Ion trajectory simulation for electrode configurations with arbitrary geometries

A multi-particle ion trajectory simulation program ITSIM 6.0 is described, which is capable of ion trajectory simulations for electrode configurations with arbitrary geometries. The electrode structures are input from a 3D drawing program AutoCAD and the electric field is calculated using a 3D field solver COMSOL. The program CreatePot acts as interface between the field solver and ITSIM 6.0. It converts the calculated electric field into a field array file readable by ITSIM 6.0 and ion trajectories are calculated by solving Newton's equation using Runge-Kutta integration methods. The accuracy of the field calculation is discussed for the ideal quadrupole ion trap in terms of applied mesh density. Electric fields of several different types of devices with 3D geometry are simulated, including ion transport through an ion optical system as a function of pressure. Ion spatial distributions, including the storage of positively charged ions only and simultaneous storage of positively/negatively charged ions in commercial linear ion traps with various geometries, are investigated using different trapping modes. Inelastic collisions and collision induced dissociation modeled using RRKM theory are studied, with emphasis on the fragmentation of n-butylbenzene inside an ideal quadrupole ion trap. The mass spectrum of 1,3-dichlorobenzene is simulated for the rectilinear ion trap device and good agreement is observed between the simulated and the experimental mass spectra. Collisional cooling using helium at different pressures is found to affect mass resolution in the rectilinear ion trap.     

Computer simulation of single-ion trajectories in paul-type ion traps

The computer simulation of single-ion trajectories using a number of computer programs is described together with associated theory. The programs permit calculation of ion trajectories while the ion is subjected to collisions with buffer gas of variable pressure, resonance excitation in any of three modes, and static or ramped DC and radiofrequency levels. Initially, the programs were designed for the calculation of ion trajectories in a quadrupole ion trap. The programs now permit such calculations for ions confined in traps having electrodes shaped to include percentages of hexapole and octupole components in the electric field as well as electrode surface geometries for which there is no closed-form expression. The Langevin collision theory is reviewed and a theoretical treatment of the multipole trap is presented.     

Realistic modeling of ion cloud motion in a Fourier transform ion cyclotron resonance cell by use of a particle-in-cell approach

Using a 'Particle-In-Cell' approach taken from plasma physics we have developed a new three-dimensional (3D) parallel computer code that today yields the highest possible accuracy of ion trajectory calculations in electromagnetic fields. This approach incorporates coulombic ion-ion and ion-image charge interactions into the calculation. The accuracy is achieved through the implementation of an improved algorithm (the so-called Boris algorithm) that mathematically eliminates cyclotron motion in a magnetic field from digital equations for ion motion dynamics. It facilitates the calculation of the cyclotron motion without numerical errors. At every time-step in the simulation the electric potential inside the cell is calculated by direct solution of Poisson's equation. Calculations are performed on a computational grid with up to 128 x 128 x 128 nodes using a fast Fourier transform algorithm. The ion populations in these simulations ranged from 1000 up to 1,000,000 ions. A maximum of 3,000,000 time-steps were employed in the ion trajectory calculations. This corresponds to an experimental detection time-scale of seconds. In addition to the ion trajectories integral time-domain signals and mass spectra were calculated. The phenomena observed include phase locking of particular m/z ions (high-resolution regime) inside larger ion clouds. A focus was placed on behavior of a cloud of ions of a single m/z value to understand the nature of Fourier transform ion cyclotron resonance (FTICR) resolution and mass accuracy in selected ion mode detection. The behavior of two and three ion clouds of different but close m/z was investigated as well. Peak coalescence effects were observed in both cases. Very complicated ion cloud dynamics in the case of three ion clouds was demonstrated. It was found that magnetic field does not influence phase locking for a cloud of ions of a single m/z. The ion cloud evolution time-scale is inversely proportional to magnetic field. The number of ions needed for peak coalescence depends quadratically on the magnetic field.     

