CHIRALITY 27:253–261 (2015)

Atomistic Modeling of IR Action Spectra Under Circularly Polarized Electromagnetic Fields: Toward Action VCD Spectra FLORENT CALVO* Laboratoire Interdisciplinaire de Physique, Université Joseph Fourier, Grenoble, France

ABSTRACT The nonlinear response and dissociation propensity of an isolated chiral molecule, camphor, to a circularly polarized infrared laser pulse was simulated by molecular dynamics as a function of the excitation wavelength. The results indicate similarities with linear absorption spectra, but also differences that are ascribable to dynamical anharmonic effects. Comparing the responses between left- and right-circularly polarized pulses in terms of dissociation probabilities, or equivalently between R- and S-camphor to a similarly polarized pulse, we find significant differences for the fingerprint C = O amide mode, with a sensitivity that could be sufficient to possibly enable vibrational circular dichroism as an action technique for probing molecular chirality and absolute conformations in the gas phase. Chirality 27:253-261, 2015. © 2015 Wiley Periodicals, Inc. KEY WORDS: vibrational circular dichroism; gas-phase spectroscopy; molecular dynamics; statistical rate theory; computational modeling; camphor Since it was first observed,1 vibrational circular dichroism (VCD) has seen major progress owing to joint advances in instrumentation and quantum chemistry, making it a useful approach to characterize chiral properties of molecules in condensed phases, including enantiomeric excess, recognition, and enantioselectivity.2–6 Molecules produced in the gas phase, typically using electrospray ionization sources, are also of fundamental interest as they represent basic building blocks of larger compounds and allow the specific contributions of the solute and solvent to binding, structure, and dynamics to be identified separately.7,8 Of increasing attention in this respect is the issue of hydration at the nanoscale, or how molecules in biological media develop their properties and functions upon discrete solvation one water molecule at a time, as in the progressive stabilization of the zwitterionic form of amino acids.9–11 Chiral properties in isolated molecules have also received increased attention in recent years, especially in the context of chiral recognition.12 Characterization techniques for isolated molecules rely heavily on mass spectrometry,13,14 which allows accurate size and charge selection, and their coupling with other devices such as drift tubes15 or ion traps in order to access their structure or kinetics upon dedicated excitation by collision, electron capture, or laser excitation. Those approaches have been used to study enantioselective interactions between chiral compounds, especially through their stability based on kinetic measurements.16,17 Chiral recognition in the gas phase has also been addressed using spectroscopies in various frequency domains.17–21 Such experiments generally proceed by measuring a depletion signal, i.e., a fragmentation propensity as a function of the excitation wavelength, the structure being again assigned after successful comparison with calculated spectra. In the case of vibrational spectroscopy, progress in light sources has prompted major advances in this field, for instance, based on the double resonance IR/UV22 or IR multiphoton dissociation (IR-MPD)23,24 techniques, with applications to systems as diverse as inorganic clusters,25 astrochemical,26 or hydrogenbonded compounds26 as well as biomolecules.17,20,27,28 With © 2015 Wiley Periodicals, Inc.

those approaches, the assignment to candidate structures relies on calculated linear absorption spectra, most often at the harmonic level, but, sometimes, taking anharmonicities arising from finite temperatures or nuclear delocalization into account through perturbation theory29,30 or classical31–33 or quantum34–37 molecular dynamics, possibly even with an explicit description of electronic structure when affordable,33 or alternatively (for the smallest systems) by solving directly the nuclear Schrödinger equation through a diverse arsenal of methods.38–41 This assignment between a dissociation probability and an absorption intensity is thus understood within linear response theory, where the exciting light is directly transferred and converted into internal energy and subsequently into the dissociating mode, giving a depletion ratio in direct correspondence with the absorption intensity. Anharmonicities are thus essential in gas phase spectroscopy, as they are responsible for the energy redistribution between the excited and dissociating modes. Furthermore, in multiphoton excitation processes such as those at play in IR-MPD or in IR resonance-enhanced multiphoton ionization (IRREMPI) nonlinear effects may occur26,42–44 due to the competition between dynamic processes involving the absorption, relaxation, and statistical decay, all with their own intrinsic time scales.45–47 Chiroptical activity and VCD are commonly addressed theoretically48 by means of quantum chemistry methods such as density-functional theory,30,49–51 within the framework of linear spectroscopy but also focusing on subtle effects such as anharmonicities30,52–54 or quantifying experimental discrepancies.55 To our best knowledge, and despite occasional measurements of VCD effects in the gas phase,56 there has been no attempt to experimentally *Correspondence to: F. Calvo, Laboratoire Interdisciplinaire de Physique, Université Joseph Fourier, Grenoble 1, 4 rue de la Physique, Grenoble, France. E-mail: fl[email protected] Received for publication 18 June 2014; Accepted 28 November 2014 DOI: 10.1002/chir.22421 Published online 16 February 2015 in Wiley Online Library (wileyonlinelibrary.com).

