Effect of Vibrational Pre-Excitation on the ... - ACS Publications

Subscriber access provided by ORTA DOGU TEKNIK UNIVERSITESI KUTUPHANESI

Article 2+

Effect of Vibrational Pre-Excitation on the Dissociation Dynamics of HOD Diptesh Dey, and Ashwani Kumar Tiwari J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b01947 • Publication Date (Web): 08 Apr 2016 Downloaded from http://pubs.acs.org on April 11, 2016

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry A is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 22

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

The Journal of Physical Chemistry

Effect of Vibrational Pre-excitation on the Dissociation Dynamics of HOD2+ Diptesh Dey and Ashwani K. Tiwari∗ Indian Institute of Science Education and Research Kolkata, Mohanpur 741246, India E-mail: [email protected] Phone: +91 (0)33 66340000. Fax: +91 (0)33 25873020

Abstract Preferential breaking of chemical bonds using few cycle, intense laser pulse to obtain desired products offer formidable challenge in understanding ultra-fast chemical reactivity. In a recent study [J. Chem. Phys. 2015, 143, 244310], it was found that carrier envelop phase (CEP) influences the bond-selective fragmentation in HOD with upto three-fold enhancement. In this paper we present a detailed theoretical study to understand the influence of initial vibrational states governing the dissociation dynamics. We have carried out a time-dependent quantum mechanical wave packet study on 3 B1 ) of HOD2+ . Analytical potential energy surface for the ground electronic state (X the ground electronic states of both the neutral molecule and dication has been developed at multi-reference configuration interaction level of theory with aug-cc-pVQZ basis set. Branching ratio is computed from the accumulated flux in H + + OD+ and D+ + OH + dissociation channels. Our investigation demonstrate a strong dependency on the initial conditions and thereby preferential cleavage of bonds can be achieved. We have also compared our results with experimental and other theoretical studies. ∗

To whom correspondence should be addressed

1 ACS Paragon Plus Environment


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

Page 2 of 22

Introduction With the advent of femtosecond laser systems in the last few decades, 1 it has become possible to probe elementary chemical processes on the scale of molecular motions. Femto-chemistry experiments provides a better understanding of the dynamics of chemical reactions at a microscopic level and therefore, it has been a subject of considerable interest. Femtosecond laser pulses have also been used as molecular scissor with the aim to selectively cleave a chemical bond to obtain desired products in a chemical reaction. 2 Recent advances in laser technology has made it possible to generate few cycle, ultrashort, intense laser fields with a pulse duration of the order of vibrational time period of A molecules. 3,4 Intensity of these fields has a magnitude typically of the order of 50V ˚

−1

i.e. it

matches with the strength of intra-molecular Coulomb forces. Exposure of molecules to such fields results in field-induced ejection of electrons, leaving behind ionic cores that experience strong Coulombic repulsion which results in the rupturing of one or more bonds. Such strong field experiments have been carried out on H2 O and HOD molecules. 4–6 Attempts have been made to understand experimental observations by carrying out quantum chemical and classical/quantum dynamical calculations. Rajgara et al. reported the formation of H2+ upon exposure of H2 O molecule to intense, ultrashort (9.3f s) laser pulses. 4 This bond formation under the influence of strong field was ultrafast as it happens within a single laser pulse. Mechanism of the formation of H2+ in this experiment was explained by Garg et al. by carrying out time-dependent quantum mechanical (TDQM) calculations on an ab initio potential energy surface (PES). 5 Their TDQM calculations showed that formation of H2+ takes place on water dication PES via a migratory mechanism. On dication PES, a proton generated from OH bond rapture, migrates towards H atom and forms H2+ molecule. Very recently, Mathur et al. reported three fold enhancement of preferential bond breaking in HOD2+ under the influence of intense 2-cycle pulse of 800nm laser light. 6 This was explained qualitatively by carrying out time-dependent quantum mechanical wave packet calculation. Legendre et al. 7 reported kinetic energy release distributions in the ion-induced fragmen2 ACS Paragon Plus Environment

