Circular Dichroism in Mass Spectrometry: Quantum Chemical

Article pubs.acs.org/JPCA

Circular Dichroism in Mass Spectrometry: Quantum Chemical Investigations for the Differences between (R)‑3Methylcyclopentanone and Its Cation Dominik Kröner* and Tina Gaebel Universität Potsdam, Chemistry Department−Theoretical Chemistry, Karl-Liebknecht-Straße 24-25, D-14476 Potsdam, Germany ABSTRACT: In mass spectrometry enantiomers can be distinguished by multiphoton ionization employing circular polarized laser pulses. The circular dichroism (CD) is detected from the normalized difference in the ion yield after excitation with light of opposite handedness. While there are cases in which fragment and parent ions exhibit the same sign of the CD in the ion yield, several experiments show that they might also differ in sign and magnitude. Supported by experimental observations it has been proposed that the parent ion, once it has been formed, is further excited by the laser, which may result in a change of the CD in the ion yield of the formed fragments compared to the parent ion. To gain a deeper insight in possible excitation pathways we calculated and compared the electronic CD absorption spectra of neutral and cationic (R)-3-methylcyclopentanone, applying density functional theory. In addition, electron wavepacket dynamics were used to compare the CD of one- and two-photon transitions. Our results support the proposed subsequent excitation of the parent ion as a possible origin of the difference of the CD in the ion yield between parent ion and fragments.

1. INTRODUCTION The distinction of isomers in a sample is an important analytical task in chemistry. While there is a large variety of methods, mass spectrometry (MS) stands out due its high sensitivity. However, distinguishing isomers in mass spectrometry is not always an easy task. While the detected fragmentation pattern carries structural information, the differentiation of constitutional isomers with small differences, such as, for example, ortho- and para-xylene, becomes already a challenge. While often MS is combined with other analytical techniques, for instance, chromatography, femtosecond laser pulses may also be optimized in computer-assisted learning loops to create distinguishable fragmentation patterns for the differentiation of structural isomers.1 An even more challenging task is the distinction of enantiomers in MS. Enantiomers are mirror images, but they cannot be superposed. Circular polarized nanosecond laser pulses can, however, be used to distinguish enantiomers of, for instance, 3-methylcyclopentanone (3MCP) in MS.2,3 More precisely, the difference in the ion yields (Y) is detected after multiphoton ionization (MPI) with either left- (LCP) or rightcircular (RCP) polarized laser light. This difference allows to define a circular dichroism (CD) in the ion yield: CD = 2(YLCP − YRCP)/(YLCP + YRCP). It is worth noting that the idea of comparing the mass spectra of two enantiospecific excitation scenarios is equivalent to an experimental proof for enantioselective laser pulse excitation proposed by us in 2003.4 Our task at that time was, however, to show that it is experimentally possible to detect the enantioselectivity of our theoretically proposed laser pulse control.5 By now, CD in MS may also be achieved using (shaped) femtosecond laser pulses.6 The pulse duration, for instance, was © 2015 American Chemical Society

shown to actually have an impact on the CD in the ion yield, where very short and intense pulses react, however, rather unspecific with the enantiomers.7 Here laser-driven electron wavepacket dynamics helped to understand the processes that take place during electronic excitation with circular polarized laser pulses.8 While at the first glance, resonance-enhanced multiphoton ionization (REMPI) appears to be the natural way for an optimal excitation of the chiral sample, nonresonant excitations have been shown to create detectable, albeit small, CDs in ion yields for (R)-propylene oxide (PO).9 Recent simulations by us indicated that during nonresonant excitations a variety of excitation pathways are induced, which all contribute to the observed CD.10 A fact that makes a prediction of the CD in ion yield, starting from the CD absorption spectrum, rather difficult. Many other aspects have been investigated to learn more about the optimal conditions for the distinction of enantiomers in MS. A particularly interesting observation is that the CD in the ion yields might differ between parent ion and fragment ions.11−13 The CD in the ion yield of the parent ion of 3MCP (m/z = 98) differs significantly in sign and size to the CD value of the fragment ion (m/z = 69) for several two-photon transitions to 3p Rydberg states.11 A similar observation was made for PO, where all of the fragment ions showed the opposite sign of the CD than the parent ion and most of them also had a larger absolute CD value.13 While there is evidence that the CD in the parent ion yield is caused by the circular dichroism in the resonant transition to an electronic excited Received: June 2, 2015 Revised: July 27, 2015 Published: July 27, 2015 9167

DOI: 10.1021/acs.jpca.5b05247 J. Phys. Chem. A 2015, 119, 9167−9177

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The Journal of Physical Chemistry A state and not by the subsequent ionization of the sample,11 the observed differences to the CD values of fragment ions indicate that further enantiospecific processes must play a role. It has been proposed that these fragments are formed from parent ions that have been further enantiospecifically excited by the circular polarized laser pulse before fragmentation takes place.12 If, for instance, the parent ion exhibits a different circular dichroism in the absorption than the neutral molecule, the observed differences could be explained. Moreover, in their experiments Logé and Boesl showed that 3MCP produces different mass spectra for an excitation with a 198 nm pulse than with two subsequent laser pulses of initially 198 nm and then 440 nm after a delay of 10 ns.12 An excitation with 440 nm alone resulted in practically no ion signal at all. Their results indicate that only the parent ion has an electronic excited state at 440 nm above its ground state, which is only available after ionization with the first laser pulse of 198 nm. In this report we study these observations by quantum chemical calculations and by a detailed comparison of the electronic structures of the neutral and ionic 3MCP. In addition, simulated electronic CD spectra of the neutral molecule and its cation help to unravel the difference of the observed CD in parent and fragment ion yields. For the twophoton excitation, laser-driven quantum electron dynamics are simulated based on the interactions of the electromagnetic field with the electric and magnetic (transition) dipole moments as well as with electric quadrupole moments. The report is structured as follows: In Section 2 the applied computational methods are described. Section 3 presents the results of our simulations including a detailed analysis. In Section 4 we summarize our findings.

functional theory (TD-DFT), employing TD-(U)CAMB3LYP/aug-cc-pVTZ. On the basis of the excitation energies Ei, UV−vis spectra are simulated, that is, the molar absorption coefficient ε as a function of the wavenumber ν̃ is determined by ε(ν)̃ = γ ∑ fi ·G(ν ̃ − νĩ)

(1)

i=1

where ν̃i = 1/λi = νi/c = Ei/(hc). In eq 1 γ = e NA/(4 me c ε0 ln(10)), with f i being the oscillator strength for the excitation to the ith electronic state; me is the electron mass; and e is the electron charge. The stick spectra are convoluted by Gaussian functions of the form G(ν ̃ − νĩ) = exp( −0.5·(ν ̃ − νĩ)2 /Δν 2̃ )/( 2π Δν)̃ with Δν̃ = 2

