Nonrotating Molecule Research Articles

Feshbach resonances of the H − 3 and D − 3 anions

Based on a series of ab initio calculations two Feshbach resonances of the H − 3 negative ion having λ(1 sa′1)2(2sa′1)2−μ(1sa′1)2(2pa′′2)2: 1 A′1 and (1sa′1)2(2sa′1)(2pa′′2): 3 A′′2 electronic structure and estimated lifetimes of more than 10−14 s are predicted. The potential energy surfaces of the Feshbach states are roughly parallel to those of the Rydberg states of neutral H 3 and show minima located between the dissociative 2pE′ ground state surfaces and the lowest Rydberg states 2sA′1 and 2pA′′2 of H 3. We have determined a number of vibrational levels of the non-rotating molecules H − 3 and D − 3 and we predict electron affinities for the mentioned two Rydberg states.

Approximate theoretical model for the five electronic states ( Ω = 5/2, 3/2, 3/2, 1/2, 1/2) arising from the ground 3d 9 configuration in nickel halide molecules and for rotational levels of the two Ω = 1/2 states in that manifold

In the first part of this paper an effective Hamiltonian for a non-rotating diatomic molecule containing only crystal-field and spin–orbit operators is set up to describe the energies of the five spin–orbit components that arise in the ground electronic configuration of the nickel monohalides. The model assumes that bonding in the nickel halides has the approximate form Ni +X −, with an electronic 3d 9 configuration plus closed shells on the Ni + moiety and a closed shell configuration on the X − moiety. From a crystal-field point of view, interactions of the positive d-hole with the cylindrically symmetrical electric charge distribution of the hypothetical NiX − closed-shell core can then be parameterized by three terms in a traditional expansion in spherical harmonics: C 0 + C 2 Y 20( θ, ϕ) + C 4 Y 40( θ, ϕ). Interaction of the hole with the magnetic field generated by its own orbital motion can be parameterized by a traditional spin–orbit interaction operator A L · S . The Hamiltonian matrix is set up in a basis set consisting of the 10 Hund’s case (a) basis functions | L, Λ; S , Σ〉 that arise when L = 2 and S = 1/2. Least-squares fits of the observed five spin–orbit components of the three lowest electronic states in NiF and NiCl are then carried out in terms of the four parameters C 0, C 2, C 4, and A which lead to good agreement, except for the two | Ω| = 1/2 states. The large equal and opposite residuals of the | Ω| = 1/2 states can be reduced to values comparable with those for the | Ω| = 3/2 and | Ω| = 5/2 states by fixing A to its value in Ni + and then introducing an empirical correction factor for one off-diagonal orbital matrix element. In the second part of this paper the usual effective Hamiltonian B( J – L – S ) 2 for a rotating diatomic molecule is used to derive expressions for the Ω-type doubling parameter p in the two | Ω| = 1/2 states. These expressions show (for certain sign conventions) that the sum of the two p values should be −2 B, but that their difference can vary between −10 B and +10 B. These theoretical results are in good agreement with the two observed p values for both NiF and NiCl. The present formalism should in principle be applicable to NiBr and NiI, and to the halides of palladium, since Pd + has a well isolated 4d 9 electronic ground configuration. Extension to metal halides having d n configurations with n < 9, or to platinum halides may present difficulties, since manifolds from the d n and d n −1 s configurations may be heavily mixed, thus requiring “too many” parameters in the electronic part of the problem. Application to linear triatomic molecules may also present problems because of the large number of vibronic perturbations made possible by their four vibrational degrees of freedom.

