Renner-Teller System Research Articles

Structure and dynamics of electronically excited molecular systems

AbstractStructure and dynamics of electronic excited states of molecular systems is of contemporary interest to understand a rich variety of processes ranging from molecular spectroscopy to reaction dynamics. Developments over the past decades have established that coupling of electronic and nuclear motion is a generic feature in polyatomic molecular systems which causes a breakdown of the Born–Oppenheimer approximation. Such a coupling leads to conical intersections in non‐linear and glancing degeneracy in linear polyatomic systems. While the former case is quite general and has wide variances depending on the nature of the coupling on the symmetry ground, the latter one is specific to the linear systems having axial symmetry. The Jahn–Teller (JT) systems form a subclass in the former category and the latter category constitutes the Renner–Teller (RT) systems. These systems are characterized by high point group symmetry and orbital degeneracy. The latter splits upon distortion along suitable symmetry reducing nuclear displacement. The JT or the RT split component states may undergo symmetry allowed coupling among another JT or RT split component states or with some non‐degenerate states. These are termed as the pseudo‐JT and pseudo‐RT coupling, respectively. We have studied a variety of photo‐induced molecular processes with the aid of ab initio quantum chemistry and first principles quantum dynamics methods. We will document here some of the important developments in the field focusing on the work done on the JT and RT systems primarily in our own laboratory.This article is categorized under: Theoretical and Physical Chemistry > Spectroscopy Software > Quantum Chemistry Structure and Mechanism > Molecular Structures

Ground state in E ⊗ e Jahn-Teller and Renner-Teller systems: Account of nonadiabaticity.

The ground and lower excited states of an E⊗e Jahn-Teller system with linear and quadratic vibronic coupling are considered, taking nonadiabaticity into account. Our calculations confirm a common opinion that in the case of a weak quadratic coupling, the ground state is doubly degenerate and the first excited state is nondegenerate for any linear coupling. However, with increasing quadratic coupling for weak linear coupling, the nondegenerate state becomes the ground state. The values of vibronic parameters are found at which the ground state changes.

Generating symmetry-adapted bases for non-Abelian point groups to be used in vibronic coupling Hamiltonians

The vibronic coupling Hamiltonian is a standard model used to describe the potential energy surfaces of systems in which non-adiabatic coupling is a key feature. This includes Jahn–Teller and Renner–Teller systems. The model approximates diabatic potential energy functions as polynomials expanded about a point of high symmetry. One must ensure the model Hamiltonian belongs to the totally symmetric irreducible representation of this point group. Here, a simple approach is presented to generate functions that form a basis for totally symmetric irreducible representations of non-Abelian groups and apply it to D∞h (2D) and O (3D). For the O group, the use of a well known basis-generating operator is also required. The functions generated for D∞h are then used to construct a ten state, four coordinate model of acetylene. The calculated absorption spectrum is compared to the experimental spectrum to serve as a validation of the approach.

Electronic states, conical intersections, and spin-rovibronic spectroscopy of the nitrogen oxide sulfide radical

Highly correlated ab initio methods are used to investigate the lowest electronic states of doublet and quartet spin multiplicities for SNO. One-dimensional cuts of the three-dimensional potential energy surfaces (3D-PESs) of these electronic states along the stretch and bend coordinate are calculated. Several avoided crossings and conical intersections are located for bent and linear configurations. The dynamics on the excited electronic states of SNO are very complex, and suggest that multi-step mechanisms should occur to populate the ground state via radiationless processes or lead to predissociation. In addition, our calculations show that the ground (X̃(2)A(')) and the first excited (Ã(2)A(")(Π)) states of this radical form a linear-bent Renner-Teller system. They correlate to the SNO(1(2)Π) state at linearity. Systematic studies of both components are performed using standard coupled cluster approaches, explicitly correlated coupled cluster technique, and multi-configurational methods in connection with large basis sets. Core-valence and scalar relativistic effects are examined. For both electronic states, the 3D-PESs are mapped in internal coordinates at the RCCSD(T)-F12b∕cc-pVTZ-F12 level. The analytical representations of these potential energy surfaces are incorporated later into perturbative and variational treatments of the nuclear motions. A set of spectroscopic parameters and spin-rovibronic levels calculated variationally are presented. Strong anharmonic resonances are found. These new results allow for the reassignment of earlier experimental IR bands of SNO trapped in cooled argon matrices.