2

500 cm−1 (where 2 2 × ln(2) Δν= ̃ full width at half maximum (fwhm) of the peak) to account for excited-state lifetimes and the vibronic fine structure of the experimental spectra. In addition to the excitation energies Ei we are, in particular, interested in electric and magnetic transition dipole moments, ̂ , which are used to μ0⃗ i = ⟨Φ0| μ ⃗ ̂|Φ⟩ i and m⃗ 0i = ⟨Φ0| m⃗ |Φ⟩ i calculate rotatory strengths according to R i = ℑ{μ0⃗ i m⃗ i0}

(2)

Note that m⃗ i0= −m⃗ 0i = m⃗ *i0 due to the (angular) momentum operator in the magnetic dipole operator: e m⃗ ̂ = 2m ∑k ( rk⃗ × pk⃗ ̂ ) for electron k at position rk⃗ with e

momentum pk⃗ ̂ . The positions of the nuclei are fixed. Rotatory strengths are usually given in 1 × 10−40 esu cm erg/G (cgs units), where 1 erg = 1 × 10−7 J, 1 G equals 1 × 10−4 T, and 1 esu corresponds to (0.1/c) m s−1 A s in SI units. The rotatory strengths Ri are used to simulated electronic CD spectra (ECD) of neutral and cationic 3MCP, according to

2. QUANTUM MECHANICAL AND DYNAMICAL METHODS First, the geometry of the neutral (R)-3MCP is optimized applying the long-range corrected CAM-B3LYP (Coulombattenuated model) density functional with the aug-cc-pVTZ basis set.14 The CAM-B3LYP functional has been found to produce realistic excitation energies for 3MCP, as shown by Rizzo et al.15 3MCP exists in several stable conformations, where the most stable one is the cyclopentanone ring being in a kind of envelope form with the methyl group in equatorial (eq) position. The methyl group in the axial (ax) position is also likely to appear in gas phase at room temperature, however, at a much lower fraction. The ratio between equatorial and axial form (eq/ax) ranges from 89:11 in theory (B3LYP/6-311+ +G(2d,2p))16 to 80:20 in cyclohexane3 or 89:11 in gas phase.17 Therefore, the axial conformer will have a very small impact on the results. Still, it is investigated in the Appendix, as it shows some differences to the equatorial form in the electronic CD.8,15 After removing an electron the cationic doublet ground state of the equatorial conformer of (R)-3MCP is optimized using unrestricted (U) CAM-B3LYP at the same level of theory. In the following, frequency analyses of both minimum-energy geometries were performed to ensure that minima are found and to identify significant differences in the normal modes of neutral and cationic species. The performed frequency analyses may also be used to simulate IR and vibrational CD (VCD) spectra of both species. Starting from the minimum-energy geometries vertical excitation energies to singlet or doublet excited states are calculated with time-dependent (linear response) density

Δε(ν)̃ = (4κ /c) ∑ νiR ̃ i·G(ν ̃ − νĩ)

(3)

i=1

with 4κ/c = (1 × 10 /22.96) dm G/(mol cm esu erg), in which 1/(4πε0 c) was replaced by 1 × 10−3 g dm3 cm G/(erg esu s2).18 All quantum chemical calculations were performed using the Gaussian09 program package.19 Furthermore, to compare one- and two-photon CD, we apply laser-driven electron wavepacket dynamics in the eigenstate representation, as described elsewhere for timedependent configuration interaction singles with perturbative doubles (TD-CIS(D)).8,20 The time-dependent Schrödinger equation is solved for 50 states by the Runge−Kutta method using a time step of 0.0025 fs. Instead of drawing on CIS(D), we use energies Ei and transition moments between ground and electronic excited states from the TD-DFT calculations, namely, electric and magnetic transition dipole moments μ⃗0i and m⃗ 0i as well as electric transition quadrupole moments Q̲ .21 In general, the electric transition quadrupole moment 0i tensors are given by Q̲ = ⟨Φ|i Q̲ ̂ |Φ⟩ j , where the electric 40

3

2

ij

quadrupole operator is defined as Q̂ αβ = ∑k qk rk⃗ ,α rk⃗ ,β with the Cartesian components α,β ∈ {x,y,z}. The electric quadrupole moment depends on the origin of the coordinate system, because the electric dipole is nonzero. We chose the center of charge as the origin. Permanent electric dipole μ⃗ii and quadrupole moments Q̲ of the excited electronic states are ii

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x-axis and the corresponding magnetic vector m⃗ 0i lies in the x− y plane to ensure an optimal interaction with the laser pulse.

obtained from TD-DFT calculations.22 The missing transition moments between electronic excited states are taken from supplementary configuration interaction singles (CIS) calculations at the same level of theory. The laser−molecule interactions are expressed by23 1 V̂ (t ) = − , 0s(t )[(De⃗ ̂ δ⃗ ̂ )† eiω(t − tc) + (De⃗ ̂ δ⃗ ̂ )e−iω(t − tc)] 2

3. RESULTS AND DISCUSSION 3.1. Change of the Molecular Structure after Ionization. In Figure 1 the optimized geometries of neutral

(4)

1 1 where D⃗ ̂ = μ ⃗ ̂ − c ez⃗ ̂ × m⃗ ̂ + 2 iQ̲ ̂ k ⃗ . Here the wavevector ω k ⃗ = e ⃗ ̂ of the laser points in z-direction, as the unit vector

c z

ez⃗ ̂ . In contrast to previous investigations,7,8 we now also consider electric quadrupole contributions, because they contribute to two-photon CD and are often in the same order of magnitude as the magnetic dipole contributions. The electric field in eq 4 is calculated as

E ⃗(t ) =

† 1 , 0s(t )[ eδ⃗ ̂ eiω(t − tc) + eδ⃗ ̂ e−iω(t − tc)] 2

(5)

where , 0 is the amplitude and ω is the frequency. The electric field strength was set to 1 GV/m, which corresponds to a mean intensity (averaged over the pulse duration) of 3 I ̅ = 16 ε0c , 0 2 ≈ 50 GW/cm2. The magnetic field B⃗ may be 1 o b t a i n e d f r o m B⃗ = e ⃗̂ × E ⃗. T h e f u n c t i o n s (t ) =

⎛ π(t − t ) ⎞ cos2⎜ t c ⎟ ⎝ p ⎠

Figure 1. (left) Comparison of the optimized geometries of neutral (light blue) and cationic (red) (R)-3-MCP ((U)CAM-B3LYP/aug-ccpVTZ). (right) Spin density of the cation.

and cationic (R)-3MCP are compared. The two minimumenergy geometries differ very little. Table 1 lists a selection of bond lengths and bond angles of the neutral and cationic structures.

c z

in eq 5 defines the shape of the laser tp

pulse for 0≤ t ≤ tp and tc = 2 , that is, the pulse duration is given by tp = 2 × fwhm, where fwhm is the full width at halfmaximum of the field. Because of the time scale of electron motion we cannot easily propagate for several nanoseconds without spending a great deal of computational time and accumulating the error over billions of timesteps (10 ns corresponds to 4× 109 time steps). Hence, the pulse duration was set to tp = 250 fs, which allows, at least, a comparison to the femtosecond pulse-driven experiments. The fwhm of the intensity is then obtained as

