HCP CPH ISOMERIZATION: Caught in the Act

Fundamental studies of vibrational resonance phenomena by multivalued resummation of the divergent Rayleigh-Schrödinger perturbation theory series: deciphering polyad structures of three H216O isotopologues

A fundamental quantitative study of the vibrational resonances of three H₂¹⁶O H,D-isotopologues with a quartic Watson Hamiltonian was carried out using the resummation of the high-order (∼λⁿ, n ≤ 203) divergent Rayleigh-Schrödinger perturbation theory (RSPT) series by quartic Padé-Hermite multivalued diagonal approximants PH^[m,m,m,m,m], m ≤ 40. The resonance condition between a pair of states is formulated as the existence of a common complex energy solution branch point inside the unit circle: |E(λ_j)|,  Re(λ_j)² + Im(λ_j)² ≤ 1. For the matrix formulation of the vibrational problem (VCI), the existence of common branch points is governed by the Katz theorem and they can be found as roots of discriminant polynomials. The main branches of the Padé-Hermite approximants typically reproduce VCI energies with high accuracy while alternative branches often fit nearby resonant states. The resummation of the RSPT series for H₂O and D₂O (up to the tenth polyad) revealed not only Fermi and Darling-Dennison resonances, but also unusual (0,2,-5) and (5,-2,0) resonance effects matching the (5,2,5) polyad structure, while the (3,2,1) structure was rigorously confirmed for HDO. It is demonstrated that the (5,2,5) polyad structure ensures good organization of high-energy resonating states and breaks down the classic (2,1,2) structure. The advocated methodology of quantitative description of resonance phenomena and revealing polyad structures is suitable for larger molecules and can be adapted to linear molecules and symmetric tops. Its application ensures rigorous classification of vibrational states and can be used in quantitative vibration-rotation spectroscopy.

Characterizing structures, energetics, and spectra of species on the 1,3[H, C, As] potential energy surfaces: A high-level theoretical contribution

The ground and the low lying electronic states of structures on the ^1,3[H, C, As] potential energy surfaces were investigated with the highly correlated theoretical approaches CCSD(T), CCSD(T)-F12b, and CASSCF/MRCI along with the series of correlation consistent (aug-cc-pVnZ, n = D, T, Q, 5) basis sets. Energetic and spectroscopic parameters were obtained at the complete basis set limit, and the effect of core-valence correlation on these properties evaluated. Fundamental frequencies were also computed with the variational configuration interaction (VCI) approach. Heats of formation at 0 and 298.15 K were estimated for HCAs and CH, AsH, CAs, and HCAs, as well as the calculation of ionization potentials for HCAs. Comparisons of the present results with literature ones for the systems HCN/HNC, HCP/HPC highlight similarities and differences among these systems. Altogether, this investigation provides a very reliable characterization of the species on the surfaces and should guide future experimental studies on these systems.

Observation of an isomerizing double-well quantum system in the condensed phase

Molecular isomerization fundamentally involves quantum states bound within a potential energy function with multiple minima. For isolated gas-phase molecules, eigenstates well above the isomerization saddle points have been characterized. However, to observe the quantum nature of isomerization, systems in which transitions between the eigenstates occur-such as condensed-phase systems-must be studied. Efforts to resolve quantum states with spectroscopic tools are typically unsuccessful for such systems. An exception is CO adsorbed on NaCl(100), which is bound with the well-known OC-Na⁺ structure. We observe an unexpected upside-down isomer (CO-Na⁺) produced by infrared laser excitation and obtain well-resolved infrared fluorescence spectra from highly energetic vibrational states of both orientational isomers. This distinctive condensed-phase system is ideally suited to spectroscopic investigations of the quantum nature of isomerization.

Intramolecular vibrational energy redistribution and the quantum ergodicity transition: a phase space perspective

The onset of facile intramolecular vibrational energy flow can be related to features in the connected network of anharmonic resonances in the classical phase space.

Relevance of the Resonance Junctions on the Arnold Web to Dynamical Tunneling and Eigenstate Delocalization

We study the competition and correspondence between the classical and quantum routes to intramolecular vibrational energy redistribution (IVR) in a three degrees of freedom model effective Hamiltonian. Specifically, we focus on the classical and the quantum dynamics near the resonance junctions on the Arnold web that are formed by an intersection of independent resonances. The regime of interest models the IVR dynamics from highly excited initial states near dissociation thresholds of molecular systems wherein both classical and purely quantum, involving dynamical tunneling, routes to IVR coexist. In the vicinity of a resonance junction, classical chaos is inevitably present, and hence one expects the quantum IVR pathways to have a strong classical component as well. We show that with increasing resonant coupling strengths the classical component of IVR leads to a transition from coherent dynamical tunneling to incoherent dynamical tunneling. Furthermore, we establish that the quantum IVR dynamics can be predicted based on the structures on the classical Arnold web. In addition, we investigate the nature of the highly excited eigenstates to identify the quantum signatures of the multiplicity-2 junctions. For the parameter regimes studies herein, by projecting the eigenstates onto the Arnold web, we find that eigenstates in the vicinity of the junctions are primarily delocalized due to dynamical tunneling.

