcosine) peptoid in implicit solvent, and the Trp-cage mini protein in explicit water.

Frequency Splitting of Chiral Phonons from Broken Time-Reversal Symmetry in CrI_{3}.

Conventional approaches for lattice dynamics based on static interatomic forces do not fully account for the effects of time-reversal-symmetry breaking in magnetic systems. Recent approaches to rectify this involve incorporating the first-order change in forces with atomic velocities under the assumption of adiabatic separation of electronic and nuclear degrees of freedom. In this Letter, we develop a first-principles method to calculate this velocity-force coupling in extended solids and show via the example of ferromagnetic CrI_{3} that, due to the slow dynamics of the spins in the system, the assumption of adiabatic separation can result in large errors for splittings of zone-center chiral modes. We demonstrate that an accurate description of the lattice dynamics requires treating magnons and phonons on the same footing.

Continuum mechanics from molecular dynamics via adiabatic time and length scale separation

Continuum mechanics from molecular dynamics via adiabatic time and length scale separation

Mass-zero constrained dynamics for simulations based on orbital-free density functional theory.

A new algorithm for efficient and fully time-reversible integration of first-principles molecular dynamics based on orbital-free density functional theory (OFDFT) is presented. The algorithm adapts to this nontrivial case, the recently introduced Mass-Zero (MaZe) constrained dynamics. The formalism ensures that full adiabatic separation is enforced between nuclear and electronic degrees of freedom and, consequently, that the exact Born-Oppenheimer probability for the nuclei is sampled. Numerical integration of the MaZe dynamics combines standard molecular dynamics algorithms, e.g., Verlet or velocity Verlet, with the SHAKE method to impose the minimum conditions on the electronic degrees of freedom as a set of constraints. The developments presented in this work, which include a bespoke adaptation of the standard SHAKE algorithm, ensure that the quasilinear scaling of OFDFT is preserved by the new method for a broad range of kinetic and exchange-correlation functionals, including nonlocal ones. The efficiency and accuracy of the approach are demonstrated via calculations of static and dynamic properties of liquid sodium in the constant energy and constant temperature ensembles.

How the Interplay among Conformational Disorder, Solvation, Local, and Charge-Transfer Excitations Affects the Absorption Spectrum and Photoinduced Dynamics of Perylene Diimide Dimers: A Molecular Dynamics/Quantum Vibronic Approach.

In this contribution we present a mixed quantum-classical dynamical approach for the computation of vibronic absorption spectra of molecular aggregates and their nonadiabatic dynamics, taking into account the coupling between local excitations (LE) and charge-transfer (CT) states. The approach is based on an adiabatic (Ad) separation between the soft degrees of freedom (DoFs) of the system and the stiff vibrations, which are described by the quantum dynamics (QD) of wave packets (WPs) moving on the coupled potential energy surfaces (PESs) of the LE and CT states. These PESs are described with a linear vibronic coupling (LVC) Hamiltonian, parameterized by an overlap-based diabatization on the grounds of time-dependent density functional theory computations. The WPs time evolution is computed with the multiconfiguration time-dependent Hartree method, using effective modes defined through a hierarchical representation of the LVC Hamiltonian. The soft DoFs are sampled with classical molecular dynamics (MD), and the coupling between the slow and fast DoFs is included by recomputing the key parameters of the LVC Hamiltonians, specifically for each MD configuration. This method, named Ad-MD|gLVC, is applied to a perylene diimide (PDI) dimer in acetonitrile and water solutions, and it is shown to accurately reproduce the change in the vibronic features of the absorption spectrum upon aggregation. Moreover, the microscopic insight offered by the MD trajectories allows for a detailed understanding of the role played by the fluctuation of the aggregate structure on the shape of the vibronic spectrum and on the population of LE and CT states. The nonadiabatic QD predicts an extremely fast (∼50 fs) energy transfer between the two LEs. CT states have only a moderate effect on the absorption spectrum, despite the fact that after photoexcitation they are shown to acquire a fast and non-negligible population, highlighting their relevance in dictating the charge separation and transport in PDI-based optical devices.

Exploring the Origins of Spectral Signatures of Strong Hydrogen Bonding in Protonated Water Clusters.

