Increasing the Mass Accuracy and Dynamic Range of Quadrupole Ion Trap Mass SpectrometersPhilip M. Remes and Jae C. Schwartz

Thermo Fisher Scientific, San Jose, CA

2 Increasing the Mass Accuracy and Dynamic Range of Quadrupole Ion Trap Mass Spectrometers

Empirical Model for Space-Charge-Induced Mass Shifts

In the empirical model, the “analyte” is the ion whose mass-to-charge ratio is under consideration (M0). “Self” interactions describe the shift induced by ions of the same mass-to-charge value (analyte ions), where S (M0) is the mass shift sensitivity to the number of analyte ions I[M0]. “Adjacent” ion interactions describe the shift induced by ions of different mass-to-charge values (Mi). A(i- M0) is the mass shift sensitivity to the number of adjacent ions I[i] at mass difference (i- M0). Self interactions are less significant than adjacent interactions, partly because the typical ion abundance is only 100-200 ions.

Equation 2 integrates the adjacent ion interactions for all ions of mass > M0. Figures 3a and 3b show the results of the calculations.

Smaller ions do not appreciably affect the analyte mass position or width because they are ejected from the trap first. The analyte ions seem to have no “memory” of adjacent ions that were already ejected.

Linearity of Interactions

It is assumed that each adjacent ion interacts with the analyte ion independently. We expect that fundamentally this is not true because the adjacent ion motion is in turn modified by other adjacent ions and the analyte ions.

In the experimental test, the mass shift was monitored for three ion populations: ∆1 Da, ∆2 Da, and equal parts ∆1 and ∆2 Da. The mixed population was expected to exhibit a mass shift that is the combination of the ∆1 Da and ∆2 Da population shifts. As shown in Figure 4, the linearity assumption appears to hold, as far as mass shifts are concerned, for typical linear ITMS operating conditions.

0 25 50 75 1000

2

4

6

8

10

Mas

s Sh

ift S

lope

(x10

-6 D

a/io

n)

ΔMass (Da)

0 200 400 600 800 10000.00

0.02

0.04

0.06

0.08

0.10

Pre

dict

ed M

ass

Shi

ft

m/z

( ) [ ] ( ) [ ]+=

⋅−+⋅=ΔLastMass

Mi

iIMiAMIMSMm5.0

00000

)(

Increasing the Mass Accuracy and Dynamic Range of Quadrupole Ion Trap Mass SpectrometersPhilip M. Remes, Jae C. SchwartzThermo Fisher Scientific, San Jose, CA

ConclusionAn empirical model for mass shift as a function of ion abundance and mass separation allows for space charge induced shifts to be corrected.

Under typical conditions, space charge interactions accumulate linearly, i.e. the effect of ion 1 and ion 2 simultaneously is the sum of their individual interactions.

Populations of 100k+ ions can be analyzed with acceptable mass accuracy (assuming no other detector non linearities).

Mass precision is also improved, especially if ESI gives a highly variable ion flux.

Simulations may point to interesting ion-ion phenomena at certain densities and mass separations.

References1. Li, G.Z.; Guan, S.; Marshall, A.G. Sympathetic cooling of trapped negative ions

by self-cooled electrons in a Fourier transform ion cyclotron resonance mass spectrometer. JASMS 1997, 8, 793-800.

2. Tolmachev, A.V.; Udseth, H.R.; Smith R.D. Modeling the ion density distribution in collisional cooling RF multipole ion guides. IJMS 2003, 222, 155-174.

AcknowledgementsWe would like to thank Scott Quarmby (Thermo Fisher Scientific, Austin) and Rob Grothe (Thermo Fisher Scientific, San Jose) for helpful discussions.

OverviewPurpose: Develop a method to correct space-charge-induced mass shifts in ion trap mass spectrometers, increasing the dynamic range of mass analysis.

Methods: Mass shifts were characterized in terms of the number of ions of interest (analyte ions), number of other ions (adjacent ions), and the mass separation between these species.

Results: 100k total ions can be mass analyzed with acceptable mass accuracy in a linear quadrupole ion trap.

IntroductionThe largest ion population that can be suitably mass analyzed by an ion trap mass spectrometer (ITMS) is limited by ion-ion interactions. These ion-ion interactions cause a shift in the observed mass-to-charge ratio and lead to peak broadening. The point at which these effects are no longer acceptable is called the spectral space charge limit. The amount of space-charge-induced mass shift and peak broadening for a given situation can be predicted based on experimental study. Therefore, these deleterious effects can be corrected and dynamic range can be increased.

MethodsSample Preparation

Thermo Scientific Pierce LTQ ESI Positive Ion Calibration Solution, a mix of caffeine, the peptide MRFA, and Ultramark 1622, was used, as well as polyethylene glycol (PEG) and angiotensin I.

Experimental Space Charge Measurements

A dual-cell linear ion trap was used for the experiments, scanning at 33 kDa/s, with an analyzer pressure of ~0.4 mTorr. Ions were isolated and then accumulated in a storage multipole before being introduced to a dual-cell linear ITMS. This allowed for simultaneous independent control of the number of ions at multiple mass-to-charge regions

Theoretical Space Charge Measurements

An ion trajectory simulation program was written to simulate the relevant portions of mass analysis in a linear ITMS. Between 128 and 20,000 ions were studied in the simulations. In each case, initial conditions were established by allowing the ions to equilibrate for 27 ms without interacting and then 3 ms with interactions.

Ion-ion interactions were calculated with an N-body method, such that the space charge force on ion i, for each dimension u, is given by Equation 1, where ru is the distance between ions i and j, and ε is a protection factor, taken to be the collision radius of a typical ion. The results are shown in Figures 1a and 1b.

FIGURE 1a. Distribution of ion-ion force magnitudes versus radius during ion storage, without resonance excitation

FIGURE 3a. Adjacent mass shift slope versus ∆mass for PEG m/z 525

FIGURE 3b. Predicted mass shift versus m/z for angiotensin I, m/z 658, [M+2H]2+, 80k total ions

Experimental Test of Space Charge Shift Correction

MS/MS was performed on various precursor ions at large ion populations, as shown in Figure 5. (For reference, current typical MS/MS targets are 10k–20k ions.) MS2

analyte positions were significantly shifted and broadened. MS3 isolated analytes were much less affected because they have no adjacent ions and can serve as a reference.

The applied correction significantly improved the mass accuracy. In addition, the low mass, mass accuracy can be improved by varying the coefficients in Equation 2 with mass. A remaining negative bias needs to be calibrated out.

Mass Precision Improvement

When electrospray ionization is not stable, the resultant ion populations can have a large variation. Under these conditions, the observed mass precision is degraded.

Figure 6 shows histograms of observed mass errors when the total ion current relative standard deviation was 15%–30% and the ion target was ~60k. The space charge correction reduced the absolute mass error and narrowed the distribution of observed masses.

All trademarks are the property of Thermo Fisher Scientific and its subsidiaries.

This information is not intended to encourage use of these products in any manners that might infringe the intellectual property rights of others.

FIGURE 4. Mass error versus number of adjacent ions for analyte ion PEG m/z 657, in the presence of equal parts m/z 658,659, only m/z 658, and only m/z 659

FIGURE 5a. Mass error for fragments of MRFA and Ultramark 1122, 70 and 90k total ions respectively

Multiply Charged Ions

The ion/ion interaction force increases with charge (Equation 1). The mass shift should therefore also be greater for highly charged species.

Figure 7a shows this experiment, where the mass shift for equal numbers of 1+ and 2+

charges was the same. Figure 7b shows simulated mass positions, where the shift for 2+ ions was twice that of 1+ ions.

Because of the conversion dynode, electron multipliers detect the number of charges and not the number of ions. Therefore, Equation 2 does not need any charge dependent factors.

