Hamiltonian for rovibrational spectra of “hot” molecules

A variational method based on the determination of rotation as a state with a constant angular momentum has been proposed for calculating rovibrational energy levels of a polyatomic molecule. By using this method, energy level values can be determined for any vibrational state with arbitrary values of vibrational quantum numbers. This makes it possible to calculate the rovibrational energy levels of the “hot” molecules.     

The mechanism of H-bond rupture: the vibrational pre-dissociation of C2H2-HCl and C2H2-DCl

Pair correlated fragment rovibrational distributions are presented following vibrational predissociation of the C2H2-DCl van der Waals dimer initiated by excitation of the asymmetric (asym) C-H stretch. The only observed fragmentation pathways are DCl (v= 0; j= 6-9)+ C2H2(nu2= 1; j= 1-5). These and previously reported data on the related C2H2-HCl species are analysed using the angular momentum (AM) method. Calculations accurately reproduce fragment rovibrational distributions following dissociation of the C2H2-HCl dimer initiated either by excitation of the asym C-H stretch or via the HCl stretch, and those from C2H2-DCl initiated via asym C-H stretch excitation. The calculations demonstrate that the dimer is bent at the moment of dissociation. Several geometries are found that lead to H-bond breakage via a clearly identified set of fragment quantum states. The results suggest a hierarchy in the disposal of excess energy and angular momentum between fragment vibration, rotation and recoil. Deposition of the largest portion of energy into a C2H2 vibrational state sets an upper limit on HCl rotation, which then determines the energy and AM remaining for C2H2 rotation and fragment recoil. Acceptor C2H2 vibrational modes follow a previously noted propensity, implying that the dissociating impulse must be able to induce appropriate nuclear motions both in the acceptor vibration and in rotation of the C2H2 fragment.     

Influence of the potential energy surface on the reaction cross section: the K + HF → KF + H system

The effect of the potential energy surface on the K + HF → KF + H cross section has been studied using reasonable Sorbie-Murrell (bent saddle point) and LEPS (collinear saddle point) potential energy surfaces (PESs). Trajectory calculations for selected initial conditions (translational energies, rovibrational levels (v, J) of HF, as well as initial parallel or perpendicular alignments between the HF rotational angular momentum and the reactants relative velocity vectors) have been performed on these PESs to compare them with experiments. The Sorbie-Murrell and LEPS-4 PESs lead to steric effect ratio results quite close to the experimental ones, once the error margins are included. The resllts point towards a bent K-F-H saddle point although the PES is very isotropic. This could explain why experimental determinations lead to suggest a collinear saddle point. The K + HF → KF + H reaction exhibits an enormous vibrational enhancement of reactivity with one quantum HF vibrational excitation, even at translational energies well above the HF(v=0) threshold, where tunnelling effect contribution to reactivity can be neglected. This behaviour has not been reproduced in the trajectory calculations and no satisfactory explanation has been obtained for this fact. Nevertheless, the HF(v=1)/HF(v=0) cross section ratio at translational energies not far from the HF(v=0) threshold and the relative cross section for HF(v=0) have been satisfactorily descibed. In what regards rotation, the best theoretical results are those corresponding to the Sorbie-Murrell PES (the cross section increases with J), although important differences with experiment appear for the J = 0–3 interval at the lower translational energy values considered (0.54 and 0.77 eV).     

Communication: state-to-state quantum dynamics study of the OH + CO → H + CO2 reaction in full dimensions (J = 0)

A full dimensional state-to-state quantum dynamics study is carried out for the prototypical complex-formation OH + CO → H + CO(2) reaction in the ground rovibrational initial state on the Lakin-Troya-Schatz-Harding potential energy surface by using the reactant-product decoupling method. With three heavy atoms and deep wells on the reaction path, the reaction represents a huge challenge for accurate quantum dynamics study. This state-to-state calculation is the first such a study on a four-atom reaction other than the H(2) + OH ? H(2)O + H and its isotope analogies. The product CO(2) vibrational and rotational state distributions, and product energy partitioning information are presented for ground initial rovibrational state with the total angular momentum J = 0.     