The effects of anharmonicity on the spectral features of strong ionic hydrogen bonds are explored through reduced dimensional studies of the couplings between the hydrogen bonding OH and the donor-acceptor OO stretching vibrations in protonated water clusters with 2-4 water molecules. Specifically, this study focuses on how the anharmonicities and couplings in these ions are reflected in the vibrational spectra by exploring the intensities of the transitions to states with excitation in both the OH and the OO stretching vibrations and changes in the frequency of the OO stretching vibration when the OH stretching vibration is excited. These questions are addressed through the application of several approximate treatments that are based on an adiabatic separation of the high-frequency OH and low-frequency OO stretching vibrations as well as low-order expansions of the potential and dipole surfaces. While an adiabatic approximation captures most of the trends found in the spectra and from an analysis of the two-dimensional model, a vibrational Franck-Condon approach fails to capture the intensities of these transitions. Of the terms in the expansion of the dipole moment function, those that are proportional to ΔrOH and ΔrOH2 are found to provide the largest contributions to the calculated intensities of the transitions involving excitation of both the OH and the OO stretches. This leads to the conclusion that the intensities of these transitions encode information about the frequency and anharmonicity of the OH stretching vibration and how they are affected by changes in the OO distance. The anharmonicity of the potential also leads to changes in the OO stretching frequency with excitation of the OH stretching vibration. The direction of this change in frequency encodes additional information about the strength of the ionic hydrogen bond.

Eyring equation and fluctuation-dissipation far away from equilibrium.

Understanding and managing the influence that either external forces or non-equilibrated environments may have on chemical processes is essential for the current and future development of theoretical chemistry. One of the central questions to solve is how to generalize the transition state theory in order to make it applicable in far from equilibrium situations. In this sense, here we propose a way to generalize Eyring's equation based on the definition of an effective thermal energy (temperature) emerging from the coupling of both fast and slow dynamic variables analyzed within the generalized Langevin dynamics scheme. This coupling makes the energy distribution of the fast degrees of freedom not equilibrate because they have been enslaved to the dynamics of the corresponding slow degrees. However, the introduction of the effective thermal energy enables us to restore an effective adiabatic separation of timescales leading to a renormalization of the generalized fluctuation-dissipation theorem. Hence, this procedure opens the possibility to deal with systems far away from equilibrium. A significant consequence of our results is that Eyring's equation is generalized to treat systems under the influence of strong external forces.

Accounting for Vibronic Features through a Mixed Quantum-Classical Scheme: Structure, Dynamics, and Absorption Spectra of a Perylene Diimide Dye in Solution.

The optical absorption spectrum of a perylene diimide (PDI) dye in acetonitrile solution is simulated using the recently developed (J. Chem. Theory Comput. 2020, 16, 1215-1231) Ad-MD|gVH method. This mixed quantum-classical (MQC) approach is based on an adiabatic (Ad) separation of soft(classical)/stiff(quantum) nuclear degrees of freedom and expresses the spectrum as a conformational average (over the soft coordinates) of vibronic spectra (for the stiff coordinates) obtained through the generalized vertical Hessian (gVH) vibronic approach. The average is performed over snapshots extracted from classical molecular dynamics (MD) runs, performed with a specifically parameterized quantum-mechanically derived force field (QMD-FF). A comprehensive assessment of the reliability of different approaches, designed to reproduce spectral shapes of flexible molecules, is here presented. First, the differences in the sampled configurational space and their consequences on the prediction of the absorption spectra are evaluated by comparing the results obtained by means of the specific QMD-FF and of a general-purpose transferable FF with those of a reference ab initio MD (AIMD) in the gas phase, in both a purely classical scheme (ensemble average) and in the Ad-MD|gVH framework. Next, classical ensemble average and MQC predictions are also obtained for the PDI dynamics in solution and compared with the results of a ″static″ approach, based on vibronic calculations carried out on a single optimized perylene diimide structure. In the classical ensemble average approach, the remarkably different samplings obtained with the two FFs lead to sizeable changes in both position and intensity of the predicted spectra, with the one computed along the QMD-FF trajectory closely matching its AIMD counterpart. Conversely, at the Ad-MD|gVH level of theory, the different samplings deliver very similar vibronic spectra, indicating that the error found in the absorption spectra obtained with the general-purpose FF mainly concerns the stiff modes. In fact, it can be effectively corrected by the quadratic extrapolation performed by gVH to locate the minima of the ground- and excited-state potential energy surfaces along such coordinates. Furthermore, in the perspective of studying the self-assembling process of PDI dyes and the vibronic spectra of large-size aggregates, the use of a molecule-specific QMD-FF also appears mandatory, considering the significant errors found in the GAFF trajectory in the flexible lateral chain populations, which dictate the supramolecular aggregation properties.

