Rovibrational Eigenstates Research Articles

Assigning quantum labels and improving accuracy for the ro-vibrational eigenstates of H3+ calculated using ScalIT

In a recent article [AIP Adv. 11, 045033 (2021)], we carried out exact quantum dynamical calculations and computed ro-vibrational energy levels and wave functions for the H3+ molecular ion up to the dissociation threshold (at J = 46) using a recently developed potential energy surface (PES) [Mol. Phys. 117, 1663 (2019)]—arguably, the most accurate to date —together with the ScalIT suite of parallel codes. In this work, we further improved the convergence accuracy and range of our ScalIT calculations for all J values up to J = 20 to a few 10–5 cm−1 (or better). In addition, we performed an ab initio assignment of the ro-vibrational energy levels, providing vibrational ‘v1, v2, |l|’ and rotational ‘J, G, U, K’ quantum labels for more than 2,200 ro-vibrational states, including every single 0 ≤ J ≤ 20 state up to and above the barrier to linearity at 10,000 cm−1. The main underlying motivation of our work is to provide a list of reliably labeled, spectroscopically accurate energy levels in a format that can be used in spectroscopic line lists, which are based on both experimental and theoretical levels. Such line lists are of huge importance in various astrochemical and astrophysical contexts.

Controlling tunneling in ammonia isotopomers.

We report results of full-dimensional variational rovibrational quantum-dynamical computations for several ammonia isotopomers, based on selected potential energy and electric dipole moment hypersurfaces. The variational rovibrational eigenstates have been used as a basis for the solution of the time-dependent Schrödinger equation for nuclear motion including coherent infrared multiphoton excitation. The theoretical and computational framework developed during this study enables the investigation of the coherent inhibition or enhancement of tunneling in ammonia isotopomers by appropriately chosen laser fields. Our quantum-dynamical computations include all vibrational and rotational degrees of freedom and assume neither the alignment nor the orientation of the molecules under investigation. Specific results include accurate rotational-vibrational levels for NH2D, NHD2, NHDMu, and NHDT, probability densities for structural parameters as a function of time from the full-dimensional wavepacket results, time-dependent chirality for the isotopically chiral molecule NHDT, and detailed analyses of the enhancement and inhibition of stereomutation dynamics.

Intermolecular rovibrational bound states of H2O[sbnd]H2 dimer from a MultiConfiguration Time Dependent Hartree approach

We compute the rovibrational eigenstates of the H2OH2 Van der Waals complex using the accurate rigid-rotor potential energy surface of Valiron et al. (2008) with the MultiConfiguration Time Dependent Hartree (MCTDH) method. The J=0–2 rovibrational bound states calculations are done with the Block Improved Relaxation procedure of MCTDH and the subsequent assignment of the states is achieved by inspection of the wavefunctions’ properties. The results of this work are found to be in close agreement with previous time independent calculations reported for this complex and therefore supports the use of the MCTDH approach for the rovibrational spectroscopic study of such weakly bound complexes.

On the use of nonrigid-molecular symmetry in nuclear motion computations employing a discrete variable representation: A case study of the bending energy levels of CH5.

A discrete-variable-representation-based symmetry adaptation algorithm is presented and implemented in the fourth-age quantum-chemical rotational-vibrational code GENIUSH. The utility of the symmetry-adapted version of GENIUSH is demonstrated by the computation of seven-dimensional bend-only vibrational and rovibrational eigenstates of the highly fluxionally symmetric CH5+ molecular ion, a prototypical astructural system. While the numerical results obtained and the symmetry labels of the computed rovibrational states of CH5+ are of considerable utility by themselves, it must also be noted that the present study confirms that the nearly unconstrained motion of the five hydrogen atoms orbiting around the central carbon atom results in highly complex rotational-vibrational quantum dynamics and renders the understanding of the high-resolution spectra of CH5+ extremely challenging.

Full-dimensional simulation of the laser-induced alignment dynamics of H2He+

ABSTRACTA theoretical approach for simulating the laser-induced alignment dynamics of non-rigid polyatomic molecules is introduced, in which the time-dependent Schrödinger equation (TDSE) is solved by expanding the laser-induced wavepacket with the field-free rovibrational eigenstates of the system. It is shown that not only the exact solution of the TDSE but also its approximated solution can be obtained, depending on the choices of the method for determining the field-free eigenstates. Laser-induced alignment of weakly bound H2He+ is investigated by adopting the present approach with high-accuracy full-dimensional variational calculations of the nuclear dynamics.

