Photofragment angular momentum distribution beyond the axial recoil approximation: predissociation

We present the quantum mechanical expressions for the angular momentum distribution of the photofragments produced in slow predissociation. The paper is based on our recent theoretical treatment [J. Chem. Phys. 123, 034307 (2005)] of the recoil angle dependence of the photofragment multipole moments which explicitly treat the role of molecular axis rotation on the electronic angular momentum polarization of the fragments. The electronic wave function of the molecule was used in the adiabatic body frame representation. The rigorous expressions for the fragment state multipoles which have been explicitly derived from the scattering wave function formalism have been used for the case of slow predissociation where a molecule lives in the excited quasibound state much longer than a rotation period. Possible radial nonadiabatic interactions were taken into consideration. The optical excitation of a single rotational branch and the broadband incoherent excitation of all possible rotational branches have been analyzed in detail. The angular momentum polarization of the photofragments has been treated in the high-J limit. The polarization of the photofragment angular momenta predicted by the theory depends on photodissociation mechanism and can in many cases be significant.     

Vector correlations in photodissociation of polarized polyatomic molecules beyond the axial recoil limit

We present the full quantum mechanical theory of the angular momentum distributions of photofragments produced in photolysis of oriented/aligned parent polyatomic molecules beyond the axial recoil limit. This paper generalizes the results of Underwood and Powis(28,29) to the case of non-axial recoil photodissociation of an arbitrary polyatomic molecule. The spherical tensor approach is used throughout this paper. We show that the recoil angular distribution of the angular momentum polarization of each of the photofragments can be presented in a universal spherical tensor form valid for photolysis in diatomic or polyatomic molecules, irrespective of the reaction mechanism. The angular distribution can be written as an expansion over the Wigner D-functions in terms of the set of the anisotropy-transforming coefficients c(K(i)q(i))(K) (k(d), K(0)) which contain all of the information about the photodissociation dynamics and can be either determined from experiment, or computed from quantum mechanical theory. An important new conservation rule is revealed through the analysis, namely that the component q(i) of the initial reagent polarization rank K(i) and the photofragment polarization rank K onto the photofragment recoil direction k is preserved in any photolysis reaction. Both laboratory and body frame expressions for the recoil angle dependence of the photofragment angular momentum polarization are presented. The parent molecule polarization is shown to lead to new terms in the obtained photofragment angular distributions compared with the isotropic case. In particular, the terms with |q(i)| > 2 can appear which are shown to manifest angular momentum helicity non-conservation in the reaction. The expressions for the coefficients c(K(i)q(i))(K) (k(d), K(0)) have been simplified using the quasiclassical approximation in the high-J limit which allows for introducing the dynamical functions and the rotation factors which describe the decreasing of the photofragment angular momentum orientation and alignment due to the rotation of the molecular axis during photodissociation. In this case, the resultant recoil angle dependence is also presented in a form where the anisotropy of the parent molecular ensemble is expressed in terms of the molecular axis distribution, rather than in terms of the molecular density matrix.     

Photodissociation dynamics of OCS at 248 nm: the S((1)D(2)) atomic angular momentum polarization

The dissociation of OCS has been investigated subsequent to excitation at 248 nm. Speed distributions, speed dependent translational anisotropy parameters, angular momentum alignment, and orientation are reported for the channel leading to S((1)D(2)). In agreement with previous experiments, two product speed regimes have been identified, correlating with differing degrees of rotational excitation in the CO coproducts. The velocity dependence of the translational anisotropy is also shown to be in agreement with previous work. However, contrary to previous interpretations, the speed dependence is shown to primarily reflect the effects of nonaxial recoil and to be consistent with predominant excitation to the 2 (1)A(') electronic state. It is proposed that the associated electronic transition moment is polarized in the molecular plane, at an angle greater than approximately 60 degrees to the initial linear OCS axis. The atomic angular momentum polarization data are interpreted in terms of a simple long-range interaction model to help identify likely surfaces populated during dissociation. Although the model neglects coherence between surfaces, the polarization data are shown to be consistent with the proposed dissociation mechanisms for the two product speed regimes. Large values for the low and high rank in-plane orientation parameters are reported. These are believed to be the first example of a polyatomic system where these effects are found to be of the same order of magnitude as the angular momentum alignment.     

