Classical Trajectories Modeling of Collisional

May 18, 2010 - The Monte Carlo method used includes simulation of the trajectories of flight of the parent (n-C4H9C6H5+) ... Paul M. Mayer , Eric Mart...
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J. Phys. Chem. A 2010, 114, 6384–6393

Monte Carlo/RRKM/Classical Trajectories Modeling of Collisional Excitation and Dissociation of n-Butylbenzene Ion in Multipole Collision Cells of Tandem Mass Spectrometers Vadim D. Knyazev*,†,‡ and Stephen E. Stein† Chemical and Biochemical Reference Data DiVision, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, and Research Center for Chemical Kinetics, Department of Chemistry, The Catholic UniVersity of America, Washington, D.C. 20064 ReceiVed: February 19, 2010; ReVised Manuscript ReceiVed: April 28, 2010

The two-channel reaction of collision-induced dissociation (CID) of the n-butylbenzene cation under the conditions of multipole collision cells of tandem mass spectrometers was studied computationally. The results were compared with the experimental data from earlier CID studies. The Monte Carlo method used includes simulation of the trajectories of flight of the parent (n-C4H9C6H5+) and the product (C7H7+ and C7H8+) ions in the electromagnetic field of multipole ion guides and collision cells, classical trajectory modeling of collisional activation and scattering of ions, and RRKM modeling of the parent ion decomposition. Experimental information on the energy dependences of the rates of the n-butylbenzene cation dissociation via two channels was used to create an RRKM model of the reaction. Effects of uncertainties in the critical parameters of the model of the reaction and the collision cells on the results of calculations were evaluated and shown to be minor. The results of modeling demonstrate a good agreement with experiment, providing support for the applied computational method in general and the use of classical trajectory modeling of collisional activation of ions in particular. 1. Introduction Collision-induced dissociation (CID) of gaseous ions is an important source of information on the properties of these ions and the corresponding parent species (e.g., refs 1-11). In a typical CID experiment performed in a three-stage tandem mass spectrometer, ions of interest are selected by the first stage of the instrument and then are vibrationally and rotationally excited via collisions with an inert gas in the second stage (collision cell). These excited ions undergo fragmentation, with products and undissociated parent ions detected by the third stage of the mass spectrometer. CID mass spectrometers are extensively used for analysis of structures of various types of molecules, including those of biological origin. However, factors determining absolute and relative abundances of ion fragments in the resultant mass spectra are not well understood. The extent and distribution of products of CID of polyatomic ions are determined by three factors: (1) the chemical mechanism of fragmentation, (2) rovibrational excitation of the parent ion as a result of collisions with the inert collider gas, and (3) kinetics of the dissociation of ions in competition with deactivating collisions and removal of ions (via scattering or detection) from the collision cell of the mass spectrometer. Among these three factors, the collisional excitation of ions is probably the one least well understood. There is an ongoing effort by a number of researchers to derive major features of collisional excitation from modeling experimental results on CID, such as dependences of ion fragmentation efficiency on collision energy, collider gas pressure, and functional group substituents affecting decomposition energy barriers. In some of these studies, energy distributions are presented in a form of * Corresponding author. E-mail: [email protected]. † National Institute of Standards and Technology. ‡ The Catholic University of America.

effective temperatures, with an implicit assumption of Boltzmann-like distribution shapes. In other studies, non-Boltzmann analytical functions with adjustable parameters are used to fit experimental data (e.g., refs 10, 12-15). A significant nonempirical effort toward understanding the characteristics of percollision activation functions was performed by Meroueh and Hase.16,17 These authors theoretically studied energy transfer in activation of small peptide ions by collisions with noble gas atoms (mostly argon) using classical trajectory calculations. Dependences of energy transfer on peptide size and conformation, relative kinetic energy of colliders, peptide temperature, intermolecular potential, and collider mass were evaluated. Rather broad energy-dependent activation functions were obtained, with considerable contributions at both small and large values of energy transferred per collision. In a more recent work, Martinez-Nunez et al.18 extended the method of Meroueh and Hase by including a Morse function term in the force field describing the potential energy surface of the ion and thus enabling theoretical modeling of both ion excitation and dissociation. These authors applied the method to modeling CID of a small ion, Cr(CO)6+, in collisions with the xenon atom collider. Effective dissociation cross sections were calculated using a combination of classical trajectory modeling of collisional excitation and fast “direct” ion dissociation with RRKM modeling of slower decomposition of vibrationally excited ions. The results of theoretical calculations were compared to the experimental data of Muntean and Armentrout obtained in the 1-5 eV range of the center-of-mass collision energy.14 The calculated collision energy dependences of ion dissociation cross sections corresponding to formation of the Cr(CO)5+, Cr(CO)4+, and Cr(CO)3+ products demonstrated a good agreement with the experimental results; formation of Cr(CO)2+ was underpredicted. This generally good accord between theory and experi-

10.1021/jp101526m  2010 American Chemical Society Published on Web 05/18/2010

Modeling of n-C4H9C6H5+ in Tandem Mass Spectrometers ment provides support for the use of classical trajectories to describe collisional activation of ions, indicating that realistic degrees of vibrational excitation can be obtained in such calculations. In a recent experimental and theoretical study,19 we combined the methodology of Meroueh and Hase with Monte Carlo simulation of ion flight through the collision cell, and RRKM modeling of ion dissociation. Reactions of dissociation of benzylammonium and tert-butyl benzylammonium ions were studied. The trajectories of the parent and the product ions flying through the hexapole RF-only collision cell of a mass spectrometer were modeled by solving classical equations of motion of a charged particle in RF electromagnetic field. Collisions of the ions with the argon collider gas were described by classical trajectory calculations similar to those of refs 16 and 17, which yielded information on vibrational and rotational excitation of ions, as well as on the changes in the value and direction of the ion velocity. Energy dependent probabilities of ion dissociation were obtained using the RRKM method; energy distributions and velocities of the products were modeled using the prior distribution model. The model explicitly included scattering of both the parent and the product ions out of the cell and the evolution of the kinetic and internal energies of ions during their flight through the collision cell. The results of the study indicated that the methodology described above is capable of successful quantitative modeling of CID in multipole collision cells, and, as part of this methodology, classical trajectory modeling realistically predicts collisional excitation of ions. However, several important parameters of the model, such as the energy barrier for ion decomposition and the initial effective internal and translational temperatures of the parent ions, were unknown (or known with poor precision) and had to be selected based on agreement between calculations and experiment. To further evaluate the performance of the methodology developed in our earlier work,19 it is highly desirable to model a CID system where all critical parameters are known with high degree of certainty, leaving no space for fitting or adjustment. For this purpose, we selected the collision induced dissociation of the n-butylbenzene cation. The reaction proceeds via two competing channels:

n-C4H9C6H5+ f C7H8+ + C3H6

(1a)

f C7H7+ + C3H7

(1b)

A large body of experimental and theoretical information on reaction 1 has been accumulated as a result of efforts by many researchers. An informative review can be found in an experimental and theoretical study of Muntean and Armentrout.15 These authors studied reaction 1 in a tandem CID mass spectrometer under very well characterized conditions (see below). The experimental results include the dependences of the cross sections for ion decomposition via channels 1a and 1b on the center of mass collision energy. The theoretical part of the work performed in ref 15 included a quantum chemical study of the reaction potential energy surface (PES) and the mechanisms of both decomposition channels, as well as modeling of the obtained experimental dependences using the RRKM method and analytical expressions for the energy dependent probability of energy transfer, which included an adjustable parameter, and for the kinetics of ion decomposition.