(

( ))t

2

fwhm I = 1 − π arcsin

4

1 2

p

Table 1. Comparison of Selected Bond Lengths and Angles between the Minimum-Energy Geometries of the Neutral and Cationic (R)-3MCP ((U)CAM-B3LYP/aug-cc-pVTZ)a

≈ 0.364t p = 91 fs. The vec-

tor eδ⃗ ̂ in eq 4 defines the polarization via eδ⃗ ̂ = π

1 2

( ex⃗ ̂ + e−iδ ey⃗ ̂ ), π

where we employ either LCP (δ = − 2 ) or RCP (δ =+ 2 ). To calculate the CD, we use the normalized difference of the populations of the excited state Si after excitation with LCP or RCP laser pulses:8 CD[Si ] = 2

PLCP[Si ] − PRCP[Si ] PLCP[Si ] + PRCP[Si ]

(6)

1 8π 2

2π

π

∫0 ∫0 ∫0

neutral

cation

a b c d e f g α β γ δ ε ζ η ω

1.520 1.526 1.537 1.529 1.518 1.201 1.516 108.4 104.7 104.5 103.1 105.2 125.7 114.2 179.9

1.546 1.523 1.525 1.533 1.553 1.178 1.521 108.7 102.9 105.2 103.4 102.8 126.8 115.6 179.7

a

Labels are used according to Figure 2, except for the C2−C1−O−C5 dihedral angle ω. Bond lengths are given in Ångstroms, and angles are given in degrees.

The P in eq 6 is the rotational average of populations of different orientations of the molecule, according to24 P=

parameter

2π

P(ϕ , θ , χ )sin(θ )dϕdθ dχ

The differences in the bond lengths range from less than one to approximately three picometers. Very small changes are also found for the bond angles. Changes are here all in the order of one to two degrees. Most notable are the contraction of the CO bond as well as the elongation of the C5−C1 and the C1−C2 single bonds (bonds e and a in Figure 2) next to it, after the molecule has been ionized. Interestingly, the contraction of the CO bond is accompanied by a reduction of the CO stretching frequency from 1851 cm−1 in case of

(7)

More precisely, the populations are evaluated for 40 molecular orientations (ϕ,θ,χ), see ref 7 for more details, and are then averaged numerically according to eq 7. Note that, for circular polarized light the third rotation angle (χ) may be omitted (at the given excitation frequencies and pulse durations). Before each propagation the molecule is oriented such that the electric transition dipole vector μ⃗ 0i of the target state Si points along the 9169


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Figure 2. Labeling of the various geometry parameters. Numbers denote carbon atoms, Latin letters denote C−C and CO bonds, and Greek letters denote bond angles.

the neutral molecule to 1750 cm−1 for the cation. Surprisingly, the CO peak in the infrared (IR) spectrum of the cation (not shown) is almost not existent: The calculated IR intensity drops from 290 km/mol in case of the neutral 3MCP to merely 1.6 km/mol for the cation. These observations are an indication for the removal of negative charge at the oxygen upon ionization, which causes (a) a weakening of the CO bond and (b) a decrease of the dipole moment of the CO group. Indeed, the change of the Mulliken charges is most pronounced for the oxygen atom when comparing neutral and cationic 3MCP; the Mulliken charge increases from −0.79 to −0.45 e. Moreover, the carbonyl C1 becomes slightly more positively charged, also weakening the C−C bonds (e and a in Figure 2) next to it. Accordingly, the frequencies of the symmetric and asymmetric C5−C1−C2 stretching modes drop significantly after ionization: While they appear at ∼830 and 1200 cm−1 for the neutral molecule, they change to 650 and 730 cm−1 in case of the cation. As such, the C−C bonds e and a toward the carbonyl C atom are potential candidates for a bond breaking (after electronic excitation) as initial step of the fragmentation. The breaking of these bonds was also proposed by Logé and Boesl.12,25 We will return to this question in Section 3.2. The spin density, shown in Figure 1, confirms our observations where electron density is mainly missing: The highest spin density is found at the oxygen, namely, in form of its nonbonding orbital, followed by the C atoms 5 and 2 or rather their bonds to the carbonyl C1 atom. It is also worth mentioning that the rotational strength for the CO stretching mode changes its sign from +1.6 to −1.9 × 10−44 esu2 cm2 after ionization (vibrational rotatory strengths are usually given in units of Debye2). For the symmetric and asymmetric C5−C1−C2 stretching mode the sign remains the same for neutral and ionized (R)-3MCP, but the value increases significantly for the symmetric vibration from 35 to 71 × 10−44 esu2 cm2 and stays almost the same for the asymmetric counterpart (from ∼31 to 28 × 10−44 esu2 cm2). To what extent these changes in the VCD spectra influence vibronic ECD spectra (for the CD in MS) cannot easily be anticipated. Still, these differences prove that the cation may behave very differently toward circular polarized light than the neutral molecule. The vertical energy difference between the neutral and cationic (R)-3MCP at the ground-state minimum-energy geometry is 9.3 eV. This is consistent with the experimentally reported ionization potential (IP) of 9.3 eV.3 3.2. Differences in the Electronic Structures. The simulated UV−vis spectra of both species are shown in Figure 3. Tables 2 and 3 list the most important excitation energies, oscillator strengths, and dominant character of the transition of neutral and ionic 3MCP, respectively.

Figure 3. Simulated UV−vis spectra of (a) the neutral and (b) the cationic (R)-3-MCP based on vertical excitation energies from TD(U)CAM-B3LYP/aug-cc-pVTZ. Stick spectra are Gaussian broadened with Δν̃ = 500 cm−1. (inset) Enlargement of the S0→ S1 peak around 290 nm. Arrows mark the laser pulse frequencies of the experimental excitation sequence described in ref 12.

Table 2. Excitation Energies and Wavelengths, Oscillator Strengths (f), Rotatory Strengths (R), Anisotropy Factors (g), and the Dominant Character of the Electronic Transition for the Lowest Eight Singlet Excited States of the Neutral Molecule (R)-3MCP (TD-CAM-B3LYP/aug-ccpVTZ) state

ΔE [eV]

λ [nm]

f

R [1 × 10−40 cgs]

g [a0 Eh/ ℏ]

main character

S1 S2

4.32 6.33

287 196

0.0001 0.0211

9.29 −9.31

65.7 −0.581

S3

6.84

181

0.0008

0.522

0.923

S4

7.02

177

0.0012

0.215

0.254

S5

7.05

176

0.0131

3.06

0.342

S6

7.60

163

0.0160

9.42

0.930

S7

7.69

161

0.0104

0.257

0.0393

S8

7.73

160

0.0250

3.48

0.223

n → π* n → Ryd (s) n → Ryd (s, px) n → Ryd (s, py) n → Ryd (s, py, pz) n → Ryd (s, px, pz) n → Ryd (s, py, px) n → Ryd (s, px, pz)