The Role of Tunneling in the Spectra of H5+ and D5+ up to 7300 cm-1.

The spectra for H5+ and D5+ are extended to cover the region between 4830 and 7300 cm-1. These spectra are obtained using mass-selected photodissociation spectroscopy. To understand the nature of the states that are accessed by the transitions in this and prior studies, we develop a four-dimensional model Hamiltonian. This Hamiltonian is expressed in terms of the two outer H2 stretches, the displacement of the shared proton from the center of mass of these two H2 groups, and the distance between the H2 groups. This choice is motivated by the large oscillator strength associated with the shared proton stretch and the fact that the spectral regions that have been probed correspond to zero, one, and two quanta of excitation in the H2 stretches. This model is analyzed using an adiabatic separation of the H2 stretches from the other two vibrations and includes the non-adiabatic couplings between H2 stretch states with the same total number of quanta of excitation in the H2 stretches. Based on the analysis of the energies and wave functions obtained from this model, we find that when there are one or more quanta of excitation in the H2 stretches the states come in pairs that reflect tunneling doublets. The states accessed by the transitions in the spectrum with the largest intensity are assigned to the members of the doublets with requisite symmetry that are localized on the lowest-energy adiabat for a given level of H2 excitation.

Classical and Quantum Signatures of Quantum Phase Transitions in a (Pseudo) Relativistic Many-Body System

We identify a (pseudo) relativistic spin-dependent analogue of the celebrated quantum phase transition driven by the formation of a bright soliton in attractive one-dimensional bosonic gases. In this new scenario, due to the simultaneous existence of the linear dispersion and the bosonic nature of the system, special care must be taken with the choice of energy region where the transition takes place. Still, due to a crucial adiabatic separation of scales, and identified through extensive numerical diagonalization, a suitable effective model describing the transition is found. The corresponding mean-field analysis based on this effective model provides accurate predictions for the location of the quantum phase transition when compared against extensive numerical simulations. Furthermore, we numerically investigate the dynamical exponents characterizing the approach from its finite-size precursors to the sharp quantum phase transition in the thermodynamic limit.

Path-integral dynamics of water using curvilinear centroids

We develop a path-integral dynamics method for water that resembles centroid molecular dynamics (CMD), except that the centroids are averages of curvilinear, rather than Cartesian, bead coordinates. The curvilinear coordinates are used explicitly only when computing the potential of mean force, the components of which are re-expressed in terms of Cartesian “quasicentroids” (so-called because they are close to the Cartesian centroids). Cartesian equations of motion are obtained by making small approximations to the quantum Boltzmann distribution. Simulations of the infrared spectra of various water models over 150–600 K show these approximations to be justified: for a two-dimensional OH-bond model, the quasicentroid molecular dynamics (QCMD) spectra lie close to the exact quantum spectra, and almost on top of the Matsubara dynamics spectra; for gas-phase water, the QCMD spectra are close to the exact quantum spectra; for liquid water and ice (using the q-TIP4P/F surface), the QCMD spectra are close to the CMD spectra at 600 K and line up with the results of thermostated ring-polymer molecular dynamics and approximate quantum calculations at 300 and 150 K. The QCMD spectra show no sign of the CMD “curvature problem” (of erroneous red shifts and broadening). In the liquid and ice simulations, the potential of mean force was evaluated on-the-fly by generalizing an adiabatic CMD algorithm to curvilinear coordinates; the full limit of adiabatic separation needed to be taken, which made the QCMD calculations 8 times more expensive than partially adiabatic CMD at 300 K, and 32 times at 150 K (and the intensities may still not be converged at this temperature). The QCMD method is probably generalizable to many other systems, provided that collective bead-coordinates can be identified that yield compact mean-field ring-polymer distributions.

