Controlling the Excited-State Dynamics of Nuclear Spin Isomers Using

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Controlling the Excited State Dynamics of Nuclear Spin Isomers Using the Dynamic Stark Effect Maria Waldl, Markus Oppel, and Leticia González J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.5b12542 • Publication Date (Web): 03 Feb 2016 Downloaded from http://pubs.acs.org on February 18, 2016

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The Journal of Physical Chemistry

Controlling the Excited State Dynamics of Nuclear Spin Isomers Using the Dynamic Stark Effect Maria Waldl, Markus Oppel, and Leticia González∗ Institut für Theoretische Chemie, Universität Wien, Währinger Str. 17, 1090 Wien, Austria E-mail: [email protected]

∗

To whom correspondence should be addressed

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ACS Paragon Plus Environment


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Abstract Stark control of chemical reactions uses intense laser pulses to distort the potential energy surfaces of a molecule, thus opening new chemical pathways. In the present paper we use the concept of Stark shifts to convert a local minimum into a local maximum of the potential energy surface, triggering constructive and destructive wave packet interferences, which then induce different dynamics on nuclear spin isomers in the electronically excited state of a quinodimethane derivative. Model quantum dynamical simulations on reduced dimensionality using optimized ultra short laser pulses demonstrate a difference of the excited state dynamics of two sets of nuclear spin isomers, which ultimately can be used to discriminate between these isomers.

Keywords Stark Effect, Nuclear Spin Isomers, Laser Control

1

Introduction

Laser control of chemical reactions has been addressed by chemists and physicists for a couple of decades. 1–3 Short, tailored laser pulses can be used to control the pathways of a nuclear wave packet moving along one or several potential energy surfaces that reflect specific changes in a chemical reaction. 4–7 Control can be exerted in different ways, for example, by using the coherent control schemes of Brumer and Shapiro, 8 or with a sequence of pulses, following the idea of Tannor-Rice, 9 where first a pump pulse creates a wave packet in an electronically excited state and a second, time-delayed pulse, targets the wave packet to a particular region of the potential energy surface. Although different variations on the latter concept have been proposed, depending on the action of the second pulse, they all rely on guiding the wave packet through the molecular potential energy surfaces with exquisite time precision. 10–12 2


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When laser fields reach a certain level of amplitude strengths, the concept of a nuclear wave packet moving along the potential energy landscape needs to be extended. Intense electric fields can induce shifts of the energy levels of a molecule, thus distorting the potential energy surfaces –a concept which is well-known as the Stark effect. 13 Using strong, non-resonant laser pulses (for example within the near infrared or THz regime), molecular potentials can be distorted without absorbing the light, but making use of the so-called dynamic or AC Stark control effect. 14 In the last years, strong fields have become an important issue in ultrafast science 15,16 and the dynamics of a number of molecular systems have been manipulated making use of fields strong enough to modify the potential energy surfaces, 17–25 and at the same time weak enough not to produce undesired ionization. An interesting application of quantum control is the possibility to use ultrashort laser pulses to separate nuclear spin isomers. Nuclear spin isomers –as ortho- and parahydrogen– are molecules which differ in the spin states of the nuclei making up the frame of the molecule. 26 Due to the indistinguishability of identical particles, in particular hydrogen, which can have its nuclear spin up or down, the different possible combinations of all the hydrogens within a molecule lead to symmetric or antisymmetric nuclear spin wave functions. Since the total wave function of a molecule must satisfy the symmetrization or Pauli postulate, which requires an overall antisymmetric wave function with respect to the exchange of two fermionic hydrogen atoms, the symmetry of the nuclear spin wave function has a direct influence on the character of the remaining components of the overall wave function of a molecule, for example, on the rotational wave function. The separation of nuclear spin isomers has the ultimate goal of producing a sample containing purely only one of the isomers. This pure sample allows one to study the physical properties of each of the isomers directly. The separation is usually done by changing the ratio between the nuclear spin isomers away from its equilibrium value at any given temperature and is still an experimental challenge. Ortho- and parahydrogen can be separated by cryogenic means for quite some time now. 27,28 However, the separation of nuclear spin isomer in polyatomic molecules

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is not straightforward. Most experimental realizations make use of the light-induced drift technique. 29 This way of separation has been successfully applied to a few number of small molecules like CH3 F, 30–33