A tri-atomic Renner-Teller system entangled with Jahn-Teller conical intersections

The present study concentrates on a situation where a Renner-Teller (RT) system is entangled with Jahn-Teller (JT) conical intersections. Studies of this type were performed in the past for contours that surround the RT seam located along the collinear axis [see, for instance, G. J. Halász, Á. Vibók, R. Baer, and M. Baer, J. Chem. Phys. 125, 094102 (2006)]. The present study is characterized by planar contours that intersect the collinear axis, thus, forming a unique type of RT-non-adiabatic coupling terms (NACT) expressed in terms of Dirac-δ functions. Consequently, to calculate the required adiabatic-to-diabatic (mixing) angles, a new approach is developed. During this study we revealed the existence of a novel molecular parameter, η, which yields the coupling between the RT and the JT NACTs. This parameter was found to be a pure number η = 22/π (and therefore independent of any particular molecular system) and is designated as Renner-Jahn coupling parameter. The present study also reveals an unexpected result of the following kind: It is well known that each (complete) group of states, responsible for either the JT-effect or the RT-effect, forms a Hilbert space of its own. However, the entanglement between these two effects forms a third effect, namely, the RT/JT effect and the states that take part in it form a different Hilbert space.

Generation of full dimensional potential energy surfaces for atmospherically important charge transfer tetratomic complexes: the case of the OMgOO+ radical cation

The weakly bound charge transfer OMgOO(+)((2)Π) ion is a quasi-linear-bent Renner-Teller system with a non-zero spin-orbit contribution. The six-dimensional potential energy surfaces (6D-PESs) for the two Renner-Teller components have been generated in internal coordinates. After benchmarking calculations, we show that the newly implemented explicitly correlated coupled cluster approach (RCCSD(T)-F12) in connection with the cc-pVTZ-F12 basis set provides an accurate description of the full 6D-PESs of this molecular system. Both components are bent with low barriers to linearity along the in-plane angles. The potentials are also very flat along the out-of-plane torsional mode. Hence, this confers a pronounced quasi linear character to OMgOO(+). Moreover, the parts of the potentials relative to the middle bond are shallow and strongly coupled to the bending motions. The parts of the PESs corresponding to the OO and MgO external diatom stretch coordinates differ strongly from those relative to the four other internal coordinates. Special care was taken to correctly account for such behaviors during the generation of the grid and fitting procedures. The present theoretical methodology can be used for mapping the 6D-PESs of other atmospherically important charge transfer complexes presenting similar features such as ONNO(+), O4(+), OOCO(+) or M-CO2(+) (where M is an alkali, magnesium or aluminum metal).

TDDFT study on quantization behaviors of nonadiabatic couplings in polyatomic systems

AbstractWe present extensive calculations on the quantization behaviors of first‐order nonadiabatic couplings (NAC) in polyatomic systems, using the method based on time‐dependent density functional theory (TDDFT). Along circular contours around Jahn–Teller conical intersections at various symmetries, such as D4h and D6h, the angular NAC are found to show apparent dependence on the contour angle, no matter how close the conical intersections are approached. This is in contrast to that the angular NAC in triatomic Jahn–Teller systems (D3h) converge to the quantized value of 1/2. The oscillatory feature of our calculated curves qualitatively resembles the analytic result of angular NAC around elliptic conical intersections in the small‐displacement limit. Furthermore, by performing the integral along the whole contour, the quantization rule on the integral of the angular NAC holds for all cases, which gives the geometric phase with a value of π. On the other hand, the angular NAC in the immediate vicinity of Renner–Teller intersections are shown to be always 1. This observation can be understood from the fact that the molecular symmetry property of the Renner–Teller intersections is always determined by the linear atomic chain. Further analysis of our results on Renner–Teller systems shows that although the quantization behavior of angular NAC can determine all NAC vectors on each atom for the triatomic systems, it cannot for the systems with more than three atoms. The NAC vectors of the latter systems are found to show both common and distinct features with respect to the atomic number and species by our TDDFT calculations. © 2012 Wiley Periodicals, Inc.

Conical intersections induced by the Renner effect: Selected systems

Conical intersections (CIs) play an important role in nonadiabatic molecular processes. We pointed out, that the Renner effect in polyatomic molecules is accompanied by symmetry-allowed CIs. Ab initio calculations and a perturbational approach have confirmed that two aligned CIs are created in the slightly bent C2H2+ molecule. In contrast, different results were obtained for the H2CN molecule. To understand this new phenomenon, additional more detailed investigations have been performed for selected Renner–Teller systems.

