Collision dynamics of proton with formaldehyde: Fragmentation and ionization Jing Wang, Cong-Zhang Gao, Florent Calvayrac, and Feng-Shou Zhang Citation: The Journal of Chemical Physics 140, 124306 (2014); doi: 10.1063/1.4868985 View online: http://dx.doi.org/10.1063/1.4868985 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/140/12?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Theoretical study on collision dynamics of H+ + CH4 at low energies J. Chem. Phys. 140, 054308 (2014); 10.1063/1.4863635 Absolute cross sections for dissociative electron attachment and dissociative ionization of cobalt tricarbonyl nitrosyl in the energy range from 0 eV to 140 eV J. Chem. Phys. 138, 044305 (2013); 10.1063/1.4776756 Fragmentation and reactivity in collisions of protonated diglycine with chemically modified perfluorinated alkylthiolate-self-assembled monolayer surfaces J. Chem. Phys. 134, 094106 (2011); 10.1063/1.3558736 Dynamics of proton-acetylene collisions at 30 eV J. Chem. Phys. 117, 1103 (2002); 10.1063/1.1485726 Momentum distribution of fragment ions produced in collisions of Ar q+ with CH 4 and CF 4 AIP Conf. Proc. 604, 291 (2002); 10.1063/1.1449352

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THE JOURNAL OF CHEMICAL PHYSICS 140, 124306 (2014)

Collision dynamics of proton with formaldehyde: Fragmentation and ionization Jing Wang,1,2 Cong-Zhang Gao,1,2 Florent Calvayrac,3 and Feng-Shou Zhang1,2,4,a) 1

The Key Laboratory of Beam Technology and Material Modification of Ministry of Education, College of Nuclear Science and Technology, Beijing Normal University, Beijing 100875, China 2 Beijing Radiation Center, Beijing 100875, China 3 Institut des Molecules et Matériaux du Mans UMR 6283, Université du Maine, LUNAM 72085 Le Mans Cedex 9, France 4 Center of Theoretical Nuclear Physics, National Laboratory of Heavy Ion Accelerator of Lanzhou, Lanzhou 730000, China

(Received 8 November 2013; accepted 7 March 2014; published online 24 March 2014) Using time-dependent density functional theory, applied to the valence electrons and coupled nonadiabatically to molecular dynamics of the ions, we study the ionization and fragmentation of formaldehyde in collision with a proton. Four different impact energies: 35 eV, 85 eV, 135 eV, and 300 eV are chosen in order to study the energy effect in the low energy region, and ten different incident orientations at 85 eV are considered for investigating the steric effect. Fragmentation ratios, single, double, and total electron ionization cross sections are calculated. For large impact parameters, these results are close to zero irrespective of the incident orientations due to a weak projectiletarget interaction. For small impact parameters, the results strongly depend on the collision energy and orientation. We also give the kinetic energy releases and scattering angles of protons, as well as the cross section of different ion fragments and the corresponding reaction channels. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4868985] I. INTRODUCTION

There has been a considerable progress in the experimental and theoretical study of ion-molecule collisions in the last several years. The progress in experiment is due to the advanced ion accelerators and detectors, which provides accurate state-to-state properties of the investigated reactions. The theoretical advance is backed up by the powerful computers and novel theoretical concepts, which allows the study of polyatomic molecules including their excitation, ionization, and dissociation. Theoretically, the electron-nuclear dynamics (END) method is a time-dependent, variational, direct, and nonadiabatic method, which provides a treatment of all electrons and nuclei. It was used to study the proton-acetylene collision at 30 eV1, 2 and the charge-transfer scattering of lowto-intermediate energies protons by O2 as well as H2 .3–6 In addition, this method then grew into the Kohn-Sham (KS) density-functional-method (DFT) version of END, the END/KSDFT method.7 The close-coupling method along with MRD-CI potential energy surfaces was employed to simulate the electron capture processes in collisions of protons with CO, C2 H4 , C2 H6 , and H2 O8–12 below 10 keV. The vibrational close-coupling rotational infinite-order sudden approximation (VCC-RIOSA) is a time-independent scattering method that requires predetermined potential energy surfaces. It was employed to research the quantum dynamics of the H+ + O2 and H+ + NO systems at low collision energies.13–15 a) Author to whom correspondence should be addressed. Electronic mail:

[email protected]