J. Phys. Chem. A, Vol. 114, No. 22, 2010 6385 The competition between the two channels of reaction 1 shifts depending on the internal energy of the excited n-C4H9C6H5+ ion. At low energies, formation of C7H8+ and propene via channel 1a dominates and at higher energies channel 1b producing C7H7+ and n-propyl radical becomes more important. The products of channel 1a are formed through a sequence of transformations consisting of an isomerization and decomposition.15 The rate-limiting “tight”20 transition state (a PES saddle point) is located somewhat below the products on the energy scale. The PES of channel 1b does not have a saddle point and the reaction occurs via separation of the C7H7+ and C3H7 moieties with a monotonically increasing potential energy;15,21,22 this channel is characterized by a “loose”20 transition state. The energy barrier for channel 1b is higher than that for channel 1a. Dependences of the rates of decomposition of the nbutylbenzene cation via channels 1a and 1b on its internal energy content have been studied by a variety of experimental techniques.23-27 The results of these studies establish the energy dependences of the rate constants of the two channels over wide ranges of energies (see below). This k(E) information, together with the well controlled conditions of the CID experiments of Muntean and Armentrout, leave very little space for any adjustments of the model of reaction 1. In the current study, an RRKM model of reaction 1 was created on the basis of the quantum chemical study of ref 15 and modified to fit the experimental k(E) dependences. Collision induced dissociation of the n-butylbenzene cation under the conditions of the CID experiments of Muntean and Armentrout15 was modeled using the method developed in ref 19. Monte Carlo simulation of several types of processes was used, including the parent and the product ions’ flight in the electromagnetic field of the octopole collision cell and the ion guide of the mass spectrometer, collisions with the xenon collider gas, rotational and vibrational excitation and changes in the values and directions of the ion velocity upon collision, and the parent ion dissociation via reaction channels 1a and 1b. Explicit accounting for the parent and the product ions scattering out of the cell was included (scattering was shown to be unimportant under the conditions of the experimental study of ref 15, see below). Classical trajectory calculations were used to model the ion-atom collisions and the resulting energy transfer and changes in ion velocities. The flexibility of the RRKM model was explored by varying the calculated k(E) dependences within the experimental envelopes of uncertainty of the k(E) dependences; the effect of these variations on the results of modeling the CID experiments was investigated. Finally, the same RRKM model and Monte Carlo method were used to simulate earlier CID experiments24,28 on reaction 1 performed in quadrupole collision cells of tandem mass spectrometers using the argon collider gas. The article is organized as follows. This section is an introduction. Section 2 describes the model of the reaction and the reactive environment, including the ion flight through collision cells and collisional excitation. Section 3 presents the results of modeling, and discussion is given in section 4. 2. The Model of Reaction 1 in a Multipole Collision Cell 2.1. The RRKM Model. The RRKM model of reaction 1 was created using quantum chemical calculations of Muntean and Armentrout15 as the basis and was adjusted to fit the experimental information on the energy dependent rate constants of the individual channels. In the initial version of the model, the vibrational frequencies and the rotational constants of the

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reactant, the products, and the transition states of reaction 1 were taken from the results of quantum chemical calculations in ref 15. The reduced moments of inertia of the internal torsional degrees of freedom were calculated using the formulas of Pitzer and Gwinn.29,30 Rotational barriers were calculated from the values of the torsional frequencies assuming sinusoidal barrier shapes. Energies of the transition states and the products relative to that of the reactant were also taken from ref 15. The lowest vibrational frequencies of the transition states for reaction channels 1a and 1b, as well as the energies of the transition states, were adjusted to fit the experimental data on the energydependent rate constants (see below). These energy-dependent rate constants, k(E), were calculated using the RRKM method.31-33 In the calculations, the position of the transition state along the reaction coordinate was assumed to be fixed, even for the barrierless “loose” transition state of channel 1b, following the approach of Muntean and Armentrout. This simplification is justified because the final results of the RRKM calculations are the k(E) dependences for both reaction channels; the details of the calculation process and model are not important as long as the k(E) dependences agree with the experimental data. The modified Beyer-Swinehart algorithm34,35 was used for calculating the density of states and the sum of states functions used in the RRKM method. Contributions from hindered rotors were treated using the formulas of ref 36. Since the positions of the transition states for both channels 1a and 1b are below those of the products on the energy scale, values of k(E) were set to zero for energies between those of the corresponding transition state and the products. Experimental data on the energy dependent rates of the two channels of reaction 1 consist of two data sets. One is the result of two studies26,27 of the rates of the reaction channel 1a as a function of the internal energy, kA(E). The other is the result of several determinations23-27 of the ratio of the rate of nbutylbenzene cation decomposition via channel 1b to that occurring via channel 1a, r(E) ) kB(E)/kA(E). Experimental data on the kA(E) dependence are presented in Figure 1. Baer et al.26 determined the values of kA(E) in the 7.5 × 104 to 1.5 × 106 s-1 range using the photoelectron photoion coincidence (PEPICO) method. Two PEPICO experimental setups were used, one located at the University of North Carolina (UNC) and the other at the University of Paris-Sud (UPSUD) in Orsay, France. The results of the two determinations shown in Figure 1 by the hollow and the filled circles, respectively, are in general good agreement but demonstrate a systematic difference, with the UNC results being about 40% higher than the UPSUD values. Oh et al.27 used the photodissociation mass-analyzed ion kinetic energy spectroscopy (PD-MIKES) technique and obtained the values of kA(E) in the (0.9-2.9) × 108 s-1 range. The authors of the PD-MIKES study report experimental uncertainties in the 20-37% range; the PEPICO study did not present uncertainty information. Experimental information on the competition between channels 1a and 1b expressed as the ratio of rate constants was reported by many groups. Figure 2 presents the results obtained in experiments utilizing charge exchange mass spectrometry (Harrison and Lin23 and Nacson and Harrison24), ion cyclotron resonance mass spectrometry (Chen et al.25), PEPICO technique (Baer et al.26), and PD-MIKES method (Oh et al.27). The combined data set covers 2 orders of magnitude of the r(E) values and is presented in Figure 2 in both linear and semilogarithmic formats. The results of different experimental studies shown on the plot are in general agreement with each other, with data scattering corresponding to an uncertainty of