Simultaneous manipulation and observation of multiple ro-vibrational eigenstates in solid para-hydrogen.

We have experimentally performed the coherent control of delocalized ro-vibrational wave packets (RVWs) of solid para-hydrogen (p-H2) by the wave packet interferometry (WPI) combined with coherent anti-Stokes Raman scattering (CARS). RVWs of solid p-H2 are delocalized in the crystal, and the wave function with wave vector k ∼ 0 is selectively excited via the stimulated Raman process. We have excited the RVW twice by a pair of femtosecond laser pulses with delay controlled by a stabilized Michelson interferometer. Using a broad-band laser pulse, multiple ro-vibrational states can be excited simultaneously. We have observed the time-dependent Ramsey fringe spectra as a function of the inter-pulse delay by a spectrally resolved CARS technique using a narrow-band probe pulse, resolving the different intermediate states. Due to the different fringe oscillation periods among those intermediate states, we can manipulate their amplitude ratio by tuning the inter-pulse delay on the sub-femtosecond time scale. The state-selective manipulation and detection of the CARS signal combined with the WPI is a general and efficient protocol for the control of the interference of multiple quantum states in various quantum systems.

Vibrational memory in quantum localized states

The rovibrational eigenenergy set of molecular systems is a key feature needed to understand and model elementary chemical reactions. A unique class of molecular systems, represented by an ${}^{4}{A}^{\ensuremath{'}\ensuremath{'}}$ excited electronic state of the ${[\mathrm{H},\mathrm{S},\mathrm{N}]}^{\ensuremath{-}}$ system comprising several distinct dipole-bound isomers, is found to contain both bent and linear minima separated by relatively small barriers. Full-dimensional nuclear-motion computations performed in Jacobi coordinates using three-dimensional potential energy surfaces describing the stable isomers and the related transition states yield rovibrational eigenstates located both below and above the barriers. The rovibrational wave functions are well localized, regardless of whether the state's energy is below or above the barriers. We also show that the states preserve the memory of the isomeric forms they ``originate from,'' which is signature of a strong vibrational memory effect above isomerization barriers.

Accurate calculations of bound rovibrational states for argon trimer.

This work presents a comprehensive quantum dynamics calculation of the bound rovibrational eigenstates of argon trimer (Ar3), using the ScalIT suite of parallel codes. The Ar3 rovibrational energy levels are computed to a very high level of accuracy (10(-3) cm(-1) or better), and up to the highest rotational and vibrational excitations for which bound states exist. For many of these rovibrational states, wavefunctions are also computed. Rare gas clusters such as Ar3 are interesting because the interatomic interactions manifest through long-range van der Waals forces, rather than through covalent chemical bonding. As a consequence, they exhibit strong Coriolis coupling between the rotational and vibrational degrees of freedom, as well as highly delocalized states, all of which renders accurate quantum dynamical calculation difficult. Moreover, with its (comparatively) deep potential well and heavy masses, Ar3 is an especially challenging rare gas trimer case. There are a great many rovibrational eigenstates to compute, and a very high density of states. Consequently, very few previous rovibrational state calculations for Ar3 may be found in the current literature-and only for the lowest-lying rotational excitations.

Iterative Diagonalization in the Multiconfigurational Time-Dependent Hartree Approach: Ro-vibrational Eigenstates

A scheme to efficiently calculate ro-vibrational (J > 0) eigenstates within the framework of the multiconfigurational time-dependent Hartree (MCTDH) approach is introduced. It employs a basis of MCTDH wave packets which is generated in the calculation of vibrational (J = 0) eigenstates via existing MCTDH-based iterative diagonalization approaches. The subsequent ro-vibrational calculations for total angular momenta J > 0 use direct products of these wave packets and the Wigner rotation matrices. In this ro-vibrational basis, the Hamiltonian matrix can be computed and diagonalized with minor numerical effort for any value of J. Accurate ro-vibrational states are obtained if the number of iterations in the J = 0 calculations and the basis set sizes in the MCTDH wave function representation are converged. Test calculations studying CH2D show that ro-vibrational eigenstates for moderately large J can be converged within wavenumber accuracy with the same MCTDH basis sets and only slightly increased iteration counts compared to purely vibrational (J = 0) calculations. If large J's are considered or very high accuracies are required, the number of iterations required to obtain convergence increases significantly. Comparing the theoretical results with experimental data for the out-of-plane bend, symmetric stretch, and antisymmetric stretch fundamentals, the accuracy of the ab initio potential energy surface employed is investigated.

