Hierarchy of effective modes for the dynamics through conical intersections in macrosystems

An extension of the effective-mode theory for the short-time dynamics through conical intersections in macrosystems [L. S. Cederbaum et al., Phys. Rev. Lett. 94, 113003 (2005)] is proposed. The macrosystem, containing a vast number of nuclear degrees of freedom (modes), is decomposed into a system part and an environment part. Only three effective modes are needed-together with the system's modes-to accurately calculate low resolution spectra and the short-time dynamics of the entire macrosystem. Here, the authors propose an iterative scheme to construct a hierarchy of additional triplets of effective modes. This naturally extends the effective-mode formulation. By taking into account more and more triplets, the dynamics are accurately predicted for longer and longer times, and more resolved spectra can be calculated. Numerical examples are presented, computed using various numbers of additional effective modes.     

Effects of higher order Jahn-Teller coupling on the nuclear dynamics

In this paper effects of higher order Jahn-Teller coupling terms on the nonadiabatic dynamics are studied. Of particular interest is the case when the potential energy surfaces of the degenerate state show pronounced anharmonicity. In order to demonstrate the effects a two-dimensional E multiply sign in circle e Jahn-Teller model system is treated which is based on the e(') stretching vibration of the photoactive (2)E(') state of NO(3) as a realistic example. The sixth order E multiply sign in circle e Jahn-Teller Hamiltonian is derived in the diabatic representation which is valid for any system with a C(3) rotation axis. This diabatization scheme is compared to lower-order Jahn-Teller Hamiltonians and to symmetry adapted as well as ad hoc approximations. Lower-order potentials result in pronounced quantitative and qualitative differences in the dynamics, including differences in the evolution of mean values, the autocorrelation functions (and thus the corresponding spectra), and the electronic population evolution. In the particular example treated, the results of fourth and fifth order potentials are very similar to the sixth order reference system. In contrast, the approximate sixth order Hamiltonians, though the corresponding adiabatic surfaces seem to be nearly identical, results in pronounced differences. The possible consequences for the dynamics of realistic systems with higher dimensionality are briefly discussed.     

Conical and glancing Jahn-Teller intersections in the cyclic trinitrogen cation

The ground and electronically excited states of cyclic N(3) (+) are characterized at the equilibrium D(3h) geometry and along the Jahn-Teller distortions. Lowest excited states are derived from single excitations from the doubly degenerate highest occupied molecular orbitals (HOMOs) to the doubly degenerate lowest unoccupied molecular orbitals (LUMOs), which give rise to two exactly and two nearly degenerate states. The interaction of two degenerate states with two other states eliminates linear terms and results in a glancing rather than conical Jahn-Teller intersection. HOMO-2-->LUMOs excitations give rise to two regular Jahn-Teller states. Optimized structures, vertical and adiabatic excitation energies, frequencies, and ionization potential (IP) are presented. IP is estimated to be 10.595 eV, in agreement with recent experiments.     

Jahn-Teller effect for short-lived states: study of the complex potential energy surfaces

The Jahn-Teller effect for bound electronic states has been investigated for many decades. In contrast, nothing is known regarding its occurrence for short-lived electronic states. Here we investigate the linear and the quadratic E multiply x e Jahn-Teller effect for degenerate resonance states with special regard to the complex potential energy surfaces. We find many new phenomena for both the real and imaginary parts of the potential energy surfaces including additional minima and intersections. Possible simplifications of the equations describing the adiabatic potential energy surfaces are discussed. We also briefly investigate other Jahn-Teller effects in linear approximation. The theoretical concepts are exemplified by calculating ab initio data for the degenerate Pi(*)-type resonance states of the tris(boramethyl)amin anion along two different doubly degenerate vibrational modes.     