For the cation the spin multiplicity of the lower electronic excited states is very close to the expected ⟨S2̂ ⟩-value of 0.75 or within the typical range of variation for the applied method. Larger deviations are found from 6.58 eV and above (188 nm and below), where the spin contamination cannot be ignored any more, such that most states are not considered to be pure doublets although they appear in the simulated UV−vis spectrum in Figure 3. The excitation energies of the neutral (R)-3MCP agree well with those published by Rizzo et al.15 but show some small differences to our own calculations based on CIS(D)/6-311+ +G(2d,2p).7 The agreement of the simulated UV−vis spectrum in Figure 3a with the experimental absorption spectra is also reasonable,3,26 as realized before,7,15 although the vibrational fine structure cannot be reproduced by our approach. The quality of high electronic excited states is not fully reliable, but they are not our major concern in this investigation. Note that the dominant character for the transitions to the Rydberg states 9170


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Table 3. Excitation Energies and Wavelengths, Oscillator Strengths ( f), Rotatory Strengths (R), Anisotropy Factors (g), and the Dominant Character of the Electronic Transition for the Lowest Eight Doublet Excited States of the Cationic Molecule (R)3MCP (TD-UCAM-B3LYP/aug-cc-pVTZ) state

ΔE [eV]

λ [nm]

f

R [1 × 10−40 cgs]

g [a0 Eh/ℏ]

main character

D1 D2 D3 D4 D5 D6 D7 D8

2.67 2.81 3.03 3.22 3.93 4.19 4.85 5.11

464 441 409 385 316 296 255 243

0.0014 0.0130 0.0058 0.0284 0.0123 0.0138 0.0627 0.0032

−7.95 14.8 4.56 −12.4 −0.0878 15.9 6.63 −13.9

−3.15 0.665 0.494 −0.293 −0.00583 1.00 0.107 −4.66

σ(C−H) → n σ′(C−H) → n σ(C−C) → n σ(C−C,C-H) → n σ′(C−C,C-H) → n σ″(C−H,C-C) → n σ(CO) → n σ′(C−C) → n

due to a crossing with D1) with clearly extended bond lengths for the C−C bonds a and c as well a slightly shortened C−C bond b. Therefore, we broke the extended bonds a and c and transferred one hydrogen from C5 to C2, forming the fragments C4H5O (m/z = 69) and C2H5 (m/z = 29) before restarting the optimization. Although again convergence was not reached after the energetic order of D1 and D2 switched during the optimization, the two fragments drifted apart with decreasing the energy, where the highest spin density was located at the C3 atom of the C2H5 fragment. Note that the same starting geometry causes the fragments to recombine if the doublet ground state D0 is optimized. Although these calculations are incomplete, they give evidence that the breaking of specific bonds in the cation after electronic excitation to D2 are energetically favorable. Hence, due to the 440 nm pulse the peak of the parent ion should decrease, and more fragment ions should be detected in the mass spectrum than in case of the 198 nm excitation only, which agrees with experimental observations.12 Note that the 10 ns delay between both excitations is more than sufficient for the cation to relax, as the geometrical changes are rather small. It is even imaginable that significantly shorter pulses with no delay will produce very similar effects. Finally, an excitation with 440 nm only should not result in any significant ionization at all, as no state is available at 440 nm (∼2.8 eV, one photon), at 5.6 eV (two photons), or at 8.4 eV (three photons) in our neutral model. In the experiment no mass spectrum is detected for 440 nm.12 3.3. Change in the Electronic Circular Dichroism. To see if the CD in the yields of the fragment ions may be changedin particular in terms of their signby an excitation of the parent cation, we first take a look at the ECD spectra of both species, see Figure 4. The simulated ECD spectrum of the neutral (R)-3MCP agrees well with the one simulated by others using the same level of theory.15 Again small differences are found in comparison to our previous results employing CIS(D)/6-311++G(2d,2p). Considering the quality of the applied methodology the experimental absorption spectrum is, for the most part (except for the missing vibrational finestructure), reproduced for the low-lying electronic states; see ref 7 for more details. The ECD spectrum of the cation shows peaks of positive and negative signs in the range of 200 to 475 nm allowing, in principle, for an enhancement or a reversal of an initial enantiospecific difference in the yields of the ionized molecules upon electronic excitation and subsequent fragmentation of the parent ion. Let us first consider resonant one-photon excitations. Here a comparison of the rotatory strengths or the peaks in the (one-

was often difficult to identify, as mixing of s- and p-type orbitals occurs. Most interesting is the direct comparison between the spectra of the (R)-3MCP molecule and its cation, see Figure 3a,b. Most remarkable is the presence of 10 partly very intense peaks above 200 nm for the cation, while for the neutral molecule only a single very weak peak at ∼290 nm is found. Above 300 nm there is no one-photon resonance in the neutral molecule possible. Although some of these electronic states of the cation offer potential electronic transition (e.g., at 255 nm) after ionization of the neutral molecule, there are, except for the peak at 290 nm, no resonant (one-photon) excitations with laser wavelengths above 200 nm available for the neutral molecule. Despite that we calculated only the (one-photon) absorption spectra, we can still discuss potential excitation pathways, if we assume that the cation is further electronically excited after it has been formed. In particular, the S0 → S2 transition of neutral 3MCP with two photons of ∼400 nm corresponds to a region in the cationic spectrum of several intense peaks. Whereas the two-photon n → π* excitation (S0 → S1) of the neutral species with ∼600 nm offers no electronic one-photon transition in the cation. However, a one-photon n → π*-excitation of the neutral molecule with ∼300 nm allows for a one-photon excitation to D6 in the cation, see Table 3. We will return to these findings later in more detail. Now, we can inspect the observations and interpretations of Logé’s and Boesl’s experiment,12 if we assume that an electronic excitation of the cation boosts the formation of fragments. In particular, an excitation with 198 nm results in our model in an S0 → S2 transition at first. Then, a second photon (2 × 6.3 eV = 12.3 eV) could ionize the molecule (IP = 9.3 eV3). However, the (relaxed) cation could not be further electronically excited, as around 198 nm we do not find any electronic state, see arrows in Figure 3. As a result the parent ion (m/z = 98) should dominate the mass spectrum and few fragment ions, formed from the cation in its electronic ground state D0, should be detected, which is consistent with experimental observations.12 If the first 198 nm laser pulse is followed by a second pulse of 440 nm (delayed by 10 ns) though, the cation would be electronically excited, namely, from D0 to D2 in our model, see Table 3. The electronically excited cation could enforce the breaking of certain bonds, leading to a fragmentation of the cation. Unfortunately an optimization of the geometry of the D2 state did not succeed. The diffuse basis functions, in particular, caused problems for the convergence of the electronic excited wave function. Starting, however, from the minimum-energy geometry of D0 an optimization with TDUCAM-B3LYP/cc-pVTZ got caught in an oscillation (possibly 9171