MRCI study on spectroscopic and molecular properties of four low-lying electronic states of the BO radical

The potential energy curves (PECs) of four low-lying electronic states of the BO radical, including two 2Σ + and two 2Π states, have been studied using the full valence complete active space self-consistent field (CASSCF) method followed by the highly accurate valence internally contracted multireference configuration interaction (MRCI) approach in combination with the cc-pV5Z basis set for internuclear separations from 0.05 to 2.0 nm. The effect on the PECs by the relativistic correction has been taken into account. With these PECs, the spectroscopic parameters ( T e , D 0, D e , R e , ω e , ω ex e , α e and B e ) of two main isotopologues ( 11B 16O and 10B 16O) have been determined. These parameters have been compared in detail with those of previous investigations reported in the literature, and excellent agreement has been found between the available data and the present results. By solving the radial Schrödinger equation of nuclear motion, 60 vibrational states for the 11B 16O(X 2Σ +), 60 for the 10B 16O(X 2Σ +), 66 for the 11B 16O(A 2Π) and 64 for the 10B 16O(A 2Π) are predicted for the non-rotating molecule. For each vibrational state of the 11B 16O(X 2Σ +), 10B 16O(X 2Σ +), 11B 16O(A 2Π) and 10B 16O(A 2Π), the vibrational level G( υ), inertial rotation constant B υ and centrifugal distortion constant D υ have been determined. Comparison with the available data shows that the present molecular constants are reliable and accurate. The ro-vibrational levels have been calculated for the X 2Σ + and A 2Π states of two main species for future laboratory research.

The polarisation of two-photon excited fluorescence in rotating molecules

We report a general theory of the two-photon excited fluorescence (TPEF) of rotating molecules under the condition of anisotropic depolarisation. The obtained expressions for the TPEF intensity are based upon the spherical tensor approach and valid for any symmetric, or asymmetric top molecule and for any photon polarisation. The expressions are written in terms of the molecular parameters M K (R, R′, t) which have clear tensor notation and contain all molecular information that can be extracted from the TPEF experiments. Two important extreme cases are discussed. If the molecular rotation period is much larger than the excited state lifetime, the obtained expressions describe the TPEF in non-rotating molecules under the condition of isotropic relaxation. The time-independent part of these expressions is in agreement with the earlier results of McClain [J. Chem. Phys., 58, 324 (1973)]. The relationship between McClain's molecular parameters and the parameters M K (R, R′, 0) is presented and analysed. If the molecular rotation period is much smaller than the excited state lifetime, the expressions describe anisotropy of fluorescence from isolated ro-vibrational molecular states. As shown, under certain approximations the expression still can be written in terms of the M-parameters which are reduced due to molecular rotation by about a factor of (2K + 1). This result manifests that the fluorescence anisotropy is reduced, but not lost due to the molecular rotation.

High-Resolution Vibrational Spectroscopy of trans-Formic Acid in Solid Parahydrogen

We report high-resolution vibrational spectra of six normal modes of trans-formic acid (FA) in rapid vapor deposited solid parahydrogen (pH(2)) with particular emphasis on the carbonyl stretching mode (nu(3)) at approximately 1770 cm(-1). Infrared spectra in the nu(3) and 2nu(3) regions reveal that even in 99.99% enriched pH(2) samples, residual orthohydrogen (oH(2)) present in the solid preferentially clusters to FA producing measurable shifts in the nu(3) transition frequency. The individual FA(oH(2))(n) cluster peaks in the size range from n = 0 to n = 5 are resolved, permitting unambiguous assignment of the nu(3) and 2nu(3) transition frequencies and linewidths for FA with a first solvation shell (n = 0) of only pH(2) molecules. This n = 0 feature is well fit by a Lorentzian line shape with a line width of 0.214(6) cm(-1) and 0.45(2) cm(-1) for nu(3) and 2nu(3), respectively, which is surprisingly broad for a small nonrotating molecule trapped in solid pH(2). Implications of the broad FA nu(3) Lorentzian line shape in terms of homogeneous and inhomogeneous broadening mechanisms are discussed.

Simplified models for anharmonic numbers and densities of vibrational states. II. All the bound states of HO 2

Anharmonic rovibrational densities of states play an important role in statistical unimolecular rate theory and suitable methods for their determination are in large demand. This article compares different approaches to their calculation using the bound states of HO 2 as an example. Nearly accurate results for this system are becoming available on the basis of ab initio calculations. After empirical correction of these results, the present work predicts a total number of bound vibrational states of 315 ± 5 (for the non-rotating molecule). Approximate methods at different levels of complexity can be validated against the results obtained. In particular, the empirical method from part I [J. Troe, Chem. Phys. 190 (1995) 381] is tested. Gaining confidence in the performance of the various methods is a necessary condition for further applications to larger molecules for which ab initio calculations are out of reach.