Page 3 of 22

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


tation dynamics of HOD2+ both by imaging technique as well as by semi-classical model calculations. They found a strong isotopic effect in the fragmentation dynamics of HOD2+ with a preferential cleavage of the O − H bond. Gervais et al. investigated the contribution of eight potential energy surfaces of the dication which can lead to the formation of H + + OD+ and D+ + OH + using classical molecular dynamics simulation. 8 They reported a very strong dependency of branching ratio between two channels on initial conditions. The branching ratio obtained in HOD2+ dissociation by Franck-Condon transition from ground state of neutral HOD molecule to HOD2+ (first initial condition) was quite different from the branching ratio obtained by Franck-Condon transition from ground and first excited states of HOD+ to the HOD2+ (second initial condition). Influence of other initial conditions, like initial rotational and vibrational states of HOD molecule, on dissociation dynamics of HOD2+ is yet to understand. Previous studies 9–19 showed that weak-field unimolecular photodissociation dynamics of HOD strongly depends on the initial vibrational state of HOD molecule. In this article, we would like to answer the question: Does the dissociation dynamics of HOD2+ depend on the initial vibrational state of HOD molecule as in the case of HOD photodissociation? To explain this, we carried out a time-dependent quantum mechanical wave packet calculation on a newly developed ab initio potential energy surface of HOD2+ generated at the multireference configurational interaction level of theory with aug-cc-pVQZ basis set. Nuclear wave packet (WP) from the ground electronic state of neutral molecule is vertically pumped to the ground electronic state of dication where it is then propagated. Branching ratio of the two dissociation channels has been computed in order to understand the influence of initial vibrational states in the fragmentation dynamics. The remainder of the paper is organized as follows. In Sec. II we describe theoretical method used in the present work. Sec. III briefly describes the functional form used to fit ab initio data points and presents the PES of neutral and dication molecules. Results are discussed and compared with previous experimental and theoretical studies in Sec. IV. Conclusions are summarized in Sec. V.



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

Page 4 of 22

Methodology Quantum dynamics of selective bond-breaking in isotopically-substituted water dication upon application of intense laser pulses to gas-phase water molecules has been studied by numerically solving the time-dependent Born-Oppenheimer Schrödinger equation 5,20,21 in internal (bond-length bond-angle) coordinates. We have considered a two degree of freedom model where only stretching of O − H and O − D bonds are allowed and the bending is neglected due to weak coupling between the stretching and bending modes. The internal kinetic energy operator in terms of associated conjugate momenta pOH and pOD is given by pˆ2 pˆ2 pˆ pˆ Tˆ = OH + OD + OH OD cosθeq , 2μOH 2μOD mO

(1)

where the reduced masses are μOH = mO mH /(mO + mH ) and μOD = mO mD /(mO + mD ), and θeq is the bond angle fixed at equilibrium value. Influence of an ultra-short, intense laser field on a molecule can be closely approximated by a δ-function pulse. Therefore, we assume a Franck-Condon (FC) transition of the initial nuclear wave packet (t = 0) in ground electronic state of HOD to the ground electronic state of HOD2+ following the δ-pulse excitation. Considering the fact that these intense pulses may also induce structural deformation in the molecule, a small error may be incorporated on promotion of the replica of the initial WP to the dication surface. Time evolution associated with the nuclear motion can then be evaluated by propagating the wave packet on dication potential energy surface as follows

Ψ(t + Δt) = exp(

ˆ −iHΔt )Ψ(t).

(2)

Since the vibrational stretching frequencies of O − H and O − D are basically local modes, the vibrational ground state wave function of HOD were obtained as a product of the wave function of individual modes calculated using Fourier Grid Hamiltonian (FGH) method. 22


Page 5 of 22

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


The eigen-frequencies compare quite well with the reported values of Amstrup and Henriksen 13 where the vibrational ground state wave function is obtained via imaginary time propagation method. 23 The action of exponential operator containing the kinetic energy part of Hamiltonian is evaluated using a two dimensional fast Fourier transform (FFT) algorithm. 24 Time propagation of the wave packet is carried out using split-operator (SO) method. 25 Extent of dissociation in the respective channels have been calculated from the time- and space-integrated outgoing flux through a dividing line for a particular nuclear coordinate given by

JH + +OD+ =

μH−OD

t 0

dt

rOD rOD

max

drOD Im Ψ(rOH , rOD , t)

min

∂Ψ (rOH , rOD , t) , × ∂rOD r OH ∗

(3)

f

where μH−OD is the (H, OD) reduced mass. Similar expression holds for the flux in D+ +OH + dissociation channel. The wave packet is multiplied by a damping function 26 in order to avoid numerical errors due to unphysical reflection from the boundaries of a finite-sized grid. Numerical parameters used in this calculation are listed in Table 1. Table 1: Grid Parameters used in the present calculation. Parameters

