Large-amplitude Internal Motions Research Articles

Gas-Phase Computational Spectroscopy: The Challenge of the Molecular Bricks of Life.

Gas-phase molecular spectroscopy is a natural playground for accurate quantum-chemical computations. However, the molecular bricks of life (e.g., DNA bases or amino acids) are challenging systems because of the unfavorable scaling of quantum-chemical models with the molecular size (active electrons) and/or the presence of large-amplitude internal motions. From the theoretical point of view, both aspects prevent the brute-force use of very accurate but very expensive state-of-the-art quantum-chemical methodologies. From the experimental point of view, both features lead to congested gas-phase spectra, whose assignment and interpretation are not at all straightforward. Based on these premises, this review focuses on the current status and perspectives of the fully a priori prediction of the spectral signatures of medium-sized molecules (containing up to two dozen atoms) in the gas phase with special reference to rotational and vibrational spectroscopies of some representative molecular bricks of life.

Inflow Dynamics in Weakly Stratified Lakes Subject to Large Isopycnal Displacements

AbstractThe effect of large‐amplitude isopycnal displacements, frequently observed in deep medium‐size arctic lakes during the ice‐free period, on the near‐ and far‐field fate of negatively buoyant river inflows is explored in this work. A three‐dimensional transport and hydrodynamic model of sub‐arctic Lake Lagarfljót was used to simulate the fate of river inflows during the summer stratification period. The intrusion dynamics are strongly affected by the amplitude and direction (downwelling/upwelling) of the isopycnal displacements induced by the wind near the river inlet. These displacements control the distance of travel of the river plume until reaching the layers with maximum density gradients (pycnocline) and, thus, the mixing ratio between the river plume and the lake water. Specifically, strong upwelling near the inlet causes the river to flow to the bottom as an underflow. Under downwelling, river plumes tend to form metalimnetic intrusions. The influence of the isopycnal displacements on the initial river fate can be parameterized using a time‐varying density Richardson number, which needs to be smoothed to account for the effects of unsteadiness. Large amplitude internal motions, of up to 70 m in Lake Lagarfljót, move deep underflows upwards to shallower basins where they could be readily incorporated into the surface mixed layer and rapidly flushed out of the lake. Metalimnetic currents associated with the V2H1 internal circulation can also accelerate riverine transport out of the lake.

The Shape of the Simplest Non-proteinogenic Amino Acid α-Aminoisobutyric Acid (Aib).

The simplest non-proteinogenic amino acid α-aminoisobutyric acid (Aib), an analogue of glycine and alanine, has been vaporized by laser ablation and probed by high-resolution Fourier transform microwave spectroscopic techniques. Comparison of the experimental rotational and 14 N nuclear quadrupole constants with that predicted ab initio has allowed the identification of three conformers of Aib exhibiting three types of hydrogen-bond interactions I (NH⋅⋅⋅O=C, cis-COOH), II (OH⋅⋅⋅N, trans-COOH), and III (N-H⋅⋅⋅O-H, cis-COOH) within the amino acid backbone. The observation of conformer III, not detected previously for related proteinogenic amino acids with a nonpolar side chain in a supersonic expansion, indicates that the presence of the methyl groups should restrict the conformational relaxation from conformer Aib-III to Aib-I. For conformer Aib-II, the rotational spectra of the 13 C isotopomers reveal a tunneling motion arising from the two equivalent methyl groups in the molecule. The observation of a single spectrum at the midpoint between those predicted for the two 13 C of the methyl groups has been explained by considering a double-minimum potential function with a low-energy interconversion barrier for a large amplitude internal motion. This singular fact has been corroborated by the anomalous centrifugal distortion effects determined in conformer Aib-II.

Two-level stochastic search of low-energy conformers for molecular spectroscopy: implementation and validation of MM and QM models.