Nonadiabatic couplings from time-dependent density functional theory. II. Successes and challenges of the pseudopotential approximation

We present extensive calculations of nonadiabatic couplings (NACs) between the electronically ground and excited states of molecules, using time-dependent density functional theory (TDDFT) within (modified) linear response [C. Hu et al. J. Chem. Phys. 127, 064103 (2007)]. Our approach is implemented in the pseudopotential framework, with the consideration of nonlinear core corrections. The features of either the ordinary Jahn-Teller conical intersections in X(3) (X=Li, Na, K, Cu, Ag, Au) trimers, or the elliptic Jahn-Teller conical intersections in NaH(2), have been well reproduced. In particular, anticipated results for the H-H(2) collision near the avoided crossing are obtained, showing appealing improvement over the first, real-time, TDDFT calculation. The other important type of intersections, Renner-Teller glancing intersection, has also been studied for several typical molecular systems (BH(2), AlH(2), CH(2)(+), SiH(2)(+)), giving results in reasonable agreement with the theoretical model. Despite these successes, it is found that for some systems, including both Jahn-Teller and Renner-Teller systems, the pseudopotential scheme might give inaccurate results for some NAC components on nonhydrogen atoms. By trying different construction schemes of pseudopotentials, e.g., using local pseudopotentials, the results of NACs are found scheme-dependent and show improvement for some cases. Since there is much freedom in constructing ab initio nonlocal pseudopotentials, our findings on TDDFT calculation of NACs in the pseudopotential scheme might be helpful to give clues for constructing more "realistic" pseudopotentials.

Spectroscopic effects of first-order relativistic vibronic coupling in linear triatomic molecules

It has recently been shown that there exists, in addition to the well-known nonrelativistic Renner-Teller coupling, a linear (that is, of the first order in the bending distortion) vibronic-coupling mechanism of relativistic (that is, spin-orbit) origin in 2II electronic states of linear molecules [L. V. Poluyanov and W. Domcke, Chem. Phys. 301, 111 (2004)]. The generic aspects of the relativistic linear vibronic-coupling mechanism have been analyzed in the present work by numerical calculations of the vibronic spectrum for appropriate models. The vibronic and spin-orbit parameters have been determined by accurate ab initio electronic-structure calculations for the X 2II states of a series of triatomic radicals and radical cations. It is shown for the example of GeCH that the relativistic linear vibronic-coupling mechanism provides a quantitative explanation of the pronounced perturbations in the vibronic spectrum of the X 2II state of GeCH, which previously have been termed "Sears resonances" [S.-G. He, H. Li, T. C. Smith, D. J. Clouthier, and A. J. Merer, J. Chem. Phys. 119, 10115 (2003)]. The X 2II vibronic spectra of the series BS2, CS2+, OCS+, and OBS illustrate the interplay of nonrelativistic and relativistic vibronic-coupling mechanisms in Renner-Teller systems.

Absorption cross sections and correlation functions of the NH2 ÃA12−X̃B12 Renner–Teller system

We present a quantum-mechanical study of absorption cross sections and correlation functions of the title system, using a spinless Hamiltonian that includes the nonadiabatic Renner-Teller (RT) coupling between the electronic states, and taking into account the nuclear-spin statistics. We consider also the stimulated emission, assuming a Boltzmann distribution of the molecular levels, and we express correlation functions in terms of wave-packet (WP) overlaps. Assuming that the body-fixed z component of the angular momentum is a constant of motion of isolated NH(2), we calculate X rotational and rovibrational, and X+A rovibronic cross sections and correlation functions at 4.2 and 300 K, up to 26 000 cm(-1) and 3000 fs. We also report the rotational spectrum at 3000 K. The number of absorbing states is large at high T, and the number of lines with appreciably intensity thus increases remarkably with T, from 67 at 4.2 K, to 847 at 300 K, and up to 10 609 at 3000 K. The cold spectrum consists only of Pi lines, due to ground-level absorption. At room and higher T, the hot spectrum presents long progressions of rovibronic lines. The strongest spectral intensities are X Pi and Phi rotational lines and A bending Sigma and Pi lines. We also find many Fermi resonances between A bending and combination states, and that approximately 50% of the lines belong to both electronic states. This latter result points out many RT couplings above 11 000 cm(-1). The theoretical intensities agree very well with the few available experimental data. The time evolution of the correlation functions reflects all internal motions, with periods ranging from approximately 750 to 2 fs, from slow rotational modes to ultrafast electronic dynamics. At low T, the correlation function is proportional to the survival probability of an initial WP, it has many recursions, and can be very regular, without decaying on the average. At high T, the correlation function is associated with the dynamics of many WPs, which present different dephasing times, and the dynamics thus becomes very irregular. The internal dynamics is nonadiabatic above 11 000 cm(-1), because the WPs move from the vertical to the linear region of the excited surface, and can jump to the ground surface owing to RT couplings.

