Geometric phase for collinear conical intersections. I. Geometric phase angle and vector potentials

We present a method for properly treating collinear conical intersections in triatomic systems. The general vector potential (gauge theory) approach for including the geometric phase effects associated with collinear conical intersections in hyperspherical coordinates is presented. The current study develops an introductory method in the treatment of collinear conical intersections by using the phase angle method. The geometric phase angle, η, in terms of purely internal coordinates is derived using the example of a spin-aligned quartet lithium triatomic system. A numerical fit and thus an analytical form for the associated vector potentials are explicitly derived for this triatomic A(3) system. The application of this methodology to AB(2) and ABC systems is also discussed.     

Dissipative geometric phase and decoherence in parity-violating chiral molecules

Within a generalized Langevin framework for open quantum systems, the cyclic evolution of a two-level system is analyzed in terms of the geometric phase extended to dissipative systems for Ohmic friction. This proposal is applied to the dynamics of chiral molecules where the tunneling and parity violating effects are competing. The effect of different system-bath coupling functions in the dissipated energy is shown to be crucial to understand the behavior of the geometric phase as well as the decoherence displayed by the corresponding interference patterns.     

A statistical theory of polydisperse block copolymer systems under weak supercrystallization

A statistical theory of conjugated macro- and microphase separation in flexile polydisperse block copolymer systems with a given arbitrary molecular structural distribution is developed in the mean field approximation. A special attention is paid to recognizing and calculating all terms having the least order of magnitude to be taken into account. To this end a special procedure is elaborated enabling to distinguish between strongly and weakly fluctuating order parameters characterizing polydisperse systems and to construct explicitly a one-field parametrization of the free energy of the systems under investigation. The contribution of so-called higher harmonics and effect of a redistribution of macromolecules among coexisting phases are taken into account therewith by a proper renormalization of the fourth vertex of the corresponding effective hamiltonian. In order to compare the presented approach and other existing theories phase diagrams of molten polydisperse diblock copolymer are built numerically in approximations corresponding to different theories. It is shown that our rigorous approach results in phase diagrams qualitatively different from the conventional ones. In particular, we predict the existence of one-phase region having a quasicrystal symmetry and regions of coexistence of this phase with disordered phase and one having the symmetry of the body-centered-oubic lattice as well as a considerable shrinking of the region of the existence of the lamellar phase.     

Second row transition metal mixed hydride-halide triatomic molecules

Summary The ground state structures and bond energies have been obtained for the triatomic MHX systems where M is the entire sequence of second row transition metal atoms and X is a halide. The most interesting results of this study appear when these systems are compared to the triatomic MH₂ and MX₂ systems. It turns out that the structure of the MHX systems are quite similar to the corresponding MH₂ systems in general. Most of the MHX systems to the right thus have bent low-spin ground states, indicating large covalent contributions to the bonding. RuHX is a special case and has a high-spin linear ground state. For the systems to the left ionicity dominates the bonding. An important result, with implications for halide ligand effects on carbonyl and olefin insertion into M-H and M-R bonds, is that the M-H bonds for the systems to the right have a different character and are significantly weaker for the MHX than for the MH₂ systems. A similar effect is noted when the M-Cl bond strengths of MCl₂ are compared to the ones in MHCl. Both these effects can be explained by a more cationic metal with mores ⁰-state character when halide ligands are present.     

化学反应中的几何相效应

锥形交叉可以通过几何相效应影响核动力学.在过去的一些年里关于锥形交叉的理论有大量的发展和进步,本文综述了分子反应动力学领域针对几何相效应研究的一些理论成果.介绍了分子反应动力学中与几何相效应直接相关的一些最新成果,同时也对这些重要结果进行了解释.我们相信几何相效应将会在非绝热化学中发挥最重要的作用.     

A Lie group method for molecular rovibrational spectra via the broken symmetry of U(r)(2)⊗U(υ)(4)

A special group chain that is appropriate for describing the rovibrational spectra of linear triatomic molecules with respect to both the vibration and the rotation of molecules as harmonic oscillators is given, and the corresponding Hamiltonian is constructed. The eigenvalue expression of the Hamiltonian is similar to the formula commonly used to calculate the rovibrational spectra of linear triatomic molecules. This method eliminates the physical uncertainty brought about by a variety of group chains. The relationships between parameters in the present expression and those in the commonly used expressions are given. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 83: 53–59, 2001     