0021-9606/2014/140(12)/124306/11/$30.00

Time-dependent density functional theory (TDDFT)16 was applied to large systems owing to its favorable scaling and low computational cost. Based on these advantages, Saalmann and Schmidt17, 18 developed an approach, in which electronic and vibrational degrees of freedom were treated simultaneously and self-consistently by combining TDDFT with classical molecular dynamics (MD). They built the basic framework for TDDFT-MD model; however, their method could not completely describe emission of electrons from the system, due to the use of a local basis set of Gaussians. Then, the TDDFT-MD method was developed by many groups to study various systems, for instance, gas-phase uracil in collision with proton,19 high-energy ion collisions with graphene fragments,20 graphite by irradiating with highly charged Ar ions,21 collisions between protons, and small molecules.22–24 The interactions of protons with molecules are of fundamental importance in several areas of astrophysics, atomic and molecular physics, and chemical physics. Therefore, the H+ + H2 CO system is an important system from the astrophysical and environmental points of view.25–27 First of all, formaldehyde is an interesting molecule worthy of attention and investigation. On the one hand, its carbonyl functional group is responsible for the strong polar nature of the molecule, and its stable C=O double bond is responsible for the sensitivity of any configuration interaction treatment for calculating its ground state energy.28 On the other hand, formaldehyde is related to the prebiotic chemicals about the young Earth29 and it may be the molecular building blocks of larger organic molecule in the interstellar medium (ISM).30 Second, the proton as a single ion-projectile is favored because of its missing electronic structure and

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capability of capturing electrons as well as its abundance in the solar wind and in the ISM. Third, so far, a great deal of work about formaldehyde has concentrated on unimolecular photodissociation,31–38 collision-induced ionization and dissociation by electrons,28, 39–43 atoms,44–50 and ions.51–53 Unfortunately, little is known about the physical process of proton impact on formaldehyde, although Jalbout30 advanced the study of a single formaldehyde reacting with a single proton + source (H+ 3 , H3 O ). He did not consider an isolated proton + (H ) due to the high energies associated with interactions involving this ion. The above facts stimulate our curiosity to directly study the collision of H+ with H2 CO to explore the origin of life on the Earth, to investigate the evolution of the organic molecule in the ISM, and to eliminate the harmful indoor gas more cheaply in the environment. In this work, we study the collision dynamics of H+ + H2 CO at low collision energies. The calculation employs the TDDFT-MD approach at the level of time-dependent local density approximation54 (TDLDA) as implemented in the code package PWTELEMAN.55, 56 The article is organized as follows. In Sec. II, the general aspects of the theoretical and numerical approach are briefly described. In Sec. III, we present separately the energy effect, the steric effect, the kinetic energy release and scattering angle of proton, the fragments, and reaction channels. Finally, in Sec. IV, we give the conclusion. II. MODEL AND METHODS

The TDLDA-MD method employs classical mechanics to describe the motions of nuclei and uses quantum mechanics to treat the dynamics of electrons. The electronic density is described by single-particle wave functions ϕ n (r), (n = 1, . . . , Nel ). Nel only considers the valence electrons, because the core electrons are energetically far below the valence levels.57, 58 The inner shell electrons and their parent nuclei constitute a whole entity which is called atomic center in a molecule or a molecular fragment. If the atomic center leaves its parent molecule alone, it is called ion. For simplicity, hereafter the whole entity is referred to as ion. Ions are treated as charged classical point particles characterized by their positions Ri , (i = 1, . . . , Nion ). In the DFT, any observable of the system are uniquely  defined by the time-dependent single-particle density ρ = n ϕn∗ ϕn .16, 59 The total energy consists of four parts: ion-ion, electronelectron, ion-electron, and the external energy. The ion-ion part includes the ion kinetic energy Ekin, ion and the ion potential Epot, ion : ion 1 ˙ i |2 , Mi | R 2 i=1

(1)

1  e2 Zi Zj . 2 i=j |Ri − Rj |

(2)

ESIC :  Ekin,el =

dr

Nel 

ϕn∗

n=1

EC =

e2 2



drdr

pˆ 2 ϕn , 2mel

ρ(r)ρ(r ) . |r − r|

(3)

(4)

The Fourier Analysis with Long Range forces (FALR) method is applied to solve the Coulomb problem in fourier representation because of its precision, robustness, and efficiency.60 The exact formulation of the xc potential is unknown, here we adopt the time-dependent adiabatic LDA (TDALDA) widely used in practical operation. It usually provides reasonable results for various systems even far from density variation limitation.61–63 The functional form of Exc is from Refs. 64 and 65 which can reproduce the PerdewWang66 results extremely well:  Exc = drρ(r)xc (ρ↑ (r), ρ↓ (r)), xc

a0 + a1 rs + a2 rs2 + a3 rs3 =− , b1 rs + b2 rs2 + b3 rs3 + b4 rs4

(5)

where the density parameter rs = {3/[4π (ρ ↑ + ρ ↓ )]}1/3 , and the constants are given in Ref. 64. For ESIC , the simple average-density SIC (ADSIC) is adopted,67 in which Nel, σ is the number of electrons with spin orientation σ , σ ∈ {↑, ↓},      ρ↑ ρσ LDA + Exc ,0 EADSI C = −Nel,↑ EC Nel,↑ Nel,↑      ρ↓ ρσ LDA + Exc 0, . (6) −Nel,↓ EC Nel,↓ Nel,↓ The ion-electron coupling interaction is described by Goedecker-Teter-Hutter pseudo-potentials (PsP) including the local and nonlocal contributions,64, 68 EP sP =

Nion   i=1

dr

Nel 

ϕn∗ VˆR(Pi sP ) ϕn .