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determine the differential nonlinear response of an isolated molecule or complex to circularly polarized infrared lasers in order to probe possible chirality effects. It is the purpose of the present report to theoretically examine the feasibility of such experiments, by conducting an atomistically resolved investigation of the nonlinear response of a chiral molecule to a circularly polarized infrared laser pulse and quantifying its fragmentation probability under realistic conditions. By varying the excitation wavelength near experimentally relevant ranges, action spectra can be evaluated, compared to linear absorption spectra, and differentiated to produce a depletion signal equivalent to conventional VCD spectra based on absorption intensities. The strategy followed here requires some estimation of sensitivities of the measured signal, which is statistical in nature, in order to assess whether a differential dissociation probability can be reliably determined outside error bars. Our application to an archetypal chiral molecule, camphor, optimistically suggests that the amide mode could be a suitable candidate for experimental testing, paving the way to future VCD spectroscopy in the gas phase. MATERIALS AND METHODS The general protocol of our simulations has been laid out in earlier papers in the case of linearly polarized laser pulses46 and it will only be sketched here. Briefly, we follow a purely classical modeling in which the molecule of interest is initially prepared at a required temperature (step 1), and subjected at time t = 0 to a single electromagnetic pulse at fixed frequency ω in the infrared range, with duration τ (step 2). At optical frequencies the wavelength exceeds the dimensions of the molecule and the field can be considered as uniform but time-dependent. Finally, after some exposure time δt
2τ the energy deposited in the molecule is converted into a dissociation probability p, accordingly with a simple but robust statistical rate theory (step 3). This entirely classical approach contrasts with the most common computational treatment of vibrational spectroscopy based on static Density Functional Theory (DFT), but has similarities to recent efforts by English et al. in the context of condensed chiral liquids subject to external electromagnetic fields.57 Camphor was chosen as an archetypal chiral molecule, having received sustained attention from experimentalists58–60 and theoreticians61–64 alike. Steps 1 and 2 are treated with full atomistic details, using the Amber ff99 force field65 with partial atomic charges that best reproduce the electrostatic potential as predicted by DFT calculations at the standard B3LYP/6-311++G** level performed with the Gaussian09 software package.66 Molecular dynamics (MD) simulations at fixed temperature T were performed using a Nosé-Hoover thermostat and a pool of 1000 independent phase space points was generated by saving snapshots successively separated by 1 ps. In step 2, each of those phase space configurations serves as an initial condition for a new trajectory, without the thermostat but in presence of the laser pulse described classically by an electromagnetic wave propagating along a random direction ! ez that mimics the random orientation of the free-flying molecule. Unless otherwise mentioned, the pulse has a Gaussian envelope of duration pffiffiffiffiffiffiffiffiffi τ = 10 ps related to the time width σ through τ ¼ 2σ 2ln2 , and it is polarized either linearly or circularly. The electric field generally reads

trajectories are propagated over a duration tpulse = 2t0 that exceeds the pulse time width. For circularly polarized waves the Ex component repffiffiffi mains but is divided by 2, and a component on ! ey is introduced as: E0 E y ¼ ± pffiffiffi f ðt Þsin½ωðt  t 0 Þ; 2

the sign depending on the handedness of circular polarization. The electric field amplitude has to be chosen, given the pulse duration, to be sufficiently high for the laser to inject enough energy in the molecule such that it can dissociate over mass spectrometric times of micro- to milliseconds. With a duration of the order of 50 ps a field strength of 2 E0 = 10 V/nm was found to produce the required results. In addition ! to the electric component, the pulse has a magnetic component B ðt Þ ! ! ! such that c B ¼ ez  E . It should be stressed here that, although of moderate intensity in the present nonrelativistic regime, the magnetic field does not negligibly act on the dynamics. Furthermore it is an essential ingredient causing circular dichroism through the presence of a magnetic dipole moment and, as such, it should not be ignored in the modeling. Step 3 of the simulation involves estimating the dissociation probability after exposure to the laser pulse. Here we assume statistical fragmentation to be the only decay channel over experimental time scales, thereby neglecting radiative emission. This approximation is justified owing to the reasonably mild excitations responsible for the dissociation, precisely allowing comparison with absorption spectra calculated in the linear response regime. We use the simple Rice-Ramsperger-Kassel (RRK) statistical rate theory which relates the internal energy Eα at trajectory α to the unimolecular dissociation rate k(Eα) as:67–69 kðE α Þ ¼

¼ E 0 f ðt Þcos½ωðt  t 0 Þ

(1)

with t0 chosen as 50 ps and E0 a field amplitude related to the laser intensity I by I ¼ cε0 E 20 =2, c and ε0 denoting the velocity of light and the dielectric permittivity of vacuum, respectively. With these notations the MD Chirality DOI 10.1002/chir

Ω0 ðE α  DÞ ; hΩðE α Þ

(3)

where Ω and Ω ’ denote the densities of vibrational states of the molecule and its lowest dissociation product, respectively, h being the Planck constant and D the dissociation energy. Additional DFT calculations were carried out to evaluate D = 3.9 eV, obtained for the dissociation of a hydrogen atom from a methyl side group, and to determine the harmonic frequencies of the parent and product molecules. From those frequencies the densities of states were evaluated using standard counting algorithms.70 More accurate rate constants could have been determined by summing over various possible dissociation channels and correcting for anharmonicities; however, mostly the prefactor of the rate constant would be affected rather than its overall behavior with increasing energy. We further note here that the choice of the approximate RRK theory with harmonic level densities is not essential to the present work, as it is mainly used to connect final energies in the MD trajectories to fragmentation probabilities through a realistic relationship. In any case, peak positions in the spectrum would not be affected by employing more accurate rate constants, and only bandwidths could be slightly altered. From the rate constant, the dissociation probability p(tobs) after a measurement time of tobs is evaluated assuming first-order kinetics, which for trajectory α simply reads:    pα ¼ 1  exp kðE α Þ t obs  t pulse :

(4)

Finally, the overall fragmentation probability is averaged over M independent trajectories {α} to yield the depletion ratio p as:

!

E ¼ E x! ex þ E y! ey and in the case of linearly polarized light only the ! ex component is nonzero as: " # ðt  t 0 Þ2 E x ¼ E 0 cos½ωðt  t 0 Þexp  2σ 2

(2)

p¼

1 X p M α α

(5)

The simulations are then repeated at different excitation wavelengths,   from which the dissociation efficiency ρ ¼ ln 1  p can be derived. In practice, we found little difference between ρ and p, and the latter quantity was chosen to define the action spectrum. The simulations can also be performed for a given enantiomer exposed to laser pulses with different circular polarizations, which leads to the corresponding probabilities p±(ω) and the differential probability

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Δp ¼ pþ p. Equivalently, a similar differential probability can be determined from the outcome of simulations of the two enantiomers but exposed to the same circularly polarized laser. The thermalized MD trajectories used a time step of 1 fs, and the trajectories exposed to the laser excitation had to employ shorter steps in order to accommodate the faster rates of variations of the electromagnetic -1 fields. Below and above 2000 cm , the time step was thus chosen as 0.5 and 0.25 fs, respectively. The spectral resolution used to calculate action -1 spectra was chosen as 1 cm .