The search for stationary points in the molecular potential energy surfaces (PES) is a problem of increasing relevance in different fields of molecular sciences especially for large, flexible systems characterized by several large-amplitude internal motions leading to shallow minima with comparable energies and separated by small barriers. After structural biology and medicinal chemistry, also high-resolution molecular spectroscopy, which is the focus of our research activity, is nowadays shifting its attention to this kind of molecular systems. In such circumstances, accurate geometrical structures and relative stabilities of all these minima are a mandatory prerequisite for the vis-à-vis comparison between computed and experimental spectra. This task raises, in turn, the problem of the best compromise between accuracy and feasibility. In our opinion, a promising route is offered by a two-level stochastic search in which a relatively inexpensive MM or QM method is used in the initial search, followed by single point energy evaluation at a higher QM level of a relatively large number of low-energy structures in order to select a final short-list of candidates, whose geometries are fully optimized at the higher QM level. Finally, the relative stabilities and properties of the final short-list of energy minima can be computed by a state-of-the-art QM approach. This strategy defines a general two-level search/three-level evaluation approach, which can be finely tuned in terms of the accuracy of the sought results. Setup of the procedure, interface with a general purpose electronic structure code and validation of the most effective low-level methods for some representative molecular systems (three already well characterized and one new) ended up with a general, robust and user-friendly tool, which can be easily used and extended also by non-specialists to aid experimental spectroscopic studies.

Internal- and rho-axis systems of molecules with one large amplitude internal motion: The geometry of rho.

The internal-axis system (IAS) of molecules with a large amplitude internal motion (LAM) is determined by integrating the kinematic equation of the IAS by Lie-group and Lie-algebraic methods. Numerical examples on hydrogen peroxide, nitrous acid, and acetaldehyde demonstrate the methods. By exploiting the special product structure of the solution matrix, simple methods are devised for calculating the transformation to the rho-axis system (RAS) along with the value of the parameter ρ characterizing a RAS rotational-LAM kinetic energy operator. The parameter ρ so calculated agrees exactly with that one obtained by the Floquet method as shown in the example of acetaldehyde. Geometrical interpretation of ρ is given. The advantageous property of the RAS over the IAS in retaining simple periodic boundary conditions is numerically demonstrated.

Fitting coupled potential energy surfaces for large systems: Method and construction of a 3-state representation for phenol photodissociation in the full 33 internal degrees of freedom using multireference configuration interaction determined data

A recently reported algorithm for representing adiabatic states coupled by conical intersections using a quasi-diabatic state Hamiltonian in four and five atom systems is extended to treat nonadiabatic processes in considerably larger molecules. The method treats all internal degrees of freedom and uses electronic structure data from ab initio multireference configuration interaction wave functions with nuclear configuration selection based on quasi-classical surface hopping trajectories. The method is shown here to be able to treat ∼30 internal degrees of freedom including dissociative and large amplitude internal motion. Two procedures are introduced which are essential to the algorithm, a null space projector which removes basis functions from the fitting process until they are needed and a partial diagonalization technique which allows for automated, but accurate, treatment of the vicinity of extended seams of conical intersections of two or more states. These procedures are described in detail. The method is illustrated using the photodissociaton of phenol, C6H5OH(X̃(1)A(')) + hv → C6H5OH(Ã(1)A('), B̃(1)A('')) → C6H5O(X̃(2)B1, Ã(2)B2) + H as a test case. Ab initio electronic structure data for the 1,2,3(1)A states of phenol, which are coupled by conical intersections, are obtained from multireference first order configuration interaction wave functions. The design of bases to simultaneously treat large amplitude motion and dissociation is described, as is the ability of the fitting procedure to smooth the irregularities in the electronic energies attributable to the orbital changes that are inherent to nonadiabatic processes.