( )= +++

=N

j zyx

uijui

rrr

rqkqF

12/3222,

ε(1)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.70.00

0.02

0.04

0.06

0.08

0.10

0.12

Probability Density

Radius (mm)

Ion-

Ion

Acc

eler

atio

n (m

m/μ

s2 )

9.3E-05

2.2E-04

4.4E-04

6.6E-04

8.8E-04

0.0011

0.0013

0.0015

0.0018

-4 -3 -2 -1 0 1 2 3 40.00

0.02

0.04

0.06

0.08

Position (mm)

Ion-

Ion

Acc

eler

atio

n (m

m/μ

s2 )

1.3E-04

0.0013

0.0024

0.0036

0.0048

0.0059

0.0071

0.0082

0.0094

0.011

0.012

Probability Density

FIGURE 1b. Distribution of ion-ion force magnitudes versus x position during mass analysis

-0.1 0.0 0.1 0.2 0.3 0.4 0.50.00

0.02

0.04

0.06

0.08

Pro

babi

lity

Den

sity

(Da-1

)

Mass Error (Da)

Measured Corrected

0 20000 40000 60000 80000 100000 120000

0.00

0.02

0.04

0.06

0.08

0.10

Ave

rage

Mas

s E

rror

(Da)

TIC

Avg Error Avg Corrected Error

0 2000 4000 6000 8000 10000 12000 14000 16000 18000-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.12

Mas

s E

rror (

Da)

Number Adjacent Ions

658,659 658 659

0 500 1000 1500 2000

682

684

686

688

690

692

694

696

Ave

rage

Pos

ition

(μs)

Ions/mm

[Μ+1]+

[Μ+2]+

[2Μ+2]2+

[2Μ+4]2+

100 200 300 400 500 600 700 800 900 1000

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

Mas

s E

rror

(Da)

m/z

MS2 Error MS3 Error MS2 Corrected Error

FIGURE 5b. Average mass error versus total ion current for Ultramark 1122

FIGURE 6. Precision of mass measurement for unstable ESI conditions, m/z 301 in angiotensin I solution

0 2000 4000 6000 8000 10000

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

Δ1 Da (Charge 1) Δ1 Da (Charge 2) Δ0.5 Da (Charge 2)

Mas

s Er

ror (

Da)

Number of Adjacent Charges

FIGURE 7a. Mass error versus adjacent ions for different ∆mass and charge. PEG m/z 657 was 1+ ion. Angiotensin m/z 648 was 2+ ion.

FIGURE 7b. Simulated average mass position for 1024 ions of m/z 524 in the presence of 128–20k adjacent ions

0 5000 10000 15000 200000.080

0.085

0.090

0.095

0.100

0.105

0.110

Ion

Ener

gy (e

V)

Number of Ions

Effect of Ion-Ion Interactions on Ion Energy

The simulations showed an unexpected behavior of ion energy versus population size, as shown in Figure 8:

• Ion energy and radius decreased with number of ions, with “kinks” at ~1000 ions/mm.

• Axial trapping size was 10 mm, so 2000 ions/mm is 20k ions.

• At larger densities, the energy and radius increase again (not shown).

The experimental ion energy was measured by decreasing the magnitude of the axial trapping barrier and measuring the number of remaining ions [1]. The experiment shows a flat region before increasing. This flat region may explain the parabolic type shape observed for the mass shifts (Figures 4 and 7).

In addition, the experimental energies were higher than the simulated ones. The simulation gas temperature was arbitrarily chosen as 300 °C but this may have been too low. A space charge “cooling” effect was observed previously in simulations at low pressure [2]. These observations have yet to be fully elucidated.

0 500 1000 1500 2000

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

0.11

0.12

0.13

Aver

age

Rad

ial K

inet

ic E

nerg

y (e

V)

Ions/mm

[M+H]+

[M+2H]+

[M+3H]+

[2M+2H]2+

[2M+4H]2+

[2M+6H]2+

FIGURE 8a. Experimental ion energy versus ion population size

FIGURE 8b. Simulated ion energy versus ion density (10 mm)

(2)

FIGURE 2. (a) Simulated RMS ion-ion interaction magnitude for 10k ions during mass analysis, (b) Average ion position during simulated mass analysis

ResultsIon-Ion Interactions During Mass Analysis

Ion-ion interactions are a complex, dynamic phenomenon. The magnitude of interactions is random and depends on specific pair-wise distances. However, the strongest ion-ion forces occur near the center of the trap (Figure 1b).

Excitation of ion oscillations somewhat decreases the magnitude of the ion-ion forces, due to a reduction in ion density. Figure 2a illustrates the reduction in average interaction force as ions are excited, and Figure 2b shows the average ion position during analysis.

100 200 300 400 500 600 700 800

-4.5

-3.0

-1.5

0.0

1.5

3.0

4.50.00

0.03

0.06

0.09

0.12100 200 300 400 500 600 700 800

Ave

rage

X P

ositi

on (m

m)

Time (μs)

Average X Position

RM

S Io

n-Io

n Ac

cele

ratio

n (m

m/μ

s)

RMS Ion-Ion Acceleration

(a)

(b)

3Thermo Scientific Poster Note • PN63578_E 06/12S

Empirical Model for Space-Charge-Induced Mass Shifts

In the empirical model, the “analyte” is the ion whose mass-to-charge ratio is under consideration (M0). “Self” interactions describe the shift induced by ions of the same mass-to-charge value (analyte ions), where S (M0) is the mass shift sensitivity to the number of analyte ions I[M0]. “Adjacent” ion interactions describe the shift induced by ions of different mass-to-charge values (Mi). A(i- M0) is the mass shift sensitivity to the number of adjacent ions I[i] at mass difference (i- M0). Self interactions are less significant than adjacent interactions, partly because the typical ion abundance is only 100-200 ions.

Equation 2 integrates the adjacent ion interactions for all ions of mass > M0. Figures 3a and 3b show the results of the calculations.

Smaller ions do not appreciably affect the analyte mass position or width because they are ejected from the trap first. The analyte ions seem to have no “memory” of adjacent ions that were already ejected.

Linearity of Interactions

It is assumed that each adjacent ion interacts with the analyte ion independently. We expect that fundamentally this is not true because the adjacent ion motion is in turn modified by other adjacent ions and the analyte ions.

In the experimental test, the mass shift was monitored for three ion populations: ∆1 Da, ∆2 Da, and equal parts ∆1 and ∆2 Da. The mixed population was expected to exhibit a mass shift that is the combination of the ∆1 Da and ∆2 Da population shifts. As shown in Figure 4, the linearity assumption appears to hold, as far as mass shifts are concerned, for typical linear ITMS operating conditions.

0 25 50 75 1000

2

4

6

8

10

Mas

s Sh

ift S

lope

(x10

-6 D

a/io

n)

ΔMass (Da)

0 200 400 600 800 10000.00

0.02

0.04

0.06

0.08

0.10

Pre

dict

ed M

ass

Shi

ft

m/z

( ) [ ] ( ) [ ]+=

⋅−+⋅=ΔLastMass

Mi

iIMiAMIMSMm5.0

00000

)(

Increasing the Mass Accuracy and Dynamic Range of Quadrupole Ion Trap Mass SpectrometersPhilip M. Remes, Jae C. SchwartzThermo Fisher Scientific, San Jose, CA

ConclusionAn empirical model for mass shift as a function of ion abundance and mass separation allows for space charge induced shifts to be corrected.

Under typical conditions, space charge interactions accumulate linearly, i.e. the effect of ion 1 and ion 2 simultaneously is the sum of their individual interactions.

Populations of 100k+ ions can be analyzed with acceptable mass accuracy (assuming no other detector non linearities).

Mass precision is also improved, especially if ESI gives a highly variable ion flux.

Simulations may point to interesting ion-ion phenomena at certain densities and mass separations.

References1. Li, G.Z.; Guan, S.; Marshall, A.G. Sympathetic cooling of trapped negative ions

by self-cooled electrons in a Fourier transform ion cyclotron resonance mass spectrometer. JASMS 1997, 8, 793-800.