Knyazev and Stein

Figure 1. Dependence of the rate constant of reaction channel 1a on the energy in active degrees of freedom of the n-butylbenzene cation. Symbols represent experimental data from Baer et al.26 (open circles, data obtained using the PEPICO instrument in the University of North Carolina; filled circles, data obtained using the PEPICO instrument in the University of Paris-Sud) and Oh et al.27 (diamonds, data obtained using the PD-MIKES method). Lines show the kA(E) dependences obtained in RRKM calculations performed in the current study, with transition state properties adjusted to fit the experimental data. The solid line represents the “central” model and the dashed lines represent the limiting “kA(plus)” and “kA(minus)” models fitted to the upper and the lower borderlines of the envelope of experimental uncertainties.

approximately (40%. Earlier studies of refs 37 and 38 performed using photodissociation mass spectrometry are in significant disagreement with the results shown in Figure 2 and are believed to be in error.26,27 Figures 1 and 2 present the kA(E) and the r(E) ) kB(E)/kA(E) data as functions of the energy in the active degrees of freedom, EACT, which include all vibrations, torsions, and one overall rotation.31-33 The values of EACT were calculated for each data point using the original data reported by the authors of refs 23-27, thermal energy values corresponding to the ion sources used in these studies, and the ionization potential of nbutylbenzene (8.66 ( 0.01 eV) reported by Baer et al.26 As described above, several lowest frequencies and energies of the transition states for channels 1a and 1b were adjusted to reproduce experimental data on energy-dependent rate constants. Specifically, in the first step of the fitting procedure, the properties of the transition state for channel 1a were adjusted to provide the best fit to the experimental data in Figure 1. The resultant calculated kA(E) dependence is shown on the plot with a solid line. In the second step, properties of the transition state for channel 1b were adjusted to fit the data in Figure 2 (solid lines). The resultant model of reaction 1 is denoted as “central” henceforth. In order to investigate the effects of uncertainties in the model on the description of CID experiments (see below), limiting variations of the model were created. First, two extra versions, denoted as “kA(minus)” and “kA(plus),” were fitted to the upper and the lower borderlines of the envelope of uncertainties in Figure 1. Properties of the transition state for channel 1b were appropriately adjusted to preserve the best fit of the r(E) ) kB(E)/kA(E) dependence. The resultant kA(E) functions are shown on the plot with dashed lines. Second, for each of these three versions of the reaction model (“central,” “kA(minus),” and “kA(plus)”) variations of the channel 1b

Modeling of n-C4H9C6H5+ in Tandem Mass Spectrometers

Figure 2. Linear (a) and semilogarithmic (b) plots of the dependence of the channel branching ratio of reaction 1 on the energy in active degrees of freedom of the n-butylbenzene cation. Symbols represent experimental data from Harrison and Lin,23 Chen et al.,25 Nacson and Harrison,24 Baer et al.,26 and Oh et al.27 Lines show the dependences of the kB(E)/kA(E) ratio obtained in RRKM calculations performed in the current study, with transition state properties adjusted to fit the experimental data. The solid line represents the “central” model; the kB(E)/kA(E) dependences obtained using the models with higher or lower kA(E) values (“kA(plus)” and “kA(minus)”) coincide with that of the “central” model and thus are not shown. The dashed lines represent variations in the calculated kB(E)/kA(E) dependences due to the use of limiting versions of the models corresponding to the upper and the lower borders of the envelope of experimental uncertainties. Shown on the plot are the kB(E)/kA(E) dependences for the two of these limiting models, “kA(minus)kB/kA(minus),” “kA(minus)kB/kA(plus).”

transition state properties were selected, thus creating more limiting models, denoted as “kA(central)kB/kA(minus),” “kA(minus)kB/kA(minus),” “kA(minus)kB/kA(plus),” etc. Here, “kB/ kA(plus)” and “kB/kA(minus)” notations correspond to the upper and the lower borders of the envelope of uncertainties in Figure 2. Dashed lines in Figure 2 illustrate the r(E) dependences for the two of these limiting models, “kA(minus)kB/kA(minus),” “kA(minus)kB/kA(plus).” The “central” and the limiting versions of the model of reaction 1 were used in Monte Carlo modeling of CID of the n-butylbenzene cation, as described below. Details of the RRKM models of reaction 1 are given in the Supporting Information (Table 1S). 2.2. Monte Carlo Modeling of CID. Modeling of the processes of ion flight through the multipole collision cells and ion guides, their collisional excitation and dissociation, as well as scattering, was aimed at most closely reproducing the experimentally obtained quantities, i.e., ion counts of the parent and the product ions. It was assumed that, for each apparatus considered, the combination of the last stage of the tandem mass spectrometer and the ion detector has the same sensitivity to all ions irrespective of their masses and chemical identities.

