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Some time ago we published our first article on the Renner-Teller (RT) model to treat the electronic interaction for a triatomic molecule [J. Chem. Phys. 124, 081106 (2006)]. The main purpose of that Communication was to suggest considering the RT phenomenon as a topological effect, just like the Jahn-Teller phenomenon. However, whereas in the first publication we just summarized a few basic features to support that idea, here in the present article, we extend the topological approach and show that all the expected features that characterize a three (multi) state RT-type'3 system of a triatomic molecule can be studied and analyzed within the framework of that approach. This, among other things, enables us to employ the topological D matrix [Phys. Rev. A 62, 032506 (2000)] to determine, a priori, under what conditions a three-state system can be diabatized. The theoretical presentation is accompanied by a detailed numerical study as carried out for the HNH system. The D-matrix analysis shows that the two original electronic states ²A1 and ²B1 (evolving from the collinear degenerate Π doublet), frequently used to study this Renner-Teller-type system, are insufficient for diabatization. This is true, in particular, for the stable ground-state configurations of the HNH molecule. However, by including just one additional electronic state—a B state (originating from a collinear Σ state)—it is found that a rigorous, meaningful three-state diabatization can be carried out for large regions of configuration space, particularly for those, near the stable configuration of NH2. This opens the way for an accurate study of this important molecule even where the electronic angular momentum deviates significantly from an integer value. [ABSTRACT FROM AUTHOR]

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 τ=1 (the Jahn-Teller values in similar situations, are τ=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 Π-states may not be sufficient in order to achieve the required accuracy. [ABSTRACT FROM AUTHOR]

In this article we present the first ab initio study of the conical intersections (cis) and their electronic nonadiabatic coupling terms (NACTs) for the {N,H2} system. Efforts were made to reveal the location of cis between the two lower, 1 2A′ and 2 2A′ states—to be designated as (1,2) cis—and the cis between the two upper, 2 2A′ and 3 2A′ states—to be designated as the (2,3) cis—of this system. We found that these cis are located along the collinear {NHH) arrangement. The study is carried out by analyzing two-state magnitudes such as the (1,2) and (2,3) adiabatic-to-diabatic transformation angles (known also as the mixing angles) and the corresponding topological phases (known also as the Berry phases or the Longuet-Higgins phases). In addition, a detailed three-state study is carried out. Here the emphasis is on driving the diagonal elements of the topological D matrix and analyzing situations for which the corresponding nonadiabatic coupling matrix is quantized. The reliability of two-state results is carefully examined by comparing them with corresponding outcomes derived for the three-state study. In addition we also calculated the potential-energy surfaces related to the two lower states and studied to what extent they are affected by the (1,2) ci. The results obtained in this treatment were found to be in full agreement with the NACT’s calculations. [ABSTRACT FROM AUTHOR]

In this paper we suggest to consider the spatial distribution of the Born-Oppenheimer nonadiabatic coupling terms as fields which are created by sources, located at degeneracy points, and which can be derived using the ordinary mathematical tools of field theory. It is shown that the curl-divergence equations as formed within a given Hilbert space [M. Baer, Chem. Phys. Lett. 35, 112 (1975)] can be converted into a set of inhomogeneous coupled Poisson equations which are solved for a given set of boundary conditions. The method is applied to the three-state Hilbert subspace of the H3 system. The numerical results are compared with ab initio calculations for which a very encouraging fit is found. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In this Communication it is suggested that various elements of the nonadiabatic coupling matrix, τjk(s) are created by the singular nonadiabatic coupling terms of the system. Moreover, given the spatial distribution of these coupling terms in the close vicinity of their singularity points yields, according to this approach, the integrated intensity of the field at every point in the region of interest. To support these statements we consider the conical intersections of the three lower states of the H+H2 system: From an ab initio treatment we obtain the nonadiabatic coupling terms around each conical intersection separately (at its close vicinity) and having those, create the field at every desired point employing vector-algebra. This approach is also used to calculate the intensity of the Curl of those matrix elements that lack their own sources [τ13(s) in the present case]. The final results are compared with relevant ab initio calculations. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In this article we consider the electronic diabatic presentation of a two-state system with the aim of earning insight regarding the distribution of conical intersections in a given region. In this process we revealed explicit relationship between the diabatic potentials and the locations of conical intersections. The study is accompanied with numerical examples as worked out for a model and ab initio potential energy surfaces of the Na+H[sub 2] system. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The three ab initio nonadiabatic coupling terms related to the three strongly coupled states of the C[sub 2]H molecule, i.e., 2²A', 3²A', and 4²A', 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. [ABSTRACT FROM AUTHOR]