Lysine Nζ-Decarboxylation Switch and Activation of the β-Lactam Sensor Domain of BlaR1 Protein of Methicillin-resistant Staphylococcus aureus

The integral membrane protein BlaR1 of methicillin-resistant Staphylococcus aureus senses the presence of β-lactam antibiotics in the milieu and transduces the information to the cytoplasm, where the biochemical events that unleash induction of antibiotic resistance mechanisms take place. We report herein by two-dimensional and three-dimensional NMR experiments of the sensor domain of BlaR1 in solution and by determination of an x-ray structure for the apo protein that Lys-392 of the antibiotic-binding site is posttranslationally modified by N(ζ)-carboxylation. Additional crystallographic and NMR data reveal that on acylation of Ser-389 by antibiotics, Lys-392 experiences N(ζ)-decarboxylation. This unique process, termed the lysine N(ζ)-decarboxylation switch, arrests the sensor domain in the activated ("on") state, necessary for signal transduction and all the subsequent biochemical processes. We present structural information on how this receptor activation process takes place, imparting longevity to the antibiotic-receptor complex that is needed for the induction of the antibiotic-resistant phenotype in methicillin-resistant S. aureus.

Rovibrational states of the H2O–H2 complex: An ab initio calculation

All bound rovibrational levels of the H(2)O-H(2) dimer are calculated for total angular momentum J = 0-5 on two recent intermolecular potential surfaces reported by Valiron et al. [J. Chem. Phys. 129, 134306 (2008)] and Hodges et al. [J. Chem. Phys. 120, 710 (2004)] obtained through ab initio calculations. The method used handles correctly the large amplitude internal motions in this complex; it involves a discrete variable representation of the intermolecular distance coordinate R and a basis of coupled free rotor wave functions for the hindered internal rotations and the overall rotation of the dimer. The basis is adapted to the permutation symmetry associated with the para/ortho (p/o) nature of both H(2)O and H(2) as well as to inversion symmetry. Dimers containing oH(2) are more strongly bound than dimers with pH(2), as expected, with dissociation energies D(0) of 33.57, 36.63, 53.60, and 59.04 cm(-1)for pH(2)O-pH(2), oH(2)O-pH(2), pH(2)O-oH(2), and oH(2)O-oH(2), respectively, on the potential of Valiron et al. that corresponds to a binding energy D(e) of 235.14 cm(-1). Rovibrational wave functions are computed as well and the nature of the bound states in the four different dimer species is discussed. Converged rovibrational levels on both potentials agree well with the high-resolution spectrum reported by Weida and Nesbitt [J. Chem. Phys. 110, 156 (1999)]; the hindered internal rotor model that was used to interpret this spectrum is qualitatively correct.

Weeding the Cosmos – FIR synchrotron spectroscopy of methanol at the Canadian Light Source

New astronomical facilities such as HIFI on the Herschel Space Observatory, the ALMA sub-mm telescope array and the SOFIA airborne infrared (IR) telescope will yield spectra from interstellar and protostellar sources with vastly increased sensitivity, resolution and frequency coverage. This creates the need for major enhancements to laboratory databases for the particularly abundant and widespread molecular species known as interstellar “weeds” in order to model and account for their lines in observed spectra in the search for new and more exotic interstellar molecular “flowers”. With its large-amplitude internal torsional motion, methanol has particularly rich spectra throughout the THz and far-infrared regions and, being widely distributed throughout the galaxy, is perhaps the most notorious interstellar weed. We have recorded new spectra for CH 3OH on the high-resolution Fourier transform spectrometer on the Far-IR beamline at the Canadian Light Source synchrotron facility. New sub-band assignments for CH 3OH are reported at high rotational and/or torsional quantum number, allowing term values for a number of new torsion–rotation substates to be determined. The aim of the program is to extend quantum number coverage of the data, improve our understanding of the energy level structure, and provide the astronomical community with better databases and models of the spectral patterns with greater predictive power for a range of astrophysical conditions.