The Jahn-Teller and Barnett effects

In the usual formulation of the Jahn-Teller effect a simplification is made in going from the adiabatic to the crude adiabatic approximation in which the electronic parts of the vibronic wavefunction are assumed independent of the nuclear coordinates. This then neglects momentum coupling in the vibronic coupling matrix. The momentum coupling has been termed the molecular Barnett effect when the active vibration transforms as the irreducible representation of a rotation in the molecular point group. Experimental evidence for the molecular Barnett effect has recently been found. In this paper the various point groups in which momentum and Barnett coupling can occur are investigated. A vibration capable of momentum coupling is contained in the asymmetric direct product of the degenerate electronic state and, as with the Jahn-Teller effect, is possible in the orbitally degenerate electronic states of molecules of all non-linear point groups. A static distortion along such a coordinate will lift the electronic degeneracy. Unlike the Jahn-Teller effect, however, in some point groups a minimum complexity of the molecule is required before such coupling can occur. In particular it will be absent in the degenerate electronic states of such simple molecules of the form X₃(D_3h); XY₃(C_3v, D_3h); XY₄(T_d); and XY₆(O_h).     

Cluster expansion of the wavefunction. Ionization potentilals of benzene

The vertical and adiabatic ionization potentiais of benzene are studied by the cluster expansion of the wavefunction theory. The calculation confirms the assignment of the photoelectron spectrum experimentally proposed by Jonsson and Lindholm. The nature of the Jahn-Teller effect in states arising from ionization of doubly degenerate π and σ orbitals is also discussed.     

On the (Emultiply sign in circlee)-Jahn-Teller conical intersections in the 3p(E') and 3d(E") Rydberg electronic states of triatomic hydrogen

The static and dynamic aspects of the Jahn-Teller (JT) interactions in the 3p(E') and 3d(E") Rydberg electronic states of H3 are analyzed theoretically. The static aspects are discussed based on recent ab initio quantum chemistry results, and the dynamic aspects are examined in terms of the vibronic spectra and nonradiative decay behavior of these states. The adiabatic potential-energy surfaces of these degenerate electronic states are derived from extensive ab initio calculations. The calculated adiabatic potential-energy surfaces are diabatized following our earlier study on this system in its 2p(E') ground electronic state. The nuclear dynamics on the resulting conically intersecting manifold of electronic states is studied by a time-dependent wave-packet approach. Calculations are performed both for the uncoupled and coupled state situations in order to understand the importance of nonadiabatic interactions due to the JT conical intersections in these excited Rydberg electronic states.     

PFI-ZEKE photoelectron spectra of the methane cation and the dynamic Jahn-Teller effect

High resolution pulsed-field-ionization (PFI) zero-kinetic-energy (ZEKE) photoelectron spectroscopy has been used to record the photoelectron spectra of CH4, CDH3, CD2H2 and CD4. The observed extensive progression of rotationally resolved transitions between 100,800 cm-1 and 104,100 cm-1 reveals for the first time the complex energy level structure of the methane cation. The high resolution enabled the determination of accurate values for the adiabatic ionization potentials of the different isotopomers. Based on a simple one-dimensional model for the pseudorotation in the different isotopomers, progress has been made towards the understanding of the Jahn-Teller effect at low energies. The static Jahn-Teller distortion in the ion could be determined directly from the vibrationless photoelectron transition in CD2H2. The analysis of the rotational structure in this spectrum with a rigid rotor model leads to an approximate experimental C2v structure. The dynamics of the other methane isotopomers near the adiabatic ionization potentials is dominated by large amplitude vibrational motions between equivalent structures. The corresponding ground state tunneling motions takes place on a picosecond time scale.     

Jahn-Teller coupling constants in the framework of the angular overlap model

The Jahn-Teller coupling constants for different symmetries are expressed as functions of the angular overlap model parameters. The resulting expressions allow an easy and straightforward evaluation of the Jahn-Teller stabilization energy; moreover the comparison among different compounds in similar series is facilitated. Two calculations on transition metal ion complexes are reported as an example.     

The Jahn-Teller effect in icosahedral molecules and complexes

The adiabatic potential surface for icosahedral systems having three-, four- and five-fold degenerate orbital states interacting with five-fold degenerate vibrations (T-v,U-v andV-v problems) is investigated. It is shown that for theT-v andV-v Jahn-Teller cases the potential surface possesses respectively a two- or three-dimensional equipotential continuum of minima. For theU-v problem the potential surface contains 15 equivalent minima. The nature of the extremum points on the adiabatic potential surfaces is elucidated. In the linear approximation to theV-v problem in the minima points the lowest potential surface is double degenerate due to the accidental occurrence of axial symmetry.     