2. Tolmachev, A.V.; Udseth, H.R.; Smith R.D. Modeling the ion density distribution in collisional cooling RF multipole ion guides. IJMS 2003, 222, 155-174.

AcknowledgementsWe would like to thank Scott Quarmby (Thermo Fisher Scientific, Austin) and Rob Grothe (Thermo Fisher Scientific, San Jose) for helpful discussions.

OverviewPurpose: Develop a method to correct space-charge-induced mass shifts in ion trap mass spectrometers, increasing the dynamic range of mass analysis.

Methods: Mass shifts were characterized in terms of the number of ions of interest (analyte ions), number of other ions (adjacent ions), and the mass separation between these species.

Results: 100k total ions can be mass analyzed with acceptable mass accuracy in a linear quadrupole ion trap.

IntroductionThe largest ion population that can be suitably mass analyzed by an ion trap mass spectrometer (ITMS) is limited by ion-ion interactions. These ion-ion interactions cause a shift in the observed mass-to-charge ratio and lead to peak broadening. The point at which these effects are no longer acceptable is called the spectral space charge limit. The amount of space-charge-induced mass shift and peak broadening for a given situation can be predicted based on experimental study. Therefore, these deleterious effects can be corrected and dynamic range can be increased.

MethodsSample Preparation

Thermo Scientific Pierce LTQ ESI Positive Ion Calibration Solution, a mix of caffeine, the peptide MRFA, and Ultramark 1622, was used, as well as polyethylene glycol (PEG) and angiotensin I.

Experimental Space Charge Measurements

A dual-cell linear ion trap was used for the experiments, scanning at 33 kDa/s, with an analyzer pressure of ~0.4 mTorr. Ions were isolated and then accumulated in a storage multipole before being introduced to a dual-cell linear ITMS. This allowed for simultaneous independent control of the number of ions at multiple mass-to-charge regions

Theoretical Space Charge Measurements

An ion trajectory simulation program was written to simulate the relevant portions of mass analysis in a linear ITMS. Between 128 and 20,000 ions were studied in the simulations. In each case, initial conditions were established by allowing the ions to equilibrate for 27 ms without interacting and then 3 ms with interactions.

Ion-ion interactions were calculated with an N-body method, such that the space charge force on ion i, for each dimension u, is given by Equation 1, where ru is the distance between ions i and j, and ε is a protection factor, taken to be the collision radius of a typical ion. The results are shown in Figures 1a and 1b.

FIGURE 1a. Distribution of ion-ion force magnitudes versus radius during ion storage, without resonance excitation

FIGURE 3a. Adjacent mass shift slope versus ∆mass for PEG m/z 525

FIGURE 3b. Predicted mass shift versus m/z for angiotensin I, m/z 658, [M+2H]2+, 80k total ions

Experimental Test of Space Charge Shift Correction

MS/MS was performed on various precursor ions at large ion populations, as shown in Figure 5. (For reference, current typical MS/MS targets are 10k–20k ions.) MS2

analyte positions were significantly shifted and broadened. MS3 isolated analytes were much less affected because they have no adjacent ions and can serve as a reference.

The applied correction significantly improved the mass accuracy. In addition, the low mass, mass accuracy can be improved by varying the coefficients in Equation 2 with mass. A remaining negative bias needs to be calibrated out.

Mass Precision Improvement

When electrospray ionization is not stable, the resultant ion populations can have a large variation. Under these conditions, the observed mass precision is degraded.

Figure 6 shows histograms of observed mass errors when the total ion current relative standard deviation was 15%–30% and the ion target was ~60k. The space charge correction reduced the absolute mass error and narrowed the distribution of observed masses.

All trademarks are the property of Thermo Fisher Scientific and its subsidiaries.

This information is not intended to encourage use of these products in any manners that might infringe the intellectual property rights of others.

FIGURE 4. Mass error versus number of adjacent ions for analyte ion PEG m/z 657, in the presence of equal parts m/z 658,659, only m/z 658, and only m/z 659

FIGURE 5a. Mass error for fragments of MRFA and Ultramark 1122, 70 and 90k total ions respectively

Multiply Charged Ions

The ion/ion interaction force increases with charge (Equation 1). The mass shift should therefore also be greater for highly charged species.

Figure 7a shows this experiment, where the mass shift for equal numbers of 1+ and 2+

charges was the same. Figure 7b shows simulated mass positions, where the shift for 2+ ions was twice that of 1+ ions.

Because of the conversion dynode, electron multipliers detect the number of charges and not the number of ions. Therefore, Equation 2 does not need any charge dependent factors.

( )= +++

=N

j zyx

uijui

rrr

rqkqF

12/3222,

ε(1)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.70.00

0.02

0.04

0.06

0.08

0.10

0.12

Probability Density

Radius (mm)

Ion-

Ion

Acc

eler

atio

n (m

m/μ

s2 )

9.3E-05

2.2E-04

4.4E-04

6.6E-04

8.8E-04

0.0011

0.0013

0.0015

0.0018

-4 -3 -2 -1 0 1 2 3 40.00

0.02

0.04

0.06

0.08

Position (mm)

Ion-

Ion

Acc

eler

atio

n (m

m/μ

s2 )

1.3E-04

0.0013

0.0024

0.0036

0.0048

0.0059

0.0071

0.0082

0.0094

0.011

0.012

Probability Density

FIGURE 1b. Distribution of ion-ion force magnitudes versus x position during mass analysis

-0.1 0.0 0.1 0.2 0.3 0.4 0.50.00

0.02

0.04

0.06

0.08

Pro

babi

lity

Den

sity

(Da-1

)

Mass Error (Da)

Measured Corrected

0 20000 40000 60000 80000 100000 120000

0.00

0.02

0.04

0.06

0.08

0.10

Ave

rage

Mas

s E

rror

(Da)

TIC

Avg Error Avg Corrected Error

0 2000 4000 6000 8000 10000 12000 14000 16000 18000-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.12

Mas

s E

rror (

Da)

Number Adjacent Ions

658,659 658 659

0 500 1000 1500 2000

682

684

686

688

690

692

694

696

Ave

rage

Pos

ition

(μs)

Ions/mm

[Μ+1]+

[Μ+2]+

[2Μ+2]2+

[2Μ+4]2+

100 200 300 400 500 600 700 800 900 1000

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

Mas

s E

rror

(Da)

m/z

MS2 Error MS3 Error MS2 Corrected Error

FIGURE 5b. Average mass error versus total ion current for Ultramark 1122

FIGURE 6. Precision of mass measurement for unstable ESI conditions, m/z 301 in angiotensin I solution

0 2000 4000 6000 8000 10000

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

Δ1 Da (Charge 1) Δ1 Da (Charge 2) Δ0.5 Da (Charge 2)

Mas

s Er

ror (

Da)

Number of Adjacent Charges

FIGURE 7a. Mass error versus adjacent ions for different ∆mass and charge. PEG m/z 657 was 1+ ion. Angiotensin m/z 648 was 2+ ion.

FIGURE 7b. Simulated average mass position for 1024 ions of m/z 524 in the presence of 128–20k adjacent ions

0 5000 10000 15000 200000.080

0.085

0.090

0.095

0.100

0.105

0.110

Ion

Ener

gy (e

V)

Number of Ions

Effect of Ion-Ion Interactions on Ion Energy

The simulations showed an unexpected behavior of ion energy versus population size, as shown in Figure 8:

• Ion energy and radius decreased with number of ions, with “kinks” at ~1000 ions/mm.

• Axial trapping size was 10 mm, so 2000 ions/mm is 20k ions.

• At larger densities, the energy and radius increase again (not shown).

The experimental ion energy was measured by decreasing the magnitude of the axial trapping barrier and measuring the number of remaining ions [1]. The experiment shows a flat region before increasing. This flat region may explain the parabolic type shape observed for the mass shifts (Figures 4 and 7).