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Boesl et al. find the opposite effect, namely, that the fragment ion with 69 amu exhibits a lower CD than the parent ion (17% vs 27%29), however, employing nanosecond laser pulses.2 While in our model the spectral width of a nanosecond pulse should not be sufficient to induce the D0→ D6 transition in the cation, this still offers no explanation why the CD value of the C4H5O+ ion is smaller than the one for the parent ion. Moreover, we only succeeded to optimize the D6 state at TDCAM-B3LYP/cc-pVTZ level of theory, but found an elongation of the C4−C5-bond, which is d in Figure 2. Although this does not allow for a reliable prediction of which fragments might be formed, the breaking of the C4−C5 bond may lead to a rearrangement where the oxygen connects to the C4 atom to form a tetrahydrofuran ring.30 The resulting (R)-2-methylene5-methyltetrahydrofuran cation certainly has a different electronic structure than the (R)-3MCP cation.30 Moreover, experimentally there are effects we cannot easily describe by our present model that play, however, an important role, for instance, the gradual change of the electronic structure of the vibrationally excited parent ion due to a beginning dissociation. Another possibility is an additional electronic excitation from D6 to D25, a state 4.14 eV (299 nm) higher in energy and still with an acceptable spin contamination (⟨S2̂ ⟩ = 0.886). The one-photon n → Ryd(s) excitation with 196 nm, see Table 2, is known to be inefficient for chiral distinction, as the CD in MS is very small (−0.3%).11 The negative sign and the relative size of the CD, that is, ∼2 orders of magnitude smaller than for n → π* (+27%29), are consistent with the g-values found in Table 2. Moreover, we do not find any electronic state at these excitation wavelengths for the cation. There are actually states around 188 nm, which could be within the spectral range of a femtosecond laser pulse. They are however not reliable, because they are strongly spin-contaminated in our calculations. The same is true for lower wavelengths, corresponding to onephoton transitions in the neutral molecule to Rydberg states with p-character, such that they will not, except for specific cases discussed below, be further considered here. This leaves us with the two-photon transitions that we simulated by electron wavepacket dynamics. The results are given in Table 4 together with one-photon results for comparison. The one-photon CD[Si] values agree qualitatively with their corresponding g-values. Note that the CD[Si] also depend on the laser field strength and decrease with increasing , 0 or increasing population in the target state.8 For that reason, the rotationally averaged populations, more precisely, the mean of PLCP and PRCP, detected in the target state are also given in Table 4. They also help to estimate the efficiency of the transition, which should also have an impact on the ion yield in MS.

Figure 4. Simulated ECD spectra of the (a) neutral and (b) cationic (R)-3-MCP (TD-(U)CAM-B3LYP/aug-cc-pVTZ). Stick spectra are broadened by Gaussian functions with Δν̃ = 500 cm−1.

photon) ECD spectra of both species give a first insight into possible enantiospecific excitation pathways. In MS it is the CD in ion yields that is detected though. Therefore, the anisotropy factor g, which is the ratio of the CD to the absorption, more Δε precisely g = ε , is probably a more suitable quantity to compare with the CD in MS, at least for long pulses and moderate field intensities. The anisotropy factor may be R calculated from quantum chemical data according to g = 4 Di , i

where Di (=|μ⃗0i|2) is the electric dipole strength of state i.27 Note that this approximation is, strictly speaking, only valid if the shapes of the CD and absorption signals are the same and the permittivity is one. Calculated values of g are given in Tables 2 and 3. The n → π* excitation of 3MCP at 290 nm (4.3 eV) is known to be highly enantiospecific, which is supported by a very high positive g-value, see Table 2. Two additional photons of this kind should ionize the molecule (3× 4.3 eV ≈ 13 eV ≫ 9.3 eV). If the created parent ion is further excited (assuming that the excess energy is stored in the kinetic energy of the ejected electron), a transition to D6 (300 nm) is possible. As the D0→ D6 transition comes with a positive CD value, the CD value of the fragments created from the electronically excited parent ion could be even higher than the one of the parent ion. This was, indeed, found experimentally for the C4H5O+ ion (m/z = 69) by the Weitzel group for femtosecond pulses.6,28 In our calculations S1 and D6 differ by 9 nm in excitation wavelength. Hence, the spectral bandwidth of roughly 4 nm (fwhm) of the applied femtosecond pulses could be just enough to induce both transitions,6 especially since vibrational progression might further broaden the peaks. Interestingly,

Table 4. CD[Si] Values and Averaged Populations P[Si] in Percent for Different Target States Si after the One- or Two-Photon Laser Pulse Excitation of (R)-3MCPa CD[Si] (P[Si]) Si S1 S2 S3 S4 S5 a

ωi 50 −0.22 0.76 0.32 0.22

(0.39) (70) (3.9) (5.6) (48)

TPCD, ref 11 ωi/2

3.0 (1.0 × 10−4) 0.36 (8.6 × 10−3) 0.37 (3.5 × 10−2) 0.27 (9.2 × 10−2)c −0.47 (0.11)d

m/z = 98 1.3 ± 0.5 −0.6 ± 0.1 −0.8 ± 0.1

m/z = 69 −0.8 1.2 −2.1 5.0 5.4

± ± ± ± ±

0.8b 0.2 0.2 0.1 0.1

All parameters are given in Section 2. bThis value is based on fragment m/z = 56. cCD value (population) determined at S5: −0.42 (6.0 × 10−3). CD value (population) determined at S4: 0.30 (1.1 × 10−2). Two-photon CD of parent and fragment ions are given for comparison, see ref 11.