13

C12 CH4 , 34 H2 CO, 35

12

C2 H4 , 36 H2 O 37,38 and CH3 OH. 39 Ortho-

and para- water has also been recently separated using the dc Stark effect, 40 by interacting with the rotational ground state of the molecules thereby inducing a different effective dipole moment within ortho- and para- water, which is used to spatially separate the isomers within a molecular beam. Interestingly, none of the previous experiments exploit the coherent properties of light to separate nuclear spin isomers. The approach presented here offers a complementary approach to the above mentioned procedures. In a series of publications, it has been shown that it is possible to discriminate nuclear spin isomers exploiting interference effects in the electronic excited state. 41–47 Recently, we reported model simulations illustrating the concept of discriminating and separating nuclear spin isomers using ultrafast pump and dump pulses. 47 In particular, we dealt with a quinodimethane derivative, the 2-[4-(cyclopenta-2,4-dien-1-ylidene)-cyclo-hexa-2,5-dien-1-ylidene]-2H-1,3-dioxole molecule (abbreviated CCD), shown in Figure 1. While in systems like H2 and H2 O, recently used in experiments as well as in theoretical investigations off nuclear spin isomers, the exchange of two fermions can be related to an overall rotation of the molecule (leading to differences in the rotational spectrum, which in turn can lead to differences in macroscopic properties - see also the studies on nuclear spin symmetry conservation and relaxation in water 48 ), in our model system the exchange of two fermionic protons is represented by an internal motion, i.e. the torsion of one part of the molecule with respect to the rest. This puts an additional constrain on the description of the total wave function of the molecule composed of its individual parts. The product of the torsional wave function with the wave function representing the nuclear spin must obey the Pauli-Principle, requiring a change of the sign of the total wave function when two protons (fermions) are exchanged. This requires, in turn, that the torsional wave function is represented as a symmetric or antisymmetric wave function, respectively.

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At very low temperature, CCD has four different nuclear spin isomers populated. 49 Two groups of nuclear spin isomers can be discriminated via their different torsional dynamics in the excited state. 46 This can be used to change the equilibrium ratio of both isomer groups by using carefully optimized ultra short laser pulses in a pump-dump like scenario. 47 The underlying principle of the proposed separation mechanism relies on the topology of the excited state potential energy surface, whose shape triggers the motion of the different parts of the excited torsional wave function towards each other. Once these different parts of the wave function meet they can start to interfere. Since different nuclear spin isomers are represented by a linear combination of localized wave functions with different signs of the coefficients, the interference will be constructive or destructive, depending on the relative phase of the localized parts of the wave packet. These different interferences finally lead to a difference in the torsional dynamics of the system, enabling one to discriminate different nuclear spin isomers. In the present paper, we show that it is possible to use the dynamical Stark field to modify the shape of a potential energy surface in order to induce wave packet interferences, which can in turn be exploited to separate nuclear spin isomers. This situation is useful if, for example, the bright state does not have the appropriate topology to trigger a motion of the wave packet and thereby inducing wave packet interferences. This is precisely the case in CCD, where the lowest-energy bright state has a similar topology as the electronic ground state and therefore does not lead to a motion of the wave packet which can promote interferences. The following section will briefly describe the theoretical methods used in the simulations. This is followed by a description of the results obtained for a simple, one-dimensional model, which was used to optimize the laser pulses, as well as the results obtained by applying the optimized pulses to the two-dimensional system which was also used in our previous work. 46,47

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Theory

2.1

Quantum Dynamics

The laser driven, excited state dynamics of a system composed, for simplicity, of two electronic states is simulated solving the time-dependent Schrödinger equation:

i











∂  Ψ0 (t)   H00 H01   Ψ0 (t)  . =   ∂t Ψ1 (t) Ψ1 (t) H10 H11

(1)

We assume the system to be preoriented, with a fixed orientation of the isomers in space. Taking into account the two torsions Φ1 and Φ2 (see Figure 1) as the degrees of freedom which define the intramolecular rotation of the hydrogens located in the fragments A, B and C of CCD, the Hamiltonian (in atomic units) of this model of reduced dimensionality can be defined as follows. The diagonal matrix elements Hii for state i are composed of three parts: Hii = T + Vi + Wi .

(2)

T is the kinetic energy operator,

T =−

1 ∂2 ∂2 1 1 ∂ ∂ , − − 2 2 2 · IA,B ∂Φ1 2 · IB,C ∂Φ2 IB ∂Φ1 ∂Φ2

(3)

describing the torsional motion, with the reduced moments of inertia

IA,B =

IA IB , (IA + IB )

(4)

IB,C =

IB IC (IB + IC )

(5)

where IA , IB and IC are the moments of inertia of the ring fragments A, B and C, respectively. Vi is the potential energy surface of state i obtained by means of ab initio CASSCF

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calculations, as described in section 2.2. Finally, Wi describes the interaction of state i with an external laser field F and contains the interaction with the dipole moment µi as well as the interaction with the polarizability αi , the latter being necessary to describe the dynamic Stark effect: Wi = −µi · F (t) − αi · F (t)2 .