Values

Description

(rOHmin , rOHmax )/a0 (rODmin , rODmax )/a0 (NrOH , NrOH ) (rOHf , rODf )/a0

(1.0,11.71) (1.0,11.71) (256,256) (8.2,8.2)

Range of rOH values Range of rOD values Number of grid points Flux analysis surface

(rOHd , rODd )/a0 Δt/f s T /ps

(8.52,8.52) 0.02419 0.48377

Starting point of WP damping Time step used in propagation Total propagation time



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

θ=180°

θ=120°

θ=60°

2

4

6

8

θ=150°

Page 6 of 22

8

6

6

4

r /a 4 OD 0

2

2

8

θ=90°

8

6

6

4

r /a 4 OD 0

2

2

8

θ=30°

8

6

6

4

r /a 4 OD 0

2

2

8

2

rOH / a0

4

6

8

rOH / a0

1 A1 ) potential Figure 1: Two-dimensional contour plots of the ground electronic state (X energy surface of HOD for different bending angles.

Potential Energy Surface 1 A1 ) surface Analytical fit of HOD(X Ab initio energies are calculated at multireference configuration interaction (MRCI) level of theory with Dunning’s augmented correlation-consisted polarized valence quadruple-ζ (augcc-pVQZ or AVQZ) basis set using MOLPRO 27 suite of programs. A set of 2257 ab initio data points were generated varying the internuclear distances from 1.0a0 to 9.0a0 with a denser grid around the equilibrium region and for bond angles of 30◦ , 60◦ , 90◦ , 120◦ , 150◦ , and 180◦ . Computed ab initio potential energy values are then fitted to a functional form using 6 ACS Paragon Plus Environment

Page 7 of 22

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


8

8

θ=180° 6

θ=150° 6

4

r /a 4 OD 0

2

2

8

8

θ=120° 6

θ=90°

4

r /a 4 OD 0

2

2

8 θ=60°

2

4

6

6

θ=30°

8

6

6

4

r /a 4 OD 0

2

2

8

2

rOH / a0

4

6

8

rOH / a0

3 B1 ) potential Figure 2: Two-dimensional contour plots of the ground electronic state (X 2+ energy surface of HOD for different bending angles.

many-body expansion method 28–30 to generate the ground state potential energy surface of HOD. For a triatomic system ABC (with A = H, B = O, and C = D) the analytic expression is written as (2) VABC (RAB , RBC , RAC ) = VA(1) + VB(1) + VC(1) + VAB (RAB ) (2) (2) + VBC (RBC ) + VAC (RAC ) (3) + VABC (RAB , RBC , RAC ).


(4)


θ = 30° θ = 60° θ = 120° θ = 150° θ = 180°

V / Hartree

0.2

0.1

0 0.2

V / Hartree

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

Page 8 of 22

0.1

(b) HOD2+, rOD = 2.0 a0 (a) HOD, rOD = 1.81 a0 θ = 30° θ = 60° θ = 90° θ = 120° θ = 150°

0

-0.1

-0.2 2

4 rOH / a0

6

8

Figure 3: Cuts of the fitted PES along with ab initio points, fixing one of the bond lengths at its equilibrium value and varying the bond angles for (a) HOD and (b) HOD2+ .

(2) The two-body term VAB is given by

c e−αAB RAB i + ci ρAB , VAB (RAB ) = 0 RAB i=1 L

(2)

(5)

with Rydberg type variables (l)

ρAB = RAB e−βAB RAB .

(6)

(2) (2) (3) Similar expressions hold for VBC and VAC . The three-body term VABC is given by

(3) VABC (RAB , RBC , RAC ) =

M

dijk ρiAB ρjBC ρkAC ,

(7)

i,j,k

with the following constraints

i + j + k = i = j = k,

(8a)

i + j + k ≤ M.