A new method for the derivation of exact vibration-rotational kinetic energy operator in internal coordinates

An efficient angular momentum method is presented and used to derive analytic expressions for the vibration-rotational kinetic energy operator of polyatomic molecules.The vibration-rotational kinetic energy operator is expressed in terms of the total angular momentum operator J,the angular momentum operator J and the momentum operator p conjugate to Z in the molecule-fixed frame Not only the method of derivation is simpler than that in the previous work,but also the expressions ot the kinetic energy operators arc more compact.Particularly,the operator is easily applied to different vibrational or rovibrational problems of the polyatomic molecules by variations of matrix elements Gn of a mass-dependent constant symmetric matrix     

Rotating full- and reduced-dimensional quantum chemical models of molecules

A flexible protocol, applicable to semirigid as well as floppy polyatomic systems, is developed for the variational solution of the rotational-vibrational Schro?dinger equation. The kinetic energy operator is expressed in terms of curvilinear coordinates, describing the internal motion, and rotational coordinates, characterizing the orientation of the frame fixed to the nonrigid body. Although the analytic form of the kinetic energy operator might be very complex, it does not need to be known a priori within this scheme as it is constructed automatically and numerically whenever needed. The internal coordinates can be chosen to best represent the system of interest and the body-fixed frame is not restricted to an embedding defined with respect to a single reference geometry. The features of the technique mentioned make it especially well suited to treat large-amplitude nuclear motions. Reduced-dimensional rovibrational models can be defined straightforwardly by introducing constraints on the generalized coordinates. In order to demonstrate the flexibility of the protocol and the associated computer code, the inversion-tunneling of the ammonia ((14)NH(3)) molecule is studied using one, two, three, four, and six active vibrational degrees of freedom, within both vibrational and rovibrational variational computations. For example, the one-dimensional inversion-tunneling model of ammonia is considered also for nonzero rotational angular momenta. It turns out to be difficult to significantly improve upon this simple model. Rotational-vibrational energy levels are presented for rotational angular momentum quantum numbers J = 0, 1, 2, 3, and 4.     

Calculation of argon trimer rovibrational spectrum

Rovibrational spectra of Ar3 are computed for total angular momenta up to J=6 using row-orthonormal hyperspherical coordinates and an expansion of the wave function on hyperspherical harmonics. The sensitivity of the spectra to the two-body potential and to the three-body corrections is analyzed. First, the best available semiempirical pair potential (HFDID1) is compared with our recent ab initio two-body potential. The ab initio vibrational energies are typically 1-2 cm-1 higher than the semiempirical ones, which is related to the slightly larger dissociation energy of the semiempirical potential. Then, the Axilrod-Teller asymptotic expansion of the three-body correction is compared with our newly developed ab initio three-body potential. The difference is found smaller than 0.3 cm-1. In addition, we define approximate quantum numbers to describe the vibration and rotation of the system. The vibration is represented by a hyper-radial mode and a two-degree-of-freedom hyperangular mode, including a vibrational angular momentum defined in an Eckart frame. The rotation is described by the total angular momentum quantum number, its projection on the axis perpendicular to the molecular plane, and a hyperangular internal momentum quantum number, related to the vibrational angular momentum by a transformation between Eckart and principal-axes-of-inertia frames. These quantum numbers provide a qualitative understanding of the spectra and, in particular, of the impact of the nuclear permutational symmetry of the system (bosonic with zero nuclear spin). Rotational constants are extracted from the spectra and are shown to be accurate only for the ground hyperangular mode.     