(7)

n=1

The external energy Eext is a time-dependent electromagnetic perturbation (e.g., a laser pulse or a by-passing ion). Here we consider simply the external Coulomb potential. The equations governing the time evolution of the system can also be divided into two parts: the electronic and ionic equation of motion. The electronic structure is governed by the Kohn-Sham (KS) Hamiltonian,

N

Ekin,ion =

Epot,ion =

hˆ KS (t) = −(¯2 ∇ 2 /2mel ) + Vion (r, t) + VC + Vxc + VSI C + Vext (r, t),

The electron-electron part contains the electron kinetic energy Ekin,el , the direct Coulomb energy EC , the exchangecorrelation energy Exc , and the self-interaction correction

(8)

where the potential of the ionic background is  composed of the individual pseudo-potentials as Vion (r, t) = i VP sP (r − Ri (t)). The behavior of the ions is derived from the external energy, the electron-ion interaction energy, and the Coulomb energy of the ionic point charges. The Hamilton’s equations of motion for ion cores are obtained by variation with respect

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to Ri and Pi , ∂ ∂Etotal Pi Ri = = , ∂t ∂Pi Mi ∂ Pi = − Ri ∂t +

Nel 

(9)

  Zi Zj e2 1 2 i=j |Ri − Rj |



ϕn |VP sP (r − Ri )|ϕn  + Vext (Ri , t) ,

(10)

n=1

Etotal = Ekin,ion + Epot,ion + Ekin,el + EC + Exc + ESI C + EP sP + Eext .

(11)

For ground-state (zero Vext gradients), the optimization of ion positions is done with the simulated annealing method.69, 70 We need to solve the static KS equation71 by the damped gradient method69 to obtain the electron ground state, hˆ KS (t0 )ϕn (r) = εn ϕn (r).

(12)

For dynamic calculation (non-zero Vext gradients), the single-particle wave function ϕ n (r, t) satisfies the timedependent KS equation, which is settled by the time-splitting method,72 i∂t ϕn (r, t) = hˆ KS (t)ϕn (r, t).

(13)

Ionic motion is treated simultaneously according to Eqs. (9) and (10), using the leap frog algorithm. As mentioned previously, we use the ground-state DFT functionals due to the nearly non-existence of excited-state DFT functionals. Although we employ the adiabatic approximation for the DFT-functional part, our method is nonadiabatic on the whole. The ionic motion is closely related to the time-dependent electron density, see Eq. (10), which provides the Ehrenfest non-adiabatic dynamics of the system. Due to the mean-field character, the Ehrenfest dynamics has some limitations: a system that was initially prepared in a pure adiabatic state will be in a mixed state when leaving the region of strong non-adiabatic coupling, this average potential will be unable to describe all reaction channels adequately. However, Ehrenfest dynamics could still give acceptable results for non-adiabatic collisions such as excited state lifetimes and decay properties of organic molecules,73 and this method will reduce to the adiabatic description if the ionic motion is slow enough to allow electrons to relax to their ground-state. In addition, while the END method is beyond Ehrenfest dynamics, it also has such a mixed state, but END can still properly predict electron-transfer total cross sections in ion-atom and ion-molecule collisions.2, 74, 75 In this model, the wave functions, densities, and potentials are discretized in a real space grid,76 it allows for a more transparent and direct coupling of electronic and ionic motion. We use 72 × 72 × 72 a3 grid points with a mesh size of a = 0.412 a0 and the corresponding electronic evolution volume V ≈ 26103 a03 . The time step is t = 6.05 × 10−4 fs. The absorbing boundary conditions55, 70 are achieved with a

mask function to avoid ejected electrons being reflected back to the numerical box when they reach the boundary. The range of impact parameters b is divided into three regions: (i) close collisions, for which b is varied in steps of 0.1 a0 from 0 a0 to 2 a0 ; (ii) intermediate collisions, for which b runs in steps of 0.2 a0 from 2 a0 to 5 a0 ; and (iii) grazing collisions, for which b is varied in steps of 1 a0 from 5 a0 to 10 a0 . Hence, there are 40 trajectories for a given incident orientation. The molecular plane of formaldehyde is in the y-z plane with C=O bond on the z axis, and the carbon atom is placed at the origin of the Cartesian coordinate system. The center of mass is at (0.0 a0 , 0.0 a0 , 1.058 a0 ). The projectile is initially located at least 20 a0 from the target.