(8b)


Page 9 of 22

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


The energy of three infinitely separated atoms, H + O + D, in their ground state has been taken to be the zero of energy. Two-dimensional contour maps of the PES for a fixed internal bond angle θ = 180◦ , 150◦ , 120◦ , 90◦ , 60◦ , and 30◦ are given in Fig. 1. Contour lines are equally spaced by 0.0075Eh , starting from −0.3675Eh . The fitted surface has a root-mean-square (r.m.s.) deviation of 0.6775kcal/mol compared to the ab initio values. Parameters resulting from the analytical fit are presented in the Supporting Information. Fig. 3(a) compares the cuts of the potential energy surface for different bond angles, fixing one of the bond length at its equilibrium value with the set of ab initio data points. Except for very small distance, at a bond angle of θ = 30◦ , the fitting is quite accurate. The ground electronic state of HOD is symmetrical with a deep potential energy well of 42910.66cm−1 with respect to D + OH asymptote for θ = 104.45◦ and equivalent dissociation channels along both the O − H and O − D separations.

3 B1 ) surface Analytical fit of HOD2+ (X Similar procedure has been adapted to generate the ground state potential energy surface of HOD2+ by fitting a set of 2557 ab initio data points calculated at the same level of theory. The internuclear distance has been varied from a denser grid around the equilibrium region to a coarser grid in the non-equilibrium regions for bond angles of 30◦ , 60◦ , 90◦ , 120◦ , 150◦ , and 180◦ to ensure an accurate fitting. The energy of three infinitely separated atoms, H + + O + D+ , in their ground state has been taken to be the zero of energy. Contour plots of the PES for a fixed internal bond angle θ = 180◦ , 150◦ , 120◦ , 90◦ , 60◦ , and 30◦ are given in Fig. 2. The fitted surface has a root-mean-square (r.m.s.) deviation of 0.9231kcal/mol compared to the ab initio values. Contour lines are equally spaced by 0.0075Eh , starting from −0.3675Eh . This contour map is very similar to the fitted PES by Garg et al. 5 but more detailed as in this case we have computed more number of data points. Their fitted surface has a r.m.s. deviation of 6.18kcal/mol. Parameters obtained from the analytical fit can be found in the Supporting Information. 9 ACS Paragon Plus Environment


Cuts of the PES for different bond angle are plotted as a function of O − H + bond length in Fig. 3(b) along with the ab initio values. Clearly, there is a very good agreement between the ab initio and fitted values. This PES is mainly repulsive with the appearance of shallow bound state on increasing bond angles. The FORTRAN subroutines describing the PES of HOD and HOD2+ will be available on request.

Results and Discussion 1

+ + H + OD D+ + OH+

0.8

0.6 Flux (J)

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

0.4

0.2

0

|0,0>

0

20

40

60

80 t / fs

100 120 140

Figure 4: Flux accumulated along the two dissociation channels as a function of time for an excitation from the vibrational ground state of HOD.

Upon Franck-Condon transition, following a δ-pulse excitation, complete population transfer occurs from HOD → HOD2+ state. The dicationic ground electronic state being very slightly bound, the initial wave packet eventually moves into either H + + OD+ or D+ + OH + channels. For an excitation from the lowest vibrational state (|0, 0) of HOD, we have plotted the fluxes obtained in both H + + OD+ and D+ + OH + product channels as a function of time in Fig. 4. Our results shows that about 74.4% of the flux moves in H + +OD+ 10 ACS Paragon Plus Environment

Page 10 of 22

Page 11 of 22

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


channel compared to about 25.5% of the flux in D+ + OH + channel. It indicates a higher probability for breaking of the O − H bond as compared to that of O − D bond. The branching ratio defined as the ratio of flux in H + + OD+ channel over D+ + OH + channel in the long time limit is found to be nearly 2.917. This finding can be explained by the difference in masses between deuterium and proton which results in different bond stretching frequencies when they are allowed to move on the same repulsive potential. Previous investigations 9–19 on the photodissociation of HOD on its first excited state potential energy surface gave similar results. It is important to mention that classical trajectory calculations 8 on HOD2+ gave the value of branching ratio 8.6 which is quite different from quantum results. They have simulated the dissociation dynamics by means of three body classical molecular dynamics on an ab initio PES generated using cc-pV5Z basis set at MRCI level of theory, for bending angles θ ≥ 80◦ and O −H distances between 1.0 to 6.5 a.u.. Their PES showed a deviation of 10−3 a.u. from the calculated data. Wigner phase space distribution was used to sample the initial conditions (i.e., positions and momenta of the atoms), which was obtained from the Wigner transform of vibrational ground state wave function of three independent harmonic oscillators. Whereas, the highly charged ion-induced HOD2+ fragmentation dynamics study using recoil ion momentum spectroscopy and classical dynamics simulation study 7 showed a branching ratio of 6.5 ± 0.5 and 13.2 : 1 respectively. Nearly two times higher branching ratio found in the classical simulation study was qualitatively argued as a possibility of the involvement of dication excited states. A proper interpretation of this observed higher branching ratio was given by Henriksen et. al. 15 for the photodissociation of HOD using semi-classical Wigner method. They have showed that actually initial momentum distribution plays the vital role on determining branching ratio and slight asymmetry (isotope effect) in the initial state has practically no role. Their results were in good agreement with exact quantum dynamical studies. Trajectories will only lead to D + OH channel when they are associated with positive value of pOD . Branching ratio gets severely overestimated on neglecting the initial momentum distribution.