Purging of a Neutrally Buoyant or a Dense Miscible Contaminant from a Rectangular Cavity. I: Case of an Incoming Laminar Boundary Layer

The flow past two-dimensional (2D) channel cavities along with the removal of neutrally buoyant or dense miscible contaminants introduced instantaneously inside the cavity are studied using eddy resolving techniques. In the simulations, the incoming boundary layer is laminar and the flow is observed not to transition to turbulence as it is convected over the cavity. As for these flow conditions the main coherent structures in the separated shear layer over the cavity are quasi-dimensional, 2D simulations are performed. It is found that the mechanism of removal of the contaminant is very different between the neutrally buoyant and buoyant cases. In the neutrally buoyant case the contaminant is purged from the cavity mostly due to the interactions between the vortices shed in the separated shear layer with the main recirculation eddies inside the cavity and with the trailing edge corner. In the simulations in which a dense contaminant is introduced inside the cavity, after the initial stages of the mass exchange process, the main phenomenon is the presence of a large amplitude internal wave motion which interacts with a strong cavity vortex situated near the trailing edge corner in between the shear layer and the density interface. The density variation across this oscillatory interface is strong. Through this interaction wisps of denser contaminant are extracted from the region beneath the density interface, before being ejected from the cavity by the separated shear layer vortices. The values of the global mass exchange coefficients for the different phases of the purging process are estimated from simple dead-zone models. As expected, the purging process is delayed in the case in which the density of the contaminant is larger than the one of the carrying fluid.

The Millimeter‐ and Submillimeter‐Wave Spectrum of Methyl Carbamate [CH 3 OC(:O)NH 2

The rotational-torsional spectrum of the syn conformer of methyl carbamate [CH3OC(:O)NH2], an isomer of the essential amino acid glycine [NH2CH2C(:O)OH], has been recorded at room temperature in the spectral region from 79 to 371 GHz. Methyl carbamate possesses a methyl group internal rotor, which gives rise to A and E torsional substates, and associated splittings in the rotational spectrum. Almost 6000 new rotational transitions arising from the vibrational ground state have been assigned, about half of them belonging to the E torsional substate. Along with some earlier data, the newly measured lines were assigned and analyzed efficiently by the integration of two program packages: CAAARS, a suite for visual, interactive mouse-assisted line assignment of asymmetric rotor spectra; and ERHAM, a program that solves the effective Hamiltonian for molecules with up to two periodic large-amplitude internal motions. This Hamiltonian was used to fit 28 spectroscopic parameters for the methyl carbamate ground vibrational state to the observed line positions with a standard deviation of 0.081 MHz. With the determined spectroscopic constants and the available dipole moment components, we are able to predict the transition frequencies and intensities of many additional lines through 400 GHz. Methyl carbamate can now be searched for over a wide frequency range in appropriate interstellar sources such as hot molecular cores.

Microwave spectrum of the heterodimers: CH 3OH–CO 2 and CH 3OH–H 2CO

Molecular complexes, dimers and heterodimers often show interesting structures, large amplitude internal motions and orientations for reaction coordinates. These properties were the motivations for the current study of the rotational spectra of the heterodimers, CH 3OH–CO 2 and CH 3OH–H 2CO, in a pulsed nozzle Fourier-transform microwave (FTMW) spectrometer. In addition to studying the normal isotopic forms, several isotopologues containing 13C or deuterium substituted atoms of each heterodimer were analyzed in order to obtain structural data of the complexes. All species showed splittings from internal rotation of the methyl group and splittings on the b-type transitions of the CH 3OH–H 2CO species suggesting rotation of the H 2CO group between equivalent structural forms. Stark effect measurements on each of the parent species provided dipole moment components. Theoretical ab initio results are compared to the experimentally determined molecular parameters.

Accurate Inertias for Large-Amplitude Motions: Improvements on Prevailing Approximations

We present a simple yet accurate method for the calculation of effective moments of inertia for large-amplitude low-frequency internal motions in molecules. Our technique makes use of the quantum-mechanical kinetic energy operator developed within the internal coordinate path Hamiltonian formalism, with the imposition of Eckart conditions on the molecular frame to separate the internal motion from overall molecular rotation. Numerical results are presented for several molecules possessing internal large-amplitude motions. These results are compared with those obtained from approximate analytic formulas proposed by Pitzer. We also give detailed examples where the conventional approximations in the current literature are not applicable for describing a single large-amplitude motion. Our straightforward algorithm yields results more accurate than those of Pitzer's method, especially for molecules with asymmetric internal rotors.