III. RESULTS AND DISCUSSION A. Energy effect

In order to study the energy effect of low-energy proton on prebiotic molecule, we deliberately choose four low collision energies (E0 = 35 eV, 85 eV, 135 eV, and 300 eV) and one specific incident orientation (the proton moves from −z to +z on the molecular plane with a displacement by an amount b in the +y direction). Fig. 1 gives the reaction channels as a function of the impact parameter for different collision energies. Two interesting reaction channels are observed: C–H bond breaking and hydrogen substitution by the incoming proton. The ionization channel without fragmentation or substitution is also found but not shown in Fig. 1. A remarkable feature is that the two interesting reactions only take place at small impact parameters (b ≤ 2.3 a0 ) and the C–H bond breaking is dominant. Note that the probabilities of bond cleavage and substitution decrease with increasing collision energy. For the case of E0 = 35 eV, the C–H bond breaking happens at b = 0.25–0.45 a0 , 0.55–1.65 a0 , 1.85–1.95 a0 , and 2.1–2.3 a0 , the substitution reaction occurs at b = 0.45–0.55 a0 and 1.95–2.1 a0 . For the case of E0 = 85 eV, the C–H bond is broken at b = 0.15–0.45 a0 , 1.25–1.75 a0 , and 1.95–2.3 a0 , the proton replaces one hydrogen atom at b = 1.75–1.95 a0 . When the collision energy increases to 135 eV, the substitution reaction disappears and the separation of C–H bond

FIG. 1. The reaction channels as a function of the impact parameter b for different collision energies.

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J. Chem. Phys. 140, 124306 (2014) TABLE I. The fragmentation ratios R(%) and the ionization cross sections σ (× 10−16 cm2 ) for different collision energies. σ s : the single ionization cross section; σ d : the double ionization cross section; σ t : the total ionization cross section. Single (SEC), double (DEC), Total (SEC + 2 DEC) electron capture cross sections by 3 He2 + colliding with formaldehyde.52

35 eV 85 eV 135 eV 300 eV

R

σs

σd

σt

SED52

DED52

Total52

3.820 3.168 3.728 2.308

8.497 8.711 9.310 9.651

1.952 1.910 2.171 2.351

12.704 12.799 14.128 14.667

... 8.630 7.755 7.807

... 3.462 3.424 3.370

... 15.554 14.602 14.547

respectively,

b R=

FIG. 2. (a) and (b) The number of escaped electrons (Nesc) at b = 0–10 a0 for different collision energies.

happens at b = 1.25–2.3 a0 . When the energy is higher (300 eV), the cleavage of C–H bond is only available at b = 1.45–2.1 a0 . The phenomenon results from the energy effect: a lower collision energy means that the incident proton moves slowly and the impact time is longer. The long interaction time is important for energy transfer from projectile to target. Then, it provides a condition for the C–H bond breaking and substitution reactions. In particular, the substitution is almost impossible to occur at high collision energy, because the kinetic energy of proton is too large for energy exchange in a short time. Figures 2(a) and 2(b) show the number of the escaped electrons (Nesc) of H2 CO induced by the proton for different collision energies. Nesc(t) = N(t = 0) − N(t), where N(t) = V drρ(r, t) is the number of electrons remaining in bound states within the finite volume V . The fractional charge of Nesc represents the ionization probability of the target after impact. For simplicity, we calculate the average Nesc. In the close collisions (b < 2.0 a0 ), Nesc(35eV) = 0.654, Nesc(85eV) = 0.522, Nesc(135eV) = 0.469, Nesc(300eV) = 0.412, a lower energy leads to a larger ionization probability. This is because the target’s strong retention of the electrons and the projectiletarget repulsion are large, which enhances the importance of the interaction time. Conversely, in the intermediate collisions (2.0 a0 ≤ b ≤ 5.0 a0 ), Nesc(35eV) = 0.415, Nesc(85eV) = 0.394, Nesc(135eV) = 0.514, Nesc(300eV) = 0.520. This implies that the higher collision energy plays an important role in the electronic excitation, due to the smaller binding force and the repulsive force. The energy effect shapes the ionization probability for 0.0 a0 ≤ b ≤5.0 a0 , but it has no effect on the target for b > 5.0 a0 , because the projectile is far from the formaldehyde. The above studies prove that the energy effect plays a key role in the ion core motions and the electron excitation. The fragmentation ratios and ionization cross sections for different energies are shown in Table I. The fragmentation ratio (R) and the ionization cross section (σ ) for one orientation can be written as an integral over the impact parameter b,