The role of axis embedding on rigid rotor decomposition analysis of variational rovibrational wave functions

Approximate rotational characterization of variational rovibrational wave functions via the rigid rotor decomposition (RRD) protocol is developed for Hamiltonians based on arbitrary sets of internal coordinates and axis embeddings. An efficient and general procedure is given that allows employing the Eckart embedding with arbitrary polyatomic Hamiltonians through a fully numerical approach. RRD tables formed by projecting rotational-vibrational wave functions into products of rigid-rotor basis functions and previously determined vibrational eigenstates yield rigid-rotor labels for rovibrational eigenstates by selecting the largest overlap. Embedding-dependent RRD analyses are performed, up to high energies and rotational excitations, for the H(2) (16)O isotopologue of the water molecule. Irrespective of the embedding chosen, the RRD procedure proves effective in providing unambiguous rotational assignments at low energies and J values. Rotational labeling of rovibrational states of H(2) (16)O proves to be increasingly difficult beyond about 10,000 cm(-1), close to the barrier to linearity of the water molecule. For medium energies and excitations the Eckart embedding yields the largest RRD coefficients, thus providing the largest number of unambiguous rotational labels.

Convergence and quantum number assignment studies of rovibrational eigenstates in a model of predissociating NeICl van der Waals complex

AbstractThis report details extensions and further analysis of the results presented in an earlier study (Elander et al., Phys Rev A 2001, 64, 012505). Rovibrational resonances in a model of the triatomic van der Waals complex NeICl were studied with a full quantum mechanical, smooth exterior dilation technique realized in a three‐dimensional finite element code. Both exact and approximate results, where Coriolis effects are neglected, are presented, and their structures are discussed. Although the helicity is a good quantum number in a one‐equation approximation, it is here demonstrated that this is not in the case when including Coriolis coupling, that is, couplings to other helicity components. The behavior of the resonance widths and the positions together with the structure of the resonance wave functions and their dependence on the total angular momentum and its projection have been studied. The dependence of the width of a given resonance on the total angular momentum was found to be weak while the dependence on the helicity is stronger. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

Robust operation of a universal set of logic gates for quantum computation using adiabatic population transfer between molecular levels

We present a robust construction of a set of logic gates operating on a system of qubits encoded in the rovibrational eigenstates of an ${\mathrm{Na}}_{2}$ molecule using the optical adiabatic population transfer (APT) phenomenon. We demonstrate the operation of a complete universal gate set for quantum computation on a two-qubit system with gate fidelities approaching 99.99%. Like other APT-based processes, the method is robust against substantial fluctuations in the intensity of the laser pulse. Our construction is easily scalable to deal with a larger number of qubits. With the aid of the set of gates thus shown we may construct pulse sequences for a wide class of quantum logic operations. We also show how to produce a representation of Bell states from a representation of product states with essentially perfect fidelity. Our scheme can be realized in all diatomic and polyatomic molecules that possess easily accessible and well characterized excited electronic states.

Spectroscopy and energetics of the acetylene molecule: dynamical complexity alongside structural simplicity