RESULTS AND DISCUSSION Assessing the Model

The most salient features of our modeling resides in the natural inclusion of nonlinear effects in the description of atomic motion, in particular anharmonicities in the potential and electric dipole moment surfaces and in the response to the field. These features can be captured at the expense of using a simplified potential energy surface, and it is important to first assess the performance of the force field with respect to IR absorption spectra for the present molecule. Linear Absorption Spectrum at Equilibrium

Figure 1 shows the IR absorption intensities of (R)-camphor obtained at zero temperature (unscaled harmonic lines) for the present Amber ff 99 model and compared to the DFT/B3LYP/6-311++G** calculations. The harmonic intensities for the force field were obtained from the square of the electric dipole moment gradient along the corresponding normal mode directions. The DFT data are in agreement with earlier comparable calculations.61–64 This agreement is of course not perfect, but reasonable in terms of peak positions, especially considering that other effects traditionally accounted for by simple scaling procedures71,72 were not included here. Additional calculations performed using the BLYP and the more recent M06-2X hybrid functionals also display variations in the peak

positions that are comparable or even greater than those obtained here with the Amber force field (results not shown). The strongest differences between the harmonic DFT and force field results are probably in the relative intensities; however, those are also notoriously difficult to predict accurately. By construction, the Amber force field contains many harmonic contributions, the major sources of anharmonicities originating from long-range interactions. For the present problem, anharmonicities are essential as the key factor allowing energy transfer between the excited modes and the dissociating bond, through complete and statistical redistribution. Anharmonicities at T = 300 K were gauged by computing the linear absorption spectrum from the Fourier transform of the electric dipole moment time autocorrelation function,37 αðωÞ∝

∞ !

 ! μ ðt Þ μ ð0Þ eiωt dt;

Z

(6)

0 ! where μ ðt Þ is the electric dipole moment at time t and the average h  i is taken over initial conditions at t = 0: !

μ ½R ðt Þ ¼

X

!

qi r i ðt Þ;

(7)

i !

r i ðt Þ being the position of atom i at time t and qi its charge. In eq. (6) the missing prefactor monotonically depends on ω and marginally affects relative intensities in a given frequency range. The anharmonic IR absorption spectrum obtained for the present force field, superimposed in Figure 1, is generally similar to the harmonic spectrum, especially for the line positions. A closer look near experimentally characteristic regions corresponding to C = O (1650–1800 cm-1) and C-H (2900–3050 cm-1) stretching modes shows band shifting to the red and blue sides, respectively, as well as some merging of closeby C-H lines reflecting thermal broadening. The relative intensities are more significantly affected by the finite temperature, indicating that the dipole moment surface also carries some anharmonicities. VCD Spectrum at Equilibrium

To further assess the model and our choice of the frequency ranges of interest, we next considered the VCD spectra, still in the linear absorption regime.We show in Figure 2 the VCD spectrum Δα(ω) of (R)-camphor predicted from DFT at the harmonic level, and the anharmonic VCD spectrum obtained at 300 K from the force field. Similar to the linear IR absorption spectrum, the VCD relative intensity was determined from the Fourier transform of the time cross-correlation function between electric and magnetic dipole moments73,74: ΔαðωÞ∝

∞D

Z

E ! μ ðt Þ mð0Þ eiωt dt;

!

(8)

0 !

where m ðt Þ is the magnetic dipole moment vector at time t, Fig. 1. Linear absorption spectra of (R)-camphor obtained at 0 K with the Amber force field and DFT/B3LYP calculations at the harmonic level, and anharmonic spectrum at 300 K obtained with the Amber force field. Two spectral regions corresponding to amide and C-H stretchings are emphasized in the upper panels. The DFT spectrum has been convoluted with a Lorentzian -1 of 5 cm width.

!

m½R ðt Þ; V ðt Þ ¼

! 1X ! q r i ðt Þ vi ðt Þ; 2 i i

(9)

!

vi ðt Þ being the velocity of atom i at time t. Chirality DOI 10.1002/chir

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Fig. 2. VCD spectrum of (R)-camphor obtained at T = 0 with DFT calculations at the harmonic level, and anharmonic VCD spectrum at 300 K obtained with the Amber force field. The harmonic signal was convoluted with a -1 Lorentzian of 5 cm width.

The VCD spectrum obtained from the present quantum chemical calculations agrees reasonably well with earlier experimental results.59 The VCD spectra display clear activities in the two ranges considered, although the various C-H stretching modes alternate in sign, making a strict comparison rather difficult. More important, the negative signal obtained for the amide mode is consistent for both descriptions, confirming the potential of this mode as a fingerprint not only for IR but also VCD spectroscopies. Modeling Action Spectra

Having established the force field to be at least of semiquantitative quality, we can now use it to model nonlinear action spectra as a response to an electromagnetic pulse. In this respect, it is instructive to consider first the qualitative effects of the laser excitation on the internal state of the molecule, and we show in Figure 3 the time variations of the kinetic temperature averaged over 100 fs upon excitation near the

C = O amide mode, that is, at frequencies close to 1700 cm-1. For the present purpose, the three trajectories were chosen exactly at the same phase space configuration, and with the same orientation of the electric field. They thus share the same initial kinetic temperature of about 330 K in this case, a bit higher than the prescribed thermostatted value (although this is perfectly allowed for a finite-size system). For these three trajectories, the pulse has actually an effect right from the beginning, the kinetic energies becoming distinguishable from one another after only a few picoseconds. This reflects the chaotic behavior of the dynamics, as expected from a many-body anharmonic system. During the first 35 ps or so, the kinetic temperature does not drift but fluctuates, as it should for a small microcanonical system. After this time, the pulse produces some significant heating, but the heating efficiency markedly depends on the frequency and polarization: heating at 1703 cm-1 is more efficient than at the lower frequency, especially in the case of linearly polarized pulses. Finally, after about 60 ps the pulses decay and the kinetic temperatures stop drifting and only fluctuate again around new equilibrium values. Judging from this figure, the amount of heating near the amide mode resonance can be quite high, the few eVs being just necessary to give rise to thermal dissociation after longer mass spectrometric times. At this stage three illustrative trajectories do not carry sufficient information to make any further conclusion, and it is necessary to discuss it on the basis of statistically averaged properties. IR Action Spectra Under Linearly Polarized Laser Pulses