In addition, the experimental energies were higher than the simulated ones. The simulation gas temperature was arbitrarily chosen as 300 °C but this may have been too low. A space charge “cooling” effect was observed previously in simulations at low pressure [2]. These observations have yet to be fully elucidated.

0 500 1000 1500 2000

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

0.11

0.12

0.13

Aver

age

Rad

ial K

inet

ic E

nerg

y (e

V)

Ions/mm

[M+H]+

[M+2H]+

[M+3H]+

[2M+2H]2+

[2M+4H]2+

[2M+6H]2+

FIGURE 8a. Experimental ion energy versus ion population size

FIGURE 8b. Simulated ion energy versus ion density (10 mm)

(2)

FIGURE 2. (a) Simulated RMS ion-ion interaction magnitude for 10k ions during mass analysis, (b) Average ion position during simulated mass analysis

ResultsIon-Ion Interactions During Mass Analysis

Ion-ion interactions are a complex, dynamic phenomenon. The magnitude of interactions is random and depends on specific pair-wise distances. However, the strongest ion-ion forces occur near the center of the trap (Figure 1b).

Excitation of ion oscillations somewhat decreases the magnitude of the ion-ion forces, due to a reduction in ion density. Figure 2a illustrates the reduction in average interaction force as ions are excited, and Figure 2b shows the average ion position during analysis.

100 200 300 400 500 600 700 800

-4.5

-3.0

-1.5

0.0

1.5

3.0

4.50.00

0.03

0.06

0.09

0.12100 200 300 400 500 600 700 800

Ave

rage

X P

ositi

on (m

m)

Time (μs)

Average X Position

RM

S Io

n-Io

n Ac

cele

ratio

n (m

m/μ

s)

RMS Ion-Ion Acceleration

(a)

(b)

4 Increasing the Mass Accuracy and Dynamic Range of Quadrupole Ion Trap Mass Spectrometers

Empirical Model for Space-Charge-Induced Mass Shifts

In the empirical model, the “analyte” is the ion whose mass-to-charge ratio is under consideration (M0). “Self” interactions describe the shift induced by ions of the same mass-to-charge value (analyte ions), where S (M0) is the mass shift sensitivity to the number of analyte ions I[M0]. “Adjacent” ion interactions describe the shift induced by ions of different mass-to-charge values (Mi). A(i- M0) is the mass shift sensitivity to the number of adjacent ions I[i] at mass difference (i- M0). Self interactions are less significant than adjacent interactions, partly because the typical ion abundance is only 100-200 ions.

Equation 2 integrates the adjacent ion interactions for all ions of mass > M0. Figures 3a and 3b show the results of the calculations.

Smaller ions do not appreciably affect the analyte mass position or width because they are ejected from the trap first. The analyte ions seem to have no “memory” of adjacent ions that were already ejected.

Linearity of Interactions

It is assumed that each adjacent ion interacts with the analyte ion independently. We expect that fundamentally this is not true because the adjacent ion motion is in turn modified by other adjacent ions and the analyte ions.

In the experimental test, the mass shift was monitored for three ion populations: ∆1 Da, ∆2 Da, and equal parts ∆1 and ∆2 Da. The mixed population was expected to exhibit a mass shift that is the combination of the ∆1 Da and ∆2 Da population shifts. As shown in Figure 4, the linearity assumption appears to hold, as far as mass shifts are concerned, for typical linear ITMS operating conditions.

0 25 50 75 1000

2

4

6

8

10

Mas

s Sh

ift S

lope

(x10

-6 D

a/io

n)

ΔMass (Da)

0 200 400 600 800 10000.00

0.02

0.04

0.06

0.08

0.10

Pre

dict

ed M

ass

Shi

ft

m/z

( ) [ ] ( ) [ ]+=

⋅−+⋅=ΔLastMass

Mi

iIMiAMIMSMm5.0

00000

)(

Increasing the Mass Accuracy and Dynamic Range of Quadrupole Ion Trap Mass SpectrometersPhilip M. Remes, Jae C. SchwartzThermo Fisher Scientific, San Jose, CA

ConclusionAn empirical model for mass shift as a function of ion abundance and mass separation allows for space charge induced shifts to be corrected.

Under typical conditions, space charge interactions accumulate linearly, i.e. the effect of ion 1 and ion 2 simultaneously is the sum of their individual interactions.

Populations of 100k+ ions can be analyzed with acceptable mass accuracy (assuming no other detector non linearities).

Mass precision is also improved, especially if ESI gives a highly variable ion flux.

Simulations may point to interesting ion-ion phenomena at certain densities and mass separations.

References1. Li, G.Z.; Guan, S.; Marshall, A.G. Sympathetic cooling of trapped negative ions

by self-cooled electrons in a Fourier transform ion cyclotron resonance mass spectrometer. JASMS 1997, 8, 793-800.

2. Tolmachev, A.V.; Udseth, H.R.; Smith R.D. Modeling the ion density distribution in collisional cooling RF multipole ion guides. IJMS 2003, 222, 155-174.

AcknowledgementsWe would like to thank Scott Quarmby (Thermo Fisher Scientific, Austin) and Rob Grothe (Thermo Fisher Scientific, San Jose) for helpful discussions.

OverviewPurpose: Develop a method to correct space-charge-induced mass shifts in ion trap mass spectrometers, increasing the dynamic range of mass analysis.

Methods: Mass shifts were characterized in terms of the number of ions of interest (analyte ions), number of other ions (adjacent ions), and the mass separation between these species.

Results: 100k total ions can be mass analyzed with acceptable mass accuracy in a linear quadrupole ion trap.

IntroductionThe largest ion population that can be suitably mass analyzed by an ion trap mass spectrometer (ITMS) is limited by ion-ion interactions. These ion-ion interactions cause a shift in the observed mass-to-charge ratio and lead to peak broadening. The point at which these effects are no longer acceptable is called the spectral space charge limit. The amount of space-charge-induced mass shift and peak broadening for a given situation can be predicted based on experimental study. Therefore, these deleterious effects can be corrected and dynamic range can be increased.

MethodsSample Preparation

Thermo Scientific Pierce LTQ ESI Positive Ion Calibration Solution, a mix of caffeine, the peptide MRFA, and Ultramark 1622, was used, as well as polyethylene glycol (PEG) and angiotensin I.

Experimental Space Charge Measurements

A dual-cell linear ion trap was used for the experiments, scanning at 33 kDa/s, with an analyzer pressure of ~0.4 mTorr. Ions were isolated and then accumulated in a storage multipole before being introduced to a dual-cell linear ITMS. This allowed for simultaneous independent control of the number of ions at multiple mass-to-charge regions

Theoretical Space Charge Measurements

An ion trajectory simulation program was written to simulate the relevant portions of mass analysis in a linear ITMS. Between 128 and 20,000 ions were studied in the simulations. In each case, initial conditions were established by allowing the ions to equilibrate for 27 ms without interacting and then 3 ms with interactions.

Ion-ion interactions were calculated with an N-body method, such that the space charge force on ion i, for each dimension u, is given by Equation 1, where ru is the distance between ions i and j, and ε is a protection factor, taken to be the collision radius of a typical ion. The results are shown in Figures 1a and 1b.

FIGURE 1a. Distribution of ion-ion force magnitudes versus radius during ion storage, without resonance excitation

FIGURE 3a. Adjacent mass shift slope versus ∆mass for PEG m/z 525

FIGURE 3b. Predicted mass shift versus m/z for angiotensin I, m/z 658, [M+2H]2+, 80k total ions

Experimental Test of Space Charge Shift Correction

MS/MS was performed on various precursor ions at large ion populations, as shown in Figure 5. (For reference, current typical MS/MS targets are 10k–20k ions.) MS2

analyte positions were significantly shifted and broadened. MS3 isolated analytes were much less affected because they have no adjacent ions and can serve as a reference.