In this Letter are presented and analyzed conical intersections which appear on the two symmetric sides of the C[sub 2v] line of the C[sub 2]H molecule. Two conical intersections (CI) of this kind, between the 3 [sup 2]A[sup ′] and 4 [sup 2]A[sup ′] electronic states, were found to be only a short distance apart, e.g., ∼0.3 Å for the CC distance of 1.25 Å. It is shown that these two CIs--to be termed CI twins--have opposite "charges" thus forming altogether a weak interaction. By increasing the CC distance, to 1.35 Å, the two twins coalesce to form a single CI. The interaction of this merged pair varies with the distance as q[sup -1] (as is the case for conical intersections) but, in contrast to ordinary CIs, does not exhibit any topological effects and its intensity is shown to be zero. These features led us to term it as a degenerate CI or concisely DCI. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A new diabatization procedure, which is expected to be reliable and easy, is implemented. The procedure takes into account two main ingredients related to diabatization, the size N of the smallest group of states that forms a Hilbert subspace and the total energy E which determines the number of open states, p, within this group of N states.

Two issues related to the size of the electronic diabatic potential energy matrix are discussed. The main advantage of the approach is that it enables a series of iterations to obtain the converged results.

A theory according to which all of the elements of the nonadiabatic coupling matrix, tau (sub jk)(q, phi), are created at the singular points of the system are presented. For the purpose of the study an angular distribution of the angular components, tau (sub phi Jk)[q (sub j)~0,tau (sub j)], at the close vicinity of their singularities, namely, around the jth singularity points q (sub j) =zero is considered.

Reports on the fully converged coupled states (CS) quantum mechanical (QM) study of the endothermic ion-molecule reaction. Comparison of the computer dynamic properties with quasi-classical trajectory (QCT); Application of the analytical potential energy surface of Pendergast, Heck, Hayes and Jacquet; Two main features of the dynamical behavior of the potential energy surface system.

Do you ever wonder what it was like when Indiana first became a state--or when it celebrated its centennial one hundred years later? For those who think about such things, such as THG: Connections' readers, the upcoming bicentennial of the Hoosier State is a long moment to contemplate and enjoy. Not only will Hoosiers celebrate the two-hundredth anniversary of becoming a state in 2016, we will also have numerous opportunities to learn about our state's history through many and varied projects that are now under way at local and state levels., Here at the Indiana Historical Society--the home for Hoosier history since 1830--we have been thinking about how best to commemorate the bicentennial in ways that are inclusive of people, from [...]

A quantum mechanical approach to treat diatom–diatom exchange processes of the type AB+CD→ABC+D is presented. The approach is based on three types of wave functions ψ0ν, ψ0λ, and χ, where the first two are (asymptotic) elastic distorted wave functions for the two arrangement channels ν and λ, and χ is a short range (square integrable) wave function describing the system in the close interaction region. The functions ψ0ν and ψ0λ are presented within the jz approximation, and to calculate χ, a perturbative-type Schrödinger equation which contains negative imaginary potentials (to form absorbing boundary conditions) is solved. The variationally stable solution is obtained employing Gaussians and local adiabatic basis sets. The actual calculation of χ is done employing the quasibreathing sphere model, where the relevant angular coordinates are selected randomly (about 50 sets like that were used) employing a Monte Carlo approach. With this approach, most detailed state-to-state cross sections were calculated for the reaction H2(n1=0, j1=0)+OH(n2=0, j2=0)→H2O(vjvKΩK)+H, where (vjv) are the usual vibrational-bending states of the water molecule, and K and ΩK are, respectively, the overall rotational quantum number and the corresponding magnetic component. The results were compared with those due to other treatments and with experiment. [ABSTRACT FROM AUTHOR]