0

P (b) b db , b 0 b db

(14)

where P(b) stands for the probability of fragmentation for an impact parameter b, P(b) = 1 for b in the fragmentation areas (only including C–H bond breaking) and P(b) = 0 for b out of the areas:  (15) σ = 2π P i+ (b) b db, where Pi + (b) is the ionization probability at impact parameter b in the final state, it is in one of possible charge states i to which it can ionize. The bound state probability Nj (t) and continuum one N¯ j (t)77 for each KS single-particle orbital are   Nj (t) = drnj (r, t) = dr|ϕj (r, t)|2 , (j = 1, . . . , Nel ), V

V

(16)  N¯ j (t) =

 drnj (r, t) =

V¯

V¯

dr|ϕj (r, t)|2 , (j = 1, . . . , Nel ), (17)

where V¯ denotes the volume which is outside the computational box. Deduced from Nj (t), the expressions of the approximate ion probabilities77 Pi + are P 0 (t) = N1 (t) · · · NNel (t), P 1+ (t) =

Nel 

N1 (t) · · · N¯ i (t)NNel (t),

(18)

(19)

i=1

P 2+ (t) =

N el −1

Nel 

N1 (t) · · · N¯ i (t) · · · N¯ j (t)NNel (t),

i=1 j =2, j >i

12

(20)

here, i=1 iPi+ (b) = Nesc(b). The total electron ionization cross section (σ t ) is the sum of the single electron ionization cross section (σ t ), the double electron ionization cross cross sections section(σ d ), and other multi-electron ionization  (σ m , 3 ≤ m ≤ 12), i.e., σ t = σ s + 2σ d + σ m . Here we only give the σ s , σ d , and σ t , because the other σ m are too small. In Table I, the increase in collision energy effectively increases the ionization cross sections, but reduces the fragmentation ratio. This is because extracting an electron from

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the target is easier than extracting an atom, the latter needs enough interaction time and proper collision configuration for large energy transfer. The ionization threshold of H2 CO is 10.88 eV and the threshold energy to obtain HCO+ from a neutral H2 CO is 12.03 eV.43, 80 Because of a lack of available data on H+ colliding with H2 CO, we use the results of 3 He2 +52 to compare. The ionization includes electron capture and direct ionization (i.e., Total (3 He2+ ) < σ t (3 He2+ )), and it can be speculated that σ t (H+ ) < σ t (3 He2 + ) form the Table I. This is because 3 He2 + has larger mass and charge than H+ . However, the two results of the same order of magnitude at least can prove that our results are credible. The low-energy proton leads to the small fragmentation probability which opens up possibilities to presence and further evolution30, 78 of H2 CO. Even if the fragmentation occurs, most products are HCO+ ions which can integrate easily with other ions to form larger molecules or molecular ions. In fact, in the solar matter, the energy of proton is between a few tenths of eV to hundreds of MeV,79 it has such a devastating impact on organic molecule. Fortunately, the Earth’s magnetic field deflects most ions, which provides a necessary protection for the life. On the other planets without magnetic field, although low-energy collision promotes the evolution of the molecule, high-energy ion rapidly destroys them.

B. Steric effect at 85 eV

There are infinite incident directions for the C2v symmetry of H2 CO. We only choose ten orientations52 at 85 eV to study the steric effect (also known as orientation effect), because these orientations are easy to interpret and some of them may easily lead to interesting reactive processes. The orientations are divided into three major categories (see insets in Fig. 3): (i) The projectile moves parallel to x axis with a displacement by an amount b in the +y, +z, and −z directions, the three orientations are marked as X+y , X+z , and X−z , respectively, and the corresponding weighting factors are w(X+z ) = w(X−z ) = 13 × 14 ≈ 8.33%, w(X+y ) = 13 × 24 ≈ 16.66% because the result of X+y is the same as the one of X−y . (ii) The proton runs parallel to y axis with b varied in the +x, +z, and −z directions, which are labeled as Y+x , Y+z , and Y−z , respectively, and w(Y+z ) = w(Y−z ) = 13 × 14 , w(Y+z ) = 13 × 24 . (iii) The proton moves parallel to z axis in both directions with b in the +x and +y directions, the four orientations O O C C , Z+y , Z+x , and Z+y , respectively, are marked as Z+x O O C C w(Z+x ) = w(Z+y ) = w(Z+x ) = w(Z+y ) = 13 × 12 × 24 . C In addition, the orientation used in Sec. III A is Z+y . Figure 3 shows that the variation of the Nesc is discriminative due to the different incident directions. For orienC O and Z+x (see Figs. 3(a) and 3(b)), the proton tations Z+x has limited opportunities to directly impact H2 CO and the Nesc is less than 0.03. For orientations X+z and X−z (see Figs. 3(c) and 3(d)), at b < 1 a0 , the Nesc exhibits a single sharp peak and the peak is about 0.3, because the

