Stark-selected beam of ground-state OCS molecules characterized by revivals of impulsive alignment

We make use of an inhomogeneous electrostatic dipole field to impart a quantum-state-dependent deflection to a pulsed beam of OCS molecules, and show that those molecules residing in the absolute ground state, X(1)Σ(+), |00(0)0>, J = 0, can be separated out by selecting the most deflected part of the molecular beam. Past the deflector, we irradiate the molecular beam by a linearly polarized pulsed nonresonant laser beam that impulsively aligns the OCS molecules. Their alignment, monitored via velocity-map imaging, is measured as a function of time, and the time dependence of the alignment is used to determine the quantum state composition of the beam. We find significant enhancements of the alignment ( = 0.84) and of state purity (>92%) for a state-selected, deflected beam compared with an undeflected beam.     

Second virial coefficients of asymmetric top molecules

A short self-contained derivation is given for the second virial coefficient B2(T) of a gas consisting of identical interacting asymmetric rigid rotors. The resulting expression is correct through variant Planck's over h2. First, the canonical partition function is derived by means of an variant Planck's over h expansion of exp[-H/(k(B)T)] due to Friedmann [Adv. Chem. Phys. 4, 225 (1962)]. The present work applies angular momentum operators and known facts from angular momentum theory. It is considerably more accessible than Friedmann's exposition, which is not based on angular momentum operators, but instead on explicit derivatives with respect to Euler angles. The partition function obtained from the variant Planck's over h expansion is applied to the derivation of an expression for B2(T) that is identical in appearance to the expression for symmetric rotors of T Pack [J. Chem. Phys. 78, 7217 (1983)]. The final equation in this work is valid for rigid rotors of any symmetry.     

Determination of alignment parameters for symmetric top molecules using nonresonant two-photon absorption

The polarization dependence of the two-photon absorption signal is described directly in terms of the matrix elements of the irreducible representation of the two-photon absorption tensor operator for an ensemble with cylindrical symmetry probed with identical photons of linear polarization. Non vanishing matrix elements are easily determined from the known tensor patterns of the specific two-photon transition. The formalism is applicable to the extraction of alignment parameters for symmetric top molecules as well as diatomics produced in collisions of unpolarized particles or in the photodissociation with a single photon of linear polarization.     

Rotational spectrum of asymmetric top molecules in combined static and laser fields

We examine the impact of the combination of a static electric field and a non-resonant linearly polarized laser field on an asymmetric top molecule. Within the rigid rotor approximation, we analyze the symmetries of the Hamiltonian for all possible field configurations. For each irreducible representation, the Schro?dinger equation is solved by a basis set expansion in terms of a linear combination of symmetric top eigenfunctions respecting the corresponding symmetries, which allows us to distinguish avoided crossings from genuine ones. Using the fluorobenzene and pyridazine molecules as prototypes, the rotational spectra and properties are analyzed for experimentally accessible static field strengths and laser intensities. Results for energy shifts, orientation, alignment, and hybridization of the angular motion are presented as the field parameters are varied. We demonstrate that a proper selection of the fields gives rise to a constrained rotational motion in three Euler angles, the wave function being oriented along the electrostatic field direction, and aligned in other two angles.     

The Fokker-Planck-Langevin model for rotational brownian motion. IV. Asymmetric top molecules

The general series expansion for the joint angular velocity-orientation conditional probability density for a fluid composed of asymmetric top molecules is derived, and expressions for the reorientational correlation functions, correlation times, spectral densities, and the correlation times relevant to magnetic relaxation via spin-rotation interactions are presented. The reorientational correlation times and spin-rotation functions computed using this Fokker-Planck-Langevin (FPL) model with isotropic friction tensor (τ_x = τ_y = τ_z) are compared with the corresponding times and functions computed with the J-diffusion limit of the extended diffusion (EDJ) model. The models are found to predict significantly different behaviour only in the regime where free rotation and precessional effects become important. The reorientation self- and cross-correlation times are shown to follow Hubbard relations in the limit of short τ_x, τ_y, τ_z. Numerical calculations of the FPL reorientational correlation functions, correlation times and spin-rotation functions show that these properties are sensitive to the anisotropies in the friction tensor in the rotational Langevin equation.     