Description of critical point nuclei within an energy-dependent geometric model

An exactly solvable version of the Bohr Hamiltonian is proposed for a unified treatment of transitional nuclei. The model employs an energy-dependent potential in the \( \beta\) shape variable which is amended with a centrifugal contribution from the \( \gamma\) and angular degrees of freedom. The parametrization of the \( \gamma\) part of the potential enables the connection between the adiabatic separation of \( \beta\) and \( \gamma\) fluctuations suitable for critical point nuclei and the exactly separable solutions specific to deformed nuclei. The fully analytical model is applied to known critical point nuclei as well as a neighbouring isotope for each case. Beside very good agreement with experiment for energies and electromagnetic transitions, numerical results also reveal specific model characteristics for critical nuclei in comparison to more or less deformed nuclei.

Adiabatic and nonadiabatic charge separation dynamics in graphene oxide quantum dots for overall water splitting

Chemical functionalization and heteroatom doping are two effective strategies for improving the conductivity of a graphene lattice. Nitrogen-doped graphene oxide quantum dot (GOQD) has been reported to possess both p- and n-conductivity that is induced by an oxygen functional group and nitrogen doping, respectively, and is suitable for catalyzing hydrogen and oxygen evolution reactions for complete water splitting. The experimental study shows that the hydrogen evolution reaction occurs considerably faster than the oxygen evolution reaction. However, the mechanism of this phenomenon remains unknown, which poses a challenge to the chemical modification of such classes of materials. In the present work, we perform nonadiabatic ab initio molecular dynamics to explore the charge separation dynamics in N-doped GOQD with oxygen functional groups. Our results show that there exists multiple charge decay channels governed by different mechanisms, which complicates the overall charge separation dynamics in N-doped GOQD. The intramolecular electron transfer mainly occurs through the nonadiabatic channel, whereas the intramolecular hole transfer mainly occurs through the adiabatic channel. There is an additional adiabatic decay channel in the p-domain, which accelerates electron–hole recombination in the p-domain. We further calculated the decoherence times and found that the decoherence of intramolecular electron transfer occurs considerably faster than that of hole transfer, which slows the quantum transition of intramolecular electron transfer. Finally, we simulated the carrier relaxation times and found that the electron relaxation is approximately one order of magnitude longer than that of the hole relaxation. Our calculation rationalizes the experimentally observed higher catalytic activity towards the hydrogen evolution compared to the oxygen evolution. More importantly, the calculation explains the fundamental roles of nitrogen doping and oxygen functional groups in the adiabatic and nonadiabatic charge decay mechanisms.

Internal Rotation and Equilibrium Structure of the Bromonitromethane Molecule According to Gas Electron Diffraction Data and Quantum Chemical Calculations

The structure and internal rotation of the bromonitromethane molecule are studied using electron diffraction analysis and quantum chemical calculations. The electron diffraction data are analyzed within the models of a general intramolecular anharmonic force field and quantum chemical pseudoconformers to account for the adiabatic separation of a large amplitude motion associated with the internal rotation of the NO2 group. The following experimental bond lengths and valence angles are obtained for the equilibrium orthogonal configuration of the molecule with Cs symmetry: re(N=O) = 1.217(5) A, re(C–N) = 1.48(2) A, re(C–Br) = 1.919(5) A, ∠еBr–C–N = 109.6(9)°, ∠еO=N=O = 125.9(9)°. The equilibrium geometry parameters are in good agreement with CCSD(T)/cc-pVTZ calculations. Thermally averaged parameters are calculated using the equilibrium geometry and quadratic and cubic quantum chemical force constants. The barrier to internal rotation cannot be determined reliably based on the electron diffraction data used in this work. There is a 82% probability that the equilibrium configuration with orthogonal C–Br and N=O bonds is most preferable, and internal rotation barrier does not exceed 280 cm-1, which agrees with CCSD(T)/cc-pVTZ calculations.