J. Chem. Phys. 140, 124306 (2014)

proton strongly affects the C=O bond. For orientations X+y and Y+x (see Figs. 3(e) and 3(f)), when 0 a0 < b < 4 a0 , the growing influences of proton leads to a larger Nesc. For Y+z and Y−z (see Figs. 3(g) and 3(h)), the collision happens on the molecular plane and the Nesc can rise to 0.6 for b < 6 a0 . The similar results can also O C and Z+y (see Figs. 3(i) be found for orientations Z+y and 3(j)) due to the coplanar collision. In Table II, the ionization cross sections (σ s , σ d , σ t ) are given for different incident directions. Because σ s , σ d , and σ t exhibit similar patterns, we only discuss the total electron ionization cross sections σ t . It strongly depends on the Nesc C O ) < σt (Z+x ) < σt (X−z ) and its order is: σt (X+z ) < σt (Z+x O C ). E(X+z , X−z )> E(Z+x , Z+x )> E(X+y , Y+x ). Qualitatively, the magnitude of these KER reflects fairly well the degree of molecular ionization and fragmentation. For orienC O , Z+x , X−z , X+y , and Y+x , the small energy tations X+z , Z+x transfer causes small ionization cross section without dissociation. For Y+z , 32 eV energy transfer only leads to a small O C , and Z+y , the fragmentation ratio R = 0.200%. For Y−z , Z+y large energy transfer results in large ionization cross section and fragmentation ratio, even the substitution. In Fig. 4, the scattering angle θ is the angle between the initial momentum of proton and the final momentum of the fastest outgoing particle. Most of them are the scattering angles of projectiles, except the angles at b = 2.0 − 2.2 a0 O C for Y−z , 1.2 − 2.0 a0 for Z+y , and 1.7 − 2.0 a0 for Z+y , at where the fastest outgoing particle is the fragment H. In Figs. 4(a), 4(b), 4(d), and 4(e), some angles are larger than 90◦ , which means that the proton hits the nucleus of the target and bounces back due to the strong Coulomb repulsion. After the fierce collision, the recoiling proton releases a large

FIG. 4. Scattering angle (black square and red circle) and the lost energy of proton (blue dotted line and green dashed line) in H+ + H2 CO collisions as functions of the impact parameter b with different impact directions at 85 eV. The arrow indicates the transition point bt .

kinetic energy, which may induce a further molecular fragmentation. Hence, the first largest peak of scattering angle is located at the edge of the peak of KER. Due to the effect of the target electron, we observe two impact-parameter regions, wherein the scattering angle has different signs. The transition point bt is indicated with an arrow, where the attraction and repulsion achieve a balance. In the repulsive region, for which b < bt , the proton penetrates the electronic cloud and sees the repulsive nuclei. The structural features of formaldehyde determine the characteristics of the scattering angle that might appear random. In the

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parameter effect on the scattering angle, we put the trajectories with different b together. At t = 11.6644 fs, the proton is very close to the formaldehyde. At t = 13.6609 fs, the strong Coulomb repulsion of the target causes the proton to scatter which presents a large arc for small impact parameters due to the steric effect. After 17.9080 fs, the proton runs away from the target, meanwhile, the target begins to oscillate after gaining kinetic energy. Take orientation X+z , for example, the proton passes through the C=O bond for b ≤ 0.3 a0 , because the forces from C and O atoms cancel out each other on average. For b = 0.4 and 0.5 a0 , the previous cancellation is not achieved, the repulsive force of O atom first deflects the projectile moving to C atom which leads to a second deflection, so there are two singularities located on both sides of the C=O bond. The scattering angles at b = 0.5 and 0.6 a0 are larger than the angles at b = 0.7 and 0.8 a0 due to the supplementary role of C atom. The peak angle is at b = 0.9 a0 where the head-on collision happens and the proton directly impacts on the O atom. For b ≥ 0.9 a0 , the protons are less affected by the C atom, the scattering angles show a regular pattern and decrease rapidly with increasing b. Similarly, for X−z , the singularities are at b = 0.8 and 0.9 a0 by two collisions. The repulsive forces of C and O atoms together result in a large deflection angle at b = 1.0 − 1.2 a0 . At b = 1.3 a0 , the projectile directly hits the C atom, and the head-on collision leads to the scattering angle peak. For orientations X+y and Y+x , the largest scattering angle is only 18.5◦ at b = 0.4 a0 , due to the small energy transfer. For the remaining six orientations, the scattering phenomena are clearly shown. In particular, if the trajectory passes through the C–H bond, the distribution of scattering angle will be more complicated and the fragmentation ratio will be inO C , and Z+y . creased, such as Y+z , Y−z , Z+y

