A harmonic adiabatic approximation to calculate highly excited vibrational levels of “floppy molecules”

Tunneling motion and splitting in the CH2OH radical: (Sub-)millimeter wave spectrum analysis

The (sub-)millimeter wave spectrum of the non-rigid CH2OH radical is investigated both experimentally and theoretically. Ab initio calculations are carried out to quantitatively characterize its potential energy surface as a function of the two large amplitude ∠H1COH and ∠H2COH dihedral angles. It is shown that the radical displays a large amplitude torsional-like motion of its CH2 group with respect to the OH group. The rotation–torsion levels computed with the help of a 4D Hamiltonian accounting for this torsional-like motion and for the overall rotation exhibit a tunneling splitting, in agreement with recent experimental investigations, and a strong rotational dependence of this tunneling splitting on the rotational quantum number K a due to the rotation–torsion Coriolis coupling. Based on an internal axis method approach, a fitting Hamiltonian accounting for tunneling effects and for the fine and hyperfine structure is built and applied to the fitting of the new (sub)-millimeter wave transitions measured in this work along with previously available high-resolution data. 778 frequencies and wavenumbers are reproduced with a unitless standard deviation of 0.79 using 27 parameters. The N = 0 tunneling splitting, which could not be determined unambiguously in the previous high-resolution investigations, is determined based on its rotational dependence.

Extreme anomalous centrifugal distortion in methylene

A new treatment is presented to account for the extreme anomalous centrifugal distortion displayed by the open-shell methylene radical. This new treatment is based on a four-dimensional approach in which both the overall rotation and the large amplitude bending mode are treated simultaneously. It accounts for the spin-rotation and spin-spin fine couplings, assumed to depend on the large amplitude bending coordinate, as well as for the hyperfine coupling. The new treatment is tested analyzing the available high-resolution data. 336 transitions, involving the ground and first excited vibrational states of the bending mode, are reproduced with a unitless standard deviation of 1.3, using 42 molecular constants. Compared to a previous analysis [S. Brünken et al., J. Chem. Phys. 123, 164315 (2005)], the present analysis is more satisfactory as it accounts for a larger dataset and the ratio of the number of data to the number of varied constants is larger. The present theoretical treatment also allows us to retrieve the bending potential and the main kinetic energy term.

Experimental and theoretical investigations of H2O-Ar

We have used continuous-wave cavity ring-down spectroscopy to record the spectrum of H₂O-Ar in the 2OH excitation range of H₂O. 24 sub-bands have been observed. Their rotational structure (T_rot = 12 K) is analyzed and the lines are fitted separately for ortho and para species together with microwave and far infrared data from the literature, with a unitless standard deviation σ=0.98 and 1.31, respectively. Their vibrational analysis is supported by a theoretical input based on an intramolecular potential energy surface obtained through ab initio calculations and computation of the rotational energy of sub-states of the complex with the water monomer in excited vibrational states up to the first hexad. For the ground and (010) vibrational states, the theoretical results agree well with experimental energies and rotational constants in the literature. For the excited vibrational states of the first hexad, they guided the assignment of the observed sub-bands. The upper state vibrational predissociation lifetime is estimated to be 3 ns from observed spectral linewidths.

Recent advances in quantum scattering calculations on polyatomic bimolecular reactions

This review surveys quantum scattering calculations on chemical reactions of polyatomic molecules in the gas phase published in the last ten years.

THE GROWING STRING METHOD FOR FLOWS OF NEWTON TRAJECTORIES BY A SECOND-ORDER METHOD

The reaction path is an important concept of theoretical chemistry. We use a definition with a reduced gradient (see Quapp et al., Theor Chem Acc100:285, 1998), also named Newton trajectory (NT). To follow a reaction path, we design a numerical scheme for a method for finding a transition state between reactant and product on the potential energy surface: the growing string (GS) method. We extend the method (see W. Quapp, J Chem Phys122:174106, 2005) by a second-order scheme for the corrector step, which includes the use of the Hessian matrix. A dramatic performance enhancement for the exactness to follow the NTs, and a dramatic reduction of the number of corrector steps are to report. Hence, we can calculate flows of NTs. The method works in nonredundant internal coordinates. The corresponding metric to work with is curvilinear. The GS calculation is interfaced with the GamessUS package (we have provided this algorithm on ). Examples for applications are the HCN isomerization pathway and NTs for the isomerization C7ax ↔ C5 of alanine dipeptide.

