Classical trajectory simulations of collisions between polyatomic molecules and a self-assembled monolayer surface

Juan José Nogueira Pérez

Nanosystems exhibit very interesting properties because of their mesoscopic size. In the last decades, the development of the experimental techniques caused a great growth in the nanotechnology field. Self-assembled monolayers (SAMs) are widely used as model for performing studies about the behaviour of these materials. SAMs have been chosen as models because they are easy to synthesize, modify and characterize. One of the processes widely analyzed in the last years, both experimentally and theoretically, is the collision between ions and neutral molecules against SAMs. These collisions give rise to a great variety of reactive and unreactive events, in particular, in the hyperthermal regime of energy (1-100 eV). The study of the mechanisms involved in these processes provides information about the nanomaterial features, and therefore, about their possible applications. Many microscopic collision characteristics cannot be observed and analyzed experimentally, and therefore simulations become an important complementary tool. The classical trajectory method has been applied faithfully in the recent past to a lot of different process, including gas/surface collisions.

The main goal of this thesis is to carry out simulations, by the classical trajectory method, of inelastic collisions between polyatomic molecules and a self-assembled monolayer surface. In particular, the projectiles employed in the simulations were CO2 and NO neutral molecules, and SiNCS+ and (CH3)2SiNCS+ ions; the target surface is formed by chains of CF3(CF2)7S adsorbed on an Au{111} support. Throughout this thesis this surface is referred as F-SAM (perfluorinated self-assembled monolayer). The program used to integrate the equations of motion was VENUS05, developed by Hase and co-workers.

When a molecule in gas phase collides against a surface, several processes can take place, as seen is Chapter 2. The most abundant ones are inelastic scattering, surface-induced dissociation (SID), charge transfer, chemical sputtering, projectile/surface reactions and physisorption. In inelastic collisions, energy transfer between the projectile and the surface occurs without chemical reaction. If the energy acquired by projectile¿s vibrational normal modes is high enough to break a bond, it could dissociate, giving rise to SID collisions. Another possible event is electron transfer from the monolayer chains or from the metallic support to the gas projectile. If this electron transfer is accompanied by the rupture of a surface group, the process is called chemical sputtering. The projectile can also react with an atom or a functional group of the monolayer, or it can be physisorbed into the monolayer by physical interaction by a mechanism called soft-landing. Soft-landing, electron transfer and, above all, inelastic scattering collisions are the events analyzed throughout this thesis. To solve the equations of motion during the classical trajectory simulation, we need to know previously the potential energy of the system.

The most important part of the potential is the intermolecular one, which is discussed in Chapter 3. Depending on the behaviour of the energy with the intermolecular distance, intermolecular interactions are classified into short-range and long-range interactions. In the former ones, the interaction energy varies abruptly with the distance, and this variation is softer for the last ones. The short-range forces arise from the repulsion between electron densities. The long-range interactions are attractive and they are classified into different types depending on the origin of their nature. Electrostatic interactions are caused by the interaction between charges and/or permanent multipole moments. Induction interactions arise from a permanent dipole or a charge in a molecule interacting with a dipole moment of another molecule induced by the first one. And dispersion interactions occur due to the forces between instantaneous multipoles. All of these interactions vary in a different way with the intermolecular distance, and they must be taken into account for building the potential energy surface. Throughout this thesis, the parameters which define the projectile intramolecular potentials were obtained by fitting vibrational frequencies computed with electronic structure methods. The analytical equation which represents the intermolecular part of the potential was determined from the adjustment of interaction energies, calculated also by quantum mechanical methods, to two-body Buckingham exp-n-m function. This means that many-body interactions are ignored. The potential parameter optimizations were performed with the help of a genetic algorithm (GA). This sort of algorithms is based on principles of natural selection and genetics. GAs generate the initial population, formed by several set of coefficients, randomly. Each set of parameters of this population, called individual, is evaluated to determine how well it enables the adjustment of the data points to the model function. The individuals with better performance are selected for creating new individuals by means of mutation and crossover operations. These new solutions are evaluated with the fitness function, and the cycle of selection, recombination and mutation is repeated until a termination criterion is satisfied. In general, GA methods provide better results than conventional optimization techniques based on the gradient or the hessian.

