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

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.     

The Jahn-Teller effect in the triply degenerate electronic state of methane radical cation

A quantum dynamics study is performed to examine the complex nuclear motion underlying the first photoelectron band of methane. The broad and highly overlapping structures of the latter are found to originate from transitions to the ground electronic state, X(2)T(2), of the methane radical cation. Ab initio calculations have also been carried out to establish the potential energy surfaces for the triply degenerate electronic manifold of CH(4)(+). A suitable diabatic vibronic Hamiltonian has been devised and the nonadiabatic effects due to Jahn-Teller conical intersections on the vibronic dynamics investigated in detail. The theoretical results show fair accord with experiment.     

Cis-trans isomerization in the S1 state of acetylene: identification of cis-well vibrational levels

A systematic analysis of the S(1)-trans (A?(1)A(u)) state of acetylene, using IR-UV double resonance along with one-photon fluorescence excitation spectra, has allowed assignment of at least part of every single vibrational state or polyad up to a vibrational energy of 4200 cm(-1). Four observed vibrational levels remain unassigned, for which no place can be found in the level structure of the trans-well. The most prominent of these lies at 46?175 cm(-1). Its (13)C isotope shift, exceptionally long radiative lifetime, unexpected rotational selection rules, and lack of significant Zeeman effect, combined with the fact that no other singlet electronic states are expected at this energy, indicate that it is a vibrational level of the S(1)-cis isomer (A?(1)A(2)). Guided by ab initio calculations [J. H. Baraban, A. R. Beck, A. H. Steeves, J. F. Stanton, and R. W. Field, J. Chem. Phys. 134, 244311 (2011)] of the cis-well vibrational frequencies, the vibrational assignments of these four levels can be established from their vibrational symmetries together with the (13)C isotope shift of the 46?175 cm(-1) level (assigned here as cis-3(1)6(1)). The S(1)-cis zero-point level is deduced to lie near 44?900 cm(-1), and the ν(6) vibrational frequency of the S(1)-cis well is found to be roughly 565 cm(-1); these values are in remarkably good agreement with the results of recent ab initio calculations. The 46?175 cm(-1) vibrational level is found to have a 3.9 cm(-1) staggering of its K-rotational structure as a result of quantum mechanical tunneling through the isomerization barrier. Such tunneling does not give rise to ammonia-type inversion doubling, because the cis and trans isomers are not equivalent; instead the odd-K rotational levels of a given vibrational level are systematically shifted relative to the even-K rotational levels, leading to a staggering of the K-structure. These various observations represent the first definite assignment of an isomer of acetylene that was previously thought to be unobservable, as well as the first high resolution spectroscopic results describing cis-trans isomerization.     

The icosahedral potential and its applications to the study of the anharmonic effects in the overtone levels of the degenerate vibrations of molecules with Ih symmetry

The splitting of the overtone levels of the T_1u, G_u, and H_g vibrations in molecules with I_h symmetry has been calculated by using the perturbation theory. To do this it was necessary to establish beforehand the icosahedral potential, employing the usual procedure in crystal field theory. The total splitting, predicted by the group theory, is obtained when the anharmonicity up to the sixth power of the coordinates is taken into account. Expressions for the intensities of the infrared-active transitions of T_1u vibrations are also proposed.

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Das ikosaedrische Potential und seine Anwendung für die Untersuchung der Anharmonizität in den Obertönen der entarteten Schwingungen von Molekülen mit Symmetrie I_h

Zusammenfassung Die Aufspaltung der Obertöne der Schwingungen T_1u, G_u und H_g in Molekülen mit Symmetrie I_h ist unter Verwendung der Störungstheorie berechnet worden. Dafür war es notwendig, das ikosaedrische Potential herzuleiten. Hierbei wurde das übliche Verfahren der Kristallfeld-Theorie angewandt. Die durch die Gruppentheorie vorhergesagte komplette Aufspaltung erhält man, wenn die Anharmonizität bis zur sechsten Potenz in den Koordinaten berücksichtigt wird. Es werden Ausdrücke für die Intensitäten der infrarot-aktiven Übergänge der Schwingungen T_1u vorgeschlagen.