J. Phys. Chem. A, Vol. 114, No. 22, 2010 6387 Thus, modeling of the events occurring in the collision cell or the collision cell/ion guide combination concentrated on the amounts of the parent and the product ions leaving the respective multipole assemblies through their exit apertures. Two experimental apparatuses were modeled. One is the double-octopole guided beam tandem mass spectrometer of Armentrout and co-workers.14,39 In this instrument, as applied to the study of reaction 1,15 thermalized (298 K) n-butylbenzene cations are focused into a two-part octopole ion guide with the combined length of 86.4 cm. The ions have well controlled values of the axial kinetic energy in the 1-10 eV range. A reaction cell (collision cell, 8.3 cm effective length) with the Xe collider gas at a pressure of 6.7 × 10-3 to 0.027 Pa (0.05-0.2 mTorr) is placed around part of the length of the first stage of the ion guide. As the parent ions traverse the collision cell part of the ion guide, a fraction of them is vibrationally excited by collisions. These excited ions can decompose via reaction channel 1a or 1b. The ions continue their flight through the remaining part of the ion guide, which gives them time available for dissociation measured in hundreds or thousands of microseconds, depending on the ion kinetic energy. The octopole ion guide utilizes relatively high value of the RF voltage (150 V at 5.0 MHz, peak to zero), which minimizes the loss of ions via scattering and ensures that most of the ions reach the last stage of the mass spectrometer, a quadrupole mass analyzer, and get detected. A detailed list of the structural and electric parameters of the apparatus used in modeling is given in the Supporting Information (Table 2S). The second apparatus is a triple-quadrupole tandem mass spectrometer described by Glish et al.40 and used by McLuckey et al.28 to study reaction 1. Here, the collision cell encloses a quadrupole ion guide (RF only, 1.85 MHz, 14 cm long). Some of the properties of the collision cell (e.g., the inscribed diameter of the quadrupole) were not reported by the authors, and thus the corresponding values were selected based on analogy with similar instruments. A detailed list of the parameters of the apparatus used in modeling is also given in the Supporting Information (Table 2S). The Monte Carlo algorithm used in the current study is described in ref 19, and only a brief overview is given here. Ions entering the hexapole through the entrance aperture are assumed to have an internal energy distribution characterized by an effective temperature TINT and a distribution of velocities orthogonal to the axis of the mass spectrometer described by an effective translational temperature TTR. Each individual ion entering the collision cell is assigned the following parameters: the kinetic energy of the motion along the cell axis EKIN, the energy of the active31-33 degrees of freedom EACT, the energy of the two-dimensional “adiabatic” overall rotation E2D, the b , and the coordinates of components of the velocity vector V the ion in the plane of the entrance aperture (X,Y). EACT and E2D are obtained using Monte Carlo selection from a thermal b directed distribution corresponding to TINT. The component of V along the cell axis, VZ, is determined by the value of EKIN; those orthogonal to the cell axis, VX and VY, are obtained via Monte Carlo selection from a thermal distribution corresponding to TTR. X and Y are randomly selected within the aperture. During the flight through the collision cell, the ion is always characterized by these parameters, which undergo evolution as a result of interaction with the RF electromagnetic field and collisions with the collider gas. If the active energy is sufficiently high, the ion can undergo decomposition via channel 1a or 1b with rate constants kDEC(A) and kDEC(B), which depend on the values of EACT and E2D. Thus, values of kDEC(A) and kDEC(B) are always

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assigned, zero in the case of low energies and nonzero (calculated from EACT and E2D) in the case of energy sufficient to overcome at least one of the barriers to decomposition. Each Monte Carlo trial begins with an ion characterized by b entering the collision EKIN, EACT, E2D, kDEC(A), kDEC(B), X, Y, and V cell. At this point, the ion path length L and lifetime with respect to reaction (decomposition) tDEC are randomly selected from appropriate distributions based on the values of the concentration of the collider gas and the rate constants of decomposition. In the beginning of the trial kDEC(A) and kDEC(B) are both equal to zero and tDEC is infinity. However, the automatic link between kDEC(A) and kDEC(B) and tDEC values is present here because this step of the algorithm is repeated via a loop later, with higher values of internal energy and generally nonzero rate constants. Then, in the next step of the algorithm, a trajectory of the ion flight through the collision cell is calculated using integration of the classical equations of motion of a charged particle in electromagnetic field. The trajectory continues until either the travel length L or the time tDEC is reached. The following outcomes of this trajectory calculation are possible: (1) scattering out of the cell, (2) exiting the collision cell through the exit aperture (detection), (3) collision with the collider gas, and (4) reaction (decomposition). Scattering means that the trajectory of the ion takes it outside the central region of the cell and the ion strikes one of the poles or the housing of the cell. In this case, the trial is terminated and the ion does not contribute to either the parent or the product signals. Exiting the collision cell (detection) means that the ion reached the end of the collision cell and exited through the exit aperture. In this case the ion is counted as contributing to the parent ion signal. If the ion reaches the end of the collision cell but strikes the part of the housing perpendicular to the axis of the cell, this event counts as scattering. Collision means that the ion collided with an atom of the collider gas. In this case, the collision event is modeled via classical trajectory calculation. This type of trajectory calculation is different from that used above in that the modeled event occurs on a significantly shorter time scale and the interaction defining the process is not that of a point charge with an electromagnetic field but of a polyatomic ion with an atom of the collider gas. Details of the ion-atom collision models and the computational procedures used are given below. After a collision occurs and its characteristics have been calculated (see below), the algorithm is looped into the first step, where the next values of the path length L and lifetime tDEC are selected. The reaction (decomposition) outcome of the trajectory run means that time equal to tDEC was reached before the distance traveled exceeded the value of L. In this case, the parent ion is replaced with a product ion (C7H8+ or C7H7+) and the corresponding values of the kinetic energy, energies of the adiabatic and active rotations, and components of the velocity vector b ′) are calculated. Calculation of these (E′KIN, E′ACT, E′2D, V quantities is performed via Monte Carlo selection from appropriate distributions of kinetic and internal energies of the ion and neutral reaction products obtained using the “prior distribution” model41 and the laws of conservation of energy and momentum. Selection of the product (C7H8+ or C7H7+) is performed in a Monte Carlo procedure based on the kDEC(B)/ kDEC(A) ratio. Trajectory of the product ion flight through the collision cell is then calculated using the same methodology that was applied to the parent ion, with the possibility of reaction excluded. The product ion can undergo collisions with the gas, with the poles or walls of the collision cell, or exit the cell

Knyazev and Stein through the exit aperture. In the latter case the ion is counted as contributing to the product ion signal. The above Monte Carlo algorithm is for a collision cell occupying the whole space of the multipole ion guide. In the experiments of Muntean and Armentrout,15 only a part of the ion guide was surrounded by a collision cell. Thus, the algorithm was modified to include the parts of the ion guide with zero collider gas pressures. In modeling these experiments, 2 × 105 Monte Carlo trials were performed for each set of conditions, i.e., ion kinetic energy and pressure in the collision cell. The results were expressed in the form of effective cross sections for reaction channels 1a and 1b, to enable comparison with the experimental results reported by the authors of ref 15. The values of cross sections were calculated from the ion counts for the detected parent and product ions using eqs 6 and 7 in Ervin and Armentrout.39 In modeling the experiment of McLuckey et al.,28 4 × 104 Monte Carlo trials were performed for each set of conditions. 2.3. The Collision Model. Classical trajectory calculations were performed to model the collisions of the ions with the monatomic collider gas (xenon and argon) and the resulting energy transfer and change in the value and direction of the ion’s velocity. The program MARINER,42 which is a customized version of VENUS96,43 was used in these calculations. For the purpose of collision simulations, the potential energy surface of the ion was represented with a force field employing three types of terms: harmonic bond stretches, harmonic bends, and torsions. This method of PES representation is well described in the literature (e.g., refs 44-46). AMBER44 force field parameters were used as the source of force constants needed to describe the PES of the polyatomic ions (nbutylbenzene, C7H7+, and C7H8+). The intermolecular potential describing the interaction between the collider atom and the polyatomic ion was of the pairwise-additive type, where the overall potential energy function is given by a sum of distancedependent potentials of interaction between the collider atom and all individual atoms of the ion. Two functions were used to represent Xe-ion interatomic potentials: the exponentialninth power expression