d

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The Journal of Physical Chemistry A The two-photon n → π* transition with 574 nm is not of particular interest, since there is no electronic state of the cation that could be excited by this wavelength. Moreover, in experiments no significant CD was found for 3MCP for the resonant two-photon n → π* enhanced ionization,6,29 which was also confirmed by theory.8,15 In contrast to ref 8 we now mainly rely on DFT than CIS data and include electric quadrupole contributions in the dynamics, such that the CD[S1] reaches significant 3%, see Table 4. However, the average population of 1 × 10−4% in S1 is not only the smallest value of all investigated cases but also possibly too small to result in a significant number of detectable ions. Taking a look at the one-photon CD[S1] value of 50% though, which is approximately twice the value found for the ion yield in MS (+27%29), we realize that a perfect one-to-one comparison between CD[Si] and the CD in ion yield is not possible, as we do not describe the ionization in our model. Nevertheless, the results of the electron dynamics give valuable insight into the initial excitation of the sample, which certainly has a significant impact on the CD detected in the ion yield, as successfully shown before.7 The CD[S2] of the two-photon n→ Ryd(s)-transition (S0 → S2 at 392 nm) shows an opposite sign to its one-photon counterpart. This agrees with experimental observations when comparing ECD (−0.3%) to TPCD (two-photon CD) of the parent ion (1.3 ± 0.5%).11 Even the fact that the magnitude of the CD[S2] value is higher for the two- than for the one-photon excitation is reproduced, although there are quantitative differences in particular to the relatively high TPCD value in MS. Interestingly, there are two states of the cation, namely, D3 and D4, in the same wavelength region; both of them, however, are too far off-resonant for the spectral width of a nanosecond pulse. Then again, the peaks are broadened in experiment, and the two doublet states differ in their ECD sign. As such, the simulated ECD spectrum in Figure 4b shows a region around 400 nm where the peaks of opposite sign partly compensate each other. Although 392 nm is still rather located in the negative arm of D4 peak, a large change of the CD of the fragments created from the electronically excited cation is not expected. Such a scenario is, in principle, also possible in experiment, giving a possible explanation why the TPCD in MS between parent ion and the fragment ion hardly changes.11 Moreover, Li et al. found no indication that the photodissociation after the two-photon n → 3s REMPI with circularly polarized nanosecond pulses is enantiospecific:3 The recorded photoelectron signal intensities showed basically the same CD as the signal intensities of the 39-fragment ion (C3H+3 ). Note that Rizzo et al. found a negative two-photon rotatory strength for the S2 state based on the same density functional and basis set but employing a different formalism based on frequency-dependent analytic response theory.15,31 At this state we cannot tell with certainty what is the reason for the difference. While Rizzo et al. employed Tinoco’s translationally invariant formalism based on the velocity forms of the electric dipole and quadrupole operators to calculate the TPCD rotational strengths, we relied on the length form of the operators, which makes the result origin-dependent. The origin dependence of the two-photon CD was, however, found to be rather weak32 and should anyway be small for the employed large basis set and the relatively small molecule.33 But it is remarkable that the number of potentially transient states, which allow for the polarization of the electronic structure,

differs: While we allow transitions between every state of our 50-level system, only six electronic excited states were considered by Rizzo et al. Indeed we obtain a negative twophoton CD[S2] of −0.31% in a two-level system of S0 and S2 instead of the positive value given in Table 4 for our 50-state model. This is evidence for the influence of transient interactions with the manifold of electronic excited states, that is, an aspect of the dynamic polarization, on the population difference in the target state. We note, however, that the transition moments between excited electronic states were obtained from CIS calculations in our simulations, see Section 2. The three following n → Ryd(p)-transitions (S3 to S5) have positive CD[Si] values for one-photon excitations in agreement with experiment. However, the corresponding two-photon values vary in their signs, see Table 4. Interestingly, Lóge and Boesl found a sign change in the two-photon CD between parent and the 69-fragment ion for this type of transitions where, except for missing data for S3 (forbidden, see oscillator strength in Table 2), the parent ions exhibit a negative sign.11 While we find the same sign for CD[S5], this is in contrast to our results for S4. The excitation energies of S4 and S5 are, however, so close that the spectral width of our 250 fs pulse of ∼24 meV (3.295ℏ/fwhmI) is sufficient to excite both states, an effect less likely for the nanosecond pulses used in experiment. Although the CD[S5] value is negative and almost twice the size as the CD[S4] value, the population found in S5, when employing light with ω4/2, is ∼1 order of magnitude smaller than the one in S4. Therefore, we do not expect that the CD of the excited parent ion would be significantly influenced by the competing S0 → S5 transition, as long as the ionization is similarly efficient starting from either state. On these grounds, the reason for the discrepancy between theory and experiment concerning the sign of the two-photon CD for S4 remains unclear. Note, however, that the oscillator strength of S5 is 1 order of magnitude larger than the one of S4, making the S0 → S5 transition much more efficient. Analogous observations are made for S5 as target state, where this time the competing S0 → S4 transition “steals” some population, but has probably no effect on the CD, in particular not for nanosecond pulses. For S0 → S5 we find, indeed, a negative two-photon CD value in agreement with the experiment.11 For the two-photon transition (362 nm) to the S3 state the sign of the 69-fragment ion is negative in MS.11 As we find a positive CD[S3] at this wavelength, the sign could only be changed by electronic excitation of the cation. Although no state is found at exactly this energy, the closest in energy is D4, which has indeed a negative rotatory strength. D4 is, however, more than 20 nm off the excitation wavelength in our calculations. Most noticeable in the mass spectra is that the TPCD of the 69-fragment ion has a positive sign for S4 and S5 and is significantly larger in magnitude than the TPCD of the parent ion.11 In our model, however, we cannot find suitable states of the cation at the corresponding wavelengths (354 or 352 nm). There are states of the cation that may be excited by a twophoton excitation, for example, D19 at 7.21 eV (172 nm) with a highly negative (one-photon) rotatory strength of −28.1 × 10−40 cgs, but they are spin-contaminated (⟨S2̂ ⟩ = 1.051). Thus, our simulations cannot give a definite explanation for these experimental findings. Probably other mechanisms play a role, for example, a highly vibrationally excited parent ion dissociates 9173


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The Journal of Physical Chemistry A first creating a different cationic structure than investigated here, which is subsequently electronically excited. In general, vertical excitations at the minimum-energy structure of the cation is not the best approach for every case, because it is missing the effect of the nuclear motion. In case of very short pulse durations, one would expect an excitation of the cation almost at the minimum-energy geometry of the neutral molecule, as there is little time for relaxation. A calculation at the S0 minimum geometry showed that basically the cation excitation energies for the states of interest are ∼0.1 to 0.3 eV lower in energy compared to the fully relaxed cation; that is, no large differences between femtosecond and nanosecond pulse ionization are expected at the first glance. For long pulse durations though, we cannot tell how the vibrational energy of the excited cation is redistributed among the modes, resulting in different excitation energies and weakened bonds. Therefore, the potential energy hypersurface of the electronic states of the cation or at least cuts along the most prominent dissociation coordinates could help to unravel more possible excitations pathways, which is a challenging task for future investigations.

change of the CD value. Still, we found indications that actually two-photon transitions in the cation might be the origin of the different CD signs in parent and fragment ions. Another reason is that the vibrational states, which were not included in our model, may also influence the observed CD. Our simulations showed that ionization can have a significant impact on the CD of, for instance, the carbonyl stretching mode. In particular for partly overlapping electronic bands the vibrational fine structure could play an important role. However, an optimization of every excited state of the cation would be required to include this effect. An energy-resolved experimental determination of the CD in the ejected photoelectrons during REMPI could provide further insight into the enantiospecific excitation pathways and the impact of the molecular vibrations. Last but not least, to fully clarify all experimental observations, presumably every possible excitation pathway had to be simulated separately. The calculation of the full potential energy surface is, however, not only very challenging, even if only the most promising reaction pathways were selected, but also far beyond this study. Our simulations actually show that, while some electronic excitation and ionization mechanisms seem to be well-described by our model, others are probably more complex than expected. Nevertheless, our simulations gave a valuable overview over possible enantiospecific excitation pathways, confirming many of the proposed mechanisms based on experimental observations. Future investigations must focus on some selected cases to gain a more detailed picture of the excitation and ionization processes.