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

Now we will focus on the effect of initial vibrational excitation on the dissociative dynamics of the dication into respective channels. At first, we made a prior vibrational excitation on the O − H stretching modes keeping the O − D mode at a zero quantum of excitation. In Fig. 5 (upper panels) we have plotted the fluxes obtained in respective channels with upto four quanta of excitation in the O−H mode. These plots indicate that as we move from |0, 0 to |1, 0 state, counter-intuitively, there is an anomalous decrease in flux for the H + + OD+ channel and an increase in flux for the D+ + OH + channel. This behaviour is different from the photodissociation of HOD, where branching ratio for |1, 0 state has a larger value than that of |0, 0 state. 17 It is also evident from Fig. 5 that the flux in H + +OD+ channel is larger for |1, 0 as compared to that of |0, 0 at early time (upto 27.5 fs). But after 27.5 fs, there is a crossing between the flux plots for |1, 0 and |0, 0 and at long time limit the flux for |0, 0 is larger compared to that of |1, 0 case. To understand this, we looked into the snapshots of the wave packet at different time and found that part of the wave packet for |1, 0 state recross towards the D+ + OH + channel. This may be attributed (non-adiabatically) to an effective bond strength (of H over D with O) as a function of the initial vibrational quantum number. As we further increase the quanta of excitation in the O − H mode, an increase in flux is obtained for the H + + OD+ channel compared to that of |1, 0 state. It is expected as now the O − H bond is more stretched which favours easy break-up of the loosely bound H + . Further vibrational excitation of the O − H mode leads to an addition of flux in the H + + OD+ channel and diminution for the D+ + OH + channel. Pre-excitation of |4, 0 state gives a maximum yield in the H + + OD+ channel, whereas, pre-excitation of |1, 0 state gives maximum yield in the D+ + OH + channel. If we reverse the process with a prior vibrational excitation in the O − D mode and zero quantum of excitation in the O − H mode then our findings support an easy break-up of O − D channel with 31.5% of flux obtained for |0, 1 state compared to 25.5% obtained for |0, 0 state. Fig. 5 (lower panels) shows the variation of flux in different channels with the progress in time. Further excitation enhances the yield in D+ + OH + channel. For pre-excitation in O − D mode, yield in D+ + OH +


Page 12 of 22

Page 13 of 22

|0,0> |1,0> |2,0> |3,0> |4,0>

1 0.9

Flux (J)

0.8

0.9 0.8 0.7

0.6

0.6

0.5

0.5

0.4

0.4

0.3

0.3

0.2

0.2 (a) H+ + OD+

0 |0,0> |0,1> |0,2> |0,3> |0,4>

1 0.9 0.8

0.1

|0,0> |0,1> |0,2> |0,3> |0,4>

1 0.9 0.8 0.7

0.6

0.6

0.5

0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1

+

+

0.1

(c) H + OD 0

(b) D+ + OH+

0

0.7

0

|0,0> |1,0> |2,0> |3,0> |4,0>

1

0.7

0.1

Flux (J)

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


50

100

+

150

t / fs

+

(d) D + OH

0 0

50

100

150

t / fs

Figure 5: Flux accumulated along the two dissociation channels as a function of time by varying the quanta of excitation of each modes.