Quantum control of isomerization by robust navigation in the energy spectrum

In this paper, we present a detailed study on the application of the quantum control technique of navigation in the energy spectrum to chemical isomerization processes, namely, CN-Li⇆ Li-CN. This technique is based on the controlled time variation of a Hamiltonian parameter, an external uniform electric field in our case. The main result of our work establishes that the navigation involved in the method is robust, in the sense that quite sizable deviations from a pre-established control parameter time profile can be introduced and still get good final results. This is specially relevant thinking of a experimental implementation of the method.

A periodic orbit bifurcation analysis of vibrationally excited isotopologues of sulfur dioxide and water molecules: symmetry breaking substitutions

Theoretical predictions and assignment of highly excited vibrational states and their organization is one of the most important challenges in molecular spectroscopy. A systematic procedure to investigate such problems is locating the principal families of periodic orbits that emanate from the stationary points of the molecule and then following their evolution with the total energy. This results in constructing continuation/bifurcation diagrams that assist in locating the critical bifurcation energies and to discover new types of vibrational modes. Another parameter that may influence the dynamics of a molecule is isotopic mass substitution. In this article, we investigate the effect of symmetry breaking by isotopic mass substitution of triatomic molecules with C(2v) symmetry in classical and quantum dynamics. Sulfur dioxide and water molecules in their ground electronic state are studied by employing accurate potential energy surfaces. Continuation/bifurcation diagrams of periodic orbits are constructed by varying the energy and the mass of one oxygen atom of sulfur dioxide and one hydrogen atom of a water molecule. The transition from normal-to-local mode vibrations is studied in terms of a pitchfork to a center-saddle elementary bifurcation of periodic orbits. The results presented in this article aim to help the assignment of experimentally obtained spectra.

Electronic spectroscopy of jet-cooled HCP+: Molecular structure, phosphorus hyperfine structure, and Renner-Teller analysis

Laser-induced fluorescence spectra of jet-cooled HCP(+) and DCP(+) have been obtained with the pulsed discharge technique using HCPDCP and argon precursor mixtures. Transitions involving all of the excited state vibrations have been observed and a set of vibrational constants has been obtained. High-resolution spectra of the (2)Pi(32) components of the 0(0) (0) bands of both isotopomers have been recorded, and these spectra show resolved phosphorus hyperfine structure which allowed the determination of the excited state Fermi contact parameter. The B values were used to obtain the ground and excited state effective geometric parameters as r(0) (")(CH)=1.077(2) A, r(0) (")(CP)=1.6013(3) A, r(0) (')(CH)=1.082(2) A, and r(0) (')(CP)=1.5331(3) A. A Renner-Teller analysis of the ground state vibrational energy levels obtained from the literature was attempted. All of the observed levels of DCP(+) and the majority of those of HCP(+) were satisfactorily fitted with a standard Renner-Teller model, but three HCP(+) levels showed large systematic deviations which could not be accommodated by reassignments or improvements in the Fermi resonance Hamiltonian. Further improvements in the theory or in the experimental data will be needed to resolve this discrepancy.

Moment of inertia, backbending, and molecular bifurcation

We predict an anomaly in highly excited bending spectra of acetylene with high vibrational angular momentum. We interpret this in terms of a vibrational shape effect with moment of inertia backbending, induced by a sequence of bifurcations with a transition from "local" to "orthogonal" modes.

Analysis of the HO2 Vibrational Spectrum on an Accurate Ab Initio Potential Energy Surface

The complete vibrational spectrum of the HO2(X(2)A' ') radical, up to the H + O2 dissociation limit, has been determined quantum mechanically on an accurate potential energy surface (PES), based on approximately 15000 ab initio points at the icMRCI+Q/aug-cc-pVQZ level of theory. The vibrational states are found to be assignable at low energies but become more irregular as the energy approaches the dissociation limit. However, even at very high energies, regularity still exists, in sharp contrast to earlier results based on the double many-body expansion (DMBE) IV potential. Several Fermi resonances have been identified, and the spectrum is fit with a spectroscopic Hamiltonian. In addition, the vibrational dynamics is analyzed using a periodic orbit approach.

