G. J. Halász

Renner-Teller/Jahn-Teller intersections along the collinear axes of polyatomic molecules: C2H2+ as a case study

Recently we discussed the Renner-Teller effect in triatomic molecules [J. Chem. Phys. 125, 094102 (2006)]. In that article the main message is that the Renner-Teller phenomenon, just like the Jahn-Teller phenomenon, is a topological effect. Now we extend this study to a tetra-atomic system, namely, the C(2)H(2) (+) ion, for which topological effects are revealed when one atom surrounds the triatom axis or when two atoms surround (at a time) the two-atom axis. The present study not only supports the findings of the previous study, in particular, the crucial role played by the topological D matrix for diabatization, but it also reveals new features which are expected to be more and more pronounced the larger the original collinear molecule. As already implied, shifting away two atoms from the collinear molecular axis does not necessarily abolish the ability of the remaining two atoms to form topological effects. Moreover, the study indicates that when the two hydrogens are shifted away, the CC axis produces two kinds of topological effects: (1) a Renner-Teller effect (characterized by a topological phase of 2pi) which is revealed when the two hydrogens surround, rigidly, this axis (as mentioned above), and (2) a Jahn-Teller effect (characterized by a topological phase of pi) which is revealed when one of the hydrogens surrounds this axis while the other hydrogen is clamped to its position.

A survey of ab initio conical intersections for the H+H2 system

In this article we present a survey of the various conical intersections which govern potential transitions between the three lower electronic states for the title molecular system. It was revealed that these three states, for a given fixed HH distance, R HH , usually form four conical intersections: two, between the two lower states and two, between the two upper states. One of the four is the well known equilateral D3h ci and the others are, essentially, C2v cis: One of them is located on the symmetry line perpendicular to the HH axis ~just like the D3h ci) and the other two are located on both sides of this symmetry line and in this way form the ci-twins. The study was carried out for four RHH-values, namely, RHH50.74, 0.5417, 0.52, and 0.4777 A. It was also established that there exists one single RHH-value designated as R HH , located in the interval

Renner-Teller nonadiabatic coupling terms: An ab-initio study of the HNH molecule

0.52, 0.53 A%, for which all four cis coalesce to become one kind of ‘‘super’’ ci which couples the three states. The numerical study was carried out employing the line integral approach for groups of two and three states. As for the two-state calculations we found that all D3h-cis, at close proximity, are circular ~ordinary! Jahn-Teller-type cis, whereas all C2v-cis, at close proximity, are elliptic Jahn-Teller cis @Chem. Phys. Lett 354, 243 ~2002!#. Particular attention is given to the 3-state quantization of the nonadiabatic coupling matrix. The quantization is found to be fulfilled in all situations as long as the regions in configuration space are not too far from the relevant cis. In the Discussion and Conclusion we discuss, among other subjects, the possibility to diabatize the adiabatic potential matrix.

Direct Signature of Light-Induced Conical Intersections in Diatomics

In this Communication we present the first theoretical/numerical treatment of nonadiabatic coupling terms (NACT) that originate from the Renner-Teller (RT) model, namely, those that follow from the splitting of an electronic level of a linear molecule when it becomes bent. These two newly formed states are characterized by different symmetries and are designated as A and B. Our main findings: (1) The RT NACTs are quantized as long as they are calculated close enough to collinear configuration of the molecule (in this case HNH). Their value is tau = 1 (the Jahn-Teller values in similar situations, are tau = (1/2)). (2) Calculation of RT NACTs at bent configurations (i.e., at a distance from the linear axis) yield decreased values, sometimes by more than 50%. This last finding implies that in strongly bent configurations the two-state Hilbert subspace (formed by the above mentioned A and B states) is affected by upper states, most likely via Jahn-Teller conical intersections. (3) This study has also important practical implications. The fact that the RT NACTs decrease in (strongly) bent situations implies that analyzing spectroscopic data employing only the two Pi-states may not be sufficient in order to achieve the required accuracy.

Quantization of the 3×3 nonadiabatic coupling matrix for three coupled states of the C2H molecule

Nonadiabatic effects are ubiquitous in physics, chemistry, and biology. They are strongly amplified by conical intersections (CIs), which are degeneracies between electronic states of triatomic or larger molecules. A few years ago it was revealed that CIs in molecular systems can be formed by laser light, even in diatomics. Because of the prevailing strong nonadiabatic couplings, the existence of such laser-induced conical intersections (LICIs) may considerably change the dynamical behavior of molecular systems. By analyzing the photodissociation process of the D2+ molecule carefully, we found a robust effect in the angular distribution of the photofragments that serves as a direct signature of the LICI, providing undoubted evidence of its existence.