4. CONCLUSIONS In MS differences in the CD values for the ion yields are detected between parent and fragment ions including the change of the sign in case of two-photon excitations. If the fragments were immediately formed from the relaxed parent ion, no such differences should be found, as the ionization step is not supposed to be enantiospecific. Therefore, after the REMPI, subsequent enantiospecific excitations of the just created parent ion are believed to alter the CD of the fragment ions formed afterward. In this report we compared the electronic structure of neutral and cationic (R)-3-MCP obtained from DFT, to learn about possible excitation pathways. Although we were not able to reproduce all experimental findings, our simulations support some of the assumptions that were made based on experimental observations. Among them we found evidence for the preferred dissociation of certain bonds after electronic excitation of the cation, a precondition for the (experimentally observed) enhanced formation of specific fragments. Furthermore, our calculations show that the subsequent excitation of the parent ion may be enantiospecific, also for wavelengths used to excite and ionize the neutral sample. Therefore, the CD observed for the fragments created from the electronically excited parent ion could, indeed, differ from the CD of the neutral molecule. However, none of the experimental cases where this effect is accompanied by a sign change of the CD could be confirmed by our simulations. This may have different reasons. For one, in all these cases two-photon excitations were induced in the neutral molecule. We used electron wavepacket dynamics based on the results of the first-principles calculations to determine a two-photon CD value from the population of the excited state. A comparison to one-photon CD values determined by the same method proved once more that the two-photon CD may be different in sign and size. This difference seems to depend particularly on interim interactions with other electronic states, that is, a two-level approach is not sufficient to describe the effect. This makes high demands on the quality of the electronic eigenfunctions also for highly excited electronic states. Because of the very small magnitude of the CD values found in theory (and experiment) small deviations in the electronic structure could result in a sign

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APPENDIX

Axial Conformer

Molecular Structures. The geometries of the neutral and cationic axial (ax) conformer of (R)-3MCP were optimized employing (U)CAM-B3LYP/aug-cc-pVTZ. Frequency analyses of the both minimum-energy geometries confirmed that minima were found. Selected geometrical parameters of the neutral and cationic (R)-3-(ax)-3MCP are compared in Table 5; the optimized geometries differ little. The most significant differences observed are the same as in the case of the equatorial (eq) conformer: The CO bond length (bond f) is shorter after ionization. In addition, a reduction of the CO stretching frequency (IR intensity) from 1849 cm−1 (280 km/ mol) in case of the neutral species to 1745 cm−1 (0.49 km/ mol) for the cation is found. At the oxygen atom, where the highest spin density of the cation is observed, the Mulliken charge increases from −0.81 to −0.47 e upon ionization. The bond lengths of the C−C bonds a and e next to the carbonyl group are increased. The interpretation of the observations are the same as in case of the (eq)-conformer, see Section 3.1. Electronic Structures. Electronic excited states for the neutral and cationic (ax)-conformer were analyzed using TD(U)CAM-B3LYP/aug-cc-pVTZ. The results are summarized in Tables 6 and 7. The corresponding UV−vis spectra were simulated as described in Section 2; they are shown in Figure 5. For the neutral species the vertical excitation energies of (ax)- and (eq)-conformer differ only by ∼1 nm. Therefore, their UV−vis spectra are very similar, compare Figurse 3a and 5a. Only a few peaks differ in intensity due to differences in the oscillator strengths between the two conformers. The excitation 9174


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The Journal of Physical Chemistry A Table 5. Comparison of Selected Bond Lengths and Angles between the Minimum-Energy Geometries of the Neutral and Cationic Axial Conformer of (R)-3MCP ((U)CAMB3LYP/aug-cc-pVTZ)a parameter

neutral

cation

a b c d e f g α β γ δ ε ζ η ω

1.520 1.528 1.542 1.531 1.519 1.201 1.524 108.6 104.9 105.0 103.0 105.4 125.7 112.1 179.9

1.546 1.528 1.529 1.534 1.552 1.178 1.521 109.1 102.9 105.6 103.2 102.6 126.3 114.0 180.0

Figure 5. Simulated UV−vis spectra of (a) the neutral and (b) the cationic (R)-3-(ax)-MCP based on vertical excitations energies from TD-(U)CAM-B3LYP/aug-cc-pVTZ. Stick spectra are Gaussianbroadened with Δν̃ = 500 cm−1. (inset) Enlargement of the S0 → S1 peak around 290 nm. Arrows mark the laser pulse frequencies of the experimental excitation sequence described in ref 12.

a Labels are used according to Figure 2, except for the C2−C1−O−C5 dihedral angle ω. Bond lengths are given in Ångstroms, and angles are given in degrees.

For the cationic species the differences between the two conformers are more pronounced. The D3 state, for instance, is ∼0.2 eV lower in energy for the (ax)- than for the (eq)conformer, whereas D6 is more than 0.3 eV higher. In addition, the oscillator strengths of many doublet states differ between the (ax)- and the (eq)-conformer. Still, the characteristics of the two spectra, see Figures 3b and 5b, are similar. No electronic state is found around 198 nm, but two doublet states, namely, D2 and D3, are close to 440 nm. Therefore, our interpretations of the results with respect to the experiment in ref 11 remain the same as for the (eq)-conformer, see Section 3.2. Electronic Circular Dichroism. The electronic CD spectra of the neutral and cationic (ax)-conformer of (R)-3MCP were simulated as described in Section 2, that is, using the rotatory strengths obtained from TD-(U)CAM-B3LYP/aug-cc-pVTZ calculations, see Tables 6 and 7. The spectra are compared in Figure 6. The ECD spectrum of the neutral (ax)-conformer agrees with the one simulated by others.15 The lowest seven electronic excited states have a negative rotatory strength in contrast to the (eq)-conformer where only R2 is negative, compare Tables 6 and 2. In comparison to a sample of the pure (eq)-conformer the CD of a mixture of (eq)- and (ax)-conformers should, hence, be decreased if one of the first seven electronic excited states is excited. In the experiment a ratio of ∼89:11 (eq/ax) is assumed at room temperature, such that most of the peaks of the Boltzmann-averaged ECD spectrum are only slightly

Table 6. Excitation Energies and Wavelengths, Oscillator Strengths ( f), Rotatory Strengths (R), Anisotropy Factors (g), and the Dominant Character of the Electronic Transition for the Lowest Eight Singlet Excited States of the Neutral (ax)-Conformer of (R)-3MCP (TD-CAM-B3LYP/ aug-cc-pVTZ) state

ΔE [eV]

λ [nm]

f

R [1 × 10−40 cgs]

g [a0 Eh/ℏ]

S1 S2 S3

4.31 6.32 6.88

288 196 180

0.0001 0.0182 0.0047

−8.39 −0.721 −2.90

−71.2 −0.0520 −0.878

S4

7.05

176

0.0045

−0.400

−0.129

S5

7.07

175

0.0067

−1.69

−0.370

S6

7.62

163

0.0104

−2.38

−0.361

S7

7.67

162

0.0085

−3.85

−0.727

S8

7.71

161

0.0055

4.09

1.19

main character n → π* n → Ryd (s) n → Ryd (s, py) n → Ryd (s, px, py) n → Ryd (s, px) n → Ryd (s, px, pz) n → Ryd (s, py, pz) n → Ryd (s, px, pz)

energies of the (ax)-conformer agree well with those found by Rizzo et al. at the same level of theory.15