Before discussing proper dissociation spectra, the intrinsic effects of the laser can be appreciated by considering first the amount of energy transferred to the molecule, as measured from the difference between the total energy at the end of the trajectory (after 100 ps) and its value at t = 0. We represent in Figure 4 the variations of the averaged energy transferred to the molecule as a function of excitation frequency in the case of linearly polarized pulses. By extension, and although //

6

absorption spectrum action spectrum harmonic spectrum

5

4

ΔE (eV)

6

5

4

6 4

3

3

2 0

2

2

1695 1710

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1

0 1650

// 1700

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Fig. 3. Typical time variations of the short-time averaged kinetic temperature of (R)-camphor exposed to three electromagnetic pulses at frequencies -1 of 1700 or 1703 cm and polarized linearly or left-circularly. The envelope of the pulse is also shown in the background. Chirality DOI 10.1002/chir

Fig. 4. Average energy transferred to (R)-camphor by the linearly polarized laser pulse as a function of its wavelength, compared to the harmonic and anharmonic absorption spectra, in the two spectral ranges of amide and C-H stretching modes. The inset shows the energy transferred upon exposure to 2 pulses of duration τ = 10 ps and peak intensity E0 = 10 V/nm (small full circles) to the same data obtained upon exposure to pulses of duration 10τ and pffiffiffiffiffi peak intensity E 0 = 10 (larger empty circles).

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MODELING ACTION VCD SPECTRA IN THE GAS PHASE

//

0.8

0.07

left-circular linear right-circular

0.6

Probability

they do not strictly represent a dissociation probability, those variations will be referred to as an action spectrum. The relation between internal energies and dissociation probability expressed by Eqs. (3) and (4) is nonlinear but monotonic, which indicates that the peak positions in the energy transferred will carry over to the actual fragmentation propensity, although the broadenings will not. The energy transferred exhibits peaks near the absorption bands, but with significantly altered features: not only the peaks are broader but they are also shifted to the red (amide mode near 1700 cm-1) or to the blue (C-H stretching modes merged into three bands near 2880, 2910, and 2980 cm-1). Compared with the harmonic spectrum, the bands in the action spectrum thus deviate even more than the anharmonic spectrum at the same initial temperature. This computational observation confirms the amplification mechanism previously identified45–47 as the cause of these apparent excessive band shifts. More precisely, the additional shifting originates from the heating of the system while still under exposure to the laser, the resonance frequencies ω being altered by temperature due to anharmonicities, at first corrective order as ω(T ) ffi ω(T = 0) × (1 + a1T + a2T 2 + ···) with a1, a2, … some constant parameters.74 The results of Figure 4 are thus consistent with a1 < 0 for the amide mode and with a1 > 0 for the C-H stretching modes, within the framework of the present Amber atomistic model. Because the laser pulse used in our modeling is rather short and intense with respect to experimental pulses, we conducted additional simulations for pulses that are 10 times longer (pulse envelope of 100 ps, total trajectory propagated over 1 ns), but carrying pffiffiffiffiffi the same intensity with a field amplitude divided by 10. Those simulations are computationally intensive and were conducted only for a limited set of frequencies near the C = O resonance, but with the same statistics. The results, shown as an inset in Figure 4, lie between the absorption spectrum and the reference data obtained with 10 ps long pulses, but with only minor differences with the latter data. The closer resemblance to the linear absorption spectrum is consistent with a more complete vibrational redistribution, but the moderate changes indicate that energy was correctly transferred from the electromagnetic pulse to the system already with the shorter pulses. This observation also provides some further justification for the statistical hypothesis used to evaluate the dissociation rate constant based on RRK theory. The energies transferred by the laser, added to the thermal energy of about 2 eV, exceed the dissociation threshold D only near ω
1700 cm-1 and 3000 cm-1, therefore those two bands should be particularly prominent in the depletion spectrum, with the remaining peaks near 2880 cm-1 and 2910 cm-1 being attenuated or even entirely vanishing. This is verified in Figure 5, where the depletion probabilities obtained for linearly and circularly polarized pulses after a measurement delay of 1 ms are represented in the two spectral ranges of interest. Noticeably, the peak near 2910 cm-1 remains visible on the action spectrum with linearly polarized light, although the averaged energy deposited by the laser only barely exceeds 1 eV. This is a consequence of the fragmentation probability pðωÞ being the average of individual probabilities pα(ω), some of the trajectories α producing a higher energy transfer than others and possibly exceeding the dissociation threshold. The two depletion spectra obtained for circularly

0.06 0.05

0.8 0.4

0.04

0.7

0.03

0.6

0.4 1695 0 1650

0.02

0.5

0.2

0.01

1700

1705

1710

// 1700

1750

2900

2950

3000

0 3050

-1

ω (cm ) Fig. 5. Fragmentation probability of (R)-camphor upon exposure to a linearly or circularly polarized pulse, as a function of laser wavelength, in the two spectral ranges of amide and C-H stretching modes.

polarized laser pulses are very similar to the spectrum under linear polarization, with a minor difference in the C = O stretching mode, which is less redshifted and slightly less intense than in the latter case. These contrasted responses are likely ascribable to intrinsic anharmonicities, as such effects are known to sometimes cause deviations relative to the harmonic limit that differ between IR and VCD spectra.30,52–54 The two action spectra obtained under circularly polarized pulses, while markedly different from the action spectrum under linearly polarized pulses, are rather similar to each other. They can be differentiated to produce an action signal equivalent to conventional VCD spectra. The differential probability ΔpðωÞ comparing the propensity of (R)-camphor to dissociate after a 100 ps exposure to circularly polarized laser pulses, and after a measurement delay of 1 ms, is represented in Figure 6 as a function of the wavelength in the two spectral ranges considered. Some error bars were evaluated here at