Ab initio non-adiabatic coupling elements: the conical intersection between the 22A' and the 32A' of the H + H2 system

The three ab initio nonadiabatic coupling terms related to the three strongly coupled states of the C2H molecule, i.e., 2 2A′, 3 2A′, and 4 2A′, were studied applying the line integral technique [M. Baer, Chem. Phys. Lett. 35, 112 (1975)]. The following was verified: (1) Due to the close proximity of the conical intersections between these three states, two-state quantization cannot always be satisfied between two successive states. (2) It is shown that in those cases where the two-state quantization fails a three-state quantization is satisfied. This three-state quantization is achieved by applying the 3×3 nonadiabatic coupling matrix that contains the three relevant nonadiabatic coupling terms. The quantization is shown to be satisfied along four different contours (in positions and sizes) surrounding the relevant conical intersections.

Effect of Light-Induced Conical Intersection on the Photodissociation Dynamics of the D2+ Molecule

Abstract The conical intersections between the 1 2 A ′ and 2 2 A ′ electronic states and the 2 2 A ′ and 3 2 A ′ electronic states of the H2+H system were characterized by line-integral calculations using ab initio non-adiabatic coupling terms. The calculations confirmed that when a contour surrounds the {1 2 A ′ ,2 2 A ′ } conical intersection but does not approach, too closely, the {2 2 A ′ ,3 2 A ′ } conical intersections the line-integral produces for the topological phase, the expected π-value [Chem. Phys. Lett., 319 (2000) 489]. Estimating the location of {2 2 A ′ ,3 2 A ′ } conical intersection, the line-integral procedure was employed again – this time for the {2 2 A ′ ,3 2 A ′ } system – confirming, in the same way, also the existence of the {2 2 A ′ ,3 2 A ′ } conical intersections.

Influence of light-induced conical intersection on the photodissociation dynamics of D2(+) starting from individual vibrational levels.

It is known that conical intersections (CIs) can be induced by laser light even in diatomics. In the close vicinity of these laser-induced CIs (LICIs) the nonadiabatic effects are infinitely strong, as is the case for naturally appearing CIs in field-free polyatomics. In the present work we study the photodissociation dynamics of the D(2)(+) molecule in an intense laser field to investigate the role of the LICI. Specifically, the kinetic energy release (KER) and the angular distribution of the photodissociation products are calculated with and without LICI for different initial conditions and for different values of the laser parameters. To do so, both one- and two-dimensional calculations were performed. In the first model the molecules were rotationally frozen, whereas in the latter one, the molecular rotation is included as a full additional dynamic variable. The results obtained undoubtedly demonstrate the strong impact of the coupling of the rotation to the vibrational and electronic motions and hence of the LICI on the dissociation dynamics of the D(2)(+) molecule.

Light-induced conical intersections for short and long laser pulses: Floquet and rotating wave approximations versus numerical exact results

Previous works have shown that dressing of diatomic molecules by standing or by running laser waves gives rise to the appearance of so-called light-induced conical intersections (LICIs). Because of the strong nonadiabatic couplings, the existence of such LICIs may significantly change the dynamical properties of a molecular system. In our former paper (J. Phys. Chem. A 2013, 117, 8528), the photodissociation dynamics of the D(2)(+) molecule were studied in the LICI framework starting the initial vibrational nuclear wave packet from the superposition of all the vibrational states initially produced by ionizing D(2). The present work complements our previous investigation by letting the initial nuclear wave packets start from different individual vibrational levels of D(2)(+), in particular, above the energy of the LICI. The kinetic energy release spectra, the total dissociation probabilities, and the angular distributions of the photofragments are calculated and discussed. An interesting phenomenon has been found in the spectra of the photofragments. Applying the light-induced adiabatic picture supported by LICI, explanations are given for the unexpected structure of the spectra.

On diabatization and the topological D-matrix: Theory and numerical studies of the H + H2 system and the C2H2 molecule

It has recently been shown that dressing of diatomic molecules by standing or by running laser waves can give rise to the appearance of the so-called light-induced conical intersections (LICIs). The effect of these LICIs on different physical properties of the diatomic molecules has been demonstrated in several publications [1–6]. In the majority of these works, the sodium dimer was chosen as an explicit showcase example and the Floquet picture was used to describe the nuclear Hamiltonian. This representation of the Hamiltonian is very illustrative and helps to understand the essence of the light-induced nonadiabatic effects. However, the natural question arises: what are the limits of the Floquet approximation? In this paper, the performance of the 2×2 Floquet Hamiltonian in the space of the ground and resonantly excited molecular electronic states is compared to that of the time-dependent exact Hamiltonian in the same space. For the latter case, we also present results employing the popular rotating wave approximation. To carry out the comparisons, different physical properties—-autocorrelation function, excited state diabatic populations and molecular alignment—have been computed. (Some figures may appear in colour only in the online journal)