Rotational State Selection And Alignment And Orientation Of Molecules In External Field

State-selection, orientation and alignment of molecules play an important role in chemical reaction dynamics. The oriented and aligned molecules are very useful for understanding stereo dynamics, photophysical or photochemical process of molecules such as dissociation, ionization, collision, and even strong-field effect. Theoretic and experimental studies in this field have been developed rapidly for many years. In this thesis, we focus on the theory for the interaction of molecular dipole moment with external electric field and use the numerical simulation to investigate the rotational state-selection of polar molecules in a hexapole electric field and the laser-field role of alignment or orientation for molecules, based on the numerical calculation for a quantum mechanical treatment of molecules and their interaction with the external field and a classical electrodynamical treatment for static electric field.We give a fundamental theoretical description of molecular rotation properties. Time-independent Schrodinger equation can be taken for the motion of molecules in a static external field. Under an electric-dipole model, we describe the pendular motion of polar molecule in uniform external electric field and show how the directional orientation of the molecules can be obtained (so called the 'brute force' method). In the case of inhomogenous static electric field, the description involves in finding the energy of molecular rotational state by building a suitable wavefunction for the rotational molecules, giving the spatial distribution of the field, and then determining the movement of the molecules in the field finally.A quantum mechanical treatment is achieved for the case of symmetric top molecules and a numerical calculation of molecular energy states can be realized by a few parameters since the molecules have a high symmetry. For asymmetric top molecules, the description is complex as many factors can have influence because of the poor symmetry of the molecule and there is no enough information on the energy states of these molecules which is necessary for the calculation. In general, for asymmetric top molecules, a linear combination of symmetric top molecular rotational wavefunctions is used in building their wavefunctions. By group theory, we analogously deal the rotational wavefunction of asymmetric top molecules with SALC (symmetry-adapted linear combination) method as LCAO-MO (Linear combination of atomic orbitals - molecular orbital). The built asymmetric top rotational wavefucntion is written as5 =I"K= ever, K=odduJ,0,M|a:+a/|The diatomic molecules and linear polyatomic molecules with doubling-splitting states, and the asymmetric top molecules with a degenerated states or having a pair of the lowest states which is close in energy and interact each other, are discussed further. Thus, we can use a two-level model to realize the process of state selection or focusing. In this model, the molecular energy and its derivative with electric field areVyJTM- W^0\2 '/2-4dW7Al, TMTli 2dEIr/(/ + 1ETMTMW° -W° the notes 7=Q,A,/,￡ and A = -im-----J-^- is the difference of the energiesbetween the two interactive states without external electric field, that is, the split value. When the split value becomes large it will be difficult to realize the role of state selection or focus under this two-level model and only the nondegenerate theory treatting the second-order Stark effect can be used.The field distribution of cylindrical-pole hexapole has been investigated. The general form of the equipotential surfaces in the field is given by0(r,0)=￡/o￡cj- cos[3{2n + \)9]Therefore, if the coefficients in the equation are determined, the field distribution can be obtained. We use a numerical treatment to determine the coefficients in this equation. Since the potential distribution obeys Laplace equation under the first boundary condition, the numerical results for the field distribution can be obtained by taking a successive over relaxation method under the square grid scale of five pointed difference numerical problem. Then we fit the numerical points to the potential equation by lest-square fitting method to get the coefficients. Selecting the different ratios of/? = p0 /rQ and under a parabola fit approximation, we havec0 = ao/32 + bo/3 + d0a0 =-0.2771 b0 = 0.5035 d0 =0.8124a, =0.1948c, = a,/?2 +b,P + dx U =-0.4115— sqrtycl + 9cfa[2 + 25c2a24 + 6cocxa6 cos66>rowhere a= it ro.The trajectories of molecules in hexapole can be determined by a Newton's differential equation,d2r _-\ dWdE dt2 m dE drSince the electric field distribution E{r,6) and the dependence of the energies W with the electric field tensor E, which decide the forces acting on the molecules, are known, we can numerically simulate the molecular motion in this hexapole field. Obviously, it is just the geometrical structure of hexapole and the selected voltage to affect the field. By choosing a suitable hexapole and selected voltage, we can realize the role of state selection or focusing. One can theoretically select the voltage as large as the ideal results are obtained. But in fact, we could not infinitely increase the selected voltage for technique difficulties. From the present theoretical analysis, we can obtain a ideal design for the hexapole with a ratio of P ol ro equal to 0.5.Under the above theoretical frame and numerical methods, we calculate the rotational state selection and beam focus in hexapole electric field for symmetric top molecule CH3CN, diatomic molecule NO, the linear triatomic molecules with the doubling states OCS, HCN, C1CN, BrCN and ICN, and the asymmetric top molecule CH2F2, SO2, (CH^O. The influences of a high-order Stark effect, the molecular properties and state energies, and the experimental parameters such as molecular beam temperature and speed, the length of the hexapole, have been discussed.We also discuss laser alignment and orientation of molecules. In this case, the motion of molecules follows a time-dependent Schro dinger equationFor linear molecules in electron ground state, the Hamiltonian isrotos9B IBFor the case of CW laser and the pulse duration of laser is longer than rotational period, we can solve this Schrodinger equation as a time-independent problem by using an effective electric field. But in short pulse laser case the time-dependent Schrodinger equation must be solved. Moreover, we only study the alignment by polarized interaction under the nonresonant laser field because the dipole interaction can be quenched. But the dipole interaction can not be neglected for a resonant laser field since the field can excite the molecules from one electric state or vibrational state to another electric state or vibrational state within a sudden time and thus the dipole interaction is larger than the polarized interaction.Using a numerical method for solving the time-dependent Schrodinger equation, we study the alignment and orientation effects for diatomic molecule IC1 and linear triatomic molecule HCN in a nonresonant and resonant pulsed laser fields, respectively. The results show that a long pulsed laser can adiabatically take molecules to pendular states, and the alignment effect dispersed after the pulse if the laser intensity reduces slowly enough. For a short-pulse, there will be more or less alignment or orientation effects left after the laser pulse turned off, and even the (cos2 6) recurrences periodly with the coherent superstition of field-free states for an ultrafast laser pulse case where the interaction is an impulse as compared to rotations, that is, an intense pulse imparts a "kick" to the molecule that rapidly transfers a large amount of angular momentum to the system. As coherence is maintained in the ultrafast case, the alignment is reconstructed at predetermined times and survives for a perfectly controllable period. An intermediate case that occurs for a pulse between long and ultrafast pulsed laser, when laser turned on pendular states appear just like molecules in long pulsed laser and when laser turned off (cos2 O^j recurrences periodly as that in ultrafast pulsed laser case, but the coherence is weak and period of (cos2 8) is poor and irregular. Moreover, the dipole interaction becomes more effect if the laser isresonant pulse, and the orientation and alignment can be obtained through dipole term. When transition occurs, the cosine between dipole moment and laser electric field and rotational wavefunction will determine the population of the final states. On all accounts, the unique properties and great applicational potential of the rotational state-selection and alignment or orientation in molecules system would inspirit us to search and investigate these domains deeply. It can be foresee that the preparing of the unique molecular system will have important value in physics and chemistry, and must advance and consummate the relate subjects.