Perimetric scale-shape coordinates for triatomic molecules

Perimetric nuclear coordinates of a triatomic molecule treat all three nuclei equivalently and are not subject to the triangle conditions. Through an appropriate orthogonal transformation they can be separated into one scale coordinate, viz., the circumference, and two shape coordinates, which are determined by the angles. The parameter space of the shape coordinates is an equilateral triangle. The basic formulas are given and the relationship between points in coordinate space and molecular shapes are elucidated. Received: 10 January 1996 / Accepted: 2 January 1997     

On the geometry of chemical reaction and phase equilibria

Kuhn-Tucker optimization theory is employed to obtain new results for the problem of the determination of equilibria in multi-phase multi-reaction systems. The results provide a complete classification of the possible types of behaviour that can occur for such systems. In this classification, there is an essential difference between the cases of systems for which no reactions have a set of stoichiometric coefficients that sum algebraically to zero, and systems for which this is not the case. The results yield a geometric interpretation that can be viewed as an extension of the corresponding interpretation of the geometry of systems undergoing phase equilibria alone. Illustrations are given of all possible cases of binary and ternary reacting systems.     

超球坐标下共线三原子反应散射的一阶Magnus数值传播法计算

使用一阶Magnus数值传播积分法计算了超球坐标描述下的共线三原子反应散射问题。应用于共线H+H_2和F+H_2体系得到了较好的结果。     

Stimulated radiative dissociation and gain measurements of Xe2Cl in solid xenon

The molecular charge transfer states of Cl-doped solid xenon form an ideal four-level laser system. UV excitation on the molecular XeCl (Bi ← X) pair potentials leads to the formation of the diatomic exciplex which relaxes with a nearly unity quantum yield to the triatomic Xe⁺₂ Cl⁻ (4²Γ) state. The radiative dissociation of the triatomic exciplex can be stimulated to provide monoenergetic atoms ≈ 1 eV above ground. While these systems are characterized by large gain coefficients, scattering losses predominate in samples prepared by standard matrix isolation techniques. Scattering losses are due to the inability of the lattice to accommodate the excess kinetic energy released in the bound to repulsive transition of the triatomic exciplex.     

A method to obtain the Eckart hamiltonian and the equations of motion of a highly deformable polyatomic system in tems of generalized coordinates

A general method that makes it possible to derive the Eckart hamiltonian and the equations of motion of a highly deformable polyatomic system in terms of generalized coordinates is presented. The overall rotation is taken into account and the method is applied to various non-reactive collisional tetratomic systems. namely (i) diatom-diatom, (ii) atom-linear symmetric triatomic and (iii) atom-bent symmetric triatomic.     

Nuclear motion on the orbitally degenerate electronic ground state of fully deuterated triatomic hydrogen

Nuclear motion in the vicinity of conical intersections of the degenerate electronic ground state of fully deuterated triatomic hydrogen, D(3), is investigated with the aid of a time-dependent wavepacket approach in hyperspherical coordinates. Vibronic energy level spectra and the eigenfunctions are examined by including, for example, (1) geometric phase (GP) correction, (2) diagonal Born-Huang (BH) correction, and (3) both GP and BH corrections to the Born-Oppenheimer adiabatic Hamiltonian and finally by considering the nonadiabatic coupling between the two electronic surfaces explicitly. It emerges from this study that inclusion of both the GP and BH corrections is insufficient to explain the spectral features observed in the experiment. The latter are recovered by considering the complete two-states coupled Hamiltonian only. This study shows that both the GP and BH corrections constitute a minor part of the surface coupling effects, in particular, on the dynamics of the upper adiabatic sheet. Most importantly, we add that the experimental signature of the GP effect appears only in the observed shift of the eigenlevels of the electronic state when compared to those obtained from a completely Born-Oppenheimer Hamiltonian. The detail fine structure of the observed band of the electronic state is shaped by the off-diagonal derivative coupling elements of the nonadiabatic coupling operator.     

化学反应的高精度从头算势能面

势能面是化学反应动力学研究的基础。近年来随着理论方法的发展与计算技术的进步,不但含三、四个原子反应体系的电子基态势能面的构建精度进一步提高,一些反应体系的多电子态耦合势能面的构建和含六个原子以上反应体系的高维从头算势能面的构建也取得了重要进展。本文结合若干典型体系势能面的构建工作,主要介绍了高精度电子基态势能面,包括Renner-Teller、旋轨耦合等非绝热效应的耦合势能面以及高维势能面方面的研究进展。     

Potential energy surface for linear triatomic molecules: An algebraic method

Recently, we proposed a new transformation between the angle of canonical coordinates and the bond angle to describe the bending motion in Potential Energy Surfaces (PES) of bent triatomic molecules. In this work we extend the transformation to include linear triatomic molecules. Results for the linear triatomic molecule N₂O are reported.     