Molecular latent space simulators

Small integration time steps limit molecular dynamics (MD) simulations to millisecond time scales. Markov state models (MSMs) and equation-free approaches learn low-dimensional kinetic models from MD simulation data by performing configurational or dynamical coarse-graining of the state space. The learned kinetic models enable the efficient generation of dynamical trajectories over vastly longer time scales than are accessible by MD, but the discretization of configurational space and/or absence of a means to reconstruct molecular configurations precludes the generation of continuous atomistic molecular trajectories. We propose latent space simulators (LSS) to learn kinetic models for continuous atomistic simulation trajectories by training three deep learning networks to (i) learn the slow collective variables of the molecular system, (ii) propagate the system dynamics within this slow latent space, and (iii) generatively reconstruct molecular configurations. We demonstrate the approach in an application to Trp-cage miniprotein to produce novel ultra-long synthetic folding trajectories that accurately reproduce atomistic molecular structure, thermodynamics, and kinetics at six orders of magnitude lower cost than MD. The dramatically lower cost of trajectory generation enables greatly improved sampling and greatly reduced statistical uncertainties in estimated thermodynamic averages and kinetic rates.

Latent space simulators learn kinetic models for atomistic simulations and generate novel trajectories at six orders of magnitude lower cost.     

A model for energy transfer in inelastic molecular collisions applicable at steady state or non-steady state and for an arbitrary distribution of collision energies

A new model for energy exchange between translational and internal degrees of freedom in atom-molecule collisions has been developed. It is suitable for both steady state conditions (e.g., a large number of collisions with thermal kinetic energies) and non-steady state conditions with an arbitrary distribution of collision energies (e.g., single high-energy collisions). In particular, it does not require that the collision energies be characterized by a quasi-thermal distribution, but nevertheless it is capable of producing a Boltzmann distribution of internal energies with the correct internal temperature under quasi-thermal conditions. The energy exchange is described by a transfer probability density that depends on the initial relative kinetic energy, the internal energy of the molecule, and the amount of energy transferred. The probability density for collisions that lead to excitation is assumed to decrease exponentially with the amount of transferred energy. The probability density for de-excitation is obtained from microscopic reversibility. The model has been implemented in the ion trap simulation program ITSIM and coupled with an Rice-Rampsberger-Kassel-Marcus (RRKM) algorithm to describe the unimolecular dissociation of populations of ions. Monte Carlo simulations of collisional energy transfer are presented. The model is validated for non-steady state conditions and for steady state conditions, and the effect of the kinetic energy dependence of the collision cross-section on internal temperature is discussed. Applications of the model to the problem of chemical mass shifts in RF ion trap mass spectrometry are shown.     

Study of the enhancement of dipolar resonant excitation by linear ion trap simulations

Resolution improvements in dipolar resonant excitation have been examined in a round-rod quadrupolar collision cell for values of the Mathieu characteristic exponent beta equal to n/p, where n and m are small integers (prime beta values) versus other beta values where n and p are not small (ordinary beta values). The trajectories of ions moving in the time-varying electric fields of a quadrupole with and without buffer-gas molecules were calculated to determine the relationship of prime and ordinary beta values to frequency resolution for resonant ion excitation and ejection. For prime beta values, the ion trajectory in the hyperbolic quadrupole field will be exactly periodic with a period of at most 4 pi p/Omega, where Omega is the angular frequency of the main drive radio-frequency (RF) potential. Ion trajectory simulations with prime beta versus ordinary beta values show that the motion of ions with prime beta values have simpler trajectories of shorter periods. Frequency response profiles (FRPs) for round-rod quadrupoles at zero pressure show that dipolar resonant excitations with prime beta values exhibit significantly narrower bandwidths than those with ordinary beta values. Simulations show that at 0.05 to 0.8 mTorr of nitrogen, it is possible to reduce the FRP bandwidth by 20% (measured at 50% depth).     

Dynamic collision-induced dissociation (DCID) in a quadrupole ion trap using a two-frequency excitation waveform: II. Effects of frequency spacing and scan rate

Dynamic CID of selected precursor ions is achieved by the application of a two-frequency excitation waveform to the end-cap electrodes during the mass instability scan of a quadrupole ion trap (QIT) mass spectrometer. This new method permits a shorter scanning time when compared with conventional on-resonance CID. When the excitation waveform consists of two closely-spaced frequencies, the relative phase-relationship of the two frequencies plays a critical role in the fragmentation dynamics. However, at wider frequency spacings (>10 kHz), these phase effects are diminished, while maintaining the efficacy of closely-spaced excitation frequencies. The fragmentation efficiencies and energetics of n-butylbenzene and tetra-alanine are studied under different experimental conditions and the results are compared at various scan rate parameters between 0.1 and 1.0 ms/Th. Although faster scan rates reduce the analysis time, the maximum observed fragmentation efficiencies rarely exceed 30%, compared with values in excess of 50% achieved at slower scan rates. The internal energies calculated from the simulations of n-butylbenzene at fast scan rates are approximately 4 eV for most experimental conditions, while at slow scan rates, internal energies above 5.5 eV are observed for a wide range of conditions. Extensive ITSIM simulations support the observation that slowing the scan rate has a similar effect on fragmentation as widening the frequency spacing between the two excitation frequencies. Both approaches generally enhance CID efficiencies and make fragmentation less dependent upon the relative phase angle between the excitation waveform and the ion motion.     