Quantum Trajectory Dynamics in Arbitrary Coordinates

The quantum trajectory approach is generalized to arbitrary coordinate systems, including curvilinear coordinates. This allows one to perform an approximate quantum trajectory propagation, which scales favorably with system size, in the same framework as standard quantum wave packet dynamics. The trajectory formulation is implemented in Jacobi coordinates for a nonrotating triatomic molecule. Wave packet reaction probabilities are computed for the O(3P) + H2 --> OH + H reaction using the approximate quantum potential. The latter is defined by the nonclassical component of the momentum operator expanded in terms of linear and exponential functions. Unlike earlier implementations with linear functions, the introduction of the exponential function provides an accurate description of asymptotic dynamics for this system and gives good agreement of approximate reaction probabilities with accurate quantum calculations.

On using Fourier series and Legendre polynomials as angular basis sets for nonrotating triatomic molecules

The numerical properties of quantum grid methods applying the Fourier series and Legendre polynomials as angular basis sets for triatomic molecule calculations are compared. The three-dimensional time-dependent wavepacket calculations ( J = 0) by using relaxation technique are performed to obtain the lowest vibrational eigenvalues of ground electronic states of OBrO and van der Waals Na⋯FH molecules. For the OBrO molecule with a deep well potential along bending mode, the numerical models using the Fourier series with fast Fourier transform technique as the angular basis set are very efficient. And the Legendre polynomials is appropriate to describe the Na⋯FH molecule with a floppy potential along bending mode.

A 2 A 2 ←X 2 B 1 absorption and Raman spectra of the OClO molecule: A three-dimensional time-dependent wave packet study

Time-dependent wave packet calculations of the (A (2)A(2)<--X (2)B(1)) absorption and Raman spectra of the OClO molecule are reported. The Fourier grid Hamiltonian method in three dimensions is employed. The X (2)B(1) ground state ab initio potential energy surface reported by Peterson is used together with his corresponding A (2)A(2) state surface or the revised surface of the A (2)A(2) state by Xie and Guo. Radau coordinates are used to describe the vibrations of a nonrotating OClO molecule. The split-operator method combined with fast Fourier transform is applied to propagate the wave function. We find that the ab initio A (2)A(2) potential energy surface better reproduces the detailed structures of the absorption spectrum at long wavelength, while the revised surface of the A (2)A(2) state, consistent with the work of Xie and Guo, better reproduces the overall shape and the energies of the vibrational levels. Both surfaces of the A (2)A(2) state can reasonably reproduce the experimental Raman spectra but neither does so in detail for the numerical model employed in the present work.

Microsolvation and vibrational shifts of OCS in helium clusters

We present a theoretical study of the solvation structure around an OCS molecule embedded in helium clusters containing 1–100 He4 atoms, obtained from diffusion Monte Carlo calculations employing an ab initio, vibrational-state dependent internuclear potential and incorporating the molecular rotational degrees of freedom. The effect of the molecular rotation is to make the local helium density around the molecule considerably more delocalized in the ellipsoidal coordinates than that seen around a nonrotating OCS molecule. We find an unexpectedly sharp energy signature associated with completion of the first solvation shell at N∼20, suggesting that strongly bound molecules like OCS could have a “magic” quantum solvation number which is not apparent from the structural quantifiers of the solvating adatoms of that shell. The frequency shifts of the asymmetric stretch transition of the OCS molecule are computed as a function of cluster size via a dynamically adiabatic decoupling scheme. The vibrational frequency shows a monotonically increasing red shift with cluster size up to the completed first solvation shell at N∼20, where it saturates to a value in good agreement with experimental measurements made for OCS in much larger clusters.