Fournier polarography revisited

A theory for Fournier polarography and higher order harmonics is presented. This is valid for reversible systems under semi-infinite diffusion to stationary and expanding plane electrodes. The algorithm is simple, accurate and exploits the identities holding for the interfacial concentrations. The computations — minimal in nature — can be carried out easily and the results given here were evaluated taking into account the presence of harmonics to, at least, the twenty-fifth order.     

A universal method for calculating isobaric-isothermal sections of ternary system phase diagrams

A method for calculating and constructing isobaric-isothermal sections of ternary system phase diagrams with the use of convex hulls was developed. The method is based on the projection of the singularities of the lower part of the Gibbs energy convex hull onto the plane of component mole fractions followed by a geometric analysis of the properties of this projection. The method is applicable to a wide range of ternary systems, it can be used to find tie-line coordinates and determine the phase compositions of all the diagram regions. The quality of the suggested algorithm was estimated, and examples of the construction of several phase diagrams are given.     

Numerical generation of hyperspherical harmonics for tetra-atomic systems

A numerical generation method of hyperspherical harmonics for tetra-atomic systems, in terms of row-orthonormal hyperspherical coordinates-a hyper-radius and eight angles-is presented. The nine-dimensional coordinate space is split into three three-dimensional spaces, the physical rotation, kinematic rotation, and kinematic invariant spaces. The eight-angle principal-axes-of-inertia hyperspherical harmonics are expanded in Wigner rotation matrices for the physical and kinematic rotation angles. The remaining two-angle harmonics defined in kinematic invariant space are expanded in a basis of trigonometric functions, and the diagonalization of the kinetic energy operator in this basis provides highly accurate harmonics. This trigonometric basis is chosen to provide a mathematically exact and finite expansion for the harmonics. Individually, each basis function does not satisfy appropriate boundary conditions at the poles of the kinetic energy operator; however, the numerically generated linear combination of these functions which constitutes the harmonic does. The size of this basis is minimized using the symmetries of the system, in particular, internal symmetries, involving different sets of coordinates in nine-dimensional space corresponding to the same physical configuration.     

Computational studies of σ-type weak interactions between NCO/NCS radicals and XY(X = H,Cl;Y = F,Cl,and Br)

The triatomic radicals NCO and NCS are of interest in atmospheric chemistry,and both the ends of these radicals can potentially serve as electron donors during the formation of σ-type hydrogen/halogen bonds with electron acceptors XY(X = H,Cl;Y = F,Cl,and Br).The geometries of the weakly bonded systems NCO/NCS···XY were determined at the MP2/aug-cc-pVDZ level of calculation.The results obtained indicate that the geometries in which the hydrogen/halogen atom is bonded at the N atom are more stable than those where it is bonded at the O/S atom,and that it is the molecular electrostatic potential(MEP)-not the electronegativity-that determines the stability of the hydrogen/halogen bond.For the same electron donor(N or O/S) in the triatomic radical and the same X atom in XY,the bond strength decreases in the order Y = F > Cl > Br.In the hydrogen/halogen bond formation process for all of the complexes studied in this work,transfer of spin electron density from the electron donor to the electron acceptor is negligible,but spin density rearranges within the triatomic radicals,being transferred to the terminal atom not interacting with XY.     

Chemischer Transport fester Lösungen. 27. Mischphasenbildung und chemischer Transport im System ZnSe/GaAs

Chemical Vapor Transport of Solid Solutions. 27. Formation of Solid Solutions and Chemical Vapor Transport in the System GaAs/ZnSe The miscibility of ZnSe and GaAs as a function of temperature has been investigated. At temperatures above 1100 °C GaAs and ZnSe form out a continous crystalline solid solution. The phase diagram of this system is presented. Mixed crystals in the system GaAs/ZnSe can be prepared by means of chemical vapor transport using iodine as transport agent. Mass spectrometric investigations have shown the formation of AsSeI(g), an up to now unknown triatomic molecule. First approximate thermodynamic Data for AsSeI(g) are given. The knowledge of AsSeI and its thermodynamic stability is necessary to understand the transport phenomena.     

The geometrical-classical limit of algebraic Hamiltonians for molecular vibrotational spectra

A classical limit, which is amenable to a geometrical interpretation, is discussed for the vibron model of molecular vibrotational spectra. Both diatomic and triatomic molecules are considered. An example of a coupling between the two stretching modes of a linear triatomic is examined in detail.