Higher energy states in the CO dimer: millimeter-wave spectra and rovibrational calculations

New extensive millimeter-wave measurements of the 12C16O dimer have been made, and more than 300 new spectral transitions have been observed in the frequency range 81-135 GHz. A joint analysis of these and previous millimeter-wave data yielded the precise location of 33 new energy levels of A+ symmetry and 20 levels of A- symmetry. These energy levels are located at 8-18 cm(-1) above the zero-point level. Some of them belong to already known stacks, and others make up 9 new stacks of the dimer. Newly determined stacks have K=0, 1, and, for the first time, 2, where K is the projection of the total angular momentum on the intermolecular axis. The energy levels from accompanying rovibrational calculations with the use of a recently developed hybrid CCSD(T)/DFT-SAPT potential are in very good agreement with experiment. Analysis of the calculated wave functions revealed that two new stacks of A+ symmetry with K=2 correspond to overall rotation of the dimer while the other newly observed stacks belong to the geared bend overtone modes. The ground vibrational states of the two "isomers" found are more or less localized at the two minima in the potential surface, whereas all the geared bend excited states show a considerable amount of delocalization.     

三原子分子振转激发态成簇现象理论研究

在只考虑弯曲振动与总角动量的耦合,而冻结伸缩振动的模型下,采用Jacobi多项式作为弯曲振动的基函数,用严格的变分法研究了H~2O分子的振转激发态的成簇现象。本文计算了H~2O分子的振转能级和函数,研究了振动激发态下转动高激发态中出现的成簇态。     

Harmonic oscillator tensors. II. angular momentum expressions of matrix elements of vibrational operators

The spatial symmetries of the harmonic oscillator and the recently found irreducible tensors constructed from the associated annihilation and creation operators are exploited to obtain new expressions for the elements of the matrix representatives of several examples of vibrational operators. Since all vibrational operators are expressible in terms of the irreducible tensors, their matrix elements reflect the angular momentum symmetry inherent in them, for the results derived here are in terms of the Clebsch–Gordan coefficients and the isoscalar factors that arise from the couplinig rule of the irreducible tensors. Familiarity with the mathematical properties of these quantities derived from the elementary theory of angular momentum facilitates the evaluation of many vibrational operators that may be of importance in the study of potentials in this basis. In particular, it is shown that the nonvanishing of matrix elements is governed by a law of conservation of angular momentum along the axis of quantization of the nondegenerate harmonic oscillator. © 1993 John Wiley & Sons, Inc.     

The role of angular momentum in collision-induced vibration-rotation relaxation in polyatomics

Vibrational relaxation of the 6(1) level of S(1)((1)B(2u)) benzene is analyzed using the angular momentum model of inelastic processes. Momentum-(rotational) angular momentum diagrams illustrate energetic and angular momentum constraints on the disposal of released energy and the effect of collision partner on resultant benzene rotational excitation. A kinematic "equivalent rotor" model is introduced that allows quantitative prediction of rotational distributions from inelastic collisions in polyatomic molecules. The method was tested by predicting K-state distributions in glyoxal-Ne as well as J-state distributions in rotationally inelastic acetylene-He collisions before being used to predict J and K distributions from vibrational relaxation of 6(1) benzene by H(2), D(2), and CH(4). Diagrammatic methods and calculations illustrate changes resulting from simultaneous collision partner excitation, a particularly effective mechanism in p-H(2) where some 70% of the available 6(1)-->0(0) energy may be disposed into 0-->2 rotation. These results support the explanation for branching ratios in 6(1)-->0(0) relaxation given by Waclawik and Lawrance and the absence of this pathway for monatomic partners. Collision-induced vibrational relaxation in molecules represents competition between the magnitude of the energy gap of a potential transition and the ability of the colliding species to generate the angular momentum (rotational and orbital) needed for the transition to proceed. Transition probability falls rapidly as DeltaJ increases and for a given molecule-collision partner pair will provide a limit to the gap that may be bridged. Energy constraints increase as collision partner mass increases, an effect that is amplified when J(i)>0. Large energy gaps are most effectively bridged using light collision partners. For efficient vibrational relaxation in polyatomics an additional requirement is that the molecular motion of the mode must be capable of generating molecular rotation on contact with the collision partner in order to meet the angular momentum requirements. We postulate that this may account for some of the striking propensities that characterize polyatomic energy transfer.     