Molecular dynamics analysis of Mg2+-dependent cleavage of a pistol ribozyme reveals a fail-safe secondary ion for catalysis

Pistol ribozymes comprise a class of small, self-cleaving RNAs discovered via comparative genomic analysis. Prior work in the field has probed the kinetics of the cleavage reaction, as well as the influence of various metal ion cofactors that accelerate the process. In the current study, we performed unbiased and unconstrained molecular dynamics simulations from two current high-resolution pistol crystal structures, and we analyzed trajectory data within the context of the currently accepted ribozyme mechanistic framework. Root-mean-squared deviations, radial distribution functions, and distributions of nucleophilic angle-of-attack reveal insights into the potential roles of three magnesium ions with respect to catalysis and overall conformational stability of the molecule. A series of simulation trajectories containing in silico mutations reveal the relatively flexible and partially interchangeable roles of two particular magnesium ions within solvated hydrogen-bonding distances from the catalytic center.     

Energetics and efficiencies of collision‐induced dissociation achieved during the mass acquisition scan in a quadrupole ion trap

Using n‐butylbenzene as a test molecule, evidence is provided that fast, efficient or highly energetic collision‐induced dissociation (CID) can be achieved during the mass acquisition ramp of a commercially available quadrupole ion trap (QIT) mass spectrometer. The method of excitation is very similar to axial modulation for mass range extension except that lower amplitude waveforms are used to excite the precursor ions within the trap instead of ejecting them from the trap. ITSIM simulations verify that fast kinetic excitation followed by kinetic‐to‐internal energy transfer occurs on the rapid time‐scale required for the recapture and mass analysis of product ions during the mass acquisition ramp. CID efficiencies larger than 50% can be obtained using this new approach and ratios of Th 91/92 of n‐butylbenzene fragment ions as large as 9 are possible, albeit at significantly reduced efficiencies. These very large ratios indicate an internal energy above 7 eV for the precursor ions indicating that fragmentation of larger ions could also be possible using this new approach. The main benefits of the new method are that no extra time is required for fragmentation or cooling and that on‐resonance conditions are guaranteed because the ions' secular frequencies are swept through the fixed frequency of excitation. Also presented are the effects of experimental variables such as excitation frequency, excitation amplitude and scan rate on the CID efficiencies and energetics. Copyright © 2005 John Wiley & Sons, Ltd.     

Collision induced dissociation of doubly-charged ions: Coulomb explosion vs. neutral loss in [Ca(urea)](2+) gas phase unimolecular reactivity via chemical dynamics simulations

In this paper we report different theoretical approaches to study the gas-phase unimolecular dissociation of the doubly-charged cation [Ca(urea)](2+), in order to rationalize recent experimental findings. Quantum mechanical plus molecular mechanical (QM/MM) direct chemical dynamics simulations were used to investigate collision induced dissociation (CID) and rotational-vibrational energy transfer for Ar + [Ca(urea)](2+) collisions. For the picosecond time-domain of the simulations, both neutral loss and Coulomb explosion reactions were found and the differences in their mechanisms elucidated. The loss of neutral urea subsequent to collision with Ar occurs via a shattering mechanism, while the formation of two singly-charged cations follows statistical (or almost statistical) dynamics. Vibrational-rotational energy transfer efficiencies obtained for trajectories that do not dissociate during the trajectory integration were used in conjunction with RRKM rate constants to approximate dissociation pathways assuming complete intramolecular vibrational energy redistribution (IVR) and statistical dynamics. This statistical limit predicts, as expected, that at long time the most stable species on the potential energy surface (PES) dominate. These results, coupled with experimental CID from which both neutral loss and Coulomb explosion products were obtained, show that the gas phase dissociation of this ion occurs by multiple mechanisms leading to different products and that reactivity on the complicated PES is dynamically complex.     