On the force–velocity relationship of a bundle of rigid bio-filaments

In various cellular processes, bio-filaments like F-actin and F-tubulin are able to exploit chemical energy associated with polymerization to perform mechanical work against an obstacle loaded with an external force. The force–velocity relationship quantitatively summarizes the nature of this process. By a stochastic dynamical model, we give, together with the evolution of a staggered bundle of Nf rigid living filaments facing a loaded wall, the corresponding force–velocity relationship. We compute the evolution of the model in the infinite wall diffusion limit and in supercritical conditions (monomer density reduced by critical density ρ^1>1), and we show that this solution remains valid for moderate non-zero values of the ratio between the wall diffusion and the chemical time scales. We consider two classical protocols: the bundle is opposed either to a constant load or to an optical trap setup, characterized by a harmonic restoring force. The constant load case leads, for each F value, to a stationary velocity Vstat(F;Nf,ρ^1) after a relaxation with characteristic time τmicro(F). When the bundle (initially taken as an assembly of filament seeds) is subjected to a harmonic restoring force (optical trap load), the bundle elongates and the load increases up to stalling over a characteristic time τOT. Extracted from this single experiment, the force–velocity VOT(F;Nf,ρ^1) curve is found to coincide with Vstat(F;Nf,ρ^1), except at low loads. We show that this result follows from the adiabatic separation between τmicro and τOT, i.e., τmicro ≪ τOT.

Internal rotation and equilibrium structure of the 2-methyl-2-nitropropane molecule from joint processing of gas phase electron diffraction data, vibrational and microwave spectroscopy data, and quantum chemical calculation results

The structure and internal rotation of the 2-methyl-2-nitropropane molecule is studied by electron diffraction and quantum chemical calculations with the use of microwave and vibrational spectroscopy data. The electron diffraction data are analyzed within the general intramolecular anharmonic force field model and the quantum chemical pseudoconformer model, considering the adiabatic separation of the degree of freedom of large amplitude motion, i.e., the internal rotation of the NO2 group. The equilibrium eclipsed configuration of the C s symmetry molecule has the following experimental bond lengths and valence angles: r e(N=O) = 1.226//1.226(8) A, r e(C–N)//r e(C–C) = 1.520//1.515/1,521(4) A, ∠еC–C–N = = 109.1/106,1(8)°, ∠еO=N=O = 124.2(6)°, ∠eC–C–Havg = 110(3)°. The equilibrium geometry parameters are well consistent with MP2/cc-pVTZ quantum chemical calculations and microwave spectroscopy data. The thermally average parameters previously obtained within the small vibration model show a satisfactory agreement with the new results. The electron diffraction data used in this work do not allow a reliable determination of the barrier to internal rotation. However, at a barrier of 203(2) cal/mol, which is derived from the microwave study, it follows from the electron diffraction data that the equilibrium configuration must correspond to an eclipsed arrangement of C–C and N=O bonds, which is also consistent with the results of quantum chemical calculations of various levels.

Multiscale enhanced sampling for protein systems: An extension via adiabatic separation

Multiscale enhanced sampling (MSES) calculates the configurational ensemble of all-atom (MM) protein systems with the help of coupling to a coarse-grained (CG) model. Here, for further improvement of the sampling efficiency, the approximation of adiabatic separation was introduced to the original MSES, by adopting a high CG temperature limit. An application to the folding of chignolin in explicit solvent demonstrated that the MSES formula based on adiabatic separation correctly sampled the canonical ensemble with excellent efficiency and robustness against the parameter selection, and thus MSES successfully achieved the scalability for applications to large protein systems.

Exciton absorption in narrow armchair graphene nanoribbons

We develop an analytical approach to the exciton optical absorption for narrow gap armchair graphene nanoribbons (AGNR). We focus on the regime of dominant size quantization in combination with the attractive electron–hole interaction. An adiabatic separation of slow and fast motions leads via the two-body Dirac equation to the isolated and coupled subband approximations. Discrete and continuous exciton states are in general coupled and form quasi-Rydberg series of purely discrete and resonance type character. The corresponding oscillator strengths and widths are derived. We show that the exciton peaks are blue-shifted, become broader and increase in magnitude upon narrowing the ribbon. At the edge of a subband the singularity related to the 1D density of states is transformed into finite absorption via the presence of the exciton. Our analytical results are in good agreement with those obtained by other methods including numerical approaches. Estimates of the expected experimental values are provided for realistic AGNR.