REDUCED GRADIENT METHODS AND THEIR RELATION TO REACTION PATHS

The reaction path is an important concept in theoretical chemistry. We discuss different definitions, their merits as well as their drawbacks: IRC (steepest descent from saddle), reduced gradient following (RGF), gradient extremals, and some others. Many properties and problems are explained by two-dimensional figures. This paper is both a review and a pointer to future research. The branching points of RGF curves are valley-ridge inflection (VRI) points of the potential energy surface. These points may serve as indicators for bifurcations of the reaction path. The VRI points are calculated with the help of Branin's method. All the important features of the potential energy surface are independent of the coordinate system. Besides the theoretical definitions, we also discuss the numerical use of the methods.

Optimal control simulation of the Deutsch-Jozsa algorithm in a two-dimensional double well coupled to an environment

The quantum Deutsch-Jozsa algorithm is implemented by using vibrational modes of a two-dimensional double well. The laser fields realizing the different gates (NOT, CNOT, and HADAMARD) on the two-qubit space are computed by the multitarget optimal control theory. The stability of the performance index is checked by coupling the system to an environment. Firstly, the two-dimensional subspace is coupled to a small number Nb of oscillators in order to simulate intramolecular vibrational energy redistribution. The complete (2+Nb)D problem is solved by the coupled harmonic adiabatic channel method which allows including coupled modes up to Nb=5. Secondly, the computational subspace is coupled to a continuous bath of oscillators in order to simulate a confined environment expected to be favorable to achieve molecular computing, for instance, molecules confined in matrices or in a fullerene. The spectral density of the bath is approximated by an Ohmic law with a cutoff for some hundreds of cm(-1). The time scale of the bath dynamics (of the order of 10 fs) is then smaller than the relaxation time and the controlled dynamics (2 ps) so that Markovian dissipative dynamics is used.

Wave packets in a bifurcating region of an energy landscape: Diels-Alder dimerization of cyclopentadiene

Quantum dynamics in a valley ridge inflection (VRI) point region is analyzed in the case of the Diels-Alder endo-dimerization of cyclopentadiene pointed out recently by [Caramella et al., J. Am. Chem. Soc. 124, 1130 (2002)]. The VRI point is located along the reaction path connecting the bispericyclic symmetrical transition structure put in evidence by Caramella et al. and the transition state of the Cope rearrangement. Dynamics is carried out by using constrained Hamiltonian methodology. The active coordinates are the first formed C-C bond length and the difference between the two other C-C bond lengths which achieve the dimerization as 4+2 or 2+4 adducts. A two-dimensional (2D) minimum-energy surface have been computed at the Becke 3 Lee-Yong-Parr6-31G* level. The energy landscape can be classified as an uphill ridge-pitchfork VRI bifurcation according to a recent classification of bifurcation events [W. Quapp, J. Mol. Struct. 695-696, 95 (2004)]. Dynamics does not describe the thermal reaction but concerns wave packets which could be prepared by pulse reagents, i.e., by coherent control. We analyze how the shape and initial location on the ground potential-energy surface are linked to the synchronous or asynchronous mechanism of the final step after the first transition state. We use a one-dimensional model of optimum control theory to check the feasibility of such a coherent preparation. The wave-packet evolution in the VRI domain is well explained by semiclassical predictions even with the negative curvature of the unstable ridge. Finally, a crude model of dissipation has been introduced to test the stability of the 2D predictions.