Selective sampling of transition paths

In this short paper, we introduce an approximate method for the quick estimate of rate constants based on a simple sampling method of reactive transition paths over high energy barriers. It makes use of the previously introduced accelerated molecular dynamics (MD) simulation method to generate initial points for trajectory shooting. The accelerated MD simulations, although with the loss of real dynamics, lead to a quick calculation of thermodynamic properties and at the same time produce an ensemble of configurations with an enhanced sampling over the phase space that is more "reactive." The forward/backward trajectory shooting as that used in the transition path sampling method is then initiated from the configurations obtained from accelerated MD simulations to generate transition paths on the original unbiased potential. This method selectively enhances sampling of successful trajectories and at the same time accelerates significantly the calculation of rate constants.     

Monte Carlo simulation of ion transport in ion mobility spectrometry

A program for simulation of ion trajectories in ion mobility spectrometry (IMS) instruments has been developed and incorporated into SIMION 7.0 [Int. J. Mass Spectrom. 200 (2000) 3–25]. Simulations were based on elastic collisions between ions and gas particles and conducted for an IMS drift tube. The program was validated by comparing the reduced mobility of helium ions derived from the simulation with the experimental data for helium ions in neon drift gas in low electric fields. Typical IMS parameters, including pressure, temperature, and flow rate of the drift gas were taken into account in the simulations. The program demonstrates capabilities of generating IMS spectra and predicting ion transport efficiency and separating ions. For the IMS drift tube studied, a correlation between imperfection of the electric field distribution and low resolution has been observed.     

Simulated ion trajectory and induced signal in ion cyclotron resonance ion traps

We present a numerical method for computation of electrostatic (trapping) and time-varying (excitation) electric fields and the resulting ion trajectory and detected time-domain-induced voltage signal in a rectangular (or cubic) ion cyclotron resonance (ICR) ion trap. The electric potential is calculated by use of the superposition principle and relaxation method with a large number of grid points (e.g., 100 × 100 × 100 for a cubic trap). Complex ICR experiments and spectra may now be simulated with high accuracy. Ion trajectories may be obtained for any combination of trapping and excitation modes, including quadrupolar or cubic trapping in static or dynamic mode; and dipolar, quadrupolar, or parametric excitation with single-frequency, frequency-sweep (chirp), or stored waveform inverse Fourier transform waveforms. The resulting ion trajectory may be represented either as its three dimensional spatial path or as two-dimensional plots of x-, y-, or z-position, velocity, or kinetic energy versus time in the absence or presence of excitation. Induced current is calculated by use of the reciprocity principle, and simulated ICR mass spectra are generated by Fourier transform of the corresponding time-domain voltage signal.     

Enhanced simulation of an RF ion funnel including gas turbulence

Electrodynamic ion funnels are used to enhance the transmission of ions in electrospray‐based ion injection systems in 0.1 to 30 Torr pressure range. Jet disrupters are commonly employed to prevent droplets and high pressure jets from entering subsequent vacuum regions. This study presents the simulation and testing of an ion funnel containing a jet disrupter using computational fluid dynamics (CFD) and SIMION ion trajectory simulations. Traditional modeling approaches have utilized approximations for the bulk fluid flow fields without including the time‐varying nature of the turbulent flow present in the system, thus yielding idealized results. In this study, the fluid flow fields are calculated using CFD. In an effort to include time dependence, a random velocity vector, whose magnitude is proportional to the square root of the turbulence kinetic energy, was calculated at each time step and added to the velocity of the background gas. These simulations predicted that the transmitted ion current is effectively modulated by the variation of the jet disrupter voltage. The addition of the random velocity vector produced results that closely matched the experiments. The simulations yielded the dependence of the transmission on the jet disrupter voltage, and the voltage necessary for maximum ion throughput was accurately predicted. In addition, the magnitude of the predicted transmission closely matched that of the experimental results. This modeling approach could be extended to similar ion transport and filtering systems in which the effects of turbulent fluid flow cannot be ignored. Copyright © 2015 John Wiley & Sons, Ltd.     

Ion trajectories in an electrostatic ion guide for external ion source fourier transform ion cyclotron resonance mass spectrometry

An electrostatic ion guide (EIG) that consists of concentric cylinder and central wire electrodes can transport ions efficiently from an external ion source to an ion cyclotron resonance (ICR) ion trap for mass analysis, with several advantages over current injection methods. Because the electrostatic force of the EIG captures ions in a stable orbit about the wire electrode, ions with initially divergent trajectories may be redirected toward the ICR ion trap for improved ion transmission efficiency. SIMION trajectory calculations (ion kinetic energy, 1–200 eV; elevation angle, 0.30 °; azimuthal angle, 0.360°) predict that ions of m/z 1000 may be transmitted through a strong (0.01 → 3.0-T) magnetic field gradient. Judicious choice of ion source position and EIG potential minimizes the spread in ion axial kinetic energy at the ICR ion trap. Advantages of the EIG include large acceptance angle, even for ions that have large initial kinetic energy and large radial displacement with respect to the central z-axis, low ion extraction voltage (5–20 V), and efficient trapping because ions need not be accelerated to high velocity to pass through the magnetic field gradient.     