V(R) ) A9 exp(-B9 × R) +

C9 R9

(2)

and the exponential-sixth power expression

V(R) ) A6 exp(-B6 × R) +

C6 R6

(3)

Here, R is the interatomic distance and A, B, and C are the parameters specific to each combination of atoms. The exponential term describes the long-range attractive part of the potential, and the sixth or ninth power term is responsible for the short-range repulsive part. Only the exponential-ninth power function was used for Ar-ion interactions. The parameters A9, B9, and C9 of the Ar-ion potential were taken from the work of Meroueh and Hase,16 who used high-level quantum chemical calculations to evaluate the interactions between Ar atoms and the constituent atoms of small peptides, and from our earlier work,19 where the same method was used for interactions of Ar with aromatic rings. The parameters for the pairwise potentials of Xe-ion interaction were determined from quantum chemical calculations performed in this work using the same

Modeling of n-C4H9C6H5+ in Tandem Mass Spectrometers procedure. QCISD(T)/6-31++G(d,p) level47 calculations with counterpoise corrections43,48 were performed to determine the energy of interaction between Xe and benzene and Xe and methane at various separations. The Stuttgart-Dresden-Bonn pseudopotentials49 was used for Xe atoms. The resultant potential energy curves were fitted with expressions 2 and 3 to obtain the requisite parameters (given in Supporting Information, Table 3S). The exponential-ninth power potential (eq 2) was used in all calculations except those performed specifically to investigate the effects of using a different potential (see below). The velocity of the relative ion-atom motion was taken from the output of calculation of the trajectory of the ion flight through the collision cell and fed into the MARINER input. Thermal velocity of the collider atom was added via a random selection from the Maxwell-Boltzmann distribution. Other input data transferred to the MARINER program were the energy of the two-dimensional overall rotation of the ion and its energy in the active degrees of freedom. The latter value was added to the zero-point energy calculated from the vibrational frequencies resulting from the force field representation of the ion PES. The initial impact parameter b and the relative orientation of the ion-atom pair were selected using Monte Carlo sampling. The b parameter ranged from 0 to the maximum value of b0 (10.0 Å), which was used in calculating the cross section (πb02) for determining the probabilities of ion-atom collisions in the Monte Carlo selection of the ion path length L before modeling the ion flight through the collision cell (see above). Initial separation of the species in MARINER calculations was 15 Å; the integration time step was in the 0.1-0.3 fs range. For each event of an ion-atom collision, an individual trajectory was calculated and the output of the MARINER program was fed to subsequent calculations within the same continuing simulation of the individual ion’s travel through the collision cell. The following data were transferred: the changes in E2D and EACT due to collision and the changes in the value and the direction of the relative velocity of the colliding species b after the collision). The new value (used to calculate EKIN and V of kDEC was calculated using the new values of E2D and EACT; this value was later used in the Monte Carlo selection of the next lifetime tDEC of the ion. 3. Results 3.1. Modeling CID Experiments in Double-Octopole Guided Beam Tandem Mass Spectrometer with Xe Collider Gas. The experiments of Muntean and Armentrout were performed with pressures in the collision cell between 6.7 × 10-3 and 0.027 Pa (0.05 and 0.2 mTorr); the results were reported as cross sections for channels 1a and 1b extrapolated to zero pressure. Figure 3 displays the results of modeling performed in the current study using the “central” model of reaction 1 at different pressures in the 3.3 × 10-3 to 0.21 Pa (0.025-1.60 mTorr). The upper plot presents the experimental data of ref 15 as heavy solid and dotted lines (channels 1a and 1b, respectively) and the results of calculations as a set of thin lines, with individual lines corresponding to different collider gas pressures. The lower plot presents the pressure dependences of the cross sections averaged over the 1-5 eV range of the center-of-mass collision energies. As can be seen from the plots, effective cross sections increase with pressure but the pressure dependences weaken at low pressures, with the average cross sections asymptotically approaching the low pressure limits. Thus, in all further calculations, cross sections obtained for the pressure of 3.3 × 10-3 Pa (0.025 mTorr) were used as the lowpressure limiting values, suitable for comparison with the reported experimental data.

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Figure 3. Effect of pressure in the collision cell on the calculated effective reaction cross sections. The upper plot (a): experimental (ref 15, heavy lines) and calculated (thin lines) dependences of the cross sections of channels 1a and 1b on the center-of-mass collision energy. The heavy solid and dotted lines display extrapolated to zero pressure experimental results for reaction channels 1a and 1b, respectively. Different thin lines were obtained in the current study using different pressures of the xenon collider gas; pressure values are listed on the legend, which refers to the upper plot. The lower plot (b) presents the pressure dependences of the calculated cross sections averaged over the 1-5 eV range of the center-of-mass collision energies. Note the logarithmic pressure scale.

The results of modeling of the experiments of Muntean and Armentrout performed using the central model (see above) are shown in Figure 4 with thin solid lines. The upper plot presents the cross sections for both reaction channels as functions of the center-of-mass collision energy; the lower plot shows the collision energy dependence of the branching ratio of the two channels. The dashed lines present the results obtained with the limiting models (“kA(minus)” and kA(plus)”). As can be seen from the plots, the results of the calculations are in general approximate agreement with the experimental data. The curves for the cross section for channel 1a as a function of the collision energy have the same qualitative shapes as the corresponding experimental dependence: zero at low energies, a rise between ∼1 and 3 eV, a maximum at around 3 eV, and a slow decay at higher energies. The absolute values of the calculated cross section are approximately a factor of 2 larger than the experimental values; the onset of the cross section growth from zero coincides with that of the experimental curve. The calculated cross section values for channel 1b, on average, agree with the experimental values. However, the calculated curves have somewhat delayed onsets compared to those of the experimental dependence, by approximately 0.3 eV; the growth rate of the calculated curve exceeds the experimental one. These features of the energy dependences of the calculated cross sections for individual channels are reflected in the collision energy dependence of the branching ratio shown on the lower plot. The calculated lines have a somewhat delayed onset and are, on average, a factor of 2 lower than the experimental values in the 3.5-5.0 eV range. The limited flexibility of the model in terms of constraints imposed by the experimental kA(E) dependence (Figure 1) is

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Figure 4. The results of modeling of the experiments of Muntean and Armentrout15 and the effects of model variations. The heavy lines display extrapolated to zero pressure experimental results. The solid thin lines show the results of calculations performed using the “central” model; the dashed thin lines show the results obtained with the limiting models, “kA(minus)” and kA(plus).” The upper plot (a): the cross sections of individual channels (1a and 1b) as functions of the centerof-mass collision energy. The lower plot (b): the C7H7+ to C7H8+ product ratio.