The parity-adapted basis set in the formulation of the photofragment angular momentum polarization problem: the role of the Coriolis interaction

We present a theoretical framework for calculating the recoil-angle dependence of the photofragment angular momentum polarization taking into account both radial and Coriolis nonadiabatic interactions in the diatomic/linear photodissociating molecules. The parity-adapted representation of the total molecular wave function has been used throughout the paper. The obtained full quantum-mechanical expressions for the photofragment state multipoles have been simplified by using the semiclassical approximation in the high-J limit and then analyzed for the cases of direct photodissociation and slow predissociation in terms of the anisotropy parameters. In both cases, each anisotropy parameter can be presented as a linear combination of the generalized dynamical functions fK(q,q',q,q') of the rank K representing contribution from different dissociation mechanisms including possible radial and Coriolis nonadiabatic transitions, coherent effects, and the rotation of the recoil axis. In the absence of the Coriolis interactions, the obtained results are equivalent to the earlier published ones. The angle-recoil dependence of the photofragment state multipoles for an arbitrary photolysis reaction is derived. As shown, the polarization of the photofragments in the photolysis of a diatomic or a polyatomic molecule can be described in terms of the anisotropy parameters irrespective of the photodissociation mechanism.     

Molecular and collective modes in ferroelectric liquid crystals studied by dielectric spectroscopy

The complex dielectric permittivity has been measured for a ferroelectric liquid crystal in the range 102-109Hz. Six different relaxations have been obtained and characterized: soft mode (SmA* and SmC* phases), Goldstone mode (SmC* phase), rotation around molecular long axis, rotation around molecular short axis, ferroelectric domain mode (SmC* phase) and an internal motion associated with a polar group. Strengths and frequencies of these modes have been obtained for the different phases for different bias fields. Using these results together with spontaneous polarization and molecular tilt measurements we have also obtained the rotational viscosities associated with the soft mode and the Goldstone mode. We explain the results in the light of the so-called Landau extended model, concluding that the biquadratic coupling between polarization and tilt is quite important with regard to the bilinear coupling. This fact has been used to explain the noticeable increase of the activation energy of the frequency of the mode related to the rotation around the molecular long axis at the SmA*-SmC* phase transition.     

Structural and electro-optical investigations of the smectic phase of chlorine-substituted banana-shaped compounds

Six members of a new homologous series of achiral banana-shaped molecules have been synthesized and studied by optical microscopy, differential scanning calorimetry, NMR spectroscopy and X-ray diffraction. According to X-ray diffraction measurements on oriented samples, four homologues form an XB2 phase behaviour. From electro-optical studies the spontaneous polarization and the tilt angle could be measured. An orientational order parameter of 0.8 was determined by 13C NMR and this is nearly independent of the temperature. NMR investigations also give information about the real conformation of the molecules in the XB2 phase. Dielectric measurements indicate that the rotation around the molecular long axis is clearly hindered because of the packing of the bent molecules within the smectic layers. which exhibits antiferroelectric switching     

Theoretical study of the photodissociation of Li(2)+ in one-color intense laser fields

A theoretical treatment of the photodissociation of the molecular ion Li(2) (+) in one-color intense laser fields, using the time-dependent wave packet approach in a Floquet Born-Oppenheimer representation, is presented. Six electronic states 1,2?(2)Σ(g)(+), 1,2?(2)Σ(u)(+), 1?(2)Π(g), and 1?(2)Π(u) are of relevance in this simulation and have been included. The dependences of the fragmental dissociation probabilities and kinetic energy release (KER) spectra on pulse width, peak intensity, polarization angle, wavelength, and initial vibrational level are analyzed to interpret the influence of control parameters of the external field. Three main dissociation channels, 1?(2)Σ(g)(+) (m = -1), 2?(2)Σ(g)(+) (m = -2), and 2?(2)Σ(u)(+) (m = -3), are seen to dominate the dissociation processes under a wide variety of laser conditions and give rise to well separated groups of KER features. Different dissociation mechanisms for the involved Floquet channels are discussed.     

Microscopic origin of spontaneous polarization in ferroelectric SC* liquid crystals

The origin of spontaneous polarization in the ferroelectric smectic C* phase is investigated within a mean-field microscopic model which describes the coupling between the tilt of molecules from the normal to the smectic layers and the rotation of a molecule around its long axis. The mean-field potential is studied which takes into account a chiral polar and a non-chiral quadrupolar biasing of the rotation of molecules around the molecular long axes. Each molecule is characterized by three transverse molecular axes: the chiral axis which turns parallel to the macroscopic C₂ axis at small tilts, the polar axis in the direction of the transverse dipole moment and the quadrupolar axis which tends to be parallel to the C₂ axis at very large tilts. A numerical analysis of the model shows that there are four different types of spontaneous polarization dependent on the temperature, including the sign-reversal type. The influence of three microscopic parameters, i.e. two angles between the three characteristic axes and the relative strength of the chiral versus the non-chiral biasing, on the type of spontaneous polarization is investigated. The relationship between the microscopic and the equivalent Landau model is established and discussed.     