     

Accurate quantum mechanical study of the Renner-Teller effect in the singlet CH2

The Renner-Teller (RT) effect between the two low-lying electronic states of singlet CH(2), a?(1)A(1) and b?(1)B(1), is studied using the multi-configuration time-dependent Hartree method with complete treatment of the RT terms. The RT terms, which are the matrix elements of the electronic orbital angular momentum operators, are calculated with ab initio methods and fitted to analytical functions. The ro-vibronic energy levels with complete treatment and constant approximation of the RT terms are calculated and compared. The influences of the geometry dependence of the RT terms on the ro-vibronic energy levels are discussed. The differences of the variation trends and influences of the RT terms between CH(2) and NH(2) are explored. In particular, as the molecule bends from linearity, the curve of the RT term (a?(1)A(1)|L(z)(2)|a?(1)A(1)() first goes down to reach a minimum and then goes up leading to decreased zero point energy and bending energy levels for the lower state of CH(2) in contrast to the case of NH(2).     

Toward spectroscopic accuracy of ab initio calculations of vibrational frequencies and related quantities: a case study of the HF molecule

Calculations at various coupled-cluster (CC) levels with and without the inclusion of linear r _{i j} -dependent terms are performed for the HF molecule in its ground state with a systematic variation of basis sets. The main emphasis is on spectroscopic properties such as the equilibrium distance r _e and the harmonic vibration frequency ω_e. Especially with the R12 methods (including linear r _{i j} -dependent terms), convergence to the basis set limit is reached. However, the results (at the basis set limit) are rather sensitive to the level of the treatment of electron correlation. The best results are found for the CCSDT1-R12 and CCSD[T]-R12 methods (CCSD[T] was previously called CCSD+T(CCSD)), while CCSD(T) overestimates ω_e by ≈6 cm⁻¹. The good agreement of conventional CCSD(T) with experiment for basis sets far from saturation (e.g. truncated at g-functions) is probably the result of a compensation of errors. The contribution of core-correlation is non-negligible and must be included (effect on ω_e≈5 cm⁻¹). Relativistic effects are also important (23 cm⁻¹), while adiabatic effects are much smaller (<1cm⁻¹) and non-adiabatic effects on ω_e can be simulated in replacing nuclear by atomic masses; for rotation nuclear masses appear to be the better choice, at least for hydrides. From a potential curve based on calculations with the CCSDT1-R12 method with relativistic corrections, the IR spectrum is computed quantum-mechanically. Both the band heads and the rotational structures of the observed spectra are reproduced with a relative error of ≈10⁻⁴ for the three isotopomers HF, DF, and TF. Received: 3 July 1998 / Accepted: 4 August 1998 / Published online: 28 October 1998     

The influence of ultrashort excitations on the vibrational dynamics in a diatomic molecule

The problem of vibrational wave packet dynamics in the system of two electronic states of a diatomic molecule, where the states are coupled by infinitely short light pulses, is solved. The electronic states were modeled by shifted harmonic oscillators with different frequencies. Exact expressions for the probability densities of the wave packets in the ground and excited states were derived. The spatial, spectral, and temporal characteristics of the wave packets, namely, the range of motion, spatial width, mean energy, spectral width (the mean number of vibrational states in a wave packet), and the autocorrelation function, were calculated as functions of the molecular parameters (the frequency ratio and the distance between the potential minima) and of the delay time between the light pulses. The possibility of controlling the mean energy and spectral width of the wave packets in the ground electronic state by varying the delay time is considered. It was shown that "squeezed" wave packets can be prepared in the ground electronic state if the upper electronic state is shallow.     