Non-Born-Oppenheimer calculations of the pure vibrational spectrum of HeH+

Very accurate calculations of the pure vibrational spectrum of the HeH(+) ion are reported. The method used does not assume the Born-Oppenheimer approximation, and the motion of both the electrons and the nuclei are treated on equal footing. In such an approach the vibrational motion cannot be decoupled from the motion of electrons, and thus the pure vibrational states are calculated as the states of the system with zero total angular momentum. The wave functions of the states are expanded in terms of explicitly correlated Gaussian basis functions multipled by even powers of the internuclear distance. The calculations yielded twelve bound states and corresponding eleven transition energies. Those are compared with the pure vibrational transition energies extracted from the experimental rovibrational spectrum.     

Identification of the transition states in the inversion of 1,4-benzodiazepines with the ab initio replica path method

The inversion of four 1,4-benzodiazepines was investigated with the ab initio "replica path method" with density functional theory at the B3LYP/6-31G* level. The reaction path constructed with this method for the inversion provides an approximate transition state (TS) geometry, which, upon further TS optimization, leads to the TS geometry characterized by a single vibrational frequency. 1,4-Benzodiazepines lacking a 5-phenyl ring have a single reaction path for the inversion with Cs symmetry at the TS. In contrast, the inversion of benzodiazepines with a 5-phenyl ring, such as the peripheral benzodiazepine receptor ligand 4'-chlorodiazepam (Ro5-4864) and its N1-desmethyl analog (Ro5-2752), can proceed through multiple reaction paths having a TS with or without Cs symmetry. Notably, the replica path method found a path connecting two asymmetric TSs of 4'-chlorodiazepam via a symmetrical TS, suggesting that these inversion paths can be readily crossed from one to another. The stabilization energies gained by 4'-chlorodiazepam and its N1-desmethyl analog from the breaking of Cs symmetry at the TS were calculated to be 0.10 and 0.07 kcal/mol, respectively. The origin of the broken symmetry of Cs was traced to the coupling of the puckering of the diazepine ring with the rotation of the chlorophenyl ring. These results show the advantages of the replica path method for locating the TSs as well as for constructing the reaction paths for the inversion of 1,4-benzodiazepines.     

Rovibrational energy transfer in the 4nu(CH) manifold of acetylene, viewed by IR-UV double-resonance spectroscopy. 4. Collision-induced quasi-continuous background effects

The 4nu(CH) rovibrational manifold around 12 700 cm(-1) in the electronic ground state, X, of acetylene (C2H2) is monitored by time-resolved infrared-ultraviolet double-resonance (IR-UV DR) spectroscopy. An IR laser pulse initially prepares rotational J states, associated with the "IR-bright" (nu1 + 3nu3) or (1 0 3 0 0)0 vibrational combination level, and subsequent collision-induced state-to-state energy transfer is probed by UV laser-induced fluorescence. Anharmonic, l-resonance, and Coriolis couplings affect the J states of interest, resulting in a congested rovibrational manifold that exhibits complex intramolecular dynamics. In preceding papers in this series, we have described three complementary forms of the IR-UV DR experiment (IR-scanned, UV-scanned, and kinetic) on collision-induced rovibrational satellites, comprising both regular even-DeltaJ features and unexpected odd-DeltaJ features. This paper examines an unusual collision-induced quasi-continuous background (CIQCB) effect that is apparently ubiquitous, accompanying regular even-DeltaJ rovibrational energy transfer and accounting for much of the observed collision-induced odd-DeltaJ satellite structure; certain IR-bright (1 0 3 0 0)0 rovibrational states (e.g., J = 12) are particularly prominent in this regard. We examine the mechanism of this CIQCB phenomenon in terms of a congested IR-dark rovibrational manifold that is populated by collisional transfer from the nearly isoenergetic IR-bright (1 0 3 0 0)0 submanifold.     