(6)

The coupling between the states i and j is mediated by the interaction with the laser field, which is described by the off diagonal element Hij ,

Hij = −µij · F (t),

(7)

where µij the transition dipole moment between states i and j and F (t) is the electric field of the laser pulse acting on the system. This field can be written as:

F (t) = F0U V sU V (t) cos(ω0U V (t)) +

(8)

(t) cos(ω0Stark (t)), F0Stark sStark 0

where the central frequencies ω0U V and ω0Stark and the amplitudes F0U V and F0Stark are the parameters to be optimized while the envelope functions sU V (t) and sStark (t) are assumed 0 to be of sin2 shape, i.e.

s(t) =

sin2 (πt/tp ), if ts < t < ts + tp

(9)

otherwise

0,

with the UV pulse duration tp = tUp V and the Stark pulse duration tStark . Possible ionization p effect of both, the UV and the Stark pulses are neglected. Throughout this work, a polarization of the laser pulse along the laboratory-fixed Z-direction was assumed, i.e. only the interaction with the z-component of the dipole vector and polarizability tensor have been taken into account. 7



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Equation 1 is solved by propagating the wave packet using the split operator 50 on a grid by means of Fourier transformation techniques. 51 As it will be explained later, due to the topology of the potential energy surface the early dynamics affecting the different spin isomers occurs only along the torsion around Φ2 . By keeping Φ1 at the equilibrium value of zero degree, we therefore restricted ourselves to this single degree of freedom when optimizing both the laser pulse parameters for the excitation from the ground to the electronically excited state as well as the parameters for the non-resonant pulse causing the dynamical Stark shift of the excited state potential. The initial wave functions for both one- and two-dimensional simulations are obtained by propagating the system using the above mentioned methods but with imaginary time. 52

2.2

Quantum Chemistry: Potentials, Dipole Moments and Polarizabilities

The potential energy surfaces and relevant properties of the CCD molecule have been calculated along the Φ1 and Φ2 torsional angles, while keeping the rest of degrees of freedom frozen. This is certainly an approximation since the employed laser fields will have an effect on other degrees of freedom; however, the present work is only intended as a proof of principle that optimized laser pulses can help to discriminate nuclear spin isomers. The method used in the electronic structure calculations is the complete active space self consistent field method. 53 In particular, a state-averaged calculation of the lowest four singlet states has been done using 12 electrons in 10 orbitals (labelled as SA4-CASSCF(12,10)), as explained in Refs. 46,47,49 All calculations were done employing the Dunning correlation corrected double zeta basis set cc-pVDZ, 54 using the program package Molpro2012. 55 The Cartesian component k = x, y, z of the polarizablities αik of states i = 0, ..., 3 have been obtained through quantum chemical calculations by replacing the general expression, 56

αik

dµki (F k ) d2 Ei (F k ) = = dF k F k =0 dF k 2 F k =0 8


(10)

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by a finite difference approximation: µki (−∆F k ) + µki (∆F k ) 2∆F k k Ei (−∆F ) − 2Ei (0) + Ei (∆F k ) = ∆F 2

αik = −

(11)

where Ei (F ) denotes the energy of state i as a function of the electric field strength F k along the Cartesian component k. µki (F k ) is the induced dipole moment along this coordinate and ∆F is the difference in the electric field. This difference has been taken as ∆F = 0.005a.u. in the calculations.

3

Results

One-dimensional (1D) energy cuts of the 2D-potential energy surfaces S0 -S3 of CCD are plotted in Figure 2. The four local minima in the electronic ground state located at Φ1 = 0◦ and 180◦ , with Φ2 = 0◦ , and Φ1 = 0◦ and 180◦ , with Φ2 = 180◦ , represent the four nuclear spin isomers. As one can see, at these geometries, the S1 and S3 states also show local minima, while the S2 excited state shows a local minimum along the Φ1 coordinate for Φ2 = 0◦ and 180◦ , and a local maximum along Φ2 for Φ1 = 0◦ and 180◦ . Therefore, in absence of an external electric field, only S2 along Φ2 shows an adequate topology to trigger wave packet interferences. Precisely for this reason, the model simulations reported in Refs. 46,47 were done exciting to this particular electronic state. The transition to this electronic excited state, however, is very weak in comparison with the bright S3 state (oscillator strength fS3 =1.595 versus fS2 =0.001 at CASSCF level of theory 46 ). Therefore, in this paper the dynamic Stark field effect is used to modify the shape of the bright S3 state, so that torsional dynamics can be triggered, which in turn can be used to discriminate the different nuclear spin isomers, thereby demonstrating how dynamic Stark fields can be useful to control torsional motion. In order to initiate the excited state dynamics we first transfer population from the ground state S0 to the excited state S3 by employing a 200 fs sin2 shaped laser pulse. Using 9