This article reviews laser-spectroscopic studies of the structure, energetics, and dynamics of processes involving small polyatomic molecules, particularly acetylene (ethyne, C2H2). The linear, centrosymmetric structure of C2H2 is deceptively simple, given that aspects of its optical spectra and dynamics have proved to be unusually complicated. The article focuses on the ground electronic state of C2H2, where rovibrational eigenstates are only approximately described in normal-mode terms, because intramolecular processes (such as anharmonic mixing, ℓ-type resonances, and Coriolis coupling) introduce extensive global and local perturbations. These tend to spoil quantum numbers and symmetries that are well-defined in low-order basis states. Such effects within the rovibrational energy states of C2H2 are systematically characterized, together with dynamical descriptions in terms of polyad models and insight into photochemical or photophysical processes that may occur at high vibrational energies, without direct electronic excitation. Time-resolved optical double-resonance spectroscopy, probed by ultraviolet-laser-induced fluorescence and pumped by either infrared absorption or coherent Raman excitation, has proved particularly useful in exploring such effects in gas-phase C2H2; techniques of this type are discussed in detail, together with other laser-spectroscopic methods that provide complementary mechanistic information. A closely related topic concerns the area of optothermal molecular-beam spectroscopy, with particular emphasis on research by the late Roger E. Miller to whose memory this article is dedicated. Key publications by Miller and coworkers, in many of which C2H2 and its isotopomers play a central role, are reviewed. These cover the following themes: structure of molecular complexes and clusters, infrared predissociation spectra, rotational and vibrational energy transfer, differential scattering, photofragmentation of oriented complexes, superfluid-helium nanodroplet spectroscopy, aerosols formed in low-temperature diffusion cells, surface scattering experiments, optically selected mass spectrometry, and characterization of biomolecules. A unifying issue that links the assorted topics of this article is the role that intramolecular perturbations can play to enhance (and sometimes suppress) the efficiency of rovibrational energy transfer in colliding molecules or in molecular complexes and clusters; C2H2 and its isotopomers have been a rich source of insight in this regard, although they continue to pose challenges to our understanding. Contents PAGE 1. Introduction 656 2. The occurrence of acetylene: connections and coincidences 657 3. Spectroscopic complexities of acetylene 659 3.1. Vibrational levels in the [Xtilde] electronic ground state 659 3.2. Anharmonic perturbations in the 4νCH vibrational manifold of C2H2 663 3.3. Local J-dependent anharmonic and ℓ-resonance perturbations 665 3.4. Local J-dependent heterogeneous Coriolis-coupling perturbations 668 3.5. Local Stark field perturbations in electric fields 671 3.6. Electronically excited states of C2H2 674 4. Acetylene as a mechanistic probe: Part of the Miller legacy 676 4.1. Optothermal spectroscopy of complexes and clusters containing C2H2 677 4.2. PHOFAD: Photofragmentation of oriented C2H2-containing complexes 680 4.3. Liquid helium nanodroplets incorporating C2H2 and its complexes 684 5. Time-resolved optical double-resonance spectroscopy of acetylene 688 5.1. Raman-ultraviolet double-resonance spectroscopy of acetylene 689 5.2. Infrared-ultraviolet double-resonance spectroscopy of acetylene 692 5.2.1. IR-UV DR studies of low-energy bending levels of acetylene 693 5.2.2. IR-UV DR studies in the νCH manifold of C2H2 695 5.2.3. IR-UV DR studies in nνCH manifolds of C2H2 above ∼6500 cm−1 698 5.2.4. IR-UV DR studies in the (νCC + 3νCH) manifold of C2H2 at ∼11 600 cm−1 699 5.2.5. IR-UV DR studies in the 4νCH manifold of C2H2 at ∼12 700 cm−1 702 5.2.6. IR-UV DR rovibrational spectroscopy of the C2H2-Ar van der Waals complex 706 5.3. Techniques that complement IR-UV DR spectroscopy of acetylene 707 6. Concluding remarks 709 Acknowledgments 710 References 710

Intensity and wavelength control of a single molecule reaction: Simulation of photodissociation of cold-trapped MgH+

Photodissociation of cold magnesium hydride ions MgH(+) leading to either Mg(+)+H or Mg+H(+) is simulated from first principles. The purpose is to study the possibility of single molecule control of the products in the presence of two laser fields. The system evolves on four electronic potential-energy curves, X(1) Sigma, A(1) Sigma, B(1) Pi, and C(1) Sigma. These potential-energy curves are calculated from first principles using multireference self-consistent field theory. The accuracy of the electronic potential curves has been checked by calculating the energies of the rovibrational eigenstates and comparing them to experimental findings. The photodissociation dynamics has furthermore been simulated by solving the time-dependent Schrodinger equation. It is shown that the branching ratio of the two dissociation channels, Mg(+)+H or Mg+H(+), can be controlled by changing the intensity and wavelength of the two driving laser fields.

Spin relaxation in isolated molecules and clusters: the interpretation of Stern-Gerlach experiments.