Fig. 6. Difference in the fragmentation probability of (R)-camphor under left- and right-circularly polarized laser pulses, compared to the conventional VCD spectrum scaled appropriately, in the two spectral ranges of C = O and C-H stretching modes. The error bars in the action VCD spectrum represent typical fluctuations among independent blocks of 200 trajectories. Chirality DOI 10.1002/chir

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CALVO

selected wavelengths by considering the five block averages over 200 trajectories and the fluctuations among them in the quantities p± . The spectrum ΔpðωÞ obtained from the whole set of trajectories shows a clear negative peak for the amide mode, and several narrower peaks for the C-H modes with alternating sign. Although those latter peaks appear qualitatively similar to the equilibrium (absorption) VCD spectrum of Figure 2, the statistical deviations are unfortunately excessively large to yield sufficient confidence. This deceptive result can be attributed to the combined consequence of the fragmentation probabilities for those modes being rather low (and of the same order of magnitude as the error bars) and the strongly fluctuating character of the VCD signal in this spectral range, further amplified by the broader nonlinear response to the pulse seen in Figure 4. Conversely, the differential action spectrum in the C = O stretching range displays a better defined intensity with position and broadening that are both similar to the equilibrium VCD spectrum. The statistical uncertainty and the absolute peak value of a few percents make this band a much better candidate for possible experimental verification of the theoretical modeling presented here. In order to further assess the sensitivity of the nonlinear response to circularly polarized pulses, we also quantified the dissociation probability of the two enantiomers to similar pulses. The response to linear pulses, while of course not expected to give any significant difference, indicates the intrinsic statistical fluctuations and, as such, provides an alternative measure of the error bars. The response of (S)-camphor should be the mirror image of that of (R)-camphor under polarization with opposite handedness, thus offering another way of evaluating the circular dichroism signal. The dissociation probabilities of (R)- and (S)-camphor upon exposure to linearly and left-circularly polarized pulses are represented in Figure. 7a, the differential response of (S)-camphor relative to its enantiomer being shown in Figure 7b for both types of polarization.

As expected, there is essentially no visible difference between the action spectra obtained for the two enantiomers under linearly polarized pulses, and the residual discrepancy inferred from Figure 7b amounts to a fraction of a percent. More interestingly, the spectrum of (S)-camphor shows very comparable variations as the reference spectrum of (R)-camphor under right-circular polarized pulse of Figure 5. In particular, the differential probability exhibits a negative peak near the same frequency of 1704 cm-1, also with very similar width and amplitude (about 2%) as was obtained in Figure 6. These results confirm that the fingerprint amide mode could indeed be of sufficient intensity and sensitivity to produce some circular dichroism in the action spectrum. We finally wish to comment on the role of anharmonicities, especially with regard to temperature and the way the system is heated by exposure to the pulse. As mentioned, and although of moderate magnitude for the present system described by the Amber force field, anharmonicities are essential to explain the differences between absorption and action spectra, because they are responsible for the energy flow from the laser field to the resonant vibrational modes and among vibrational modes themselves. Their practical importance can be further discussed in the light of temperature effects. We show in Figure 8a the dissociation probability of (R)-camphor under linearly and circularly polarized pulses in the 1690–1720 cm-1 range, after thermalization at 600 K instead of 300 K as previously. The main effect of temperature is to broaden the absorption band, although line redshifting remains of modest amplitude. The effect on the action spectra is also a severely broader band, resulting from contributions that add to each other. First, intrinsic anharmonicities are naturally responsible for thermal broadening of the absorption peaks owing to facilitated off-resonance excitation in the presence of mode couplings. Second, the thermal energy shifts by a further 2 eV, making statistical dissociation more likely in the entire spectral range.

Fig. 7. (a) Dissociation probability of (R)- and (S)-camphor under linearly and left-circularly polarized pulses, after thermalization at 300 K and as a function of laser wavelength near the amide mode. (b) Differential probability for the dissociation of (R) versus (S) camphor molecules, under linearly or left circularly polarized pulses.

Fig. 8. (a) Dissociation probability of (R)-camphor upon exposure to a linearly or circularly polarized laser pulse, after thermalization at 600 K and as a function of laser wavelength near the amide mode. (b) Differential probability between left- and right-circularly polarized pulses. For both panels, the absorption IR and VCD spectra have been scaled appropriately.

Chirality DOI 10.1002/chir

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MODELING ACTION VCD SPECTRA IN THE GAS PHASE

The differential fragmentation probability Δp corresponding to the above responses p± after thermalization at 600 K is depicted in Figure 8b together with the equilibrium VCD spectrum at the same temperature. Error bars were again added to measure the statistical fluctuations among five independent blocks of 200 trajectories. Interestingly, and although the depletion signal is globally stronger and broader, the differential action spectrum only carries the larger broadening but loses in intensity, to the extent that it is now comparable or even lower than the estimated uncertainties. With respect to Figure 6, the most significant differences thus lie in a loss of sensitivity, whereas the equilibrium VCD spectrum is not so much altered. This temperature dependence of the differential action spectrum is at variance with the commonly known robustness of conventional VCD spectra against temperature changes.5 The practical usefulness of the method under scrutiny here will ultimately be dictated by experimental considerations, starting of course with feasibility. Testing should first be conducted on enantiomerically pure samples, positive results already providing a proof of concept. Success could then encourage or trigger further applications along the lines of traditional VCD spectroscopy but for isolated molecules, beyond absolute structural assignment, and extending toward enantiomeric characterization, chiral recognition, etc.

including anharmonic corrections,30 will suffice to assist experimental characterization. Besides the use of a force field, another important approximation had to be made in the modeling of a single short but intense laser pulse. Although the total energy that must be deposited in the system should remain in excess of several eVs for dissociation to be detectable over less than milliseconds, the actual exposure time in multiphoton irradiation experiments is closer to microseconds and in the form of multiple micropulses.23 A limited set of calculations performed with longer but less intense pulses indeed suggests that nonlinear effects might become less strong owing to a more complete vibrational relaxation between successive photon absorption events. One way to also avoid using such intense pulses in experiments would be through the so-called messenger technique, in which a weakly bound atom or molecule is physisorbed on the system of interest, its dissociation being probed as the main channel conveying successful absorption. Extension to circular dichroism would of course require that the chiral properties of the molecule of interest, notably its response to the polarized laser field, are preserved upon adsorption of the messenger species. ACKNOWLEDGMENT

The author thanks Dr. Anne Zehnacker-Rentien for very useful suggestions and comments.