Accurate theoretical prediction of vibrational frequencies in an inhomogeneous dynamic environment: a case study of a glutamate molecule in water solution and in a protein-bound form

We propose a hierarchical approach to model vibrational frequencies of a ligand in a strongly fluctuating inhomogeneous environment such as a liquid solution or when bound to a macromolecule, e.g., a protein. Vibrational frequencies typically measured experimentally are ensemble averaged quantities which result (in part) from the influence of the strongly fluctuating solvent. Solvent fluctuations can be sampled effectively by a classical molecular simulation, which in our model serves as the first, low level of the hierarchy. At the second high level of the hierarchy a small subset of system coordinates is used to construct a patch of the potential surface (ab initio) relevant to the vibration in question. This subset of coordinates is under the influence of an instantaneous external force exerted by the environment. The force is calculated at the lower level of the hierarchy. The proposed methodology is applied to model vibrational frequencies of a glutamate in water and when bound to the Glutamate receptor protein and its mutant. Our results are in close agreement with the experimental values and frequency shifts measured by the Jayaraman group by the Fourier transform infrared spectroscopy [Q. Cheng et al., Biochem. 41, 1602 (2002)]. Our methodology proved useful in successfully reproducing vibrational frequencies of a ligand in such a soft, flexible, and strongly inhomogeneous protein as the Glutamate receptor.     

Contrasting singlet-triplet dynamical behavior of two vibrational levels of the acetylene S1 2(1)3(1)B2 polyad

Surface electron ejection by laser-excited metastables (SEELEM) and LIF spectra of acetylene were simultaneously recorded in the regions of the A1Au-X1Sigmag+ nominal 2(1)3(1)4(2) Ka=1<--00 and 2(1)3(1)6(2) Ka=1<--00 bands near 46,140 cm(-1). The upper states of these two bands are separated by only approximately 100 cm(-1), and the two S1 vibrational levels are known to be strongly mixed by anharmonic and Coriolis interactions. Strikingly different patterns were observed in the SEELEM spectra in the regions of the 2(1)3(1)4(2) and 2(1)3(1)6(2) vibrational levels. Because the equilibrium structure of the T3 electronic state is known to be nonplanar, excitation of nu4 (torsion) and nu6 (antisymmetric in-plane bend) are expected respectively to promote and suppress vibrational overlap between low-lying S1 and T3 vibrational levels. The nearly 50:50 mixed 2(1)3(1)4(2)-2(1)3(1)6(2) character of the S1 vibrational levels rules out this simple Franck-Condon explanation for the different appearance of the SEELEM spectra. A simple model is applied to the SEELEM/LIF spectra to explain the differences between spectral patterns in terms of a T3 doorway-mediated singlet-triplet coupling model.     

Quantum chemical predictions of the vibrational spectra of polyatomic molecules. The uracil molecule and two derivatives

This work describes the different scaling procedures used to correct the quantum-chemical theoretical predictions of the IR and Raman vibrational wavenumbers. Examples of each case are shown, with special attention to the uracil molecule and some derivatives. The results obtained with different semiempirical and ab initio methods, and basis sets, are compared and discussed. A comprehensive compendium of the main scale factors and scaling equations available to obtain the scaled wavenumbers is also shown.     

Ab initio study of torsional vibrations of the fluoral molecule in the ground state

A comparative analysis of various approximations used to solve the problem on the torsional motion of the CF₃ group in the trifluoroacetaldehyde molecule is presented. It is considered how the estimates of torsional transition frequencies are affected by the choice of a basis set for an ab initio calculation, by the method of inclusion of electron correlation, by the geometrical model of the molecule, and by the method of determination of nuclear energy levels. The results are also considered for the related acetaldehyde molecule. The Appendix briefly defines the structure of the energy levels of torsional symmetric top vibrations. M. V. Lomonosov Moscow State University. Translated fromZhurnal Strukturnoi Khimii, Vol. 39, No. 3, pp. 514–521, May–June, 1998.     

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.     