Periodic orbits in biological molecules: Phase space structures and selectivity in alanine dipeptide

Small and large molecules may localize their energy in specific bonds or generally in vibrational modes for extended periods of time, an effect which may have dramatic consequences in reaction dynamics. Periodic orbits offer the means to identify phase space regions with localized motions. The author demonstrate that techniques to locate periodic orbits developed for small molecules can be applied to large molecules such as alanine dipeptide. The widely used empirical force fields are employed and principal families of periodic orbits associated with local-type motions and emanated from the lowest energy minima and saddle points are investigated. Continuation of these families at high energies unravels the stable and unstable regions of phase space as well as elementary bifurcations such as saddle nodes.

Characterization of singlet ground and low-lying electronic excited states of phosphaethyne and isophosphaethyne

The singlet ground ((approximate)X(1)Sigma1+) and excited (1Sigma-,1Delta) states of HCP and HPC have been systematically investigated using ab initio molecular electronic structure theory. For the ground state, geometries of the two linear stationary points have been optimized and physical properties have been predicted utilizing restricted self-consistent field theory, coupled cluster theory with single and double excitations (CCSD), CCSD with perturbative triple corrections [CCSD(T)], and CCSD with partial iterative triple excitations (CCSDT-3 and CC3). Physical properties computed for the global minimum ((approximate)X(1)Sigma+HCP) include harmonic vibrational frequencies with the cc-pV5Z CCSD(T) method of omega1=3344 cm(-1), omega2=689 cm(-1), and omega3=1298 cm(-1). Linear HPC, a stationary point of Hessian index 2, is predicted to lie 75.2 kcal mol(-1) above the global minimum HCP. The dissociation energy D0[HCP((approximate)X(1)Sigma+)-->H(2S)+CP(X2Sigma+)] of HCP is predicted to be 119.0 kcal mol(-1), which is very close to the experimental lower limit of 119.1 kcal mol(-1). Eight singlet excited states were examined and their physical properties were determined employing three equation-of-motion coupled cluster methods (EOM-CCSD, EOM-CCSDT-3, and EOM-CC3). Four stationary points were located on the lowest-lying excited state potential energy surface, 1Sigma- -->1A", with excitation energies Te of 101.4 kcal mol(-1) (1A"HCP), 104.6 kcal mol(-1)(1Sigma-HCP), 122.3 kcal mol(-1)(1A" HPC), and 171.6 kcal mol(-1)(1Sigma-HPC) at the cc-pVQZ EOM-CCSDT-3 level of theory. The physical properties of the 1A" state with a predicted bond angle of 129.5 degrees compare well with the experimentally reported first singlet state ((approximate)A1A"). The excitation energy predicted for this excitation is T0=99.4 kcal mol(-1) (34 800 cm(-1),4.31 eV), in essentially perfect agreement with the experimental value of T0=99.3 kcal mol(-1)(34 746 cm(-1),4.308 eV). For the second lowest-lying excited singlet surface, 1Delta-->1A', four stationary points were found with Te values of 111.2 kcal mol(-1) (2(1)A' HCP), 112.4 kcal mol(-1) (1Delta HPC), 125.6 kcal mol(-1)(2(1)A' HCP), and 177.8 kcal mol(-1)(1Delta HPC). The predicted CP bond length and frequencies of the 2(1)A' state with a bond angle of 89.8 degrees (1.707 A, 666 and 979 cm(-1)) compare reasonably well with those for the experimentally reported (approximate)C(1)A' state (1.69 A, 615 and 969 cm(-1)). However, the excitation energy and bond angle do not agree well: theoretical values of 108.7 kcal mol(-1) and 89.8 degrees versus experimental values of 115.1 kcal mol(-1) and 113 degrees. of 115.1 kcal mol(-1) and 113 degrees.

Quantum mechanical and quasiclassical investigations of the time domain nonadiabatic dynamics of NO2 close to the bottom of the XA12‐AB22 conical intersection

We use the effective Hamiltonian that we recently fitted against the first 306 experimentally observed vibronic transitions of NO2 [Joyeux et al., J. Chem. Phys. 119, 5923 (2003)] to investigate the time domain nonadiabatic dynamics of this molecule on the coupled X 2A1 and A 2B2 electronic states, using both quantum mechanical and quasiclassical techniques. From the quantum mechanical point of view, we show that the transfer of population to the electronic ground state originating from a wave packet launched on the excited state occurs in a stepwise fashion. The evolution of wave packets launched on the electronic ground state is instead more complex because the crossing seam is located close to the bottom of the electronic excited state. We next use the mapping formalism, which replaces the discrete electronic degrees of freedom by continuous ones, to obtain a classical description of the coupled electronic states. We propagate Gaussian swarms of trajectories to show that this approach can be used to calculate the populations in each electronic state. We finally propose a very simple trajectory surface hopping model, which assumes that trajectories have a constant probability to jump onto the other state in a particular region of the phase space and a null hopping probability outside from this region. Quasiclassical calculations show that this model enables a precise estimation of complex quantities, as for example the projection of the instantaneous probability density on given planes.