Theoretical study of the He-HF+ complex. II. Rovibronic states from coupled diabatic potential energy surfaces.

The bound rovibronic levels of the He-HF+ complex were calculated for total angular momentum J=1/2, 3/2, 5/2, 7/2, and 9/2 with the use of ab initio diabatic intermolecular potentials presented in Paper I and the inclusion of spin-orbit coupling. The character of the rovibronic states was interpreted by a series of calculations with the intermolecular distance R fixed at values ranging from 1.5 to 8.5 A and by analysis of the wave functions. In this analysis we used approximate angular momentum quantum numbers defined with respect to a dimer body-fixed (BF) frame with its z axis parallel to the intermolecular vector R and with respect to a molecule-fixed (MF) frame with its z axis parallel to the HF+ bond. The linear equilibrium geometry makes the He-HF+ complex a Renner-Teller system. We found both sets of quantum numbers, BF and MF, useful to understand the characteristics of the Renner-Teller effect in this system. In addition to the properties of a "normal" semirigid molecule Renner-Teller system it shows typical features caused by large-amplitude internal (bending) motion. We also present spectroscopic data: stretch and bend frequencies, spin-orbit splittings, parity splittings, and rotational constants.

Electronic states of HNO + and HON +

The three-dimensional CASSCF-MRCI potential energy functions have been calculated for the X 2 A ′ and A 2 A ″ electronic states of the HNO + and HON + isomers. In both cases, these two states form a bent-linear Renner–Teller pair in 2Π symmetry. The barriers to linearity of the X state are calculated to be 6846 cm −1 for HNO + and 8050 cm −1 for HON + (RCCSD(T)). Both isomers possess a conical intersection arising from the crossing between the first excited 2Σ + state and the X 2Π state along the collinear ( NO +( X 1Σ +)+ H( 2 S)) dissociation path. The barrier for isomerisation has been calculated to be 19457 cm −1 (MRCI) and the HNO + isomer is more stable than HON + by 5819 cm −1. The rovibronic levels in the HNO + Renner–Teller system have been calculated by a variational method taking into account the coupling of the rovibrational, electronic and electron spin angular momenta. Since for HON + the barrier to dissociation of the X 2 A ′ ground state is located below the barrier to linearity, only low lying vibrational levels have been calculated for this isomer.

The ion-molecule reaction O+ (4S) + N2(X1Σ+) → NO+ (X1Σ +, v′) + N(4S) and the predissociation of the A2Σ+ and B2Π states of N2O+

The potential energy surfaces (PESs) for several electronic states involved in the reaction O+ (4S) + N2(X1Σ+) → NO+ (X1Σ +, v′) + N(4S) and the role of the ionic N2O+ intermediate have been investigated by ab initio calculations. The 4A″ PES, which correlates with the ground state educts, has a barrier of about 1 eV, and therefore at low collision energies the reaction cannot take place adiabatically on this surface. However, the spin-orbit coupling in the entrance channel allows the system to pass into the Renner-Teller system of the X2 Π electronic ground state of the N2O+ intermediate. The reaction then proceeds on these surfaces up to the region in the exit channel where a similar coupling allows it to reach the product quartet asymptote. At collision energies higher than about 1 eV, the reaction proceeds mainly on the adiabatic PES of the 4A″ state. The A2Σ+ state of N2O+ predissociates via a vibronic coupling with the B2Π state, and in bent structures via a spin-orbit coupling with the 4A″ component of the 4II state. The electronic structure of the B2Π state is found to be of crucial importance for the understanding of the reactive processes in low lying electronic states of N2O+.

Spectroscopic verification of the theoretical reassignment of H2O+ Ã-state vibrational levels

A Franck–Condon analysis of a low-resolution (4 nm FWHM) H2O+ à 2A1–X̃ 2B1 spectrum is presented in order to support recent ab initio calculations of the H2O+ X̃/à Renner–Teller system that call for a reassignment of the Ã-state vibrational levels [Brommer et al., J. Chem. Phys. 98, 5222 (1993)]. ÖX̃ luminescence with well-resolved vibronic bands is observed from near-resonant Kr+(2P1/2)+H2O charge–transfer collisions. It is demonstrated that the intensity of vibronic progressions is only truthfully reproduced if the previously calculated vibronic transition moments [Jungen, Hallin, and Merer, Mol. Phys. 40, 25 (1980)] are applied to the reassigned states, thus confirming the ab initio work.