Anisotropy of dielectric relaxation in crystal form II of poly(vinylidene fluoride)

The anisotropy of the crystalline relaxation (α relaxation) in oriented poly(vinylidene fluoride) in crystal form II has been studied. The dielectric increment Δε is analyzed on the basis of the two-site model. A linear relation between Δε/χξ and cos²θ is obtained, where χ is the degree of crystallinity, ξ is the ratio of the internal field to the applied field, and θ is the angle between the applied electric field and the molecular axis. The dipole moment changes direction only along the molecular axis in the relaxation in crystal form II; the molecular motion cannot be explained by chain rotation around the molecular axis. Possible models for the α relaxation are proposed: change in conformation with internal rotation can occur in the crystalline chains, and defects in the crystalline regions play an important role in the α relaxation.     

Molecular and electronic structure of halogen-substituted phosphaalkenes

Peculiarities of the molecular and electronic structure of P- and C-halogen-substituted phosphaalkenes have been considered on the basis of results of X-ray diffraction studies and quantumchemical calculations. Introduction of an electronegative halogen atom is shown to have an insignificant effect on the intramolecular bond angle distribution, whereas the influence on the P=C bond length is noticeable. Thus, in P-substituted phosphaalkenes it substantially increases the polarization of the P=C bond (which causes its noticeable shortening). In C-substituted phosphaalkenes the effect of halogen atoms is less pronounced: decreasing the P=C bond polarization leads only to its slight elongation. In addition, a considerable elongation of the phosphorus-halogen bond in comparison with three-coordination phosphorus compounds is a peculiarity of the molecular structure of P-halogen-substituted phosphaalkenes.     

Heme distortions in sperm-whale carbonmonoxy myoglobin: correlations between rotational strengths and heme distortions in MD-generated structures

We have investigated the effects of heme rotational isomerism in sperm-whale carbonmonoxymyoglobin using computational techniques. Several molecular dynamics simulations have been performed for the two rotational isomers A and B, which are related by a 180 degrees rotation around the alpha-gamma axis of the heme, of sperm-whale carbonmonoxy myoglobin in water. Both neutron diffraction and NMR structures were used as starting structures. In the absence of an experimental structure, the structure of isomer B was generated by rotating the heme in the structure of isomer A. Distortions of the heme from planarity were characterized by normal coordinate structural decomposition and by the angle of twist of the pyrrole rings from the heme plane. The heme distortions of the neutron diffraction structure were conserved in the MD trajectories, but in the NMR-based trajectories, where the heme distortions are less well defined, they differ from the original heme deformations. The protein matrix induced similar distortions on the hemes in orientations A and B. Our results suggest that the binding site prefers a particular macrocycle conformation, and a 180 degrees rotation of the heme does not significantly alter the protein's preference for this conformation. The intrinsic rotational strengths of the two Soret transitions, separated according to their polarization in the heme plane, show strong correlations with the ruffling deformation and the average twist angle of the pyrrole rings. The total rotational strength, which includes contributions from the chromophores in the protein, shows a weaker correlation with heme distortions.     

Static-lattice theory of crystalline HCN.: II. Elastic and piezoelectric properties

An effective dipole potential is used to calculate the elastic and piezoelectric coefficients for a static-lattice model of tetragonal HCN, using the generalized thermodynamic theory of internal strain. The model is unstable with respect to molecular rotation away from the tetragonal axis, owing to the use of a point effective dipole. An improved potential would represent the molecule as a set of polarizable point dipoles. Isotropic pressures makes HCN expand along the tetragonal axis as it contracts perpendicular to the axis, because of strong elastic cross-linking. The piezoelectric stress coefficient for shear strain is dominated by the contribution from molecular rotation. Both physical and thermodynamic coefficients are calculated; the differences between the coefficients, which arise from the permanent polarization in HCN, are especially marked in the strain coefficient.     