Spectroscopic analysis of asymmetric top free radicals——Application to pure rotational spectra of NO_2 in the ground vibronic state

Several key problems involved in the analyses of spectra of asymmetric top molecules, i.e., the effective Hamiltonian, the representation and basis vector, identification of energy levels, the selection rules, the relative intensity, and Zeeman tuning rate, were elucidated systematically. Introducing the high-order centrifugal distortion terms into the effective Hamiltonian, the precision for calculation has been improved substantially, which allows us to analyze the high-lying rotational transitions. A global analysis of all available spectra of 14N16O2 in the ground vibronic state has been made to obtain a set of molecular constants of 14N16O2 in the ground vibronic state which is the most precise and extensive so far. Using the improved parameters, some FIR LMR lines left unassigned hitherto have been identified successfully.     

Extended rotational diffusion and orientational relaxation of symmetric top molecules in a strong dc electric field: second-rank orientational correlation functions

Second-rank orientational correlation functions (pertaining to Kerr effect relaxation and Raman scattering) are obtained using the extended rotational diffusion (J-diffusion) model of symmetric top polar molecules in a strong constant external field. It is shown that the shape of the molecule noticeably affects all second-rank correlation functions and relaxation times in the rare collision limit. In the opposite limit of frequent collisions, the quantities of interest are shown to be shape independent as a consequence of vanishingly small inertial effects. An interpolation formula for the orientation relaxation times in the intermediate regime between the rare and frequent collision limits is also given.     

Role of rotational temperature in adiabatic molecular alignment

One-dimensional alignment of molecules in the adiabatic limit, where the pulse duration greatly exceeds the molecular rotational periods, is studied experimentally. Four different asymmetric top molecules (iodobenzene, p-diiodobenzene, 3,4-dibromothiophene, and 4,4'-dibromobiphenyl), rotationally cooled through a high pressure supersonic pulsed valve, are aligned by a 9-ns-long pulse. Their orientations are measured through Coulomb explosion, induced by a 130-fs-long pulse, and by recording the direction of the recoiling ions. The paper focuses on the crucial role of the initial rotational temperature for the degree of alignment. In particular, we show that at molecular temperatures in the 1 K range very strong alignment is obtained already at intensities of a few times 10(11) W/cm2 for all four molecules. At the highest intensities (approximately 10(12) W/cm2) the molecules can tolerate without ionizing >or=0.92 in the case of iodobenzene. This is the strongest degree of alignment ever reported for any molecule.     

A computer assisted procedure of assignments of vibration–rotation bands of asymmetric and symmetric top molecules

An advanced graphically oriented interactive program package for assignments of complex (perturbed) vibration–rotation spectra of asymmetric and symmetric top molecules has been developed. In addition to the well known Loomis–Wood algorithm, the new procedure takes advantage of a precise knowledge of the lower (e.g. ground) vibrational state energies, works with a realistic approximation of effective Hamiltonians for lower as well as upper vibrational states, and allows an instant combination difference inspection of spectral lines by the graphical representation of the appropriate parts of the analyzed experimental spectrum. Being constrained to the combination difference checking, the new algorithm can directly assign the correct rotational quantum numbers as well as ‘quality weights’ estimating relative accuracies of the identified lines.     

Spectroscopic analysis of asymmetric top free radicals

Several key problems involved in the analyses of spectra of asymmetric top molecules, i.e., the effective Hamiltonian, the representation and basis vector, identification of energy levels, the selection rules, the relative intensity, and Zeeman tuning rate, were elucidated systematically. Introducing the high-order centrifugal distortion terms into the effective Hamiltonian, the precision for calculation has been improved substantially, which allows us to analyze the high-lying rotational transitions. A global analysis of all available spectra of¹⁴N¹⁶O₂ in the ground vibronic state has been made to obtain a set of molecular constants of¹⁴N¹⁶O₂ in the ground vibronic state which is the most precise and extensive so far. Using the improved parameters, some FIR LMR lines left unassigned hitherto have been identified successfully.     