D. The evolution of the electron density and major fragments at 85 eV

FIG. 5. Superimposed configurations obtained from the trajectories with different impact parameters for the ten orientations. For clarity, the configurations are given at 8.00415 fs, 11.66440 fs, 13.66090 fs, and 17.90800 fs, respectively. Red ball: oxygen atom; blue ball: carbon atom; white ball: hydrogen atom; green ball: proton. Axes are given on the left.

attractive region, for which b > bt , the projectile is attracted by the electronic cloud and displays a small scattering angle. The characteristic features of the protons are understood more explicitly in Fig. 5, it shows the evolution of the ion motion for each orientation. In order to investigate the impact

To achieve a more profound understanding of the molecular ionization and dissociation processes, Fig. 6 presents the evolution of ion coordinates and electron densities. For b = 0.2 a0 , the proton hits C atom and recoils, meanwhile it captures electrons and transfers energy to H atom. The cleavage of C–H bond is significant. For b = 0.4 a0 , the proton is scattered with an entirely different emergent angle and the smaller energy transfer delays the C–H bond breaking. For b = 0.7 a0 , the capture ionization and C–H bond breaking disappear and the direct ionization grows. For b = 1.3 a0 and 1.5 a0 , the direct ionization is dominant, but the separation of C–H bond becomes more and more apparent. For b = 1.8 a0 and 1.9 a0 , the head-on collisions first kick the H atom at 13.31 fs, then the targets release the projectile with captured electron due to the long dwell time for charge transfer. For b = 2.4 a0 , 2.6 a0 , and 3.4 a0 , the capture ionization prevails again, but the oscillation amplitude of C–H bond reduces, because the influence of the projectile diminishes. Obviously, the capture ionization plays a dominant role in the target ionization and the direct ionization takes second place.

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FIG. 7. Time evolution of bond length at 85 eV with different impact parameters b = 2.4 a0 , 2.6 a0 , and 3.4 a0 . Black solid line: C=O bond; red dashed line: C–H1 bond; blue dotted line: C–H2 bond.

FIG. 6. Time evolution of ionic motions and electron densities for orientation C at 85 eV with different impact parameters b. The various colors repreZ+y sent different densities. Green ball: proton; red ball: hydrogen atom; yellow ball: carbon atom; blue ball: oxygen atom. “C=/=H” means the C–H bond breaking.

The reason of the different dynamic behaviors lies in different energy transfer. For example, take the cases of b = 0.7, 1.5, and 1.8 a0 : E = 6.56 eV for b = 0.7 a0 , E = 15.75 eV for b = 1.4 a0 , and E = 65.19 eV for b = 1.8 a0 . The 6.56 eV kinetic energy for b = 0.7 a0 cannot break the C–H bond but it can stimulate the direct ionization. For b = 1.5 a0 , the larger energy transfer causes the cleavage of C–H bond, but the final kinetic energy of proton is still large and the interaction time is not long enough for the projectile to capture the electron. However, for b = 1.8 a0 , the head-on collision

transfers most of the kinetic energy from the projectile to the H atom, which leads in the cleavage of the C–H bond. But the remaining fragment still cannot retain the proton, because the final kinetic energy of the proton is 19.81 eV, which is large enough for projectile to escape. On the other hand, the interaction time is longer, t ≈ 3.63 fs, it facilitates the electron capture by proton. Fig. 7 shows the changes in C=O and C–H bonds at 2.4 a0 , 2.6 a0 , and 3.4 a0 . For b = 2.4 a0 , the proton induces the C–H1 bond to vibrate with a large amplitude. For b = 2.6 a0 , the amplitude of C–H1 bond is smaller, as time proceeds, the amplitude of C–H1 bond reduces and the oscillating amplitudes of C=O and C–H2 bonds increase. For larger impact parameter b = 3.4 a0 , the small vibration of the system takes place. It suggests that selecting suitable impact parameter can effectively control the intensity of system response. Table III gives the different reaction channels for each products, here we focus on the ion fragments. Molecular ion H2 CO+ is the major ion product and its cross section is 4.219 × 10−16 cm2 . This molecular ion is produced through reaction channels (2)–(5) and the reaction channel (3) makes greater contribution than channel (2). The reactions (4,5) are rare due to the small probability of substitution. During formaldehyde ionization, its oxygen atom delivers a non-bonding electron then the spin density becomes large on the oxygen atom of

TABLE III. Reaction channels for proton-formaldehyde collision. (1) (2) (3) (4) (5)

No response Only direct ionization Only electron capture Substitution with ionization Substitution without ionization