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a frequency of ω U V = 4.835eV and a maximum amplitude of F0U V = 0.285GV /m, more than 98% of the population is transferred into the excited state. As in our previous works, 46,47,49 the potential barrier along the Φ2 coordinate is much lower than along Φ1 . Thus, for simplicity, the second non-resonant laser pulse, responsible for the dynamical Stark shift, has only been optimized using a 1D-model, where the torsional angle Φ1 is fixed and only Φ2 is varied. Optimizing the same process along using Φ1 as the active coordinate could require much higher laser intensities. Additionally, any dynamics triggered along the Φ1 coordinate would immediately couple with a motion along Φ2 , deteriorating the discrimination between nuclear spin isomers. Figure 3 shows the potential energy together with the permanent and transition dipole moment as well as the dipole induced static polarizability as a function of the torsion along Φ2 for the two electronic states involved in the laser pulse optimization, the ground state S0 and the third electronically excited state S3 . The large values of the intra state dipole moment µ33 in combination with a large polarizability α33 at the equilibrium values of Φ2 = 0◦ and Φ2 = 180◦ along the z component are expected to shape the potential energy surface of the S3 excited state so that a temporal maximum is induced at the Franck-Condon window at the vicinity of the equilibrium values, which in turn should be able to trigger the desired wave packet motion, i.e. wave packet interferences in the excited state. Note that the corresponding values for the dipole moment and for the polarizabilities along the x and y components are 5 times smaller. We therefore assume an alignment of the molecule along the laboratory fixed Z-axis, ignoring the interaction of the laser pulse with the x and y components. The optimal laser parameters of the non-resonant low frequency laser pulse were found performing a systematic scan of the frequencies and amplitudes of the Stark pulse, varying the frequency ω Stark between 0.002 and 0.015 eV and the amplitude F0Stark between 2 and 6 GV/m. As a measure of the control achieved, an adequate observable that can be compared along the propagation is required. An obvious choice would be to follow directly the expectation value of the torsion, < Ψ|Φˆ2 |Ψ >. However, since the system is symmetric with

10


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respect to the torsion around Φ2 (and Φ1 ), this expectation value is always exactly zero. More suitable to distinguish between different nuclear spin isomers is to look at the variance (dispersion) of the latter operator, which is defined as: DΦ2 =< Ψ|Φˆ22 |Ψ > − < Ψ|Φˆ2 |Ψ >2 .

(12)

A direct measure of the difference in the excited state dynamics of two nuclear spin isomers showing constructive or destructive interferences, respectively, is the difference between their corresponding dispersion: ∆D = DΦs 2 − DΦa 2

(13)

with DΦs 2 and DΦa 2 being the dispersion of the isomers labeled s and a, respectively. The final aim of optimizing the Stark pulse is to find a time tf where the system shows a sizeable dispersion difference, according to equation 13. This is motivated by one of our previous works, 47 where it was shown that it is possible to use a dump pulse to bring the different excited nuclear spin isomers back to the electronic ground state, at the time where the dynamics of the two nuclear spin isomers exhibits the maximal difference. The initial nuclear spin isomers along the Φ2 coordinate, represented by a symmetric and antisymmetric torsional wave functions, respectively, are shown in Fig. 4. These wave functions are used as the starting wave functions for the propagation at t = 0. Figure 5 shows the difference in dispersion as a function of the varied laser pulse parameters. Clearly, the difference in the dispersion is larger for higher field amplitudes F0Stark as well as larger frequencies ω Stark . Looking closely, one can identify small peaks in the upper left corner, for field amplitudes between 5 and 6 GV/m and frequencies between 0.008 and 0.013 eV. A careful analysis of the data shows that a local maximum can be found at F0Stark =5.56 GV/m and ω Stark =0.0105 eV. Accordingly, these values have been chosen as the optimal parameters of the control pulse. The optimal frequency of the Stark pulse is thereby a compromise between two effects: i) the optimal modification of the topology of

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the potential energy surface into the right shape, i.e. triggering a motion of both parts of the wave packet towards each other; and ii) the right timing to allow the wave packet to start moving, while the ongoing Stark pulse is already changing its electric field towards the opposite value, which in turn stops the motion of the wave packets. Figure 6a shows the dispersion as a function of time of both the symmetric and antisymmetric torsional wave functions propagated under the influence of the optimal laser pulse (figure 6b) composed of the parameters mentioned above. The non-resonant low frequency laser induces a periodic modification of the potential which in turn triggers the torsional dynamics of the wave packets. Shortly after 2200 fs the two distinct parts of the starting wave functions start to interfere. Since there is a sign difference in the linear combination of the initial wave functions, the interference patterns show different destructive or constructive interference behavior, leading finally to a difference in the dynamics of both isomers. This difference manifests itself in a difference of the dispersion of the wave function. Having shown for this reduced 1D-model along Φ2 that control over nuclear spin isomers is possible by choosing the right combination of the UV and Stark pulse, we analyze the effect of the optimized pulse sequence on the 2D model, including both Φ2 and Φ1 torsional angles. We therefore use the pulses from the 1D simulations and propagate the system on the 2D potential energy surfaces along both torsional angles Φ1 and Φ2 for both relevant electronically excited states S0 and S3 . The starting wave functions representing the different nuclear spin isomers are now linear combinations of four single wave packets localized within the four mimina of the potential energy surface of the electronic ground state, see also Ref. 46,47 The optimized laser pulse sequence is robust against the additional degree of freedom, showing the same effect as in the 1D case. Depending on the relative sign of the starting wave function along Φ2 a difference in the dispersion of the symmetric and antisymmetric linear combination can be seen, whereas different signs (i.e. a symmetric or antisymmetric combination) along Φ1 does not lead to any difference in the torsional dynamics in the electronically excited state. To understand this behavior, the (time dependent) light-induced