Phase space optimization of quantum representations: Three-body systems and the bound states of HCO

In an earlier paper [J. Chem. Phys. 111, 4869 (1999)] we introduced a quasiclassical phase space approach for generating a nearly optimal direct-product basis for representing an arbitrary quantum Hamiltonian within a given energy range of interest. From a few reduced-dimensional integrals, the method determines the optimal one-dimensional marginal Hamiltonians, whose eigenstates comprise the direct-product basis. In this paper the method is applied to three-body vibrational systems expressed in radial and angular coordinates. Numerical results are obtained for the bound state eigenenergies of the nonrotating HCO molecule, determined to ∼0.01 cm−1 accuracy using a phase space optimized direct-product basis of 1972 functions. This represents a computational reduction of several orders of magnitude, in comparison with previous calculations.

Selecting molecules in the vibrational and rotational ground state by deflection

A beam of diatomic molecules scattered off a standing wave laser mode splits according to the rovibrational quantum state of the molecules. Our numerical calculation shows that single state resolution can be achieved by properly tuned, monochromatic light. The proposed scheme allows for selecting non-vibrating and non-rotating molecules from a thermal beam, implementing a laser Maxwell's demon to prepare a rovibrationally cold molecular ensemble.

An ab initio direct-trajectory study of the photodissociation of ClOOCl

The photodissociation of chlorine peroxide, ClOOCl, is studied with classical trajectories where the energy and gradient are computed on the fly by means of the state-averaged (sa) complete active space self-consistent field (CASSCF) with the DZP(+) basis set. We show that six electronically excited states are involved in the process of decomposition, which proceeds via several competing pathways and at least three electronically unique fragment channels. The problem is treated in four-dimensional (4D) (C2 constraint) and five-dimensional (5D) (planar constraint) frameworks in order to model the mechanisms of synchronous and asynchronous or stepwise dissociation, respectively. A single trajectory with the initial conditions of a nonvibrating, nonrotating molecule is propagated on each excited state surface for an average time of 10 fs for the purposes of determining the early stages of bond breaking. We show that even in such a short propagation time the pathway competition can be more or less unambiguously understood. The results indicate that in the regime of a 308 nm photolysis, the major dissociation fragments are Cl atoms and O2 molecules, both in the ground state. The higher energy regime of a 248 nm photoexcitation yields additional fragments, e.g., ClO(X 2Π), O(3P) and ClOO(X 2A″,1 2A′). We have achieved an overall qualitative agreement with experiment that more than 70% of the available energy is transferred into the translational energy of the products for the case of the synchronous concerted dissociation. In all the cases, the rotational excitation of produced molecular oxygen is very high, while its vibration is in v=0. Implications of the results on the stratospheric ozone depletion cycle are also presented.

Vibrational resonances of non-rotating HCN in the excited

A multi reference internally contracted configuration interaction (MRCI) method is used to generate the potential energy function (PEF) of the excited electronic state of HCN molecule. The analytic representation of the PEF is employed to calculate complex eigenvalues (resonance positions and widths) by a discrete variable representation (DVR) of the Hamiltonian for the non-rotating (J =0) molecule. The computational method used is a variant of the filter-diagonalization technique based on a recursive polynomial expansion of the absorbing-boundary-conditions (ABC) Green operator. Reasonable agreement with existing experimental data is found.

Recursion polynomial expansion of the Green’s function with absorbing boundary conditions: Calculations of resonances of HCO by filter diagonalization

An iterative method for calculating resonance positions and widths is developed. The system Hamiltonian with an asymptotic complex absorbing potential is represented by a large and sparse matrix. A small set of ‘‘good’’ basis functions suitable for diagonalizing the Hamiltonian matrix in a given energy window is generated by acting with a polynomial expansion of the imaginary part of the system Green’s function onto a generic initial wave packet. As an application to a realistic three-dimensional system, the calculation of 65 resonances of the nonrotating HCO molecule up to the energy 9000 cm−1 is presented. The method is shown to be rapidly convergent and accurate, especially for narrow resonances.