Table 7. Excitation Energies and Wavelengths, Oscillator Strengths ( f), Rotatory Strengths (R), Anisotropy Factors (g), and the Dominant Character of the Electronic Transition for the Lowest Eight Doublet Excited States of the Cationic (ax)-Conformer of (R)-3MCP (TD-UCAM-B3LYP/aug-cc-pVTZ) state

ΔE [eV]

λ [nm]

f

R [1 × 10−40 cgs]

g [a0 Eh/ℏ]

main character

D1 D2 D3 D4 D5 D6 D7 D8

2.68 2.79 2.84 3.23 3.93 4.52 4.69 4.98

463 445 436 384 315 274 264 249

0.0055 0.0008 0.0076 0.0119 0.0072 0.0041 0.0408 0.0137

−1.38 2.27 −5.87 5.97 −5.56 −2.75 1.00 −20.9

−0.140 1.74 −0.459 0.337 −0.629 −0.625 0.0239 −1.57

σ(C−H) → n σ′(C−H) → n σ(C−C) → n σ(C−C,C-H) → n σ′(C−H,C-C) → n σ″(C−C,C-H) → n σ(CO,C−C) → n σ′(C−C,CO) → n

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Table 8. CD[Si] Values and Averaged Populations P[Si] in Percent for Different Target States Si after the One- or TwoPhoton Laser Pulse Excitation of the (ax)-Conformer of (R)3MCPa CD[Si] (P[Si]) Si

ωi

S1 S2 S3 S4 S5

−53 (0.77) −2.3 × 10−2 (64) −0.61 (21) −5.4 × 10−2 (20)b −0.20 (28)

ωi/2 −3.1 −0.86 0.56 −0.71 −0.37

(4.6 (6.4 (2.7 (4.8 (2.8

× × × × ×

10−4) 10−3) 10−2) 10−2)c 10−2)d

a All parameters are given in Section 2. bRotational averaging based on 144 orientations. cCD value (population) determined at S5: −0.42 (1.5 × 10−3). dCD value (population) determined at S4: −0.65 (6.0 × 10−3).

Figure 6. Simulated ECD spectra of the (a) neutral and (b) cationic (R)-3-(ax)-MCP (TD-(U)CAM-B3LYP/aug-cc-pVTZ). Stick spectra are broadened by Gaussian functions with Δν̃ = 500 cm−1.

For the two-photon n → Ryd(s) excitation with 392 nm we find again different signs of the CD[S2] for the two conformers. Although the absolute value of the CD[S2] of the (ax)conformer (−0.86%) is more than 2 times higher than the one of the (eq)-conformer (0.36%), the CD value of the mixture differs with 0.26% little from the value of the pure (eq)conformer. The excitation wavelength for the D0 → D4 transition is with 384 nm close enough to 392 nm to be excited by a femtosecond pulse. The rotatory strength for this transition is positive, which is consistent with experimental observations. Therefore, in a realistic mixture of conformers the (ax)-conformer does not qualitatively change the results found for the pure (eq)-conformer, see Section 3.3. The influence of the (ax)-conformer remains small also for the two-photon transitions to the states S3, S4, and S5. The corresponding excitation wavelengths are all off-resonant to any state in the (ax)-cation, see gap in the ECD spectrum in Figure 6b around 350 nm, such that the influence of the (ax)conformer is negligible for these scenarios, too. Moreover, we recall that the excitation frequencies in experiment are dominated by those of the (eq)-conformer. Therefore, the excited-state populations of the (ax)-conformer will be smaller than those given in Table 8; that is, the CD will be even less influenced (not shown).

decreased with respect to the spectrum of the pure (eq)conformer.15 An exception is the rotatory strength of S7, which should change its sign when allowing for 11% of (ax)conformers. As we are mainly interested in resonant electronic transitions in the cation right after the ionization of the neutral molecule, we look for possible excitation pathways. First we consider resonant one-photon excitations in the pure (ax)-conformer. For the n → π* excitation at 288 nm we cannot find any suitable electronic transition in the cation, as states D5 and D6 differ too much in their excitation wavelength (315 and 274 nm) even for the femtosecond pulses applied in experiment.6 Therefore, the presence of the (ax)-conformer should not change the considerations made for the (eq)-conformer, see Section 3.3. The same is true for the one-photon n → Ryd(s) excitation with 196 nm where we do not expect any significant effect of the (ax)-conformer as the anisotropy factor for this transition (S0 → S2) is almost zero for (R)-3-(ax)-MCP, and no suitable doublet electronic excited state is found at 196 nm for the cation. Like for the (eq)-conformer, laser pulse-induced one- and two-photon transitions in the neutral (ax)-conformer of (R)3MCP were simulated by wavepacket dynamics, as described in Section 2. The (ax)-conformer is initially oriented such that the electric and magnetic transition dipole vectors of the target state Si lie in the x−y plane for an optimal interaction with the laser pulse. Thus, the initial orientations may differ from those of the (eq)-conformer. The resulting CD[Si] values are listed in Table 8. Note that we set the laser pulse frequencies ωi to the excitation energies (ΔEi/ℏ) of the (ax)-conformer, which differ slightly from those of the (eq)-conformer; that is, the pure (ax)-conformer is considered to estimate its maximal possible influence. For the (ax)-conformer the two-photon n → π* excitation with 576 nm results in a negative CD[S1] (−3.1%) in contrast to the (eq)-conformer (3.0%), see Table 4. Moreover, the averaged population in S1 is more than 4 times higher for the (ax)- than for the (eq)-conformer. Therefore, we scale the populations PLCP and PRCP of the (eq)- and (ax)-conformers by 89% (eq) or 11% (ax) and calculate from the weighted average the CD[S1] of the mixture. The CD[S1] of the mixture remains positive but decreases to 0.80%. Still, the presence of the (ax)conformer does not change the interpretation of the result, see Section 3.3.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Fruitful discussions with U. Boesl (Munich) and K.-M. Weitzel (Marburg) are gratefully acknowledged. D.K. thanks the German Research Foundation for funding (Project No. Kr 2942/2).

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REFERENCES

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multiplied by 1/2 to obtain the employed m⃗ ij in atomic units (eℏ/me). Electric transition quadrupole moments Q̲ between ground and 0i

electronic excited state i, obtained from the transition density, must be divided by √2. (22) Wiberg, K. B.; Hadad, C. M.; LePage, T. J.; Breneman, C. M.; Frisch, M. J. An Analysis of the Effect of Electron Correlation on Charge Density Distributions. J. Phys. Chem. 1992, 96, 671−679. 9177


Circular Dichroism in Mass Spectrometry: Quantum Chemical

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