illustrated by the dashed lines in Figure 4. Average differences between the cross sections obtained for the reaction channel 1a using the “central” and the limiting models are only 14% at collision energies above 1.5 eV. The effects of variations in the model allowed by the uncertainties in the kB(E)/kA(E) ratio (Figure 2) are illustrated in Figure 5. Here, the thin solid lines present the results obtained with the “kA(minus)” model and the dashed lines show the changes caused by using the variations of this model: “kA(minus)kB/kA(minus)” and “kA(minus)kB/ kA(plus).” Again, the changes caused by these model variations are minor. Calculations with TTR increased from 298 to 1000 K or with the reaction ∆Ho0 varied within the experimental uncertainties15 resulted in no observable changes. Finally, the variability in the results of calculation caused by different analytical representations of the ion-collider atom potentials is illustrated in Figure 6, where different thin lines display the cross sections and the branching ratio results obtained using the two alternative formulas for these intermolecular potentials: expressions 2 and 3. The differences between the calculated cross section values are minor; the calculated branching fractions do not depend on the intermolecular potential representation. 3.2. Modeling CID Experiments in Quadrupole Collision Cells of Tandem Mass Spectrometers with Ar Collider Gas. Three groups performed CID experiments on the n-butylbenzene cation using quadrupole collision cells with argon collider gas as parts of tandem mass spectrometers. In all of these studies, the C7H7+ to C7H8+ product ratio was determined as a function of either the ion kinetic energy, EKIN, or the center-of-mass collision energy, ECOLL. Two of the studies24,50 used the same model of triple-quadrupole mass spectrometer (Sciex Inc., model TAGA 600051-53). Nevertheless, the results of these two studies on the EKIN dependence of the C7H7+ to C7H8+ ratio are in quantitative disagreement (see Figure 1S in the Supporting

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Figure 5. The effects of model variations in modeling of the experiments of Muntean and Armentrout.15 The heavy lines display extrapolated to zero pressure experimental results. The solid thin lines show the results of calculations performed using model “kA(minus)”; the dashed thin lines show results obtained with the limiting models, “kA(minus)kB/kA(minus)” and “kA(minus)kB/kA(plus).” The upper plot (a): the cross sections of individual channels (1a and 1b) as functions of the center-of-mass collision energy. The lower plot (b): the C7H7+ to C7H8+ product ratio.

Figure 6. The effects of model variations due to different representations of intermolecular potentials in modeling of the experiments of Muntean and Armentrout.15 The heavy lines display extrapolated to zero pressure experimental results. The thin lines show the results of calculations performed using the “central” model with the ion-atom potentials described by the exponential ninth power expression (eq 2) (solid lines) and the exponential sixth power expression (eq 3) (dashed lines). The upper plot (a): the cross sections of individual channels (1a and 1b) as functions of the center-of-mass collision energy. The lower plot (b): the C7H7+ to C7H8+ product ratio.

Information). Dawson and Sun50 obtained the values of this product ratio that changes from 1 at EKIN just above zero to 5 at ∼40 eV and declines to below 4 at EKIN > 70 eV. The

Modeling of n-C4H9C6H5+ in Tandem Mass Spectrometers

Figure 7. The results of modeling of the experiments of McLuckey et al.28 and Nacson and Harrison.24 The plots show the dependences of the C7H7+ to C7H8+ ratio as a function of the ion kinetic energy, EKIN (lower horizontal axis) and the center-of-mass collision energy, ECOLL (upper horizontal axis). Experimental data from refs 28 (filled circles) and 24 (open circles). The thin lines represent the calculated curves: three for the pressure of the argon collider gas of 0.013 Pa (0.1 mTorr, solid, long-dash, and short-dash lines, exit aperture diameters of 0.4, 0.2, and 1.27 cm, respectively) and 0.053 Pa (0.4 mTorr, dash-dotted line). Error bars represent random computational uncertainties (1σ) of the Monte Carlo method.

experiments of Nacson and Harrison24 resulted in lower values of the C7H7+ to C7H8+ ratio: 0.5 at EKIN equal to 10 eV and gradually rising to 2.5 at EKIN above 40 eV, where the dependence is saturated. Only some of the details of the collision cell design are reported in refs 24, 50-52. The pressure in the collision cell is not uniform, as the argon collider gas is introduced through a jet positioned close to the middle of the cell length and directed perpendicular to the cell axis. Instead of the collision cell pressure, the authors report estimated values of the “target density”, an integral of the collider gas concentration over the distance, which was kept below 1 × 1014 molecules cm-2 in ref 50 and at 1 × 1014 molecules cm-2 in ref 24. The third study, that of McLuckey et al.,28 used a magnetic sector-quadrupole-quadrupole tandem mass spectrometer described in ref 40. Only some of the details of the design are reported in refs 40 and 28 (see Table 2S in the Supporting Information). The range of pressures of argon in the collision cell used in experiments is reported as 0.013-0.053 Pa (0.1-0.4 mTorr); pressures used in individual experiments are not reported. The results of McLuckey et al. on the kinetic energy dependence of the C7H7+ to C7H8+ ratio are in perfect agreement with the later results of Nacson and Harrison24 (Figure 7). Given the agreement between the results of refs 28 and 24, we select the combined data set from these studies as the experimental target for modeling CID of n-butylbenzene cation in a quadrupole collision cell with argon collider gas. The parameters of the quadrupole cell used in modeling are those of McLuckey et al.28 (Table 2S in the Supporting Information). Several important parameters were not reported by the authors and had to be assigned based on analogy with other similar systems. In particular, the inscribed diameter of the quadrupole, amplitude of the RF voltage, and the diameters of the entrance and the exit apertures are unknown. Reference 40 reports that the quadrupole has a maximum peak-to-peak RF amplitude of 2000 V and a maximum mass of 500 Da. In modeling, it was assumed that RF voltage is scaled proportionately to the mass of the parent ion, giving the value of 268 V for the peak-to-