Microwave spectra of mono- 13C substituted acetone, (CH 3) 2CO

The microwave spectra of the two mono- 13C isotopic forms of acetone are reported for the first time. Measurements were carried out from 11 to 25 GHz with a pulsed-beam Fourier-transform microwave spectrometer. Because overall rotation interacts with the internal rotations of the methyl groups, the spectra were analyzed with an effective rotational Hamiltonian for molecules with two periodic large-amplitude internal motions. In acetone-2- 13C, the methyl groups are equivalent; in acetone-1- 13C, they are not. The molecular structure has been re-examined by including rotational constant data on other isotopic forms reported previously. An equilibrium structure for acetone has been derived from the observed rotational constants and vibration–rotation constants calculated from ab initio force fields.

New applications of the genetic algorithm for the interpretation of high-resolution spectra

Rotationally resolved electronic spectroscopy yields a wealth of information on molecular structures in different electronic states. Unfortunately, for large molecules the spectra get rapidly very congested owing to close-lying vibronic bands, other isotopomers with similar zero-point energy shifts, or large-amplitude internal motions. A straightforward assignment of single rovibronic lines and, therefore, line position assigned fits are impossible. An alternative approach is unassigned fits of the spectra using genetic algorithms (GAs) with special cost functions for evaluation of the quality of the fit. This paper decribes the improvements we established on the GA method discussed before (J.A. Hageman, R. Wehrens, R. de Gelder, W.L. Meerts, and L.M.C. Buydens. J. Chem. Phys. 113, 7955 (2000)). In particular, we succeeded in obtaining a dramatic reduction in computing time that made it possible to apply the GA process in a large number of cases. A completely automated fit of a rotationally resolved laser-induced fluorescence spectrum without any prior knowledge of the molecular parameters can now be performed in less than 1 h. We demonstrate the power of the method on a number of typical examples such as very dense rovibronic spectra of van der Waals clusters and overlapping spectra due to different isotopomers. The discussed results demonstrate the extreme power of the GA in automated fitting and assigning of complex spectra. It opens the road to the analysis of complex spectra of biomolecules and their building blocks. Key words: high-resolution spectroscopy, genetic algorithm, biomolecules, structure, van der Waals clusters.

Theoretical study of the He-HF+ complex. II. Rovibronic states from coupled diabatic potential energy surfaces.

The bound rovibronic levels of the He-HF+ complex were calculated for total angular momentum J=1/2, 3/2, 5/2, 7/2, and 9/2 with the use of ab initio diabatic intermolecular potentials presented in Paper I and the inclusion of spin-orbit coupling. The character of the rovibronic states was interpreted by a series of calculations with the intermolecular distance R fixed at values ranging from 1.5 to 8.5 A and by analysis of the wave functions. In this analysis we used approximate angular momentum quantum numbers defined with respect to a dimer body-fixed (BF) frame with its z axis parallel to the intermolecular vector R and with respect to a molecule-fixed (MF) frame with its z axis parallel to the HF+ bond. The linear equilibrium geometry makes the He-HF+ complex a Renner-Teller system. We found both sets of quantum numbers, BF and MF, useful to understand the characteristics of the Renner-Teller effect in this system. In addition to the properties of a "normal" semirigid molecule Renner-Teller system it shows typical features caused by large-amplitude internal (bending) motion. We also present spectroscopic data: stretch and bend frequencies, spin-orbit splittings, parity splittings, and rotational constants.

Rho-axis-system Hamiltonian for molecules with one large amplitude internal motion

The rho-axis system and the rho-axis-system Hamiltonian were devised and formulated to describe the rotational–internal–rotational motion of molecules possessing certain local geometrical symmetries. Nevertheless, they were employed to molecules without the required symmetries and apparently lying outside the range of their applicability. To justify such applications and to facilitate first-principles calculation of the corresponding spectroscopic parameters, the rho-axis-system and the rho-axis system Hamiltonian must be derived without assuming or imposing symmetry constraints. A derivation satisfying this requirement is described, and the rho-axis method is extended to molecules having a large amplitude internal motion of any kind.