Assignment and extraction of dynamics of a small molecule with a complex vibrational spectrum: thiophosgene

The dispersed fluorescence spectrum of the ground electronic state of thiophosgene, SCCl2, is analyzed in a very complex region of vibrational excitation, 7000-9000 cm(-1). The final result is that most of the inferred excited vibrational levels are assigned in terms of approximate constants of the motion. Furthermore, each level is associated with a rung on a ladder of quantum states on the basis of common reduced dimension fundamental motions. The resulting ladders cannot be identified by any experimental means, and it is the interspersing in energy of their rungs that makes the spectrum complex even after the process of level separation into polyads. Van Vleck perturbation theory is used to create polyad constants of the motion and a spectroscopic Hamiltonian from a potential fitted to experimental data. The eigen functions of this spectroscopic Hamiltonian are rewritten as semiclassical wave functions and transformed to a representation that allows us to analyze and assign the spectra with no other work other than to utilize concepts from nonlinear dynamics.     

Theory of electron tunneling through a bridge molecule with two electronic levels at low temperatures

A theory of electron tunneling through a single-center bridge redox group that has two electronic levels participating in the electron transfer process is presented. The temperature is presumed to be low enough to ignore activation redox conversions of the bridge group. Salient features of this system are due both to the presence of two electroactive states of the bridge group and to relaxation processes along the reaction coordinate. The processes in question make the tunneling current time-dependent at fixed potentials and can bring about hysteresis in current-voltage curves when cycling the bias potential. Effects of inelastic tunneling with excitation of vibrations of a local quantum degree of freedom are considered.     

Intramolecular vibrational energy redistribution in the highly excited fluoroform molecule: a quantum mechanical study using the multiconfiguration time-dependent Hartree algorithm

The present paper is devoted to a detailed study of the intramolecular vibrational energy redistribution in fluoroform initiated by a local mode excitation of the CH stretch [nnu(CH) (n=1,...,4)]. All nine internal degrees of freedom are explicitly taken into account and the full quantum mechanical simulation is performed by means of the multiconfiguration time-dependent Hartree algorithm. The existence of different time scales considerably complicates the dynamics. The mode-to-mode energy transfer is analyzed by calculating the evolution of the partial energies of all vibrational modes. This study emphasizes the crucial role played by the two-dimensional FCH bending modes which act as an energy reservoir. The fast energy flow into these bending modes significantly hinders an energy flow from the CH chromophore. Finally, our results are compared with those obtained previously with the wave operator sorting algorithm approach.     

Photostability of electronically excited polyacenes: a case study of vibronic coupling in the naphthalene radical cation

Novel issues of electronic nonadiabatic coupling in the excited state dynamics of prototypical naphthalene radical cation of polycyclic aromatic hydrocarbon of the polyacene family are theoretically investigated. A benchmark ab initio quantum dynamical study is performed and its complex vibronic spectra and nonradiative decay are examined. The findings are in very good accord with the experiment, unambiguously establishing the crucial role of intricate electron-nuclear coupling in the photoinduced dynamical processes of this system.     

Homoclinic motions in the vibrational spectra of floppy systems: the LiCN molecule

Recent experimental and theoretical methods allowed the efficient investigation of highly excited rovibrational states of molecular systems. At these levels of excitation the correspondence principle holds, and then classical mechanics can provide intuitive views of the involved processes. In this respect, we have recently shown that for completely hyperbolic systems, homoclinic motions, which are known to organize the classical chaotic region in Hamiltonian systems, imprint a clear signature in the corresponding highly excited quantum spectra. In this Communication we show that this result also holds in mixed systems, by considering an application to the floppy LiNCLiCN molecular system.     

Solubility of small molecule in ionic liquids: a model study on the ionic size effect

Recently, the solvent power of ionic liquid (IL) has been described based on Flory-Huggins (FH) theory assuming that the volumes of the components are the same (J. Phys. Chem. B, 2006, 110, 16205). Here, we extended the FH theory to derive the solvent power in the case of different sizes (molar volumes) of the IL's components based on "polymer-like" model. Applying this model, the effect of ionic size on the solvent power of ionic liquids has been investigated. It was found that the effect of size can be characterized by introducing the effective volume (V+ and V-) of each site of the ion, and for the equivalent ionic liquid, the larger effective volume of the ionic liquid has the larger solvent power. Our results are in excellent agreement with the experimental solubility data in various ionic liquids.