Calculation of the rotational constants A and C for isotopic species of slightly perturbed CH3CN symmetric top molecules

A technique which was employed earlier to calculate the rotational constants of CH₃CCH has been extended to the ground and two vibrational levels in thev ₈ vibration of CH₃CN for several isotopic species. The moments of inertia and a computer iteration technique over experimental data for each isotopic species were employed to evaluate the constantA _v in an excited vibrational state for a symmetric top molecule. This method gave good estimates forA _v for each isotope. The angle of bending and the orientation of each molecular system in reference frames, one fixed on the carbon atom at the -CN site and the other at the center of mass, were explored. These results are discussed in this paper. The method, which was applied by Tam and Roberts to the nv₁₀,n=1, 2, 3, 4, vibrations of CH₃CCH earlier and which was extended to thev ₁₀=1 vibration of CH₃CCH with¹³C isotopic species, has been applied to¹³C isotopic species of CH₃CN and seems to be a useful tool to extract the value ofA ₀. Each of these molecules shows reasonable dependency ofA _v over vibrational levels. Values ofA _v calculated from the geometrical model are in good agreement with those obtained by fitting the terms in the frequency equations, which containedA _v , to the experimental data through an iteration technique in which the value ofA was allowed to vary.     

Collisional induced rotational excitation ofN-atomic molecules

A simple model for collisional rotational excitation of diatomic molecules presented previously (in excellent agreement with experiments and computations for electron-Na₂ collisions at about 300 eV) is extended toN-atomic molecules. Special attention is given to highly symmetric cases, where all molecular atoms are equivalent (with the possible exception of a different atom in the centre). Selection rules, propensity rules and rotational rainbow structures in differential state-to-state cross sections are discussed.     

Detection of collision-induced rotational alignment in counterpropagating beam scattering

Collision-induced rotational alignment of NH₃ scattered from He is detected in a counterpropagating pulsed molecular beam scattering experiment. Starting from an isotope distribution of the initial rotational angular momentum, the generation of a highly aligned product ensemble due to inelastic scattering is observed. For all probed state-resolved differential cross sections the alignment changes from negative values for backward scattering to positive values at small deflection angles which is in qualitative agreement with predictions from a geometric apse model. The degree of alignment strongly depends on the final rotational state, indicating a correlation with the involved energy transfer.     

Optimal molecular alignment and orientation through rotational ladder climbing

We study the control by electromagnetic fields of molecular alignment and orientation in a linear, rigid-rotor model. With the help of a monotonically convergent algorithm, we find that the optimal field is in the microwave part of the spectrum and acts by resonantly exciting the rotation of the molecule progressively from the ground state, i.e., by rotational ladder climbing. This mechanism is present not only when maximizing orientation or alignment, but also when using prescribed target states that simultaneously optimize the efficiency of orientation/alignment and its duration. The extension of the optimization method to consider a finite rotational temperature is also presented.     

The rotational partition function for linear molecules

An important function in the statistical treatment of a gas of linear molecules is This sum is convenient to use mainly when α is large and alternate expressions, generally asymptotic expansions, are often used when α is small. In this paper, the sum is evaluated to yield a single expression that is valid for large and small values of α. The expression is composed of three terms, each of which involves the theta functions of Jacobi. One term is in the form of an integral, but is small relative to the other two and easily evaluated by numerical means. The expression is readily differentiated and can be used for the general evaluation of the rotational partition function for gases of linear molecules at all temperatures. This revised version was published online in July 2006 with corrections to the Cover Date.     

Long-range interactions in molecules and rotational coupling

We report a case study on Na₂ of the influence of rotational coupling for molecular states directly below the dissociation limit, where the electronic binding energy and the hyperfine interactions are of similar magnitude and the rotational energy can be varied from small to large compared to the former energies. The experimental observation and the theoretical analysis are important for obtaining precise data concerning long-range interactions and extrapolation to the dissociation limit, which are required for describing cold collisions in atomic traps. A consistent model for all observations with rotational quantum number J′ up to 41 is developed which involves few atomic parameters and demonstrates that these are sufficient to describe molecular levels few μeV below the dissociation energy.     

Measurement of the field-free alignment of diatomic molecules

An apparatus was constructed to experimentally quantify the field-free alignment of diatomic molecules irradiated by strong femtosecond laser pulses. In this apparatus, both homodyne and pure heterodyne detections were realized. The alignment signal is proportional to [ - 1/3](2) for homodyne detection and ( - 1/3) for pure heterodyne detection, where theta is the polar angle between the molecular axis and the laser polarization direction. Fourier transform spectra of the homodyne signal and the pure heterodyne signal were also studied. By comparing the alignment signal and its Fourier transform spectrum with the numerical calculation of the time-dependent Schr?dinger equation, we demonstrated that the pure heterodyne signal directly reproduced the alignment parameter , and its Fourier transform spectrum provided information regarding the populations of different J states in the rotational wavepacket.