CONCLUSION

As a fundamental property of organic molecules, chirality can be probed by spectroscopies based on electronic or vibrational circular dichroism. While these methods have become highly accurate in condensed phases, they remain unexploited for isolated molecules produced in the gas phase, despite impressive advances in optical and infrared spectroscopies that monitor depletion ratio by mass spectrometry. In particular, the advent of tunable coherent sources based on synchrotron light or free-electron lasers with the increasing accuracy and predictiveness of quantum chemistry approaches have had a significant impact on the structural assignment of isolated molecules. The possibility to carry differential vibrational spectroscopy under circularly polarized lasers would greatly enlarge the capabilities of such spectroscopies and pave the way to a wealth of applications. While the present work did not provide any direct experimental comparison, it was designed to motivate such experiments and evaluate the feasibility of VCD in nonlinear gas phase action spectroscopy. By calculating the differential fragmentation probabilities for the archetypal compound of camphor under left- and right-circularly polarized laser pulses, we precisely assessed the nonlinear response that is the gas-phase action counterpart to standard equilibrium VCD signals. The atomistic approach followed here is entirely classical in its description of interatomic forces, electric and magnetic dipole moments, as well as in the way the laser interacts with the molecule. However, this multiscale modeling remains realistic in the sense that it accounts for the various important processes of absorption, redistribution, and relaxation by statistical dissociation, all with their own time scales. Because of the numerous MD trajectories that are required to achieve sufficient statistics, such a multiscale modeling is currently out of reach at the ab initio level; however, it can be hoped that conventional quantum chemistry techniques to compute IR and VCD linear spectra, possibly

LITERATURE CITED 1. Holzwarth G, Hsu EC, Mosher HS, Faulkner TR, Moscowitz A. Infrared circular dichroism of carbon-hydrogen and carbon-deuterium stretching modes. Observations J Am Chem Soc 1974;96:251–252. 2. Nafie LA, Keiderling TA, Stephens PJ. Vibrational circular dichroism. J Am Chem Soc 1976;98:2715–2723. 3. Polavarapu PL. Renaissance in chiroptical spectroscopic methods for molecular structure determination. Chem Rec 2007;7:125–136. 4. He Y, Wang B, Dukor RK, Nafie LA. Determination of absolute configuration of chiral molecules using vibrational optical activity: a review. Appl Spectrosc 2011;65:699–723. 5. Berova N, Nakanishi K, Woody RW, editors. Circular dichroism: principles and applications, 2nd ed. New York: Wiley-VCH; 2000. 6. Guo C, Shah RD, Dukor RK, Cao X, Freedman TB, Nafie LA. Determination of enantiomeric excess in samples of chiral molecules using Fourier transform vibrational circular dichroism spectroscopy: simulation of realtime reaction monitoring. Anal Chem 2004;76:6956–6966. 7. Weinkauf R, Schermann JP, de Vries MS, Kleinermanns K. Molecular physics of building blocks of life under isolated or defined conditions. Eur Phys J D 2002;20:309–316. 8. Kim SK, Schermann JP, Ha T. Biomolecular structures: from isolated molecules to the cell crowded medium. Phys Chem Chem Phys 2010;12:3334–3335. 9. Jockusch RA, Lemoff AS, Williams ER. Hydration of valine-cation complexes in the gas phase: on the number of water molecules necessary to form a zwitterion. J Phys Chem A 2001;105:10929–10942. 10. Blom MN, Compagnon I, Polfer NC, von Helden G, Meijer G, Suhai S, Paizs B, Oomens J. Stepwise solvation of an amino acid: the appearance of zwitterionic structures. J Phys Chem A 2007;111:7309–7316. 11. Kong XL, Tsai IA, Sabu S, Han CC, Lee YT, Chang HC, Tu SY, Kung AH, Wu CC. Progressive stabilization of zwitterionic structures in H(Ser)(2-8) (+) studied by infrared photodissociation spectroscopy. Angew Chem Int Ed 2006;45:4130–4134. 12. Zehnacker A, editor. Chiral recognition in the gas phase. Boca Raton, FL: CRC Press Taylor & Francis Group; 2010. 13. Schug KA, Lindner W. Chiral analysis by MS. Anal Chem 2003;75: 25A–31A. 14. Schalley CA. Molecular recognition and supramolecular chemistry in the gas phase. Mass Spectrom Rev 2001;20:253–309. Chirality DOI 10.1002/chir