Electronic structure calculations, discussed in Chapter 4, allow to evaluate the energy (and many other properties) of a given system. They are classified into ab initio, semiempirical and density functional theory (DFT) techniques. Semiempirical methods were not employed in this thesis. The ab initio methods use the real Hamiltonian, without doing any type of simplification in it. They often give us the most accurate results. Both semiempirical and ab initio techniques try to find the wavefunction that describes the system in the best way. For doing that, some methods optimize the molecular orbital coefficients so that the energy calculated from them is as low as possible, that is, they are based on the variational theorem. Other methods use the perturbation theory for computing the energy. On the other hand, density functional theory methods employ the electron density, instead the wavefunction, for obtaining the energy of the system. They also apply the variational theory, optimizing the molecular orbital coefficients for obtaining an electron density which in turn provides the lowest possible energy. All quantum mechanical methods employed in this thesis are under the Born-Oppenheimer approximation, that is, they suppose that the system remains in the same electronic state all time without undergoing nonadiabatic transitions. Moreover, relativistic effects are not considered in this type of calculations. In particular, the methods employed here are RI-MP2, CCSD(T), RIJ-DFT-D and SAC-CI. All these techniques are based on the Hartree-Fock (HF) method, which treats the electron correlation in an average (and simplified) way in order to make easier the resolution of the Schrödinger equation. Particularly, in the HF approach each electron is considered to be moving move in the field of the nuclei and the average field of the other N-1 electrons. This means that the electron correlation is not totally taken into account. A series of improvements, comprised as post-Hartree-Fock methods, were developed in order to introduce correctly the correlation energy. After computing the potential energy surface, the next step in the classical trajectory recipe is to select the initial coordinates and momenta of all atoms composing our system. This election is commonly called sampling of initial conditions.

Chapter 5 touches in detail the methods employed in this thesis for doing this sampling. In general, these techniques are based on Monte Carlo formulas, that is, the process requires certain degree of randomness. An important issue for simulations which involve surfaces is the use of periodic boundary conditions. This technique allows to replicate the primary cell, which represents the surface, infinitely along the space. The replicas of the primary cell are named image cells. In this way, when a particle leaves the primary cell in direction, for instance, +X, an image particle enters the primary cell from an image cell found in the ¿ X direction. Using periodic boundary conditions, the simulations are more realistic because we are imitating, with quite lot accuracy, a surface of macroscopic size. Once the potential energy surface is known and the initial conditions are chosen, the classical equations of motion (Newton or Hamilton equations) can be solved. Such equation requires a numerical resolution. There exists a great variety of algorithms to solve this type of equations (Chapter 5). In a general way, these techniques are classified into two groups: one-step and multistep methods. The one-step methods, called Runge-Kutta algorithms, permit the calculation of coordinates qn+1 and momenta pn+1 at step n+1 , given the values of the previous step qn and pn . On the other hand, multistep methods require more than one previous value of q and p , and consequently, they are more accurate that one-step techniques; if the method is of th-order, it needs the coordinates and momenta of n previous steps. This means that multistep algorithms are non-self-starting, and so a Runge-Kutta method is necessary at the beginning of the trajectory. The equations of motion are solved for a given number of steps or up to the process of interest finishes. Then, several properties can be computed classically from the final coordinates and momenta. Moreover, since the coordinates and momenta are known at any time, one can compute other time-dependent interesting features of the system.