A detailed three-dimensional quantum mechanical study of the (Ar+H2)+ system along the energy range 0.4 eV≤Etot≤1.65 eV is presented. The main difference between this new treatment and the previously published one [J. Chem. Phys. 87, 465 (1987)] is the employment of a new version of the reactive infinite-order sudden approximation (IOSA), which is based on the ordinary inelastic IOSA carried out for an optical potential. In the numerical treatment we include three surfaces (only two were included in the previous treatment), one which correlates with the Ar+H+2 system and two which correlate with the two spin states of Ar+(2Pj); j=3/2,1/2. The results are compared with both trajectory-surface-hopping calculations and with experiments. In most cases, very good agreement is obtained. [ABSTRACT FROM AUTHOR]

In this work we examined the possibility that characteristic heavy–light–heavy collinear oscillatory behavior of the reactive probability functions will also be apparent in three-dimensional partial cross sections. The study was carried out using the quasiclassical trajectory method for ClHCl and IHI. For this study the DIM-3C potential energy surfaces were employed. It was found that whereas in general the collinear features were reproduced in three dimensions, the prospects for them to be detected experimentally exist for only part of them. [ABSTRACT FROM AUTHOR]

Investigates the F+D[sub 2]...DF+D reaction in a high resolution crossed molecular beam scattering experiment at a collision energy of 90 meV. Presentation of a three dimensional quantum mechanical calculation; Rotational state distributions of the DF molecules; Differences between calculated and experimental results.

This work describes a new approach to treating quantum mechanical scattering problems. It is based on expanding the wave function in terms of an infinite set of localized Gaussian functions and employing the features of a Toeplitz matrix. [ABSTRACT FROM AUTHOR]

A comprehensive theoretical investigation of vibrational excitation and vibronic charge transfer in the H++O2 collision at ECM=23 eV is reported. The calculations of differential and integral scattering observables are undertaken within both the quantal infinite order sudden (QIOS) and the vibronic semiclassical (VSC) approximations. They involve 2×15 vibronic expansions associated with the diabatic states determined by Grimbert et al. [Chem. Phys. 124, 187 (1988)] using a so-called effective model potential (EMP) method. A quadripartite comparison involving experimental data of Noll and Toennies [J. Chem. Phys. 85, 3313 (1986)], results of a QIOS treatment of Gianturco et al. [Phys. Rev. A 42, 3926 (1990)] based on DIM potentials and the present QIOS, and VSC results is presented. From the comparison of the theoretical and experimental results we find that the present calculations based on the EMP reproduce much better the experimental data than those based on the DIM potentials. Though differences are found between the present QIOS and VSC results, the experimental data do not help deciding between the two theories. The relative merits of the QIOS and VSC approaches are put forward and discussed. By scrutinizing intermediate results of lengthy calculations we have been able to bring out elementary models in them. Pure vibrational excitation is found to be a prominent process in this system and charge transfer substantially affects it. [ABSTRACT FROM AUTHOR]

In this work possible quantum mechanical effects for the three dimensional reactive D+H2→HD+H reaction are discussed. The study is carried out by comparing quantum mechanical and quasiclassical backscattered differential cross sections as a function of collision energy. A strong quantum effect is detected for the v=0–>v’=0 transition in the energy range around Etr=13 kcal/mol. [ABSTRACT FROM AUTHOR]