260

CALVO

15. Dwivedi P, Wu C, Matz LM, Clowers BH, Siems WF, Hill HH. Gas-phase chiral separations by ion mobility spectrometry. Anal Chem 2006;78: 8200–8206. 16. Wu LM, Tao WA, Cooks RG. Kinetic method for the simultaneous chiral analysis of different amino acids in mixtures. Int J Mass spectrom 2003;38:386–393. 17. Sen A, Le Barbu-Debus K, Scuderi D, Zehnacker-Rentien A. Mass spectrometry study and infrared spectroscopy of the complex between camphor and the two enantiomers of protonated alanine: the role of higher-energy conformers in the enantioselectivity of the dissociation rate constants. Chirality 2013;25:436–443. 18. Dunbar RC, Steill JD, Oomens J. Chirality-induced conformational preferences in peptide-metal ion binding revealed by IR spectroscopy. J Am Chem Soc 2011;133:1212–1215. 19. Wu RH, McMahon TB. An investigation of protonation sites and conformations of protonated amino acids by IRMPD spectroscopy. Chem Phys Chem 2008;9:2826–2835. 20. Seurre N, Le Barbu-Debus K, Lahmani F, Zehnacker A, Borho N, Suhm MA. Chiral recognition between lactic acid derivatives and an aromatic alcohol in a supersonic expansion: electronic and vibrational spectroscopy. Phys Chem Chem Phys 2006;8:1007–1016. 21. Scuderi D, Maître P, Rondino F, Le Barbu-Debus K, Lepère V, Zehnacker-Rentien A. Chiral recognition in cinchona alkaloid protonated dimers: mass spectrometry and UV photodissociation studies. J Phys Chem A 2010;114:3306–3312. 22. Chin W, Piuzzi IF, Dimicoli I, Mons M. Probing the competition between secondary structures and local preferences in gas phase isolated peptide backbones. Phys Chem Chem Phys 2006;8:1033–1048. 23. Brodbelt JS, Wilsson JJ. Infrared multiphoton dissociation in quadrupole ion traps. Mass Spectrom Rev 2009;28:390–424. 24. Eyler JR. Infrared multiple photon dissociation spectroscopy of ions in penning traps. Mass Spectrom Rev 2009;28:448–467. 25. Gruene P, Rayner DM, Redlich B, van der Meer AFG, Lyon JT, Meijer G, Fielicke A. Structures of neutral Au7, Au19, and Au20 clusters in the gas phase. Science 2008;321:674–676. 26. Oomens J, Tielens AGGM, Sartakov BG, von Helden G, Meijer G. Laboratory infrared spectroscopy of cationic polycyclic aromatic hydrocarbon molecules. Astrophys J 2003;591:968–985. 27. Ebata T, Fujii A, Mikami N. Vibrational spectroscopy of small-sized hydrogen-bonded clusters and their ions. Int Rev Phys Chem 1998;17:331–361. 28. Polfer NC, Oomens J. Vibrational spectroscopy of bare and solvated ionic complexes of biological relevance. Mass Spectrom Rev 2009;28:586–607. 29. Barone V. Anharmonic vibrational properties by a fully automated secondorder perturbative approach. J Chem Phys 2005;122:014108. 30. Cappelli C, Bloino J, Lipparini F, Barone V. Toward ab initio anharmonic vibrational circular dichroism spectra in the condensed phase. J Phys Chem Lett 2012;3:1766–1773. 31. Greathouse JA, Cygan RT, Simmons BA. Vibrational spectra of methane clathrate hydrates from molecular dynamics simulation. J Phys Chem B 2006;110:6428–6431. 32. Rossi M, Blum V, Kupser P, von Helden G, Bierau F, Pagel K, Meijer G, + Scheffler M. Secondary structure of Ag-Alan-LysH polyalanine peptides (n = 5,10,15) in vacuo: helical or not? J Phys Chem Lett 2010;1:3465–3470. 33. Gaigeot M-P. Theoretical spectroscopy of floppy peptides at room temperature. A DFTMD perspective: gas and aqueous phase. Phys Chem Chem Phys 2010;12:3336–3359. 34. Shiga M, Nakayama A. Ab initio path integral ring polymer molecular dynamics: vibrational spectra of molecules. Chem Phys Lett 2007;451: 175–181. 35. Vendrell O, Gatti F, Meyer HD. Strong isotope effects in the infrared spectrum of the zundel cation. Angew Chem Int Ed 2008;48:352–355. 36. Huang X, Habershon S, Bowman JM. Comparison of quantum, classical, and ring-polymer molecular dynamics: infra-red spectra of Cl (H2O) and + H (H2O)2. Chem Phys Lett 2008;450:253–257. 37. Ramírez M, López-Ciudad T, Kumar P, Marx D. Quantum corrections to classical time-correlation functions: hydrogen bonding and anharmonic floppy modes. J Chem Phys 2004;121:3973–3983. 38. Jung JO, Gerber RB. Vibrational wave functions and spectroscopy of (H2O)n, n = 2, 3, 4, 5: vibrational self-consistent field with correlation corrections. J Chem Phys 1996;105:10332–10348. Chirality DOI 10.1002/chir