H·+ H·+ H·+ H·+ H·+

(6) (7) (8)

C–H break without ionization C–H break with direct ionization C–H break with electron capture

H · + + H2 CO → H · + + H2 CO → H · + + H2 CO →

HCO + H + H · + HCO+ + H + H · + + e− HCO+ + H + H ·

(9) (10) (11)

C=O break without ionization C=O break with direct ionization C=O break with electron capture

H · + + H2 CO → H · + + H2 CO → H · + + H2 CO →

CH2 + O + H · + · + + e− CH+ 2 +O+H + CH2 + O + H ·

+ H2 CO → + H2 CO → + H2 CO → + H2 CO → + H2 CO →

H2 CO + H · + H2 CO+ + H · + + e− H2 CO+ + H · H · HCO+ + H+ + e− H · HCO+ + H

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the radical cation while the positive charge is located on the methylene group.43, 81 The cross section for HCO+ is 0.319 × 10−16 cm2 and it comes from a C–H bond split by the reaction channels (7,8). Note that for the cleavage of C–H bond, the probability of the fragmentation into the fragment pair (HCO+ , H) is significantly larger than the one of the fragmentation into the fragment pair (HCO, H+ ) for all impact parameters. This can be attribute to the Stevenson’s rule: the fragment of lowest ionization energy is favored to retain the charge and becomes the ionic product.43 Because IE(HCO) = 8.12 eV and IE(H) = 13.6 eV, the (HCO+ , H) needs much smaller ionization energy than (HCO, H+ ) and the charge is located on HCO to form HCO+ ion. The final structure of HCO+ is a linear geometry.82 The large cross section of HCO+ indicates that the C–H bond cleavage possesses an important part of fragmentation. −16 The cross section for the minor CH+ 2 is 0.003 × 10 2 cm and the fragment results from a C=O bond breaking by the reaction channels (10,11). According to Stevenson’s rule, + the CH+ 2 ion is formed rather than O , because the IE(CH2 ) = 10.40 eV and IE(O) = 13.62 eV. In addition, due to the dominant position of capture ionization in molecular ionization, the reaction channels (3), (8), and (11) make greater contributions to fragmentation than channels (2), (7), and (10), respectively. IV. CONCLUSIONS

In the framework of the time-dependent local density approximation, applied to valence electrons, and coupled nonadiabatically to molecular dynamics of ions, we explore in detail the influences of the collision energy and configuration on the collision scenario. We find that in some cases, the molecule after the impact will be excited to produce ionization and fragmentation. We use four different low collision energies (35 eV, 85 eV, 135 eV, 300 eV) for the same incident orientation to study the energy effect, we find that the probabilities of C–H bond rupture and substitution reactions decrease with increasing collision energy. To the contrary, a higher energy can result in a larger ionization cross section. This is because the energy transfer from proton to nucleus requires longer interaction time than the energy transfer from proton to electron. We choose ten different incident orientations at 85 eV to explore the steric effect, and we obtain that the steric effect is obvious. The order of total ionization cross section C O ) < σt (Z+x ) < σt (X−z ) < σt (X+y ) σ t is: σt (X+z ) < σt (Z+x O C < σt (Y+x ) < σt (Y+z ) < σt (Z+y ) < σt (Y−z ) < σt (Z+y ). For C O orientations X+z , Z+x , Z+x , X−z , X+y , and Y+x , the ionization cross section is small and no fragmentation happens. O C , Y−z , and Z+y , the ionInstead, for orientations Y+z , Z+y ization cross section is larger and both C–H bond breaking and substitution occur. The latter collision configurations are conducive to energy transfer, because the trajectory of the proton is settled on the molecular plane and coplanar collision happens. The steric effect also affects the kinetic energy release and scattering angle of proton. The general order of en-

J. Chem. Phys. 140, 124306 (2014) O , ergy transfer for different orientations is: E(Y−z , Z+y C O C Z+y ) > E(Y+z ) > E(X+z , X−z ) > E(Z+x , Z+x ) > E (X+y , Y+x ). It proves that the bond breaking needs a large energy transfer. We obtain three ion fragments: H2 CO+ , HCO+ , and CH+ 2 due to the Stevenson’s rule. The molecular capture ionization is the dominant reaction channel, its cross section of forming H2 CO+ is large and reaches up to 4.219 × 10−16 cm2 , and the other ionic cross sections are small due to their small fragmentation ratios.

ACKNOWLEDGMENTS

This work was supported by the National Natural Science Foundation of China under Grant Nos. 11025524 and 11161130520, National Basic Research Program of China under Grant No. 2010CB832903, and the European Commission’s 7th Framework Programme (FP7-PEOPLE-2010IRSES) under Grant Agreement Project No. 269131. 1 S.

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