J. Phys. Chem. A, Vol. 114, No. 22, 2010 6391 zero amplitude. The inscribed diameter was set to twice the diameter of the rods, 1.27 cm. The diameters of the entrance and the exit apertures were set to 0.40 cm. The exit aperture can have significant effect on the fraction of ions that get transmitted or scattered. Thus, the effects of varying the exit diameter parameters were studied: calculations were repeated with the narrow (0.20 cm) and the wide (1.27 cm diameter, i.e., completely open exit side of the collision cell) versions of the exit aperture. The pressure of the collider gas was varied between 0.013 and 0.053 Pa (0.1 and 0.4 mTorr), which corresponds to the (0.45-1.81) × 1014 molecules cm-2 “target density.” In addition, calculations directed at evaluating effects of increased ion scattering were performed: one set of calculations with the amplitude of RF voltage decreased by a factor of 8 (35 V), and a set with the increased value of TTR (from 298 to 2000 K). The results of modeling are presented in Figure 7 together with the experimental data of refs 28 and 24. The plots show the dependences of the C7H7+ to C7H8+ ratio on the ion kinetic energy, EKIN (lower horizontal axis) and the center-of-mass collision energy, ECOLL (upper horizontal axis). The calculated curves include those at 0.013 Pa (0.1 mTorr, three curves with varying exit apertures) and 0.053 Pa (0.4 mTorr). Varying the exit aperture has no effect on the C7H7+ to C7H8+ ratio, although the fraction of transmitted parent and product ions is strongly affected. Additional calculations with the models using decreased RF voltage or increased TTR also resulted in significantly increased fraction of ions scattered out of the collision cell. However, the same C7H7+ to C7H8+ ratios were obtained within the uncertainties of calculations. Higher pressure in the collision cell results, on average, in 17% lower C7H7+ to C7H8+ ratio. The range of collision energies in Figure 7 is approximately four times larger than the corresponding ranges in Figures 4-6, where the calculated and the experimental data for the Xe collider gas are presented. Comparing the figures, one can see that the low-energy part of Figure 7 (ECOLL < 5 eV) is similar to the lower plots of Figures 4-6. The calculated values of the C7H7+ to C7H8+ ratio are lower than the experimental ones, with a tendency to “catch up” with increasing collision energy. The plot in Figure 7 extends to higher ECOLL values and displays the calculated curves being higher than the experimental ones at ECOLL above 6-7 eV. On average, the calculated and the experimental values of the C7H7+ to C7H8+ ratio are in general agreement within approximately a factor of 2. 4. Discussion In our previous work, in which the Monte Carlo method of modeling CID in multipole collision cells used in the current study was developed,19 good agreement between the experimental and the calculated fragmentation efficiency curves was obtained for two reactive systems, dissociation of the benzylammonium and the tert-butyl benzylammonium ions. However, since a number of important parameters of the models were unknown, they were treated as adjustable. The main motivation behind the current study was to verify and validate the same theoretical method using a reactive system, the properties of which are known to the extent that would remove the need for adjustable parameters. The reaction of decomposition of the n-butylbenzene cation in multipole collision cells and ion guides satisfies this requirement. Especially valuable is the ability to compare the results of calculations with the experimental data of Muntean and Armentrout15 obtained under well-defined and controlled conditions. As described above, well established experimental knowledge of energy-dependent rate constants puts

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strict boundaries on the model properties, and varying these properties within the limits imposed by the experimental uncertainties of the kA(E) and the kB(E)/kA(E) functions results in only relatively small changes in the results of CID modeling. Two other important model parameters that had to be selected in ref 19 based on fitting experimental data, the internal and the translational effective temperatures of the ions, are either known under the conditions of the experiments of Muntean and Armentrout (TINT ) 298 K) or have no effect on the results (see above). Scattering of ions out of the collision cell at low pressures was shown to have a significant effect on ion fragmentation efficiency in ref 19. In the current work, due to the high values of the RF voltage used in the experiments of ref 15, scattering does not affect the results of modeling of these experiments in any notable way: the cross sections and the channel branching ratios calculated without taking scattering into account have the same values as with explicit accounting for scattering. Under the conditions of the experiments of McLuckey et al.28 and Nacson and Harrison,24 scattering of ions can be an important process, depending on the values of the RF voltage. However, the only experimental quantity reported in these studies that is suitable for comparison with the results of modeling is the dependence of the branching ratio of the two channels of reaction 1 on the kinetic energy. As described above, this ratio was shown to be not sensitive to RF voltage or other parameters influencing the degree of ion scattering. The overall agreement between the experimental and the calculated CID data can be characterized as generally good, with deviations not exceeding a factor of 2 for the effective cross sections of ion dissociation via channels 1a and 1b, and for the channel branching ratio. The collider gas pressures used in the experiments by Muntean and Armentrout,15 McLuckey et al.,28 and Nacson and Harrison24 modeled here correspond to conditions of mostly single ion-atom collisions. Thus, the results are most sensitive to the properties of the per-collision activation function, P(E, E′, ECOLL), the probability of energy transfer from energy E′ to energy E upon a collision with a collider gas atom or molecule with the relative kinetic energy ECOLL. The success of modeling performed in the current study indicates that the classical trajectory method used by Meroueh and Hase16,17 for small peptides and incorporated here in the general Monte Carlo algorithm of modeling the entirety of processes occurring in multipole CID collision cells, generally, adequately describes the P(E, E′, ECOLL) function. This conclusion is in agreement with the results of MartinezNunez et al.18 who modeled the CID of Cr(CO)6+ in the octopole collision cell/ion guide apparatus used by Muntean and Armentrout15 (see above, in the Introduction). The computational results of these authors are also is general agreement with experiment. The major difference between the method used in the current study and that applied by Martinez-Nunez et al. is in the use of explicit accounting for the ion flight in the electromagnetic field of the multipole, its random collisions with the collider gas, and kinetics of its decomposition during the flight. Acknowledgment. The authors express their thanks to Dr. K. F. Lim and Dr. W. L. Hase for providing them with the copies of quasiclassical trajectory modeling programs (MARINER and VENUS). Supporting Information Available: A supplement including the detailed characteristics of the modeled multipole collision cells, parameters of the pairwise ion-atom potentials obtained in quantum chemical calculations, and literature data on the