39. Light JC, Carrington T. Discrete-variable representations and their utilization. Adv Chem Phys 2000;114:264–310. 40. Carbonnière P, Dargelos A, Pouchan C. The VCI-P code: an iterative variation-perturbation scheme for efficient computations of anharmonic vibrational levels and IR intensities of polyatomic molecules. Theor Chem Acc 2010;125:543–554. 41. Christiansen O. Selected new developments in vibrational structure theory: potential construction and vibrational wave function calculations. Phys Chem Chem Phys 2012;14:6672–6687. 42. Banisaukas J, Szczepanski J, Eyler J, Vala M, Hirata S, Head-Gordon M, Oomens J, Meijer G, von Helden G. Vibrational and electronic spectroscopy of acenaphthylene and its cation. J Phys Chem A 2003;107: 782–793. 43. Lorenz UJ, Solcà N, Lemaire J, Maître P, Dopfer O. Infrared spectra of isolated protonated polycyclic aromatic hydrocarbons: protonated naphthalene. Angew Chem Int Ed 2007;46:6714–6716. 44. Atkins CG, Rajabi K, Gillis EAL, Fridgen TD. Infrared multiple photon dissociation spectra of proton- and sodium bound glycine dimers in the N–H and O–H stretching region. J Phys Chem A 2008;112: 10220–10225. 45. Oomens J, Sartakov BG, Meijer G, von Helden G. Gas-phase Infrared multiple photon dissociation spectroscopy of mass-selected molecular ions. Int J Mass Spectrom 2006;254:1–19. 46. Calvo F, Parneix P. Amplification of anharmonicities in multiphoton vibrational action spectra. Chem Phys Chem 2012;13:212–220. 47. Parneix P, Basire M, Calvo F. Accurate modeling of infrared multiple photon dissociation spectra: the dynamical role of anharmonicities. J Phys Chem A 2013;117:3954–3959. 48. Stephens PJ. Theory of vibrational circular dichroism. J Phys Chem 1985;89:748–752. 49. Cheeseman JR, Frisch MJ, Devlin FJ, Stephens PJ. Ab initio calculation of atomic axial tensors and vibrational rotational strengths using density functional theory. Chem Phys Lett 1996;252:211–220. 50. Stephens PJ, Devlin FJ. Determination of the structure of chiral molecules using ab initio vibrational circular dichroism spectroscopy. Chirality 2000;12:172–179. 51. Schwerdtfeger P, Kühn A, Bast R, Laerdahl JK, Faglioni F, Lazzeretti P. The vibrational spectrum of camphor from ab initio and density functional theory and parity violation in the C–C*–CO bending mode. Chem Phys Lett 2004;383:496–501. 52. Bak KL, Bludsky O, Jørgensen P. Ab initio calculations of anharmonic vibrational circular dichroism intensities of trans-2,3-dideuteriooxirane. J Chem Phys 1995;103:10548–10555. 53. Abbate S, Castiglioni E, Gangemi F, Gangemi R, Longhi G, Ruzziconi R, Spizzichino S. Harmonic and anharmonic features of IR and NIR absorption and VCD spectra of chiral 4-X-[2.2] paracyclophanes. J Phys Chem A 2007;111:7031–7040. 54. Mori H, Yamagishi A, Sato H. Theoretical study on vibrational circular dichroism spectra of tris(acetylacetonato)metal(III) complexes: anharmonic effects and low-lying excited states. J Chem Phys 2011;135:084506. 55. Covington CL, Polavarapu PL. Similarity in dissymetry factor spectra: a quantitative measure of comparison between experimental and predicted vibrational circular dichroism. J Phys Chem A 2013;117:3377–3386. 56. Šebestký J, Bour P. Raman optical activity of methyloxirane gas and liquid. J Phys Chem Lett 2011;2:498–502. 57. English NJ, Kusalik PG, Woods SA. Coupling of translational and rotational motion in chiral liquids in electromagnetic and circularly polarised electric fields. J Chem Phys 2012;136:094508. 58. Nafie LA. Polarization modulation FTIR spectroscopy. In: Mackenzie MW, editor. Advances in applied Fourier transform infrared spectroscopy. New York: Wiley; 1988, p 67–104. 59. Guo C, Shah RD, Dukor RK, Freedman TB, Cao X, Nafie LA. Fourier -1 transform vibrational circular dichroism from 800 to 10,000 cm ; near IR-VCD spectral standards for terpenes and related molecules. Vib Spectrosc 2006;42:254–272. 60. Debie E, Jaspers L, Bultink P, Herrebout W, Van der Veken B. Induced solvent chirality: a VCD study of camphor in CDCl3. Chem Phys Lett 2008;450:426–430. 61. Devlin FJ, Stephens PJ, Cheeseman JR, Frisch MJ. Prediction of vibrational circular dichroism spectra using density functional theory: camphor and fenchone. J Am Chem Soc 1996;118:6327–6328.

MODELING ACTION VCD SPECTRA IN THE GAS PHASE 62. Morita HE, Kodama TS, Tanaka T. Chirality of camphor derivatives by density functional theory. Chirality 2006;18:783–789. 63. Abbate S, Burgi LF, Gangemi F, Gangemi R, Lebon F, Longhi G, Pultz VM, Lightner DA. Comparative analysis of IR and vibrational circular dichroism spectra for a series of camphor-related molecules. J Phys Chem A 2009;113:11390–11405. 64. Gangemi F, Gangemi R, Longhi G, Abbate S. Calculations of overtone NIR and NIR-VCD spectra in the local mode approximation: camphor and camphorquinone. Vib Spectrosc 2009;50:257–267. 65. Wang JM, Cieplak P, Kollman PA. How well does a restrained electrostatic potential (RESP) model perform in calculating conformational energies of organic and biological molecules? J Comput Chem 2000;21:1049–1074. 66. Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Scalmani G, Barone V, Mennucci B, Petersson GA, Nakatsuji H, Caricato M, Li X, Hratchian HP, Izmaylov AF, Bloino J, Zheng G, Sonnenberg JL, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Vreven T, Montgomery JA, Jr, Peralta JE, Ogliaro F, Bearpark M, Heyd JJ, Brothers E, Kudin KN, Staroverov VN, Kobayashi R, Normand J, Raghavachari K, Rendell A, Burant JC, Iyengar SS, Tomasi J, Cossi M, Rega N, Millam MJ, Klene M, Knox JE, Cross JB, Bakken V, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Martin RL, Morokuma K, Zakrzewski VG, Voth GA, Salvador P, Dannenberg JJ, Dapprich S, Daniels AD, Farkas O, Foresman JB, Ortiz JV, Cioslowski J, Fox DJ. Gaussian 09, Revision A.02. Wallingford, CT: Gaussian; 2009.

261

67. Rice OK, Ramsperger HC. Theories of unimolecular gas reactions at low pressures. J Am Chem Soc 1927;49:1617–1629. 68. Kassel LS. Studies in homogeneous gas reactions. I J Phys Chem 1928;32:225–242. 69. Kassel LS. Studies in homogeneous gas reactions. II. Introduction of quantum theory J Phys Chem 1928;32:1065–1079. 70. Beyer T, Swinehart DF. Algorithm 448 number of multiply restricted partitions. Commun ACM 1973;16:379–379. 71. Scott AP, Radom LJ. Harmonic vibrational frequencies: an evaluation of Hartree-Fock, Møller-Plesset, quadratic configuration interaction, density functional theory, and semiempirical scale factors. J Phys Chem 1996;100:16502–16513. 72. Basire M, Parneix P, Calvo F. Finite-temperature IR spectroscopy of polyatomic molecules: a theoretical assessment of scaling factors. J Phys Chem A 2010;114:3139–3146. 73. Abbate S, Longhi G, Kwon K, Moscowitz A. The use of cross-correlation functions in the analysis of circular dichroism spectra. J Chem Phys 1998;108:50–62. 74. Yang S, Cho M. Direct calculations of vibrational absorption and circular dichroism spectra of alanine dipeptide analog in water: quantum mechanical/molecular mechanical molecular dynamics simulations. J Chem Phys 2009;131:135102. 75. Calvo F, Doye JPK, Wales DJ. Characterization of anharmonicities on complex potential surfaces: perturbation theory and simulation. J Chem Phys 2001;115:9627–9636.

Chirality DOI 10.1002/chir