12


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potentials or dressed states 57–59 are obtained according to

ViLIP (t) = Vi + Wi (t) = Vi − µi · F (t) − αi · F (t)2

(14)

for the S3 state along both torsional coordinates. These are depicted in Figure 7 for both, the most negative (at 2160fs, figure 7b) and most positive (at 2360fs, figure 7c), electric field strengths, which in turn correspond to a maximal modification of the potential energy surface towards negative energies (at a maximal field strength at 2360 fs) or towards positive energies (at the minimal field strength at 2160fs), respectively, together with the unmodified potential energy surface, figure 7a. As one can see, both torsional degrees of freedom are affected by the non resonant low frequency laser pulse. However, the desired effect of converting a local potential minimum to a local maximum, which then can trigger the motion of the wave function along the coordinate of interest, is only effective along Φ2 and not along Φ1 . This means that for Φ2 the local potential well, which initially traps the wave packet, can be converted into a local maximum. In contrast, Φ1 always shows a barrier between 0 and 180 degrees, which blocks any possible interference of the wave packet along this coordinate. This particular behavior of the potential energy surface justifies the initial approach of first finding an optimal laser pulse sequence for a simple 1D case along Φ2 before applying the same sequence to the 2D model. Figure 8 shows the difference in the dispersion of Φ2 for the two different starting wave functions for a 2D-propagation using the optimal laser pulse parameters obtained by the procedure described above. The time evolution of the dispersion itself is shown as an inset. Again, as in the 1D case, the dispersion values are identical for both nuclear spin isomers during the first ca. 1700 fs, which is the time that the wave packet needs to start interfering. In contrast to the 1D case and also in contrast to our previous work, where the system was excited to the second electronically excited state, S2 , there is a drop of the value of the dispersion at 1000fs, i.e. close to the beginning of the simulation. This drop is caused by an initial compression of the wave packet along the torsional degree

13



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of freedom and this, in turn, is caused by a slightly less shallow potential energy well in the S3 state in contrast to the S0 state. Soon after, at 1500fs, this compression is compensated by the initial dispersion of the wave packet due to the movement of the different parts of the wave function along the Φ2 coordinate, which is caused by the change of the topology of the potential energy surface by the non resonant Stark laser pulse, cf. Figure 7. In the second half of the propagation, after 2000fs, the differences between both wave packets become noticeable. At this point, the different parts of the wave packet start to interfere within the Φ2 coordinate and again, as in the one dimensional case, one can have both constructive and destructive interference, depending on the initial phase of the starting wave function. Figure 9 depicts as an example a snapshot of the wave function in the S3 state at 2200 fs for the case a of symmetric initial wave function Ψs . One can clearly see the spreading of the wave packet along the Φ2 coordinate, causing interference between both individual parts and thus affecting the excited state dynamics. This interference along Φ2 will clearly depend on the sign pattern of the initial wave function (symmetric or antisymmetric) and thus cause a different interference pattern for both cases. Any sign difference along the Φ1 coordinate will, at least within the present time scale of up to 4000 fs, not cause any difference in the dynamics along the Φ1 coordinate since there is always a barrier between both potential wells keeping both parts of the wave packet well apart along this coordinate. In order to differentiate and discriminate nuclear spin isomers along Φ1 one would need to follow a slightly different strategy, for example by finding an optimized laser pulse sequence which in particular affects the potential energy barrier along Φ1 or by choosing other, more appropriate electronically excited states of the molecule.

4

Conclusion

This paper shows for 2-[4-(cyclopenta-2,4-dien-1-ylidene)-cyclohexa-2,5-dien-1-ylidene]-2H-1,3-dioxole, a quinodimethane derivate, the possibility to use the dynamical Stark effect

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to control the ratio between different nuclear spin isomers. The effect of the Stark shift is simulated using quantum dynamical wave packet propatations in one and two degrees of freedom based on potential energy surfaces, dipole moments and polarizabilities, which were calculated using quantum chemical ab initio methods. A moderate strong field is employed to change the topology of a potential energy, converting a local minimum into a local maximum. This temporally local maximum is used to trigger wave packet interferences, so that nuclear spin isomers can be differentiated. It was therefore demonstrated that one can use the dynamical Stark effect to drive the torsional dynamics of the excited state of the molecule along the desired pathway, such that, due to constructive or destructive interferences different nuclear spin isomers behave differently. This difference in the dynamics could be used in a pump-dump like experiment to separate the different nuclear spin isomers by changing the ratio between the isomers away from its equilibrium value.