The applied correction significantly improved the mass accuracy. In addition, the low mass, mass accuracy can be improved by varying the coefficients in Equation 2 with mass. A remaining negative bias needs to be calibrated out.

Mass Precision Improvement

When electrospray ionization is not stable, the resultant ion populations can have a large variation. Under these conditions, the observed mass precision is degraded.

Figure 6 shows histograms of observed mass errors when the total ion current relative standard deviation was 15%–30% and the ion target was ~60k. The space charge correction reduced the absolute mass error and narrowed the distribution of observed masses.

All trademarks are the property of Thermo Fisher Scientific and its subsidiaries.

This information is not intended to encourage use of these products in any manners that might infringe the intellectual property rights of others.

FIGURE 4. Mass error versus number of adjacent ions for analyte ion PEG m/z 657, in the presence of equal parts m/z 658,659, only m/z 658, and only m/z 659

FIGURE 5a. Mass error for fragments of MRFA and Ultramark 1122, 70 and 90k total ions respectively

Multiply Charged Ions

The ion/ion interaction force increases with charge (Equation 1). The mass shift should therefore also be greater for highly charged species.

Figure 7a shows this experiment, where the mass shift for equal numbers of 1+ and 2+

charges was the same. Figure 7b shows simulated mass positions, where the shift for 2+ ions was twice that of 1+ ions.

Because of the conversion dynode, electron multipliers detect the number of charges and not the number of ions. Therefore, Equation 2 does not need any charge dependent factors.

( )= +++

=N

j zyx

uijui

rrr

rqkqF

12/3222,

ε(1)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.70.00

0.02

0.04

0.06

0.08

0.10

0.12

Probability Density

Radius (mm)

Ion-

Ion

Acc

eler

atio

n (m

m/μ

s2 )

9.3E-05

2.2E-04

4.4E-04

6.6E-04

8.8E-04

0.0011

0.0013

0.0015

0.0018

-4 -3 -2 -1 0 1 2 3 40.00

0.02

0.04

0.06

0.08

Position (mm)

Ion-

Ion

Acc

eler

atio

n (m

m/μ

s2 )

1.3E-04

0.0013

0.0024

0.0036

0.0048

0.0059

0.0071

0.0082

0.0094

0.011

0.012

Probability Density

FIGURE 1b. Distribution of ion-ion force magnitudes versus x position during mass analysis

-0.1 0.0 0.1 0.2 0.3 0.4 0.50.00

0.02

0.04

0.06

0.08

Pro

babi

lity

Den

sity

(Da-1

)

Mass Error (Da)

Measured Corrected

0 20000 40000 60000 80000 100000 120000

0.00

0.02

0.04

0.06

0.08

0.10

Ave

rage

Mas

s E

rror

(Da)

TIC

Avg Error Avg Corrected Error

0 2000 4000 6000 8000 10000 12000 14000 16000 18000-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.12

Mas

s E

rror (

Da)

Number Adjacent Ions

658,659 658 659

0 500 1000 1500 2000

682

684

686

688

690

692

694

696

Ave

rage

Pos

ition

(μs)

Ions/mm

[Μ+1]+

[Μ+2]+

[2Μ+2]2+

[2Μ+4]2+

100 200 300 400 500 600 700 800 900 1000

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

Mas

s E

rror

(Da)

m/z

MS2 Error MS3 Error MS2 Corrected Error

FIGURE 5b. Average mass error versus total ion current for Ultramark 1122

FIGURE 6. Precision of mass measurement for unstable ESI conditions, m/z 301 in angiotensin I solution

0 2000 4000 6000 8000 10000

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

Δ1 Da (Charge 1) Δ1 Da (Charge 2) Δ0.5 Da (Charge 2)

Mas

s Er

ror (

Da)

Number of Adjacent Charges

FIGURE 7a. Mass error versus adjacent ions for different ∆mass and charge. PEG m/z 657 was 1+ ion. Angiotensin m/z 648 was 2+ ion.

FIGURE 7b. Simulated average mass position for 1024 ions of m/z 524 in the presence of 128–20k adjacent ions

0 5000 10000 15000 200000.080

0.085

0.090

0.095

0.100

0.105

0.110

Ion

Ener

gy (e

V)

Number of Ions

Effect of Ion-Ion Interactions on Ion Energy

The simulations showed an unexpected behavior of ion energy versus population size, as shown in Figure 8:

• Ion energy and radius decreased with number of ions, with “kinks” at ~1000 ions/mm.

• Axial trapping size was 10 mm, so 2000 ions/mm is 20k ions.

• At larger densities, the energy and radius increase again (not shown).

The experimental ion energy was measured by decreasing the magnitude of the axial trapping barrier and measuring the number of remaining ions [1]. The experiment shows a flat region before increasing. This flat region may explain the parabolic type shape observed for the mass shifts (Figures 4 and 7).

In addition, the experimental energies were higher than the simulated ones. The simulation gas temperature was arbitrarily chosen as 300 °C but this may have been too low. A space charge “cooling” effect was observed previously in simulations at low pressure [2]. These observations have yet to be fully elucidated.

0 500 1000 1500 2000

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

0.11

0.12

0.13

Aver

age

Rad

ial K

inet

ic E

nerg

y (e

V)

Ions/mm

[M+H]+

[M+2H]+

[M+3H]+

[2M+2H]2+

[2M+4H]2+

[2M+6H]2+

FIGURE 8a. Experimental ion energy versus ion population size

FIGURE 8b. Simulated ion energy versus ion density (10 mm)

(2)

FIGURE 2. (a) Simulated RMS ion-ion interaction magnitude for 10k ions during mass analysis, (b) Average ion position during simulated mass analysis

ResultsIon-Ion Interactions During Mass Analysis

Ion-ion interactions are a complex, dynamic phenomenon. The magnitude of interactions is random and depends on specific pair-wise distances. However, the strongest ion-ion forces occur near the center of the trap (Figure 1b).

Excitation of ion oscillations somewhat decreases the magnitude of the ion-ion forces, due to a reduction in ion density. Figure 2a illustrates the reduction in average interaction force as ions are excited, and Figure 2b shows the average ion position during analysis.

100 200 300 400 500 600 700 800

-4.5

-3.0

-1.5

0.0

1.5

3.0

4.50.00

0.03

0.06

0.09

0.12100 200 300 400 500 600 700 800

Ave

rage

X P

ositi

on (m

m)

Time (μs)

Average X Position

RM

S Io

n-Io

n Ac

cele

ratio

n (m

m/μ

s)

RMS Ion-Ion Acceleration

(a)

(b)

5Thermo Scientific Poster Note • PN63578_E 06/12S

Empirical Model for Space-Charge-Induced Mass Shifts

In the empirical model, the “analyte” is the ion whose mass-to-charge ratio is under consideration (M0). “Self” interactions describe the shift induced by ions of the same mass-to-charge value (analyte ions), where S (M0) is the mass shift sensitivity to the number of analyte ions I[M0]. “Adjacent” ion interactions describe the shift induced by ions of different mass-to-charge values (Mi). A(i- M0) is the mass shift sensitivity to the number of adjacent ions I[i] at mass difference (i- M0). Self interactions are less significant than adjacent interactions, partly because the typical ion abundance is only 100-200 ions.

Equation 2 integrates the adjacent ion interactions for all ions of mass > M0. Figures 3a and 3b show the results of the calculations.

Smaller ions do not appreciably affect the analyte mass position or width because they are ejected from the trap first. The analyte ions seem to have no “memory” of adjacent ions that were already ejected.

Linearity of Interactions

It is assumed that each adjacent ion interacts with the analyte ion independently. We expect that fundamentally this is not true because the adjacent ion motion is in turn modified by other adjacent ions and the analyte ions.

In the experimental test, the mass shift was monitored for three ion populations: ∆1 Da, ∆2 Da, and equal parts ∆1 and ∆2 Da. The mixed population was expected to exhibit a mass shift that is the combination of the ∆1 Da and ∆2 Da population shifts. As shown in Figure 4, the linearity assumption appears to hold, as far as mass shifts are concerned, for typical linear ITMS operating conditions.