Photochemistry of the model phototropic system involving flavins and indoles. I. Fluorescence polarization and MO calculations of the direction of the electronic transition moments in flavins

Abstract— The fluorescence polarization spectra of riboflavin, lumiflavin, and alloxazine under different conditions have been obtained. It has been shown that the polarization spectrum of riboflavin is not affected significantly by media such as D₂O-glycerol (50: 50) and castor oil. Our data do not indicate the anomalous spectral shift of riboflavin in castor oil, in contrast to the previous finding described by Thomas. The electronic structures of lumiflavin and alloxazine are similar to that of riboflavin, as revealed by the fluorescence polarization measurements and the molecular orbital calculations. The Pariser-Parr-Pople semiempirical SCF ASMO CI computations have been performed to compare the calculated transition moments with the polarization data. The theory predicts an angle of 42° between the 450 and 365 nm transition oscillators, in reasonable agreement with the experimental angle of about 49°. It has been shown, from the comparison of the calculated and observed spectral quantities, that the pseudo-heteroatom model for treating methyl groups in the flavin molecule is not adequate. The group orbital and inductive approximations appear to be satisfactory. Finally, the implication of the present findings has been briefly discussed in connection with phototropism.     

Absolute orientation of molecules at interfaces

A method to determine the absolute orientation of molecules at liquid interfaces by sum frequency generation (SFG) is reported. It is based on measurements of the orientations of two nonparallel vibrationally active chromophores in the molecule of interest combined with a rotation matrix formulation to obtain the absolute molecular orientation. We chose m-tolunitrile, a planar molecule adsorbed to the air/water interface, as a proof-of-method experiment. Quantitative analysis of different polarization sum frequency intensities facilitate unique peak assignments of the methyl and nitrile groups of m-tolunitrile. The SFG analysis of the measurement yields a nitrile group tilting at 53 degrees to the surface normal, and the C3 axis of the methyl group is almost upright at 23 degrees with respect to the surface normal. Using a rotation matrix formulation, we found that the angle between the surface plane and the m-tolunitrile molecular plane is 70 degrees.     

Orientational motions of vibrational chromophores in molecules at the air/water interface with time-resolved sum frequency generation

The first time-resolved experiments in which interfacial molecules are pumped to excited electronic states and probed by vibrational sum frequency generation (SFG) are reported. This method was used to measure the out-of-plane rotation dynamics, i.e. time dependent changes in the polar angle, of a vibrational chromophore of an interfacial molecule. The chromophore is the carbonyl group, the rotation observed is that of the -C=O bond axis, with respect to the interfacial normal, and the interfacial molecule is coumarin 314 (C314) at the air/water interface. The orientational relaxation time was found to be 220+/-20 ps, which is much faster than the orientational relaxation time of the permanent dipole moment axis of C314 at the same interface, as obtained from pump-second harmonic probe experiments. Possible effects on the rotation of the -C=O bond axis due to the carbonyl group hydrogen bonding with interfacial water are discussed. From the measured equilibrium orientation of the permanent dipole moment axis and the carbonyl axis, and knowledge of their relative orientation in the molecule, the absolute orientation of C314 at the air/water interface is obtained.     

13C N.M.R. and 14N N.Q.R. in ferroelectric liquid crystals Polar versus quadrupolar ordering

¹³C nuclear magnetic resonance and ¹⁴N nuclear quadrupole resonance spectra of ferroelectric smectic C*liquid crystals and their non-chiral analogues allow for a microscopic determination of the polar and quadrupolar (or bipolar) biasing of rotation around the long molecular axis as well as for a determination of the anisotropy in the fluctuations of this axis. The results show that the microscopic origin of the biquadratic coupling between the polarization and the tilt, which has been recently introduced into the extended Landau model of the S_A-S*_C transition, is the quadrupolar (or bipolar) rotational bias induced by the anisotropy in the fluctuations of the long molecular axis. The tilt induced anisotropy in the fluctuations is practically identical in chiral and non-chiral smectic C phases.     

Geometry and electronic structure of the dimethyl sulfoxide dimer. Calculation by the MNDO method

The geometric and electronic structure of the complex formed by dipole-dipole interaction between two molecules of DMSO in the "head-to-tail" orientation were calculated by the MNDO quantum-chemical method. The minimum total energy corresponds to a distance of 5.5 Å between the sulfur atoms, and the angle between the axis of the molecular dipoles is 16.4°. This agrees with calculations for liquid DMSO by molecular dynamics. The large equilibrium distance between the DMSO molecules explains its low density in the liquid phase and the high intensity of microwave absorption due to free volume sufficient for rotation of one molecule in the complex in relation to the dipole axis of the other.N. D. Zelinskii Institute of Organic Chemistry, Russian Academy of Sciences, 117334 Moscow. Translated fromIzvestiya Akademii Nauk, Seriya Khimicheskaya, No. 6, pp. 1340–1344, June, 1992.     