Acknowledgement Rana Obaid, Daniel Kinzel and Jörn Manz are thanked for fruitful discussions. Financial support by the Deutsche Forschungsgemeinschaft via projects GO1059/7-3 and MA515/25-3 is gratefully acknowledged.

References (1) Gordon, R. J.; Rice, S. A. Active Control of the Dynamics of Atoms and Molecules. Ann. Rev. Phys. Chem. 1997, 48, 601–641. (2) Rice, S. A. Perspectives on the Control of Quantum Many-Body Dynamics: Applications to Chemical Reactions. Adv. Phys. Chem. 1997, 101, 213–283. (3) Rice, S. A.; Zhao, M. Optical Control of Molecular Dynamics; Wiley: New York, 2000. (4) Brixner, T.; Gerber, G. Quantum Control of Gas-Phase and Liquid-Phase Femtochemistry. ChemPhysChem 2003, 4, 418–438. 15



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(5) Dantus, M.; Lozovoy, V. V. Experimental Coherent Laser Control of Physicochemical Processes. Chemical Reviews 2004, 104, 1813–1860. (6) Ohmori, K. Wave-Packet and Coherent Control Dynamics. Annual Review of Physical Chemistry 2009, 60, 487–511. (7) Lozovoy, V. V.; Dantus, M. Laser Control of Physicochemical Processes; Experiments and Applications. Annu. Rep. Prog. Chem., Sect. C: Phys. Chem. 2006, 102, 227–258. (8) Shapiro, M.; Brumer, P. Quantum Control of Molecular Processes, 2nd ed.; Wiley: New York, 2012. (9) Tannor, D. J.; Kosloff, R.; Rice, A. Coherent Pulse Sequence Induced Control of Selectivity of Reactions: Exact Quantum Mechanical Calculations. J. Chem. Phys. 1986, 85, 5805–5820. (10) Elghobashi, N.; González, L.; Manz, J. Quantum Model Simulations of Symmetry Breaking and Control of Bond Selective Dissociation of FHF− using IR+UV Laser Pulses. J. Chem. Phys. 2004, 120, 8002–8014. (11) Elghobashi, N.; Krause, P.; Manz, J.; Oppel, M. IR + UV Laser Pulse Control of Momenta Directed to Specific Products: Quantum Model Simulations for HOD* -> H + OD versus HO + D. Phys. Chem. Chem. Phys. 2003, 5, 4806–4813. (12) Machholm, M.; Henriksen, N. E. Two-pulse Laser Control for Selective Photofragment Orientation. J. Chem. Phys. 1999, 111, 3051–3057. (13) Stark, J. Observation of the Separation of Spectral Lines by an Electric Field. Nature 1913, 92, 401–404. (14) Carmichael, H. J.; Walls, D. F. A Quantum-mechanical Master Equation Treatment of the Dynamical Stark Effect. J. Phys. B 1976, 9, 1199–1219.

16


Page 16 of 29

Page 17 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(15) Townsend, D.; Sussman, B. J.; Stolow, A. A Stark Future for Quantum Control. J. Phys. Chem. A 2011, 115, 357–373. (16) Sola, I. R.; Gonzalez-Vazquez, J.; de Nalda, R.; Banares, L. Strong Field Laser Control of Photochemistry. Phys. Chem. Chem. Phys. 2015, 17, 13183–13200. (17) Sussman, B. J.; Townsend, D.; Ivanov, M. Y.; Stolow, A. Dynamic Stark Control of Photochemical Processes. Science 2006, 314, 278–281. (18) Sanz-Sanz, C.; Richings, G. W.; Worth, G. A. Dynamic Stark Control: Model Studies based on the Photodissociation of IBr. Faraday Discuss. 2011, 153, 275–291. (19) Han, Y.-C.; Yuan, K.-J.; Hu, W.-H.; Cong, S.-L. Control of Photodissociation and Photoionization of the NaI Molecule by Dynamic Stark Effect. J. Chem. Phys. 2009, 130, 044308. (20) Kinzel, D.; Marquetand, P.; González, L. Stark Control of a Chiral Fluoroethylene Derivative. J. Phys. Chem. A 2012, 116, 2743–2749. (21) Richings, G. W.; Worth, G. A. Non-Resonant Dynamic Stark Control at a Conical Intersection: The Photodissociation of Ammonia. J. Phys. Chem. A 2012, 116, 11228– 11240. (22) Balerdi, G.; Corrales, M. E.; Gitzinger, G.; González-Vázquez, J.; Solá, I. R.; Loriot, V.; Nalda, R. d.; Bañares, L. Dynamic StarkSshift of the 3 R1 Rydberg State of CH3 I. EPJ Web of Conferences 2013, 41, 02035. (23) Vindel-Zandbergen, P.; Falge, M.; Chang, B. Y.; Engel, V.; Sola, I. R. Manipulating the Singlet-triplet Transition in Ion Strings by Nonresonant Dynamic Stark Effect. Theor Chem Acc 2013, 132, 1–10. (24) Sala, M.; Saab, M.; Lasorne, B.; Gatti, F.; Guérin, S. Laser Control of the Radiationless Decay in Pyrazine using the Dynamic Stark Effect. J. Chem. Phys. 2014, 140, 194309. 17