Nonadiabatic couplings from time-dependent density functional theory: formulation in the Casida formalism and practical scheme within modified linear response

We present an efficient method to compute nonadiabatic couplings (NACs) between the electronically ground and excited states of molecules, within the framework of time-dependent density functional theory (TDDFT) in frequency domain. Based on the comparison of dynamic polarizability formulated both in the many-body wave function form and the Casida formalism, a rigorous expression is established for NACs, which is similar to the calculation of oscillator strength in the Casida formalism. The adiabatic local density approximation (ALDA) gives results in reasonable accuracy as long as the conical intersection (ci) is not approached too closely, while its performance quickly degrades near the ci point. This behavior is consistent with the real-time TDDFT calculation. Through the use of modified linear response theory together with the ground-state-component separation scheme, the performance of ALDA can be greatly improved, not only in the vicinity of ci but also for Rydberg transitions and charge-transfer excitations. Several calculation examples, including the quantization of NACs from the Jahn-Teller effect in the H3 system, have been given to show that TDDFT can efficiently give NACs with an accuracy comparable to that of wave-function-based methods.     

Effects of ethynyl substituents on the electronic structure of cyclobutadiene

The effects of ethynyl substitution on the electronic structure of cyclobutadiene are investigated in this work. Ethynyl substituted cyclobutadienes may be involved in Bergman cyclization reactions and are possible intermediates in the formation of fullerenes and graphitic sheets. Prediction of the electronic structure of cyclobutadiene is challenging for single-reference ab initio methods because of Jahn-Teller distortions and the diradical character of the singlet state. The equation-of-motion spin-flip coupled-cluster with single and double excitations (EOM-SF-CCSD) method accurately describes diradical states and is used to determine vertical and adiabatic singlet-triplet energy splittings in the substituted cyclobutadienes. The adiabatic singlet-triplet gaps decrease upon substituent addition, but the singlet states remain lower in energy. However, the results are affected by spin-contamination of the reference state and deteriorate when an unrestricted HF reference is employed. Additional insights in the electronic structure of cyclobutadienes are obtained by analyzing natural charges and spin densities. The substituents pull the charge out of the cyclobutadiene ring; however, the natural charges and spin densities are found to be nearly independent of the geometry and spin state.     

Is the B state of Na3 a case of Berry's phase?

The B state of Na₃ is often cited as an example of fractional quantization of the pseudorotational motion on the lower adiabatic surface of theE×e Jahn-Teller system. Recently, an alternative interpretation of the experimental results was given which is based on a pseudo-Jahn-Teller treatment and implies integer quantization. We present rotationally resolved spectra of a number of vibronic bands of the Na₃ B-X system and believe that they can only be explained in terms of integer quantum numbersj of the vibronic angular momentum.     

The EEL epectrum of the triplet exciton of C60 and the theoretical analysis of its vibronic structure

The electron energy loss (EEL) spectrum of the triplet exciton of the (111) surface of solid C₆₀ has been recorded at 105 K. Its rich vibronic structure is suggestive of a high degree of molecular distortion that occurs upon excitation. The static Jahn-Teller distortion of the isolated molecule, along the adiabatic potential energy surface of T₁, is determined by quantum-chemical calculations and the relaxed molecular structure is found to belong to the D_5d point group symmetry. The vibrational force field is evaluated at the distorted structure and used to simulate the EEL intensities of phonon-assisted transitions in the strong coupling regime.     

铜镁铝三元水滑石的姜-泰勒效应

采用密度泛函理论(DFT),用CASTEP程序模块,对类水滑石(CuxMg3-xAl-LDHs,x=0-3)周期性模型进行几何全优化,通过分析各体系的结构参数、电子排布、氢键、Mulliken电荷布居、结合能,总结出体系中的姜-泰勒效应和结构稳定性规律.结果表明,姜-泰勒效应不仅存在于d轨道未排满的Cu2+中,在p轨道未排满的Mg2+中也可能存在,且未饱和的d、p轨道共同影响着金属离子姜-泰勒畸变的大小.在CuxMg3-xAl-LDHs(x=0-3)中,铝八面体和镁八面体分别以稳定的拉长的八面体形式存在.而随着Cu2+的增加,铜八面体逐渐从压扁的八面体向稳定的拉长的八面体形式转变,体系获得了逐渐增多的姜-泰勒稳定化能.总体上,随着Cu2+的增加,体系中姜-泰勒效应导致的畸变使主客体间的氢键和静电作用力均有减弱趋势,且体系的结合能绝对值逐渐减小,故体系稳定性下降.这有助于从理论上进一步认识含铜水滑石的姜-泰勒效应.     