0 25 50 75 1000

2

4

6

8

10

Mas

s Sh

ift S

lope

(x10

-6 D

a/io

n)

ΔMass (Da)

0 200 400 600 800 10000.00

0.02

0.04

0.06

0.08

0.10

Pre

dict

ed M

ass

Shi

ft

m/z

( ) [ ] ( ) [ ]+=

⋅−+⋅=ΔLastMass

Mi

iIMiAMIMSMm5.0

00000

)(

Increasing the Mass Accuracy and Dynamic Range of Quadrupole Ion Trap Mass SpectrometersPhilip M. Remes, Jae C. SchwartzThermo Fisher Scientific, San Jose, CA

ConclusionAn empirical model for mass shift as a function of ion abundance and mass separation allows for space charge induced shifts to be corrected.

Under typical conditions, space charge interactions accumulate linearly, i.e. the effect of ion 1 and ion 2 simultaneously is the sum of their individual interactions.

Populations of 100k+ ions can be analyzed with acceptable mass accuracy (assuming no other detector non linearities).

Mass precision is also improved, especially if ESI gives a highly variable ion flux.

Simulations may point to interesting ion-ion phenomena at certain densities and mass separations.

References1. Li, G.Z.; Guan, S.; Marshall, A.G. Sympathetic cooling of trapped negative ions

by self-cooled electrons in a Fourier transform ion cyclotron resonance mass spectrometer. JASMS 1997, 8, 793-800.

2. Tolmachev, A.V.; Udseth, H.R.; Smith R.D. Modeling the ion density distribution in collisional cooling RF multipole ion guides. IJMS 2003, 222, 155-174.

AcknowledgementsWe would like to thank Scott Quarmby (Thermo Fisher Scientific, Austin) and Rob Grothe (Thermo Fisher Scientific, San Jose) for helpful discussions.

OverviewPurpose: Develop a method to correct space-charge-induced mass shifts in ion trap mass spectrometers, increasing the dynamic range of mass analysis.

Methods: Mass shifts were characterized in terms of the number of ions of interest (analyte ions), number of other ions (adjacent ions), and the mass separation between these species.

Results: 100k total ions can be mass analyzed with acceptable mass accuracy in a linear quadrupole ion trap.

IntroductionThe largest ion population that can be suitably mass analyzed by an ion trap mass spectrometer (ITMS) is limited by ion-ion interactions. These ion-ion interactions cause a shift in the observed mass-to-charge ratio and lead to peak broadening. The point at which these effects are no longer acceptable is called the spectral space charge limit. The amount of space-charge-induced mass shift and peak broadening for a given situation can be predicted based on experimental study. Therefore, these deleterious effects can be corrected and dynamic range can be increased.

MethodsSample Preparation

Thermo Scientific Pierce LTQ ESI Positive Ion Calibration Solution, a mix of caffeine, the peptide MRFA, and Ultramark 1622, was used, as well as polyethylene glycol (PEG) and angiotensin I.

Experimental Space Charge Measurements

A dual-cell linear ion trap was used for the experiments, scanning at 33 kDa/s, with an analyzer pressure of ~0.4 mTorr. Ions were isolated and then accumulated in a storage multipole before being introduced to a dual-cell linear ITMS. This allowed for simultaneous independent control of the number of ions at multiple mass-to-charge regions

Theoretical Space Charge Measurements

An ion trajectory simulation program was written to simulate the relevant portions of mass analysis in a linear ITMS. Between 128 and 20,000 ions were studied in the simulations. In each case, initial conditions were established by allowing the ions to equilibrate for 27 ms without interacting and then 3 ms with interactions.

Ion-ion interactions were calculated with an N-body method, such that the space charge force on ion i, for each dimension u, is given by Equation 1, where ru is the distance between ions i and j, and ε is a protection factor, taken to be the collision radius of a typical ion. The results are shown in Figures 1a and 1b.

FIGURE 1a. Distribution of ion-ion force magnitudes versus radius during ion storage, without resonance excitation

FIGURE 3a. Adjacent mass shift slope versus ∆mass for PEG m/z 525

FIGURE 3b. Predicted mass shift versus m/z for angiotensin I, m/z 658, [M+2H]2+, 80k total ions

Experimental Test of Space Charge Shift Correction

MS/MS was performed on various precursor ions at large ion populations, as shown in Figure 5. (For reference, current typical MS/MS targets are 10k–20k ions.) MS2

analyte positions were significantly shifted and broadened. MS3 isolated analytes were much less affected because they have no adjacent ions and can serve as a reference.

The applied correction significantly improved the mass accuracy. In addition, the low mass, mass accuracy can be improved by varying the coefficients in Equation 2 with mass. A remaining negative bias needs to be calibrated out.

Mass Precision Improvement

When electrospray ionization is not stable, the resultant ion populations can have a large variation. Under these conditions, the observed mass precision is degraded.

Figure 6 shows histograms of observed mass errors when the total ion current relative standard deviation was 15%–30% and the ion target was ~60k. The space charge correction reduced the absolute mass error and narrowed the distribution of observed masses.

All trademarks are the property of Thermo Fisher Scientific and its subsidiaries.

This information is not intended to encourage use of these products in any manners that might infringe the intellectual property rights of others.

FIGURE 4. Mass error versus number of adjacent ions for analyte ion PEG m/z 657, in the presence of equal parts m/z 658,659, only m/z 658, and only m/z 659

FIGURE 5a. Mass error for fragments of MRFA and Ultramark 1122, 70 and 90k total ions respectively

Multiply Charged Ions

The ion/ion interaction force increases with charge (Equation 1). The mass shift should therefore also be greater for highly charged species.

Figure 7a shows this experiment, where the mass shift for equal numbers of 1+ and 2+

charges was the same. Figure 7b shows simulated mass positions, where the shift for 2+ ions was twice that of 1+ ions.

Because of the conversion dynode, electron multipliers detect the number of charges and not the number of ions. Therefore, Equation 2 does not need any charge dependent factors.

( )= +++

=N

j zyx

uijui

rrr

rqkqF

12/3222,

ε(1)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.70.00

0.02

0.04

0.06

0.08

0.10

0.12

Probability Density

Radius (mm)

Ion-

Ion

Acc

eler

atio

n (m

m/μ

s2 )

9.3E-05

2.2E-04

4.4E-04

6.6E-04

8.8E-04

0.0011

0.0013

0.0015

0.0018

-4 -3 -2 -1 0 1 2 3 40.00

0.02

0.04

0.06

0.08

Position (mm)

Ion-

Ion

Acc

eler

atio

n (m

m/μ

s2 )

1.3E-04

0.0013

0.0024

0.0036

0.0048

0.0059

0.0071

0.0082

0.0094

0.011

0.012

Probability Density

FIGURE 1b. Distribution of ion-ion force magnitudes versus x position during mass analysis

-0.1 0.0 0.1 0.2 0.3 0.4 0.50.00

0.02

0.04

0.06

0.08

Pro

babi

lity

Den

sity

(Da-1

)

Mass Error (Da)

Measured Corrected

0 20000 40000 60000 80000 100000 120000

0.00

0.02

0.04

0.06

0.08

0.10

Ave

rage

Mas

s E

rror

(Da)

TIC

Avg Error Avg Corrected Error

0 2000 4000 6000 8000 10000 12000 14000 16000 18000-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.12

Mas

s E

rror (

Da)

Number Adjacent Ions

658,659 658 659

0 500 1000 1500 2000

682

684

686

688

690

692

694

696

Ave

rage

Pos

ition

(μs)

Ions/mm

[Μ+1]+

[Μ+2]+

[2Μ+2]2+

[2Μ+4]2+

100 200 300 400 500 600 700 800 900 1000

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

Mas

s E

rror

(Da)

m/z

MS2 Error MS3 Error MS2 Corrected Error

FIGURE 5b. Average mass error versus total ion current for Ultramark 1122

FIGURE 6. Precision of mass measurement for unstable ESI conditions, m/z 301 in angiotensin I solution

0 2000 4000 6000 8000 10000

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

Δ1 Da (Charge 1) Δ1 Da (Charge 2) Δ0.5 Da (Charge 2)

Mas

s Er

ror (

Da)

Number of Adjacent Charges

FIGURE 7a. Mass error versus adjacent ions for different ∆mass and charge. PEG m/z 657 was 1+ ion. Angiotensin m/z 648 was 2+ ion.