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(25) Scheit, S.; Arasaki, Y.; Takatsuka, K. Control Scheme of Nonadiabatic Transitions with the Dynamical Shift of Potential Curve Crossing. J. Chem. Phys. 2014, 140, 244115. (26) Bonhoeffer, K.; Harteck, P. Weitere Versuche mit Parawasserstoff. Naturwissenschaften 1929, 17, 321–322. (27) Sandler, Y. L. The Adsorption and Ortho-Para Conversion of Hydrogen on Diamagnetic Solids. II. The Relative Adsorbabilities of Orthohydrogen and Parahydrogen. J. Phys. Chem. 1954, 58, 58–61. (28) Cunningham, C. M.; Johnston, H. L. The Surface Catalysis of the Ortho- to ParaConversion in Liquid Hydrogen by Paramagnetic Oxides on Alumina. J. Am. Chem. Soc. 1958, 80, 2377–2382. (29) Gel’mukhanov, F. K.; Shalagin, A. M. Light-induced Diffusion of Gases. J. Exp. Theor. Phys. Lett. 1979, 29, 711. (30) Panfilov, V.; Strunin, V.; Chapovsky, P. L. Light-induced Drift of CH3 F Molecules. Sov. Phys. J. Exp. Theor. Phys. 1983, 58, 510–515. (31) Chapovsky, P. L.; Krasnoperov, L. N.; Panfilov, V. N.; Strunin, V. P. Studies on Separation and Conversation of Spin Modification of CH3 F Molecules. Chem. Phys. 1985, 97, 449–455. (32) Bakarev, A. E.; Chapovsky, P. L. Anomalously large Isotopic Effect Observed in the Conversion of Different Nuclear-spin Modifications of CH3 F Molecules. J. Exp. Theor. Phys. Lett. 1986, 44, 4–6. (33) Chapovsky, P. L. Conversion of Nuclear Spin Modifications of CH3 F Molecules in the Gaseous Phase. Sov. Phys. J. Exp. Theor. Phys. 1990, 70, 895–901. (34) Chapovsky, P.; Cosléou, J.; Herlemont, F.; Khelkhal, M.; Legrand, J. Separation and

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Page 18 of 29

Page 19 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Conversion of Nuclear Spin Isomers of Ethylene. Chem. Phys. Letters 2000, 322, 424– 428. (35) Peters, G.; Schramm, B. Nuclear Spin State Relaxation in Formaldehyde: Dependence of the Rate Constant on Pressure. Chem. Phys. Letters 1999, 302, 181–186. (36) Sun, Z.-D.; Takagi, K.; Matsushima, F. Separation and Conversion Dynamics of Four Nuclear Spin Isomers of Ethylene. Science 2005, 310, 1938–1941. (37) Tikhonov, V. I.; Volkov, A. A. Separation of Water into Its Ortho and Para Isomers. Science 2002, 296, 2363. (38) Kravchuk, T.; Reznikov, M.; Tichonov, P.; Avidor, N.; Meir, Y.; Bekkerman, A.; Alexandrowicz, G. A Magnetically Focused Molecular Beam of Ortho-Water. Science 2011, 331, 319–321. (39) Sun, Z.-D.; Ge, M.; Zheng, Y. Separation and Conversion Dynamics of Nuclear-Spin Isomers of Gaseous Methanol. Nat Commun 2015, 6, 6877. (40) Horke, D. A.; Chang, Y.-P.; Długoł¸ecki, K.; Küpper, J. Separating Para and Ortho Water. Angew. Chem. Intern. Ed. 2014, 53, 11965–11968. (41) Deeb, O.; Leibscher, M.; Manz, J.; von Muellern, W.; Seideman, T. Toward Separation of Nuclear Spin Isomers with Coherent Light. ChemPhysChem 2007, 8, 322–328. (42) Grohmann, T.; Deeb, O.; Leibscher, M. Quantum Separation of Para- and Orthofulvene with Coherent Light: The Influence of the Conical Intersection. Chem. Phys. 2007, 338, 252 – 258. (43) Belz, S.; Grohmann, T.; Leibscher, M. Quantum Dynamical Simulations for Nuclear Spin Selective Laser Control of Ortho- and Para-fulvene. J. Chem. Phys. 2009, 131, 034305.