Absorption spectrum and assignment of the Chappuis band of ozone

New global diabatic potential energy surfaces of the electronic states 1B1 and 1A2 of ozone and the non-adiabatic coupling surface between them are constructed from electronic structure calculations. These surfaces are used to study the visible photodissociation in the Chappuis band by means of quantum mechanical calculations. The calculated absorption spectrum and its absolute intensity are in good agreement with the experimental results. A vibrational assignment of the diffuse structures in the Chappuis band system is proposed on the basis of the nodal structures of the underlying resonance states.

Resonances of CH2(ãA11) and their roles in unimolecular and bimolecular reactions

Low-lying resonances of the CH2(a 1A1) system (J=0) in an accurate ab initio potential energy surface are studied using a filter-diagonalization method. The width of these resonances fluctuates by more than two orders of magnitude and on average increases with the energy. Analysis of the resonance states concludes that the unimolecular decay of the excited molecular system near the dissociation threshold is neither mode specific nor statistical state specific. This is apparently due to remnant regularity embedded in the largely chaotic classical phase space, as evidenced by periodic orbit analysis. As a result, the Rice-Ramsperger-Kassel-Marcus and statistical adiabatic channel models overestimate the average unimolecular decay rate. The implications of the resonances for the bimolecular C(1D)+H2 reaction are also discussed.

On dynamical tunneling and classical resonances

This work establishes a firm relationship between classical nonlinear resonances and the phenomenon of dynamical tunneling. It is shown that the classical phase space with its hierarchy of resonance islands completely characterizes dynamical tunneling and explicit forms of the dynamical barriers can be obtained only by identifying the key resonances. Relationship between the phase space viewpoint and the quantum mechanical superexchange approach is discussed in near-integrable and mixed regular-chaotic situations. For near-integrable systems with sufficient anharmonicity the effect of multiple resonances, i.e., resonance-assisted tunneling, can be incorporated approximately. It is also argued that the presumed relation of avoided crossings to nonlinear resonances does not have to be invoked in order to understand dynamical tunneling. For molecules with low density of states the resonance-assisted mechanism is expected to be dominant.

Quantum level structures at a Fermi resonance with angular momentum: classical periodic orbits, catastrophe maps and quantum monodromy

The Xiao-Kellman catastrophe map, for the classification of classical periodic orbits of the standard 2:1 Fermi resonance Hamiltonian is extended to species with finite vibrational angular momentum. The influence of the classical periodic orbit structure on different organizations of the quantum mechanical eigenvalues, in the four regions of the map, is strikingly demonstrated. The quantum eigenvalue lattices in angular momentum and energy space show dislocations attributable to a topological effect, termed quantum monodromy. Analogues with quantum monodromy in quasi-linear molecules and LiCN/LiNC isomerisation are demonstrated.

The Huggins band of ozone: A theoretical analysis

The Huggins band of ozone is investigated by means of dynamics calculations using a new (diabatic) potential energy surface for the 3 (1)A'(1B2) state. The good overall agreement of the calculated spectrum of vibrational energies and intensities with the experimental spectrum, especially at low to intermediate excitation energies, is considered as evidence that the Huggins band is due to the two C(s) potential wells of the 1B2 state rather than the single C2v well of the 2 (1)A'(1A1) state. The vibrational assignment of the "cold bands," based on the nodal structure of wave functions, on the whole supports the most recent experimental assignment [J. Chem. Phys. 115, 9311 (2001)]. The quantum mechanical spectrum is analyzed in terms of classical periodic orbits and the structure of the classical phase space.

Semiclassical dynamics of the van der Waals states in O3(X 1A1)

We present the analysis and the semiclassical quantization of the van der Waals states of ozone in the ground electronic state X1A1. Progressions of these states dominate the spectrum of O3 at threshold. Periodic orbits are used to perform assignment and quantization of the vibrational states. Semiclassical quantization is numerically accurate despite the fact that the classical phase space is chaotic while the nodal patterns of the quantum mechanical wave functions are regular. The lifetimes of recombination of the van der Waals states into the "normal" ozone are also discussed.