Knyazev and Stein C7H7+ to C7H8+ ratio as function of the ion kinetic energy (Tables 1S-3S, Figure 1S). This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Chapman, J. R., Ed. Mass Spectrometry of Protein and Peptides; Humana Press: Totowa, NJ, 2000. (2) Glish, G. L.; Vachet, R. W. Nat. ReV. Drug DiscoVery 2003, 2, 140–150. (3) Lin, D.; Tabb, D. L.; Yates, J. R. I. Biochim. Biophys. Acta 2003, 1646, 1–10. (4) Aebersold, R. J. Am. Soc. Mass Spectrom. 2003, 14, 685–695. (5) McLuckey, S. A.; Wells, J. M. Chem. ReV. 2001, 101, 571–606. (6) Shukla, A. K.; Futrell, J. H. J. Mass Spectrom. 2000, 35, 1069– 1090. (7) McLuckey, S. A. J. Am. Soc. Mass Spectrom. 1992, 3, 559–614. (8) McLuckey, S. A.; Goeringer, D. E. J. Mass. Spectrom. 1997, 32, 461–474. (9) Paizs, B.; Suhai, S. Mass Spectr. ReV. 2005, 24, 508–548. (10) Armentrout, P. B. J. Am. Soc. Mass. Spectrom. 2002, 13, 419– 434. (11) Armentrout, P. B. J. Chem. Phys. 2007, 126, 234302. (12) Laskin, J.; Byrd, M.; Futrell, J. Int. J. Mass Spectrom. 2000, 195, 285–302. (13) Laskin, J.; Futrell, J. H. J. Phys. Chem. A 2000, 104, 5484–5494. (14) Muntean, F.; Armentrout, P. B. J. Chem. Phys. 2001, 115, 1213– 1228. (15) Muntean, F.; Armentrout, P. B. J. Phys. Chem. A 2003, 107, 7413– 7422. (16) Meroueh, O.; Hase, W. L. J. Phys. Chem. A 1999, 103, 3981– 3990. (17) Meroueh, O.; Hase, W. L. Int. J. Mass Spectrom. 2000, 201, 233– 244. (18) Martinez-Nunez, E.; Fernandez-Ramos, A.; Vasquez, S. A.; Marques, J.; Xue, M.; Hase, W. L. J. Chem. Phys. 2005, 123, 154311. (19) Knyazev, V. D.; Stein, S. E. J. Am. Soc. Mass Spectrom. 2010, 21, 425-439. (20) Benson, S. W. Thermochemical Kinetics, 2nd ed.; John Wiley and Sons: New York, 1976. (21) Troe, J.; Ushakov, V. G.; Viggiano, A. A. J. Phys. Chem. A 2006, 110, 1491–1499. (22) Fernandez, A. I.; Viggiano, A. A.; Troe, J. J. Phys. Chem. A 2006, 110, 8467–8476. (23) Harrison, A. G.; Lin, M. S. Int. J. Mass Spectrom. Ion Phys. 1983, 51, 353–356. (24) Nacson, S.; Harrison, A. G. Int. J. Mass Spectrom. Ion Processes 1985, 63, 325–337. (25) Chen, J. H.; Hays, J. D.; Dunbar, R. C. J. Phys. Chem. 1984, 88, 4759–4764. (26) Baer, T.; Dutuit, O.; Mestdagh, H.; Rolando, C. J. Phys. Chem. A 1988, 92, 5674–5679. (27) Oh, S. T.; Choe, J. C.; Kim, M. S. J. Phys. Chem. 1996, 100, 13367– 13374. (28) McLuckey, S. A.; Sallans, L.; Cody, R. B.; Burnier, R. C.; Verma, S.; Freiser, B. S.; Cooks, R. G. Int. J. Mass Spectrom. Ion Phys. 1982, 44, 215–229. (29) Pitzer, K. S. J. Chem. Phys. 1946, 14, 239–243. (30) Pitzer, K. S.; Gwinn, W. D. J. Chem. Phys. 1942, 10, 428. (31) Robinson, P. J.; Holbrook, K. A. Unimolecular Reactions; WileyInterscience: New York, 1972. (32) Gilbert, R. G.; Smith, S. C. Theory of Unimolecular and Recombination Reactions; Blackwell: Oxford, 1990. (33) Holbrook, K. A.; Pilling, M. J.; Robertson, S. H. Unimolecular Reactions, 2nd ed.; Wiley: New York, 1996. (34) Beyer, T.; Swinehart, D. F. Commun. Assoc. Comput. Mach. 1973, 16, 379. (35) Astholz, D. C.; Troe, J.; Wieters, W. J. Chem. Phys. 1979, 70, 5107. (36) Knyazev, V. D. J. Phys. Chem. A 1998, 102, 3916–3922. (37) Mukhtar, E. S.; Griffiths, I. W.; Harris, F. M.; Beynon, J. H. Int. J. Mass. Spectrom. Ion. Phys. 1981, 37, 159–166. (38) Welch, M. J.; Pereles, D. J.; White, E. Org. Mass Spectrom. 1985, 20, 425–426. (39) Ervin, K. M.; Armentrout, P. B. 1985, 83, 166–189. (40) Glish, G. L.; McLuckey, S. A.; Ridley, T. Y.; Cooks, R. G. Int. J. Mass Spectrom. Ion Processes 1982, 41, 157–177. (41) Baer, T.; Hase, W. L. Unimolecular Reaction Dynamics; Oxford University Press: New York, 1996. (42) Lim, K. F.; Hase, W. L. http://www.deakin.edu.au/∼Lim/, 1990.

Modeling of n-C4H9C6H5+ in Tandem Mass Spectrometers (43) Hase, W. L.; Duchovic, R. J.; Hu, X.; Komornicki, A.; Lim, K. F.; Lu, D.-H.; Peslherbe, G. H.; Swamy, K. N.; Vande Linde, S. R.; Varandas, A.; Wang, H.; Wolf, R. J. QCPE Bull. 1996, 16 (4), 43. (44) Cornell, W. D.; Cieplak, P.; Bayly, C. I.; Gould, I. R.; Merz, K. M.; Ferguson, D. M.; Spellmeyer, D. C.; Fox, T.; Caldwell, J. W.; Kollman, P. A. J. Am. Chem. Soc. 1995, 117, 5179–5197. (45) Jorgensen, W. L.; Maxwell, D. S.; Tirado-Rives, J. J. Am. Chem. Soc. 1996, 118, 11225–11236. (46) Price, M. L. P.; Ostrovsky, D.; Jorgensen, W. L. J. Comput. Chem. 2001, 22, 1340–1352. (47) Pople, J. A.; Head-Gordon, M.; Raghavachari, K. J. Chem. Phys. 1987, 87, 5968–5975. (48) Friedman, M. H.; Yergey, A. L.; Campana, J. E. J. Phys. E: Sci. Instrum. 1982, 15, 53–61.

J. Phys. Chem. A, Vol. 114, No. 22, 2010 6393 (49) Martin, J. M. L.; Sundermann, A. J. Chem. Phys. 2001, 114, 3408– 3420. (50) Dawson, P. H.; Sun, W.-F. Int. J. Mass Spectrom. Ion Processes 1982, 44, 51–59. (51) Dawson, P. H.; French, J. B.; Buckley, J. A.; Douglas, D. J.; Simmons, D. Organic Mass Spectrom. 1982, 17, 212–219. (52) Dawson, P. H.; French, J. B.; Buckley, J. A.; Douglas, D. J.; Simmons, D. Organic Mass Spectrom. 1982, 17, 205–211. (53) Certain commercial instruments and materials are identified in this article to adequately specify the procedures. In no case does such identification imply recommendation or endorsement by NIST, nor does it imply that the instruments or materials are necessarily the best available for this purpose.

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