channel increases with increase in quanta of excitation, whereas yield in H + + OD+ channel decreases with increase in quanta of excitation. This can be explained in a similar way due to an increase in the stretching of the bond upon further excitation. The branching ratio obtained for |0, 4 state is found to be 0.816 (i.e. less than unity), with about 45% of flux in the H + + OD+ channel and 55.1% of flux in the D+ + OH + channel. Corresponding branching ratios and fluxes obtained are reported in Table 2. To examine the sensitivity of branching ratio to vibrational pre-excitation, the branching ratio for different vibrational modes are plotted in Fig. 6 (upper panel). It is clear that on exciting O − H mode from 0 to 1, value of branching ratio decreases from 2.917 to 2.123. On



3.5 |4,0> Branching Ratio (Γ)

3

|0,0>

|3,0> |2,0>

2.5 |1,0> 2

|0,1>

1.5 1

|0,2> (a) Present study

0.5

Γ-stabilize/Γ-unstabilize

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

Page 14 of 22

3.0

|0,3>

|0,4>

|nOH, nOD> (b) Mathur et al.

2.5

2.0

1.5 -180

-90 -45 0 45 90 CEP / degrees

180

Figure 6: (a) Theoretically observed branching ratio for different vibrational initial states and (b) experimentally obtained CEP-stabilized branching ratio.

further pre-excitation of the O − H mode, branching ratio starts increasing with the increase in quanta of excitation. Pre-exciting O − D mode, branching ratio decreases with increase in quanta of excitation. Furthermore, value of the branching ratio is greater than unity for pre-excited states |0, 1 and |0, 2. In case of |0, 3 state it is almost unity, suggesting an equal probability of cleavage of either of the bonds. Whereas, |0, 4 pre-excitation causes the branching ratio to become even lesser than unity. It suggests that the cleavage of O−D bond is preferred over the cleave of O − H bond for this state. These branching ratio values are compared with the recently reported CEP-dependent experimental values of branching ratio 6 (lower panel of Fig. 6). In this experiment, HOD molecules were exposed to very intense


Page 15 of 22

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


2-cycle 800nm laser pulses resulting in the formation of dication which finally dissociates into either H + + OD+ or D+ + OH + . It is clear from Fig. 6 that the branching ratio versus vibrational mode plot and branching ratio versus CEP plot have very similar structure. This suggest that CEP-dependency of branching ratio is probably due to the fact that laser pulses with different CEP causes excitation in the vibrational modes of HOD before it ionizes to dication. It has been shown in a previous study 31 on state-selective vibrational excitation of H2+ that CEP plays an important role on population transfer. To fully understand the CEP-dependency of branching ratio, one really needs to carry out coupled electron-nuclear dynamics under the influence of intense laser fields. These studies are in progress and will be published subsequently. Table 2: Branching ratio obtained for Franck-Condon transition from different initial states |nOH , nOD

(H + + OD+ )

(D+ + OH + )

H + +OD + D + +OH +

|0, 0 |1, 0 |0, 1 |2, 0 |0, 2 |3, 0 |0, 3 |4, 0 |0, 4

0.744 0.669 0.620 0.704 0.550 0.731 0.495 0.747 0.450

0.255 0.315 0.368 0.282 0.452 0.255 0.505 0.237 0.551

2.917 2.123 1.684 2.496 1.216 2.866 0.980 3.151 0.816

In order to check the sensitivity of branching ratio on the bending angle we have performed calculations at other fixed angles and our results are tabulated in Table 3. Almost negligible effect is found for the bending angles ranging from 110 − 180◦ in which range PES shows a bound state, suggesting the validity of our two degree of freedom model.



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

Table 3: Branching ratio dependency on bending angle |nOH , nOD 0, 0

1, 0

0, 1

2, 0

0, 2

3, 0

0, 3

4, 0

0, 4

θ◦ 179.88 150 120 179.88 150 120 179.88 150 120 179.88 150 120 179.88 150 120 179.88 150 120 179.88 150 120 179.88 150 120 179.88 150 120

H + +OD+ D + +OH +

2.917 3.04 3.407 2.123 2.18 2.27 1.684 1.73 1.951 2.496 2.52 2.55 1.216 1.25 1.39 2.123 2.18 2.27 2.866 2.90 2.92 3.151 3.205 3.264 0.816 0.83 0.91