19



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(44) Grohmann, T.; Leibscher, M. Nuclear Spin Selective Alignment of Ethylene and Analogues. J. Chem. Phys. 2011, 134, 204316. (45) Floß, J.; Grohmann, T.; Leibscher, M.; Seideman, T. Nuclear Spin Selective Laser Control of Rotational and Torsional Dynamics. J. Chem. Phys. 2012, 136, 084309. (46) Obaid, R.; Kinzel, D.; Oppel, M.; González, L. Discrimination of Nuclear Spin Isomers Exploiting the Excited State Dynamics of a Quinodimethane Derivative. J. Chem. Phys. 2014, 141, 164323. (47) Obaid, R.; Kinzel, D.; Oppel, M.; González, L. Separating Nuclear Spin Isomers using a Pump-Dump Laser Scheme. Theor Chem Acc 2015, 134, 46. (48) Tanner, C. M.; Quack, M.; Schmidiger, D. Nuclear Spin Symmetry Conservation and Relaxation in Water (1H216O) Studied by Cavity Ring-Down (CRD) Spectroscopy of Supersonic Jets. J. Phys. Chem. A 2013, 117, 10105–10118. (49) Belz, S.; Deeb, O.; González, L.; Grohman, T.; Kinzel, D.; Leibscher, M.; Manz, J.; Obaid, R.; Oppel, M.; Xavier, G. D. et al. Nuclear Spin Selective Torsional States: Implications of Molecular Symmetry. Z. Phys. Chem. 2013, 227, 1021–1048. (50) Feit, M. D.; Fleck Jr., J. A. Solution of the Schrödinger Equation by a Spectral Method. J. Chem. Phys. 1983, 78, 301–308. (51) Leforestier, C.; Bisseling, R. H.; Cerjan, C.; Feit, M. D.; Friesner, R.; Guldberg, A.; Hammerich, A.; Jolicard, G.; Karrlein, W.; Meyer, H.-D. et al. A Comparison of Different Propagation Schemes for the Time Dependent Schrödinger Equation. J. Comput. Phys. 1991, 94, 59–80. (52) Lehtovaara, L.; Toivanen, J.; Eloranta, J. Solution of Time-independent Schrödinger Equation by the Imaginary Time Propagation Method. J. Comput. Phys. 2007, 221, 148–157. 20


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(53) Roos, B. O.; Taylor, P. R.; Siegbahn, P. E. M. A Complete Active Space SCF Method (CASSCF) using a Density Matrix Formulated Super-CI Approach. Chem. Phys. 1980, 48, 157–173. (54) Dunning Jr., T. H. Gaussian Basis Sets for use in Correlated Molecular Calculations. I. The Atoms Boron through Neon and Hydrogen. J. Chem. Phys. 1989, 90, 1007–1023. (55) Werner, H.-J.; Knowles, P. J.; Knizia, G.; Manby, F. R.; Schütz, M.; Celani, P.; Korona, T.; Lindh, R.; Mitrushenkov, A.; Rauhut, G. et al. MOLPRO, version 2012.1, a Package of Ab Initio Programs. http://www.molpro.net, accessed: 2016-01-27. (56) Koch, V.; Andrae, D. Static Electric Dipole Polarizabilities for Isoelectronic Sequences. Int. J. Quantum Chem. 2011, 111, 891–903. (57) A. D. Bandrauk, E. E. A.; Gauthier, J.-M. In Molecules in Laser Fields; Bandrauk, A. D., Ed.; Marcel Dekker, New York, 1993. (58) Garraway, B. M.; Suominen, K.-A. Adiabatic Passage by Light-Induced Potentials in Molecules. Phys. Rev. Lett. 1998, 80, 932–935. (59) Chang, B. Y.; Shin, S.; Santamaria, J.; Sola, I. R. Bond Breaking in Light-induced Potentials. J. Chem. Phys. 2009, 130, 124320.

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Z

C 2

B

X

1

A

Figure 1: Sketch of the quinodimethane derivative 2-[4-(cyclopenta-2,4-dien-1-ylidene)-cyclohexa-2,5-dien-1-ylidene]-2H-1,3-dioxole (abbreviated CCD), which is used as an example to demonstrate the discrimination of nuclear spin isomers making use of the dynamic Stark effect. A, B and C depicts the three fragments inducing the two torsional motions along Φ1 and Φ2 . While these torsions are hindered in the electronic ground state, the molecule can rotate around these angles in the electronically excited states. The character (symmetric or antisymmetric) of this torsional fraction of the overall wave function is complementary to the character of the nuclear spin wave function, leading to a difference in the torsional motion for the different nuclear spin isomers.

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Figure 7: Electronic excited state potential S3 without (a) and with (b-c) the effect of external fields. The potential energy surface is time-dependent modified through the dynamic Stark effect by means of the non-resonant low frequency laser pulse shown in Fig. 6b). Depicted are the most positive (b) and most negative (c) interaction with the electric field strength at 2160 fs and 2360 fs, respectively.

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Controlling the Excited-State Dynamics of Nuclear Spin Isomers Using

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