Assessing an impulsive model for rotational energy partitioning to acetyl radicals from the photodissociation of acetyl chloride at 235 nm

This work uses the photodissociation of acetyl chloride to assess the utility of a recently proposed impulsive model when the dissociation occurs on an excited electronic state that is not repulsive in the Franck-Condon region. The impulsive model explicitly includes an average over the vibrational quantum states of acetyl chloride when it calculates an impact parameter for fission of the C-Cl bond, as well as the distribution of thermal energy in the photolytic precursor. The experimentally determined stability of the resulting acetyl radical to subsequent dissociation is the key observable that allows us to test the model's ability to predict the partitioning of energy between rotation and vibration of the radical. We compare the model's predictions for three different assumed geometries at which the impulsive force might act, generating the relative kinetic energy and the concomitant rotational energy in the acetyl radical. Assuming that the impulsive force acts at the transition state for C-Cl fission on the S(1) excited state gives a poor prediction; the model predicts far more energy in rotation of the acetyl radical than is consistent with the measured velocity map imaging spectrum of the stable radicals. The best prediction results from using a geometry derived from the classical trajectory calculations on the excited state potential energy surface. We discuss the insight gained into the excited state dissociation dynamics of acetyl chloride and, more generally, the utility of using the impulsive model in conjunction with excited state trajectory calculations to predict the partitioning of internal energy between rotation and vibration for radicals produced from the photolysis of halogenated precursors.     

Conformational identification of tryptamine embedded in superfluid helium droplets using electronic polarization spectroscopy

We report electronic polarization spectroscopy of tryptamine embedded in superfluid helium droplets. In a dc electric field, dependence of laser induced fluorescence from tryptamine on the polarization direction of the excitation laser is measured. Among the three observed major conformers A, D, and E, conformers D and E display preference for perpendicular excitation relative to the orientation field, while conformer A is insensitive to the polarization direction of the excitation laser. We attribute the behavior of conformer A to the fact that the angle between the permanent dipole and the transition dipole is close to the magic angle. Using a linear variation method, we can reproduce the polarization preference of the three conformers and determine the angle between the transition dipole and the permanent dipole. Since the side chain exerts small effect on the direction of the transition dipole in the frame of the indole chromophore, all three conformers have a common transition dipole more or less in the indole plane at an angle of approximately 60 degrees relative to the long axis of the chromophore. The orientation of the side chain, on the other hand, determines the size and direction of the permanent dipole, thereby affecting the angle between the permanent dipole and the transition dipole. For conformer D in the droplet, our results agree with the Anti(ph) structure, rather than the Anti(py) structure. Our work demonstrates that polarization spectroscopy is effective in conformational identification for molecules that contain a known chromophore. Although coupling of the electronic transition with the helium matrix is not negligible, it does not affect the direction of the transition dipole.     

Quantum effect on the internal proton transfer and structural fluctuation in the H+ 5 cluster

The thermal equilibrium state of H+(5) is investigated by means of an ab initio path integral molecular dynamics (PIMD) method, in which degrees of freedom of both nuclei and electrons at finite temperature are quantized within the adiabatic approximation. The second-order Moller-Plesset force field has been employed for the present ab initio PIMD. At 5-200 K, H+(5) is shown to have the structure that the proton is surrounded by the two H(2) units without any exchange of an atom between the central proton and the H(2) unit. At 5 K, the quantum tunneling of the central proton occurs more easily when the distance between the two H(2) units is shortened. At the high temperature of 200 K, the central proton is more delocalized in space between the two H(2) units, with less correlation with the stretching of the distance between the two H(2) units. As for the rotation of the H(2) units around the C(2) axis of H+(5) , the dihedral angle distribution is homogeneous at all temperatures, suggesting that the two H(2) units freely rotate around the C(2) axis, while this quantum effect on the rotation of the H(2) units becomes more weakened with increasing temperature. The influence of the structural fluctuation of H+(5) on molecular orbital energies has been examined to conclude that the highest occupied molecular orbital-lowest unoccupied molecular orbital energy gap is largely reduced with the increase of temperature because of the spatial expansion of the whole cluster.