Intra- and intermolecular energy transfer in highly excited ozone complexes

The energy transfer of highly excited ozone molecules is investigated by means of classical trajectories. Both intramolecular energy redistribution and the intermolecular energy transfer in collisions with argon atoms are considered. The sign and magnitude of the intramolecular energy flow between the vibrational and the rotational degrees of freedom crucially depend on the projection K(a) of the total angular momentum of ozone on the body-fixed a axis. The intermolecular energy transfer in single collisions between O(3) and Ar is dominated by transfer of the rotational energy. In accordance with previous theoretical predictions, the direct vibrational de-excitation is exceedingly small. Vibration-rotation relaxation in multiple Ar+O(3) collisions is also studied. It is found that the relaxation proceeds in two clearly distinguishable steps: (1) During the time between collisions, the vibrational degrees of freedom are "cooled" by transfer of energy to rotation; even at low pressure equilibration of the internal energy is slow compared to the time between collisions. (2) In collisions, mainly the rotational modes are "cool" by energy transfer to argon.     

Torsion-vibration coupling in methanol: the adiabatic approximation and intramolecular vibrational redistribution scaling

The four-dimensional model Hamiltonian of Wang and Perry [J. Chem. Phys. 109, 10795 (1998)] is used to compare the approximate adiabatic separation of the torsion and CH stretches in methanol to an exact solution of the same Hamiltonian. The adiabatic approximation accounts for the pattern of the energy levels in the lowest torsional states, including the inverted tunneling splittings, but does not account for the pattern of systematic two- and four-fold near degeneracies at high torsional excitation. In the adiabatic basis, the nonadiabatic couplings mix the torsional and vibrational degrees of freedom and hence are a source for intramolecular vibrational redistribution (IVR). These IVR matrix elements are found to decrease by only a factor of 2 or 3 with each higher coupling order, in agreement with the results of Pearman and Gruebele [Z. Phys. Chem. Munich 214, 1439 (2000)]. This gentle scaling behavior, which contrasts with a steeper falloff with coupling order in more rigid molecules, points to a more important role for direct high-order couplings in torsional molecules. In this model, the scaling behavior derives from a single coupling term that is low order in the torsional angular momentum in combination with one-dimensional torsional functions that include contributions from many torsional angular momenta.     

Quantum dynamics of rovibrational transitions in H2-H2 collisions: internal energy and rotational angular momentum conservation effects

We present a full dimensional quantum mechanical treatment of collisions between two H(2) molecules over a wide range of energies. Elastic and state-to-state inelastic cross sections for ortho-H(2)?+ para-H(2) and ortho-H(2)?+ ortho-H(2) collisions have been computed for different initial rovibrational levels of the molecules. For rovibrationally excited molecules, it has been found that state-to-state transitions are highly specific. Inelastic collisions that conserve the total rotational angular momentum of the diatoms and that involve small changes in the internal energy are found to be highly efficient. The effectiveness of these quasiresonant processes increases with decreasing collision energy and they become highly state-selective at ultracold temperatures. They are found to be more dominant for rotational energy exchange than for vibrational transitions. For non-reactive collisions between ortho- and para-H(2) molecules for which rotational energy exchange is forbidden, the quasiresonant mechanism involves a purely vibrational energy transfer albeit with less efficiency. When inelastic collisions are dominated by a quasiresonant transition calculations using a reduced basis set involving only the quasiresonant channels yield nearly identical results as the full basis set calculation leading to dramatic savings in computational cost.     

Rovibrational momentum densities of diatomic molecules in the rigid rotor-harmonic oscillator approximation

The rigid rotor-harmonic oscillator model in the momentum representation is used to examine the rovibrational momentum density of a diatomic molecule. The effects on this function of rotational and vibrational excitation, thermal averaging, and nuclear spin statistics are exhibited in calculations on N₂ and thehydrogen halides, and a brief comparison with electron momentum densities is made.