FIGURE 7b. Simulated average mass position for 1024 ions of m/z 524 in the presence of 128–20k adjacent ions

0 5000 10000 15000 200000.080

0.085

0.090

0.095

0.100

0.105

0.110

Ion

Ener

gy (e

V)

Number of Ions

Effect of Ion-Ion Interactions on Ion Energy

The simulations showed an unexpected behavior of ion energy versus population size, as shown in Figure 8:

• Ion energy and radius decreased with number of ions, with “kinks” at ~1000 ions/mm.

• Axial trapping size was 10 mm, so 2000 ions/mm is 20k ions.

• At larger densities, the energy and radius increase again (not shown).

The experimental ion energy was measured by decreasing the magnitude of the axial trapping barrier and measuring the number of remaining ions [1]. The experiment shows a flat region before increasing. This flat region may explain the parabolic type shape observed for the mass shifts (Figures 4 and 7).

In addition, the experimental energies were higher than the simulated ones. The simulation gas temperature was arbitrarily chosen as 300 °C but this may have been too low. A space charge “cooling” effect was observed previously in simulations at low pressure [2]. These observations have yet to be fully elucidated.

0 500 1000 1500 2000

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

0.11

0.12

0.13

Aver

age

Rad

ial K

inet

ic E

nerg

y (e

V)

Ions/mm

[M+H]+

[M+2H]+

[M+3H]+

[2M+2H]2+

[2M+4H]2+

[2M+6H]2+

FIGURE 8a. Experimental ion energy versus ion population size

FIGURE 8b. Simulated ion energy versus ion density (10 mm)

(2)

FIGURE 2. (a) Simulated RMS ion-ion interaction magnitude for 10k ions during mass analysis, (b) Average ion position during simulated mass analysis

ResultsIon-Ion Interactions During Mass Analysis

Ion-ion interactions are a complex, dynamic phenomenon. The magnitude of interactions is random and depends on specific pair-wise distances. However, the strongest ion-ion forces occur near the center of the trap (Figure 1b).

Excitation of ion oscillations somewhat decreases the magnitude of the ion-ion forces, due to a reduction in ion density. Figure 2a illustrates the reduction in average interaction force as ions are excited, and Figure 2b shows the average ion position during analysis.

100 200 300 400 500 600 700 800

-4.5

-3.0

-1.5

0.0

1.5

3.0

4.50.00

0.03

0.06

0.09

0.12100 200 300 400 500 600 700 800

Ave

rage

X P

ositi

on (m

m)

Time (μs)

Average X Position

RM

S Io

n-Io

n Ac

cele

ratio

n (m

m/μ

s)

RMS Ion-Ion Acceleration

(a)

(b)

6 Increasing the Mass Accuracy and Dynamic Range of Quadrupole Ion Trap Mass Spectrometers

Empirical Model for Space-Charge-Induced Mass Shifts

In the empirical model, the “analyte” is the ion whose mass-to-charge ratio is under consideration (M0). “Self” interactions describe the shift induced by ions of the same mass-to-charge value (analyte ions), where S (M0) is the mass shift sensitivity to the number of analyte ions I[M0]. “Adjacent” ion interactions describe the shift induced by ions of different mass-to-charge values (Mi). A(i- M0) is the mass shift sensitivity to the number of adjacent ions I[i] at mass difference (i- M0). Self interactions are less significant than adjacent interactions, partly because the typical ion abundance is only 100-200 ions.

Equation 2 integrates the adjacent ion interactions for all ions of mass > M0. Figures 3a and 3b show the results of the calculations.

Smaller ions do not appreciably affect the analyte mass position or width because they are ejected from the trap first. The analyte ions seem to have no “memory” of adjacent ions that were already ejected.

Linearity of Interactions

It is assumed that each adjacent ion interacts with the analyte ion independently. We expect that fundamentally this is not true because the adjacent ion motion is in turn modified by other adjacent ions and the analyte ions.

In the experimental test, the mass shift was monitored for three ion populations: ∆1 Da, ∆2 Da, and equal parts ∆1 and ∆2 Da. The mixed population was expected to exhibit a mass shift that is the combination of the ∆1 Da and ∆2 Da population shifts. As shown in Figure 4, the linearity assumption appears to hold, as far as mass shifts are concerned, for typical linear ITMS operating conditions.

0 25 50 75 1000

2

4

6

8

10

Mas

s Sh

ift S

lope

(x10

-6 D

a/io

n)

ΔMass (Da)

0 200 400 600 800 10000.00

0.02

0.04

0.06

0.08

0.10

Pre

dict

ed M

ass

Shi

ft

m/z

( ) [ ] ( ) [ ]+=

⋅−+⋅=ΔLastMass

Mi

iIMiAMIMSMm5.0

00000

)(

Increasing the Mass Accuracy and Dynamic Range of Quadrupole Ion Trap Mass SpectrometersPhilip M. Remes, Jae C. SchwartzThermo Fisher Scientific, San Jose, CA

ConclusionAn empirical model for mass shift as a function of ion abundance and mass separation allows for space charge induced shifts to be corrected.

Under typical conditions, space charge interactions accumulate linearly, i.e. the effect of ion 1 and ion 2 simultaneously is the sum of their individual interactions.

Populations of 100k+ ions can be analyzed with acceptable mass accuracy (assuming no other detector non linearities).

Mass precision is also improved, especially if ESI gives a highly variable ion flux.

Simulations may point to interesting ion-ion phenomena at certain densities and mass separations.

References1. Li, G.Z.; Guan, S.; Marshall, A.G. Sympathetic cooling of trapped negative ions

by self-cooled electrons in a Fourier transform ion cyclotron resonance mass spectrometer. JASMS 1997, 8, 793-800.

2. Tolmachev, A.V.; Udseth, H.R.; Smith R.D. Modeling the ion density distribution in collisional cooling RF multipole ion guides. IJMS 2003, 222, 155-174.

AcknowledgementsWe would like to thank Scott Quarmby (Thermo Fisher Scientific, Austin) and Rob Grothe (Thermo Fisher Scientific, San Jose) for helpful discussions.

OverviewPurpose: Develop a method to correct space-charge-induced mass shifts in ion trap mass spectrometers, increasing the dynamic range of mass analysis.

Methods: Mass shifts were characterized in terms of the number of ions of interest (analyte ions), number of other ions (adjacent ions), and the mass separation between these species.

Results: 100k total ions can be mass analyzed with acceptable mass accuracy in a linear quadrupole ion trap.

IntroductionThe largest ion population that can be suitably mass analyzed by an ion trap mass spectrometer (ITMS) is limited by ion-ion interactions. These ion-ion interactions cause a shift in the observed mass-to-charge ratio and lead to peak broadening. The point at which these effects are no longer acceptable is called the spectral space charge limit. The amount of space-charge-induced mass shift and peak broadening for a given situation can be predicted based on experimental study. Therefore, these deleterious effects can be corrected and dynamic range can be increased.

MethodsSample Preparation

Thermo Scientific Pierce LTQ ESI Positive Ion Calibration Solution, a mix of caffeine, the peptide MRFA, and Ultramark 1622, was used, as well as polyethylene glycol (PEG) and angiotensin I.