Fingerprints of Delocalized Transition States in Quantum Dynamics

Reactions with delocalized transition states (plateau reactions) can be characterized statically by their energy profile along the reaction path, where they exhibit a broad, flat region instead of one or several well-defined saddle points on the potential energy surface. Employing our new, highly flexible quantum dynamics code to perform two-dimensional and effective four-dimensional quantum wave packet propagations on ab initio based model potentials, we show that plateau reactions can also be discerned from the other standard reaction types by their dynamics.

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.

Propagation with distributed Gaussians as a sparse, adaptive basis for higher-dimensional quantum dynamics

A simple quantum wavepacket propagation algorithm is presented, designed to produce a very compact, non-direct product representation in higher-dimensional cases. Instead of moving basis functions around, localized basis functions at pre-defined centers are added to and deleted from the representation, generating an active basis function set strictly localized to the region where the moving wavepacket has significantly non-zero values. Simple one-dimensional examples prove this property, as well as the ability of the algorithm to accommodate splitting and rejoining of an arbitrary number of wavefunction pieces, and tunnelling through potential energy barriers. It is argued that future applications to higher-dimensional examples will be less expensive than with traditional direct-product bases, since making the basis adaptive has a lower scaling than the elementary steps necessary for any propagation algorithm itself.

The all-Cartesian reaction plane Hamiltonian: Formulation and application to the H-atom transfer in tropolone

In this work we present an all-Cartesian reaction surface approach, where the large amplitude coordinates span the so-called reaction plane, that is, the unique plane defined by the two minima and the saddle-point structure of an isomerization reaction. Orthogonal modes are treated within harmonic approximation which gives the total Hamiltonian an almost separable form that is suitable for multidimensional quantum dynamics calculations. The reaction plane Hamiltonian is constructed for the H-atom transfer in tropolone as an example for a system with an intramolecular O...H-O hydrogen bond. We find ground-state tunneling splittings of 3.5 and 0.16 cm(-1) for the normal and deuterated species, respectively. We calculated infrared-absorption spectra for a four-dimensional model focusing on the low-frequency region. Here, we identify a reaction mode which is closely connected to the tautomerization that is reflected in the increase of tunneling splitting to 18 cm(-1) upon excitation.

The potential energy surface of the Ar-CO complex obtained using high-resolution data

A potential energy surface is retrieved for the Ar-CO complex by carrying out a global analysis of its high-resolution spectroscopic data. The data set consists of already published microwave and infrared data and of new microwave transitions which are presented in the paper. The theoretical approach used to reproduce the spectrum is based on a model Hamiltonian which accounts simultaneously for the two large amplitude van der Waals modes and for the overall rotation of the complex. Only the vCO = 0 state is considered. The root-mean-square deviation of the analysis is 18 MHz for the microwave data and 1.4 x 10(-3) cm(-1) for the infrared energy difference data. Fifteen parameters corresponding to the potential energy function are determined in addition to two kinetic energy parameters and two distortion-type parameters. The potential energy surface derived is in good agreement with the one obtained by Shin, Shin, and Tao [J. Chem. Phys. 104, 183 (1996)].

Improved RGF method to find saddle points

The predictor-corrector method for following a reduced gradient (RGF) to determine saddle points [Quapp, W. et al., J Comput Chem 1998, 19, 1087] is further accelerated by a modification allowing an implied corrector step per predictor but almost without additional costs. The stability and robustness of the RGF method are improved, and the new version in addition reduces the number of gradient and Hessian calculations.

One-dimensional quantum description of the bending vibrations of HCN/CNH for high values of the total angular momentum

For high values of the quantum number of the total angular momentum J (up to J = 20), quantum mechanical eigenstates (eigenvalues and eigenfunctions) are calculated by the method of Gatti et al. (J. Mol. Spectrosc. 181 (1997) 403) for the bending deformations of HCN and CNH. In particular, we have examined the l-type resonances in highly excited rovibrational states within the framework of a one-dimensional model, i.e. along the reaction pathway for the isomerization reaction HCN/CNH. The potential energy surface used is that of Bowman et al. (J. Chem. Phys. 99 (1993) 308).