Page 16 of 22

Page 17 of 22

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


Summary and Conclusion We have performed a time-dependent quantum mechanical wave packet calculation to study the influence of different vibrational initial states on the dissociation dynamics of HOD2+ on a newly developed PES. The ab initio data points were generated at MRCI level of theory and then fitted to a functional form using many-body expansion technique. Dissociation of water dication is assumed to take place in its ground electronic state following a Franck-Condon transition of the nuclear WP of the parent HOD molecule in its ground electronic state. The observed branching ratio of 2.917 (from |0, 0) indicates a strong preference for the cleavage of O − H bond rather than O − D. Classical dynamics simulation suggests a branching ratio of 8.6, which is quite high. The reason for this is that initial momentum distribution and not the slight asymmetry in initial state which plays the vital role in determining branching ratio. With a prior vibrational excitation of O − H mode, initially there is a decrease in branching ratio, after which it starts increasing on further excitation. Whereas, vibrational pre-excitation of O − D mode causes the branching ratio to gradually decrease. Pre-exciting vibrational modes causes the respective bonds to stretch and therefore an increase in flux for that channel. The above study indicates a possibility to selectively dissociate a molecule into respective channels with simply exciting its vibrational modes, similar to the recent study on selective breaking of bonds using different CEP-dependent pulses.

Acknowledgement D.D. gratefully acknowledges the University Grants Commission (UGC), New Delhi for the Senior Research Fellowship.

Supporting Information Coefficients used for analytical fitting of HOD and HOD2+ potential energy surfaces.



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

References (1) Zewail, A. H. Femtochemistry: Atomic-Scale Dynamics of the Chemical Bond Using Ultrafast Lasers. Angew. Chem. Int. Ed. 2000, 39, 2586–2631. (2) Crim, F. F. State- and Bond-Selected Unimolecular Reactions. Science 1990, 249, 1387–1392. (3) Dota, K.; Garg, M.; Tiwari, A. K.; Dharmadhikari, J. A.; Dharmadhikari, A. K.; Mathur, D. Intense Two-Cycle Laser Pulses Induce Time-Dependent Bond Hardening in a Polyatomic Molecule. Phys. Rev. Lett. 2012, 108, 073602(1)–073602(4). (4) Rajgara, F. A.; Dharmadhikari, A. K.; Mathur, D.; Safvan, C. P. Strong fields induce ultrafast rearrangement of H atoms in H2O. J. Chem. Phys. 2009, 130, 231104(1)– 231104(4). (5) Garg, M.; Tiwari, A. K.; Mathur, D. Quantum dynamics of proton migration in H2O dications: H2+ formation on ultrafast timescales. J. Chem. Phys. 2012, 136, 024320(1)– 024320(9). (6) Mathur, D.; Dota, K.; Dey, D.; Tiwari, A. K.; Dharmadhikari, J. A.; Dharmadhikari, A. K.; De, S.; Vasa, P. Quantum dynamics of proton migration in H2O dications: H2+ formation on ultrafast timescales. J. Chem. Phys. 2015, 143, 244310(1)– 244310(9). (7) Legendre, S.; Giglio, E.; Tarisien, M.; Cassimi, A.; Gervais, B.; Adoui, L. Isotopic effects in water dication fragmentation. J. Phys. Chem. B: A Mol. Opt. Phys. 2005, 38, L233–L241. (8) Gervais, B.; Giglio, E.; Adoui, L.; Cassimi, A.; Duflot, D.; Galassi, M. E. The H2O2+ potential energy surfaces dissociating into H+/OH+: Theoretical analysis of the isotopic effect. J. Chem. Phys. 2009, 131, 024302(1)–024302(9). 18 ACS Paragon Plus Environment