Experimental Space Charge Measurements

A dual-cell linear ion trap was used for the experiments, scanning at 33 kDa/s, with an analyzer pressure of ~0.4 mTorr. Ions were isolated and then accumulated in a storage multipole before being introduced to a dual-cell linear ITMS. This allowed for simultaneous independent control of the number of ions at multiple mass-to-charge regions

Theoretical Space Charge Measurements

An ion trajectory simulation program was written to simulate the relevant portions of mass analysis in a linear ITMS. Between 128 and 20,000 ions were studied in the simulations. In each case, initial conditions were established by allowing the ions to equilibrate for 27 ms without interacting and then 3 ms with interactions.

Ion-ion interactions were calculated with an N-body method, such that the space charge force on ion i, for each dimension u, is given by Equation 1, where ru is the distance between ions i and j, and ε is a protection factor, taken to be the collision radius of a typical ion. The results are shown in Figures 1a and 1b.

FIGURE 1a. Distribution of ion-ion force magnitudes versus radius during ion storage, without resonance excitation

FIGURE 3a. Adjacent mass shift slope versus ∆mass for PEG m/z 525

FIGURE 3b. Predicted mass shift versus m/z for angiotensin I, m/z 658, [M+2H]2+, 80k total ions

Experimental Test of Space Charge Shift Correction

MS/MS was performed on various precursor ions at large ion populations, as shown in Figure 5. (For reference, current typical MS/MS targets are 10k–20k ions.) MS2

analyte positions were significantly shifted and broadened. MS3 isolated analytes were much less affected because they have no adjacent ions and can serve as a reference.

The applied correction significantly improved the mass accuracy. In addition, the low mass, mass accuracy can be improved by varying the coefficients in Equation 2 with mass. A remaining negative bias needs to be calibrated out.

Mass Precision Improvement

When electrospray ionization is not stable, the resultant ion populations can have a large variation. Under these conditions, the observed mass precision is degraded.

Figure 6 shows histograms of observed mass errors when the total ion current relative standard deviation was 15%–30% and the ion target was ~60k. The space charge correction reduced the absolute mass error and narrowed the distribution of observed masses.

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FIGURE 4. Mass error versus number of adjacent ions for analyte ion PEG m/z 657, in the presence of equal parts m/z 658,659, only m/z 658, and only m/z 659

FIGURE 5a. Mass error for fragments of MRFA and Ultramark 1122, 70 and 90k total ions respectively

Multiply Charged Ions

The ion/ion interaction force increases with charge (Equation 1). The mass shift should therefore also be greater for highly charged species.

Figure 7a shows this experiment, where the mass shift for equal numbers of 1+ and 2+

charges was the same. Figure 7b shows simulated mass positions, where the shift for 2+ ions was twice that of 1+ ions.

Because of the conversion dynode, electron multipliers detect the number of charges and not the number of ions. Therefore, Equation 2 does not need any charge dependent factors.

( )= +++

=N

j zyx

uijui

rrr

rqkqF

12/3222,

ε(1)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.70.00

0.02

0.04

0.06

0.08

0.10

0.12

Probability Density

Radius (mm)

Ion-

Ion

Acc

eler

atio

n (m

m/μ

s2 )

9.3E-05

2.2E-04

4.4E-04

6.6E-04

8.8E-04

0.0011

0.0013

0.0015

0.0018

-4 -3 -2 -1 0 1 2 3 40.00

0.02

0.04

0.06

0.08

Position (mm)

Ion-

Ion

Acc

eler

atio

n (m

m/μ

s2 )

1.3E-04

0.0013

0.0024

0.0036

0.0048

0.0059

0.0071

0.0082

0.0094

0.011

0.012

Probability Density

FIGURE 1b. Distribution of ion-ion force magnitudes versus x position during mass analysis

-0.1 0.0 0.1 0.2 0.3 0.4 0.50.00

0.02

0.04

0.06

0.08

Pro

babi

lity

Den

sity

(Da-1

)

Mass Error (Da)

Measured Corrected

0 20000 40000 60000 80000 100000 120000

0.00

0.02

0.04

0.06

0.08

0.10

Ave

rage

Mas

s E

rror

(Da)

TIC

Avg Error Avg Corrected Error

0 2000 4000 6000 8000 10000 12000 14000 16000 18000-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.12

Mas

s E

rror (

Da)

Number Adjacent Ions

658,659 658 659

0 500 1000 1500 2000

682

684

686

688

690

692

694

696

Ave

rage

Pos

ition

(μs)

Ions/mm

[Μ+1]+

[Μ+2]+

[2Μ+2]2+

[2Μ+4]2+

100 200 300 400 500 600 700 800 900 1000

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

Mas

s E

rror

(Da)

m/z

MS2 Error MS3 Error MS2 Corrected Error

FIGURE 5b. Average mass error versus total ion current for Ultramark 1122

FIGURE 6. Precision of mass measurement for unstable ESI conditions, m/z 301 in angiotensin I solution

0 2000 4000 6000 8000 10000

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

Δ1 Da (Charge 1) Δ1 Da (Charge 2) Δ0.5 Da (Charge 2)

Mas

s Er

ror (

Da)

Number of Adjacent Charges

FIGURE 7a. Mass error versus adjacent ions for different ∆mass and charge. PEG m/z 657 was 1+ ion. Angiotensin m/z 648 was 2+ ion.

FIGURE 7b. Simulated average mass position for 1024 ions of m/z 524 in the presence of 128–20k adjacent ions

0 5000 10000 15000 200000.080

0.085

0.090

0.095

0.100

0.105

0.110

Ion

Ener

gy (e

V)

Number of Ions

Effect of Ion-Ion Interactions on Ion Energy

The simulations showed an unexpected behavior of ion energy versus population size, as shown in Figure 8:

• Ion energy and radius decreased with number of ions, with “kinks” at ~1000 ions/mm.

• Axial trapping size was 10 mm, so 2000 ions/mm is 20k ions.

• At larger densities, the energy and radius increase again (not shown).

The experimental ion energy was measured by decreasing the magnitude of the axial trapping barrier and measuring the number of remaining ions [1]. The experiment shows a flat region before increasing. This flat region may explain the parabolic type shape observed for the mass shifts (Figures 4 and 7).

In addition, the experimental energies were higher than the simulated ones. The simulation gas temperature was arbitrarily chosen as 300 °C but this may have been too low. A space charge “cooling” effect was observed previously in simulations at low pressure [2]. These observations have yet to be fully elucidated.

0 500 1000 1500 2000

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

0.11

0.12

0.13

Aver

age

Rad

ial K

inet

ic E

nerg

y (e

V)

Ions/mm

[M+H]+

[M+2H]+

[M+3H]+

[2M+2H]2+

[2M+4H]2+

[2M+6H]2+

FIGURE 8a. Experimental ion energy versus ion population size

FIGURE 8b. Simulated ion energy versus ion density (10 mm)

(2)

FIGURE 2. (a) Simulated RMS ion-ion interaction magnitude for 10k ions during mass analysis, (b) Average ion position during simulated mass analysis

ResultsIon-Ion Interactions During Mass Analysis

Ion-ion interactions are a complex, dynamic phenomenon. The magnitude of interactions is random and depends on specific pair-wise distances. However, the strongest ion-ion forces occur near the center of the trap (Figure 1b).

Excitation of ion oscillations somewhat decreases the magnitude of the ion-ion forces, due to a reduction in ion density. Figure 2a illustrates the reduction in average interaction force as ions are excited, and Figure 2b shows the average ion position during analysis.

100 200 300 400 500 600 700 800

-4.5

-3.0

-1.5

0.0

1.5

3.0

4.50.00

0.03

0.06

0.09

0.12100 200 300 400 500 600 700 800

Ave

rage

X P

ositi

on (m

m)

Time (μs)

Average X Position

RM

S Io

n-Io

n Ac

cele

ratio

n (m

m/μ

s)

RMS Ion-Ion Acceleration

(a)

(b)

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