Total state-selected and state-to-state absolute cross sections for the reactions, H+2(X,v’=0–4)+Ar→H2(X,v) +Ar+(2P3/2,1/2) [reaction (I)], ArH++H [reaction (II)], and H++H+Ar [reaction (III)], have been measured in the center-of-mass collision energy (Ec.m.) range of 0.48–100 eV. Experimental state-selected cross sections for reactions (I) and (II) measured at Ec.m.=0.48–0.95 eV are in agreement with those reported previously by Tanaka, Kato, and Koyano [J. Chem. Phys. 75, 4941 (1981)]. The experiment shows that prominent features of the cross sections for reactions (I) and (II) are governed by the close resonance of the H+2(X,v’=2)+Ar and H2(X,v=0)+Ar+(2P1/2) vibronic states. At Ec.m.≤3 eV, the vibrational state-selected cross section for the charge transfer reaction (I) is peaked at v’=2.The enhancement of the charge transfer cross section for v’=2 as compared to other v’ states of reactant H+2 increases as Ec.m. is decreased. The state-to-state cross sections for reaction (I),measured at Ec.m.≤3 eV, show that the enhancement for the charge transfer cross section for v’=2 is due to the preferential population of Ar+(2P1/2). At Ec.m.=0.48–0.95 eV and v’=2, nearly 80% of the charge transfer product Ar+ ions are formed in the 2P1/2 state. However, at Ec.m.>5 eV, the intensity for charge transfer product Ar+(2P3/2) is greater than that for Ar+(2P1/2). Contrary to the strong vibrational dependence of the cross section for reaction (I), the cross section for reaction (II) is only weakly dependent on the vibrational state of H+2. At Ec.m.≤3 eV, the cross section for the formation of ArH+ is the lowest for v’=2 compared to other v’ states, an observation attributed to the competition of the nearly resonant Ar+(2P1/2)+H2(X,v=0) charge transfer channel. The cross section for reaction (II) decreases with increasing Ec.m..At Ec.m.≥20 eV, the... [ABSTRACT FROM AUTHOR]

Total state-selected and state-to-state absolute cross sections for the reactions Ar+(2P3/2,1/2)+H2(X,v=0)→Ar (1S0)+H+2(X,v’) [reaction (1)], ArH++H [reaction (2)], and H++H+Ar [reaction (3)] have been measured in the center-of-mass collision energy Ec.m. range of 0.24–19.1 eV. Absolute spin–orbit state transition total cross sections (σ3/2→1/2,σ1/2→3/2) for the collisions of Ar+(2P3/2,1/2) with H2 at Ec.m.=1.2–19.1 eV have been obtained.The measured state-selected cross sections for reaction (1) [σ3/2,1/2(H+2)] reveal that at Ec.m.≤5 eV, σ1/2(H+2) is greater than σ3/2(H+2), while the reverse is observed at Ec.m.≥7 eV. The total state-to-state absolute cross sections for reaction (1) (σ3/2,1/2→v’) show unambiguously that in the Ec.m. range of 0.16–3.9 eV the dominant product channel formed in the reaction of Ar+(2P1/2)+H2(X,v=0) is H+2(X,v’=2)+Ar. These observations support the conclusion that at low Ec.m. the outcome of charge transfer collisions is governed mostly by the close energy resonance effect. However, at sufficiently high Ec.m.(>6 eV) the charge transfer of Ar+(2P3/2)+H2 is favored compared to that of Ar+(2P1/2)+H2.The relative values measured for X1/2→v’[≡σ1/2→v’/σ1/2 (H+2)] are in good accord with those predicted from calculations using the state-to-state cross sections for the H+2(X,v’=0–4)+Ar charge transfer reaction and the relation based on microscopic reversibility. The experimental values for X3/2→v’[≡σ3/2→v’/σ3/2 (H+2)] and those predicted using the microscopic reversibility argument are also in fair agreement. The spin–orbit effect for the cross section of reaction (2) [σ3/2,1/2(ArH+)] is significantly less than that for reaction (1). Both σ3/2(ArH+) and σ1/2(ArH+) decrease rapidly as Ec.m. is... [ABSTRACT FROM AUTHOR]