In the first three works of this thesis, discussed in Chapters 6, 7 and 8, the collision of the CO2 molecule against an F-SAM surface was analyzed. The potential energy surface has already been calculated in a previous work developed in our research group. In this simulations the influence of collision energy on the dynamics, and the role of the surface mass was investigated. The F-SAM potential was described employing two different models. The first one was an all-atom (AA) model where all atoms are considered explicitly, that is, the structure of the surface is not simplified. The second model employed, called united atom (UA) model, treats the -CF3 and -CF2- groups as single pseudo-atoms. The results indicate that the UA model overestimates the efficiency of energy transfer to the surface because the UA F-SAM surface is softer than the AA one. The simulations also show that the mass of the surface atoms plays an important role in the dynamics. The amount of energy transferred to the monolayer increases when the mass is reduced because of the rise in chain flexibility. Analysis of rotational quantum number distributions and Doppler profiles shows that the results obtained with the AA model are in good agreement with experiments. Several UA models for the F-SAM were developed in order to improve the results obtained by the old one. One of these new UA models, in which the CF3 and CF2 units were rotated randomly for computing an average potential, was demonstrated to be very useful because it is 3 times faster thanthe AA model but without affecting significantly the accuracy of the results with respect to the AA model. Other topic analyzed for the CO2/F-SAM collisions was the CO2 vibrational relaxation due to the interaction between the projectile and the surface. The coupling between the two degenerate bends of the CO2 molecule generates a vibrational angular momentum. Thus, excitations of these degenerate bends provide a good opportunity to investigate vibrational energy transfer between carbon dioxide and the surface. Before the collision with the monolayer, we observed unphysical bend energy leakage from the CO2. After a detailed analysis of this issue, we found that trajectories that conserved their bend energies fulfill a particular relationship between the phases of the stretching and bending normal modes. An analysis of the vibrational temperatures provides again a reasonably good agreement with the experiments, and shows that the time scale needed to achieve bend energy accommodation is at least 50 ps.

A detailed analysis of energy transfer and stereodynamics for NO/F-SAM collisions was performed in Chapter 9. There, the potential energy surface was obtained by fitting energies calculated at the fp-CCSD(T)/CBS level of theory to two-body Buckingham formulas. We found in the dynamics that thermal accommodation of the rotational degrees of freedom in NO is explained in terms of a minimum number of moderate variations in the direction of the rotational angular momentum. In addition, the energy transfer behavior with the collision energy was explained by a new model, based on the adiabaticity parameter, which adjusts accurately the dynamics data. This model predicts 100% efficiency of energy transfer to the surface in the high collision energy limit. The stereodynamics analysis shows that the two preferred rotational motions of the scattered molecules are corkscrew and cartwheel. The available experimental data were compared with the simulations and we found again a good agreement.

In Chapter 10, intermolecular potential energy curves for SiNCS+/F-SAM and (CH3)2SiNCS+/F-SAM were constructed with the help of a genetic algorithm. A DFT functional which accounts for dispersion forces, based on the B97 functional, was validated by comparing with fp-CCSD(T)/CBS calculations. In this work, we found that the equation formed by a Lennard-Jones potential with an electrostatic term, employed in most of the universal force fields, is not suitable for adjusting simultaneously the short and the long range of energies. Comparisons between SiNCS+/CF4 and SiNCS+/mini-SAM and between (CH3)2SiNCS+/CF4 and (CH3)2SiNCS+/mini-SAM potential energy curves, where the mini-SAM is a model formed by nine chains of CF3(CF2)2CF3, demonstrated the validity of using the C and F atoms of the CF4 molecule for representing the atoms of the F-SAM chains during the parameterization.

In the last work of this thesis, simulations of SiNCS+/F-SAM and (CH3)2SiNCS+/F-SAM were carried out to try to explain experimental results. In particular, Cooks and co-workers found in their experiments that the biggest ion undergoes soft-landing, whereas the smallest ion is not trapped into the surface. For the moment, the simulations results obtained so far do not explain clearly this different behavior of both ions. Even so, it seems that electron transfer from the gold surface to the SiNCS+ ion, giving rise to ion neutralization, may be a reasonable reason to explain the fact that this ion is not detected in the sputtering spectrum. But additional analysis and calculations are necessary to reach firm conclusions. In general, under the above results, we can conclude that the classical trajectory approach is a reliable and useful technique for modeling gas/surface inelastic collisions. The development of the potential energy surface is the most relevant stage in the whole theoretical process since the behavior of the system depends strongly on the forces involved in the system. The sampling of the initial conditions must be done carefully in order to mimic appropriately the experimental conditions.


Supervised by:
Saulo A. Vázquez Rodríguez and Emilio Martinez Nuñez

Defence University:
University of Santiago de Compostela

Year of Defence:

Francisco Javier Aoiz Moleres (Chair), Antonio Fernández Ramos (Secretary), Jorge Manuel Campos Marques (Committee member), Jesús Rodríguez Otero (Committee member) and Pascal Larregaray (Committee member)