Atomic thermal motions studied by variable-temperature X-ray diffraction and related to non-linear optical properties of crystalline meta-dinitrobenzene.

The meta-dinitrobenzene crystal structure has been determined at five temperatures in the 100-300 K temperature range. The thermal expansion coefficients have been calculated from the temperature variation of the lattice parameters. Rigid-body motion analysis with allowance for large-amplitude internal motions provided the T, L and S tensors' values at the temperatures studied and was used to characterize the torsional motion of two nitro groups in the molecule. Frequencies of the translational and librational modes and of the torsional modes of the nitro groups have been compared with the wave numbers at the maximum of bands in the low-frequency Raman and IR spectra. Ab initio calculations were performed in order to assess the contribution from large-amplitude internal motions to the static first-order hyperpolarizability of the m-dinitrobenzene molecule.

Quantum dynamics of methanol: Hamiltonian, representation and intensity considerations

Employing a body-fixed axis system and Jacobi coordinates, a model for the vibration–torsion–rotation Hamiltonian of the CH 3OH molecule with large-amplitude internal motions has been derived. This Hamiltonian is expressed in terms of Jacobi coordinates and is partitioned in the form H A+ H B+ H int, where H A and H B are the rovibrational Hamiltonians of methyl group CH 3 and asymmetric rotor OH, and H int represents their interactions. The resulting Hamiltonian is used to carry out a pure quantum mechanical calculation for this kind of molecule or to construct the potential surface using observed data. The detailed discussion of the Hamiltonian is presented for the model with a rigid methyl group and a rigid OH, which describes five lower frequency vibrational modes and pure rotation in the molecule. We discuss the advantages of body-fixed Jacobi form of the Hamiltonian and solution strategies for practical programming. The properties of labels of the energy states, potential function and dipole moments are investigated according to the molecular symmetry group G 6 of methanol. Finally, the developed formulation is used to calculate the energy levels of CO-stretching–torsion–rotation for lower rotational excitation ( J⩽5). Comparison of the calculated results with experimental ones is presented.

Application of Permutation–Inversion Group Theory to the Interpretation of the Microwave Absorption Spectrum of Dimethyl Methylphosphonate

The G36 permutation–inversion group theoretical tunneling–rotational formalism originally developed for the methanol dimer has been modified (for the subgroup G18) and extended (to the larger group G54) for application to dimethyl methylphosphonate, CH3P(O)(OCH3)2, which has three large-amplitude methyl top internal rotation motions and one large-amplitude methoxy interchange motion. Energy levels of this chiral molecule are conveniently labeled by symmetry species corresponding to a mixed set of irreducible and reducible representations of G18 denoted by A1, A2, E, E1sep, E2sep, and Gsep. The separably degenerate species (with subscript sep) consist of pairs of irreducible representations of G18 whose energies are degenerate for Hamiltonians invariant to time reversal. All characters of these separably degenerate representations are real. Comparison of the group-theoretically derived splitting patterns with Fourier transform microwave and ab initio results from the preceding paper permit drawing a semiquantitative energy level diagram showing how a given Ka=0 level splits into A1⊕A2⊕2E⊕E1sep⊕E2sep⊕2Gsep components when the large-amplitude motions are turned on in the following order: (i) low-barrier methyl top internal rotation, (ii) medium-barrier methyl top internal rotation, (iii) top–top interaction, and (iv) methoxy interchange motion. (Internal rotation of the high-barrier methyl top is ignored.) Spectral splitting patterns observed for Ka=1–1 transitions are also quite regular, being either the same as, or mirror images of, the Ka=0–0 patterns. Theoretical work on Ka>0 splitting patterns is in progress.