Page 18 of 22

Page 19 of 22

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


(9) Vander Wal, R. L.; Scott, J. L.; Crim, F. F. Selectively breaking the OH bond in HOD. J. Chem. Phys. 1990, 92, 803–805. (10) Bar, I.; Cohen, Y.; David, D.; Rosenwaks, S.; Valentini, J. J. Direct observation of preferential bond fission by excitation of a vibrational fundamental: Photodissociation of HOD (0,0,1). J. Chem. Phys. 1990, 93, 2146–2148. (11) Zhang, J.; Imre, D. G.; Frederick, J. H. HOD spectroscopy and photodissociation dynamics: selectivity in hydroxyl/hydroxyl-d bond breaking. J. Phys. Chem. 1989, 93, 1840–1851. (12) Imre, D. G.; Zhang, J. Dynamics and selective bond breaking in photodissociation. Chem. Phys. 1989, 139, 89–121. (13) Amstrup, B.; Henriksen, N. E. Control of HOD photodissociation dynamics via bondselective infrared multiphoton excitation and a femtosecond ultraviolet laser pulse. J. Chem. Phys. 1992, 97, 8285–8295. (14) Engel, V.; Schinke, R. Isotope effects in the fragmentation of water: The photodissociation of HOD in the first absorption band. J. Chem. Phys. 1988, 88, 6831–6837. (15) Henriksen, N. E.; Møller, K. B.; Engel, V. Isotope effects in the photofragmentation of symmetric molecules: The branching ratio of ODOH in water. J. Chem. Phys. 2005, 122, 204320(1)–204320(6). (16) Sarma, M.; Adhikari, S.; Mishra, M. K. Selective control of {HOD} photodissociation using low quanta OD excitation and field optimized initial state (FOIST) based combination of states and colors. Chem. Phys. Lett. 2006, 420, 321–329. (17) Sarma, M.; Adhikari, S.; Mishra, M. K. An Examination of the Expectation Value Profiles for Average Stretch and Momentum in OH and OD Bonds of the HOD Molecule



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

To Determine Their Role in Selective Photodissociation. J. Phys. Chem. A 2008, 112, 13302–13307. (18) Sarma, M.; Mishra, M. K. Role of Photolysis Frequency in Enhanced Selectivity and Yield for Controlled Bond Breaking in HOD. J. Phys. Chem. A 2008, 112, 4895–4905. (19) Rao, B. J.; Varandas, A. J. C. Subfemtosecond Quantum Nuclear Dynamics in Water Isotopomers. J. Phys. Chem. A 2015, 119, 4856–4863. (20) Balakrishnan, N.; Kalyanaraman, C.; Sathyamurthy, N. Time-dependent quantum mechanical approach to reactive scattering and related processes. Phys. Rep. 1997, 280, 79–144. (21) Dey, D.; Tiwari, A. K. Time-dependent quantum mechanical approach to reactive scattering and related processes. Eur. Phys. J. D 2014, 68, 169(1)–169(8). (22) Marston, C. C.; BalintKurti, G. G. The Fourier grid Hamiltonian method for bound state eigenvalues and eigenfunctions. J. Chem. Phys. 1989, 91, 3571–3576. (23) Kosloff, R.; Tal-Ezer, H. A direct relaxation method for calculating eigenfunctions and eigenvalues of the schrdinger equation on a grid. Chem. Phys. Lett. 1986, 127, 223–230. (24) Kosloff, D.; Kosloff, D. A fourier method solution for the time dependent Schrdinger equation as a tool in molecular dynamics. J Comput. Phys. 1983, 52, 35–53. (25) Feit, M. D.; Fleck, J., J. A.; Steiger, A. Solution of the Schrdinger equation by a spectral method. J Comput. Phys. 1982, 47, 412–433. (26) Mahapatra, S.; Sathyamurthy, N. Negative imaginary potentials in time-dependent quantum molecular scattering. J Chem. Soc., Faraday Trans. 1997, 93, 773–779. (27) Werner, H.-J. et al. MOLPRO, version 2010.1, a package of ab initio programs. 2010; see http://www.molpro.net. 20 ACS Paragon Plus Environment

Page 20 of 22

Page 21 of 22

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


(28) Aguado, A.; Tablero, C.; Paniagua, M. Global fit of ab initio potential energy surfaces I. Triatomic systems. Comput. Phys. Comm. 1998, 108, 259–266. (29) Aguado, A.; Paniagua, M. A new functional form to obtain analytical potentials of triatomic molecules. J. Chem. Phys. 1992, 96, 1265–1275. (30) Murrell, J. N.; Carter, S.; Farantos, S. C.; Huxley, P.; Varandas, A. J. C. Molecular Potential Energy Functions; Wiley, Chichester, 1984. (31) Paramonov, G. K.; K¨ uhn, O. State-Selective Vibrational Excitation and Dissociation of H2+ by Strong Infrared Laser Pulses: Below-Resonant versus Resonant Laser Fields and ElectronField Following. J. Phys. Chem. A 2012, 116, 11388–11397.



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

Graphical TOC Entry

!"!#


Page 22 of 22

Effect of Vibrational Pre-Excitation on the ... - ACS Publications

Recommend Documents