Intramolecular spin relaxation may occur in isolated molecules or clusters provided that the density of rovibrational eigenstates is sufficiently high to serve as an energy bath and angular momentum is conserved. In the coupled, zero-field limit, total angular momentum (J) is the sum of spin (S) and rotational (N) momenta such that J and M(J) are good angular momentum quantum numbers. In the coupled limit, transitions between Zeeman levels (Delta M(J)++0) cannot occur in the absence of an external torque. However, in the high-field limit, J and M(J) are no longer good quantum numbers, as N and S are decoupled and only their projections on the z axis defined by the external field are invariant. In this case M(N) and M(S) remain as good quantum numbers so that angular momentum conserving transitions can occur subject to the selection rule Delta M(N)=-Delta M(S). Determination of the magnetic moments of isolated molecules and clusters via a thermodynamics-based analysis requires that their magnetizations are measured at sufficiently large fields that spin-rotation effects become negligible and the Zeeman level structure approaches the free-spin case.

Experimental implementation of the Deutsch-Jozsa algorithm for three-qubit functions using pure coherent molecular superpositions

The Deutsch-Jozsa algorithm is experimentally demonstrated for three-qubit functions using pure coherent superpositions of ${\mathrm{Li}}_{2}$ rovibrational eigenstates. The function's character, either constant or balanced, is evaluated by first imprinting the function, using a phase-shaped femtosecond pulse, on a coherent superposition of the molecular states, and then projecting the superposition onto an ionic final state, using a second femtosecond pulse at a specific time delay.

Experimental coherent computation of a multiple-input AND gate using pure molecular superpositions

Pure coherent superpositions of Li 2 rovibrational eigenstates are used for the experimental coherent computation of a classical multiple-input AND logical gate. The input sets of Boolean values are imprinted into the phases of the eigenstates by shaped femtosecond pulses. The computation is carried out by the coherence and field-free time evolution. The Boolean result is given by the existence/nonexistence of a specific pre-determined superposition at a given delay time; it is read via projection onto an ionic state by a second femtosecond pulse. As an example, the gate is used in solving a yes/no computational decision problem.

Propagation of 3D Wave Packets for Nonzero Total Angular Momentum Using the Split Operator Method

Three-dimensional wave packet calculations for total angular momentum quantum number J ≥ 0 have been performed in Jacobi coordinates. To be able to use the split operator propagator together with the fast Fourier transform method, the wave function is transformed and a modified Hamiltonian obtained. The filter diagonalization method has been used to determine a few rovibrational eigenstates of the H2O molecule on the lowest potential energy surface. Good agreement with previous work is obtained.

Fully coupled six-dimensional calculations of rovibrational eigenstates of floppy four-atom molecules

A methodology for rigorous and efficient quantum 6D calculation of the vibration-rotation levels of floppy four-atom molecules is reviewed. The rovibrational Hamiltonian in the diatom–diatom Jacobi coordinates is employed. The distance between the diatomic centers of mass is discretized by means of the discrete variable representation (DVR). At each DVR point, a 5D Hamiltonian is diagonalized. The quasiadiabatic basis of the 5D eigenvectors reduces greatly the dimension of the final Hamiltonian matrix, allowing its direct diagonalization to give the rovibrational energy levels and wave functions. The methodology lends itself well to implementation on parallel computers.

Global potential energy surfaces for the H3+ system. Analytical representation of the adiabatic ground-state 1 1A′ potential

Adiabatic global potential energy surfaces, for singlet and triplet states of A′ and A″ symmetries, were computed for an extensive grid for a total of 8469 conformations of H3+ system at full configuration interaction ab initio level and using an extended basis set that has also been optimized for excited states. An accurate (root-mean-square error lower than 20 cm−1) global fit to the ground-state potential is obtained using a diatomics-in-molecules approach corrected by several symmetrized three-body terms with a total of 96 linear parameters and 3 nonlinear parameters. This produces an accurate global potential which represents all aspects of ground-state H3+ including the absolute minimum, the avoided crossing and dissociation limits, satisfying the correct symmetry properties of the system. The rovibrational eigenstates have been calculated up to total angular momentum J=20 using hyperspherical coordinates with symmetry adapted basis functions. The infrared spectra thus reproduced is within 1 cm−1 with respect to the experimental values for several transitions.