A fast Fourier transform method for the quasiclassical selection of initial rovibrational states of triatomic molecules

This paper describes the use of an exact fast Fourier transform method to prepare specified vibrational–rotational states of triatomic molecules. The method determines the Fourier coefficients needed to describe the coordinates and momenta of a vibrating–rotating triatomic molecule. Once the Fourier coefficients of a particular state are determined, it is possible to easily generate as many random sets of initial Cartesian coordinates and momenta as desired. All the members of each set will correspond to the particular vibrational–rotational state selected. For example, in the case of the ground vibrational state of a nonrotating water molecule, the calculated actions of 100 sets of initial conditions produced actions within 0.001ℏ of the specified quantization values and energies within 5 cm−1 of the semiclassical eigenvalue. The numerical procedure is straightforward for states in which all the fundamental frequencies are independent. However, for states for which the fundamental frequencies become commensurate (resonance states), there are additional complications. In these cases it is necessary to determine a new set of ‘‘fundamental’’ frequencies and to modify the quantization conditions. Once these adjustments are made, good results are obtained for resonance states. The major problems are in labeling the large number of Fourier coefficients and the presence of regions of chaotic motion. Results are presented for the vibrational states of H2O and HCN and the rovibrational states of H2O.

Simplified models for anharmonic numbers and densities of vibrational states. I. Application to NO2 and H3+

Numbers and densities of vibrational states of non-rotating polyatomic molecules are calculated by a simplified model which accounts for Morse anharmonicities of stretching and for generalized empirical stretch-bend couplings of bending modes. At energies above the dissociation limit, adiabatic channel maxima restrict the molecular phase space. The model is applied to the NO2(X̃ 2A1), NO2(Ã 2B2), and H3+ systems for which satisfactory agreement with the available experimental or calculational results is obtained.

Multiconfiguration response calculations on the Cameron bands of the CO molecule

The spin-forbidden electronic transition a 3Π–X 1Σ+ of the CO molecule constituting the Cameron band system has been studied by multiconfiguration linear and quadratic response methods. A vibrational analysis of the a 3Π and the X 1Σ+ states based on the obtained potential energy and transition mement curves was carried out for emission from the v′= 0, 1 vibronic levels of the a3Π0,1 spin-sublevels of the upper state to the different lowest v″ vibrational levels of the ground state. The oscillator strength of the 0–0 band is calculated to be 1.35 × 10–7, which is in agreement with literature values. The Einstein coefficients for the 10 vibronic transitions of the non-rotating molecule have been compared with literature values. The lifetime of the lowest a 3Π0, J= 0, e level is estimated to be 3.15 s.

Control of molecular vibrational excitation and dissociation by chirped intense infrared laser pulses. Rotational effects

We extend our previous studies on control of dissociation and vibrational excitation of a diatomic molecule using chirped, intense, infrared laser pulses [Phys. Rev. Lett. 65, 2355 (1990)]. The present model includes molecular rotations and a realistic molecular dipole function. The results obtained from numerical integration of the time-dependent Schrödinger equation show a considerable sensitivity of dissociation probabilities to the initial rotational quantum number. Although rotational effects generally decrease the excitation efficiency compared to previous nonrotating molecule results, the dissociation probability induced by chirped pulses is still four to eight orders of magnitudes greater than that for monochromatic pulse dissociation.

Rotational structure in the Hopfield series of N2

The Hopfield Rydberg series of 14N2 have been reinvestigated both at room temperature under equilibrium conditions and at a rotational temperature of ∼20 K in supersonically expanding nitrogen. High-resolution absorption spectra of the preionizing resonances in the region from 143 000 to 151 100 cm−1 have been recorded photographically as well as photoelectrically using, respectively, the 10.6 m vuv spectrograph of the National Research Council in Ottawa, Canada, and the 6.65 m scanning spectrometer at the Photon Factory synchrotron facility in Tsukuba, Japan. The photoelectric measurements have been reduced to absolute photoabsorption cross sections. The rotationally cold spectra show strikingly regular patterns of absorption peaks and window resonances that are accounted for, semiquantitatively, by the calculated total ionization cross sections for the nonrotating molecule [M. Raoult et al., J. Phys. B 16, 4601 (1983), and unpublished work by H. Le Rouzo and M. Raoult, quoted by C. H. Greene and Ch. Jungen, in Adv. At. Mol. Phys. 21, 51 (1985)]. The complexity of the room temperature spectra is rotationally induced; it does not call for an interpretation in terms of strong interactions with an unidentified perturber state as suggested by Baig and Connerade [J. Phys. B 19, L605 (1986)].