Potential energy surfaces and Jahn-Teller effect on CH4...NO complexes

The potential energy surface of the CH(4)...NO van der Waals complexes was explored at the RCCSD(T)/aug-cc-pVTZ level including the full counterpoise correction to the basis set superposition error. The Jahn-Teller distortion of the C(3v) configurations for the CH bonded and CH(3) face complexes was analyzed. From this distortion, two A(') and A(") adiabatic surfaces were considered. The estimated zero point energy of C(s) configurations is above the barrier of the C(3v) ones. Therefore, the CH(3) face complexes are dynamic Jahn-Teller systems. The D(0) (140 cm(-1) for A(") state and 100 cm(-1) for A(')) values obtained are in good agreement with the experimental values (103+/-2 cm(-1)) recently reported.     

Vibronic structure of the permanganate absorption spectrum from time-dependent density functional calculations

The UV absorption spectrum of the permanganate anion is a prototype transition-metal complex spectrum. Despite this being a simple d0 Td system, for which a beautiful spectrum with detailed vibrational structure has been available since 1967, the assignment of the second and third bands is still very controversial. The issue can be resolved only by an elucidation of the intricate vibronic structure of the spectrum. We investigate the vibronic coupling by means of linear-response time-dependent density functional calculations. By means of a diabatizing scheme that employs the transition densities obtained in the TDDFT calculations in many geometries around Re, we construct a Taylor series expansion in the normal coordinates of a diabatic potential energy matrix, coupling 24 excited states. The simulated vibronic structure is in good agreement with the experimental absorption spectrum after the adjustment of some of the calculated vertical excitation energies. The peculiar blurred vibronic structure of the second band, which is a very distinctive feature of the experimental spectrum, is fully reproduced in the calculations. It is caused by the double-well shape of the adiabatic energy surface along the Jahn-Teller active e mode of the allowed 1E state arising from the second 1T2 state, which exhibits a Jahn-Teller splitting into 1B2 and 1E states. We trace the double-well shape to an avoided crossing between two diabatic states with different orbital-excitation character. The crossing can be explained at the molecular orbital level from the Jahn-Teller splitting of the set of 7t2{3d(xy), 3d(xz), 3d(yz)} orbitals (the LUMO + 1), to which the excitations characterizing the diabatic states take place. In contrast to its character in the two well regions, at Re the 2(1)T2 state is not predominantly an excitation to the LUMO + 1, but has more HOMO - 1 --> LUMO (2e = {3d(x2-y2), 3d(z2)}) character. The changing character of the 2(1)T2 - 1E state along the e mode implies that the assignment of the experimental bands to single orbital transitions is too simplistic intrinsically. This spectrum, and notably the blurring of the vibronic structure in the second band, can be understood only from the extensive configurational mixing and vibronic coupling between the excited states. This solves the long-standing assignment problem of these bands.     

Uncertainty evaluation for the adiabatic temperature rise in isoperibol calorimetry

This article describes a practical approach for evaluating the uncertainty of results for determinations of the adiabatic (corrected) temperature rise in isoperibol calorimetry. The methodology is firmly based on the recommendations of the Guide to the expression of uncertainty in measurement (GUM). Although developed for a specific modification of the Regnault?CPfaundler method, the approach is sufficiently general to make it applicable to virtually any other scheme for the evaluation of temperature?Ctime curves in temperature-rise calorimetry.     

Adiabatic and diabatic representations for atom-molecule collisions: Treatment of the collinear arrangement

In this work some aspects of the atom-molecule interactions are extended to include electronic transitions. The main emphasis is directed towards the close relationship between the adiabatic and the diabatic representations. We show how one may transform from the adiabatic scheme to the diabatic one without losing physical information and with minimal amount of numerical efforts. The case of two surfaces (or two electronic states) is treated in particular detail. The main outcome of this study is that, although the electronic information regarding the atom-molecule interaction is given in the adiabatic scheme, one should transform to the diabatic scheme when treating the nuclear interactions.