Classical trajectories and RRKM modeling of collisional excitation and dissociation of benzylammonium and <Emphasis Type="Italic">tert</Emphasis>-butyl benzylammonium ions in a quadrupole-hexapole-quadrupole tandem mass spectrometer

Collision-induced dissociation of the benzylammonium and the 4-tert-butyl benzylammonium ions was studied experimentally in an electrospray ionization quadrupole-hexapole-quadrupole tandem mass spectrometer. Ion fragmentation efficiencies were determined as functions of the kinetic energy of ions and the collider gas (argon) pressure. A theoretical Monte Carlo model of ion collisional excitation, scattering, and decomposition was developed. The model includes simulation of the trajectories of the parent and the product ions flight through the hexapole collision cell, quasiclassical trajectory modeling of collisional activation and scattering of ions, and Rice-Ramsperger-Kassel-Marcus (RRKM) modeling of the parent ion decomposition. The results of modeling demonstrate a general agreement between calculations and experiment. Calculated values of ion fragmentation efficiency are sensitive to initial vibrational excitation of ions, scattering of product ions from the collision cell, and distribution of initial ion velocities orthogonal to the axis of the collision cell. Three critical parameters of the model were adjusted to reproduce the experimental data on the dissociation of the benzylammonium ion: reaction enthalpy and initial internal and translational temperatures of the ions. Subsequent application of the model to decomposition of the t-butyl benzylammonium ion required adjustment of the internal ion temperature only. Energy distribution functions obtained in modeling depend on the average numbers of collisions between the ion and the atoms of the collider gas and, in general, have non-Boltzmann shapes.     

State(R)-state(TS)-state(P) theoretical study of H+H_2 system

The calculation of H + H2 system by symplectic quasiclassical trajectory (SQCT) shows that there are two types of collision trajectories A and B, i.e., type A trajectory passes the saddle point of transition state (TS), whereas type B trajectory does not pass the saddle point of transition state. Not all the reactants of type A trajectory are reactive, while not all of type B trajectory are nonreactive. The partition and reactivity of these two types of trajectories are affected by reactant state(R), furthermore, the types of trajectories affect the state and angle distributions of products. Not only the rudiment framework for theoretical study on state(R)-state(TS)-state(P) is established, but also the further understanding of transition state theory (TST) of Eyring is investigated in this paper.     

Classical line shapes based on analytical solutions of bimolecular trajectories in collision induced emission

The classical theory of collision induced emission (CIE) from pairs of dissimilar atoms is studied. This radiation emitted by accelerating dipoles is produced essentially by their overlap and exchange interaction at short range. This classical calculation is based on exact collinear solutions of the trajectories of two spherical particles in a head-on collision under the influence of a Morse potential with a well of arbitrary depth. Without too restrictive conditions a variety of simple solutions in closed form is obtained that illustrates the connection between collision dynamics and CIE. Depending on the well depth and energy of the particles, they may radiate in the far infrared to infrared or visible and shorter wavelength regions. The results are characterized by a fixed total energy. Nevertheless, a connection is demonstrated between the line shape in CIE computed through the trajectory and that based on the emission of a thermally equilibrated system.     

State(R)-state(TS)-state(P) theoretical study of H + H<Subscript>2</Subscript> system

The calculation of H + H₂ system by symplectic quasiclassical trajectory (SQCT) shows that there are two types of collision trajectories A and B, i.e., type A trajectory passes the saddle point of transition state (TS), whereas type B trajectory does not pass the saddle point of transition state. Not all the reactants of type A trajectory are reactive, while not all of type B trajectory are nonreactive. The partition and reactivity of these two types of trajectories are affected by reactant state(R), furthermore, the types of trajectories affect the state and angle distributions of products. Not only the rudiment framework for theoretical study on state(R)-state(TS)-state(P) is established, but also the further understanding of transition state theory (TST) of Eyring is investigated in this paper.