Theoretical study of the Renner-Teller Ã2A1-[Xtilde]2B1system of NH2

Three-dimensional potential energy functions of the à 2B1-[Xtilde] 2A1 bent-bent Renner-Teller system of NH2 have been generated and used in calculations of the rovibronic energy levels (J ⩽ 9>/2) by a variational approach accounting for anharmonicity, rotation-vibration, electronic angular momenta and electron-spin coupling effects. For low values of N, the theoretical rovibronic term values up to about 20 000 cm-1 agree with available experimental data to within a few wavenumbers. For the first time, all existing rovibronic states for N = 0 and 1 are given and assigned up to 18 000 cm-1. For higher levels including stretching modes the Fermi polyads have been used in the assignments.

Selective mode excitations in the electronic ground states of water, deuterium hydroxide, silylene and amidogen

Based on ab initio three-dimensional functions of potential energy, electric dipole and transition moments, the rovibronic energy levels, eigenfunctions, and radiative transition probabilitiw have been calculated for several triatomic molecules (H 2 O, HDO, SiH 2 , and the Renner-Teller system of NH 2 ). Using ultrashort infrared picosecond laser pulses, the state-selective multiphoton excitations of the υ 1 =4 (symmetric stretching) vibrational eigenstate of these molecules as well as the corresponding diatomics OH, SiH, and NH have been investigated. The OH stretching mode in HDO and in H 2 O can be selectively populated. Strong anharmonic coupling (SiH 2 ) or Renner-Teller coupling to another electronic state (NH 2 ) may, however, considerably reduce the achievable state selectivity

Theoretical rotational-vibrational spectra of theX 3 B 1,a 1 A 1 andb 1 B 1 states of NH 2 +

The three-dimensional potential energy functions have been calculated from highly correlated multireference configuration interaction electronic wavefunctions for theX 3 B 1,a 1 A 1, andb 1 B 1 states of the NH 2 + ion. For the quasi-linear electronic ground state this information and the electric dipole moment functions have been used to calculate spectroscopic constants, line intensities and rotationally resolved absorption spectra. For thea 1 A 1-b 1 B 1 bent/quasi-linear Renner-Teller system ro-vibronic energy levels have been obtained from a variational approach accounting for anharmonicity, rotation-vibration and electronic angular momenta coupling effects. The vibronic levels are given for energies up to 13 500 cm−1 for the bending levels and up to 8000 cm−1 for the stretching and combination levels.

Vibronic spectrum of the CS +2 ion in the X 2Π g state

Based on ab initio electronic structure calculations, the three-dimensional potential energy functions for the X 2Π g Renner—Teller system of CS + 2 have been generated and used in variational beyond Born—Oppenheimer calculations of the rovibronic energy levels. All vibronic levels ( J  P) for energies up to 2500 cm −1 are given for K = 0–3. Available experimental data agree to within 10 cm −1 with the theoretical results. From the compositions of the rovibronic wavefunctions new assignments are made for levels within the Fermi polyads 2ν 1 + ν 2 = 2, 4 and 6. The positions of many so far unknown energy levels are predicted.

Theoretical spin–rovibronic 2A1(Πu)–2B1 spectrum of the H2O+, HDO+, and D2O+ cations

Based on extensive ab initio multiconfiguration reference configuration interaction (MRCI) electronic structure calculations, three-dimensional potential energy functions for the A 2A1(Πu)–X 2B1 linear/bent Renner–Teller systems of H2O+, HDO+, and D2O+ have been generated and used in beyond Born–Oppenheimer calculations of the spin–rovibronic energy levels by a variational approach. The effects of anharmonicity, rotation–vibration, electronic angular momenta, and spin coupling effects have been accounted for. For H2O+, HDO+, and D2O+ vibronic band origins for the bending levels to Ka=5 and for selected stretching and combination levels are given. Almost all experimentally known data have been reproduced with an accuracy better than 10 cm−1 after minor modifications of the ab initio potential energy functions. Our calculated values will facilitate further experimental assignments. A consistent interpretation of the photoelectron spectra for the different isotopes of water is given. Previous assignments of the bending modes in the A 2A1 state have been revised by two quantum numbers.